This is the gsll Reference Manual, version 0, generated automatically by Declt version 4.0 beta 2 "William Riker" on Sun Dec 15 06:19:45 2024 GMT+0.
gsll/init
gsll/floating-point
gsll/mathematical
gsll/data
gsll/special-functions
gsll/linear-algebra
gsll/eigensystems
gsll/fast-fourier-transforms
gsll/random
gsll/statistics
gsll/histogram
gsll/calculus
gsll/ordinary-differential-equations
gsll/interpolation
gsll/solve-minimize-fit
gsll/physical-constants
gsll/test-unit
gsll/tests
gsll/gsll.asd
gsll/init/init.lisp
gsll/init/libgsl.lisp
gsll/init/gsl-version.lisp
gsll/init/utility.lisp
gsll/init/forms.lisp
gsll/init/conditions.lisp
gsll/init/callback-compile-defs.lisp
gsll/init/mobject.lisp
gsll/init/callback-included.lisp
gsll/init/callback.lisp
gsll/init/types.lisp
gsll/init/callback-struct.lisp
gsll/init/funcallable.lisp
gsll/init/interface.lisp
gsll/init/defmfun.lisp
gsll/init/defmfun-array.lisp
gsll/init/defmfun-single.lisp
gsll/init/body-expand.lisp
gsll/init/generate-examples.lisp
gsll/init/generic.lisp
gsll/floating-point/ieee-modes.lisp
gsll/floating-point/floating-point.lisp
gsll/mathematical/mathematical.lisp
gsll/mathematical/complex.lisp
gsll/data/array-structs.lisp
gsll/data/foreign-array.lisp
gsll/data/vector.lisp
gsll/data/matrix.lisp
gsll/data/both.lisp
gsll/data/array-tests.lisp
gsll/data/permutation.lisp
gsll/data/combination.lisp
gsll/polynomial.lisp
gsll/special-functions/sf-result.lisp
gsll/special-functions/return-structures.lisp
gsll/special-functions/airy.lisp
gsll/special-functions/bessel.lisp
gsll/special-functions/clausen.lisp
gsll/special-functions/coulomb.lisp
gsll/special-functions/coupling.lisp
gsll/special-functions/dawson.lisp
gsll/special-functions/debye.lisp
gsll/special-functions/dilogarithm.lisp
gsll/special-functions/elementary.lisp
gsll/special-functions/elliptic-integrals.lisp
gsll/special-functions/elliptic-functions.lisp
gsll/special-functions/error-functions.lisp
gsll/special-functions/exponential-functions.lisp
gsll/special-functions/exponential-integrals.lisp
gsll/special-functions/fermi-dirac.lisp
gsll/special-functions/gamma.lisp
gsll/special-functions/gegenbauer.lisp
gsll/special-functions/hypergeometric.lisp
gsll/special-functions/laguerre.lisp
gsll/special-functions/lambert.lisp
gsll/special-functions/legendre.lisp
gsll/special-functions/logarithm.lisp
gsll/special-functions/mathieu.lisp
gsll/special-functions/power.lisp
gsll/special-functions/psi.lisp
gsll/special-functions/synchrotron.lisp
gsll/special-functions/transport.lisp
gsll/special-functions/trigonometry.lisp
gsll/special-functions/zeta.lisp
gsll/sorting.lisp
gsll/linear-algebra/blas1.lisp
gsll/linear-algebra/blas2.lisp
gsll/linear-algebra/blas3.lisp
gsll/linear-algebra/matrix-generation.lisp
gsll/linear-algebra/exponential.lisp
gsll/linear-algebra/lu.lisp
gsll/linear-algebra/qr.lisp
gsll/linear-algebra/qrpt.lisp
gsll/linear-algebra/svd.lisp
gsll/linear-algebra/cholesky.lisp
gsll/linear-algebra/diagonal.lisp
gsll/linear-algebra/householder.lisp
gsll/eigensystems/symmetric-hermitian.lisp
gsll/eigensystems/eigen-struct.lisp
gsll/eigensystems/nonsymmetric.lisp
gsll/eigensystems/generalized.lisp
gsll/eigensystems/nonsymmetric-generalized.lisp
gsll/fast-fourier-transforms/wavetable-workspace.lisp
gsll/fast-fourier-transforms/forward.lisp
gsll/fast-fourier-transforms/backward.lisp
gsll/fast-fourier-transforms/inverse.lisp
gsll/fast-fourier-transforms/select-direction.lisp
gsll/fast-fourier-transforms/unpack.lisp
gsll/fast-fourier-transforms/discrete.lisp
gsll/fast-fourier-transforms/extras.lisp
gsll/fast-fourier-transforms/example.lisp
gsll/random/rng-types.lisp
gsll/random/generators.lisp
gsll/random/quasi.lisp
gsll/random/tests.lisp
gsll/random/gaussian.lisp
gsll/random/gaussian-tail.lisp
gsll/random/gaussian-bivariate.lisp
gsll/random/exponential.lisp
gsll/random/laplace.lisp
gsll/random/exponential-power.lisp
gsll/random/cauchy.lisp
gsll/random/rayleigh.lisp
gsll/random/rayleigh-tail.lisp
gsll/random/landau.lisp
gsll/random/levy.lisp
gsll/random/gamma.lisp
gsll/random/flat.lisp
gsll/random/lognormal.lisp
gsll/random/chi-squared.lisp
gsll/random/fdist.lisp
gsll/random/tdist.lisp
gsll/random/beta.lisp
gsll/random/logistic.lisp
gsll/random/pareto.lisp
gsll/random/spherical-vector.lisp
gsll/random/weibull.lisp
gsll/random/gumbel1.lisp
gsll/random/gumbel2.lisp
gsll/random/dirichlet.lisp
gsll/random/discrete.lisp
gsll/random/poisson.lisp
gsll/random/bernoulli.lisp
gsll/random/binomial.lisp
gsll/random/multinomial.lisp
gsll/random/negative-binomial.lisp
gsll/random/geometric.lisp
gsll/random/hypergeometric.lisp
gsll/random/logarithmic.lisp
gsll/random/shuffling-sampling.lisp
gsll/statistics/mean-variance.lisp
gsll/statistics/absolute-deviation.lisp
gsll/statistics/higher-moments.lisp
gsll/statistics/autocorrelation.lisp
gsll/statistics/covariance.lisp
gsll/statistics/median-percentile.lisp
gsll/histogram/histogram.lisp
gsll/histogram/updating-accessing.lisp
gsll/histogram/statistics.lisp
gsll/histogram/operations.lisp
gsll/histogram/probability-distribution.lisp
gsll/histogram/ntuple.lisp
gsll/calculus/numerical-integration.lisp
gsll/calculus/numerical-integration-with-tables.lisp
gsll/calculus/monte-carlo-structs.lisp
gsll/calculus/monte-carlo.lisp
gsll/calculus/numerical-differentiation.lisp
gsll/ordinary-differential-equations/ode-system.lisp
gsll/ordinary-differential-equations/ode-struct.lisp
gsll/ordinary-differential-equations/stepping.lisp
gsll/ordinary-differential-equations/control.lisp
gsll/ordinary-differential-equations/evolution.lisp
gsll/ordinary-differential-equations/ode-example.lisp
gsll/interpolation/interpolation.lisp
gsll/interpolation/types.lisp
gsll/interpolation/lookup.lisp
gsll/interpolation/evaluation.lisp
gsll/interpolation/spline-example.lisp
gsll/chebyshev.lisp
gsll/series-struct.lisp
gsll/series-acceleration.lisp
gsll/wavelet.lisp
gsll/hankel.lisp
gsll/solve-minimize-fit/generic.lisp
gsll/solve-minimize-fit/solver-struct.lisp
gsll/solve-minimize-fit/roots-one.lisp
gsll/solve-minimize-fit/minimization-one.lisp
gsll/solve-minimize-fit/roots-multi.lisp
gsll/solve-minimize-fit/minimization-multi.lisp
gsll/solve-minimize-fit/linear-least-squares.lisp
gsll/solve-minimize-fit/nonlinear-least-squares.lisp
gsll/solve-minimize-fit/simulated-annealing.lisp
gsll/basis-splines.lisp
gsll/physical-constants/mksa.lisp
gsll/physical-constants/cgsm.lisp
gsll/physical-constants/num.lisp
gsll/physical-constants/export.lisp
gsll/test-unit/machine.lisp
gsll/test-unit/augment.lisp
gsll/tests/absolute-deviation.lisp
gsll/tests/absolute-sum.lisp
gsll/tests/airy.lisp
gsll/tests/autocorrelation.lisp
gsll/tests/axpy.lisp
gsll/tests/basis-spline.lisp
gsll/tests/bernoulli.lisp
gsll/tests/bessel.lisp
gsll/tests/beta.lisp
gsll/tests/binomial.lisp
gsll/tests/blas-copy.lisp
gsll/tests/blas-swap.lisp
gsll/tests/cauchy.lisp
gsll/tests/cdot.lisp
gsll/tests/chebyshev.lisp
gsll/tests/chi-squared.lisp
gsll/tests/cholesky.lisp
gsll/tests/clausen.lisp
gsll/tests/column.lisp
gsll/tests/combination.lisp
gsll/tests/coulomb.lisp
gsll/tests/coupling.lisp
gsll/tests/correlation.lisp
gsll/tests/covariance.lisp
gsll/tests/dawson.lisp
gsll/tests/debye.lisp
gsll/tests/dilogarithm.lisp
gsll/tests/dirichlet.lisp
gsll/tests/discrete.lisp
gsll/tests/dot.lisp
gsll/tests/eigensystems.lisp
gsll/tests/elementary.lisp
gsll/tests/elliptic-functions.lisp
gsll/tests/elliptic-integrals.lisp
gsll/tests/error-functions.lisp
gsll/tests/euclidean-norm.lisp
gsll/tests/exponential-functions.lisp
gsll/tests/exponential-integrals.lisp
gsll/tests/exponential.lisp
gsll/tests/exponential-power.lisp
gsll/tests/fast-fourier-transform.lisp
gsll/tests/fdist.lisp
gsll/tests/fermi-dirac.lisp
gsll/tests/flat.lisp
gsll/tests/gamma.lisp
gsll/tests/gamma-randist.lisp
gsll/tests/gaussian-bivariate.lisp
gsll/tests/gaussian.lisp
gsll/tests/gaussian-tail.lisp
gsll/tests/gegenbauer.lisp
gsll/tests/geometric.lisp
gsll/tests/givens.lisp
gsll/tests/gumbel1.lisp
gsll/tests/gumbel2.lisp
gsll/tests/hankel.lisp
gsll/tests/higher-moments.lisp
gsll/tests/histogram.lisp
gsll/tests/householder.lisp
gsll/tests/hypergeometric.lisp
gsll/tests/hypergeometric-randist.lisp
gsll/tests/index-max.lisp
gsll/tests/interpolation.lisp
gsll/tests/inverse-matrix-product.lisp
gsll/tests/laguerre.lisp
gsll/tests/lambert.lisp
gsll/tests/landau.lisp
gsll/tests/laplace.lisp
gsll/tests/legendre.lisp
gsll/tests/levy.lisp
gsll/tests/linear-least-squares.lisp
gsll/tests/logarithmic.lisp
gsll/tests/logarithm.lisp
gsll/tests/logistic.lisp
gsll/tests/lognormal.lisp
gsll/tests/lu.lisp
gsll/tests/mathematical.lisp
gsll/tests/mathieu.lisp
gsll/tests/matrix-div.lisp
gsll/tests/matrix-max-index.lisp
gsll/tests/matrix-max.lisp
gsll/tests/matrix-mean.lisp
gsll/tests/matrix-min.lisp
gsll/tests/matrix-min-index.lisp
gsll/tests/matrix-minmax-index.lisp
gsll/tests/matrix-minmax.lisp
gsll/tests/matrix-sub.lisp
gsll/tests/matrix-add.lisp
gsll/tests/matrix-mult.lisp
gsll/tests/matrix-product-hermitian.lisp
gsll/tests/matrix-product.lisp
gsll/tests/matrix-product-nonsquare.lisp
gsll/tests/matrix-product-symmetric.lisp
gsll/tests/matrix-product-triangular.lisp
gsll/tests/matrix-set-all.lisp
gsll/tests/matrix-set-zero.lisp
gsll/tests/matrix-standard-deviation.lisp
gsll/tests/matrix-standard-deviation-with-fixed-mean.lisp
gsll/tests/matrix-standard-deviation-with-mean.lisp
gsll/tests/matrix-swap.lisp
gsll/tests/matrix-transpose-copy.lisp
gsll/tests/matrix-transpose.lisp
gsll/tests/matrix-variance.lisp
gsll/tests/matrix-variance-with-fixed-mean.lisp
gsll/tests/matrix-variance-with-mean.lisp
gsll/tests/median-percentile.lisp
gsll/tests/minimization-one.lisp
gsll/tests/minimization-multi.lisp
gsll/tests/monte-carlo.lisp
gsll/tests/multinomial.lisp
gsll/tests/negative-binomial.lisp
gsll/tests/nonlinear-least-squares.lisp
gsll/tests/ntuple.lisp
gsll/tests/numerical-differentiation.lisp
gsll/tests/numerical-integration.lisp
gsll/tests/ode.lisp
gsll/tests/pareto.lisp
gsll/tests/permutation.lisp
gsll/tests/poisson.lisp
gsll/tests/polynomial.lisp
gsll/tests/power.lisp
gsll/tests/psi.lisp
gsll/tests/qr.lisp
gsll/tests/qrpt.lisp
gsll/tests/quasi-random-number-generators.lisp
gsll/tests/random-number-generators.lisp
gsll/tests/rank-1-update.lisp
gsll/tests/rayleigh.lisp
gsll/tests/rayleigh-tail.lisp
gsll/tests/roots-multi.lisp
gsll/tests/roots-one.lisp
gsll/tests/row.lisp
gsll/tests/scale.lisp
gsll/tests/series-acceleration.lisp
gsll/tests/set-basis.lisp
gsll/tests/setf-column.lisp
gsll/tests/setf-row.lisp
gsll/tests/set-identity.lisp
gsll/tests/shuffling-sampling.lisp
gsll/tests/sort-matrix-largest.lisp
gsll/tests/sort-matrix.lisp
gsll/tests/sort-matrix-smallest.lisp
gsll/tests/sort-vector-index.lisp
gsll/tests/sort-vector-largest-index.lisp
gsll/tests/sort-vector-largest.lisp
gsll/tests/sort-vector.lisp
gsll/tests/sort-vector-smallest-index.lisp
gsll/tests/sort-vector-smallest.lisp
gsll/tests/spherical-vector.lisp
gsll/tests/svd.lisp
gsll/tests/swap-columns.lisp
gsll/tests/swap-elements.lisp
gsll/tests/swap-row-column.lisp
gsll/tests/swap-rows.lisp
gsll/tests/synchrotron.lisp
gsll/tests/tdist.lisp
gsll/tests/transport.lisp
gsll/tests/trigonometry.lisp
gsll/tests/vector-div.lisp
gsll/tests/vector-max-index.lisp
gsll/tests/vector-max.lisp
gsll/tests/vector-mean.lisp
gsll/tests/vector-min.lisp
gsll/tests/vector-min-index.lisp
gsll/tests/vector-minmax-index.lisp
gsll/tests/vector-minmax.lisp
gsll/tests/vector-sub.lisp
gsll/tests/vector-add.lisp
gsll/tests/vector-mult.lisp
gsll/tests/vector-reverse.lisp
gsll/tests/vector-set-all.lisp
gsll/tests/vector-set-zero.lisp
gsll/tests/vector-standard-deviation.lisp
gsll/tests/vector-standard-deviation-with-fixed-mean.lisp
gsll/tests/vector-standard-deviation-with-mean.lisp
gsll/tests/vector-swap.lisp
gsll/tests/vector-variance.lisp
gsll/tests/vector-variance-with-fixed-mean.lisp
gsll/tests/vector-variance-with-mean.lisp
gsll/tests/weibull.lisp
gsll/tests/zeta.lisp
The main system appears first, followed by any subsystem dependency.
gsll
GNU Scientific Library for Lisp.
Liam M. Healy
GPL v3
0
cffi-grovel
(system).
foreign-array
(system).
cffi-grovel
(system).
trivial-garbage
(system).
alexandria
(system).
metabang-bind
(system).
lisp-unit
(system).
trivial-features
(system).
init
(module).
floating-point
(module).
mathematical
(module).
data
(module).
polynomial.lisp
(file).
special-functions
(module).
sorting.lisp
(file).
linear-algebra
(module).
eigensystems
(module).
fast-fourier-transforms
(module).
random
(module).
statistics
(module).
histogram
(module).
calculus
(module).
ordinary-differential-equations
(module).
interpolation
(module).
chebyshev.lisp
(file).
series-struct.lisp
(file).
series-acceleration.lisp
(file).
wavelet.lisp
(file).
hankel.lisp
(file).
solve-minimize-fit
(module).
basis-splines.lisp
(file).
physical-constants
(module).
test-unit
(module).
tests
(module).
Modules are listed depth-first from the system components tree.
gsll/init
gsll/floating-point
gsll/mathematical
gsll/data
gsll/special-functions
gsll/linear-algebra
gsll/eigensystems
gsll/fast-fourier-transforms
gsll/random
gsll/statistics
gsll/histogram
gsll/calculus
gsll/ordinary-differential-equations
gsll/interpolation
gsll/solve-minimize-fit
gsll/physical-constants
gsll/test-unit
gsll/tests
gsll/init
gsll
(system).
init.lisp
(file).
libgsl.lisp
(file).
gsl-version.lisp
(file).
utility.lisp
(file).
forms.lisp
(file).
conditions.lisp
(file).
callback-compile-defs.lisp
(file).
mobject.lisp
(file).
callback-included.lisp
(file).
callback.lisp
(file).
types.lisp
(file).
callback-struct.lisp
(file).
funcallable.lisp
(file).
interface.lisp
(file).
defmfun.lisp
(file).
defmfun-array.lisp
(file).
defmfun-single.lisp
(file).
body-expand.lisp
(file).
generate-examples.lisp
(file).
generic.lisp
(file).
gsll/floating-point
init
(module).
gsll
(system).
ieee-modes.lisp
(file).
floating-point.lisp
(file).
gsll/mathematical
init
(module).
gsll
(system).
mathematical.lisp
(file).
complex.lisp
(file).
gsll/data
init
(module).
gsll
(system).
array-structs.lisp
(file).
foreign-array.lisp
(file).
vector.lisp
(file).
matrix.lisp
(file).
both.lisp
(file).
array-tests.lisp
(file).
permutation.lisp
(file).
combination.lisp
(file).
gsll/special-functions
init
(module).
mathematical
(module).
gsll
(system).
sf-result.lisp
(file).
return-structures.lisp
(file).
airy.lisp
(file).
bessel.lisp
(file).
clausen.lisp
(file).
coulomb.lisp
(file).
coupling.lisp
(file).
dawson.lisp
(file).
debye.lisp
(file).
dilogarithm.lisp
(file).
elementary.lisp
(file).
elliptic-integrals.lisp
(file).
elliptic-functions.lisp
(file).
error-functions.lisp
(file).
exponential-functions.lisp
(file).
exponential-integrals.lisp
(file).
fermi-dirac.lisp
(file).
gamma.lisp
(file).
gegenbauer.lisp
(file).
hypergeometric.lisp
(file).
laguerre.lisp
(file).
lambert.lisp
(file).
legendre.lisp
(file).
logarithm.lisp
(file).
mathieu.lisp
(file).
power.lisp
(file).
psi.lisp
(file).
synchrotron.lisp
(file).
transport.lisp
(file).
trigonometry.lisp
(file).
zeta.lisp
(file).
gsll/linear-algebra
init
(module).
data
(module).
special-functions
(module).
gsll
(system).
blas1.lisp
(file).
blas2.lisp
(file).
blas3.lisp
(file).
matrix-generation.lisp
(file).
exponential.lisp
(file).
lu.lisp
(file).
qr.lisp
(file).
qrpt.lisp
(file).
svd.lisp
(file).
cholesky.lisp
(file).
diagonal.lisp
(file).
householder.lisp
(file).
gsll/eigensystems
gsll
(system).
symmetric-hermitian.lisp
(file).
eigen-struct.lisp
(file).
nonsymmetric.lisp
(file).
generalized.lisp
(file).
nonsymmetric-generalized.lisp
(file).
gsll/fast-fourier-transforms
gsll
(system).
wavetable-workspace.lisp
(file).
forward.lisp
(file).
backward.lisp
(file).
inverse.lisp
(file).
select-direction.lisp
(file).
unpack.lisp
(file).
discrete.lisp
(file).
extras.lisp
(file).
example.lisp
(file).
gsll/random
gsll
(system).
rng-types.lisp
(file).
generators.lisp
(file).
quasi.lisp
(file).
tests.lisp
(file).
gaussian.lisp
(file).
gaussian-tail.lisp
(file).
gaussian-bivariate.lisp
(file).
exponential.lisp
(file).
laplace.lisp
(file).
exponential-power.lisp
(file).
cauchy.lisp
(file).
rayleigh.lisp
(file).
rayleigh-tail.lisp
(file).
landau.lisp
(file).
levy.lisp
(file).
gamma.lisp
(file).
flat.lisp
(file).
lognormal.lisp
(file).
chi-squared.lisp
(file).
fdist.lisp
(file).
tdist.lisp
(file).
beta.lisp
(file).
logistic.lisp
(file).
pareto.lisp
(file).
spherical-vector.lisp
(file).
weibull.lisp
(file).
gumbel1.lisp
(file).
gumbel2.lisp
(file).
dirichlet.lisp
(file).
discrete.lisp
(file).
poisson.lisp
(file).
bernoulli.lisp
(file).
binomial.lisp
(file).
multinomial.lisp
(file).
negative-binomial.lisp
(file).
geometric.lisp
(file).
hypergeometric.lisp
(file).
logarithmic.lisp
(file).
shuffling-sampling.lisp
(file).
gsll/statistics
gsll
(system).
mean-variance.lisp
(file).
absolute-deviation.lisp
(file).
higher-moments.lisp
(file).
autocorrelation.lisp
(file).
covariance.lisp
(file).
median-percentile.lisp
(file).
gsll/histogram
init
(module).
linear-algebra
(module).
random
(module).
gsll
(system).
histogram.lisp
(file).
updating-accessing.lisp
(file).
statistics.lisp
(file).
operations.lisp
(file).
probability-distribution.lisp
(file).
ntuple.lisp
(file).
gsll/calculus
init
(module).
mathematical
(module).
data
(module).
random
(module).
gsll
(system).
numerical-integration.lisp
(file).
numerical-integration-with-tables.lisp
(file).
monte-carlo-structs.lisp
(file).
monte-carlo.lisp
(file).
numerical-differentiation.lisp
(file).
gsll/ordinary-differential-equations
init
(module).
gsll
(system).
ode-system.lisp
(file).
ode-struct.lisp
(file).
stepping.lisp
(file).
control.lisp
(file).
evolution.lisp
(file).
ode-example.lisp
(file).
gsll/interpolation
init
(module).
mathematical
(module).
gsll
(system).
interpolation.lisp
(file).
types.lisp
(file).
lookup.lisp
(file).
evaluation.lisp
(file).
spline-example.lisp
(file).
gsll/solve-minimize-fit
init
(module).
mathematical
(module).
data
(module).
random
(module).
gsll
(system).
generic.lisp
(file).
solver-struct.lisp
(file).
roots-one.lisp
(file).
minimization-one.lisp
(file).
roots-multi.lisp
(file).
minimization-multi.lisp
(file).
linear-least-squares.lisp
(file).
nonlinear-least-squares.lisp
(file).
simulated-annealing.lisp
(file).
gsll/physical-constants
init
(module).
gsll
(system).
mksa.lisp
(file).
cgsm.lisp
(file).
num.lisp
(file).
export.lisp
(file).
gsll/test-unit
gsll
(system).
machine.lisp
(file).
augment.lisp
(file).
gsll/tests
test-unit
(module).
gsll
(system).
absolute-deviation.lisp
(file).
absolute-sum.lisp
(file).
airy.lisp
(file).
autocorrelation.lisp
(file).
axpy.lisp
(file).
basis-spline.lisp
(file).
bernoulli.lisp
(file).
bessel.lisp
(file).
beta.lisp
(file).
binomial.lisp
(file).
blas-copy.lisp
(file).
blas-swap.lisp
(file).
cauchy.lisp
(file).
cdot.lisp
(file).
chebyshev.lisp
(file).
chi-squared.lisp
(file).
cholesky.lisp
(file).
clausen.lisp
(file).
column.lisp
(file).
combination.lisp
(file).
coulomb.lisp
(file).
coupling.lisp
(file).
correlation.lisp
(file).
covariance.lisp
(file).
dawson.lisp
(file).
debye.lisp
(file).
dilogarithm.lisp
(file).
dirichlet.lisp
(file).
discrete.lisp
(file).
dot.lisp
(file).
eigensystems.lisp
(file).
elementary.lisp
(file).
elliptic-functions.lisp
(file).
elliptic-integrals.lisp
(file).
error-functions.lisp
(file).
euclidean-norm.lisp
(file).
exponential-functions.lisp
(file).
exponential-integrals.lisp
(file).
exponential.lisp
(file).
exponential-power.lisp
(file).
fast-fourier-transform.lisp
(file).
fdist.lisp
(file).
fermi-dirac.lisp
(file).
flat.lisp
(file).
gamma.lisp
(file).
gamma-randist.lisp
(file).
gaussian-bivariate.lisp
(file).
gaussian.lisp
(file).
gaussian-tail.lisp
(file).
gegenbauer.lisp
(file).
geometric.lisp
(file).
givens.lisp
(file).
gumbel1.lisp
(file).
gumbel2.lisp
(file).
hankel.lisp
(file).
higher-moments.lisp
(file).
histogram.lisp
(file).
householder.lisp
(file).
hypergeometric.lisp
(file).
hypergeometric-randist.lisp
(file).
index-max.lisp
(file).
interpolation.lisp
(file).
inverse-matrix-product.lisp
(file).
laguerre.lisp
(file).
lambert.lisp
(file).
landau.lisp
(file).
laplace.lisp
(file).
legendre.lisp
(file).
levy.lisp
(file).
linear-least-squares.lisp
(file).
logarithmic.lisp
(file).
logarithm.lisp
(file).
logistic.lisp
(file).
lognormal.lisp
(file).
lu.lisp
(file).
mathematical.lisp
(file).
mathieu.lisp
(file).
matrix-div.lisp
(file).
matrix-max-index.lisp
(file).
matrix-max.lisp
(file).
matrix-mean.lisp
(file).
matrix-min.lisp
(file).
matrix-min-index.lisp
(file).
matrix-minmax-index.lisp
(file).
matrix-minmax.lisp
(file).
matrix-sub.lisp
(file).
matrix-add.lisp
(file).
matrix-mult.lisp
(file).
matrix-product-hermitian.lisp
(file).
matrix-product.lisp
(file).
matrix-product-nonsquare.lisp
(file).
matrix-product-symmetric.lisp
(file).
matrix-product-triangular.lisp
(file).
matrix-set-all.lisp
(file).
matrix-set-zero.lisp
(file).
matrix-standard-deviation.lisp
(file).
matrix-standard-deviation-with-fixed-mean.lisp
(file).
matrix-standard-deviation-with-mean.lisp
(file).
matrix-swap.lisp
(file).
matrix-transpose-copy.lisp
(file).
matrix-transpose.lisp
(file).
matrix-variance.lisp
(file).
matrix-variance-with-fixed-mean.lisp
(file).
matrix-variance-with-mean.lisp
(file).
median-percentile.lisp
(file).
minimization-one.lisp
(file).
minimization-multi.lisp
(file).
monte-carlo.lisp
(file).
multinomial.lisp
(file).
negative-binomial.lisp
(file).
nonlinear-least-squares.lisp
(file).
ntuple.lisp
(file).
numerical-differentiation.lisp
(file).
numerical-integration.lisp
(file).
ode.lisp
(file).
pareto.lisp
(file).
permutation.lisp
(file).
poisson.lisp
(file).
polynomial.lisp
(file).
power.lisp
(file).
psi.lisp
(file).
qr.lisp
(file).
qrpt.lisp
(file).
quasi-random-number-generators.lisp
(file).
random-number-generators.lisp
(file).
rank-1-update.lisp
(file).
rayleigh.lisp
(file).
rayleigh-tail.lisp
(file).
roots-multi.lisp
(file).
roots-one.lisp
(file).
row.lisp
(file).
scale.lisp
(file).
series-acceleration.lisp
(file).
set-basis.lisp
(file).
setf-column.lisp
(file).
setf-row.lisp
(file).
set-identity.lisp
(file).
shuffling-sampling.lisp
(file).
sort-matrix-largest.lisp
(file).
sort-matrix.lisp
(file).
sort-matrix-smallest.lisp
(file).
sort-vector-index.lisp
(file).
sort-vector-largest-index.lisp
(file).
sort-vector-largest.lisp
(file).
sort-vector.lisp
(file).
sort-vector-smallest-index.lisp
(file).
sort-vector-smallest.lisp
(file).
spherical-vector.lisp
(file).
svd.lisp
(file).
swap-columns.lisp
(file).
swap-elements.lisp
(file).
swap-row-column.lisp
(file).
swap-rows.lisp
(file).
synchrotron.lisp
(file).
tdist.lisp
(file).
transport.lisp
(file).
trigonometry.lisp
(file).
vector-div.lisp
(file).
vector-max-index.lisp
(file).
vector-max.lisp
(file).
vector-mean.lisp
(file).
vector-min.lisp
(file).
vector-min-index.lisp
(file).
vector-minmax-index.lisp
(file).
vector-minmax.lisp
(file).
vector-sub.lisp
(file).
vector-add.lisp
(file).
vector-mult.lisp
(file).
vector-reverse.lisp
(file).
vector-set-all.lisp
(file).
vector-set-zero.lisp
(file).
vector-standard-deviation.lisp
(file).
vector-standard-deviation-with-fixed-mean.lisp
(file).
vector-standard-deviation-with-mean.lisp
(file).
vector-swap.lisp
(file).
vector-variance.lisp
(file).
vector-variance-with-fixed-mean.lisp
(file).
vector-variance-with-mean.lisp
(file).
weibull.lisp
(file).
zeta.lisp
(file).
Files are sorted by type and then listed depth-first from the systems components trees.
gsll/gsll.asd
gsll/init/init.lisp
gsll/init/libgsl.lisp
gsll/init/gsl-version.lisp
gsll/init/utility.lisp
gsll/init/forms.lisp
gsll/init/conditions.lisp
gsll/init/callback-compile-defs.lisp
gsll/init/mobject.lisp
gsll/init/callback-included.lisp
gsll/init/callback.lisp
gsll/init/types.lisp
gsll/init/callback-struct.lisp
gsll/init/funcallable.lisp
gsll/init/interface.lisp
gsll/init/defmfun.lisp
gsll/init/defmfun-array.lisp
gsll/init/defmfun-single.lisp
gsll/init/body-expand.lisp
gsll/init/generate-examples.lisp
gsll/init/generic.lisp
gsll/floating-point/ieee-modes.lisp
gsll/floating-point/floating-point.lisp
gsll/mathematical/mathematical.lisp
gsll/mathematical/complex.lisp
gsll/data/array-structs.lisp
gsll/data/foreign-array.lisp
gsll/data/vector.lisp
gsll/data/matrix.lisp
gsll/data/both.lisp
gsll/data/array-tests.lisp
gsll/data/permutation.lisp
gsll/data/combination.lisp
gsll/polynomial.lisp
gsll/special-functions/sf-result.lisp
gsll/special-functions/return-structures.lisp
gsll/special-functions/airy.lisp
gsll/special-functions/bessel.lisp
gsll/special-functions/clausen.lisp
gsll/special-functions/coulomb.lisp
gsll/special-functions/coupling.lisp
gsll/special-functions/dawson.lisp
gsll/special-functions/debye.lisp
gsll/special-functions/dilogarithm.lisp
gsll/special-functions/elementary.lisp
gsll/special-functions/elliptic-integrals.lisp
gsll/special-functions/elliptic-functions.lisp
gsll/special-functions/error-functions.lisp
gsll/special-functions/exponential-functions.lisp
gsll/special-functions/exponential-integrals.lisp
gsll/special-functions/fermi-dirac.lisp
gsll/special-functions/gamma.lisp
gsll/special-functions/gegenbauer.lisp
gsll/special-functions/hypergeometric.lisp
gsll/special-functions/laguerre.lisp
gsll/special-functions/lambert.lisp
gsll/special-functions/legendre.lisp
gsll/special-functions/logarithm.lisp
gsll/special-functions/mathieu.lisp
gsll/special-functions/power.lisp
gsll/special-functions/psi.lisp
gsll/special-functions/synchrotron.lisp
gsll/special-functions/transport.lisp
gsll/special-functions/trigonometry.lisp
gsll/special-functions/zeta.lisp
gsll/sorting.lisp
gsll/linear-algebra/blas1.lisp
gsll/linear-algebra/blas2.lisp
gsll/linear-algebra/blas3.lisp
gsll/linear-algebra/matrix-generation.lisp
gsll/linear-algebra/exponential.lisp
gsll/linear-algebra/lu.lisp
gsll/linear-algebra/qr.lisp
gsll/linear-algebra/qrpt.lisp
gsll/linear-algebra/svd.lisp
gsll/linear-algebra/cholesky.lisp
gsll/linear-algebra/diagonal.lisp
gsll/linear-algebra/householder.lisp
gsll/eigensystems/symmetric-hermitian.lisp
gsll/eigensystems/eigen-struct.lisp
gsll/eigensystems/nonsymmetric.lisp
gsll/eigensystems/generalized.lisp
gsll/eigensystems/nonsymmetric-generalized.lisp
gsll/fast-fourier-transforms/wavetable-workspace.lisp
gsll/fast-fourier-transforms/forward.lisp
gsll/fast-fourier-transforms/backward.lisp
gsll/fast-fourier-transforms/inverse.lisp
gsll/fast-fourier-transforms/select-direction.lisp
gsll/fast-fourier-transforms/unpack.lisp
gsll/fast-fourier-transforms/discrete.lisp
gsll/fast-fourier-transforms/extras.lisp
gsll/fast-fourier-transforms/example.lisp
gsll/random/rng-types.lisp
gsll/random/generators.lisp
gsll/random/quasi.lisp
gsll/random/tests.lisp
gsll/random/gaussian.lisp
gsll/random/gaussian-tail.lisp
gsll/random/gaussian-bivariate.lisp
gsll/random/exponential.lisp
gsll/random/laplace.lisp
gsll/random/exponential-power.lisp
gsll/random/cauchy.lisp
gsll/random/rayleigh.lisp
gsll/random/rayleigh-tail.lisp
gsll/random/landau.lisp
gsll/random/levy.lisp
gsll/random/gamma.lisp
gsll/random/flat.lisp
gsll/random/lognormal.lisp
gsll/random/chi-squared.lisp
gsll/random/fdist.lisp
gsll/random/tdist.lisp
gsll/random/beta.lisp
gsll/random/logistic.lisp
gsll/random/pareto.lisp
gsll/random/spherical-vector.lisp
gsll/random/weibull.lisp
gsll/random/gumbel1.lisp
gsll/random/gumbel2.lisp
gsll/random/dirichlet.lisp
gsll/random/discrete.lisp
gsll/random/poisson.lisp
gsll/random/bernoulli.lisp
gsll/random/binomial.lisp
gsll/random/multinomial.lisp
gsll/random/negative-binomial.lisp
gsll/random/geometric.lisp
gsll/random/hypergeometric.lisp
gsll/random/logarithmic.lisp
gsll/random/shuffling-sampling.lisp
gsll/statistics/mean-variance.lisp
gsll/statistics/absolute-deviation.lisp
gsll/statistics/higher-moments.lisp
gsll/statistics/autocorrelation.lisp
gsll/statistics/covariance.lisp
gsll/statistics/median-percentile.lisp
gsll/histogram/histogram.lisp
gsll/histogram/updating-accessing.lisp
gsll/histogram/statistics.lisp
gsll/histogram/operations.lisp
gsll/histogram/probability-distribution.lisp
gsll/histogram/ntuple.lisp
gsll/calculus/numerical-integration.lisp
gsll/calculus/numerical-integration-with-tables.lisp
gsll/calculus/monte-carlo-structs.lisp
gsll/calculus/monte-carlo.lisp
gsll/calculus/numerical-differentiation.lisp
gsll/ordinary-differential-equations/ode-system.lisp
gsll/ordinary-differential-equations/ode-struct.lisp
gsll/ordinary-differential-equations/stepping.lisp
gsll/ordinary-differential-equations/control.lisp
gsll/ordinary-differential-equations/evolution.lisp
gsll/ordinary-differential-equations/ode-example.lisp
gsll/interpolation/interpolation.lisp
gsll/interpolation/types.lisp
gsll/interpolation/lookup.lisp
gsll/interpolation/evaluation.lisp
gsll/interpolation/spline-example.lisp
gsll/chebyshev.lisp
gsll/series-struct.lisp
gsll/series-acceleration.lisp
gsll/wavelet.lisp
gsll/hankel.lisp
gsll/solve-minimize-fit/generic.lisp
gsll/solve-minimize-fit/solver-struct.lisp
gsll/solve-minimize-fit/roots-one.lisp
gsll/solve-minimize-fit/minimization-one.lisp
gsll/solve-minimize-fit/roots-multi.lisp
gsll/solve-minimize-fit/minimization-multi.lisp
gsll/solve-minimize-fit/linear-least-squares.lisp
gsll/solve-minimize-fit/nonlinear-least-squares.lisp
gsll/solve-minimize-fit/simulated-annealing.lisp
gsll/basis-splines.lisp
gsll/physical-constants/mksa.lisp
gsll/physical-constants/cgsm.lisp
gsll/physical-constants/num.lisp
gsll/physical-constants/export.lisp
gsll/test-unit/machine.lisp
gsll/test-unit/augment.lisp
gsll/tests/absolute-deviation.lisp
gsll/tests/absolute-sum.lisp
gsll/tests/airy.lisp
gsll/tests/autocorrelation.lisp
gsll/tests/axpy.lisp
gsll/tests/basis-spline.lisp
gsll/tests/bernoulli.lisp
gsll/tests/bessel.lisp
gsll/tests/beta.lisp
gsll/tests/binomial.lisp
gsll/tests/blas-copy.lisp
gsll/tests/blas-swap.lisp
gsll/tests/cauchy.lisp
gsll/tests/cdot.lisp
gsll/tests/chebyshev.lisp
gsll/tests/chi-squared.lisp
gsll/tests/cholesky.lisp
gsll/tests/clausen.lisp
gsll/tests/column.lisp
gsll/tests/combination.lisp
gsll/tests/coulomb.lisp
gsll/tests/coupling.lisp
gsll/tests/correlation.lisp
gsll/tests/covariance.lisp
gsll/tests/dawson.lisp
gsll/tests/debye.lisp
gsll/tests/dilogarithm.lisp
gsll/tests/dirichlet.lisp
gsll/tests/discrete.lisp
gsll/tests/dot.lisp
gsll/tests/eigensystems.lisp
gsll/tests/elementary.lisp
gsll/tests/elliptic-functions.lisp
gsll/tests/elliptic-integrals.lisp
gsll/tests/error-functions.lisp
gsll/tests/euclidean-norm.lisp
gsll/tests/exponential-functions.lisp
gsll/tests/exponential-integrals.lisp
gsll/tests/exponential.lisp
gsll/tests/exponential-power.lisp
gsll/tests/fast-fourier-transform.lisp
gsll/tests/fdist.lisp
gsll/tests/fermi-dirac.lisp
gsll/tests/flat.lisp
gsll/tests/gamma.lisp
gsll/tests/gamma-randist.lisp
gsll/tests/gaussian-bivariate.lisp
gsll/tests/gaussian.lisp
gsll/tests/gaussian-tail.lisp
gsll/tests/gegenbauer.lisp
gsll/tests/geometric.lisp
gsll/tests/givens.lisp
gsll/tests/gumbel1.lisp
gsll/tests/gumbel2.lisp
gsll/tests/hankel.lisp
gsll/tests/higher-moments.lisp
gsll/tests/histogram.lisp
gsll/tests/householder.lisp
gsll/tests/hypergeometric.lisp
gsll/tests/hypergeometric-randist.lisp
gsll/tests/index-max.lisp
gsll/tests/interpolation.lisp
gsll/tests/inverse-matrix-product.lisp
gsll/tests/laguerre.lisp
gsll/tests/lambert.lisp
gsll/tests/landau.lisp
gsll/tests/laplace.lisp
gsll/tests/legendre.lisp
gsll/tests/levy.lisp
gsll/tests/linear-least-squares.lisp
gsll/tests/logarithmic.lisp
gsll/tests/logarithm.lisp
gsll/tests/logistic.lisp
gsll/tests/lognormal.lisp
gsll/tests/lu.lisp
gsll/tests/mathematical.lisp
gsll/tests/mathieu.lisp
gsll/tests/matrix-div.lisp
gsll/tests/matrix-max-index.lisp
gsll/tests/matrix-max.lisp
gsll/tests/matrix-mean.lisp
gsll/tests/matrix-min.lisp
gsll/tests/matrix-min-index.lisp
gsll/tests/matrix-minmax-index.lisp
gsll/tests/matrix-minmax.lisp
gsll/tests/matrix-sub.lisp
gsll/tests/matrix-add.lisp
gsll/tests/matrix-mult.lisp
gsll/tests/matrix-product-hermitian.lisp
gsll/tests/matrix-product.lisp
gsll/tests/matrix-product-nonsquare.lisp
gsll/tests/matrix-product-symmetric.lisp
gsll/tests/matrix-product-triangular.lisp
gsll/tests/matrix-set-all.lisp
gsll/tests/matrix-set-zero.lisp
gsll/tests/matrix-standard-deviation.lisp
gsll/tests/matrix-standard-deviation-with-fixed-mean.lisp
gsll/tests/matrix-standard-deviation-with-mean.lisp
gsll/tests/matrix-swap.lisp
gsll/tests/matrix-transpose-copy.lisp
gsll/tests/matrix-transpose.lisp
gsll/tests/matrix-variance.lisp
gsll/tests/matrix-variance-with-fixed-mean.lisp
gsll/tests/matrix-variance-with-mean.lisp
gsll/tests/median-percentile.lisp
gsll/tests/minimization-one.lisp
gsll/tests/minimization-multi.lisp
gsll/tests/monte-carlo.lisp
gsll/tests/multinomial.lisp
gsll/tests/negative-binomial.lisp
gsll/tests/nonlinear-least-squares.lisp
gsll/tests/ntuple.lisp
gsll/tests/numerical-differentiation.lisp
gsll/tests/numerical-integration.lisp
gsll/tests/ode.lisp
gsll/tests/pareto.lisp
gsll/tests/permutation.lisp
gsll/tests/poisson.lisp
gsll/tests/polynomial.lisp
gsll/tests/power.lisp
gsll/tests/psi.lisp
gsll/tests/qr.lisp
gsll/tests/qrpt.lisp
gsll/tests/quasi-random-number-generators.lisp
gsll/tests/random-number-generators.lisp
gsll/tests/rank-1-update.lisp
gsll/tests/rayleigh.lisp
gsll/tests/rayleigh-tail.lisp
gsll/tests/roots-multi.lisp
gsll/tests/roots-one.lisp
gsll/tests/row.lisp
gsll/tests/scale.lisp
gsll/tests/series-acceleration.lisp
gsll/tests/set-basis.lisp
gsll/tests/setf-column.lisp
gsll/tests/setf-row.lisp
gsll/tests/set-identity.lisp
gsll/tests/shuffling-sampling.lisp
gsll/tests/sort-matrix-largest.lisp
gsll/tests/sort-matrix.lisp
gsll/tests/sort-matrix-smallest.lisp
gsll/tests/sort-vector-index.lisp
gsll/tests/sort-vector-largest-index.lisp
gsll/tests/sort-vector-largest.lisp
gsll/tests/sort-vector.lisp
gsll/tests/sort-vector-smallest-index.lisp
gsll/tests/sort-vector-smallest.lisp
gsll/tests/spherical-vector.lisp
gsll/tests/svd.lisp
gsll/tests/swap-columns.lisp
gsll/tests/swap-elements.lisp
gsll/tests/swap-row-column.lisp
gsll/tests/swap-rows.lisp
gsll/tests/synchrotron.lisp
gsll/tests/tdist.lisp
gsll/tests/transport.lisp
gsll/tests/trigonometry.lisp
gsll/tests/vector-div.lisp
gsll/tests/vector-max-index.lisp
gsll/tests/vector-max.lisp
gsll/tests/vector-mean.lisp
gsll/tests/vector-min.lisp
gsll/tests/vector-min-index.lisp
gsll/tests/vector-minmax-index.lisp
gsll/tests/vector-minmax.lisp
gsll/tests/vector-sub.lisp
gsll/tests/vector-add.lisp
gsll/tests/vector-mult.lisp
gsll/tests/vector-reverse.lisp
gsll/tests/vector-set-all.lisp
gsll/tests/vector-set-zero.lisp
gsll/tests/vector-standard-deviation.lisp
gsll/tests/vector-standard-deviation-with-fixed-mean.lisp
gsll/tests/vector-standard-deviation-with-mean.lisp
gsll/tests/vector-swap.lisp
gsll/tests/vector-variance.lisp
gsll/tests/vector-variance-with-fixed-mean.lisp
gsll/tests/vector-variance-with-mean.lisp
gsll/tests/weibull.lisp
gsll/tests/zeta.lisp
gsll/init/init.lisp
init
(module).
gsll
.
gsl-config-pathname
(function).
gsll/init/gsl-version.lisp
init.lisp
(file).
init
(module).
*gsl-version*
(symbol macro).
%var-accessor-*gsl-version*
(function).
(setf %var-accessor-*gsl-version*)
(function).
have-at-least-gsl-version
(function).
gsll/init/utility.lisp
init.lisp
(file).
init
(module).
make-symbol-cardinal
(function).
make-symbol-cardinals
(function).
mappend
(function).
gsll/init/forms.lisp
init.lisp
(file).
init
(module).
*defmfun-llk*
(special variable).
*defmfun-optk*
(special variable).
after-llk
(function).
arglist-plain-and-categories
(function).
category-for-argument
(function).
eql-specializer
(function).
gsll/init/conditions.lisp
init.lisp
(file).
libgsl.lisp
(file).
init
(module).
bad-function-supplied
(condition).
cache-limit-exceeded
(condition).
divergence
(condition).
exceeded-maximum-iterations
(condition).
factorization-failure
(condition).
failure-to-reach-tolerance
(condition).
failure-to-reach-tolerance-f
(condition).
failure-to-reach-tolerance-g
(condition).
failure-to-reach-tolerance-x
(condition).
generic-failure-1
(condition).
generic-failure-2
(condition).
gsl-condition
(condition).
gsl-division-by-zero
(condition).
gsl-eof
(condition).
input-domain
(condition).
input-range
(condition).
invalid-argument
(condition).
invalid-pointer
(condition).
invalid-tolerance
(condition).
jacobian-not-improving
(condition).
loss-of-accuracy
(condition).
memory-allocation-failure
(condition).
no-progress
(condition).
nonconformant-dimensions
(condition).
nonsquare-matrix
(condition).
overflow
(condition).
return-value-on-error
(macro).
roundoff-failure
(condition).
runaway-iteration
(condition).
sanity-check-failure
(condition).
singularity
(condition).
table-limit-exceeded
(condition).
underflow
(condition).
unimplemented-feature
(condition).
unsupported-feature
(condition).
*errorno-keyword*
(special variable).
+continue+
(constant).
+ebadfunc+
(constant).
+ebadlen+
(constant).
+ebadtol+
(constant).
+ecache+
(constant).
+ediverge+
(constant).
+edom+
(constant).
+efactor+
(constant).
+efailed+
(constant).
+efault+
(constant).
+einval+
(constant).
+eloss+
(constant).
+emaxiter+
(constant).
+enomem+
(constant).
+enoprog+
(constant).
+enoprogj+
(constant).
+enotsqr+
(constant).
+eof+
(constant).
+eovrflw+
(constant).
+erange+
(constant).
+eround+
(constant).
+erunaway+
(constant).
+esanity+
(constant).
+esing+
(constant).
+etable+
(constant).
+etol+
(constant).
+etolf+
(constant).
+etolg+
(constant).
+etolx+
(constant).
+eundrflw+
(constant).
+eunimpl+
(constant).
+eunsup+
(constant).
+ezerodiv+
(constant).
+failure+
(constant).
+success+
(constant).
define-gsl-condition
(macro).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-number
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
error-text
(reader method).
establish-handler
(function).
explanation
(reader method).
line-number
(reader method).
lookup-condition
(function).
signal-gsl-error
(function).
signal-gsl-warning
(function).
source-file
(reader method).
unspecified-errno
(condition).
gsll/init/callback-compile-defs.lisp
init.lisp
(file).
init
(module).
*callbacks-for-classes*
(special variable).
get-callbacks-for-class
(function).
make-cbstruct-object
(function).
make-mobject-defmcallbacks
(function).
mobject-cbvname
(function).
mobject-cbvnames
(function).
mobject-fnvname
(function).
mobject-fnvnames
(function).
mobject-variable-name
(function).
record-callbacks-for-class
(function).
gsll/init/mobject.lisp
init.lisp
(file).
callback-compile-defs.lisp
(file).
init
(module).
allocate
(generic function).
defmobject
(macro).
foreign-pointer-method
(macro).
initialize-suffix-switched-foreign
(function).
make-initialize-instance
(function).
make-reinitialize-instance
(function).
mobject
(class).
mobject-maker
(function).
mpointer
(method).
mpointer
(reader method).
plural-symbol
(function).
singular-symbol
(function).
singularize
(function).
symbol-keyword-symbol
(function).
gsll/init/callback-included.lisp
mobject.lisp
(file).
init
(module).
dimensions
(reader method).
print-object
(method).
callback-included
(class).
callback-included-cl
(class).
callback-set-dynamic
(function).
callback-struct
(reader method).
cbinfo
(reader method).
def-ci-subclass
(macro).
def-ci-subclass-1d
(macro).
dimension-names
(reader method).
funcallables
(reader method).
functions
(reader method).
scalarsp
(reader method).
gsll/init/callback.lisp
init.lisp
(file).
utility.lisp
(file).
forms.lisp
(file).
callback-included.lisp
(file).
init
(module).
callback-args
(function).
callback-remove-arg
(function).
callback-replace-arg
(function).
callback-set-slots
(function).
callback-symbol-set
(function).
cbd-dimensions
(function).
cbd-functions
(function).
defmcallback
(macro).
make-cbstruct
(function).
make-defmcallbacks
(function).
number-of-callbacks
(function).
parse-callback-argspec
(function).
parse-callback-fnspec
(function).
parse-callback-static
(function).
set-cbstruct
(function).
set-parameters
(function).
set-slot-function
(function).
set-structure-slot
(function).
gsll/init/types.lisp
init.lisp
(file).
libgsl.lisp
(file).
init
(module).
*blas-splice-fp-types*
(special variable).
*cstd-blas-mapping*
(special variable).
*cstd-gsl-mapping*
(special variable).
*gsl-splice-fp-types*
(special variable).
*gsl-splice-int-types*
(special variable).
cl-gsl
(function).
gsll/init/callback-struct.lisp
types.lisp
(file).
libgsl.lisp
(file).
init
(module).
gsll/init/funcallable.lisp
init.lisp
(file).
utility.lisp
(file).
init
(module).
all-io
(function).
array-element-refs
(function).
callback-set-mvb
(function).
faify-form
(function).
make-compiled-funcallable
(function).
make-funcallable-form
(function).
make-funcallables-for-object
(function).
reference-foreign-element
(function).
value-from-dimensions
(function).
vspecs-direction
(function).
gsll/init/interface.lisp
init.lisp
(file).
conditions.lisp
(file).
init
(module).
gsl-lookup
(function).
*gsl-symbol-equivalence*
(special variable).
*special-c-return*
(special variable).
check-gsl-status
(function).
check-null-pointer
(function).
cl-argument-types
(function).
cl-symbols
(function).
declaration-form
(function).
defmpar
(macro).
map-name
(function).
success-continue
(function).
success-failure
(function).
wfo-declare
(function).
gsll/init/defmfun.lisp
init.lisp
(file).
forms.lisp
(file).
interface.lisp
(file).
init
(module).
body-optional-arg
(function).
defmfun
(macro).
expand-defmfun-method
(function).
expand-defmfun-optional
(function).
expand-defmfun-wrap
(function).
optional-args-to-switch-gsl-functions
(function).
with-defmfun-key-args
(macro).
wrap-index-export
(function).
wrap-progn
(function).
gsll/init/defmfun-array.lisp
init.lisp
(file).
defmfun.lisp
(file).
callback-included.lisp
(file).
init
(module).
actual-array-c-type
(function).
actual-array-class
(function).
actual-class-arglist
(function).
actual-element-c-type
(function).
actual-gsl-function-name
(function).
element-type-select
(function).
expand-defmfun-arrays
(function).
expand-defmfun-defmethods
(function).
expand-defmfun-generic
(function).
generate-methods
(function).
gsll/init/defmfun-single.lisp
init.lisp
(file).
defmfun.lisp
(file).
mobject.lisp
(file).
callback.lisp
(file).
init
(module).
name
(reader method).
body-no-optional-arg
(function).
complete-definition
(function).
defgeneric-method-p
(function).
gsl-name
(reader method).
gsl-version
(reader method).
obsolete-gsl-version
(condition).
stupid-code-walk-find-variables
(function).
variables-used-in-c-arguments
(function).
wrap-letlike
(function).
gsll/init/body-expand.lisp
init.lisp
(file).
defmfun.lisp
(file).
mobject.lisp
(file).
callback.lisp
(file).
init
(module).
body-expand
(function).
cl-convert-form
(function).
creturn-st
(function).
defmfun-return
(function).
values-unless-singleton
(function).
gsll/init/generate-examples.lisp
init.lisp
(file).
init
(module).
examples
(function).
*all-generated-tests*
(special variable).
*double-float-pool*
(special variable).
*signed-byte-pool*
(special variable).
*unsigned-byte-pool*
(special variable).
array-default
(function).
delete-test-definition
(function).
generate-all-array-tests
(macro).
generate-all-array-tests-body
(function).
make-list-from-pool
(function).
save-test
(macro).
scalar-default
(function).
stupid-code-walk-eval-some
(function).
gsll/init/generic.lisp
init
(module).
parameter
(generic function).
(setf parameter)
(generic function).
gsll/floating-point/ieee-modes.lisp
floating-point
(module).
set-floating-point-modes
(function).
gsll/floating-point/floating-point.lisp
floating-point
(module).
float-as-integer
(function).
format-ieee754-bits
(function).
integer-as-float
(function).
decode-ieee754
(function).
ieee754-sign-bit
(function).
next-float
(function).
gsll/mathematical/mathematical.lisp
mathematical
(module).
+nan+
(constant).
+negative-infinity+
(constant).
+positive-infinity+
(constant).
double-float-unequal
(function).
exp-1
(function).
finitep
(function).
gsl-asinh
(function).
gsl-atanh
(function).
hypotenuse*
(function).
infinityp
(function).
log+1
(function).
nanp
(function).
gsll/mathematical/complex.lisp
mathematical
(module).
argument
(function).
cx-add
(function).
cx-add-imag
(function).
cx-add-real
(function).
cx-arccos
(function).
cx-arccos-real
(function).
cx-arccosh
(function).
cx-arccosh-real
(function).
cx-arccot
(function).
cx-arccoth
(function).
cx-arccsc
(function).
cx-arccsc-real
(function).
cx-arccsch
(function).
cx-arcsec
(function).
cx-arcsec-real
(function).
cx-arcsech
(function).
cx-arcsin
(function).
cx-arcsin-real
(function).
cx-arcsinh
(function).
cx-arctan
(function).
cx-arctanh
(function).
cx-arctanh-real
(function).
cx-conjugate
(function).
cx-cos
(function).
cx-cosh
(function).
cx-cot
(function).
cx-coth
(function).
cx-csc
(function).
cx-csch
(function).
cx-div
(function).
cx-div-imag
(function).
cx-div-real
(function).
cx-exp
(function).
cx-expt
(function).
cx-expt-real
(function).
cx-inverse
(function).
cx-log
(function).
cx-log10
(function).
cx-logb
(function).
cx-mul
(function).
cx-mul-imag
(function).
cx-mul-real
(function).
cx-negative
(function).
cx-sec
(function).
cx-sech
(function).
cx-sin
(function).
cx-sinh
(function).
cx-sqrt
(function).
cx-sqrt-real
(function).
cx-sub
(function).
cx-sub-imag
(function).
cx-sub-real
(function).
cx-tan
(function).
cx-tanh
(function).
log-modulus
(function).
modulus
(function).
modulus2
(function).
gsll/data/foreign-array.lisp
array-structs.lisp
(file).
data
(module).
make-foreign-array-from-mpointer
(function).
make-gsl-metadata
(function).
mpointer
(method).
gsll/data/vector.lisp
foreign-array.lisp
(file).
array-structs.lisp
(file).
data
(module).
set-basis
(generic function).
swap-elements
(generic function).
vector-reverse
(generic function).
gsll/data/matrix.lisp
foreign-array.lisp
(file).
vector.lisp
(file).
array-structs.lisp
(file).
data
(module).
column
(generic function).
(setf column)
(generic function).
matrix-transpose
(generic function).
matrix-transpose*
(generic function).
row
(generic function).
(setf row)
(generic function).
set-identity
(generic function).
swap-columns
(generic function).
swap-row-column
(generic function).
swap-rows
(generic function).
gsll/data/both.lisp
foreign-array.lisp
(file).
vector.lisp
(file).
matrix.lisp
(file).
data
(module).
elt*
(generic function).
elt+
(generic function).
elt-
(generic function).
elt/
(generic function).
maref
(macro).
(setf maref)
(setf expander).
max-index
(generic function).
min-index
(generic function).
minmax
(generic function).
minmax-index
(generic function).
mmax
(generic function).
mmin
(generic function).
mminusp
(generic function).
mplusp
(generic function).
mzerop
(generic function).
non-negative-p
(generic function).
set-all
(generic function).
set-zero
(generic function).
swap
(generic function).
access-value-int
(function).
alloc-from-block
(generic function).
set-maref
(macro).
gsll/data/permutation.lisp
foreign-array.lisp
(file).
array-structs.lisp
(file).
data
(module).
aref
(method).
canonical-cycles
(function).
canonical-to-linear
(function).
copy
(method).
dimensions
(method).
initialize-instance
(method).
inversions
(function).
linear-cycles
(function).
linear-to-canonical
(function).
make-permutation
(function).
permutation
(class).
permutation*
(function).
permutation-data
(function).
permutation-inverse
(function).
permutation-next
(function).
permutation-previous
(function).
permutation-reverse
(function).
permute
(generic function).
permute-inverse
(generic function).
print-object
(method).
reinitialize-instance
(method).
set-identity
(method).
size
(method).
swap-elements
(method).
validp
(generic function).
allocate
(method).
generate-all-permutations
(function).
generate-all-permutations-backwards
(function).
perm-copy
(function).
gsll/data/combination.lisp
foreign-array.lisp
(file).
array-structs.lisp
(file).
data
(module).
combination-next
(function).
combination-previous
(function).
combination-range
(function).
copy
(method).
init-first
(function).
init-last
(function).
initialize-instance
(method).
make-combination
(function).
print-object
(method).
size
(method).
validp
(method).
comb-copy
(function).
combination
(class).
gsll/polynomial.lisp
gsll
(system).
divided-difference
(function).
evaluate
(method).
evaluate
(method).
evaluate
(method).
evaluate-with-derivatives
(function).
initialize-instance
(method).
make-polynomial-complex-workspace
(function).
polynomial-complex-workspace
(class).
polynomial-solve
(function).
solve-cubic
(function).
solve-cubic-complex
(function).
solve-quadratic
(function).
solve-quadratic-complex
(function).
taylor-divided-difference
(function).
allocate
(method).
gsll/special-functions/return-structures.lisp
sf-result.lisp
(file).
special-functions
(module).
*default-sf-array-size*
(special variable).
complex-with-error
(function).
values-with-errors
(function).
vdf
(function).
vdf-size
(function).
gsll/special-functions/airy.lisp
return-structures.lisp
(file).
special-functions
(module).
airy-ai
(function).
airy-ai-deriv
(function).
airy-ai-deriv-scaled
(function).
airy-ai-scaled
(function).
airy-bi
(function).
airy-bi-deriv
(function).
airy-bi-deriv-scaled
(function).
airy-bi-scaled
(function).
airy-zero-ai
(function).
airy-zero-ai-deriv
(function).
airy-zero-bi
(function).
airy-zero-bi-deriv
(function).
gsll/special-functions/bessel.lisp
return-structures.lisp
(file).
special-functions
(module).
bessel-lnknu
(function).
bessel-zero-j0
(function).
bessel-zero-j1
(function).
bessel-zero-jnu
(function).
cylindrical-bessel-i
(generic function).
cylindrical-bessel-i-scaled
(generic function).
cylindrical-bessel-i0
(function).
cylindrical-bessel-i0-scaled
(function).
cylindrical-bessel-i1
(function).
cylindrical-bessel-i1-scaled
(function).
cylindrical-bessel-in-array
(function).
cylindrical-bessel-in-scaled-array
(function).
cylindrical-bessel-j
(generic function).
cylindrical-bessel-j-array-order
(function).
cylindrical-bessel-j-array-x
(function).
cylindrical-bessel-j0
(function).
cylindrical-bessel-j1
(function).
cylindrical-bessel-k
(generic function).
cylindrical-bessel-k-scaled
(generic function).
cylindrical-bessel-k0
(function).
cylindrical-bessel-k0-scaled
(function).
cylindrical-bessel-k1
(function).
cylindrical-bessel-k1-scaled
(function).
cylindrical-bessel-kn-array
(function).
cylindrical-bessel-kn-scaled-array
(function).
cylindrical-bessel-y
(generic function).
cylindrical-bessel-y0
(function).
cylindrical-bessel-y1
(function).
cylindrical-bessel-yn-array
(function).
spherical-bessel-i0-scaled
(function).
spherical-bessel-i1-scaled
(function).
spherical-bessel-i2-scaled
(function).
spherical-bessel-il-scaled
(function).
spherical-bessel-il-scaled-array
(function).
spherical-bessel-j0
(function).
spherical-bessel-j1
(function).
spherical-bessel-j2
(function).
spherical-bessel-jl
(function).
spherical-bessel-jl-array
(function).
spherical-bessel-jl-steed-array
(function).
spherical-bessel-k0-scaled
(function).
spherical-bessel-k1-scaled
(function).
spherical-bessel-k2-scaled
(function).
spherical-bessel-kl-scaled
(function).
spherical-bessel-kl-scaled-array
(function).
spherical-bessel-y0
(function).
spherical-bessel-y1
(function).
spherical-bessel-y2
(function).
spherical-bessel-yl
(function).
spherical-bessel-yl-array
(function).
gsll/special-functions/clausen.lisp
return-structures.lisp
(file).
special-functions
(module).
clausen
(function).
gsll/special-functions/coulomb.lisp
return-structures.lisp
(file).
special-functions
(module).
coulomb-cl
(function).
coulomb-cl-array
(function).
coulomb-wave-f-array
(function).
coulomb-wave-fg
(function).
coulomb-wave-fg-array
(function).
coulomb-wave-fgp-array
(function).
coulomb-wave-sphf-array
(function).
hydrogenicr
(function).
hydrogenicr-1
(function).
gsll/special-functions/coupling.lisp
return-structures.lisp
(file).
special-functions
(module).
coupling-3j
(function).
coupling-6j
(function).
coupling-9j
(function).
gsll/special-functions/dawson.lisp
return-structures.lisp
(file).
special-functions
(module).
dawson
(function).
gsll/special-functions/debye.lisp
return-structures.lisp
(file).
special-functions
(module).
gsll/special-functions/dilogarithm.lisp
return-structures.lisp
(file).
special-functions
(module).
dilogarithm
(generic function).
gsll/special-functions/elementary.lisp
return-structures.lisp
(file).
special-functions
(module).
multiply
(function).
multiply-err
(function).
gsll/special-functions/elliptic-integrals.lisp
return-structures.lisp
(file).
special-functions
(module).
elliptic-integral-d
(function).
elliptic-integral-e
(function).
elliptic-integral-e-complete
(function).
elliptic-integral-f
(function).
elliptic-integral-k-complete
(function).
elliptic-integral-p
(function).
elliptic-integral-rc
(function).
elliptic-integral-rd
(function).
elliptic-integral-rf
(function).
elliptic-integral-rj
(function).
gsll/special-functions/elliptic-functions.lisp
return-structures.lisp
(file).
special-functions
(module).
jacobian-elliptic-functions
(function).
*elljac-a*
(special variable).
*elljac-b*
(special variable).
*elljac-c*
(special variable).
*elljac-c2*
(special variable).
*elljac-k*
(special variable).
gsll/special-functions/error-functions.lisp
return-structures.lisp
(file).
special-functions
(module).
gsll/special-functions/exponential-functions.lisp
return-structures.lisp
(file).
special-functions
(module).
exp-err
(function).
exp-err-scaled
(function).
exp-mult
(function).
exp-mult-err
(function).
exp-mult-err-scaled
(function).
exp-mult-scaled
(function).
exp-scaled
(function).
expm1
(function).
exprel
(function).
exprel-2
(function).
exprel-n
(function).
gsl-exp
(function).
gsll/special-functions/exponential-integrals.lisp
return-structures.lisp
(file).
special-functions
(module).
atanint
(function).
chi
(function).
ci
(function).
exponential-integral-3
(function).
exponential-integral-e1
(function).
exponential-integral-e2
(function).
exponential-integral-ei
(function).
exponential-integral-en
(function).
shi
(function).
si
(function).
gsll/special-functions/fermi-dirac.lisp
return-structures.lisp
(file).
special-functions
(module).
fermi-dirac-0
(function).
fermi-dirac-1
(function).
fermi-dirac-1/2
(function).
fermi-dirac-2
(function).
fermi-dirac-3/2
(function).
fermi-dirac-inc-0
(function).
fermi-dirac-integral
(function).
fermi-dirac-m1
(function).
fermi-dirac-m1/2
(function).
gsll/special-functions/gamma.lisp
return-structures.lisp
(file).
special-functions
(module).
1/gamma
(function).
beta
(function).
choose
(function).
complementary-incomplete-gamma
(function).
double-factorial
(function).
factorial
(function).
gamma
(function).
gamma*
(function).
incomplete-beta
(function).
incomplete-gamma
(function).
log-beta
(function).
log-choose
(function).
log-double-factorial
(function).
log-factorial
(function).
log-gamma
(function).
log-gamma-complex
(function).
log-gamma-sign
(function).
log-pochammer
(function).
log-pochammer-sign
(function).
nonnormalized-incomplete-gamma
(function).
pochammer
(function).
relative-pochammer
(function).
taylor-coefficient
(function).
+gamma-xmax+
(constant).
gsll/special-functions/gegenbauer.lisp
return-structures.lisp
(file).
special-functions
(module).
gegenbauer
(function).
gegenbauer-1
(function).
gegenbauer-2
(function).
gegenbauer-3
(function).
gegenbauer-array
(function).
gsll/special-functions/hypergeometric.lisp
return-structures.lisp
(file).
special-functions
(module).
hypergeometric-0f1
(function).
hypergeometric-1f1
(generic function).
hypergeometric-2f0
(function).
hypergeometric-2f1
(function).
hypergeometric-2f1-conj
(function).
hypergeometric-2f1-conj-renorm
(function).
hypergeometric-2f1-renorm
(function).
hypergeometric-u
(generic function).
hypergeometric-u-e10
(generic function).
gsll/special-functions/laguerre.lisp
return-structures.lisp
(file).
special-functions
(module).
laguerre
(function).
laguerre-1
(function).
laguerre-2
(function).
laguerre-3
(function).
gsll/special-functions/lambert.lisp
return-structures.lisp
(file).
special-functions
(module).
lambert-w0
(function).
lambert-wm1
(function).
gsll/special-functions/legendre.lisp
return-structures.lisp
(file).
special-functions
(module).
legendre-conicalp-0
(function).
legendre-conicalp-1
(function).
legendre-conicalp-half
(function).
legendre-conicalp-mhalf
(function).
legendre-h3d
(function).
legendre-h3d-0
(function).
legendre-h3d-1
(function).
legendre-h3d-array
(function).
legendre-p1
(function).
legendre-p2
(function).
legendre-p3
(function).
legendre-pl
(function).
legendre-pl-array
(function).
legendre-pl-deriv-array
(function).
legendre-plm
(function).
legendre-q0
(function).
legendre-q1
(function).
legendre-ql
(function).
legendre-regular-cylindrical-conical
(function).
legendre-regular-spherical-conical
(function).
legendre-sphplm
(function).
gsll/special-functions/logarithm.lisp
return-structures.lisp
(file).
special-functions
(module).
gsl-log
(generic function).
log-1+x
(function).
log-1+x-m1
(function).
log-abs
(function).
gsll/special-functions/mathieu.lisp
return-structures.lisp
(file).
special-functions
(module).
initialize-instance
(method).
make-mathieu
(function).
mathieu
(class).
mathieu-a
(function).
mathieu-a-array
(function).
mathieu-b
(function).
mathieu-b-array
(function).
mathieu-ce
(function).
mathieu-ce-array
(function).
mathieu-mc
(function).
mathieu-mc-array
(function).
mathieu-ms
(function).
mathieu-ms-array
(function).
mathieu-se
(function).
mathieu-se-array
(function).
allocate
(method).
gsll/special-functions/power.lisp
return-structures.lisp
(file).
special-functions
(module).
pow
(function).
gsll/special-functions/psi.lisp
return-structures.lisp
(file).
special-functions
(module).
gsll/special-functions/synchrotron.lisp
return-structures.lisp
(file).
special-functions
(module).
synchrotron-1
(function).
synchrotron-2
(function).
gsll/special-functions/transport.lisp
return-structures.lisp
(file).
special-functions
(module).
transport-2
(function).
transport-3
(function).
transport-4
(function).
transport-5
(function).
gsll/special-functions/trigonometry.lisp
return-structures.lisp
(file).
special-functions
(module).
cos-err
(function).
gsl-cos
(generic function).
gsl-sin
(generic function).
hypotenuse
(function).
log-cosh
(function).
log-sin
(function).
log-sinh
(function).
polar-to-rectangular
(function).
rectangular-to-polar
(function).
restrict-positive
(function).
restrict-symmetric
(function).
sin-err
(function).
sinc
(function).
gsll/special-functions/zeta.lisp
return-structures.lisp
(file).
special-functions
(module).
eta
(function).
hurwitz-zeta
(function).
zeta
(generic function).
zeta-1
(generic function).
gsll/sorting.lisp
gsll
(system).
heapsort
(function).
heapsort-index
(function).
msort
(generic function).
sort-index
(generic function).
sort-largest
(generic function).
sort-largest-index
(generic function).
sort-smallest
(generic function).
sort-smallest-index
(generic function).
sort-vector
(generic function).
sort-vector-index
(generic function).
sort-vector-largest
(generic function).
sort-vector-largest-index
(generic function).
sort-vector-smallest
(generic function).
sort-vector-smallest-index
(generic function).
defcomparison
(macro).
gsll/linear-algebra/blas1.lisp
linear-algebra
(module).
absolute-sum
(generic function).
axpy
(generic function).
blas-copy
(generic function).
blas-swap
(generic function).
cdot
(generic function).
euclidean-norm
(generic function).
givens-rotation
(generic function).
givens-rotation-m
(generic function).
index-max
(generic function).
modified-givens-rotation
(generic function).
modified-givens-rotation-m
(generic function).
scale
(generic function).
sdot
(function).
gsll/linear-algebra/blas2.lisp
linear-algebra
(module).
conjugate-rank-1-update
(generic function).
hermitian-rank-1-update
(generic function).
hermitian-rank-2-update
(generic function).
inverse-matrix-product
(generic function).
matrix-product
(generic function).
matrix-product-hermitian
(generic function).
matrix-product-symmetric
(generic function).
matrix-product-triangular
(generic function).
rank-1-update
(generic function).
symmetric-rank-1-update
(generic function).
symmetric-rank-2-update
(generic function).
matrix-product-dimensions
(function).
gsll/linear-algebra/blas3.lisp
blas2.lisp
(file).
linear-algebra
(module).
hermitian-rank-1-update
(method).
hermitian-rank-1-update
(method).
hermitian-rank-2-update
(method).
hermitian-rank-2-update
(method).
inverse-matrix-product
(method).
inverse-matrix-product
(method).
inverse-matrix-product
(method).
inverse-matrix-product
(method).
matrix-product
(method).
matrix-product
(method).
matrix-product
(method).
matrix-product
(method).
matrix-product-hermitian
(method).
matrix-product-hermitian
(method).
matrix-product-symmetric
(method).
matrix-product-symmetric
(method).
matrix-product-symmetric
(method).
matrix-product-symmetric
(method).
matrix-product-triangular
(method).
matrix-product-triangular
(method).
matrix-product-triangular
(method).
matrix-product-triangular
(method).
symmetric-rank-1-update
(method).
symmetric-rank-1-update
(method).
symmetric-rank-1-update
(method).
symmetric-rank-1-update
(method).
symmetric-rank-2-update
(method).
symmetric-rank-2-update
(method).
symmetric-rank-2-update
(method).
symmetric-rank-2-update
(method).
gsll/linear-algebra/matrix-generation.lisp
linear-algebra
(module).
*hilb12*
(special variable).
*hilb12-soln*
(special variable).
*hilb2*
(special variable).
*hilb2-soln*
(special variable).
*hilb3*
(special variable).
*hilb3-soln*
(special variable).
*hilb4*
(special variable).
*hilb4-soln*
(special variable).
*m35*
(special variable).
*m53*
(special variable).
*s35*
(special variable).
*s53*
(special variable).
*vander12*
(special variable).
*vander12-soln*
(special variable).
*vander2*
(special variable).
*vander2-soln*
(special variable).
*vander3*
(special variable).
*vander3-soln*
(special variable).
*vander4*
(special variable).
*vander4-soln*
(special variable).
constant-matrix
(function).
create-complex-matrix
(function).
create-general-matrix
(function).
create-hilbert-matrix
(function).
create-matrix
(function).
create-moler-matrix
(function).
create-rhs-vector
(function).
create-row-matrix
(function).
create-singular-matrix
(function).
create-vandermonde-matrix
(function).
gsll/linear-algebra/exponential.lisp
linear-algebra
(module).
matrix-exponential
(function).
gsll/linear-algebra/lu.lisp
linear-algebra
(module).
lu-decomposition
(generic function).
lu-determinant
(generic function).
lu-invert
(generic function).
lu-log-determinant
(generic function).
lu-refine
(generic function).
lu-sgndet
(generic function).
lu-solve
(generic function).
test-lu-solve-dim
(function).
gsll/linear-algebra/qr.lisp
linear-algebra
(module).
qr-decomposition
(function).
qr-qrsolve
(function).
qr-qtvector
(function).
qr-qvector
(function).
qr-rsolve
(function).
qr-solve
(function).
qr-solve-least-squares
(function).
qr-unpack
(function).
qr-update
(function).
r-solve
(function).
test-qr-decomp-dim
(function).
test-qr-lssolve-dim
(function).
test-qr-qrsolve-dim
(function).
test-qr-solve-dim
(function).
test-qr-update-dim
(function).
gsll/linear-algebra/qrpt.lisp
linear-algebra
(module).
qrpt-decomposition
(function).
qrpt-decomposition*
(function).
qrpt-qrsolve
(function).
qrpt-rsolve
(function).
qrpt-solve
(function).
qrpt-update
(function).
test-qrpt-decomp-dim
(function).
test-qrpt-qrsolve-dim
(function).
test-qrpt-solve-dim
(function).
gsll/linear-algebra/svd.lisp
linear-algebra
(module).
sv-decomposition
(function).
sv-jacobi-decomposition
(function).
sv-modified-decomposition
(function).
sv-solve
(function).
test-sv-solve-dim
(function).
gsll/linear-algebra/cholesky.lisp
linear-algebra
(module).
cholesky-decomposition
(generic function).
cholesky-invert
(function).
cholesky-solve
(generic function).
test-cholesky-decomp-dim
(function).
test-cholesky-invert-dim
(function).
test-cholesky-solve-dim
(function).
gsll/linear-algebra/diagonal.lisp
linear-algebra
(module).
bidiagonal-decomposition
(function).
bidiagonal-unpack
(function).
bidiagonal-unpack-diagonal-superdiagonal
(function).
bidiagonal-unpack2
(function).
solve-cyclic-tridiagonal
(function).
solve-symmetric-cyclic-tridiagonal
(function).
solve-symmetric-tridiagonal
(function).
solve-tridiagonal
(function).
tridiagonal-decomposition
(generic function).
tridiagonal-unpack
(generic function).
tridiagonal-unpack-t
(generic function).
solve-tridiagonal-example
(function).
gsll/linear-algebra/householder.lisp
linear-algebra
(module).
householder-hm
(function).
householder-hv
(function).
householder-mh
(function).
householder-solve
(function).
householder-transform
(function).
test-hh-solve-dim
(function).
gsll/eigensystems/symmetric-hermitian.lisp
eigensystems
(module).
eigen-herm
(class).
eigen-hermv
(class).
eigen-symm
(class).
eigen-symmv
(class).
eigenvalues
(generic function).
eigenvalues-eigenvectors
(generic function).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
make-eigen-herm
(function).
make-eigen-hermv
(function).
make-eigen-symm
(function).
make-eigen-symmv
(function).
sort-eigenvalues-eigenvectors
(generic function).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
eigenvalue-eigenvectors-example
(function).
gsll/eigensystems/nonsymmetric.lisp
eigen-struct.lisp
(file).
eigensystems
(module).
eigen-nonsymm
(class).
eigen-nonsymmv
(class).
eigenvalues-eigenvectors-nonsymm
(function).
eigenvalues-nonsymm
(function).
initialize-instance
(method).
initialize-instance
(method).
make-eigen-nonsymm
(function).
make-eigen-nonsymmv
(function).
allocate
(method).
allocate
(method).
set-parameters-nonsymmetric
(function).
gsll/eigensystems/generalized.lisp
eigensystems
(module).
eigen-genherm
(class).
eigen-genhermv
(class).
eigen-gensymm
(class).
eigen-gensymmv
(class).
eigenvalues-eigenvectors-gensymm
(generic function).
eigenvalues-gensymm
(generic function).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
make-eigen-genherm
(function).
make-eigen-genhermv
(function).
make-eigen-gensymm
(function).
make-eigen-gensymmv
(function).
gsll/eigensystems/nonsymmetric-generalized.lisp
eigensystems
(module).
eigen-gen
(class).
eigen-genv
(class).
eigenvalues-eigenvectors-gen
(function).
eigenvalues-gen
(function).
initialize-instance
(method).
initialize-instance
(method).
make-eigen-gen
(function).
make-eigen-genv
(function).
allocate
(method).
allocate
(method).
set-parameters-gen
(function).
gsll/fast-fourier-transforms/wavetable-workspace.lisp
fast-fourier-transforms
(module).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
make-fft-wavetable
(function).
make-fft-workspace
(function).
with-fourier-transform-environment
(macro).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
fft-complex-wavetable-double-float
(class).
fft-complex-wavetable-single-float
(class).
fft-complex-workspace-double-float
(class).
fft-complex-workspace-single-float
(class).
fft-half-complex-wavetable-double-float
(class).
fft-half-complex-wavetable-single-float
(class).
fft-real-wavetable-double-float
(class).
fft-real-wavetable-single-float
(class).
fft-real-workspace-double-float
(class).
fft-real-workspace-single-float
(class).
make-fft-complex-wavetable-double-float
(function).
make-fft-complex-wavetable-single-float
(function).
make-fft-complex-workspace-double-float
(function).
make-fft-complex-workspace-single-float
(function).
make-fft-half-complex-wavetable-double-float
(function).
make-fft-half-complex-wavetable-single-float
(function).
make-fft-real-wavetable-double-float
(function).
make-fft-real-wavetable-single-float
(function).
make-fft-real-workspace-double-float
(function).
make-fft-real-workspace-single-float
(function).
gsll/fast-fourier-transforms/forward.lisp
fast-fourier-transforms
(module).
forward-fourier-transform
(function).
forward-fourier-transform-dif-radix2
(generic function).
forward-fourier-transform-halfcomplex-nonradix2
(generic function).
forward-fourier-transform-halfcomplex-radix2
(generic function).
forward-fourier-transform-nonradix2
(generic function).
forward-fourier-transform-radix2
(generic function).
power-of-2-p
(function).
gsll/fast-fourier-transforms/backward.lisp
fast-fourier-transforms
(module).
backward-fourier-transform
(function).
backward-fourier-transform-dif-radix2
(generic function).
backward-fourier-transform-halfcomplex-nonradix2
(generic function).
backward-fourier-transform-halfcomplex-radix2
(generic function).
backward-fourier-transform-nonradix2
(generic function).
backward-fourier-transform-radix2
(generic function).
gsll/fast-fourier-transforms/inverse.lisp
fast-fourier-transforms
(module).
inverse-fourier-transform
(function).
inverse-fourier-transform-dif-radix2
(generic function).
inverse-fourier-transform-halfcomplex-nonradix2
(generic function).
inverse-fourier-transform-halfcomplex-radix2
(generic function).
inverse-fourier-transform-nonradix2
(generic function).
inverse-fourier-transform-radix2
(generic function).
gsll/fast-fourier-transforms/select-direction.lisp
fast-fourier-transforms
(module).
fourier-transform
(function).
fourier-transform-dif-radix2
(generic function).
fourier-transform-radix2
(generic function).
gsll/fast-fourier-transforms/unpack.lisp
fast-fourier-transforms
(module).
unpack
(function).
fft-half-complex-radix2-unpack
(generic function).
fft-half-complex-unpack
(generic function).
fft-real-unpack
(generic function).
gsll/fast-fourier-transforms/discrete.lisp
fast-fourier-transforms
(module).
backward-discrete-fourier-transform
(generic function).
discrete-fourier-transform
(generic function).
forward-discrete-fourier-transform
(generic function).
inverse-discrete-fourier-transform
(generic function).
gsll/fast-fourier-transforms/extras.lisp
fast-fourier-transforms
(module).
fft-frequency-vector
(function).
fft-inverse-shift
(function).
fft-shift
(function).
fft-frequency-split
(function).
fft-frequency-step
(function).
fft-highest-frequency
(function).
gsll/fast-fourier-transforms/example.lisp
fast-fourier-transforms
(module).
copy-with-stride
(function).
fft-pulse-test
(function).
make-and-init-vector
(function).
make-urand-vector
(function).
realpart-vector
(function).
reset-urand
(function).
size-vector-scalar
(function).
test-complex-fft-noise
(function).
test-fft-noise
(function).
test-real-fft-noise
(function).
urand
(function).
vector/length
(function).
gsll/random/rng-types.lisp
random
(module).
+borosh13+
(symbol macro).
+cmrg+
(symbol macro).
+coveyou+
(symbol macro).
+default-type+
(symbol macro).
+fishman18+
(symbol macro).
+fishman20+
(symbol macro).
+fishman2x+
(symbol macro).
+gfsr4+
(symbol macro).
+knuthran+
(symbol macro).
+knuthran2+
(symbol macro).
+knuthran2002+
(symbol macro).
+lecuyer21+
(symbol macro).
+minstd+
(symbol macro).
+mrg+
(symbol macro).
+mt19937+
(symbol macro).
+mt19937-1998+
(symbol macro).
+mt19937-1999+
(symbol macro).
+r250+
(symbol macro).
+ran0+
(symbol macro).
+ran1+
(symbol macro).
+ran2+
(symbol macro).
+ran3+
(symbol macro).
+rand+
(symbol macro).
+rand48+
(symbol macro).
+random128_bsd+
(symbol macro).
+random128_glibc2+
(symbol macro).
+random128_libc5+
(symbol macro).
+random256_bsd+
(symbol macro).
+random256_glibc2+
(symbol macro).
+random256_libc5+
(symbol macro).
+random32_bsd+
(symbol macro).
+random32_glibc2+
(symbol macro).
+random32_libc5+
(symbol macro).
+random64_bsd+
(symbol macro).
+random64_glibc2+
(symbol macro).
+random64_libc5+
(symbol macro).
+random8_bsd+
(symbol macro).
+random8_glibc2+
(symbol macro).
+random8_libc5+
(symbol macro).
+random_bsd+
(symbol macro).
+random_glibc2+
(symbol macro).
+random_libc5+
(symbol macro).
+randu+
(symbol macro).
+ranf+
(symbol macro).
+ranlux+
(symbol macro).
+ranlux389+
(symbol macro).
+ranlxd1+
(symbol macro).
+ranlxd2+
(symbol macro).
+ranlxs0+
(symbol macro).
+ranlxs1+
(symbol macro).
+ranlxs2+
(symbol macro).
+ranmar+
(symbol macro).
+slatec+
(symbol macro).
+taus+
(symbol macro).
+taus113+
(symbol macro).
+taus2+
(symbol macro).
+transputer+
(symbol macro).
+tt800+
(symbol macro).
+uni+
(symbol macro).
+uni32+
(symbol macro).
+vax+
(symbol macro).
+waterman14+
(symbol macro).
+zuf+
(symbol macro).
all-random-number-generators
(function).
rng-environment-setup
(function).
%var-accessor-+borosh13+
(function).
(setf %var-accessor-+borosh13+)
(function).
%var-accessor-+cmrg+
(function).
(setf %var-accessor-+cmrg+)
(function).
%var-accessor-+coveyou+
(function).
(setf %var-accessor-+coveyou+)
(function).
%var-accessor-+default-type+
(function).
(setf %var-accessor-+default-type+)
(function).
%var-accessor-+fishman18+
(function).
(setf %var-accessor-+fishman18+)
(function).
%var-accessor-+fishman20+
(function).
(setf %var-accessor-+fishman20+)
(function).
%var-accessor-+fishman2x+
(function).
(setf %var-accessor-+fishman2x+)
(function).
%var-accessor-+gfsr4+
(function).
(setf %var-accessor-+gfsr4+)
(function).
%var-accessor-+knuthran+
(function).
(setf %var-accessor-+knuthran+)
(function).
%var-accessor-+knuthran2+
(function).
(setf %var-accessor-+knuthran2+)
(function).
%var-accessor-+knuthran2002+
(function).
(setf %var-accessor-+knuthran2002+)
(function).
%var-accessor-+lecuyer21+
(function).
(setf %var-accessor-+lecuyer21+)
(function).
%var-accessor-+minstd+
(function).
(setf %var-accessor-+minstd+)
(function).
%var-accessor-+mrg+
(function).
(setf %var-accessor-+mrg+)
(function).
%var-accessor-+mt19937+
(function).
(setf %var-accessor-+mt19937+)
(function).
%var-accessor-+mt19937-1998+
(function).
(setf %var-accessor-+mt19937-1998+)
(function).
%var-accessor-+mt19937-1999+
(function).
(setf %var-accessor-+mt19937-1999+)
(function).
%var-accessor-+r250+
(function).
(setf %var-accessor-+r250+)
(function).
%var-accessor-+ran0+
(function).
(setf %var-accessor-+ran0+)
(function).
%var-accessor-+ran1+
(function).
(setf %var-accessor-+ran1+)
(function).
%var-accessor-+ran2+
(function).
(setf %var-accessor-+ran2+)
(function).
%var-accessor-+ran3+
(function).
(setf %var-accessor-+ran3+)
(function).
%var-accessor-+rand+
(function).
(setf %var-accessor-+rand+)
(function).
%var-accessor-+rand48+
(function).
(setf %var-accessor-+rand48+)
(function).
%var-accessor-+random128_bsd+
(function).
(setf %var-accessor-+random128_bsd+)
(function).
%var-accessor-+random128_glibc2+
(function).
(setf %var-accessor-+random128_glibc2+)
(function).
%var-accessor-+random128_libc5+
(function).
(setf %var-accessor-+random128_libc5+)
(function).
%var-accessor-+random256_bsd+
(function).
(setf %var-accessor-+random256_bsd+)
(function).
%var-accessor-+random256_glibc2+
(function).
(setf %var-accessor-+random256_glibc2+)
(function).
%var-accessor-+random256_libc5+
(function).
(setf %var-accessor-+random256_libc5+)
(function).
%var-accessor-+random32_bsd+
(function).
(setf %var-accessor-+random32_bsd+)
(function).
%var-accessor-+random32_glibc2+
(function).
(setf %var-accessor-+random32_glibc2+)
(function).
%var-accessor-+random32_libc5+
(function).
(setf %var-accessor-+random32_libc5+)
(function).
%var-accessor-+random64_bsd+
(function).
(setf %var-accessor-+random64_bsd+)
(function).
%var-accessor-+random64_glibc2+
(function).
(setf %var-accessor-+random64_glibc2+)
(function).
%var-accessor-+random64_libc5+
(function).
(setf %var-accessor-+random64_libc5+)
(function).
%var-accessor-+random8_bsd+
(function).
(setf %var-accessor-+random8_bsd+)
(function).
%var-accessor-+random8_glibc2+
(function).
(setf %var-accessor-+random8_glibc2+)
(function).
%var-accessor-+random8_libc5+
(function).
(setf %var-accessor-+random8_libc5+)
(function).
%var-accessor-+random_bsd+
(function).
(setf %var-accessor-+random_bsd+)
(function).
%var-accessor-+random_glibc2+
(function).
(setf %var-accessor-+random_glibc2+)
(function).
%var-accessor-+random_libc5+
(function).
(setf %var-accessor-+random_libc5+)
(function).
%var-accessor-+randu+
(function).
(setf %var-accessor-+randu+)
(function).
%var-accessor-+ranf+
(function).
(setf %var-accessor-+ranf+)
(function).
%var-accessor-+ranlux+
(function).
(setf %var-accessor-+ranlux+)
(function).
%var-accessor-+ranlux389+
(function).
(setf %var-accessor-+ranlux389+)
(function).
%var-accessor-+ranlxd1+
(function).
(setf %var-accessor-+ranlxd1+)
(function).
%var-accessor-+ranlxd2+
(function).
(setf %var-accessor-+ranlxd2+)
(function).
%var-accessor-+ranlxs0+
(function).
(setf %var-accessor-+ranlxs0+)
(function).
%var-accessor-+ranlxs1+
(function).
(setf %var-accessor-+ranlxs1+)
(function).
%var-accessor-+ranlxs2+
(function).
(setf %var-accessor-+ranlxs2+)
(function).
%var-accessor-+ranmar+
(function).
(setf %var-accessor-+ranmar+)
(function).
%var-accessor-+slatec+
(function).
(setf %var-accessor-+slatec+)
(function).
%var-accessor-+taus+
(function).
(setf %var-accessor-+taus+)
(function).
%var-accessor-+taus113+
(function).
(setf %var-accessor-+taus113+)
(function).
%var-accessor-+taus2+
(function).
(setf %var-accessor-+taus2+)
(function).
%var-accessor-+transputer+
(function).
(setf %var-accessor-+transputer+)
(function).
%var-accessor-+tt800+
(function).
(setf %var-accessor-+tt800+)
(function).
%var-accessor-+uni+
(function).
(setf %var-accessor-+uni+)
(function).
%var-accessor-+uni32+
(function).
(setf %var-accessor-+uni32+)
(function).
%var-accessor-+vax+
(function).
(setf %var-accessor-+vax+)
(function).
%var-accessor-+waterman14+
(function).
(setf %var-accessor-+waterman14+)
(function).
%var-accessor-+zuf+
(function).
(setf %var-accessor-+zuf+)
(function).
def-rng-type
(macro).
rng-types-setup
(function).
gsll/random/generators.lisp
rng-types.lisp
(file).
random
(module).
+default-seed+
(symbol macro).
copy
(method).
get-random-number
(function).
gsl-random-state
(function).
initialize-instance
(method).
make-random-number-generator
(function).
name
(method).
print-object
(method).
random-number-generator
(class).
reinitialize-instance
(method).
rng-max
(function).
rng-min
(function).
rng-state
(generic function).
sample
(generic function).
size
(method).
%var-accessor-+default-seed+
(function).
(setf %var-accessor-+default-seed+)
(function).
allocate
(method).
rng-clone
(function).
rng-copy
(function).
gsll/random/quasi.lisp
rng-types.lisp
(file).
generators.lisp
(file).
random
(module).
+halton+
(symbol macro).
+niederreiter2+
(symbol macro).
+reverse-halton+
(symbol macro).
+sobol+
(symbol macro).
copy
(method).
initialize-instance
(method).
make-quasi-random-number-generator
(function).
name
(method).
qrng-get
(function).
quasi-random-number-generator
(class).
reinitialize-instance
(method).
rng-state
(method).
size
(method).
%var-accessor-+halton+
(function).
(setf %var-accessor-+halton+)
(function).
%var-accessor-+niederreiter2+
(function).
(setf %var-accessor-+niederreiter2+)
(function).
%var-accessor-+reverse-halton+
(function).
(setf %var-accessor-+reverse-halton+)
(function).
%var-accessor-+sobol+
(function).
(setf %var-accessor-+sobol+)
(function).
allocate
(method).
quasi-clone
(function).
quasi-copy
(function).
gsll/random/tests.lisp
rng-types.lisp
(file).
random
(module).
*pdf-number-of-tries*
(special variable).
+gslt-bin-size+
(constant).
+gslt-bins+
(constant).
+gslt-lower-limit+
(constant).
+gslt-upper-limit+
(constant).
+initial-number-of-samples+
(constant).
bin-samples
(function).
distribution-bin-integral
(function).
limits-check
(function).
testpdf
(function).
gsll/random/gaussian.lisp
rng-types.lisp
(file).
random
(module).
gaussian-p
(function).
gaussian-pdf
(function).
gaussian-pinv
(function).
gaussian-q
(function).
gaussian-qinv
(function).
sample
(method).
sample
(method).
sample
(method).
sample
(method).
sample
(method).
ugaussian-p
(function).
ugaussian-pdf
(function).
ugaussian-pinv
(function).
ugaussian-q
(function).
ugaussian-qinv
(function).
gsll/random/gaussian-tail.lisp
rng-types.lisp
(file).
random
(module).
gaussian-tail-pdf
(function).
sample
(method).
sample
(method).
ugaussian-tail-pdf
(function).
gsll/random/gaussian-bivariate.lisp
rng-types.lisp
(file).
random
(module).
bivariate-gaussian-pdf
(function).
sample
(method).
gsll/random/exponential.lisp
rng-types.lisp
(file).
random
(module).
exponential-p
(function).
exponential-pdf
(function).
exponential-pinv
(function).
exponential-q
(function).
exponential-qinv
(function).
sample
(method).
gsll/random/laplace.lisp
rng-types.lisp
(file).
random
(module).
laplace-p
(function).
laplace-pdf
(function).
laplace-pinv
(function).
laplace-q
(function).
laplace-qinv
(function).
sample
(method).
gsll/random/exponential-power.lisp
rng-types.lisp
(file).
random
(module).
exponential-power-p
(function).
exponential-power-pdf
(function).
exponential-power-q
(function).
sample
(method).
gsll/random/cauchy.lisp
rng-types.lisp
(file).
random
(module).
cauchy-p
(function).
cauchy-pdf
(function).
cauchy-pinv
(function).
cauchy-q
(function).
cauchy-qinv
(function).
sample
(method).
gsll/random/rayleigh.lisp
rng-types.lisp
(file).
random
(module).
rayleigh-p
(function).
rayleigh-pdf
(function).
rayleigh-pinv
(function).
rayleigh-q
(function).
rayleigh-qinv
(function).
sample
(method).
gsll/random/rayleigh-tail.lisp
rng-types.lisp
(file).
random
(module).
rayleigh-tail-pdf
(function).
sample
(method).
gsll/random/landau.lisp
rng-types.lisp
(file).
random
(module).
landau-pdf
(function).
sample
(method).
gsll/random/levy.lisp
rng-types.lisp
(file).
random
(module).
gsll/random/gamma.lisp
rng-types.lisp
(file).
random
(module).
gamma-p
(function).
gamma-pdf
(function).
gamma-pinv
(function).
gamma-q
(function).
gamma-qinv
(function).
sample
(method).
sample
(method).
gsll/random/flat.lisp
rng-types.lisp
(file).
random
(module).
gsll/random/lognormal.lisp
rng-types.lisp
(file).
random
(module).
lognormal-p
(function).
lognormal-pdf
(function).
lognormal-pinv
(function).
lognormal-q
(function).
lognormal-qinv
(function).
sample
(method).
gsll/random/chi-squared.lisp
rng-types.lisp
(file).
random
(module).
chi-squared-p
(function).
chi-squared-pdf
(function).
chi-squared-pinv
(function).
chi-squared-q
(function).
chi-squared-qinv
(function).
sample
(method).
gsll/random/fdist.lisp
rng-types.lisp
(file).
random
(module).
fdist-p
(function).
fdist-pdf
(function).
fdist-pinv
(function).
fdist-q
(function).
fdist-qinv
(function).
sample
(method).
gsll/random/tdist.lisp
rng-types.lisp
(file).
random
(module).
sample
(method).
tdist-p
(function).
tdist-pdf
(function).
tdist-pinv
(function).
tdist-q
(function).
tdist-qinv
(function).
gsll/random/beta.lisp
rng-types.lisp
(file).
random
(module).
gsll/random/logistic.lisp
rng-types.lisp
(file).
random
(module).
logistic-p
(function).
logistic-pdf
(function).
logistic-pinv
(function).
logistic-q
(function).
logistic-qinv
(function).
sample
(method).
gsll/random/pareto.lisp
rng-types.lisp
(file).
random
(module).
pareto-p
(function).
pareto-pdf
(function).
pareto-pinv
(function).
pareto-q
(function).
pareto-qinv
(function).
sample
(method).
gsll/random/spherical-vector.lisp
rng-types.lisp
(file).
random
(module).
gsll/random/weibull.lisp
rng-types.lisp
(file).
random
(module).
sample
(method).
weibull-p
(function).
weibull-pdf
(function).
weibull-pinv
(function).
weibull-q
(function).
weibull-qinv
(function).
gsll/random/gumbel1.lisp
rng-types.lisp
(file).
random
(module).
gumbel1-p
(function).
gumbel1-pdf
(function).
gumbel1-pinv
(function).
gumbel1-q
(function).
gumbel1-qinv
(function).
sample
(method).
gsll/random/gumbel2.lisp
rng-types.lisp
(file).
random
(module).
gumbel2-p
(function).
gumbel2-pdf
(function).
gumbel2-pinv
(function).
gumbel2-q
(function).
gumbel2-qinv
(function).
sample
(method).
gsll/random/dirichlet.lisp
rng-types.lisp
(file).
random
(module).
dirichlet-log-pdf
(function).
dirichlet-pdf
(function).
sample
(method).
gsll/random/discrete.lisp
rng-types.lisp
(file).
random
(module).
discrete-pdf
(function).
discrete-random
(class).
initialize-instance
(method).
make-discrete-random
(function).
sample
(method).
allocate
(method).
gsll/random/poisson.lisp
rng-types.lisp
(file).
random
(module).
poisson-p
(function).
poisson-pdf
(function).
poisson-q
(function).
sample
(method).
gsll/random/bernoulli.lisp
rng-types.lisp
(file).
random
(module).
bernoulli-pdf
(function).
sample
(method).
gsll/random/binomial.lisp
rng-types.lisp
(file).
random
(module).
binomial
(function).
binomial-p
(function).
binomial-pdf
(function).
binomial-q
(function).
gsll/random/multinomial.lisp
rng-types.lisp
(file).
random
(module).
multinomial-log-pdf
(function).
multinomial-pdf
(function).
sample
(method).
gsll/random/negative-binomial.lisp
rng-types.lisp
(file).
random
(module).
negative-binomial-p
(function).
negative-binomial-pdf
(function).
negative-binomial-q
(function).
pascal-p
(function).
pascal-pdf
(function).
pascal-q
(function).
sample
(method).
sample
(method).
gsll/random/geometric.lisp
rng-types.lisp
(file).
random
(module).
geometric-p
(function).
geometric-pdf
(function).
geometric-q
(function).
sample
(method).
gsll/random/hypergeometric.lisp
rng-types.lisp
(file).
random
(module).
hypergeometric-p
(function).
hypergeometric-pdf
(function).
hypergeometric-q
(function).
sample
(method).
gsll/random/logarithmic.lisp
rng-types.lisp
(file).
random
(module).
logarithmic-pdf
(function).
sample
(method).
gsll/random/shuffling-sampling.lisp
rng-types.lisp
(file).
random
(module).
gsll/statistics/mean-variance.lisp
statistics
(module).
mean
(generic function).
standard-deviation
(generic function).
standard-deviation-with-fixed-mean
(generic function).
variance
(generic function).
variance-with-fixed-mean
(generic function).
weighted-mean
(generic function).
weighted-standard-deviation
(generic function).
weighted-standard-deviation-with-fixed-mean
(generic function).
weighted-variance
(generic function).
weighted-variance-with-fixed-mean
(generic function).
gsll/statistics/absolute-deviation.lisp
statistics
(module).
absolute-deviation
(generic function).
weighted-absolute-deviation
(generic function).
gsll/statistics/higher-moments.lisp
statistics
(module).
kurtosis
(generic function).
skewness
(generic function).
weighted-kurtosis
(generic function).
weighted-skewness
(generic function).
gsll/statistics/autocorrelation.lisp
statistics
(module).
autocorrelation
(generic function).
gsll/statistics/covariance.lisp
statistics
(module).
correlation
(generic function).
covariance
(generic function).
gsll/statistics/median-percentile.lisp
statistics
(module).
gsll/histogram/histogram.lisp
histogram
(module).
copy
(method).
copy
(method).
histogram
(class).
histogram2d
(class).
initialize-instance
(method).
initialize-instance
(method).
make-histogram
(function).
make-histogram2d
(function).
reinitialize-instance
(method).
reinitialize-instance
(method).
set-ranges-uniform
(generic function).
allocate
(method).
allocate
(method).
histo-clone
(function).
histo-copy
(function).
histo2d-clone
(function).
histo2d-copy
(function).
histogram-c-tclass
(class).
view-bin-as-foreign-array
(function).
view-range-as-foreign-array
(function).
gsll/histogram/updating-accessing.lisp
histogram.lisp
(file).
histogram
(module).
aref
(method).
aref
(method).
dimensions
(method).
dimensions
(method).
histogram-find
(function).
increment
(generic function).
max-range
(generic function).
min-range
(generic function).
range
(generic function).
set-zero
(method).
set-zero
(method).
gsll/histogram/statistics.lisp
histogram.lisp
(file).
histogram
(module).
gsll/histogram/operations.lisp
histogram.lisp
(file).
histogram
(module).
gsll/histogram/probability-distribution.lisp
histogram.lisp
(file).
histogram
(module).
histogram-pdf
(class).
histogram2d-pdf
(class).
initialize-instance
(method).
initialize-instance
(method).
make-histogram-pdf
(function).
make-histogram2d-pdf
(function).
reinitialize-instance
(method).
reinitialize-instance
(method).
sample
(method).
sample
(method).
sample
(method).
sample
(method).
gsll/histogram/ntuple.lisp
histogram
(module).
bookdata-ntuple
(function).
close-ntuple
(function).
create-ntuple
(function).
open-ntuple
(function).
project-ntuple
(function).
read-ntuple
(function).
write-ntuple
(function).
*ntuple-example-data-file*
(special variable).
*ntuple-example-scale*
(special variable).
make-ntuple-example-data
(function).
ntuple-data-tclass
(class).
ntuple-example-histogramming
(function).
ntuple-example-make-read
(function).
ntuple-example-read
(function).
ntuple-example-sel-func
(function).
ntuple-example-val-func
(function).
ntuple-example-values
(function).
gsll/calculus/numerical-integration.lisp
calculus
(module).
*default-absolute-error*
(special variable).
*default-relative-error*
(special variable).
initialize-instance
(method).
integration-qag
(function).
integration-qagi
(function).
integration-qagil
(function).
integration-qagiu
(function).
integration-qagp
(function).
integration-qags
(function).
integration-qawc
(function).
integration-qng
(function).
integration-workspace
(class).
make-integration-workspace
(function).
allocate
(method).
integration-test-f1
(function).
integration-test-f11
(function).
integration-test-f15
(function).
integration-test-f16
(function).
integration-test-f3
(function).
integration-test-f454
(function).
integration-test-f455
(function).
integration-test-f459
(function).
integration-test-myfn1
(function).
integration-test-myfn2
(function).
gsll/calculus/numerical-integration-with-tables.lisp
numerical-integration.lisp
(file).
calculus
(module).
initialize-instance
(method).
initialize-instance
(method).
integration-qawf
(function).
integration-qawo
(function).
integration-qaws
(function).
make-qawo-table
(function).
make-qaws-table
(function).
qawo-table
(class).
qaws-table
(class).
reinitialize-instance
(method).
reinitialize-instance
(method).
allocate
(method).
allocate
(method).
integration-test-f456
(function).
integration-test-f457
(function).
integration-test-f458
(function).
gsll/calculus/monte-carlo.lisp
calculus
(module).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
make-monte-carlo-miser
(function).
make-monte-carlo-plain
(function).
make-monte-carlo-vegas
(function).
monte-carlo-integrate-miser
(function).
monte-carlo-integrate-plain
(function).
monte-carlo-integrate-vegas
(function).
monte-carlo-miser
(class).
monte-carlo-plain
(class).
monte-carlo-vegas
(class).
parameter
(method).
parameter
(method).
(setf parameter)
(method).
(setf parameter)
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
*mc-lower*
(special variable).
*mc-upper*
(special variable).
*monte-carlo-default-samples-per-dimension*
(special variable).
allocate
(method).
allocate
(method).
allocate
(method).
get-mcm-parameters
(function).
get-mcv-parameters
(function).
mcrw
(function).
random-walk-miser-example
(function).
random-walk-plain-example
(function).
random-walk-vegas-example
(function).
set-mcm-parameters
(function).
set-mcv-parameters
(function).
gsll/calculus/numerical-differentiation.lisp
calculus
(module).
backward-derivative
(function).
central-derivative
(function).
forward-derivative
(function).
deriv-f1-d
(function).
deriv-f2
(function).
deriv-f2-d
(function).
deriv-f3
(function).
deriv-f3-d
(function).
deriv-f4
(function).
deriv-f4-d
(function).
deriv-f5
(function).
deriv-f5-d
(function).
deriv-f6-d
(function).
gsll/ordinary-differential-equations/ode-system.lisp
ordinary-differential-equations
(module).
with-ode-integration
(macro).
gsll/ordinary-differential-equations/ode-struct.lisp
ordinary-differential-equations
(module).
gsll/ordinary-differential-equations/stepping.lisp
ode-struct.lisp
(file).
ordinary-differential-equations
(module).
+step-bsimp+
(symbol macro).
+step-gear1+
(symbol macro).
+step-gear2+
(symbol macro).
+step-rk2+
(symbol macro).
+step-rk2imp+
(symbol macro).
+step-rk4+
(symbol macro).
+step-rk4imp+
(symbol macro).
+step-rk8pd+
(symbol macro).
+step-rkck+
(symbol macro).
+step-rkf45+
(symbol macro).
apply-step
(function).
initialize-instance
(method).
make-ode-stepper
(function).
name
(method).
ode-stepper
(class).
reinitialize-instance
(method).
step-order
(function).
%var-accessor-+step-bsimp+
(function).
(setf %var-accessor-+step-bsimp+)
(function).
%var-accessor-+step-gear1+
(function).
(setf %var-accessor-+step-gear1+)
(function).
%var-accessor-+step-gear2+
(function).
(setf %var-accessor-+step-gear2+)
(function).
%var-accessor-+step-rk2+
(function).
(setf %var-accessor-+step-rk2+)
(function).
%var-accessor-+step-rk2imp+
(function).
(setf %var-accessor-+step-rk2imp+)
(function).
%var-accessor-+step-rk4+
(function).
(setf %var-accessor-+step-rk4+)
(function).
%var-accessor-+step-rk4imp+
(function).
(setf %var-accessor-+step-rk4imp+)
(function).
%var-accessor-+step-rk8pd+
(function).
(setf %var-accessor-+step-rk8pd+)
(function).
%var-accessor-+step-rkck+
(function).
(setf %var-accessor-+step-rkck+)
(function).
%var-accessor-+step-rkf45+
(function).
(setf %var-accessor-+step-rkf45+)
(function).
allocate
(method).
gsll/ordinary-differential-equations/control.lisp
ordinary-differential-equations
(module).
adjust-stepsize
(function).
control-alloc
(function).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
initialize-instance
(method).
make-scaled-control
(function).
make-standard-control
(function).
make-y-control
(function).
make-yp-control
(function).
name
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
scaled-control
(class).
standard-control
(class).
y-control
(class).
yp-control
(class).
allocate
(method).
allocate
(method).
allocate
(method).
allocate
(method).
ode-control
(class).
gsll/ordinary-differential-equations/evolution.lisp
ordinary-differential-equations
(module).
apply-evolution
(function).
initialize-instance
(method).
make-ode-evolution
(function).
ode-evolution
(class).
reinitialize-instance
(method).
allocate
(method).
gsll/ordinary-differential-equations/ode-example.lisp
ode-system.lisp
(file).
stepping.lisp
(file).
ordinary-differential-equations
(module).
*max-iter*
(special variable).
integrate-vanderpol
(function).
vanderpol
(function).
vanderpol-jacobian
(function).
gsll/interpolation/interpolation.lisp
interpolation
(module).
initialize-instance
(method).
initialize-instance
(method).
interpolation
(class).
make-interpolation
(function).
make-spline
(function).
reinitialize-instance
(method).
reinitialize-instance
(method).
spline
(class).
gsll/interpolation/types.lisp
interpolation.lisp
(file).
interpolation
(module).
+akima-interpolation+
(symbol macro).
+cubic-spline-interpolation+
(symbol macro).
+linear-interpolation+
(symbol macro).
+periodic-akima-interpolation+
(symbol macro).
+periodic-cubic-spline-interpolation+
(symbol macro).
+polynomial-interpolation+
(symbol macro).
minimum-size
(generic function).
name
(method).
name
(method).
%var-accessor-+akima-interpolation+
(function).
(setf %var-accessor-+akima-interpolation+)
(function).
%var-accessor-+cubic-spline-interpolation+
(function).
(setf %var-accessor-+cubic-spline-interpolation+)
(function).
%var-accessor-+linear-interpolation+
(function).
(setf %var-accessor-+linear-interpolation+)
(function).
%var-accessor-+periodic-akima-interpolation+
(function).
(setf %var-accessor-+periodic-akima-interpolation+)
(function).
%var-accessor-+periodic-cubic-spline-interpolation+
(function).
(setf %var-accessor-+periodic-cubic-spline-interpolation+)
(function).
%var-accessor-+polynomial-interpolation+
(function).
(setf %var-accessor-+polynomial-interpolation+)
(function).
gsll/interpolation/lookup.lisp
interpolation
(module).
accelerated-interpolation-search
(function).
acceleration
(class).
initialize-instance
(method).
interpolation-search
(function).
make-acceleration
(function).
allocate
(method).
gsll/interpolation/evaluation.lisp
interpolation
(module).
evaluate
(method).
evaluate
(method).
evaluate-derivative
(generic function).
evaluate-integral
(generic function).
evaluate-second-derivative
(generic function).
gsll/interpolation/spline-example.lisp
types.lisp
(file).
interpolation
(module).
evaluate-integral-example
(function).
spline-example
(function).
gsll/chebyshev.lisp
init
(module).
gsll
(system).
chebyshev
(class).
coefficients
(function).
derivative-chebyshev
(function).
evaluate
(method).
evaluate-chebyshev-error
(function).
initialize-instance
(method).
integral-chebyshev
(function).
make-chebyshev
(function).
order
(method).
reinitialize-instance
(method).
size
(method).
allocate
(method).
chebyshev-point-example
(function).
chebyshev-step
(function).
chebyshev-table-example
(function).
gsll/series-acceleration.lisp
init
(module).
mathematical
(module).
series-struct.lisp
(file).
gsll
(system).
accelerate
(function).
accelerate-truncated
(function).
initialize-instance
(method).
initialize-instance
(method).
levin
(class).
levin-truncated
(class).
make-levin
(function).
make-levin-truncated
(function).
acceleration-example
(function).
allocate
(method).
allocate
(method).
levin-value
(function).
gsll/wavelet.lisp
gsll
(system).
+bspline-wavelet+
(symbol macro).
+bspline-wavelet-centered+
(symbol macro).
+daubechies-wavelet+
(symbol macro).
+daubechies-wavelet-centered+
(symbol macro).
+haar-wavelet+
(symbol macro).
+haar-wavelet-centered+
(symbol macro).
initialize-instance
(method).
initialize-instance
(method).
make-wavelet
(function).
make-wavelet-workspace
(function).
name
(method).
wavelet
(class).
wavelet-2d-nonstandard-transform
(function).
wavelet-2d-nonstandard-transform-forward
(function).
wavelet-2d-nonstandard-transform-inverse
(function).
wavelet-2d-nonstandard-transform-matrix
(function).
wavelet-2d-nonstandard-transform-matrix-forward
(function).
wavelet-2d-nonstandard-transform-matrix-inverse
(function).
wavelet-2d-transform
(function).
wavelet-2d-transform-forward
(function).
wavelet-2d-transform-inverse
(function).
wavelet-2d-transform-matrix
(function).
wavelet-2d-transform-matrix-forward
(function).
wavelet-2d-transform-matrix-inverse
(function).
wavelet-transform
(function).
wavelet-transform-forward
(function).
wavelet-transform-inverse
(function).
wavelet-workspace
(class).
%var-accessor-+bspline-wavelet+
(function).
(setf %var-accessor-+bspline-wavelet+)
(function).
%var-accessor-+bspline-wavelet-centered+
(function).
(setf %var-accessor-+bspline-wavelet-centered+)
(function).
%var-accessor-+daubechies-wavelet+
(function).
(setf %var-accessor-+daubechies-wavelet+)
(function).
%var-accessor-+daubechies-wavelet-centered+
(function).
(setf %var-accessor-+daubechies-wavelet-centered+)
(function).
%var-accessor-+haar-wavelet+
(function).
(setf %var-accessor-+haar-wavelet+)
(function).
%var-accessor-+haar-wavelet-centered+
(function).
(setf %var-accessor-+haar-wavelet-centered+)
(function).
*wavelet-sample*
(special variable).
allocate
(method).
allocate
(method).
forward-backward
(function).
wavelet-example
(function).
wavelet-forward-example
(function).
gsll/hankel.lisp
gsll
(system).
apply-hankel
(function).
hankel
(class).
initialize-instance
(method).
make-hankel
(function).
reinitialize-instance
(method).
sample-k-hankel
(function).
sample-x-hankel
(function).
allocate
(method).
gsll/solve-minimize-fit/generic.lisp
solve-minimize-fit
(module).
function-value
(generic function).
iterate
(generic function).
last-step
(generic function).
solution
(generic function).
gsll/solve-minimize-fit/solver-struct.lisp
solve-minimize-fit
(module).
gsll/solve-minimize-fit/roots-one.lisp
generic.lisp
(file).
solve-minimize-fit
(module).
+bisection-fsolver+
(symbol macro).
+brent-fsolver+
(symbol macro).
+false-position-fsolver+
(symbol macro).
+newton-fdfsolver+
(symbol macro).
+secant-fdfsolver+
(symbol macro).
+steffenson-fdfsolver+
(symbol macro).
fsolver-lower
(function).
fsolver-upper
(function).
initialize-instance
(method).
initialize-instance
(method).
iterate
(method).
iterate
(method).
make-one-dimensional-root-solver-f
(function).
make-one-dimensional-root-solver-fdf
(function).
name
(method).
name
(method).
one-dimensional-root-solver-f
(class).
one-dimensional-root-solver-fdf
(class).
reinitialize-instance
(method).
reinitialize-instance
(method).
root-test-delta
(function).
root-test-interval
(function).
root-test-residual
(function).
solution
(method).
solution
(method).
%var-accessor-+bisection-fsolver+
(function).
(setf %var-accessor-+bisection-fsolver+)
(function).
%var-accessor-+brent-fsolver+
(function).
(setf %var-accessor-+brent-fsolver+)
(function).
%var-accessor-+false-position-fsolver+
(function).
(setf %var-accessor-+false-position-fsolver+)
(function).
%var-accessor-+newton-fdfsolver+
(function).
(setf %var-accessor-+newton-fdfsolver+)
(function).
%var-accessor-+secant-fdfsolver+
(function).
(setf %var-accessor-+secant-fdfsolver+)
(function).
%var-accessor-+steffenson-fdfsolver+
(function).
(setf %var-accessor-+steffenson-fdfsolver+)
(function).
allocate
(method).
allocate
(method).
quadratic
(function).
quadratic-and-derivative
(function).
quadratic-derivative
(function).
roots-one-example-derivative
(function).
roots-one-example-no-derivative
(function).
gsll/solve-minimize-fit/minimization-one.lisp
generic.lisp
(file).
solve-minimize-fit
(module).
+brent-fminimizer+
(symbol macro).
+golden-section-fminimizer+
(symbol macro).
+quad-golden-fminimizer+
(symbol macro).
fminimizer-f-lower
(function).
fminimizer-f-upper
(function).
fminimizer-x-lower
(function).
fminimizer-x-upper
(function).
function-value
(method).
initialize-instance
(method).
iterate
(method).
make-one-dimensional-minimizer
(function).
min-test-interval
(function).
name
(method).
one-dimensional-minimizer
(class).
reinitialize-instance
(method).
solution
(method).
%var-accessor-+brent-fminimizer+
(function).
(setf %var-accessor-+brent-fminimizer+)
(function).
%var-accessor-+golden-section-fminimizer+
(function).
(setf %var-accessor-+golden-section-fminimizer+)
(function).
%var-accessor-+quad-golden-fminimizer+
(function).
(setf %var-accessor-+quad-golden-fminimizer+)
(function).
allocate
(method).
minimization-one-example
(function).
gsll/solve-minimize-fit/roots-multi.lisp
roots-one.lisp
(file).
generic.lisp
(file).
solver-struct.lisp
(file).
solve-minimize-fit
(module).
+broyden+
(symbol macro).
+discrete-newton+
(symbol macro).
+gnewton-mfdfsolver+
(symbol macro).
+hybrid-scaled+
(symbol macro).
+hybrid-unscaled+
(symbol macro).
+newton-mfdfsolver+
(symbol macro).
+powells-hybrid+
(symbol macro).
+powells-hybrid-unscaled+
(symbol macro).
function-value
(method).
function-value
(method).
initialize-instance
(method).
initialize-instance
(method).
iterate
(method).
iterate
(method).
last-step
(method).
last-step
(method).
make-multi-dimensional-root-solver-f
(function).
make-multi-dimensional-root-solver-fdf
(function).
multi-dimensional-root-solver-f
(class).
multi-dimensional-root-solver-fdf
(class).
multiroot-test-delta
(function).
multiroot-test-residual
(function).
name
(method).
name
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
solution
(method).
solution
(method).
%var-accessor-+broyden+
(function).
(setf %var-accessor-+broyden+)
(function).
%var-accessor-+discrete-newton+
(function).
(setf %var-accessor-+discrete-newton+)
(function).
%var-accessor-+gnewton-mfdfsolver+
(function).
(setf %var-accessor-+gnewton-mfdfsolver+)
(function).
%var-accessor-+hybrid-scaled+
(function).
(setf %var-accessor-+hybrid-scaled+)
(function).
%var-accessor-+hybrid-unscaled+
(function).
(setf %var-accessor-+hybrid-unscaled+)
(function).
%var-accessor-+newton-mfdfsolver+
(function).
(setf %var-accessor-+newton-mfdfsolver+)
(function).
%var-accessor-+powells-hybrid+
(function).
(setf %var-accessor-+powells-hybrid+)
(function).
%var-accessor-+powells-hybrid-unscaled+
(function).
(setf %var-accessor-+powells-hybrid-unscaled+)
(function).
*powell-a*
(special variable).
*rosenbrock-a*
(special variable).
*rosenbrock-b*
(special variable).
allocate
(method).
allocate
(method).
multiroot-slot
(function).
powell
(function).
roots-multi-example-derivative
(function).
roots-multi-example-no-derivative
(function).
rosenbrock
(function).
rosenbrock-df
(function).
rosenbrock-fdf
(function).
gsll/solve-minimize-fit/minimization-multi.lisp
generic.lisp
(file).
solve-minimize-fit
(module).
+conjugate-fletcher-reeves+
(symbol macro).
+conjugate-polak-ribiere+
(symbol macro).
+simplex-nelder-mead+
(symbol macro).
+simplex-nelder-mead-on2+
(symbol macro).
+simplex-nelder-mead-random+
(symbol macro).
+vector-bfgs+
(symbol macro).
+vector-bfgs2+
(symbol macro).
function-value
(method).
function-value
(method).
initialize-instance
(method).
initialize-instance
(method).
iterate
(method).
iterate
(method).
make-multi-dimensional-minimizer-f
(function).
make-multi-dimensional-minimizer-fdf
(function).
mfdfminimizer-gradient
(function).
mfdfminimizer-restart
(function).
min-test-gradient
(function).
min-test-size
(function).
multi-dimensional-minimizer-f
(class).
multi-dimensional-minimizer-fdf
(class).
name
(method).
name
(method).
reinitialize-instance
(method).
reinitialize-instance
(method).
size
(method).
solution
(method).
solution
(method).
%var-accessor-+conjugate-fletcher-reeves+
(function).
(setf %var-accessor-+conjugate-fletcher-reeves+)
(function).
%var-accessor-+conjugate-polak-ribiere+
(function).
(setf %var-accessor-+conjugate-polak-ribiere+)
(function).
%var-accessor-+simplex-nelder-mead+
(function).
(setf %var-accessor-+simplex-nelder-mead+)
(function).
%var-accessor-+simplex-nelder-mead-on2+
(function).
(setf %var-accessor-+simplex-nelder-mead-on2+)
(function).
%var-accessor-+simplex-nelder-mead-random+
(function).
(setf %var-accessor-+simplex-nelder-mead-random+)
(function).
%var-accessor-+vector-bfgs+
(function).
(setf %var-accessor-+vector-bfgs+)
(function).
%var-accessor-+vector-bfgs2+
(function).
(setf %var-accessor-+vector-bfgs2+)
(function).
*paraboloid-center*
(special variable).
allocate
(method).
allocate
(method).
multimin-example-derivative
(function).
multimin-example-derivative-scalars
(function).
multimin-example-no-derivative
(function).
paraboloid-and-derivative
(function).
paraboloid-and-derivative-scalar
(function).
paraboloid-derivative
(function).
paraboloid-derivative-scalar
(function).
paraboloid-scalar
(function).
paraboloid-vector
(function).
gsll/solve-minimize-fit/linear-least-squares.lisp
solve-minimize-fit
(module).
fit-workspace
(class).
initialize-instance
(method).
linear-estimate
(function).
linear-fit
(function).
linear-mfit
(function).
make-fit-workspace
(function).
multi-linear-estimate
(function).
multi-linear-residuals
(function).
multiplier-estimate
(function).
multiplier-fit
(function).
allocate
(method).
default-covariance
(function).
default-lls-workspace
(function).
linear-least-squares-multivariate-example
(function).
linear-least-squares-univariate-example
(function).
linear-mfit-nosvd
(function).
linear-mfit-svd
(function).
mv-linear-least-squares-data
(function).
size-array
(function).
gsll/solve-minimize-fit/nonlinear-least-squares.lisp
generic.lisp
(file).
solver-struct.lisp
(file).
solve-minimize-fit
(module).
+levenberg-marquardt+
(symbol macro).
+levenberg-marquardt-unscaled+
(symbol macro).
fit-gradient
(function).
fit-test-delta
(function).
fit-test-gradient
(function).
function-value
(method).
initialize-instance
(method).
initialize-instance
(method).
iterate
(method).
iterate
(method).
jacobian
(function).
last-step
(method).
ls-covariance
(function).
make-jacobian-matrix
(function).
make-nonlinear-fdffit
(function).
make-nonlinear-ffit
(function).
name
(method).
name
(method).
nonlinear-fdffit
(class).
nonlinear-ffit
(class).
reinitialize-instance
(method).
reinitialize-instance
(method).
solution
(method).
solution
(method).
%var-accessor-+levenberg-marquardt+
(function).
(setf %var-accessor-+levenberg-marquardt+)
(function).
%var-accessor-+levenberg-marquardt-unscaled+
(function).
(setf %var-accessor-+levenberg-marquardt-unscaled+)
(function).
*nlls-example-data*
(special variable).
allocate
(method).
allocate
(method).
copy-exponent-fit-data
(function).
exponent-fit-data
(structure).
exponent-fit-data-n
(reader).
(setf exponent-fit-data-n)
(writer).
exponent-fit-data-p
(function).
exponent-fit-data-sigma
(reader).
(setf exponent-fit-data-sigma)
(writer).
exponent-fit-data-y
(reader).
(setf exponent-fit-data-y)
(writer).
exponential-residual
(function).
exponential-residual-derivative
(function).
exponential-residual-fdf
(function).
generate-nlls-data
(function).
make-exponent-fit-data
(function).
nonlinear-least-squares-example
(function).
norm-f
(function).
gsll/solve-minimize-fit/simulated-annealing.lisp
solve-minimize-fit
(module).
simulated-annealing
(function).
*pointer-offset*
(special variable).
copy-sa-state
(function).
make-new-sa-state
(function).
make-sa-states
(function).
sa-state-value
(function).
simulated-annealing-example
(function).
simulated-annealing-int
(function).
simulated-annealing-parameters-tclass
(class).
simulated-annealing-test
(function).
state-pointer
(function).
trivial-example-energy
(function).
trivial-example-metric
(function).
trivial-example-step
(function).
trivial-test-energy
(function).
gsll/basis-splines.lisp
gsll
(system).
basis-spline
(class).
breakpoint
(function).
evaluate
(method).
greville-abscissa
(function).
initialize-instance
(method).
knots
(function).
make-basis-spline
(function).
number-of-breakpoints
(function).
number-of-coefficients
(function).
order
(method).
uniform-knots
(function).
allocate
(method).
bspline-example
(function).
gsll/test-unit/augment.lisp
machine.lisp
(file).
test-unit
(module).
+test-factor+
(constant).
+test-sigma+
(constant).
+test-sqrt-tol0+
(constant).
+test-tol0+
(constant).
+test-tol1+
(constant).
+test-tol2+
(constant).
+test-tol3+
(constant).
+test-tol4+
(constant).
+test-tol5+
(constant).
+test-tol6+
(constant).
assert-neginf
(macro).
assert-posinf
(macro).
assert-sf-scale
(macro).
assert-to-tolerance
(macro).
sf-check-results
(function).
sf-check-single
(function).
sf-frac-diff
(function).
gsll/tests/fast-fourier-transform.lisp
tests
(module).
*allowed-ticks*
(special variable).
all-fft-test-forms
(macro).
fft-complex-off-stride-check
(function).
fft-complex-result-check
(macro).
fft-real-result-check
(macro).
fft-test-forms
(function).
Packages are listed by definition order.
gsll
gsl
cffi
.
common-lisp
.
antik-user
.
*default-absolute-error*
(special variable).
*default-relative-error*
(special variable).
*gsl-version*
(symbol macro).
+akima-interpolation+
(symbol macro).
+bisection-fsolver+
(symbol macro).
+borosh13+
(symbol macro).
+brent-fminimizer+
(symbol macro).
+brent-fsolver+
(symbol macro).
+broyden+
(symbol macro).
+bspline-wavelet+
(symbol macro).
+bspline-wavelet-centered+
(symbol macro).
+cmrg+
(symbol macro).
+conjugate-fletcher-reeves+
(symbol macro).
+conjugate-polak-ribiere+
(symbol macro).
+coveyou+
(symbol macro).
+cubic-spline-interpolation+
(symbol macro).
+daubechies-wavelet+
(symbol macro).
+daubechies-wavelet-centered+
(symbol macro).
+default-seed+
(symbol macro).
+default-type+
(symbol macro).
+discrete-newton+
(symbol macro).
+false-position-fsolver+
(symbol macro).
+fishman18+
(symbol macro).
+fishman20+
(symbol macro).
+fishman2x+
(symbol macro).
+gfsr4+
(symbol macro).
+gnewton-mfdfsolver+
(symbol macro).
+golden-section-fminimizer+
(symbol macro).
+haar-wavelet+
(symbol macro).
+haar-wavelet-centered+
(symbol macro).
+halton+
(symbol macro).
+hybrid-scaled+
(symbol macro).
+hybrid-unscaled+
(symbol macro).
+knuthran+
(symbol macro).
+knuthran2+
(symbol macro).
+knuthran2002+
(symbol macro).
+lecuyer21+
(symbol macro).
+levenberg-marquardt+
(symbol macro).
+levenberg-marquardt-unscaled+
(symbol macro).
+linear-interpolation+
(symbol macro).
+minstd+
(symbol macro).
+mrg+
(symbol macro).
+mt19937+
(symbol macro).
+mt19937-1998+
(symbol macro).
+mt19937-1999+
(symbol macro).
+nan+
(constant).
+negative-infinity+
(constant).
+newton-fdfsolver+
(symbol macro).
+newton-mfdfsolver+
(symbol macro).
+niederreiter2+
(symbol macro).
+periodic-akima-interpolation+
(symbol macro).
+periodic-cubic-spline-interpolation+
(symbol macro).
+polynomial-interpolation+
(symbol macro).
+positive-infinity+
(constant).
+powells-hybrid+
(symbol macro).
+powells-hybrid-unscaled+
(symbol macro).
+quad-golden-fminimizer+
(symbol macro).
+r250+
(symbol macro).
+ran0+
(symbol macro).
+ran1+
(symbol macro).
+ran2+
(symbol macro).
+ran3+
(symbol macro).
+rand+
(symbol macro).
+rand48+
(symbol macro).
+random128_bsd+
(symbol macro).
+random128_glibc2+
(symbol macro).
+random128_libc5+
(symbol macro).
+random256_bsd+
(symbol macro).
+random256_glibc2+
(symbol macro).
+random256_libc5+
(symbol macro).
+random32_bsd+
(symbol macro).
+random32_glibc2+
(symbol macro).
+random32_libc5+
(symbol macro).
+random64_bsd+
(symbol macro).
+random64_glibc2+
(symbol macro).
+random64_libc5+
(symbol macro).
+random8_bsd+
(symbol macro).
+random8_glibc2+
(symbol macro).
+random8_libc5+
(symbol macro).
+random_bsd+
(symbol macro).
+random_glibc2+
(symbol macro).
+random_libc5+
(symbol macro).
+randu+
(symbol macro).
+ranf+
(symbol macro).
+ranlux+
(symbol macro).
+ranlux389+
(symbol macro).
+ranlxd1+
(symbol macro).
+ranlxd2+
(symbol macro).
+ranlxs0+
(symbol macro).
+ranlxs1+
(symbol macro).
+ranlxs2+
(symbol macro).
+ranmar+
(symbol macro).
+reverse-halton+
(symbol macro).
+secant-fdfsolver+
(symbol macro).
+simplex-nelder-mead+
(symbol macro).
+simplex-nelder-mead-on2+
(symbol macro).
+simplex-nelder-mead-random+
(symbol macro).
+slatec+
(symbol macro).
+sobol+
(symbol macro).
+steffenson-fdfsolver+
(symbol macro).
+step-bsimp+
(symbol macro).
+step-gear1+
(symbol macro).
+step-gear2+
(symbol macro).
+step-rk2+
(symbol macro).
+step-rk2imp+
(symbol macro).
+step-rk4+
(symbol macro).
+step-rk4imp+
(symbol macro).
+step-rk8pd+
(symbol macro).
+step-rkck+
(symbol macro).
+step-rkf45+
(symbol macro).
+taus+
(symbol macro).
+taus113+
(symbol macro).
+taus2+
(symbol macro).
+transputer+
(symbol macro).
+tt800+
(symbol macro).
+uni+
(symbol macro).
+uni32+
(symbol macro).
+vax+
(symbol macro).
+vector-bfgs+
(symbol macro).
+vector-bfgs2+
(symbol macro).
+waterman14+
(symbol macro).
+zuf+
(symbol macro).
1/gamma
(function).
absolute-deviation
(generic function).
absolute-sum
(generic function).
accelerate
(function).
accelerate-truncated
(function).
accelerated-interpolation-search
(function).
acceleration
(class).
adjust-stepsize
(function).
airy-ai
(function).
airy-ai-deriv
(function).
airy-ai-deriv-scaled
(function).
airy-ai-scaled
(function).
airy-bi
(function).
airy-bi-deriv
(function).
airy-bi-deriv-scaled
(function).
airy-bi-scaled
(function).
airy-zero-ai
(function).
airy-zero-ai-deriv
(function).
airy-zero-bi
(function).
airy-zero-bi-deriv
(function).
all-random-number-generators
(function).
apply-evolution
(function).
apply-hankel
(function).
apply-step
(function).
argument
(function).
atanint
(function).
autocorrelation
(generic function).
axpy
(generic function).
backward-derivative
(function).
backward-discrete-fourier-transform
(generic function).
backward-fourier-transform
(function).
bad-function-supplied
(condition).
basis-spline
(class).
bernoulli-pdf
(function).
bessel-lnknu
(function).
bessel-zero-j0
(function).
bessel-zero-j1
(function).
bessel-zero-jnu
(function).
beta
(function).
beta-p
(function).
beta-pdf
(function).
beta-pinv
(function).
beta-q
(function).
beta-qinv
(function).
bidiagonal-decomposition
(function).
bidiagonal-unpack
(function).
bidiagonal-unpack-diagonal-superdiagonal
(function).
bidiagonal-unpack2
(function).
binomial
(function).
binomial-p
(function).
binomial-pdf
(function).
binomial-q
(function).
bivariate-gaussian-pdf
(function).
blas-copy
(generic function).
blas-swap
(generic function).
bookdata-ntuple
(function).
breakpoint
(function).
cache-limit-exceeded
(condition).
canonical-cycles
(function).
canonical-to-linear
(function).
cauchy-p
(function).
cauchy-pdf
(function).
cauchy-pinv
(function).
cauchy-q
(function).
cauchy-qinv
(function).
cdot
(generic function).
central-derivative
(function).
chebyshev
(class).
chi
(function).
chi-squared-p
(function).
chi-squared-pdf
(function).
chi-squared-pinv
(function).
chi-squared-q
(function).
chi-squared-qinv
(function).
cholesky-decomposition
(generic function).
cholesky-invert
(function).
cholesky-solve
(generic function).
choose
(function).
ci
(function).
clausen
(function).
close-ntuple
(function).
coefficients
(function).
column
(generic function).
(setf column)
(generic function).
combination-next
(function).
combination-previous
(function).
combination-range
(function).
complementary-incomplete-gamma
(function).
conjugate-rank-1-update
(generic function).
control-alloc
(function).
correlation
(generic function).
cos-err
(function).
coulomb-cl
(function).
coulomb-cl-array
(function).
coulomb-wave-f-array
(function).
coulomb-wave-fg
(function).
coulomb-wave-fg-array
(function).
coulomb-wave-fgp-array
(function).
coulomb-wave-sphf-array
(function).
coupling-3j
(function).
coupling-6j
(function).
coupling-9j
(function).
covariance
(generic function).
create-ntuple
(function).
cx-add
(function).
cx-add-imag
(function).
cx-add-real
(function).
cx-arccos
(function).
cx-arccos-real
(function).
cx-arccosh
(function).
cx-arccosh-real
(function).
cx-arccot
(function).
cx-arccoth
(function).
cx-arccsc
(function).
cx-arccsc-real
(function).
cx-arccsch
(function).
cx-arcsec
(function).
cx-arcsec-real
(function).
cx-arcsech
(function).
cx-arcsin
(function).
cx-arcsin-real
(function).
cx-arcsinh
(function).
cx-arctan
(function).
cx-arctanh
(function).
cx-arctanh-real
(function).
cx-conjugate
(function).
cx-cos
(function).
cx-cosh
(function).
cx-cot
(function).
cx-coth
(function).
cx-csc
(function).
cx-csch
(function).
cx-div
(function).
cx-div-imag
(function).
cx-div-real
(function).
cx-exp
(function).
cx-expt
(function).
cx-expt-real
(function).
cx-inverse
(function).
cx-log
(function).
cx-log10
(function).
cx-logb
(function).
cx-mul
(function).
cx-mul-imag
(function).
cx-mul-real
(function).
cx-negative
(function).
cx-sec
(function).
cx-sech
(function).
cx-sin
(function).
cx-sinh
(function).
cx-sqrt
(function).
cx-sqrt-real
(function).
cx-sub
(function).
cx-sub-imag
(function).
cx-sub-real
(function).
cx-tan
(function).
cx-tanh
(function).
cylindrical-bessel-i
(generic function).
cylindrical-bessel-i-scaled
(generic function).
cylindrical-bessel-i0
(function).
cylindrical-bessel-i0-scaled
(function).
cylindrical-bessel-i1
(function).
cylindrical-bessel-i1-scaled
(function).
cylindrical-bessel-in-array
(function).
cylindrical-bessel-in-scaled-array
(function).
cylindrical-bessel-j
(generic function).
cylindrical-bessel-j-array-order
(function).
cylindrical-bessel-j-array-x
(function).
cylindrical-bessel-j0
(function).
cylindrical-bessel-j1
(function).
cylindrical-bessel-k
(generic function).
cylindrical-bessel-k-scaled
(generic function).
cylindrical-bessel-k0
(function).
cylindrical-bessel-k0-scaled
(function).
cylindrical-bessel-k1
(function).
cylindrical-bessel-k1-scaled
(function).
cylindrical-bessel-kn-array
(function).
cylindrical-bessel-kn-scaled-array
(function).
cylindrical-bessel-y
(generic function).
cylindrical-bessel-y0
(function).
cylindrical-bessel-y1
(function).
cylindrical-bessel-yn-array
(function).
dawson
(function).
debye-1
(function).
debye-2
(function).
debye-3
(function).
debye-4
(function).
derivative-chebyshev
(function).
dilogarithm
(generic function).
dirichlet-log-pdf
(function).
dirichlet-pdf
(function).
discrete-fourier-transform
(generic function).
discrete-pdf
(function).
discrete-random
(class).
divergence
(condition).
divided-difference
(function).
double-factorial
(function).
double-float-unequal
(function).
eigen-gen
(class).
eigen-genherm
(class).
eigen-genhermv
(class).
eigen-gensymm
(class).
eigen-gensymmv
(class).
eigen-genv
(class).
eigen-herm
(class).
eigen-hermv
(class).
eigen-nonsymm
(class).
eigen-nonsymmv
(class).
eigen-symm
(class).
eigen-symmv
(class).
eigenvalues
(generic function).
eigenvalues-eigenvectors
(generic function).
eigenvalues-eigenvectors-gen
(function).
eigenvalues-eigenvectors-gensymm
(generic function).
eigenvalues-eigenvectors-nonsymm
(function).
eigenvalues-gen
(function).
eigenvalues-gensymm
(generic function).
eigenvalues-nonsymm
(function).
elliptic-integral-d
(function).
elliptic-integral-e
(function).
elliptic-integral-e-complete
(function).
elliptic-integral-f
(function).
elliptic-integral-k-complete
(function).
elliptic-integral-p
(function).
elliptic-integral-rc
(function).
elliptic-integral-rd
(function).
elliptic-integral-rf
(function).
elliptic-integral-rj
(function).
elt*
(generic function).
elt+
(generic function).
elt-
(generic function).
elt/
(generic function).
equal-bins-p
(generic function).
erf
(function).
erf-q
(function).
erf-z
(function).
erfc
(function).
eta
(function).
euclidean-norm
(generic function).
evaluate
(generic function).
evaluate-chebyshev-error
(function).
evaluate-derivative
(generic function).
evaluate-integral
(generic function).
evaluate-second-derivative
(generic function).
evaluate-with-derivatives
(function).
examples
(function).
exceeded-maximum-iterations
(condition).
exp-1
(function).
exp-err
(function).
exp-err-scaled
(function).
exp-mult
(function).
exp-mult-err
(function).
exp-mult-err-scaled
(function).
exp-mult-scaled
(function).
exp-scaled
(function).
expm1
(function).
exponential-integral-3
(function).
exponential-integral-e1
(function).
exponential-integral-e2
(function).
exponential-integral-ei
(function).
exponential-integral-en
(function).
exponential-p
(function).
exponential-pdf
(function).
exponential-pinv
(function).
exponential-power-p
(function).
exponential-power-pdf
(function).
exponential-power-q
(function).
exponential-q
(function).
exponential-qinv
(function).
exprel
(function).
exprel-2
(function).
exprel-n
(function).
factorial
(function).
factorization-failure
(condition).
failure-to-reach-tolerance
(condition).
failure-to-reach-tolerance-f
(condition).
failure-to-reach-tolerance-g
(condition).
failure-to-reach-tolerance-x
(condition).
fdist-p
(function).
fdist-pdf
(function).
fdist-pinv
(function).
fdist-q
(function).
fdist-qinv
(function).
fermi-dirac-0
(function).
fermi-dirac-1
(function).
fermi-dirac-1/2
(function).
fermi-dirac-2
(function).
fermi-dirac-3/2
(function).
fermi-dirac-inc-0
(function).
fermi-dirac-integral
(function).
fermi-dirac-m1
(function).
fermi-dirac-m1/2
(function).
fft-frequency-vector
(function).
fft-inverse-shift
(function).
fft-shift
(function).
finitep
(function).
fit-gradient
(function).
fit-test-delta
(function).
fit-test-gradient
(function).
fit-workspace
(class).
flat-p
(function).
flat-pdf
(function).
flat-pinv
(function).
flat-q
(function).
flat-qinv
(function).
float-as-integer
(function).
fminimizer-f-lower
(function).
fminimizer-f-upper
(function).
fminimizer-x-lower
(function).
fminimizer-x-upper
(function).
format-ieee754-bits
(function).
forward-derivative
(function).
forward-discrete-fourier-transform
(generic function).
forward-fourier-transform
(function).
fourier-transform
(function).
fsolver-lower
(function).
fsolver-upper
(function).
function-value
(generic function).
gamma
(function).
gamma*
(function).
gamma-p
(function).
gamma-pdf
(function).
gamma-pinv
(function).
gamma-q
(function).
gamma-qinv
(function).
gaussian-p
(function).
gaussian-pdf
(function).
gaussian-pinv
(function).
gaussian-q
(function).
gaussian-qinv
(function).
gaussian-tail-pdf
(function).
gegenbauer
(function).
gegenbauer-1
(function).
gegenbauer-2
(function).
gegenbauer-3
(function).
gegenbauer-array
(function).
generic-failure-1
(condition).
generic-failure-2
(condition).
geometric-p
(function).
geometric-pdf
(function).
geometric-q
(function).
get-random-number
(function).
givens-rotation
(generic function).
givens-rotation-m
(generic function).
greville-abscissa
(function).
gsl-asinh
(function).
gsl-atanh
(function).
gsl-condition
(condition).
gsl-cos
(generic function).
gsl-division-by-zero
(condition).
gsl-eof
(condition).
gsl-exp
(function).
gsl-log
(generic function).
gsl-lookup
(function).
gsl-random-state
(function).
gsl-sin
(generic function).
gumbel1-p
(function).
gumbel1-pdf
(function).
gumbel1-pinv
(function).
gumbel1-q
(function).
gumbel1-qinv
(function).
gumbel2-p
(function).
gumbel2-pdf
(function).
gumbel2-pinv
(function).
gumbel2-q
(function).
gumbel2-qinv
(function).
hankel
(class).
hazard
(function).
heapsort
(function).
heapsort-index
(function).
hermitian-rank-1-update
(generic function).
hermitian-rank-2-update
(generic function).
histogram
(class).
histogram-covariance
(function).
histogram-find
(function).
histogram-pdf
(class).
histogram2d
(class).
histogram2d-pdf
(class).
householder-hm
(function).
householder-hv
(function).
householder-mh
(function).
householder-solve
(function).
householder-transform
(function).
hurwitz-zeta
(function).
hydrogenicr
(function).
hydrogenicr-1
(function).
hypergeometric-0f1
(function).
hypergeometric-1f1
(generic function).
hypergeometric-2f0
(function).
hypergeometric-2f1
(function).
hypergeometric-2f1-conj
(function).
hypergeometric-2f1-conj-renorm
(function).
hypergeometric-2f1-renorm
(function).
hypergeometric-p
(function).
hypergeometric-pdf
(function).
hypergeometric-q
(function).
hypergeometric-u
(generic function).
hypergeometric-u-e10
(generic function).
hypotenuse
(function).
hypotenuse*
(function).
incomplete-beta
(function).
incomplete-gamma
(function).
increment
(generic function).
index-max
(generic function).
infinityp
(function).
init-first
(function).
init-last
(function).
input-domain
(condition).
input-range
(condition).
integer-as-float
(function).
integral-chebyshev
(function).
integration-qag
(function).
integration-qagi
(function).
integration-qagil
(function).
integration-qagiu
(function).
integration-qagp
(function).
integration-qags
(function).
integration-qawc
(function).
integration-qawf
(function).
integration-qawo
(function).
integration-qaws
(function).
integration-qng
(function).
integration-workspace
(class).
interpolation
(class).
interpolation-search
(function).
invalid-argument
(condition).
invalid-pointer
(condition).
invalid-tolerance
(condition).
inverse-discrete-fourier-transform
(generic function).
inverse-fourier-transform
(function).
inverse-matrix-product
(generic function).
inversions
(function).
iterate
(generic function).
jacobian
(function).
jacobian-elliptic-functions
(function).
jacobian-not-improving
(condition).
knots
(function).
kurtosis
(generic function).
laguerre
(function).
laguerre-1
(function).
laguerre-2
(function).
laguerre-3
(function).
lambert-w0
(function).
lambert-wm1
(function).
landau-pdf
(function).
laplace-p
(function).
laplace-pdf
(function).
laplace-pinv
(function).
laplace-q
(function).
laplace-qinv
(function).
last-step
(generic function).
legendre-conicalp-0
(function).
legendre-conicalp-1
(function).
legendre-conicalp-half
(function).
legendre-conicalp-mhalf
(function).
legendre-h3d
(function).
legendre-h3d-0
(function).
legendre-h3d-1
(function).
legendre-h3d-array
(function).
legendre-p1
(function).
legendre-p2
(function).
legendre-p3
(function).
legendre-pl
(function).
legendre-pl-array
(function).
legendre-pl-deriv-array
(function).
legendre-plm
(function).
legendre-q0
(function).
legendre-q1
(function).
legendre-ql
(function).
legendre-regular-cylindrical-conical
(function).
legendre-regular-spherical-conical
(function).
legendre-sphplm
(function).
levin
(class).
levin-truncated
(class).
linear-cycles
(function).
linear-estimate
(function).
linear-fit
(function).
linear-mfit
(function).
linear-to-canonical
(function).
log+1
(function).
log-1+x
(function).
log-1+x-m1
(function).
log-abs
(function).
log-beta
(function).
log-choose
(function).
log-cosh
(function).
log-double-factorial
(function).
log-erfc
(function).
log-factorial
(function).
log-gamma
(function).
log-gamma-complex
(function).
log-gamma-sign
(function).
log-modulus
(function).
log-pochammer
(function).
log-pochammer-sign
(function).
log-sin
(function).
log-sinh
(function).
logarithmic-pdf
(function).
logistic-p
(function).
logistic-pdf
(function).
logistic-pinv
(function).
logistic-q
(function).
logistic-qinv
(function).
lognormal-p
(function).
lognormal-pdf
(function).
lognormal-pinv
(function).
lognormal-q
(function).
lognormal-qinv
(function).
loss-of-accuracy
(condition).
ls-covariance
(function).
lu-decomposition
(generic function).
lu-determinant
(generic function).
lu-invert
(generic function).
lu-log-determinant
(generic function).
lu-refine
(generic function).
lu-sgndet
(generic function).
lu-solve
(generic function).
make-acceleration
(function).
make-basis-spline
(function).
make-chebyshev
(function).
make-combination
(function).
make-discrete-random
(function).
make-eigen-gen
(function).
make-eigen-genherm
(function).
make-eigen-genhermv
(function).
make-eigen-gensymm
(function).
make-eigen-gensymmv
(function).
make-eigen-genv
(function).
make-eigen-herm
(function).
make-eigen-hermv
(function).
make-eigen-nonsymm
(function).
make-eigen-nonsymmv
(function).
make-eigen-symm
(function).
make-eigen-symmv
(function).
make-fft-wavetable
(function).
make-fft-workspace
(function).
make-fit-workspace
(function).
make-hankel
(function).
make-histogram
(function).
make-histogram-pdf
(function).
make-histogram2d
(function).
make-histogram2d-pdf
(function).
make-integration-workspace
(function).
make-interpolation
(function).
make-jacobian-matrix
(function).
make-levin
(function).
make-levin-truncated
(function).
make-mathieu
(function).
make-monte-carlo-miser
(function).
make-monte-carlo-plain
(function).
make-monte-carlo-vegas
(function).
make-multi-dimensional-minimizer-f
(function).
make-multi-dimensional-minimizer-fdf
(function).
make-multi-dimensional-root-solver-f
(function).
make-multi-dimensional-root-solver-fdf
(function).
make-nonlinear-fdffit
(function).
make-nonlinear-ffit
(function).
make-ode-evolution
(function).
make-ode-stepper
(function).
make-one-dimensional-minimizer
(function).
make-one-dimensional-root-solver-f
(function).
make-one-dimensional-root-solver-fdf
(function).
make-permutation
(function).
make-polynomial-complex-workspace
(function).
make-qawo-table
(function).
make-qaws-table
(function).
make-quasi-random-number-generator
(function).
make-random-number-generator
(function).
make-scaled-control
(function).
make-spline
(function).
make-standard-control
(function).
make-wavelet
(function).
make-wavelet-workspace
(function).
make-y-control
(function).
make-yp-control
(function).
maref
(macro).
(setf maref)
(setf expander).
mathieu
(class).
mathieu-a
(function).
mathieu-a-array
(function).
mathieu-b
(function).
mathieu-b-array
(function).
mathieu-ce
(function).
mathieu-ce-array
(function).
mathieu-mc
(function).
mathieu-mc-array
(function).
mathieu-ms
(function).
mathieu-ms-array
(function).
mathieu-se
(function).
mathieu-se-array
(function).
matrix-exponential
(function).
matrix-product
(generic function).
matrix-product-hermitian
(generic function).
matrix-product-symmetric
(generic function).
matrix-product-triangular
(generic function).
matrix-transpose
(generic function).
matrix-transpose*
(generic function).
max-index
(generic function).
max-range
(generic function).
mean
(generic function).
median
(generic function).
memory-allocation-failure
(condition).
mfdfminimizer-gradient
(function).
mfdfminimizer-restart
(function).
min-index
(generic function).
min-range
(generic function).
min-test-gradient
(function).
min-test-interval
(function).
min-test-size
(function).
minimum-size
(generic function).
minmax
(generic function).
minmax-index
(generic function).
mmax
(generic function).
mmin
(generic function).
mminusp
(generic function).
modified-givens-rotation
(generic function).
modified-givens-rotation-m
(generic function).
modulus
(function).
modulus2
(function).
monte-carlo-integrate-miser
(function).
monte-carlo-integrate-plain
(function).
monte-carlo-integrate-vegas
(function).
monte-carlo-miser
(class).
monte-carlo-plain
(class).
monte-carlo-vegas
(class).
mplusp
(generic function).
msort
(generic function).
multi-dimensional-minimizer-f
(class).
multi-dimensional-minimizer-fdf
(class).
multi-dimensional-root-solver-f
(class).
multi-dimensional-root-solver-fdf
(class).
multi-linear-estimate
(function).
multi-linear-residuals
(function).
multinomial-log-pdf
(function).
multinomial-pdf
(function).
multiplier-estimate
(function).
multiplier-fit
(function).
multiply
(function).
multiply-err
(function).
multiroot-test-delta
(function).
multiroot-test-residual
(function).
mzerop
(generic function).
name
(generic function).
nanp
(function).
negative-binomial-p
(function).
negative-binomial-pdf
(function).
negative-binomial-q
(function).
no-progress
(condition).
non-negative-p
(generic function).
nonconformant-dimensions
(condition).
nonlinear-fdffit
(class).
nonlinear-ffit
(class).
nonnormalized-incomplete-gamma
(function).
nonsquare-matrix
(condition).
number-of-breakpoints
(function).
number-of-coefficients
(function).
ode-evolution
(class).
ode-stepper
(class).
one-dimensional-minimizer
(class).
one-dimensional-root-solver-f
(class).
one-dimensional-root-solver-fdf
(class).
open-ntuple
(function).
order
(generic function).
overflow
(condition).
parameter
(generic function).
(setf parameter)
(generic function).
pareto-p
(function).
pareto-pdf
(function).
pareto-pinv
(function).
pareto-q
(function).
pareto-qinv
(function).
pascal-p
(function).
pascal-pdf
(function).
pascal-q
(function).
permutation
(class).
permutation*
(function).
permutation-data
(function).
permutation-inverse
(function).
permutation-next
(function).
permutation-previous
(function).
permutation-reverse
(function).
permute
(generic function).
permute-inverse
(generic function).
pochammer
(function).
poisson-p
(function).
poisson-pdf
(function).
poisson-q
(function).
polar-to-rectangular
(function).
polynomial-complex-workspace
(class).
polynomial-solve
(function).
pow
(function).
project-ntuple
(function).
psi
(generic function).
psi-1
(generic function).
psi-1+iy
(function).
psi-n
(function).
qawo-table
(class).
qaws-table
(class).
qr-decomposition
(function).
qr-qrsolve
(function).
qr-qtvector
(function).
qr-qvector
(function).
qr-rsolve
(function).
qr-solve
(function).
qr-solve-least-squares
(function).
qr-unpack
(function).
qr-update
(function).
qrng-get
(function).
qrpt-decomposition
(function).
qrpt-decomposition*
(function).
qrpt-qrsolve
(function).
qrpt-rsolve
(function).
qrpt-solve
(function).
qrpt-update
(function).
quantile
(generic function).
quasi-random-number-generator
(class).
r-solve
(function).
random-number-generator
(class).
range
(generic function).
rank-1-update
(generic function).
rayleigh-p
(function).
rayleigh-pdf
(function).
rayleigh-pinv
(function).
rayleigh-q
(function).
rayleigh-qinv
(function).
rayleigh-tail-pdf
(function).
read-ntuple
(function).
rectangular-to-polar
(function).
relative-pochammer
(function).
restrict-positive
(function).
restrict-symmetric
(function).
return-value-on-error
(macro).
rng-environment-setup
(function).
rng-max
(function).
rng-min
(function).
rng-state
(generic function).
root-test-delta
(function).
root-test-interval
(function).
root-test-residual
(function).
roundoff-failure
(condition).
row
(generic function).
(setf row)
(generic function).
runaway-iteration
(condition).
sample
(generic function).
sample-k-hankel
(function).
sample-x-hankel
(function).
sanity-check-failure
(condition).
scale
(generic function).
scaled-control
(class).
sdot
(function).
set-all
(generic function).
set-basis
(generic function).
set-floating-point-modes
(function).
set-identity
(generic function).
set-ranges-uniform
(generic function).
set-zero
(generic function).
shi
(function).
shift
(generic function).
si
(function).
sigma
(generic function).
simulated-annealing
(function).
sin-err
(function).
sinc
(function).
singularity
(condition).
size
(generic function).
skewness
(generic function).
solution
(generic function).
solve-cubic
(function).
solve-cubic-complex
(function).
solve-cyclic-tridiagonal
(function).
solve-quadratic
(function).
solve-quadratic-complex
(function).
solve-symmetric-cyclic-tridiagonal
(function).
solve-symmetric-tridiagonal
(function).
solve-tridiagonal
(function).
sort-eigenvalues-eigenvectors
(generic function).
sort-index
(generic function).
sort-largest
(generic function).
sort-largest-index
(generic function).
sort-smallest
(generic function).
sort-smallest-index
(generic function).
sort-vector
(generic function).
sort-vector-index
(generic function).
sort-vector-largest
(generic function).
sort-vector-largest-index
(generic function).
sort-vector-smallest
(generic function).
sort-vector-smallest-index
(generic function).
spherical-bessel-i0-scaled
(function).
spherical-bessel-i1-scaled
(function).
spherical-bessel-i2-scaled
(function).
spherical-bessel-il-scaled
(function).
spherical-bessel-il-scaled-array
(function).
spherical-bessel-j0
(function).
spherical-bessel-j1
(function).
spherical-bessel-j2
(function).
spherical-bessel-jl
(function).
spherical-bessel-jl-array
(function).
spherical-bessel-jl-steed-array
(function).
spherical-bessel-k0-scaled
(function).
spherical-bessel-k1-scaled
(function).
spherical-bessel-k2-scaled
(function).
spherical-bessel-kl-scaled
(function).
spherical-bessel-kl-scaled-array
(function).
spherical-bessel-y0
(function).
spherical-bessel-y1
(function).
spherical-bessel-y2
(function).
spherical-bessel-yl
(function).
spherical-bessel-yl-array
(function).
spline
(class).
standard-control
(class).
standard-deviation
(generic function).
standard-deviation-with-fixed-mean
(generic function).
step-order
(function).
sum
(generic function).
sv-decomposition
(function).
sv-jacobi-decomposition
(function).
sv-modified-decomposition
(function).
sv-solve
(function).
swap
(generic function).
swap-columns
(generic function).
swap-elements
(generic function).
swap-row-column
(generic function).
swap-rows
(generic function).
symmetric-rank-1-update
(generic function).
symmetric-rank-2-update
(generic function).
synchrotron-1
(function).
synchrotron-2
(function).
table-limit-exceeded
(condition).
taylor-coefficient
(function).
taylor-divided-difference
(function).
tdist-p
(function).
tdist-pdf
(function).
tdist-pinv
(function).
tdist-q
(function).
tdist-qinv
(function).
transport-2
(function).
transport-3
(function).
transport-4
(function).
transport-5
(function).
tridiagonal-decomposition
(generic function).
tridiagonal-unpack
(generic function).
tridiagonal-unpack-t
(generic function).
ugaussian-p
(function).
ugaussian-pdf
(function).
ugaussian-pinv
(function).
ugaussian-q
(function).
ugaussian-qinv
(function).
ugaussian-tail-pdf
(function).
underflow
(condition).
uniform-knots
(function).
unimplemented-feature
(condition).
unpack
(function).
unsupported-feature
(condition).
validp
(generic function).
variance
(generic function).
variance-with-fixed-mean
(generic function).
vector-reverse
(generic function).
wavelet
(class).
wavelet-2d-nonstandard-transform
(function).
wavelet-2d-nonstandard-transform-forward
(function).
wavelet-2d-nonstandard-transform-inverse
(function).
wavelet-2d-nonstandard-transform-matrix
(function).
wavelet-2d-nonstandard-transform-matrix-forward
(function).
wavelet-2d-nonstandard-transform-matrix-inverse
(function).
wavelet-2d-transform
(function).
wavelet-2d-transform-forward
(function).
wavelet-2d-transform-inverse
(function).
wavelet-2d-transform-matrix
(function).
wavelet-2d-transform-matrix-forward
(function).
wavelet-2d-transform-matrix-inverse
(function).
wavelet-transform
(function).
wavelet-transform-forward
(function).
wavelet-transform-inverse
(function).
wavelet-workspace
(class).
weibull-p
(function).
weibull-pdf
(function).
weibull-pinv
(function).
weibull-q
(function).
weibull-qinv
(function).
weighted-absolute-deviation
(generic function).
weighted-kurtosis
(generic function).
weighted-mean
(generic function).
weighted-skewness
(generic function).
weighted-standard-deviation
(generic function).
weighted-standard-deviation-with-fixed-mean
(generic function).
weighted-variance
(generic function).
weighted-variance-with-fixed-mean
(generic function).
with-fourier-transform-environment
(macro).
with-ode-integration
(macro).
write-ntuple
(function).
y-control
(class).
yp-control
(class).
zeta
(generic function).
zeta-1
(generic function).
%var-accessor-*gsl-version*
(function).
(setf %var-accessor-*gsl-version*)
(function).
%var-accessor-+akima-interpolation+
(function).
(setf %var-accessor-+akima-interpolation+)
(function).
%var-accessor-+bisection-fsolver+
(function).
(setf %var-accessor-+bisection-fsolver+)
(function).
%var-accessor-+borosh13+
(function).
(setf %var-accessor-+borosh13+)
(function).
%var-accessor-+brent-fminimizer+
(function).
(setf %var-accessor-+brent-fminimizer+)
(function).
%var-accessor-+brent-fsolver+
(function).
(setf %var-accessor-+brent-fsolver+)
(function).
%var-accessor-+broyden+
(function).
(setf %var-accessor-+broyden+)
(function).
%var-accessor-+bspline-wavelet+
(function).
(setf %var-accessor-+bspline-wavelet+)
(function).
%var-accessor-+bspline-wavelet-centered+
(function).
(setf %var-accessor-+bspline-wavelet-centered+)
(function).
%var-accessor-+cmrg+
(function).
(setf %var-accessor-+cmrg+)
(function).
%var-accessor-+conjugate-fletcher-reeves+
(function).
(setf %var-accessor-+conjugate-fletcher-reeves+)
(function).
%var-accessor-+conjugate-polak-ribiere+
(function).
(setf %var-accessor-+conjugate-polak-ribiere+)
(function).
%var-accessor-+coveyou+
(function).
(setf %var-accessor-+coveyou+)
(function).
%var-accessor-+cubic-spline-interpolation+
(function).
(setf %var-accessor-+cubic-spline-interpolation+)
(function).
%var-accessor-+daubechies-wavelet+
(function).
(setf %var-accessor-+daubechies-wavelet+)
(function).
%var-accessor-+daubechies-wavelet-centered+
(function).
(setf %var-accessor-+daubechies-wavelet-centered+)
(function).
%var-accessor-+default-seed+
(function).
(setf %var-accessor-+default-seed+)
(function).
%var-accessor-+default-type+
(function).
(setf %var-accessor-+default-type+)
(function).
%var-accessor-+discrete-newton+
(function).
(setf %var-accessor-+discrete-newton+)
(function).
%var-accessor-+false-position-fsolver+
(function).
(setf %var-accessor-+false-position-fsolver+)
(function).
%var-accessor-+fishman18+
(function).
(setf %var-accessor-+fishman18+)
(function).
%var-accessor-+fishman20+
(function).
(setf %var-accessor-+fishman20+)
(function).
%var-accessor-+fishman2x+
(function).
(setf %var-accessor-+fishman2x+)
(function).
%var-accessor-+gfsr4+
(function).
(setf %var-accessor-+gfsr4+)
(function).
%var-accessor-+gnewton-mfdfsolver+
(function).
(setf %var-accessor-+gnewton-mfdfsolver+)
(function).
%var-accessor-+golden-section-fminimizer+
(function).
(setf %var-accessor-+golden-section-fminimizer+)
(function).
%var-accessor-+haar-wavelet+
(function).
(setf %var-accessor-+haar-wavelet+)
(function).
%var-accessor-+haar-wavelet-centered+
(function).
(setf %var-accessor-+haar-wavelet-centered+)
(function).
%var-accessor-+halton+
(function).
(setf %var-accessor-+halton+)
(function).
%var-accessor-+hybrid-scaled+
(function).
(setf %var-accessor-+hybrid-scaled+)
(function).
%var-accessor-+hybrid-unscaled+
(function).
(setf %var-accessor-+hybrid-unscaled+)
(function).
%var-accessor-+knuthran+
(function).
(setf %var-accessor-+knuthran+)
(function).
%var-accessor-+knuthran2+
(function).
(setf %var-accessor-+knuthran2+)
(function).
%var-accessor-+knuthran2002+
(function).
(setf %var-accessor-+knuthran2002+)
(function).
%var-accessor-+lecuyer21+
(function).
(setf %var-accessor-+lecuyer21+)
(function).
%var-accessor-+levenberg-marquardt+
(function).
(setf %var-accessor-+levenberg-marquardt+)
(function).
%var-accessor-+levenberg-marquardt-unscaled+
(function).
(setf %var-accessor-+levenberg-marquardt-unscaled+)
(function).
%var-accessor-+linear-interpolation+
(function).
(setf %var-accessor-+linear-interpolation+)
(function).
%var-accessor-+minstd+
(function).
(setf %var-accessor-+minstd+)
(function).
%var-accessor-+mrg+
(function).
(setf %var-accessor-+mrg+)
(function).
%var-accessor-+mt19937+
(function).
(setf %var-accessor-+mt19937+)
(function).
%var-accessor-+mt19937-1998+
(function).
(setf %var-accessor-+mt19937-1998+)
(function).
%var-accessor-+mt19937-1999+
(function).
(setf %var-accessor-+mt19937-1999+)
(function).
%var-accessor-+newton-fdfsolver+
(function).
(setf %var-accessor-+newton-fdfsolver+)
(function).
%var-accessor-+newton-mfdfsolver+
(function).
(setf %var-accessor-+newton-mfdfsolver+)
(function).
%var-accessor-+niederreiter2+
(function).
(setf %var-accessor-+niederreiter2+)
(function).
%var-accessor-+periodic-akima-interpolation+
(function).
(setf %var-accessor-+periodic-akima-interpolation+)
(function).
%var-accessor-+periodic-cubic-spline-interpolation+
(function).
(setf %var-accessor-+periodic-cubic-spline-interpolation+)
(function).
%var-accessor-+polynomial-interpolation+
(function).
(setf %var-accessor-+polynomial-interpolation+)
(function).
%var-accessor-+powells-hybrid+
(function).
(setf %var-accessor-+powells-hybrid+)
(function).
%var-accessor-+powells-hybrid-unscaled+
(function).
(setf %var-accessor-+powells-hybrid-unscaled+)
(function).
%var-accessor-+quad-golden-fminimizer+
(function).
(setf %var-accessor-+quad-golden-fminimizer+)
(function).
%var-accessor-+r250+
(function).
(setf %var-accessor-+r250+)
(function).
%var-accessor-+ran0+
(function).
(setf %var-accessor-+ran0+)
(function).
%var-accessor-+ran1+
(function).
(setf %var-accessor-+ran1+)
(function).
%var-accessor-+ran2+
(function).
(setf %var-accessor-+ran2+)
(function).
%var-accessor-+ran3+
(function).
(setf %var-accessor-+ran3+)
(function).
%var-accessor-+rand+
(function).
(setf %var-accessor-+rand+)
(function).
%var-accessor-+rand48+
(function).
(setf %var-accessor-+rand48+)
(function).
%var-accessor-+random128_bsd+
(function).
(setf %var-accessor-+random128_bsd+)
(function).
%var-accessor-+random128_glibc2+
(function).
(setf %var-accessor-+random128_glibc2+)
(function).
%var-accessor-+random128_libc5+
(function).
(setf %var-accessor-+random128_libc5+)
(function).
%var-accessor-+random256_bsd+
(function).
(setf %var-accessor-+random256_bsd+)
(function).
%var-accessor-+random256_glibc2+
(function).
(setf %var-accessor-+random256_glibc2+)
(function).
%var-accessor-+random256_libc5+
(function).
(setf %var-accessor-+random256_libc5+)
(function).
%var-accessor-+random32_bsd+
(function).
(setf %var-accessor-+random32_bsd+)
(function).
%var-accessor-+random32_glibc2+
(function).
(setf %var-accessor-+random32_glibc2+)
(function).
%var-accessor-+random32_libc5+
(function).
(setf %var-accessor-+random32_libc5+)
(function).
%var-accessor-+random64_bsd+
(function).
(setf %var-accessor-+random64_bsd+)
(function).
%var-accessor-+random64_glibc2+
(function).
(setf %var-accessor-+random64_glibc2+)
(function).
%var-accessor-+random64_libc5+
(function).
(setf %var-accessor-+random64_libc5+)
(function).
%var-accessor-+random8_bsd+
(function).
(setf %var-accessor-+random8_bsd+)
(function).
%var-accessor-+random8_glibc2+
(function).
(setf %var-accessor-+random8_glibc2+)
(function).
%var-accessor-+random8_libc5+
(function).
(setf %var-accessor-+random8_libc5+)
(function).
%var-accessor-+random_bsd+
(function).
(setf %var-accessor-+random_bsd+)
(function).
%var-accessor-+random_glibc2+
(function).
(setf %var-accessor-+random_glibc2+)
(function).
%var-accessor-+random_libc5+
(function).
(setf %var-accessor-+random_libc5+)
(function).
%var-accessor-+randu+
(function).
(setf %var-accessor-+randu+)
(function).
%var-accessor-+ranf+
(function).
(setf %var-accessor-+ranf+)
(function).
%var-accessor-+ranlux+
(function).
(setf %var-accessor-+ranlux+)
(function).
%var-accessor-+ranlux389+
(function).
(setf %var-accessor-+ranlux389+)
(function).
%var-accessor-+ranlxd1+
(function).
(setf %var-accessor-+ranlxd1+)
(function).
%var-accessor-+ranlxd2+
(function).
(setf %var-accessor-+ranlxd2+)
(function).
%var-accessor-+ranlxs0+
(function).
(setf %var-accessor-+ranlxs0+)
(function).
%var-accessor-+ranlxs1+
(function).
(setf %var-accessor-+ranlxs1+)
(function).
%var-accessor-+ranlxs2+
(function).
(setf %var-accessor-+ranlxs2+)
(function).
%var-accessor-+ranmar+
(function).
(setf %var-accessor-+ranmar+)
(function).
%var-accessor-+reverse-halton+
(function).
(setf %var-accessor-+reverse-halton+)
(function).
%var-accessor-+secant-fdfsolver+
(function).
(setf %var-accessor-+secant-fdfsolver+)
(function).
%var-accessor-+simplex-nelder-mead+
(function).
(setf %var-accessor-+simplex-nelder-mead+)
(function).
%var-accessor-+simplex-nelder-mead-on2+
(function).
(setf %var-accessor-+simplex-nelder-mead-on2+)
(function).
%var-accessor-+simplex-nelder-mead-random+
(function).
(setf %var-accessor-+simplex-nelder-mead-random+)
(function).
%var-accessor-+slatec+
(function).
(setf %var-accessor-+slatec+)
(function).
%var-accessor-+sobol+
(function).
(setf %var-accessor-+sobol+)
(function).
%var-accessor-+steffenson-fdfsolver+
(function).
(setf %var-accessor-+steffenson-fdfsolver+)
(function).
%var-accessor-+step-bsimp+
(function).
(setf %var-accessor-+step-bsimp+)
(function).
%var-accessor-+step-gear1+
(function).
(setf %var-accessor-+step-gear1+)
(function).
%var-accessor-+step-gear2+
(function).
(setf %var-accessor-+step-gear2+)
(function).
%var-accessor-+step-rk2+
(function).
(setf %var-accessor-+step-rk2+)
(function).
%var-accessor-+step-rk2imp+
(function).
(setf %var-accessor-+step-rk2imp+)
(function).
%var-accessor-+step-rk4+
(function).
(setf %var-accessor-+step-rk4+)
(function).
%var-accessor-+step-rk4imp+
(function).
(setf %var-accessor-+step-rk4imp+)
(function).
%var-accessor-+step-rk8pd+
(function).
(setf %var-accessor-+step-rk8pd+)
(function).
%var-accessor-+step-rkck+
(function).
(setf %var-accessor-+step-rkck+)
(function).
%var-accessor-+step-rkf45+
(function).
(setf %var-accessor-+step-rkf45+)
(function).
%var-accessor-+taus+
(function).
(setf %var-accessor-+taus+)
(function).
%var-accessor-+taus113+
(function).
(setf %var-accessor-+taus113+)
(function).
%var-accessor-+taus2+
(function).
(setf %var-accessor-+taus2+)
(function).
%var-accessor-+transputer+
(function).
(setf %var-accessor-+transputer+)
(function).
%var-accessor-+tt800+
(function).
(setf %var-accessor-+tt800+)
(function).
%var-accessor-+uni+
(function).
(setf %var-accessor-+uni+)
(function).
%var-accessor-+uni32+
(function).
(setf %var-accessor-+uni32+)
(function).
%var-accessor-+vax+
(function).
(setf %var-accessor-+vax+)
(function).
%var-accessor-+vector-bfgs+
(function).
(setf %var-accessor-+vector-bfgs+)
(function).
%var-accessor-+vector-bfgs2+
(function).
(setf %var-accessor-+vector-bfgs2+)
(function).
%var-accessor-+waterman14+
(function).
(setf %var-accessor-+waterman14+)
(function).
%var-accessor-+zuf+
(function).
(setf %var-accessor-+zuf+)
(function).
*all-generated-tests*
(special variable).
*allowed-ticks*
(special variable).
*blas-splice-fp-types*
(special variable).
*callbacks-for-classes*
(special variable).
*cstd-blas-mapping*
(special variable).
*cstd-gsl-mapping*
(special variable).
*default-sf-array-size*
(special variable).
*defmfun-llk*
(special variable).
*defmfun-optk*
(special variable).
*double-float-pool*
(special variable).
*elljac-a*
(special variable).
*elljac-b*
(special variable).
*elljac-c*
(special variable).
*elljac-c2*
(special variable).
*elljac-k*
(special variable).
*errorno-keyword*
(special variable).
*gsl-splice-fp-types*
(special variable).
*gsl-splice-int-types*
(special variable).
*gsl-symbol-equivalence*
(special variable).
*hilb12*
(special variable).
*hilb12-soln*
(special variable).
*hilb2*
(special variable).
*hilb2-soln*
(special variable).
*hilb3*
(special variable).
*hilb3-soln*
(special variable).
*hilb4*
(special variable).
*hilb4-soln*
(special variable).
*m35*
(special variable).
*m53*
(special variable).
*max-iter*
(special variable).
*mc-lower*
(special variable).
*mc-upper*
(special variable).
*monte-carlo-default-samples-per-dimension*
(special variable).
*nlls-example-data*
(special variable).
*ntuple-example-data-file*
(special variable).
*ntuple-example-scale*
(special variable).
*paraboloid-center*
(special variable).
*pdf-number-of-tries*
(special variable).
*pointer-offset*
(special variable).
*powell-a*
(special variable).
*rosenbrock-a*
(special variable).
*rosenbrock-b*
(special variable).
*s35*
(special variable).
*s53*
(special variable).
*signed-byte-pool*
(special variable).
*special-c-return*
(special variable).
*unsigned-byte-pool*
(special variable).
*vander12*
(special variable).
*vander12-soln*
(special variable).
*vander2*
(special variable).
*vander2-soln*
(special variable).
*vander3*
(special variable).
*vander3-soln*
(special variable).
*vander4*
(special variable).
*vander4-soln*
(special variable).
*wavelet-sample*
(special variable).
+continue+
(constant).
+ebadfunc+
(constant).
+ebadlen+
(constant).
+ebadtol+
(constant).
+ecache+
(constant).
+ediverge+
(constant).
+edom+
(constant).
+efactor+
(constant).
+efailed+
(constant).
+efault+
(constant).
+einval+
(constant).
+eloss+
(constant).
+emaxiter+
(constant).
+enomem+
(constant).
+enoprog+
(constant).
+enoprogj+
(constant).
+enotsqr+
(constant).
+eof+
(constant).
+eovrflw+
(constant).
+erange+
(constant).
+eround+
(constant).
+erunaway+
(constant).
+esanity+
(constant).
+esing+
(constant).
+etable+
(constant).
+etol+
(constant).
+etolf+
(constant).
+etolg+
(constant).
+etolx+
(constant).
+eundrflw+
(constant).
+eunimpl+
(constant).
+eunsup+
(constant).
+exp-x+
(constant).
+ezerodiv+
(constant).
+failure+
(constant).
+gamma-xmax+
(constant).
+gslt-bin-size+
(constant).
+gslt-bins+
(constant).
+gslt-lower-limit+
(constant).
+gslt-upper-limit+
(constant).
+initial-number-of-samples+
(constant).
+ln2+
(constant).
+success+
(constant).
+test-factor+
(constant).
+test-sigma+
(constant).
+test-sqrt-tol0+
(constant).
+test-tol0+
(constant).
+test-tol1+
(constant).
+test-tol2+
(constant).
+test-tol3+
(constant).
+test-tol4+
(constant).
+test-tol5+
(constant).
+test-tol6+
(constant).
acceleration-example
(function).
access-value-int
(function).
actual-array-c-type
(function).
actual-array-class
(function).
actual-class-arglist
(function).
actual-element-c-type
(function).
actual-gsl-function-name
(function).
after-llk
(function).
all-fft-test-forms
(macro).
all-io
(function).
alloc-from-block
(generic function).
allocate
(generic function).
arglist-plain-and-categories
(function).
array-default
(function).
array-element-refs
(function).
assert-neginf
(macro).
assert-posinf
(macro).
assert-sf-scale
(macro).
assert-to-tolerance
(macro).
backward-fourier-transform-dif-radix2
(generic function).
backward-fourier-transform-halfcomplex-nonradix2
(generic function).
backward-fourier-transform-halfcomplex-radix2
(generic function).
backward-fourier-transform-nonradix2
(generic function).
backward-fourier-transform-radix2
(generic function).
bin-samples
(function).
body-expand
(function).
body-no-optional-arg
(function).
body-optional-arg
(function).
bspline-example
(function).
callback-args
(function).
callback-included
(class).
callback-included-cl
(class).
callback-remove-arg
(function).
callback-replace-arg
(function).
callback-set-dynamic
(function).
callback-set-mvb
(function).
callback-set-slots
(function).
callback-struct
(generic reader).
callback-symbol-set
(function).
category-for-argument
(function).
cbd-dimensions
(function).
cbd-functions
(function).
cbinfo
(generic reader).
chebyshev-point-example
(function).
chebyshev-step
(function).
chebyshev-table-example
(function).
check-gsl-status
(function).
check-null-pointer
(function).
cl-argument-types
(function).
cl-convert-form
(function).
cl-gsl
(function).
cl-symbols
(function).
comb-copy
(function).
combination
(class).
complete-definition
(function).
complex-with-error
(function).
constant-matrix
(function).
copy-exponent-fit-data
(function).
copy-sa-state
(function).
copy-with-stride
(function).
create-complex-matrix
(function).
create-general-matrix
(function).
create-hilbert-matrix
(function).
create-matrix
(function).
create-moler-matrix
(function).
create-rhs-vector
(function).
create-row-matrix
(function).
create-singular-matrix
(function).
create-vandermonde-matrix
(function).
creturn-st
(function).
declaration-form
(function).
decode-ieee754
(function).
def-ci-subclass
(macro).
def-ci-subclass-1d
(macro).
def-rng-type
(macro).
default-covariance
(function).
default-lls-workspace
(function).
defcomparison
(macro).
defgeneric-method-p
(function).
define-gsl-condition
(macro).
defmcallback
(macro).
defmfun
(macro).
defmfun-return
(function).
defmobject
(macro).
defmpar
(macro).
delete-test-definition
(function).
deriv-f1-d
(function).
deriv-f2
(function).
deriv-f2-d
(function).
deriv-f3
(function).
deriv-f3-d
(function).
deriv-f4
(function).
deriv-f4-d
(function).
deriv-f5
(function).
deriv-f5-d
(function).
deriv-f6-d
(function).
dimension-names
(generic reader).
distribution-bin-integral
(function).
dpi
(constant).
eigenvalue-eigenvectors-example
(function).
element-type-select
(function).
eql-specializer
(function).
error-number
(generic reader).
error-text
(generic reader).
establish-handler
(function).
evaluate-integral-example
(function).
expand-defmfun-arrays
(function).
expand-defmfun-defmethods
(function).
expand-defmfun-generic
(function).
expand-defmfun-method
(function).
expand-defmfun-optional
(function).
expand-defmfun-wrap
(function).
explanation
(generic reader).
exponent-fit-data
(structure).
exponent-fit-data-n
(reader).
(setf exponent-fit-data-n)
(writer).
exponent-fit-data-p
(function).
exponent-fit-data-sigma
(reader).
(setf exponent-fit-data-sigma)
(writer).
exponent-fit-data-y
(reader).
(setf exponent-fit-data-y)
(writer).
exponential-residual
(function).
exponential-residual-derivative
(function).
exponential-residual-fdf
(function).
faify-form
(function).
fft-complex-off-stride-check
(function).
fft-complex-result-check
(macro).
fft-complex-wavetable-double-float
(class).
fft-complex-wavetable-single-float
(class).
fft-complex-workspace-double-float
(class).
fft-complex-workspace-single-float
(class).
fft-frequency-split
(function).
fft-frequency-step
(function).
fft-half-complex-radix2-unpack
(generic function).
fft-half-complex-unpack
(generic function).
fft-half-complex-wavetable-double-float
(class).
fft-half-complex-wavetable-single-float
(class).
fft-highest-frequency
(function).
fft-pulse-test
(function).
fft-real-result-check
(macro).
fft-real-unpack
(generic function).
fft-real-wavetable-double-float
(class).
fft-real-wavetable-single-float
(class).
fft-real-workspace-double-float
(class).
fft-real-workspace-single-float
(class).
fft-test-forms
(function).
foreign-pointer-method
(macro).
forward-backward
(function).
forward-fourier-transform-dif-radix2
(generic function).
forward-fourier-transform-halfcomplex-nonradix2
(generic function).
forward-fourier-transform-halfcomplex-radix2
(generic function).
forward-fourier-transform-nonradix2
(generic function).
forward-fourier-transform-radix2
(generic function).
fourier-transform-dif-radix2
(generic function).
fourier-transform-radix2
(generic function).
funcallables
(generic reader).
functions
(generic reader).
generate-all-array-tests
(macro).
generate-all-array-tests-body
(function).
generate-all-permutations
(function).
generate-all-permutations-backwards
(function).
generate-methods
(function).
generate-nlls-data
(function).
get-callbacks-for-class
(function).
get-mcm-parameters
(function).
get-mcv-parameters
(function).
gsl-config-pathname
(function).
gsl-name
(generic reader).
gsl-version
(generic reader).
have-at-least-gsl-version
(function).
histo-clone
(function).
histo-copy
(function).
histo2d-clone
(function).
histo2d-copy
(function).
histogram-c-tclass
(class).
ieee754-sign-bit
(function).
initialize-suffix-switched-foreign
(function).
integrate-vanderpol
(function).
integration-test-f1
(function).
integration-test-f11
(function).
integration-test-f15
(function).
integration-test-f16
(function).
integration-test-f3
(function).
integration-test-f454
(function).
integration-test-f455
(function).
integration-test-f456
(function).
integration-test-f457
(function).
integration-test-f458
(function).
integration-test-f459
(function).
integration-test-myfn1
(function).
integration-test-myfn2
(function).
inverse-fourier-transform-dif-radix2
(generic function).
inverse-fourier-transform-halfcomplex-nonradix2
(generic function).
inverse-fourier-transform-halfcomplex-radix2
(generic function).
inverse-fourier-transform-nonradix2
(generic function).
inverse-fourier-transform-radix2
(generic function).
levin-value
(function).
limits-check
(function).
line-number
(generic reader).
linear-least-squares-multivariate-example
(function).
linear-least-squares-univariate-example
(function).
linear-mfit-nosvd
(function).
linear-mfit-svd
(function).
lookup-condition
(function).
make-and-init-vector
(function).
make-cbstruct
(function).
make-cbstruct-object
(function).
make-compiled-funcallable
(function).
make-defmcallbacks
(function).
make-exponent-fit-data
(function).
make-fft-complex-wavetable-double-float
(function).
make-fft-complex-wavetable-single-float
(function).
make-fft-complex-workspace-double-float
(function).
make-fft-complex-workspace-single-float
(function).
make-fft-half-complex-wavetable-double-float
(function).
make-fft-half-complex-wavetable-single-float
(function).
make-fft-real-wavetable-double-float
(function).
make-fft-real-wavetable-single-float
(function).
make-fft-real-workspace-double-float
(function).
make-fft-real-workspace-single-float
(function).
make-foreign-array-from-mpointer
(function).
make-funcallable-form
(function).
make-funcallables-for-object
(function).
make-gsl-metadata
(function).
make-initialize-instance
(function).
make-list-from-pool
(function).
make-mobject-defmcallbacks
(function).
make-new-sa-state
(function).
make-ntuple-example-data
(function).
make-reinitialize-instance
(function).
make-sa-states
(function).
make-symbol-cardinal
(function).
make-symbol-cardinals
(function).
make-urand-vector
(function).
map-name
(function).
mappend
(function).
matrix-product-dimensions
(function).
mcrw
(function).
mean-2x
(function).
mean-2y
(function).
minimization-one-example
(function).
mobject
(class).
mobject-cbvname
(function).
mobject-cbvnames
(function).
mobject-fnvname
(function).
mobject-fnvnames
(function).
mobject-maker
(function).
mobject-variable-name
(function).
mpointer
(generic function).
multimin-example-derivative
(function).
multimin-example-derivative-scalars
(function).
multimin-example-no-derivative
(function).
multiroot-slot
(function).
mv-linear-least-squares-data
(function).
next-float
(function).
nonlinear-least-squares-example
(function).
norm-f
(function).
ntuple-data-tclass
(class).
ntuple-example-histogramming
(function).
ntuple-example-make-read
(function).
ntuple-example-read
(function).
ntuple-example-sel-func
(function).
ntuple-example-val-func
(function).
ntuple-example-values
(function).
number-of-callbacks
(function).
obsolete-gsl-version
(condition).
ode-control
(class).
optional-args-to-switch-gsl-functions
(function).
paraboloid-and-derivative
(function).
paraboloid-and-derivative-scalar
(function).
paraboloid-derivative
(function).
paraboloid-derivative-scalar
(function).
paraboloid-scalar
(function).
paraboloid-vector
(function).
parse-callback-argspec
(function).
parse-callback-fnspec
(function).
parse-callback-static
(function).
perm-copy
(function).
plural-symbol
(function).
pmnil
(macro).
powell
(function).
power-of-2-p
(function).
quadratic
(function).
quadratic-and-derivative
(function).
quadratic-derivative
(function).
quasi-clone
(function).
quasi-copy
(function).
random-walk-miser-example
(function).
random-walk-plain-example
(function).
random-walk-vegas-example
(function).
realpart-vector
(function).
record-callbacks-for-class
(function).
reference-foreign-element
(function).
reset-urand
(function).
rng-clone
(function).
rng-copy
(function).
rng-types-setup
(function).
roots-multi-example-derivative
(function).
roots-multi-example-no-derivative
(function).
roots-one-example-derivative
(function).
roots-one-example-no-derivative
(function).
rosenbrock
(function).
rosenbrock-df
(function).
rosenbrock-fdf
(function).
sa-state-value
(function).
save-test
(macro).
scalar-default
(function).
scalarsp
(generic reader).
set-cbstruct
(function).
set-maref
(macro).
set-mcm-parameters
(function).
set-mcv-parameters
(function).
set-parameters
(function).
set-parameters-gen
(function).
set-parameters-nonsymmetric
(function).
set-slot-function
(function).
set-structure-slot
(function).
sf-check-results
(function).
sf-check-single
(function).
sf-frac-diff
(function).
sigma-2x
(function).
sigma-2y
(function).
signal-gsl-error
(function).
signal-gsl-warning
(function).
simulated-annealing-example
(function).
simulated-annealing-int
(function).
simulated-annealing-parameters-tclass
(class).
simulated-annealing-test
(function).
singular-symbol
(function).
singularize
(function).
size-array
(function).
size-vector-scalar
(function).
solve-tridiagonal-example
(function).
source-file
(generic reader).
spline-example
(function).
state-pointer
(function).
stupid-code-walk-eval-some
(function).
stupid-code-walk-find-variables
(function).
success-continue
(function).
success-failure
(function).
symbol-keyword-symbol
(function).
test-cholesky-decomp-dim
(function).
test-cholesky-invert-dim
(function).
test-cholesky-solve-dim
(function).
test-complex-fft-noise
(function).
test-fft-noise
(function).
test-hh-solve-dim
(function).
test-lu-solve-dim
(function).
test-qr-decomp-dim
(function).
test-qr-lssolve-dim
(function).
test-qr-qrsolve-dim
(function).
test-qr-solve-dim
(function).
test-qr-update-dim
(function).
test-qrpt-decomp-dim
(function).
test-qrpt-qrsolve-dim
(function).
test-qrpt-solve-dim
(function).
test-real-fft-noise
(function).
test-sv-solve-dim
(function).
testpdf
(function).
trivial-example-energy
(function).
trivial-example-metric
(function).
trivial-example-step
(function).
trivial-test-energy
(function).
unspecified-errno
(condition).
urand
(function).
value-from-dimensions
(function).
values-unless-singleton
(function).
values-with-errors
(function).
vanderpol
(function).
vanderpol-jacobian
(function).
variables-used-in-c-arguments
(function).
vdf
(function).
vdf-size
(function).
vector/length
(function).
view-bin-as-foreign-array
(function).
view-range-as-foreign-array
(function).
vspecs-direction
(function).
wavelet-example
(function).
wavelet-forward-example
(function).
wfo-declare
(function).
with-defmfun-key-args
(macro).
wrap-index-export
(function).
wrap-letlike
(function).
wrap-progn
(function).
Definitions are sorted by export status, category, package, and then by lexicographic order.
The default absolute error used in numerical integration.
gsll
.
The default relative error used in numerical integration.
gsll
.
Get or set (setf maref) the array element from the GSL mpointer. The class-name is the specific subclass name of grid:foreign-array.
gsll
.
Return the value(s) (a value or list of values) in case the specified GSL error is signalled in the body.
gsll
.
Create an environment where all FFTs will be performed on vectors of the
same type and with the same length. This allows to calculculate and reuse the
wavetable and workspace only once.
The first and second arguments will be bound to the wavetable and workspace, the third argument is the element type of the vectors to be FFT’d and the fourth argument indicates the length of the vectors to which FFTs will be applied. Optionally, T can be given as a fifth argument if the element type of the vectors is real, but must be considered as half-complex.
gsll
.
Environment for integration of ordinary differential equations when dependent variables are individually named scalars.
gsll
.
The reciprocal of the gamma function, 1/Gamma(x) using the real Lanczos method.
gsll
.
From the terms of a series in array, compute the extrapolated
limit of the series using a Levin u-transform. Additional
working space must be provided in levin. The extrapolated sum is
returned with an estimate of the absolute error. The actual
term-by-term sum is returned in
w->sum_plain. The algorithm calculates the truncation error
(the difference between two successive extrapolations) and round-off
error (propagated from the individual terms) to choose an optimal
number of terms for the extrapolation.
gsll
.
From the terms of a series in array, compute the extrapolated
limit of the series using a Levin u-transform. Additional
working space must be provided in levin. The extrapolated sum is
returned with an estimate of the absolute error. The actual
term-by-term sum is returned in w->sum_plain. The algorithm
terminates when the difference between two successive extrapolations
reaches a minimum or is sufficiently small. The difference between
these two values is used as estimate of the error and is stored in
abserr_trunc. To improve the reliability of the algorithm the
extrapolated values are replaced by moving averages when calculating
the truncation error, smoothing out any fluctuations.
gsll
.
Search the data array x-array of size, using the given acceleration.
This is how lookups are performed during evaluation of an interpolation. The
function returns an index i such that x_array[i] <= x < x_array[i+1]}.
gsll
.
Adjust the step-size using the control function
and the current values of current-y, y-error and dydt.
The stepping function stepper is also needed to determine the order
of the method. If the error in the y-values y-error is found to be
too large then the step-size is reduced and the function returns
:step-size-decreased. If the error is sufficiently small then
step-size may be increased and :step-size-increased is returned. The
function returns :step-size-unchanged if the step-size is
unchanged. The goal of the function is to estimate the largest
step-size which satisfies the user-specified accuracy requirements for
the current point.
gsll
.
The Airy function derivative Ai’(x).
The scaled Airy function derivative S_A(x) Ai’(x).
For x>0 the scaling factor S_A(x) is exp(+(2/3) x^(3/2)),
and is 1 for x<0.
The scaled Airy function S_A(x) Ai(x).
For x>0 the scaling factor S_A(x) is exp(+(2/3) x^(3/2)),
and is 1 for x<0.
The Airy function derivative Bi’(x).
The scaled Airy function derivative S_B(x) Bi’(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0.
The scaled Airy function S_B(x) Bi(x).
For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)),
and is 1 for x<0.
The location of the s-th zero of the Airy function Ai(x).
The location of the s-th zero of the Airy function derivative Ai’(x).
The location of the s-th zero of the Airy function Bi(x).
The location of the s-th zero of the Airy function derivative Bi’(x).
A list of all random number generator types.
gsll
.
Advance the system (e, dydt) from time
and position y using the stepping function step.
The new time and position are stored in time and y on output.
The initial step-size supplied, but this will be modified
using the control function to achieve the appropriate error
bound if necessary. The routine may make several calls to step in
order to determine the optimum step-size. If the step-size has been
changed the value of step-size will be modified on output. The maximum
time max-time is guaranteed not to be exceeded by the time-step. On the
final time-step the value of time will be set to t1 exactly.
gsll
.
Apply the transform to the array array-in
whose size is equal to the size of the transform. The result is stored
in the array array-out which must be of the same length.
gsll
.
Apply the stepping function stepper to the system of equations
defined by make-ode-stepper, using the step size step-size to
advance the system from time time and state y to time t +
step-size. The new state of the system is stored in y on output,
with an estimate of the absolute error in each component stored in
yerr If the argument dydt-in is not null it should point an array
containing the derivatives for the system at time t on input. This
is optional as the derivatives will be computed internally if they
are not provided, but allows the reuse of existing derivative
information. On output the new derivatives of the system at time
t + step-size will be stored in dydt-out if it is not null.
User-supplied functions defined in the system dydt
should signal an error or return the correct value.
gsll
.
The Arctangent integral, which is defined as AtanInt(x) = int_0^x dt arctan(t)/t.
gsll
.
Compute the numerical derivative of the function at the point x using an adaptive backward difference algorithm with a step-size of step. The function is evaluated only at points less than x, and never at x itself. The derivative is returned in result and an estimate of its absolute error is returned as the second value. This function should be used if f(x) has a discontinuity at x, or is undefined for values greater than x. This function is equivalent to calling #’forward-derivative with a negative step-size.
gsll
.
Perform a backward fast Fourier transform on the given vector. If the length of the vector is not a power of 2, and the user has a suitable wavetable and/or workspace, these can be supplied as keyword arguments. If the vector is real, it is assumed to be in half-complex form. If the length of the vector is a power of 2, use of a non-radix-2 transform can be forced.
gsll
.
The probability p(k) of obtaining
k from a Bernoulli distribution with probability parameter
p, using the formula given in #’sample :bernoulli.
gsll
.
The logarithm of the irregular modified Bessel function of fractional order nu, ln(K_nu(x)) for x>0, nu>0.
gsll
.
The location of the s-th positive zero of the Bessel function J_0(x).
gsll
.
The location of the s-th positive zero of the Bessel function J_1(x).
gsll
.
These routines compute the location of the s-th positive zero of the Bessel function J_nu(x). The current implementation does not support negative values of nu.
gsll
.
The Beta Function, B(a,b) = Gamma(a)Gamma(b)/Gamma(a+b)} for a > 0, b > 0.
gsll
.
The cumulative distribution functions
P(x) for the beta distribution with parameters a and b.
The probability density p(x) at x
for a beta distribution with parameters a and b, using the
formula given in #’sample :beta.
The inverse cumulative distribution functions
P(x) for the beta distribution with parameters a and b.
The cumulative distribution functions
Q(x) for the beta distribution with parameters a and b.
The inverse cumulative distribution functions
Q(x) for the beta distribution with parameters a and b.
Factorize the M-by-N matrix A into
bidiagonal form U B V^T. The diagonal and superdiagonal of the
matrix B are stored in the diagonal and superdiagonal of A,
The orthogonal matrices U and V are stored as compressed
Householder vectors in the remaining elements of A. The
Householder coefficients are stored in the vectors tau-U and
tau-V. The length of tau-U must equal the number of
elements in the diagonal of A and the length of tau-V should
be one element shorter.
gsll
.
Unpack the bidiagonal decomposition of A given by
#’bidiagonal-decomposition (A, tau-U, tau-V)
into the separate orthogonal matrices U, V, and the diagonal
vector diag and superdiagonal superdiag. Note that U
is stored as a compact M-by-N orthogonal matrix satisfying
U^T U = I for efficiency.
gsll
.
Unpack the diagonal and superdiagonal of the bidiagonal decomposition of A given by #’bidiagonal-decomposition, into the diagonal vector diag and superdiagonal vector superdiag.
gsll
.
Unpack the bidiagonal decomposition of A given by
#’bidiagonal-decomposition (A, tau-U, tau-V)
into the separate orthogonal matrices U, V and the diagonal
vector diag and superdiagonal superdiag. The matrix U
is stored in-place in A.
gsll
.
A random integer from the binomial distribution,
the number of successes in n independent trials with probability
p. The probability distribution for binomial variates is,
p(k) = {n! over k! (n-k)!} p^k (1-p)^{n-k}
0 <= k <= n.
gsll
.
The cumulative distribution functions
P(k) for the Binomial distribution with parameters p and n.
gsll
.
The probability p(k) of obtaining k
from a binomial distribution with parameters p and n, using
the formula given in #’binomial.
gsll
.
The cumulative distribution functions Q(k) for the Binomial distribution with parameters p and n.
gsll
.
The probability density p(x,y) at
(x,y) for a bivariate Gaussian distribution with standard
deviations sigma_x, sigma_y and correlation coefficient
rho, using the formula given for #’sample :bivariate-gaussian.
gsll
.
The ith breakpoint of the basis spline bspline.
gsll
.
Count the number of cycles in the permutation q, given in canonical form.
gsll
.
Convert a permutation q in canonical form back into linear form storing it in the output argument p.
gsll
.
The cumulative distribution functions
P(x) for the Cauchy distribution with scale parameter a.
gsll
.
The probability density p(x) at x
for a Cauchy distribution with scale parameter a, using the formula
given for #’sample :cauchy.
gsll
.
The inverse cumulative distribution functions
P(x) for the Cauchy distribution with scale parameter a.
gsll
.
The cumulative distribution functions
Q(x) for the Cauchy distribution with scale parameter a.
gsll
.
The inverse cumulative distribution functions
Q(x) for the Cauchy distribution with scale parameter a.
gsll
.
Compute the numerical derivative of the function
at the point x using an adaptive central difference algorithm with
a step-size of step. The derivative and an
estimate of its absolute error is returned.
The initial value of step is used to estimate an optimal step-size,
based on the scaling of the truncation error and round-off error in the
derivative calculation. The derivative is computed using a 5-point rule
for equally spaced abscissae at x-step, x-step/2, x,
x+step/2, x, with an error estimate taken from the difference
between the 5-point rule and the corresponding 3-point rule x-step,
x, x+step. Note that the value of the function at x
does not contribute to the derivative calculation, so only 4-points are
actually used.
gsll
.
The integral
Chi(x) := Re[ gamma_E + log(x) + int_0^x dt (cosh[t]-1)/t],
where gamma_E} is the Euler constant.
gsll
.
The cumulative distribution functions
P(x) for the chi-squared distribution with nu degrees of freedom.
gsll
.
The probability density p(x) at x
for a chi-squared distribution with nu degrees of freedom, using
the formula given in #’sample :chi-squared.
gsll
.
The inverse cumulative distribution functions
P(x) for the chi-squared distribution with nu degrees of freedom.
gsll
.
The cumulative distribution functions
Q(x) for the chi-squared distribution with nu degrees of freedom.
gsll
.
The inverse cumulative distribution functions
Q(x) for the chi-squared distribution with nu degrees of freedom.
gsll
.
Compute the inverse of the matrix cholesky which must have been previously computed by #’cholesky-decomposition. The inverse of the original matrix is stored in cholesky on output.
gsll
.
The combinatorial factor (n choose m) = n!/(m!(n-m)!).
gsll
.
The Cosine integral Ci(x) = -int_x^infty dt cos(t)/t for x > 0.
gsll
.
Closes the ntuple file and frees its associated allocated memory.
gsll
.
The Chebyshev coefficient array as a CL array (foreign-friendly).
gsll
.
Advance the combination c to the next combination in lexicographic order and return c. If no further combinations are available it returns NIL. Starting with the first combination and repeatedly applying this function will iterate through all possible combinations of a given order.
gsll
.
Step backwards from the combination c to the previous combination in lexicographic order, returning c. If no previous combination is available it returns NIL with c unmodified.
gsll
.
The range (n), or maximum possible value (n in the (n k) notation) of the combination c.
gsll
.
The complementary normalized incomplete Gamma Function
P(a,x) = 1/Gamma(a) int_0^x dt t^{a-1} exp(-t)}
for a > 0, x >= 0. Note that Abramowitz & Stegun
call P(a,x) the incomplete gamma function (section 6.5).
gsll
.
Return a pointer to a newly allocated instance of a
control function of type control-type. This function is only needed for
defining new types of control functions. For most purposes the standard
control functions described above should be sufficient.
gsll
.
The cosine of an angle x with an associated absolute error dx, cos(x pm dx).
gsll
.
The Coulomb wave function normalization constant C_L(eta) for L > -1.
gsll
.
The Coulomb wave function normalization constant C_L(eta) for L = Lmin ... Lmin + kmax, Lmin > -1.
gsll
.
The Coulomb wave function F_L(eta,x) for
L = Lmin ... Lmin + kmax, storing the results in fc-array.
In the case of overflow the exponent is stored in the second value returned.
gsll
.
The Coulomb wave functions F_L(eta,x),
G_{L-k}(eta,x) and their derivatives F’_L(eta,x), G’_{L-k}(eta,x)
with respect to x. The parameters are restricted to L, L-k > -1/2},
x > 0 and integer k. Note that L itself is not restricted to being
an integer. The results are stored in the parameters F, G for the
function values and Fp, Gp for the derivative values. If an
overflow occurs, the condition ’overflow is signalled and scaling
exponents are stored in the modifiable parameters exp-F, exp-G.
gsll
.
The functions F_L(eta,x),
G_L(eta,x) for L = Lmin ... Lmin + kmax storing the
results in fc_array and gc_array. In the case of overflow the
exponents are stored in F_exponent and G_exponent.
gsll
.
The functions F_L(eta,x),
G_L(eta,x) and their derivatives F’_L(eta,x),
G’_L(eta,x) for L = Lmin ... Lmin + kmax storing the
results in fc_array, gc_array, fcp_array and gcp_array.
In the case of overflow the exponents are stored in F_exponent
and G_exponent.
gsll
.
The Coulomb wave function divided by the argument
F_L(eta, x)/x for L = Lmin ... Lmin + kmax, storing the
results in fc_array. In the case of overflow the exponent is
stored in F_exponent. This function reduces to spherical Bessel
functions in the limit eta to 0.
gsll
.
The Wigner 3-j coefficient,
pmatrix{ja & jb & jccr
ma & mb & mccr}
where the arguments are given in half-integer units,
ja = two_ja/2, ma = two_ma/2, etc.
gsll
.
The Wigner 6-j coefficient,
ja & jb & jc
jd & je & jf
where the arguments are given in half-integer units, ja =
two_ja/2, ma = two_ma/2, etc.
gsll
.
The Wigner 9-j coefficient,
ja & jb & jc
jd & je & jf
jg & jh & ji
where the arguments are given in half-integer units,
ja = two_ja/2, ma = two_ma/2, etc.
gsll
.
Create a new write-only ntuple file filename for
ntuples of size and return a pointer to the newly created
ntuple struct. Any existing file with the same name is truncated to
zero length and overwritten. A pointer to memory for the current ntuple
row data must be supplied—this is used to copy ntuples
in and out of the file.
gsll
.
The regular modified cylindrical Bessel function of zeroth order, I_0(x).
gsll
.
The scaled regular modified cylindrical Bessel function of zeroth order, exp(-|x|) I_0(x).
gsll
.
The regular modified cylindrical Bessel function of first order, I_1(x).
gsll
.
The scaled regular modified cylindrical Bessel function of first order, exp(-|x|) I_1(x).
gsll
.
The values of the regular modified cylindrical Bessel functions
I_n(x) for n from from nmin to nmin+length(array)-1 inclusive.
The values are computed using recurrence relations for efficiency, and
therefore may differ slightly from the exact values.
gsll
.
The values of the scaled regular modified cylindrical Bessel
functions I_n(x) for n from from nmin to nmin+length(array)-1
inclusive. The values are computed using recurrence
relations for efficiency, and therefore may differ slightly from the
exact values.
gsll
.
The values of the regular cylindrical Bessel functions J_n(x)
for n from nmin to nmin+length(array)-1 inclusive.
The values are computed using recurrence relations for efficiency,
and therefore may differ slightly from the exact values.
gsll
.
The regular cylindrical Bessel function of
fractional order nu, J_nu(x), evaluated at a series of
x values. The array v contains the x values.
They are assumed to be strictly ordered and positive.
The array is over-written with the values of J_nu(x_i).
gsll
.
The regular cylindrical Bessel function of zeroth order, J_0(x).
gsll
.
The regular cylindrical Bessel function of first order, J_1(x).
gsll
.
The irregular modified cylindrical Bessel function of zeroth order, K_0(x).
gsll
.
The scaled irregular modified cylindrical Bessel function of zeroth order, exp(-|x|) K_0(x).
gsll
.
The irregular modified cylindrical Bessel function of first order, K_1(x).
gsll
.
The scaled irregular modified cylindrical Bessel function of first order, exp(-|x|) K_1(x).
gsll
.
The values of the irregular modified cylindrical Bessel functions
K_n(x) for n from from nmin to nmin+length(array)-1 inclusive.
The values are computed using recurrence relations for efficiency, and
therefore may differ slightly from the exact values.
gsll
.
The values of the scaled irregular cylindrical
Bessel functions exp(x) K_n(x) for n from from nmin to
nmin+length(array)-1 inclusive.
The start of the range nmin must be positive
or zero. The domain of the function is x>0. The values are
computed using recurrence relations for efficiency, and therefore
may differ slightly from the exact values.
gsll
.
The irregular cylindrical Bessel function of zeroth order, Y_0(x).
gsll
.
The irregular cylindrical Bessel function of first order, Y_1(x).
gsll
.
The values of the irregular cylindrical Bessel functions
Y_n(x) for n from from nmin to
nmin+length(array)-1 inclusive. The values are computed using
recurrence relations for efficiency, and therefore may differ slightly
from the exact values.
gsll
.
The first-order Debye function D_1(x) = (1/x) int_0^x dt (t/(e^t - 1)).
gsll
.
The second-order Debye function
D_2(x) = (2/x^2) int_0^x dt (t^2/(e^t - 1)).
gsll
.
The third-order Debye function
D_3(x) = (3/x^3) int_0^x dt (t^3/(e^t - 1)).
gsll
.
The fourth-order Debye function
D_4(x) = (4/x^4) int_0^x dt (t^4/(e^t - 1)).
gsll
.
Compute the derivative of the Chebyshev series, storing
the derivative coefficients in the previously allocated series.
The two series must have been allocated with the same order.
gsll
.
The logarithm of the probability density
p(theta_1, ... , theta_K)
for a Dirichlet distribution with parameters
alpha[K].
gsll
.
The probability density p(theta_1, ... , theta_K)
at theta[K] for a Dirichlet distribution with parameters
alpha[K], using the formula given for #’sample :dirichlet.
gsll
.
The probability P[k] of observing the variable k.
Since P[k] is not stored as part of the lookup table, it must be
recomputed; this computation takes O(K), so if K is large
and you care about the original array P[k] used to create the
lookup table, then you should just keep this original array P[k]
around.
gsll
.
Compute a divided-difference representation of the interpolating polynomial for the points (xa, ya) stored in the arrays of equal length. On output the divided-differences of (xa,ya) are stored in the array dd, of the same length.
gsll
.
This function determines whether x and y are approximately equal
to a relative accuracy epsilon.
The relative accuracy is measured using an interval of size 2
delta, where delta = 2^k epsilon and k is the maximum
base-2 exponent of x and y as computed by the function
frexp().
If x and y lie within this interval, they are considered approximately equal and the function returns nil. Otherwise if x < y, the function returns -1, or if x > y, the function returns +1.
gsll
.
Compute eigenvalues and right eigenvectors of the n-by-n real
generalized nonsymmetric matrix pair (A, B). The eigenvalues are
stored in (alpha, beta) and the eigenvectors are stored in evec. It
first calls eigenvalues-gen to compute the eigenvalues, Schur forms,
and Schur vectors. Then it finds eigenvectors of the Schur forms and
backtransforms them using the Schur vectors. The Schur vectors are
destroyed in the process, but can be saved by using setting
shur-vectors true. The computed eigenvectors are normalized to have
unit magnitude. On output, (A, B) contains the generalized Schur
form (S, T).
If compute-shur-form-s is true, the full Schur form S will be computed. If it is NIL, S will not be computed (this is the default setting). S is a quasi upper triangular matrix with 1-by-1 and 2-by-2 blocks on its diagonal. 1-by-1 blocks correspond to real eigenvalues, and 2-by-2 blocks correspond to complex eigenvalues.
If compute-shur-form-t true, the full Schur form T will be
computed. If it is NIL, T will not be
computed (this is the default setting). T is an upper triangular
matrix with non-negative elements on its diagonal. Any 2-by-2
blocks in S will correspond to a 2-by-2 diagonal block in T.
gsll
.
Compute eigenvalues and right eigenvectors of the n-by-n real nonsymmetric matrix A. It first calls #’eigenvalues-nonsymm to compute the eigenvalues, Schur form T, and Schur vectors. Then it finds eigenvectors of T and backtransforms them using the Schur vectors. The Schur vectors are destroyed in the process, but can be saved by specifying binding shur-vectors to a vector of length n, or t to have it automatically made. The computed eigenvectors are normalized to have unit magnitude. On output, the upper portion of A contains the Schur form T. If #’eigenvalues-nonsymm fails, no eigenvectors are computed, and an error code is returned.
gsll
.
Compute the eigenvalues of the real generalized nonsymmetric matrix
pair (A, B), and store them as pairs in (alpha, beta), where alpha
is complex and beta is real. If beta_i is non-zero, then lambda =
alpha_i / beta_i is an eigenvalue. Likewise, if alpha_i is
non-zero, then mu = beta_i / alpha_i is an eigenvalue of the
alternate problem mu A y = B y. The elements of beta are
normalized to be non-negative.
If S is desired, it is stored in A on output. If T is desired, it
is stored in B on output. The ordering of eigenvalues in (alpha,
beta) follows the ordering of the diagonal blocks in the Schur
forms S and T. In rare cases, this function may fail to find all
eigenvalues. If this occurs, an error code is returned.
If compute-shur-form-s is true, the full Schur form S will be computed. If it is NIL, S will not be computed (this is the default setting). S is a quasi upper triangular matrix with 1-by-1 and 2-by-2 blocks on its diagonal. 1-by-1 blocks correspond to real eigenvalues, and 2-by-2 blocks correspond to complex eigenvalues.
If compute-shur-form-t true, the full Schur form T will be
computed. If it is NIL, T will not be
computed (this is the default setting). T is an upper triangular
matrix with non-negative elements on its diagonal. Any 2-by-2
blocks in S will correspond to a 2-by-2 diagonal block in T.
gsll
.
Compute the eigenvalues of the real nonsymmetric matrix A and
stores them in the vector ’eigenvalues. If T is desired, it is
stored in the upper portion of A on output. Otherwise, on output,
the diagonal of A will contain the 1-by-1 real eigenvalues and
2-by-2 complex conjugate eigenvalue systems, and the rest of A is
destroyed. In rare cases, this function may fail to find all
eigenvalues. If this happens, a warning is signalled and the number
of converged eigenvalues is returned as a second value. The
converged eigenvalues are stored in the beginning of eval.
If compute-shur-form is true, the full Schur form T will be computed.
If it is set to nil, T will not be computed (this is
the default setting). Computing the full Schur form requires
approximately 1.5-2 times the number of flops.
If balance is true, a balancing transformation is applied to the
matrix prior to computing eigenvalues. This transformation is
designed to make the rows and columns of the matrix have comparable
norms, and can result in more accurate eigenvalues for matrices
whose entries vary widely in magnitude. See Balancing for more
information. Note that the balancing transformation does not
preserve the orthogonality of the Schur vectors, so if you wish to
compute the Schur vectors with you will obtain the Schur vectors of
the balanced matrix instead of the original matrix. The relationship
will be
T = Q^t D^(-1) A D Q
where Q is the matrix of Schur vectors for the balanced matrix, and D
is the balancing transformation. Then this function will compute
a matrix Z which satisfies
T = Z^(-1) A Z
with Z = D Q. Note that Z will not be orthogonal. For this reason, balancing is not performed by default.
gsll
.
The incomplete elliptic integral D(phi,k) which is defined through the Carlson form RD(x,y,z) by the relation D(phi,k) = 1/3 (sin phi)^3 RD (1-sin^2(phi), 1-k^2 sin^2(phi), 1).
gsll
.
The incomplete elliptic integral of the second kind, E(phi,k). Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
gsll
.
The complete elliptic integral of the second kind, E(k).
Note that Abramowitz & Stegun define this function in terms of the
parameter m = k^2.
gsll
.
The incomplete elliptic integral of the first kind, F(phi,k). Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
gsll
.
The complete elliptic integral of the first kind, K(k). Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
gsll
.
The incomplete elliptic integral of the third kind, P(phi,k,n). Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and sin^2(alpha) = k^2, with the change of sign n to -n.
gsll
.
The incomplete elliptic integral RC(x,y).
gsll
.
The incomplete elliptic integral RD(x,y,z).
gsll
.
The incomplete elliptic integral RF(x,y,z).
gsll
.
The incomplete elliptic integral RJ(x,y,z,p).
gsll
.
The error function erf(x), where
erf(x) = (2/sqrt(pi)) int_0^x dt exp(-t^2).
gsll
.
The upper tail of the Gaussian probability function Q(x) = (1/sqrt{2pi}) int_x^infty dt exp(-t^2/2)}.
gsll
.
The Gaussian probability density function Z(x) = (1/sqrt{2pi}) exp(-x^2/2)}.
gsll
.
The complementary error function
erfc(x) = 1 - erf(x) = (2/sqrt(pi)) int_x^infty exp(-t^2).
gsll
.
Evaluate the Chebyshev series at a point x, returning result and an estimate of its absolute error. If order is supplied, evaluate to at most the given order.
gsll
.
Evaluates a polynomial and its derivatives and stores the results in the array @var{res} of size @var{lenres}. The output array contains the values of @math{d^k P/d x^k} for the specified value of @var{x} starting with @math{k = 0}. The optional argument ’derivatives may be either a vector-double-float, or a non-negative integer. If the former, the function value and derivatives are put in the vector supplied; if the latter, a new vector-double-float is created with the specified length.
gsll
.
If no argument is supplied, list the names of the example categories. If a category name is given as the argument, give the list of examples in that category.
gsll
.
exp(x)-1, computed in a way that is accurate for small x.
gsll
.
Exponentiate x with an associated absolute error dx.
gsll
.
Exponentiate x with an associated absolute error dx and with extended numeric range.
gsll
.
Exponentiate x and multiply by the factor y to return the product y exp(x).
gsll
.
The product y exp(x) for the quantities x, y with associated absolute errors dx, dy.
gsll
.
The product y exp(x) for the quantities x, y with associated absolute errors dx, dy and with extended numeric range.
gsll
.
The product y exp(x) with extended numeric range.
gsll
.
The exponential function scaled. This function may be useful if the value of exp(x) would overflow the numeric range of double.
gsll
.
exp(x)-1 using an algorithm that is accurate for small x.
gsll
.
The third-order exponential integral Ei_3(x) = int_0^xdt exp(-t^3) for x >= 0.
gsll
.
The exponential integral
E_1(x)}, E_1(x) := Re int_1^infty dt exp(-xt)/t..
gsll
.
The second-order exponential integral
E_2(x)}, E_2(x) := Re int_1^infty dt exp(-xt)/t^2.
gsll
.
The exponential integral Ei(x),
Ei(x) := - PVleft(int_{-x}^infty dt exp(-t)/tright).
gsll
.
The exponential integral E_n(x) of order n, E_n(x) := Re int_1^infty dt exp(-xt)/t^n.
gsll
.
The cumulative distribution function
P(x) for the exponential distribution with mean mu.
gsll
.
The probability density p(x) at x
for an exponential distribution with mean mu, using the formula
given for #’sample :exponential.
gsll
.
The inverse cumulative distribution function
P(x) for the exponential distribution with mean mu.
gsll
.
The cumulative distribution function
P(x), for the exponential power distribution with
parameters a and b.
gsll
.
The probability density p(x) at x
for an exponential power distribution with scale parameter a
and exponent b, using the formula given for #’sample :exponential-power.
gsll
.
The cumulative distribution functions Q(x) for the exponential power distribution with parameters a and b.
gsll
.
The cumulative distribution function
Q(x) for the exponential distribution with mean mu.
gsll
.
The inverse cumulative distribution function
Q(x) for the exponential distribution with mean mu.
gsll
.
(exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + ...
gsll
.
2(exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + ...
gsll
.
N-relative exponential, which is the n-th generalization of the functions #’exprel and #’exprel-2.
gsll
.
The factorial n!, related to the Gamma function by n! = Gamma(n+1).
gsll
.
The cumulative distribution functions P(x) for the fdist distribution with nu1 and nu2 degrees of freedom.
gsll
.
The probability density p(x) at x
for an F-distribution with nu1 and nu2 degrees of freedom,
using the formula given #’sample :fdist.
gsll
.
The inverse cumulative distribution functions P(x) for the fdist distribution with nu1 and nu2 degrees of freedom.
gsll
.
The cumulative distribution functions Q(x) for the fdist distribution with nu1 and nu2 degrees of freedom.
gsll
.
The inverse cumulative distribution functions Q(x) for the fdist distribution with nu1 and nu2 degrees of freedom.
gsll
.
The complete Fermi-Dirac integral with an index of 0. This integral is given by F_0(x) = ln(1 + e^x).
gsll
.
The complete Fermi-Dirac integral with an index of 1, F_1(x) = int_0^infty dt (t /(exp(t-x)+1)).
gsll
.
The complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) int_0^infty dt (t^2 /(exp(t-x)+1)).
gsll
.
The incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = ln(1 + e^{b-x}) - (b-x).
gsll
.
The complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/Gamma(j+1)) int_0^infty dt (t^j /(exp(t-x)+1)).
gsll
.
The complete Fermi-Dirac integral with an index of -1. This integral is given by F_{-1}(x) = e^x / (1 + e^x).
gsll
.
The complete Fermi-Dirac integral F_{-1/2}(x).
gsll
.
Make and return a vector that contains the sample frequencies of an FFT
that has been applied to a vector with the given size and :sample-spacing.
If :shifted is T, then the vector will contain the sample frequencies after
FFT-SHIFT has been applied to the result of an FFT.
gsll
.
Return a copy of a vector where the zero and positive frequency components are shifted to the beginning, i.e. ordered so that it is suitable for an inverse FFT.
gsll
.
Return a copy of a vector that is the result of an FFT, with the zero and positive frequencies shifted to the center and end, so that the data is suitable for e.g. plotting.
gsll
.
Compute the gradient of Phi(x) = (1/2) ||F(x)||^2 from the Jacobian matrix and the function values using the formula g = J^T f.
gsll
.
Test for the convergence of the sequence by comparing the
last step with the absolute error and relative
error to the current position. The test returns T
if |last-step_i| < absolute-error + relative-error |current-position_i|
for each component i of current-position and returns NIL otherwise.
gsll
.
Test the residual gradient against the absolute
error bound. Mathematically, the gradient should be
exactly zero at the minimum. The test returns T if the
following condition is achieved: sum_i |gradient_i| < absolute-error
and returns NIL otherwise. This criterion is suitable
for situations where the precise location of the minimum
is unimportant provided a value can be found where the gradient is small
enough.
gsll
.
The cumulative distribution functions
P(x) for a uniform distribution from a to b.
The probability density p(x) at x
for a uniform distribution from a to b, using the formula
given for #’sample :flat.
The inverse cumulative distribution functions P(x) for a uniform distribution from a to b.
The cumulative distribution functions
Q(x) for a uniform distribution from a to b.
The inverse cumulative distribution functions Q(x) for a uniform distribution from a to b.
The sequence integer corresponding to the float
which satisfies three properties:
1) For two floats (< a b), then
(< (float-as-integer a) (float-as-integer b)).
2) If two floats (< a b) are adjacent, then
(= (1+ (float-as-integer a)) (float-as-integer b)).
3) (zerop (float-as-integer 0.0))
The absolute value of the integer is the integer of the
IEEE754 representation without the sign bit, and the
sign of the integer agrees with the sign of the float.
To get the IEEE754 integer, specify ’single-float or
’double-float to ieee754.
gsll
.
The value of the function at the current estimate of the lower bound for the minimizer.
gsll
.
The value of the function at the current estimate of the upper bound for the minimizer.
gsll
.
The current lower bound of the interval for the minimizer.
gsll
.
The current upper bound of the interval for the minimizer.
gsll
.
Format as binary each of the three pieces that make the IEEE 754 floating point representation for a float.
gsll
.
Compute the numerical derivative of the function
at the point x using an adaptive forward difference algorithm with
a step-size of step. The function is evaluated only at points greater
than x and never at x itself. The derivative is returned in
result and an estimate of its absolute error is returned as the
second value. This function should be used if f(x) has a
discontinuity at x, or is undefined for values less than x.
The initial value of step is used to estimate an optimal step-size,
based on the scaling of the truncation error and round-off error in
the derivative calculation. The derivative at x is computed
using an “open” 4-point rule for equally spaced abscissae at
x+step/4, x+step/2, x+3step/4, x+step,
with an error estimate taken from the difference between the 4-point
rule and the corresponding 2-point rule x+step/2,
x+step.
gsll
.
Perform a forward fast Fourier transform on the given vector. If the length of the vector is not a power of 2, and the user has a suitable wavetable and/or workspace, these can be supplied as keyword arguments. If the (real) vector is in half-complex form, then the key argument :half-complex should be non-NIL. If the length of the vector is a power of 2, use of a non-radix-2 transform can be forced.
gsll
.
Perform a fast Fourier transform on the given vector in the selected direction. The direction argument is one of :backward or :forward.
gsll
.
The lower end of the current bracketing interval for the solver.
gsll
.
The upper end of the current bracketing interval for the solver.
gsll
.
The Gamma function Gamma(x), subject to x
not being a negative integer. The function is computed using the real
Lanczos method. The maximum value of x such that
Gamma(x) is not considered an overflow is given by +gamma-xmax+.
gsll
.
The regulated Gamma Function Gamma^*(x)
for x > 0, given by
Gamma^*(x) = Gamma(x)/(sqrt{2pi} x^{(x-1/2)} exp(-x))
= (1 + {1 over 12x} + ...)
for x to infinity.
gsll
.
The cumulative distribution functions
P(x) for the Gamma distribution with parameters a and b.
gsll
.
The probability density p(x) at x
for a gamma distribution with parameters a and b, using the
formula given in #’sample :gamma.
gsll
.
The inverse cumulative distribution functions
P(x) for the Gamma distribution with parameters a and b.
gsll
.
The cumulative distribution functions
Q(x) for the Gamma distribution with parameters a and b.
gsll
.
The inverse cumulative distribution functions
Q(x) for the Gamma distribution with parameters a and b.
gsll
.
The cumulative distribution function P(x) for the Gaussian distribution with standard deviation sigma.
gsll
.
Compute the probability density p(x) at x
for a Gaussian distribution with standard deviation sigma.
gsll
.
The inverse cumulative distribution function P(x) for the Gaussian distribution with standard deviation sigma.
gsll
.
The cumulative distribution function Q(x) for the Gaussian distribution with standard deviation sigma.
gsll
.
The inverse cumulative distribution function Q(x) for the Gaussian distribution with standard deviation sigma.
gsll
.
The probability density p(x) at x
for a Gaussian tail distribution with standard deviation sigma and
lower limit a, using the formula given for gaussian-tail.
gsll
.
The Gegenbauer polynomial C^{(lambda)}_n(x)} for a specific value of n, lambda, x subject to lambda > -1/2, n >= 0.
gsll
.
The Gegenbauer polynomial C^{(lambda)}_1(x)}.
gsll
.
The Gegenbauer polynomial C^{(lambda)}_2(x)}.
gsll
.
The Gegenbauer polynomial C^{(lambda)}_3(x)}.
gsll
.
Compute an array of Gegenbauer polynomials C^{(lambda)}_n(X)} for n = 0, 1, 2, ..., length(array)-1}, subject to lambda > -1/2.
gsll
.
The cumulative distribution functions
P(k) for the geometric distribution with parameter p.
gsll
.
The probability p(k) of obtaining k
from a geometric distribution with probability parameter p, using
the formula given in #’sample :geometric.
gsll
.
The cumulative distribution functions
Q(k) for the geometric distribution with parameters p.
gsll
.
Generate a random integer. The
minimum and maximum values depend on the algorithm used, but all
integers in the range [min, max] are equally likely. The
values of min and max can determined using the auxiliary
functions #’rng-max and #’rng-min.
gsll
.
Returns the location of the @math{i}-th Greville abscissa for the given B-spline basis. For the ill-defined case when @math{k=1}, the implementation chooses to return breakpoint interval midpoints.
gsll
.
Find the GSLL (Lisp) equivalent of the GSL symbol.
gsll
.
The complete state of a given random number generator, specified as a vector of bytes.
gsll
.
The cumulative distribution functions
P(x) for the Type-1 Gumbel distribution with
parameters a and b.
gsll
.
The probability density p(x) at x
for a Type-1 Gumbel distribution with parameters a and b,
using the formula given for #’sample :gumbel1.
gsll
.
The inverse cumulative distribution functions P(x) for the Type-1 Gumbel distribution with parameters a and b.
gsll
.
The cumulative distribution functions
Q(x) for the Type-1 Gumbel distribution with
parameters a and b.
gsll
.
The inverse cumulative distribution functions Q(x) for the Type-1 Gumbel distribution with parameters a and b.
gsll
.
The cumulative distribution functions
P(x) for the Type-2 Gumbel distribution with
parameters a and b.
gsll
.
The probability density p(x) at x
for a Type-2 Gumbel distribution with parameters a and b,
using the formula given in #’sample :gumbel2.
gsll
.
The inverse cumulative distribution functions P(x) for the Type-2 Gumbel distribution with parameters a and b.
gsll
.
The cumulative distribution functions
Q(x) for the Type-2 Gumbel distribution with
parameters a and b.
gsll
.
The inverse cumulative distribution functions Q(x) for the Type-2 Gumbel distribution with parameters a and b.
gsll
.
Sort the count elements of the array of size specified
into ascending order using the comparison
function. The type of the comparison function is defined by,
A comparison function should return a negative integer if the first
argument is less than the second argument, zero if the two arguments
are equal and a positive integer if the first argument is greater than
the second argument.
gsll
.
Indirectly sort the count elements of the array
array, each of size given, into ascending order using the
comparison function. The resulting permutation is stored
in p, an array of length n. The elements of p give the
index of the array element which would have been stored in that position
if the array had been sorted in place. The first element of p
gives the index of the least element in array, and the last
element of p gives the index of the greatest element in
array. The array itself is not changed.
gsll
.
The covariance of the histogrammed x and y variables, where
the histogram is regarded as a probability
distribution. Negative bin values are ignored for the purposes
of this calculation.
gsll
.
Finds the bin number which covers the coordinate value in
the histogram. The bin is located using a binary search. The
search includes an optimization for histograms with uniform
range, and will return the correct bin immediately in this
case. If the value is found in the range of the histogram
then the function returns the index. If value lies outside
the valid range of the histogram then the error input-domain is
signalled.
gsll
.
Apply the Householder matrix P defined by the
scalar tau and the vector v to the left-hand side of the
matrix A. On output the result P A is stored in A.
gsll
.
Apply the Householder transformation P defined by the scalar tau and the vector v to the vector w. On output the result P w is stored in w.
gsll
.
Apply the Householder matrix P defined by the
scalar tau and the vector v to the right-hand side of the
matrix A. On output the result A P is stored in A.
gsll
.
Solve the system A x = b directly using Householder
transformations. If x-spec is NIL (default), the solution will
replace b. If x-spec is T, then an array will be created and the
solution returned in it. If x-spec is a grid:foreign-array, the solution will
be returned in it. If x-spec is non-NIL, on output the solution is
stored in x and b is not modified. The matrix A is destroyed by
the Householder transformations. The solution is returned from the
function call.
gsll
.
Prepare a Householder transformation P = I - tau v v^T
which can be used to zero all the elements of the input vector except
the first. Returned values are the transformation, which is stored
in the vector v, and the scalar tau.
gsll
.
The Hurwitz zeta function zeta(s,q) for s > 1, q > 0.
The n-th normalized hydrogenic bound state radial wavefunction,
R_n := {2 Z^{3/2} over n^2} left({2Z over n}right)^l
sqrt{(n-l-1)! over (n+l)!} exp(-Z r/n) L^{2l+1}_{n-l-1}(2Z/n r).
The normalization is chosen such that the wavefunction psi is given by
psi(n,l,r) = R_n Y_{lm}.
gsll
.
The lowest-order normalized hydrogenic bound state radial wavefunction R_1 := 2Z sqrt{Z} exp(-Z r).
gsll
.
The hypergeometric function
2F0(a,b,x). The series representation
is a divergent hypergeometric series. However, for x < 0 we
have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)
gsll
.
The Gauss hypergeometric function
2F1(a,b,c,x) for |x| < 1. If the arguments
(a,b,c,x) are too close to a singularity then the function can
signal the error ’exceeded-maximum-iterations when the series
approximation converges too slowly. This occurs in the region of
x=1, c - a - b = m for integer m.
gsll
.
The Gauss hypergeometric function 2F1(a, a*, c, x) with complex parameters for |x| < 1.
gsll
.
The renormalized Gauss hypergeometric function 2F1(a, a*, c, x) / Gamma(c) for |x| < 1.
gsll
.
The renormalized Gauss hypergeometric function 2F1(a,b,c,x) / Gamma(c) for |x| < 1.
gsll
.
The cumulative distribution functions P(k) for the hypergeometric distribution with parameters n1, n2 and tt.
gsll
.
The probability p(k) of obtaining k
from a hypergeometric distribution with parameters n1, n2,
tt, using the formula given in #’sample :hypergeometric.
gsll
.
The cumulative distribution functions Q(k) for the hypergeometric distribution with parameters n1, n2, and tt.
gsll
.
The hypotenuse sqrt{x^2 + y^2} computed in a way that avoids overflow.
gsll
.
The normalized incomplete Beta function
B_x(a,b)/B(a,b) where
B_x(a,b) = int_0^x t^{a-1} (1-t)^{b-1} dt
for a > 0, b > 0, and 0 <= x <= 1.
gsll
.
The normalized incomplete Gamma Function
Q(a,x) = 1/Gamma(a) int_x^infty dt t^{a-1} exp(-t) for a > 0, x >= 0.
gsll
.
Return +1 if x is positive infinity, -1 if negative infinity
nil if finite. Some platforms will return only +1 for either sign.
gsll
.
Initialize the combination c to the lexicographically first combination, i.e. (0,1,2,...,k-1).
gsll
.
Initialize the combination c to the lexicographically last combination, i.e. (n-k,n-k+1,...,n-1).
gsll
.
Construct the floating point number from its integer representation,
either sequence or IEEE754.
Also return the number in rational form.
The integer may be either a signed integer produced by
float-as-integer, or an IEEE754 integer. Acceptable
float-type is either ’double-float or ’single-float.
gsll
.
Compute the integral of the Chebyshev series, storing
the integral coefficients in the previously allocated series.
The two series must have been allocated with the same order.
The lower limit of the integration is taken to be the left hand
end of the range lower-limit.
gsll
.
Apply an integration rule adaptively until an estimate
of the integral of f over (a,b) is achieved within the
desired absolute and relative error limits, absolute-error and
relative-error. The function returns the final approximation,
and an estimate of the absolute error. The integration rule
is determined by the value of method, which should
be chosen from the following symbolic names,
:gauss15 :gauss21 :gauss31 :gauss41 :gauss51 :gauss61
corresponding to the 15, 21, 31, 41, 51 and 61 point Gauss-Kronrod
rules. The higher-order rules give better accuracy for smooth functions,
while lower-order rules save time when the function contains local
difficulties, such as discontinuities.
On each iteration the adaptive integration strategy bisects the interval
with the largest error estimate. The subintervals and their results are
stored in the memory provided by workspace. The maximum number of
subintervals is given by ’limit, which may not exceed the allocated
size of the workspace.
gsll
.
Compute the integral of the function f over the
infinite interval (-infty,+infty). The integral is mapped onto the
semi-open interval (0,1] using the transformation x = (1-t)/t,
int_{-infty}^{+infty} dx , f(x)
= int_0^1 dt , (f((1-t)/t) + f(-(1-t)/t))/t^2.
It is then integrated using the QAGS algorithm. The normal 21-point
Gauss-Kronrod rule of QAGS is replaced by a 15-point rule, because the
transformation can generate an integrable singularity at the origin. In
this case a lower-order rule is more efficient.
gsll
.
Compute the integral of the function f over the
semi-infinite interval (-infty,b). The integral is mapped onto the
semi-open interval (0,1] using the transformation x = b - (1-t)/t,
int_{-infty}^{b} dx, f(x) = int_0^1 dt, f(b - (1-t)/t)/t^2
and then integrated using the QAGS algorithm.
gsll
.
Compute the integral of the function f over the
semi-infinite interval (a,+infty). The integral is mapped onto the
semi-open interval (0,1] using the transformation x = a + (1-t)/t,
int_{a}^{+infty} dx, f(x) = int_0^1 dt f(a + (1-t)/t)/t^2
and then integrated using the QAGS algorithm.
gsll
.
Apply the adaptive integration algorithm QAGS taking
account of the user-supplied locations of singular points. The array
points should contain the endpoints of the
integration ranges defined by the integration region and locations of
the singularities. For example, to integrate over the region
(a,b) with break-points at x_1, x_2, x_3 (where
a < x_1 < x_2 < x_3 < b) then an array with
(setf (data array) #(a x_1 x_2 x_3 b)) should be used.
If you know the locations of the singular points in the integration
region then this routine will be faster than #’integration-QAGS.
gsll
.
Apply the Gauss-Kronrod 21-point integration rule
adaptively until an estimate of the integral of f over
(a,b) is achieved within the desired absolute and relative error
limits, absolute-error and relative-error. The results are extrapolated
using the epsilon-algorithm, which accelerates the convergence of the
integral in the presence of discontinuities and integrable
singularities. The function returns the final approximation from the
extrapolation, and an estimate of the absolute error. The subintervals
and their results are stored in the
memory provided by workspace. The maximum number of subintervals
is given by limit, which may not exceed the allocated size of the
workspace.
gsll
.
Compute the Cauchy principal value of the integral of
f over (a,b), with a singularity at c,
I = int_a^b dx, {f(x)/x - c} = lim_{epsilon -> 0}
{int_a^{c-epsilon} dx, {f(x)/x - c} + int_{c+epsilon}^b dx,
{f(x) over x - c}}
The adaptive bisection algorithm of QAG is used, with modifications to
ensure that subdivisions do not occur at the singular point x = c.
When a subinterval contains the point x = c or is close to
it then a special 25-point modified Clenshaw-Curtis rule is used to control
the singularity. Further away from the singularity the algorithm
uses an ordinary 15-point Gauss-Kronrod integration rule.
gsll
.
This function attempts to compute a Fourier integral of the
function f over the semi-infinite interval [a,+infty).
I = int_a^{+infty} dx f(x) sin(omega x)
I = int_a^{+infty} dx f(x) cos(omega x)
The parameter omega and choice of sin or cos is taken from the
table wf (the length L can take any value, since it is overridden
by this function to a value appropriate for the fourier
integration). The integral is computed using the QAWO algorithm
over each of the subintervals,
C_1 = [a, a + c]
C_2 = [a + c, a + 2 c]
... = ...
C_k = [a + (k-1) c, a + k c]
where c = (2 floor(|omega|) + 1) pi/|omega|. The width c is
chosen to cover an odd number of periods so that the contributions
from the intervals alternate in sign and are monotonically
decreasing when f is positive and monotonically decreasing. The
sum of this sequence of contributions is accelerated using the
epsilon-algorithm.
This function works to an overall absolute tolerance of
abserr. The following strategy is used: on each interval C_k the
algorithm tries to achieve the tolerance
TOL_k = u_k abserr
where u_k = (1 - p)p^{k-1} and p = 9/10. The sum of the geometric
series of contributions from each interval gives an overall
tolerance of abserr.
If the integration of a subinterval leads to difficulties then the
accuracy requirement for subsequent intervals is relaxed,
TOL_k = u_k max(abserr, max_{i<k}{E_i})
where E_k is the estimated error on the interval C_k.
The subintervals and their results are stored in the memory provided by workspace. The maximum number of subintervals is given by limit, which may not exceed the allocated size of the workspace. The integration over each subinterval uses the memory provided by cycle_workspace as workspace for the QAWO algorithm.
gsll
.
Use an adaptive algorithm to compute the integral of f over (a,b)
with the weight function sin(omega x) or cos(omega x) defined
by the table wf,
I = int_a^b dx f(x) sin(omega x)
I = int_a^b dx f(x) cos(omega x)
The results are extrapolated using the epsilon-algorithm to
accelerate the convergence of the integral. The function returns
the final approximation from the extrapolation, result, and an
estimate of the absolute error, abserr. The subintervals and their
results are stored in the memory provided by workspace. The maximum
number of subintervals is given by limit, which may not exceed the
allocated size of the workspace.
Those subintervals with large widths d where domega > 4 are computed using a 25-point Clenshaw-Curtis integration rule, which handles the oscillatory behavior. Subintervals with a small widths where domega < 4 are computed using a 15-point Gauss-Kronrod integration.
gsll
.
Compute the integral of the function f(x) over the interval (a,b)
with the singular weight function (x-a)^alpha (b-x)^beta
log^mu (x-a) log^nu (b-x). The parameters of the weight
function (alpha, beta, mu, nu) are used to make the default table. The
integral is
I = int_a^b dx f(x) (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x).
The adaptive bisection algorithm of QAG is used. When a
subinterval contains one of the endpoints then a special 25-point
modified Clenshaw-Curtis rule is used to control the
singularities. For subintervals which do not include the endpoints
an ordinary 15-point Gauss-Kronrod integration rule is used.
gsll
.
Apply the Gauss-Kronrod 10-point, 21-point, 43-point and
87-point integration rules in succession until an estimate of the
integral of f over (a,b) is achieved within the desired
absolute and relative error limits, absolute-error and relative-error. The
function returns the final approximation, an estimate of
the absolute error, and the number of function evaluations
used. The Gauss-Kronrod rules are designed in such a way
that each rule uses all the results of its predecessors, in order to
minimize the total number of function evaluations.
gsll
.
Find the index i of the array x-array such
that x-array[i] <= x < x-array[i+1]. The index is searched for
in the range [low-index, high-index].
gsll
.
Perform a inverse fast Fourier transform on the given vector. If the length of the vector is not a power of 2, and the user has a suitable wavetable and/or workspace, these can be supplied as keyword arguments. If the vector is real, it is assumed to be in half-complex form. If the length of the vector is a power of 2, use of a non-radix-2 transform can be forced.
gsll
.
Count the number of inversions in the permutation
p. An inversion is any pair of elements that are not in order.
For example, the permutation 2031 has three inversions, corresponding to
the pairs (2,0) (2,1) and (3,1). The identity permutation has no
inversions.
gsll
.
The Jacobian matrix for the current iteration of the solver.
gsll
.
The Jacobian elliptic functions sn(u|m),
cn(u|m), dn(u|m) computed by descending Landen transformations.
gsll
.
Compute the knots associated with the given breakpoints and store them in the workspace.
gsll
.
The generalized Laguerre polynomials L^a_n(x) for a > -1, n >= 0.
gsll
.
The generalized Laguerre polynomial L^a_1(x) using explicit representations.
gsll
.
The generalized Laguerre polynomial L^a_2(x) using explicit representations.
gsll
.
The generalized Laguerre polynomial L^a_3(x) using explicit representations.
gsll
.
The principal branch of the Lambert W function, W_0(x).
gsll
.
The secondary real-valued branch of the Lambert W function, W_{-1}(x).
gsll
.
The probability density p(x) at x
for the Landau distribution using an approximation to the formula given
in #’sample :landau.
gsll
.
The cumulative distribution function
P(x) for the laplace distribution with width a.
gsll
.
The probability density p(x) at x
for a Laplace distribution with width a, using the formula
given for #’sample :laplace.
gsll
.
The inverse cumulative distribution function P(x) for the laplace distribution with width a.
gsll
.
The cumulative distribution function
Q(x) for the laplace distribution with width a.
gsll
.
The inverse cumulative distribution function Q(x) for the laplace distribution with width a.
gsll
.
The conical function P^0_{-1/2 + i lambda(x)} for x > -1.
gsll
.
The conical function
P^1_{-1/2 + i lambda}(x)} for x > -1.
gsll
.
The irregular Spherical Conical Function P^{1/2}_{-1/2 + i lambda}(x) for x > -1.
gsll
.
The regular Spherical Conical Function P^{-1/2}_{-1/2 + i lambda}(x) for x > -1.
gsll
.
The l-th radial eigenfunction of the
Laplacian on the 3-dimensional hyperbolic space
eta >= 0, l >= 0. In the flat limit this takes the form
L^{H3d}_l(lambda,eta) = j_l(lambdaeta).
gsll
.
The zeroth radial eigenfunction of the Laplacian on the
3-dimensional hyperbolic space,
L^{H3d}_0(lambda,eta) := sin(lambdaeta)/(lambdasinh(eta))
for eta >= 0. In the flat limit this takes the form
L^{H3d}_0(lambda,eta) = j_0(lambdaeta).
gsll
.
The first radial eigenfunction of the Laplacian on
the 3-dimensional hyperbolic space,
L^{H3d}_1(lambda,eta) := 1/sqrt{lambda^2 + 1}
sin(lambda eta)/(lambda sinh(eta)) (coth(eta) - lambda cot(lambdaeta))}
for eta >= 0. In the flat limit this takes the form
L^{H3d}_1(lambda,eta) = j_1(lambdaeta)}.
gsll
.
An array of radial eigenfunctions L^{H3d}_l(lambda, eta) for 0 <= l <= length(array).
gsll
.
The Legendre polynomials P_1(x) using an explicit representation.
gsll
.
The Legendre polynomials P_2(x) using an explicit representation.
gsll
.
The Legendre polynomials P_3(x) using an explicit representation.
gsll
.
The Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1.
gsll
.
Compute an array of Legendre polynomials P_l(x) for l = 0, ..., length(array), |x| <= 1.
gsll
.
Compute an array of Legendre polynomials derivatives dP_l(x)/dx, for l = 0, ..., length(array), |x| <= 1.
gsll
.
The associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1.
gsll
.
The Legendre function Q_l(x) for x > -1, x /= 1, l >= 0.
gsll
.
The Regular Cylindrical Conical Function P^{-m}_{-1/2 + i lambda}(x) for x > -1, m >= -1.
gsll
.
The Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + i lambda}(x) for x > -1, l >= -1.
gsll
.
The normalized associated Legendre polynomial sqrt{(2l+1)/(4pi) sqrt{(l-m)!/(l+m)!} P_l^m(x) suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. These routines avoid the overflows that occur for the standard normalization of P_l^m(x).
gsll
.
Count the number of cycles in the permutation p, given in linear form.
gsll
.
Use the best-fit linear regression coefficients
c0, c1 and their covariance
cov00, cov01, cov11 to compute the fitted function
y and its standard deviation y-error for the model
Y = c_0 + c_1 X at the point x.
gsll
.
Compute the best-fit linear regression coefficients
c0, c1 of the model Y = c_0 + c_1 X for the weighted or unweighted
dataset (x, y), two vectors of equal length with strides
x-stride and y-stride, and return as the first two values.
The vector weight if given, of the same length
and stride w-stride, specifies the weight of each datapoint. The
weight is the reciprocal of the variance for each datapoint in y.
The covariance matrix for the parameters (c0, c1) is
computed using the weights and returned via the parameters
(cov00, cov01, c0v01) as the next three values. The weighted or
unweighted sum of squares of the residuals from the best-fit line,
chi^2, is returned as the last value.
Returns: c0, c1, cov00, cov01, cov11, sumsq.
Returns: intercept, slope, intercept variance, covariance, slope variance, sum square of residuals.
gsll
.
Compute the best-fit parameters c of the weighted or unweighted
model y = X c for the observations y and optional weights
and the model matrix X. The covariance matrix of
the model parameters is computed with the given weights. The
weighted sum of squares of the residuals from the best-fit,
chi^2, is returned as the last value.
The best-fit is found by singular value decomposition of the matrix
model using the preallocated workspace provided. The modified
Golub-Reinsch SVD algorithm is used for the unweighted solution,
with column scaling to improve the accuracy of the singular values.
Any components which have zero singular value (to machine
precision) are discarded from the fit.
If tolerance is a double-float, the SVD algorithm is used.
If it is nil the non-svd algorithm is used.
gsll
.
Compute the canonical form of the permutation p and stores it in the output argument q.
gsll
.
log(1+x), computed in a way that is accurate for small x.
gsll
.
log(1 + x) for x > -1 using an algorithm that is accurate for small x.
gsll
.
log(1 + x) - x for x > -1 using an algorithm that is accurate for small x.
gsll
.
The natural logarithm of the magnitude of x, log(|x|), for x ne 0.
gsll
.
The logarithm of the Beta Function, log(B(a,b)) for a > 0, b > 0.
gsll
.
The logarithm of (n choose m). This is
equivalent to the sum log(n!) - log(m!) - log((n-m)!).
gsll
.
Logarithm of cosh function, special functions These routines compute log(cosh(x)) for any x.
gsll
.
Compute the logarithm of the double factorial of n, log(n!!).
gsll
.
The logarithm of the complementary error function log(erfc(x)).
gsll
.
The logarithm of the factorial of n, log(n!).
The algorithm is faster than computing
ln(Gamma(n+1)) via #’log-gamma for n < 170, but defers for larger n.
gsll
.
The logarithm of the Gamma function,
log(Gamma(x)), subject to x not a being negative
integer. For x<0 the real part of log(Gamma(x)) is
returned, which is equivalent to log(|Gamma(x)|). The function
is computed using the real Lanczos method.
gsll
.
Compute log(Gamma(z)) for complex z=z_r+i z_i
and z not a negative integer, using the complex Lanczos
method. The returned parameters are lnr = log|Gamma(z)| and
arg = arg(Gamma(z)) in (-pi,pi]. Note that the phase
part (arg) is not well-determined when |z| is very large,
due to inevitable roundoff in restricting to (-pi,pi]. This
will result in a :ELOSS error when it occurs. The absolute
value part (lnr), however, never suffers from loss of precision.
gsll
.
Compute the sign of the gamma function and the logarithm of
its magnitude, subject to x not being a negative integer. The
function is computed using the real Lanczos method. The value of the
gamma function can be reconstructed using the relation Gamma(x) =
sgn * exp(resultlg)}.
gsll
.
The logarithm of the magnitude of the complex number.
gsll
.
The logarithm of the Pochhammer symbol,
log((a)_x) = log(Gamma(a + x)/Gamma(a)) for a > 0, a+x > 0.
gsll
.
The logarithm of the Pochhammer symbol and its sign.
The computed parameters are result =
log(|(a)_x|) and sgn = sgn((a)_x) where (a)_x :=
Gamma(a + x)/Gamma(a), subject to a, a+x not being negative integers.
gsll
.
This function computes the logarithm of the complex sine, log(sin(z_r + i z_i)) storing the real and imaginary parts in szr, szi.
gsll
.
Logarithm of sinh function, special functions These routines compute log(sinh(x)) for x > 0.
gsll
.
The probability p(k) of obtaining k
from a logarithmic distribution with probability parameter p,
using the formula given in #’sample :logarithmic.
gsll
.
The cumulative distribution functions
P(x) for the logistic distribution with scale parameter a.
gsll
.
The probability density p(x) at x
for a logistic distribution with scale parameter a, using the
formula given in #’sample :logistic.
gsll
.
The inverse cumulative distribution functions
P(x) for the logistic distribution with scale parameter a.
gsll
.
The cumulative distribution functions
Q(x) for the logistic distribution with scale parameter a.
gsll
.
The inverse cumulative distribution functions
Q(x) for the logistic distribution with scale parameter a.
gsll
.
The cumulative distribution functions
P(x) for the lognormal distribution with parameters zeta and sigma.
gsll
.
The probability density p(x) at X
for a lognormal distribution with parameters zeta and sigma,
using the formula given in #’sample :lognormal.
gsll
.
The inverse cumulative distribution functions P(x) for the lognormal distribution with parameters zeta and sigma.
gsll
.
The cumulative distribution functions
Q(x) for the lognormal distribution with parameters
zeta and sigma.
gsll
.
The inverse cumulative distribution functions
Q(x) for the lognormal distribution with parameters
zeta and sigma.
gsll
.
Compute the covariance matrix of the best-fit parameters
using the Jacobian matrix J. The relative error
is used to remove linear-dependent columns when J is
rank deficient. The covariance matrix is given by
C = (J^T J)^{-1}
and is computed by QR decomposition of J with column-pivoting. Any
columns of R which satisfy |R_{kk}| <= relative-error |R_{11}|
are considered linearly-dependent and are excluded from the covariance
matrix (the corresponding rows and columns of the covariance matrix are
set to zero).
If the minimisation uses the weighted least-squares function
f_i = (Y(x, t_i) - y_i) / sigma_i then the covariance
matrix above gives the statistical error on the best-fit parameters
resulting from the gaussian errors sigma_i on
the underlying data y_i. This can be verified from the relation
delta f = J delta c and the fact that the fluctuations in f
from the data y_i are normalised by sigma_i and
so satisfy <delta f delta f^T> = I.
For an unweighted least-squares function f_i = (Y(x, t_i) -
y_i) the covariance matrix above should be multiplied by the variance
of the residuals about the best-fit sigma^2 = sum (y_i - Y(x,t_i))^2 / (n-p)
to give the variance-covariance matrix sigma^2 C.
This estimates the statistical error on the
best-fit parameters from the scatter of the underlying data.
For more information about covariance matrices see the GSL documentation Fitting Overview.
gsll
.
Create the GSL object representing a acceleration for interpolation (class ACCELERATION).
Make an accelerator object, which is a
kind of iterator for interpolation lookups. It tracks the state of
lookups, thus allowing for application of various acceleration
strategies.
gsll
.
Create the GSL object representing a basis spline (class BASIS-SPLINE). Allocate a workspace for computing B-splines. The number of breakpoints is given by number-of-breakpoints. This leads to n = nbreak + k - 2 basis functions where k = order. Cubic B-splines are specified by k = 4. The size of the workspace is O(5k + nbreak).
gsll
.
Create the GSL object representing a Chebyshev series (class CHEBYSHEV). Make a Chebyshev series of specified order.
gsll
.
Make the object representing a combination of k things from a set of n. If initialize is T, initialize as the first k values (init-first). If n is a combination, make a new combination with the same specification. If initialize is also T, copy it.
gsll
.
Create the GSL object representing a lookup table for the discrete random number generator (class DISCRETE-RANDOM).
Make a structure that contains the lookup
table for the discrete random number generator. The array probabilities contains
the probabilities of the discrete events; these array elements must all be
positive, but they needn’t add up to one (so you can think of them more
generally as “weights”)—the preprocessor will normalize appropriately.
This return value is used as an argument to #’discrete.
gsll
.
Create the GSL object representing a generalized nonsymmetric eigenvalue workspace (class EIGEN-GEN).
Make a workspace for computing eigenvalues of n-by-n real
generalized nonsymmetric eigensystems. The size of the workspace
is O(n).
gsll
.
Create the GSL object representing a hermitian generalized eigenvalue workspace (class EIGEN-GENHERM).
Make a workspace for computing eigenvalues of n-by-n complex
generalized hermitian-definite eigensystems. The size of the
workspace is O(3n).
gsll
.
Create the GSL object representing a hermitian generalized eigensystem workspace (class EIGEN-GENHERMV).
Make a workspace for computing eigenvalues and eigenvectors of
n-by-n complex generalized hermitian-definite eigensystems. The
size of the workspace is O(5n).
gsll
.
Create the GSL object representing a symmetric generalized eigenvalue workspace (class EIGEN-GENSYMM).
Make a workspace for computing eigenvalues of n-by-n real
generalized symmetric-definite eigensystems. The size of the workspace
is O(2n).
gsll
.
Create the GSL object representing a symmetric generalized eigensystem workspace (class EIGEN-GENSYMMV).
Make a workspace for computing eigenvalues and eigenvectors of
n-by-n real generalized symmetric-definite eigensystems. The size
of the workspace is O(4n).
gsll
.
Create the GSL object representing a generalized nonsymmetric eigenvector and eigenvalue workspace (class EIGEN-GENV).
Make a workspace for computin geigenvalues and eigenvectors of
n-by-n real generalized nonsymmetric eigensystems. The size of the
workspace is O(7n).
gsll
.
Create the GSL object representing a Hermitian eigenvalue workspace (class EIGEN-HERM).
Make a workspace for computing eigenvalues of
n-by-n complex Hermitian matrices. The size of the workspace
is O(3n).
gsll
.
Create the GSL object representing a Hermitian eigensystem workspace (class EIGEN-HERMV).
Make a workspace for computing eigenvalues and
eigenvectors of n-by-n complex hermitian matrices. The size of
the workspace is O(5n).
gsll
.
Create the GSL object representing a non-symmetric eigenvalue workspace (class EIGEN-NONSYMM).
Make a workspace for computing eigenvalues of
n-by-n real non-symmetric matrices. The size of the workspace
is O(2n).
gsll
.
Create the GSL object representing a non-symmetric eigenvector and eigenvalue workspace (class EIGEN-NONSYMMV).
Make a workspace for computing for computing eigenvalues and
eigenvectors of n-by-n real nonsymmetric matrices. The size of the
workspace is O(5n).
gsll
.
Create the GSL object representing a symmetric eigenvalue workspace (class EIGEN-SYMM).
Make a workspace for computing eigenvalues of
n-by-n real symmetric matrices. The size of the workspace
is O(2n).
gsll
.
Create the GSL object representing a symmetric eigensystem workspace (class EIGEN-SYMMV).
Make a workspace for computing eigenvalues and
eigenvectors of n-by-n real symmetric matrices. The size of
the workspace is O(4n).
gsll
.
Make a wavetable for an FFT of the given element type and length. T can be given as an optional third argument if the wavetable is meant for a Fourier transform on a half-complex vector.
gsll
.
Make a wavetable for an FFT of the given element type and length.
gsll
.
Create the GSL object representing a multi-dimensional root solver with function only (class FIT-WORKSPACE). Make a workspace for a multidimensional linear least-squares fit.
gsll
.
Create the GSL object representing a discrete Hankel Transform (class HANKEL). Allocate a Discrete Hankel transform object of the given size and optionally initialize the transform for the given values of nu and x.
gsll
.
Create the GSL object representing a one-dimensional histogram, including bin boundaries and bin contents (class HISTOGRAM).
gsll
.
Create the GSL object representing a one-dimensional histogram PDF (class HISTOGRAM-PDF).
Optionally initialize the probability distribution pdf with the contents
of the histogram. If any of the bins are negative then an
input-domain error is signalled because a probability distribution
cannot contain negative values.
gsll
.
Create the GSL object representing a two-dimensional histogram, including bin boundaries and bin contents. (class HISTOGRAM2D).
gsll
.
Create the GSL object representing a two-dimensional histogram PDF (class HISTOGRAM2D-PDF).
Optionally initialize the probability distribution pdf with the contents
of the histogram. If any of the bins are negative then an
input-domain error is signalled because a probability distribution
cannot contain negative values.
gsll
.
Create the GSL object representing a integration workspace (class INTEGRATION-WORKSPACE).
Make a workspace sufficient to hold n double
precision intervals, their integration results and error estimates.
gsll
.
Create the GSL object representing a interpolation (class INTERPOLATION).
Make an interpolation object of type for size data-points,
and optionally initialize the interpolation object interp for the
data (xa,ya) where xa and ya are vectors. The interpolation object does not save
the data arrays xa and ya and only stores the static state
computed from the data. The xa data array is always assumed to be
strictly ordered; the behavior for other arrangements is not defined.
gsll
.
Make an empty Jacobian matrix for nonlinear least squares.
gsll
.
Create the GSL object representing a Levin u-transform (class LEVIN).
Make a workspace for a Levin u-transform of n
terms. The size of the workspace is O(2n^2 + 3n).
gsll
.
Create the GSL object representing a truncated Levin u-transform (class LEVIN-TRUNCATED).
Make a workspace for a Levin u-transform of n
terms, without error estimation. The size of the workspace is
O(3n).
gsll
.
Create the GSL object representing a workspace for Mathieu functions (class MATHIEU). Make a workspace needed for some Mathieu functions.
gsll
.
Create the GSL object representing a miser Monte Carlo integration (class MONTE-CARLO-MISER).
Make and initialize a workspace for Monte Carlo integration in
dimension dim. The workspace is used to maintain
the state of the integration.
gsll
.
Create the GSL object representing a plain Monte Carlo integration (class MONTE-CARLO-PLAIN). Make and initialize a workspace for Monte Carlo integration in dimension dim.
gsll
.
Create the GSL object representing a vegas Monte Carlo integration (class MONTE-CARLO-VEGAS).
Make and initialize a workspace for Monte Carlo integration in
dimension dim. The workspace is used to maintain
the state of the integration. Returns a pointer to vegas-state.
gsll
.
Create the GSL object representing a multi-dimensional minimizer with function only (class MULTI-DIMENSIONAL-MINIMIZER-F).
Make an instance of a minimizer for a function of the given
dimensions without derivative. Optionally initialize the minimizer
to minimize the function starting from the initial point. The size
of the initial trial steps is given in vector step-size. The
precise meaning of this parameter depends on the method used.
gsll
.
Create the GSL object representing a multi-dimensional minimizer with function and derivative (class MULTI-DIMENSIONAL-MINIMIZER-FDF).
Make an instance of a minimizer for a function of the given
dimensions with a derivative. Optionally initialize the minimizer
to minimize the function starting from the initial point. The size
of the first trial step is given by step-size. The accuracy of the
line minimization is specified by tolernace. The precise meaning
of this parameter depends on the method used. Typically the line
minimization is considered successful if the gradient of the
function g is orthogonal to the current search direction p to a
relative accuracy of tolerance, where dot(p,g) < tol |p| |g|.
gsll
.
Create the GSL object representing a multi-dimensional root solver with function only (class MULTI-DIMENSIONAL-ROOT-SOLVER-F).
Make an instance of a solver of the type specified for a system of
the specified number of dimensions. Optionally
set or reset an existing solver to use the function and the
initial guess gsl-vector. If scalarsp is T, the functions will
be supplied scalars, and should return scalars.
gsll
.
Create the GSL object representing a multi-dimensional root solver with function and derivative (class MULTI-DIMENSIONAL-ROOT-SOLVER-FDF).
Make an instance of a derivative solver of the type specified for
a system of the specified number of dimensions. Optionally
set or reset an existing solver to use the function and derivative
(fdf) and the initial guess. If scalarsp is T, the functions will
be supplied, and should return scalars.
gsll
.
Create the GSL object representing a nonlinear least squares fit with function and derivative (class NONLINEAR-FDFFIT).
The number of observations must be greater than or
equal to parameters.
gsll
.
Create the GSL object representing a nonlinear least squares fit with function only (class NONLINEAR-FFIT). The number of observations must be greater than or equal to parameters.
gsll
.
Create the GSL object representing a evolution for ordinary differential equations (class ODE-EVOLUTION). Make an object to advance the ODE solution.
gsll
.
Create the GSL object representing a stepper for ordinary differential equations (class ODE-STEPPER).
Make a stepper for ordinary differential equations. The type is
one of the GSL-supplied types defined in stepping.lisp, and
dimensions is the number of dependent variables. This instance
should be reinitialized whenever the next use of it will not be a
continuation of a previous step.
gsll
.
Create the GSL object representing a one-dimensional minimizer (class ONE-DIMENSIONAL-MINIMIZER).
Make an instance of a minimizer of the given type. Specify
a guess of the minimum point, the search interval
(x-minimum x-lower x-upper) and optionally
function values at those points (f-minimum f-lower f-upper).
gsll
.
Create the GSL object representing a one-dimensional root solver with function only (class ONE-DIMENSIONAL-ROOT-SOLVER-F).
gsll
.
Create the GSL object representing a one-dimensional root solver with function and derivative (class ONE-DIMENSIONAL-ROOT-SOLVER-FDF).
gsll
.
Create the GSL object representing a permutation (class PERMUTATION).
gsll
.
Create the GSL object representing a complex workspace for polynomials (class POLYNOMIAL-COMPLEX-WORKSPACE).
gsll
.
Create the GSL object representing a table for QAWO numerical integration method (class QAWO-TABLE).
Make a table describing a sine or cosine weight function W(x) with
the parameters (omega, L),
W(x) = sin(omega x)
W(x) = cos(omega x)
The parameter L must be the length of the interval over which the
function will be integrated L = b - a. The choice of sine or cosine
is made with the parameter trig which should be one of :cosine or :sine.
This makes a table of the trigonometric coefficients required in the
integration process. The parameter n determines the number of levels
of coefficients that are computed. Each level corresponds to one
bisection of the interval L, so that n levels are sufficient for
subintervals down to the length L/2^n. An error of class
’table-limit-exceeded is signalled if the number of levels is
insufficient for the requested accuracy.
gsll
.
Create the GSL object representing a table for QAWS numerical integration method (class QAWS-TABLE).
Make and initialize a table for the QAWS
adaptive integration method for singular functions.
It a singular weight function W(x) with the parameters (alpha, beta, mu, nu),
W(x) = (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x)
where alpha > -1, beta > -1, and mu = 0, 1, nu = 0, 1. The
weight function can take four different forms depending on the
values of mu and nu,
W(x) = (x-a)^alpha (b-x)^beta (mu = 0, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) (mu = 1, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(b-x) (mu = 0, nu = 1)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) log(b-x) (mu = 1, nu = 1)
The singular points (a,b) do not have to be specified until the
integral is computed, where they are the endpoints of the integration
range.
gsll
.
Create the GSL object representing a quasi random number generator (class QUASI-RANDOM-NUMBER-GENERATOR).
Make and optionally initialize the generator q to its starting point.
Note that quasi-random sequences do not use a seed and always produce
the same set of values.
gsll
.
Create the GSL object representing a random number generator (class RANDOM-NUMBER-GENERATOR).
Make and optionally initialize (or ‘seed’) the random number
generator of the specified type. If the generator is seeded with
the same value of s on two different runs, the same stream of
random numbers will be generated by successive calls. If different
values of s are supplied, then the generated streams of random
numbers should be completely different. If the seed s is zero then
the standard seed from the original implementation is used instead.
For example, the original Fortran source code for the *ranlux*
generator used a seed of 314159265, and so choosing s equal to zero
reproduces this when using *ranlux*.
gsll
.
Create the GSL object representing a scaled control for ordinary differential equations (class SCALED-CONTROL).
Create a new control object which uses the same algorithm
as #’new-standard-control but with an absolute error
which is scaled for each component by the array absolute-error.
The formula for D_i for this control object is
D_i = epsilon_{abs} s_i + epsilon_{rel} * (a_{y} |y_i| + a_{dydt} h |y’_i|)
where s_i is the i-th component of the array absolute-scale.
The same error control heuristic is used by the Matlab ode suite.
gsll
.
Create the GSL object representing a spline (class SPLINE). Make an interpolation object of type for size data-points.
gsll
.
Create the GSL object representing a standard control for ordinary differential equations (class STANDARD-CONTROL).
The standard control object is a four parameter heuristic based on
absolute and relative errors absolute-error and relative-error, and
scaling factors y-scaling and dydt-scaling for the system state y(t) and derivatives
y’(t) respectively.
The step-size adjustment procedure for this method begins by computing
the desired error level D_i for each component,
D_i = epsilon_{absolute} + epsilon_{relative} * (a_{y} |y_i| + a_{dydt} h |y’_i|)
and comparing it with the observed error E_i = |yerr_i|. If the
observed error E exceeds the desired error level D by more
than 10% for any component then the method reduces the step-size by an
appropriate factor,
h_{new} = h_{old} * S * (E/D)^{-1/q}
where g is the consistency order of the method (e.g. q=4 for
4(5) embedded RK), and S is a safety factor of 0.9. The ratio
E/D is taken to be the maximum of the ratios E_i/D_i.
If the observed error E is less than 50% of the desired error
level D for the maximum ratio E_i/D_i then the algorithm
takes the opportunity to increase the step-size to bring the error in
line with the desired level,
h_{new} = h_{old} * S * (E/D)^{-1/(q+1)}
This encompasses all the standard error scaling methods. To avoid
uncontrolled changes in the stepsize, the overall scaling factor is
limited to the range 1/5 to 5.
gsll
.
Create the GSL object representing a wavelet (class WAVELET). Make and initialize a wavelet object of type ’type. The parameter ’member selects the specific member of the wavelet family. A memory-allocation-failure error indicates either lack of memory or an unsupported member requested.
gsll
.
Create the GSL object representing a wavelet workspace (class WAVELET-WORKSPACE).
Make a workspace for the discrete wavelet transform.
To perform a one-dimensional transform on size elements, a workspace
of size size must be provided. For two-dimensional transforms of
size-by-size matrices it is sufficient to allocate a workspace of
size, since the transform operates on individual rows and
columns.
gsll
.
Create the GSL object representing a y control for ordinary differential equations (class Y-CONTROL).
Create a new control object which will keep the local
error on each step within an absolute error of absolute-error and
relative error of relative-error with respect to the solution y_i(t).
This is equivalent to the standard control object with y-scaling=1 and
dydt-scaling=0.
gsll
.
Create the GSL object representing a yp control for ordinary differential equations (class YP-CONTROL).
Create a new control object which will keep the local
error on each step within an absolute error of absolute-error and
relative error of relative-error with respect to the derivatives of the
solution y’_i(t). This is equivalent to the standard control
object with y-scaling=0 and dydt-scaling=1.
gsll
.
Compute the characteristic value a_n(q) of the Mathieu function ce_n(q,x) respectively.
gsll
.
Compute a series of Mathieu characteristic values a_n(q) for n from minimum-order to minimum-order + size - 1 inclusive, where size is either the numerical value supplied in size-or-array, or the the length of the vector supplied there.
gsll
.
Compute the characteristic values b_n(q) of the Mathieu function se_n(q,x), respectively.
gsll
.
Compute a series of Mathieu characteristic values b_n(q) for n from minimum-order to minimum-order + size - 1 inclusive, where size is either the numerical value supplied in size-or-array, or the the length of the vector supplied there.
gsll
.
Compute the angular Mathieu functions ce_n(q,x).
gsll
.
Compute a series of the angular Mathieu function ce_n(q) for n from minimum-order to minimum-order + size - 1 inclusive, where size is either the numerical value supplied in size-or-array, or the the length of the vector supplied there.
gsll
.
Compute the radial j-th kind Mathieu functions Mc_n^{(j)}(q,x) of order n. The allowed values of j are 1 and 2. The functions for j = 3,4 can be computed as M_n^{(3)} = M_n^{(1)} + iM_n^{(2)} and M_n^{(4)} = M_n^{(1)} - iM_n^{(2)}, where M_n^{(j)} = Mc_n^{(j)} or Ms_n^{(j)}.
gsll
.
Compute a series of the radial Mathieu function of kind j for n from minimum-order to minimum-order + size inclusive, where size is either the numerical value supplied in size-or-array, or the the length of the vector supplied there.
gsll
.
Compute the radial j-th kind Mathieu functions Ms_n^{(j)}(q,x) of order n. The allowed values of j are 1 and 2. The functions for j = 3,4 can be computed as M_n^{(3)} = M_n^{(1)} + iM_n^{(2)} and M_n^{(4)} = M_n^{(1)} - iM_n^{(2)}, where M_n^{(j)} = Mc_n^{(j)} or Ms_n^{(j)}.
gsll
.
Compute a series of the radial Mathieu function of kind j for n from minimum-order to minimum-order + size inclusive, where size is either the numerical value supplied in size-or-array, or the the length of the vector supplied there.
gsll
.
Compute the angular Mathieu functions se_n(q,x).
gsll
.
Compute a series of the angular Mathieu function se_n(q) for n from minimum-order to minimum-order + size - 1 inclusive, where size is either the numerical value supplied in size-or-array, or the the length of the vector supplied there.
gsll
.
Calculate the matrix exponential by the scaling and
squaring method described in Moler + Van Loan,
SIAM Rev 20, 801 (1978). The matrix to be exponentiated
is matrix, the returned exponential is exponential.
The mode argument allows
choosing an optimal strategy, from the table
given in the paper, for a given precision.
gsll
.
The current best estimate of the gradient for the minimizer.
gsll
.
Reset the minimizer to use the current point as a new starting point.
gsll
.
Test the norm of the gradient against the
absolute tolerance absolute-error. The gradient of a multidimensional
function goes to zero at a minimum. The test returns T
if |g| < epsabs is achieved, and NIL otherwise. A suitable choice of
absolute-error can be made from the desired accuracy in the function for
small variations in x. The relationship between these quantities
delta f = g delta x.
gsll
.
Test for the convergence of the interval [lower,upper]
with absolute error and relative error specified.
The test returns T if the following condition is achieved:
|a - b| < epsabs + epsrel min(|a|,|b|)
when the interval x = [a,b] does not include the origin. If the
interval includes the origin then min(|a|,|b|) is replaced by
zero (which is the minimum value of |x| over the interval). This
ensures that the relative error is accurately estimated for minima close
to the origin.
This condition on the interval also implies that any estimate of the
minimum x_m in the interval satisfies the same condition with respect
to the true minimum x_m^*,
|x_m - x_m^*| < epsabs + epsrel x_m^*
assuming that the true minimum x_m^* is contained within the interval.
gsll
.
Test the minimizer specific characteristic size (if applicable to
the used minimizer) against absolute tolerance absolute-error. The test
returns T if the size is smaller than tolerance, and NIL otherwise.
gsll
.
Uses the miser Monte Carlo algorithm to integrate the
function f over the hypercubic region defined by the
lower and upper limits in the arrays ’lower-limits and
’upper-limits, each a gsl-vector of the samelength
The integration uses a fixed number
of function calls number-of-samples, and obtains random sampling points using
the random number generator ’generator. A previously allocated workspace
’state must be supplied. The result of the integration is returned
with an estimated absolute error.
gsll
.
Uses the plain Monte Carlo algorithm to integrate the
function f over the hypercubic region defined by the
lower and upper limits in the arrays ’lower-limits and
’upper-limits, each a gsl-vector of length dim.
The integration uses a fixed number
of function calls number-of-samples, and obtains random sampling points using
the random number generator ’generator. A previously allocated workspace
’state must be supplied. The result of the integration is returned
with an estimated absolute error.
gsll
.
Uses the vegas Monte Carlo algorithm to integrate the function f over the dim-dimensional hypercubic region defined by the lower and upper limits in the arrays x1 and xu, each of the same length. The integration uses a fixed number of function calls number-of-samples, and obtains random sampling points using the random number generator r. A previously allocated workspace s must be supplied. The result of the integration is returned with an estimated absolute error. The result and its error estimate are based on a weighted average of independent samples. The chi-squared per degree of freedom for the weighted average is returned via the state struct component, s->chisq, and must be consistent with 1 for the weighted average to be reliable.
gsll
.
Use the best-fit multilinear regression coefficients
and their covariance matrix to compute the fitted function value
y and its standard deviation for the model y = x.c
at the point x.
gsll
.
Compute the vector of residuals r = y - X c for the observations y, coefficients c and matrix of predictor variables X.
gsll
.
Compute the natural logarithm of the probability P(n_1, n_2, ..., n_K)
of sampling n[K] from a multinomial distribution
with parameters p[K], using the formula given for #’sample :multinomial.
gsll
.
Compute the probability P(n_1, n_2, ..., n_K)
of sampling n[K] from a multinomial distribution
with parameters p[K], using the formula given for #’sample :multinomial.
gsll
.
Use the best-fit linear regression coefficient
c1 and its covariance cov11 to compute the fitted function
y and its standard deviation y-error for the model
Y = c_0 + c_1 X at the point x.
gsll
.
Compute the best-fit linear regression coefficient
c1 of the model Y = c_1 X for the weighted or unweighted datasets
(x, y), two vectors of equal length with strides
x-stride and y-stride. The vector weight of the same length
and of stride w-stide specifies the weight of each datapoint. The
weight is the reciprocal of the variance for each datapoint in y.
The variance of the parameter c1 is computed using the weights
and returned as the second value. The weighted sum of
squares of the residuals from the best-fit line, chi^2, is
returned as the last value.
gsll
.
Multiplies two double-floats returning the product and associated error.
gsll
.
Multiplies two double floats x and y with associated absolute errors dx and dy. The product xy +/- xy sqrt((dx/x)^2 +(dy/y)^2) is returned.
gsll
.
Test for the convergence of the sequence by comparing the
last step dx with the absolute error and relative
errors given to the current position x. The test returns
T if the following condition is achieved:
|dx_i| < epsabs + epsrel |x_i|
for each component of x and returns NIL otherwise.
gsll
.
Test the residual value f against the absolute error,
returning T if the following condition is achieved:
sum_i |f_i| < absolute_error
and returns NIL otherwise. This criterion is suitable
for situations where the precise location of the root x is
unimportant provided a value can be found where the
residual is small enough.
gsll
.
The cumulative distribution functions P(k) for the negative binomial distribution with parameters p and n.
gsll
.
The probability p(k) of obtaining k
from a negative binomial distribution with parameters p and
n, using the formula given in #’sample :negative-binomial.
gsll
.
The cumulative distribution functions Q(k) for the negative binomial distribution with parameters p and n.
gsll
.
The incomplete Gamma Function
Gamma(a,x), without the normalization factor
included in the previously defined functions:
Gamma(a,x) = int_x^infty dt t^{a-1} exp(-t)
for a real and x >= 0.
gsll
.
The number of breakpoints of the basis spline bspline.
gsll
.
Open an existing ntuple file filename for reading
and return a pointer to a corresponding ntuple struct. The ntuples in
the file must have size size. A pointer to memory for the current
ntuple row data must be supplied—this is used to copy
ntuples in and out of the file.
gsll
.
The cumulative distribution functions
P(x) for the Pareto distribution with exponent a and scale b.
gsll
.
The probability density p(x) at x
for a Pareto distribution with exponent a and scale b, using
the formula given in #’sample :pareto.
gsll
.
The inverse cumulative distribution functions
P(x) for the Pareto distribution with exponent a and scale b.
gsll
.
The cumulative distribution functions
Q(x) for the Pareto distribution with exponent a and scale b.
gsll
.
The inverse cumulative distribution functions
Q(x) for the Pareto distribution with exponent a and scale b.
gsll
.
The cumulative distribution functions P(k) for the Pascal distribution with parameters p and n.
gsll
.
The probability p(k) of obtaining k
from a Pascal distribution with parameters p and
n, using the formula given in #’sample :pascal.
gsll
.
The cumulative distribution functions Q(k) for the Pascal distribution with parameters p and n.
gsll
.
Combine the two permutations pa and pb into a single permutation p where p = pa . pb. The permutation p is equivalent to applying pb first and then pa.
gsll
.
A pointer to the array of elements in the permutation p.
gsll
.
Find the inverse of the permutation p.
gsll
.
Advance the permutation p to the next permutation
in lexicographic order and return p and T. If no further
permutations are available, return p and NIL with
p unmodified. Starting with the identity permutation and
repeatedly applying this function will iterate through all possible
permutations of a given order.
gsll
.
Step backwards from the permutation p to the
previous permutation in lexicographic order, returning p and T.
If no previous permutation is available, return
p and NIL with p unmodified.
gsll
.
Reverse the order of the elements of the permutation p.
gsll
.
The Pochhammer symbol (a)_x := Gamma(a +
x)/Gamma(a), subject to a and a+x not being negative
integers. The Pochhammer symbol is also known as the Apell symbol and
sometimes written as (a,x).
gsll
.
The cumulative distribution functions
P(k) for the Poisson distribution with parameter mu.
gsll
.
The probability p(k) of obtaining k
from a Poisson distribution with mean mu using the formula
given in #’sample :poisson.
gsll
.
The cumulative distribution functions
Q(k) for the Poisson distribution with parameter mu.
gsll
.
Convert the polar coordinates (r, theta) to
rectilinear coordinates (x, y), x = rcos(theta), y = rsin(theta).
gsll
.
Arguments are: a vector-double-float of coefficients, a complex
vector of length one less than coefficients that will hold the
answer, and a workspace made by make-polynomial-complex-workspace.
The roots of the general polynomial
P(x) = a_0 + a_1 x + a_2 x^2 + ... + a_{n-1} x^{n-1} using
balanced-QR reduction of the companion matrix. The coefficient of the
highest order term must be non-zero.
gsll
.
The power x^n for integer n. The
power is computed using the minimum number of multiplications. For
example, x^8 is computed as ((x^2)^2)^2, requiring only 3
multiplications. For reasons of efficiency, these functions do not
check for overflow or underflow conditions.
gsll
.
Update the histogram from the ntuple
using the functions value-function and select-function. For each
ntuple row where the selection function select-function is non-zero the
corresponding value of that row is computed using the function
value-function and added to the histogram. Those ntuple rows where
select-function returns zero are ignored. New entries are added to
the histogram, so subsequent calls can be used to accumulate further
data in the same histogram.
gsll
.
The real part of the digamma function on the line 1+i y, Re[psi(1 + i y)].
The polygamma function psi^{(m)}(x)} for m >= 0, x > 0.
Factorize the M-by-N matrix A into the QR decomposition A = Q R.
On output the diagonal and
upper triangular part of the input matrix contain the matrix
R. The vector tau and the columns of the lower triangular
part of the matrix A contain the Householder coefficients and
Householder vectors which encode the orthogonal matrix Q. The
vector tau must be of length k=min(M,N). The matrix
Q is related to these components by, Q = Q_k ... Q_2 Q_1
where Q_i = I - tau_i v_i v_i^T and v_i is the
Householder vector v_i = (0,...,1,A(i+1,i),A(i+2,i),...,A(m,i)).
This is the same storage scheme as used by lapack.
The algorithm used to perform the decomposition is Householder QR (Golub & Van Loan, Matrix Computations, Algorithm 5.2.1).
Solves the system R x = Q^T b for x. It can
be used when the QR decomposition of a matrix is available in
unpacked form as Q, R).
Apply the matrix Q^T encoded in the decomposition
(QR, tau) to the vector v, storing the result Q^T v in v.
The matrix multiplication is carried out directly using
the encoding of the Householder vectors without needing to form the full
matrix Q^T.
Apply the matrix Q encoded in the decomposition
(QR, tau) to the vector v, storing the result Q v in v.
The matrix multiplication is carried out directly using
the encoding of the Householder vectors without needing to form the full
matrix Q.
Solve the triangular system R x = b for x. It may be useful if the
product b’ = Q^T b has already been computed using QR-QTvec. If
x-spec is NIL (default), the solution will replace b. If x-spec is
T, then an array will be created and the solution returned in it.
If x-spec is a grid:foreign-array, the solution will be returned in it. If
x-spec is non-NIL, on output the solution is stored in x and b is
not modified. The solution is returned from the function call.
Solve the square system A x = b using the QR decomposition of A
into (QR, tau) given by QR-decomp. The least-squares solution for
rectangular systems can be found using QR-lssolve. If x-spec is
NIL (default), the solution will replace b. If x-spec is T, then
an array will be created and the solution returned in it. If
x-spec is a grid:foreign-array, the solution will be returned in it. If x-spec
is non-NIL, on output the solution is stored in x and b is not
modified. The solution is returned from the function call.
The least squares solution to the overdetermined system A x = b where the matrix A has more rows than columns. The least squares solution minimizes the Euclidean norm of the residual, ||Ax - b||.The routine uses the QR decomposition of A into (QR, tau) given by #’QR-decomposition. The solution is returned in x. The residual is computed as a by-product and stored in residual.
Unpack the encoded QR decomposition (QR, tau) into the matrices Q and R where Q is M-by-M and R is M-by-N.
Perform a rank-1 update w v^T of the QR
decomposition (Q, R). The update is given by Q’R’ = Q R + w v^T
where the output matrices Q’ and R’ are also
orthogonal and right triangular. Note that w is destroyed by the
update.
Store the next point from the sequence generator q
in the array. The space available for it must match the
dimension of the generator. The point will lie in the range
0 < x_i < 1 for each x_i.
gsll
.
Factorizes the M-by-N matrix A into
the QRP^T decomposition A = Q R P^T. On output the
diagonal and upper triangular part of the input matrix contain the
matrix R. The permutation matrix P is stored in the
permutation. The sign of the permutation is given by
signum. It has the value (-1)^n, where n is the
number of interchanges in the permutation. The vector tau and the
columns of the lower triangular part of the matrix A contain the
Householder coefficients and vectors which encode the orthogonal matrix
Q. The vector tau must be of length k=min(M,N). The
matrix Q is related to these components by, Q = Q_k ... Q_2 Q_1
where Q_i = I - tau_i v_i v_i^T and v_i is the Householder vector
v_i = (0,...,1,A(i+1,i),A(i+2,i),...,A(m,i)). This is the same storage scheme
as used by lapack. The vector norm is a workspace of length
N used for column pivoting.
The algorithm used to perform the decomposition is Householder QR with column pivoting (Golub & Van Loan, Matrix Computations, Algorithm 5.4.1).
Factorize the matrix A into the decomposition
A = Q R P^T without modifying A itself and storing the
output in the separate matrices q and r.
Solve the square system R P^T x = Q^T b for
x. It can be used when the QR decomposition of a matrix is
available in unpacked form as (Q, R).
Solve the triangular system R P^T x = b in-place for the N-by-N
matrix R contained in QR. On input x should contain the right-hand
side b, which is replaced by the solution on output. If x-spec is
NIL (default), the solution will replace b. If x-spec is T, then an
array will be created and the solution returned in it. If x-spec is
a grid:foreign-array, the solution will be returned in it. If x-spec is
non-NIL, on output the solution is stored in x and b is not
modified. The solution is returned from the function call.
Solve the square system A x = b using the QRP^T decomposition of A
into (QR, tau, permutation) given by #’QRPT-decomposition. If x-spec is
NIL (default), the solution will replace b. If x-spec is T, then
an array will be created and the solution returned in it. If
x-spec is a grid:foreign-array, the solution will be returned in it. If x-spec
is non-NIL, on output the solution is stored in x and b is not
modified. The solution is returned from the function call.
Perform a rank-1 update w v^T of the QRP^T
decomposition (Q, R, p). The update is given by
Q’R’ = Q R + w v^T where the output matrices Q’ and
R’ are also orthogonal and right triangular. Note that w is
destroyed by the update. The permutation is not changed.
Solve the triangular system R x = b in-place. On input x should
contain the right-hand side b, which is replaced by the solution on
output. If x-spec is NIL (default), the solution will replace b.
If x-spec is T, then an array will be created and the solution
returned in it. If x-spec is a grid:foreign-array, the solution will be
returned in it. If x-spec is non-NIL, on output the solution is
stored in x and b is not modified. The solution is returned from
the function call.
The cumulative distribution function
P(x) for the Rayleigh distribution with scale
parameter sigma.
gsll
.
The probability density p(x) at x
for a Rayleigh distribution with scale parameter sigma, using the
formula given for #’sample :rayleigh.
gsll
.
The inverse cumulative distribution function P(x)} for the Rayleigh distribution with scale parameter sigma.
gsll
.
The cumulative distribution function
Q(x) for the Rayleigh distribution with scale
parameter sigma.
gsll
.
The inverse cumulative distribution function Q(x) for the Rayleigh distribution with scale parameter sigma.
gsll
.
The probability density p(x) at x
for a Rayleigh tail distribution with scale parameter sigma and
lower limit a, using the formula given in #’sample :rayleigh-tail.
gsll
.
Read the current row of the ntuple file and stores the value.
gsll
.
Convert the rectilinear coordinates (x, y) to
polar coordinates (r, theta), such that x =
r cos(theta)}, y = r sin(theta). The argument theta
lies in the range [-pi, pi].
gsll
.
The relative Pochhammer symbol ((a)_x - 1)/x where (a)_x := Gamma(a + x)/Gamma(a)}.
gsll
.
Force the angle theta to lie in the range [0,2pi).
gsll
.
Force the angle theta to lie in the range (-pi,pi].
gsll
.
Read the environment variables GSL_RNG_TYPE and GSL_RNG_SEED and use their values to set the corresponding library variables *default-type* and *default-seed*
gsll
.
The largest value that #’get-random-number can return.
gsll
.
The smallest value that #’get-random-number
can return. Usually this value is zero. There are some generators with
algorithms that cannot return zero, and for these generators the minimum
value is 1.
gsll
.
Test for the convergence of the sequence ... x0, x1
with absolute error absolute-error and relative error
relative-error. The test returns T if the following
condition is achieved,
|x_1 - x_0| < epsabs + epsrel |x_1|
and returns NIL otherwise.
gsll
.
Test for the convergence of the interval [lower,upper]
with absolute error absolute-error and relative error
relative-error. This returns T
if the following condition is achieved,
|a - b| < epsabs + epsrel min(|a|,|b|)
when the interval x = [a,b] does not include the origin. If the
interval includes the origin then min(|a|,|b|) is replaced by
zero (which is the minimum value of |x| over the interval). This
ensures that the relative error is accurately estimated for roots close
to the origin.
This condition on the interval also implies that any estimate of the
root r in the interval satisfies the same condition with respect
to the true root r^*, |r - r^*| < epsabs + epsrel r^*
assuming that the true root r^* is contained within the interval.
gsll
.
Tests the residual value f against the absolute
error bound absolute-error. The test returns T if the
following condition is achieved,
|f| < epsabs
and returns NIL otherwise. This criterion is suitable
for situations where the precise location of the root, x, is
unimportant provided a value can be found where the residual,
|f(x)|, is small enough.
gsll
.
The value of the n-th sample point in k-space, j_{nu,n+1}/X}.
gsll
.
The value of the n-th sample point in the unit interval, (j_{nu,n+1}/j_{nu,M}) X, which are the points where the function f(t) is assumed to be sampled.
gsll
.
Sum of a scalar and a dot product for single-floats.
gsll
.
Set the IEEE 754 precision, rounding mode, and exception mask.
gsll
.
Perform a simulated annealing search through a given space. The space is specified by providing the functions energy-function and metric-function. The simulated annealing steps are generated using the random number generator and the function step-function. The starting configuration of the system should be given by state-values. The parameters n-tries, iterations-fixed-T, step-size, k, t-initial, mu-t, t-min control the run by providing the temperature schedule and other tunable parameters to the algorithm. On exit the best result achieved during the search is returned. If the annealing process has been successful this should be a good approximation to the optimal point in the space. The simulated annealing routines require several user-specified functions to define the configuration space and energy function.
gsll
.
Compute the sine of an angle x with
an associated absolute error dx, sin(x pm dx).
gsll
.
Find the real roots of the cubic equation, x^3 + a x^2 + b x + c = 0
with a leading coefficient of unity. The roots are given
in ascending order. Three values are always returned;
if a root is not real, the value returned for it will be NIL.
gsll
.
Find the complex roots of the cubic equation, x^3 + a x^2 + b x + c = 0 with a leading coefficient of unity. Three values are always returned; if a root does not exist, the value returned for it will be NIL.
gsll
.
Solve the general N-by-N system A x = b where A is cyclic
tridiagonal (N >= 3). The cyclic super-diagonal and
sub-diagonal vectors must have the same number of
elements as the diagonal vector diag. The form of A for the
4-by-4 case is
A = ( d_0 e_0 0 f_3 )
( f_0 d_1 e_1 0 )
( 0 f_1 d_2 e_2 )
( e_3 0 f_2 d_3 ).
gsll
.
The real roots of the quadratic equation a x^2 + b x + c = 0. Two values are always returned; if the roots are not real, these values are NIL.
gsll
.
The complex roots of the quadratic equation a x^2 + b x + c = 0. Two values are always returned; if a root does not exist, the value returned will be NIL.
gsll
.
Solve the general N-by-N system A x = b where A is symmetric
cyclic tridiagonal (N >= 3). The cyclic
off-diagonal vector must have the same number of elements as the
diagonal vector diag. The form of A for the 4-by-4 case is
shown below,
A = ( d_0 e_0 0 e_3 )
( e_0 d_1 e_1 0 )
( 0 e_1 d_2 e_2 )
( e_3 0 e_2 d_3 )
gsll
.
Solve the general N-by-N system A x = b where A is
symmetric tridiagonal (N >= 2). The off-diagonal vector
must be one element shorter than the diagonal vector diag.
The form of A for the 4-by-4 case is
A = ( d_0 e_0 0 0 )
( e_0 d_1 e_1 0 )
( 0 e_1 d_2 e_2 )
( 0 0 e_2 d_3 ).
gsll
.
Solve the general N-by-N system A x = b where A is tridiagonal
(N >= 2). The super-diagonal and
sub-diagonal vectors must be one element shorter
than the diagonal vector diag. The form of A for the 4-by-4
case is
A = ( d_0 e_0 0 0 )
( f_0 d_1 e_1 0 )
( 0 f_1 d_2 e_2 )
( 0 0 f_2 d_3 ).
gsll
.
The scaled regular modified spherical Bessel function of zeroth order, exp(-|x|) i_0(x).
gsll
.
The scaled regular modified spherical Bessel function of first order, exp(-|x|) i_1(x).
gsll
.
The scaled regular modified spherical Bessel function of second order, exp(-|x|) i_2(x).
gsll
.
The scaled regular modified spherical Bessel function of order l, exp(-|x|) i_l(x).
gsll
.
The values of the scaled regular modified cylindrical Bessel
functions exp(-|x|) i_l(x) for l from 0 to length(array)-1
inclusive. The values are computed using recurrence relations
for efficiency, and therefore may differ slightly from the exact values.
gsll
.
The regular spherical Bessel function of zeroth order, j_0(x) = sin(x)/x.
gsll
.
The regular spherical Bessel function of first order, j_1(x) = (sin(x)/x - cos(x))/x.
gsll
.
The regular spherical Bessel function of second order, j_2(x) = ((3/x^2 - 1)sin(x) - 3cos(x)/x)/x.
gsll
.
The regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0.
gsll
.
The values of the regular spherical Bessel
functions j_l(x) for l from 0 to length(array)-1 and x >= 0.
The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
gsll
.
Uses Steed’s method to compute the values of the regular spherical Bessel functions j_l(x) for l from 0 to length(array)-1 inclusive for x >= 0. The Steed/Barnett algorithm is described in Comp. Phys. Comm. 21, 297 (1981). Steed’s method is more stable than the recurrence used in the other functions but is also slower.
gsll
.
The scaled irregular modified spherical Bessel function of zeroth order, exp(x) k_0(x), for x>0.
gsll
.
The scaled irregular modified spherical Bessel function of first order, exp(x) k_1(x), for x>0.
gsll
.
The scaled irregular modified spherical Bessel function of second order, exp(x) k_2(x), for x>0.
gsll
.
The scaled irregular modified spherical Bessel function of order l, exp(x) k_l(x), for x>0.
gsll
.
The values of the scaled irregular modified spherical Bessel functions exp(x) k_l(x) for l from 0 to length(array)-1 inclusive x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.
gsll
.
The irregular spherical Bessel function of zeroth order, y_0(x) = -cos(x)/x.
gsll
.
The irregular spherical Bessel function of first order, y_1(x) = -(cos(x)/x + sin(x))/x.
gsll
.
The irregular spherical Bessel function of second order, y_2(x) = (-3/x^3 + 1/x)cos(x) - (3/x^2)sin(x).
gsll
.
The irregular spherical Bessel function of order l, y_l(x), for l >= 0.
gsll
.
The irregular spherical Bessel functions y_l(x) for l
from 0 to length(array)-1. The values are computed using
recurrence relations for efficiency,
and therefore may differ slightly from the exact values.
gsll
.
The order of the stepping function on the previous
step, which can vary if the stepping function itself is adaptive.
gsll
.
Factorize the M-by-N matrix A into
the singular value decomposition A = U S V^T for M >= N.
On output the matrix A is replaced by U. The diagonal elements
of the singular value matrix S
are stored in the vector S. The singular values are non-negative
and form a non-increasing sequence from S_1 to S_N. The
matrix V contains the elements of V in untransposed
form. To form the product U S V^T it is necessary to take the
transpose of V. A workspace of length N is required in work.
This routine uses the Golub-Reinsch SVD algorithm.
The SVD of the M-by-N matrix A using one-sided Jacobi orthogonalization for M >= N. The Jacobi method can compute singular values to higher relative accuracy than Golub-Reinsch algorithms (see references for details).
The SVD using the modified Golub-Reinsch algorithm, which is faster for M >> N. It requires the vector work of length N and the N-by-N matrix X as additional working space.
Solve the system A x = b using the singular value
decomposition (U, S, V) of A given by #’SV-decomposition.
Only non-zero singular values are used in computing the solution. The
parts of the solution corresponding to singular values of zero are
ignored. Other singular values can be edited out by setting them to
zero before calling this function.
In the over-determined case where A has more rows than columns the system is solved in the least squares sense, returning the solution x which minimizes ||A x - b||_2.
The first synchrotron function x int_x^infty dt K_{5/3}(t)} for x >= 0.
gsll
.
The second synchrotron function x K_{2/3}(x)} for x >= 0.
gsll
.
Compute the Taylor coefficient x^n / n! for x >= 0, n >= 0.
gsll
.
Convert the divided-difference representation of a
polynomial to a Taylor expansion. The divided-difference representation
is supplied in the arrays dd and xa of the same length.
On output the Taylor coefficients of the polynomial expanded about the
point xp are stored in the array coefficients which has the same length
as xa and dd.
gsll
.
The cumulative distribution functions
P(x) for the tdist distribution with nu degrees of freedom.
gsll
.
The probability density p(x) at x
for a t-distribution with nu degrees of freedom, using the formula
given in #’sample :tdist.
gsll
.
The inverse cumulative distribution functions
P(x) for the tdist distribution with nu degrees of freedom.
gsll
.
The cumulative distribution functions
Q(x) for the tdist distribution with nu degrees of freedom.
gsll
.
The inverse cumulative distribution functions
Q(x) for the tdist distribution with nu degrees of freedom.
gsll
.
The cumulative distribution function P(x) for the Gaussian distribution with unit standard deviation.
gsll
.
Compute results for the unit Gaussian distribution,
equivalent to the #’gaussian-pdf with a standard deviation of one,
sigma = 1.
gsll
.
The inverse cumulative distribution function P(x) for the Gaussian distribution with unit standard deviation.
gsll
.
The cumulative distribution function Q(x) for the Gaussian distribution with unit standard deviation.
gsll
.
The inverse cumulative distribution function Q(x) for the Gaussian distribution with unit standard deviation.
gsll
.
Equivalent to gaussian-tail-pdf with sigma=1.
gsll
.
Compute knots uniformly on the interval [a, b] and store them in the workspace.
gsll
.
gsll
.
Compute the two-dimensional wavelet transform in non-standard form.
gsll
.
Compute the two-dimensional wavelet transform in non-standard form.
gsll
.
Compute the two-dimensional wavelet transform in non-standard form.
gsll
.
Compute the non-standard form of the two-dimensional in-place wavelet transform on a matrix.
gsll
.
Compute the non-standard form of the two-dimensional in-place wavelet transform on a matrix.
gsll
.
Compute the non-standard form of the two-dimensional in-place wavelet transform on a matrix.
gsll
.
Compute in-place forward and inverse discrete wavelet transforms
in standard and non-standard forms on the
array data stored in row-major form with dimensions
and physical row length tda. The dimensions must
be equal (square matrix) and are restricted to powers of two. For the
transform version of the function the argument direction can be
either :forward or :backward. A
workspace of the appropriate size must be provided. On exit,
the appropriate elements of the array data are replaced by their
two-dimensional wavelet transform.
An error invalid-argument is signalled if the matrix is not square
with dimension a power of 2, or if insufficient
workspace is provided.
gsll
.
Compute two-dimensional in-place forward and inverse
discrete wavelet transforms in standard and non-standard forms on the
array data stored in row-major form with dimensions size1
and size2 and physical row length tda. The dimensions must
be equal (square matrix) and are restricted to powers of two. A
workspace of the appropriate size must be provided. On exit,
the appropriate elements of the array data are replaced by their
two-dimensional wavelet transform.
An error invalid-argument is signalled if the matrix is not square
with dimension a power of 2, or if insufficient
workspace is provided.
gsll
.
Compute two-dimensional in-place forward and inverse discrete
wavelet transforms in standard and non-standard forms on the array
data stored in row-major form with dimensions size1 and size2 and
physical row length tda. The dimensions must be equal (square matrix)
and are restricted to powers of two. A workspace of the appropriate
size must be provided. On exit, the appropriate elements of the array
data are replaced by their two-dimensional wavelet transform. An
error invalid-argument is signalled if the matrix is not square with dimension
a power of 2, or if insufficient workspace is provided.
gsll
.
Compute the two-dimensional in-place wavelet transform on a matrix.
gsll
.
Compute the two-dimensional in-place wavelet transform on a matrix.
gsll
.
Compute the two-dimensional in-place wavelet transform on a matrix.
gsll
.
Compute in-place forward and inverse discrete wavelet
transforms on the array data. The length of the
transform n is restricted to powers
of two. For the transform version of the function the argument
dir can be either :forward or :backward. A workspace
of the same length as data must be provided.
For the forward transform, the elements of the original array are
replaced by the discrete wavelet
transform f_i -> w_{j,k}
in a packed triangular storage layout,
where j is the index of the level j = 0 ... J-1
and k is the index of the coefficient within each level,
k = 0 ... (2^j)-1. The total number of levels is J = log_2(n).
The output data has the following form,
(s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0},cdots, d_{j,k},cdots, d_{J-1,2^{J-1} - 1})
where the first element is the smoothing coefficient
s_{-1,0}, followed by the detail coefficients d_{j,k} for each level j.
The backward transform inverts these coefficients to obtain
the original data.
gsll
.
Compute in-place forward and inverse discrete wavelet
transforms on the array data. The length of the transform
is restricted to powers of two.
A workspace of the same length as data must be provided.
For the forward transform, the elements of the original array are
replaced by the discrete wavelet transform
f_i -> w_{j,k} in a packed triangular storage layout,
where j is the index of the level j = 0 ... J-1
and k is the index of the coefficient within each level,
k = 0 ... (2^j)-1. The total number of levels is J = log_2(n).
The output data has the following form,
(s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0},cdots, d_{j,k},cdots, d_{J-1,2^{J-1} - 1})
where the first element is the smoothing coefficient s_{-1,0},
followed by the detail coefficients d_{j,k} for each level j.
The backward transform inverts these coefficients to obtain
the original data.
gsll
.
Compute in-place inverse discrete wavelet
transforms on the array data. The length of the transform
is restricted to powers of two.
A workspace of the same length as data must be provided.
For the forward transform, the elements of the original array are
replaced by the discrete wavelet transform
f_i -> w_{j,k} in a packed triangular storage layout,
where j is the index of the level j = 0 ... J-1
and k is the index of the coefficient within each level,
k = 0 ... (2^j)-1. The total number of levels is J = log_2(n).
The output data has the following form,
(s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0},cdots, d_{j,k},cdots, d_{J-1,2^{J-1} - 1})
where the first element is the smoothing coefficient s_{-1,0},
followed by the detail coefficients d_{j,k} for each level j.
The backward transform inverts these coefficients to obtain
the original data.
gsll
.
The cumulative distribution functions
P(x) for the Weibull distribution with scale a and exponent b.
gsll
.
The probability density p(x) at x
for a Weibull distribution with scale a and exponent b,
using the formula given in #’sample :weibull.
gsll
.
The inverse cumulative distribution functions
P(x) for the Weibull distribution scale a and exponent b.
gsll
.
The cumulative distribution functions
Q(x) for the Weibull distribution with scale a and exponent b.
gsll
.
The inverse cumulative distribution functions
Q(x) for the Weibull distribution exponent a and scale b.
gsll
.
Write the current ntuple ntuple->ntuple_data of size ntuple->size to the corresponding file.
gsll
.
The absolute deviation from the mean of data. The absolute deviation from the mean is defined as absdev = (1/N) sum |x_i - Hatmu| where x_i are the elements of the dataset data. The absolute deviation from the mean provides a more robust measure of the width of a distribution than the variance. If ’mean is not supplied, this function computes the mean of data via a call to #’mean. With mean supplied, this function is useful if you have already computed the mean of data (and want to avoid recomputing it), or wish to calculate the absolute deviation relative to another value (such as zero, or the median).
gsll
.
vector-single-float
) &optional mean) ¶vector-double-float
) &optional mean) ¶vector-signed-byte-8
) &optional mean) ¶vector-unsigned-byte-8
) &optional mean) ¶vector-signed-byte-16
) &optional mean) ¶vector-unsigned-byte-16
) &optional mean) ¶vector-signed-byte-32
) &optional mean) ¶vector-unsigned-byte-32
) &optional mean) ¶vector-signed-byte-64
) &optional mean) ¶vector-unsigned-byte-64
) &optional mean) ¶The absolute sum sum |x_i| of the elements of the vector x.
The lag-1 autocorrelation of the dataset data.
a_1 = {sum_{i = 1}^{n} (x_{i} - Hatmu) (x_{i-1} - Hatmu)
over
sum_{i = 1}^{n} (x_{i} - Hatmu) (x_{i} - Hatmu)}.
gsll
.
vector-single-float
) &optional mean) ¶vector-double-float
) &optional mean) ¶vector-signed-byte-8
) &optional mean) ¶vector-unsigned-byte-8
) &optional mean) ¶vector-signed-byte-16
) &optional mean) ¶vector-unsigned-byte-16
) &optional mean) ¶vector-signed-byte-32
) &optional mean) ¶vector-unsigned-byte-32
) &optional mean) ¶vector-signed-byte-64
) &optional mean) ¶vector-unsigned-byte-64
) &optional mean) ¶Compute the sum y = alpha x + y for the vectors x and y.
Backward discrete Fourier transform provided to check the FFT routines.
Copy the elements of the vector x into the vector y.
gsll
.
vector-single-float
) (y vector-single-float
)) ¶vector-double-float
) (y vector-double-float
)) ¶vector-complex-single-float
) (y vector-complex-single-float
)) ¶vector-complex-double-float
) (y vector-complex-double-float
)) ¶Exchange the elements of the vectors.
gsll
.
vector-single-float
) (vec2 vector-single-float
)) ¶vector-double-float
) (vec2 vector-double-float
)) ¶vector-complex-single-float
) (vec2 vector-complex-single-float
)) ¶vector-complex-double-float
) (vec2 vector-complex-double-float
)) ¶The complex conjugate scalar product x^H y for the vectors.
Factorize the positive-definite square matrix A into the Cholesky decomposition A = L L^T (real) or A = L L^H (complex). On output the diagonal and lower triangular part of the input matrix A contain the matrix L. The upper triangular part of the input matrix contains L^T, the diagonal terms being identical for both L and L^T. If the matrix is not positive-definite then the decomposition will fail, returning the error input-domain.
Solve the system A x = b using the Cholesky
decomposition of A into the matrix given by
#’cholesky-decomposition. If x-spec is NIL (default), the solution
will replace b. If x-spec is T, then an array will be created and the
solution returned in it. If x-spec is a grid:foreign-array, the solution will
be returned in it.
Copy the elements of the ith column of the matrix into the vector. The length of the vector must be the same as the length of the column.
gsll
.
matrix-single-float
) i &optional vector) ¶matrix-double-float
) i &optional vector) ¶matrix-complex-single-float
) i &optional vector) ¶matrix-complex-double-float
) i &optional vector) ¶matrix-signed-byte-8
) i &optional vector) ¶matrix-unsigned-byte-8
) i &optional vector) ¶matrix-signed-byte-16
) i &optional vector) ¶matrix-unsigned-byte-16
) i &optional vector) ¶matrix-signed-byte-32
) i &optional vector) ¶matrix-unsigned-byte-32
) i &optional vector) ¶matrix-signed-byte-64
) i &optional vector) ¶matrix-unsigned-byte-64
) i &optional vector) ¶Copy the elements of the vector into the ith column of the matrix. The length of the vector must be the same as the length of the column.
gsll
.
matrix-single-float
) i) ¶matrix-double-float
) i) ¶matrix-complex-single-float
) i) ¶matrix-complex-double-float
) i) ¶matrix-signed-byte-8
) i) ¶matrix-unsigned-byte-8
) i) ¶matrix-signed-byte-16
) i) ¶matrix-unsigned-byte-16
) i) ¶matrix-signed-byte-32
) i) ¶matrix-unsigned-byte-32
) i) ¶matrix-signed-byte-64
) i) ¶matrix-unsigned-byte-64
) i) ¶The conjugate rank-1 update A = alpha x y^H + A of the matrix A.
gsll
.
vector-complex-single-float
) (y vector-complex-single-float
) (a matrix-complex-single-float
)) ¶vector-complex-double-float
) (y vector-complex-double-float
) (a matrix-complex-double-float
)) ¶Efficiently compute the Pearson correlation coefficient between the datasets data1 and data2 which must both be of the same length
gsll
.
vector-single-float
) (data2 vector-single-float
)) ¶vector-double-float
) (data2 vector-double-float
)) ¶vector-signed-byte-8
) (data2 vector-signed-byte-8
)) ¶vector-unsigned-byte-8
) (data2 vector-unsigned-byte-8
)) ¶vector-signed-byte-16
) (data2 vector-signed-byte-16
)) ¶vector-unsigned-byte-16
) (data2 vector-unsigned-byte-16
)) ¶vector-signed-byte-32
) (data2 vector-signed-byte-32
)) ¶vector-unsigned-byte-32
) (data2 vector-unsigned-byte-32
)) ¶vector-signed-byte-64
) (data2 vector-signed-byte-64
)) ¶vector-unsigned-byte-64
) (data2 vector-unsigned-byte-64
)) ¶The covariance of the datasets data1 and data2 which must
be of the same length,
covar = {1 over (n - 1)} sum_{i = 1}^{n}
(x_{i} - Hat x) (y_{i} - Hat y).
gsll
.
vector-single-float
) (data2 vector-single-float
) &optional mean1 mean2) ¶vector-double-float
) (data2 vector-double-float
) &optional mean1 mean2) ¶vector-signed-byte-8
) (data2 vector-signed-byte-8
) &optional mean1 mean2) ¶vector-unsigned-byte-8
) (data2 vector-unsigned-byte-8
) &optional mean1 mean2) ¶vector-signed-byte-16
) (data2 vector-signed-byte-16
) &optional mean1 mean2) ¶vector-unsigned-byte-16
) (data2 vector-unsigned-byte-16
) &optional mean1 mean2) ¶vector-signed-byte-32
) (data2 vector-signed-byte-32
) &optional mean1 mean2) ¶vector-unsigned-byte-32
) (data2 vector-unsigned-byte-32
) &optional mean1 mean2) ¶vector-signed-byte-64
) (data2 vector-signed-byte-64
) &optional mean1 mean2) ¶vector-unsigned-byte-64
) (data2 vector-unsigned-byte-64
) &optional mean1 mean2) ¶The regular modified cylindrical Bessel function of order n, I_n(x).
The scaled regular modified cylindrical Bessel function of order n, exp(-|x|) I_n(x)}.
gsll
.
float
) x) ¶The scaled regular modified Bessel function of fractional order nu, exp(-|x|)I_nu(x) for x>0, nu>0.
integer
) x) ¶The scaled regular modified cylindrical Bessel function of order n, exp(-|x|) I_n(x)}.
The regular cylindrical Bessel function of order n, J_n(x).
The irregular modified cylindrical Bessel function of order n, K_n(x).
The scaled irregular modified cylindrical Bessel function of order n, exp(-|x|) K_n(x).
The irregular cylindrical Bessel function of order n, Y_n(x).
The dilogarithm.
Discrete Fourier transform in selectable direction provided to check the FFT routines.
Eigenvalues of the real symmetric or complex hermitian matrix A. Additional workspace of the appropriate size and type must be provided in w. The diagonal and lower triangular part of A are destroyed during the computation, but the strict upper triangular part is not referenced. For the complex hermitian case, The imaginary parts of the diagonal are assumed to be zero and are not referenced. The eigenvalues are stored in the vector eigenvalues and are unordered.
The eigenvalues and eigenvectors of the real symmetric or complex hermitian matrix A. Additional workspace of the appropriate size must be provided in w. The diagonal and lower triangular part of A are destroyed during the computation, but the strict upper triangular part is not referenced. For complex hermitian matrices, the imaginary parts of the diagonal are assumed to be zero and are not referenced. The eigenvalues are stored in the vector eigenvalues and are unordered. The corresponding eigenvectors are stored in the columns of the matrix eigenvectors. For example, the eigenvector in the first column corresponds to the first eigenvalue. The eigenvectors are guaranteed to be mutually orthogonal and normalised to unit magnitude.
Computes the eigenvalues and eigenvectors of the real generalized symmetric-definite matrix pair (A, B), and stores them in eval and evec respectively. The computed eigenvectors are normalized to have unit magnitude. On output, B contains its Cholesky decomposition and A is destroyed.
gsll
.
matrix-double-float
) (b matrix-double-float
) &optional eigenvalues eigenvectors ws) ¶matrix-complex-double-float
) (b matrix-complex-double-float
) &optional eigenvalues eigenvectors ws) ¶Compute the eigenvalues of the real generalized symmetric-definite matrix pair (A, B), and stores them in eval, using the method outlined above. On output, B contains its Cholesky decomposition and A is destroyed.
Multiply the elements of a by the elements of b. The two must have the same dimensions.
gsll
.
histogram2d
) scale) ¶Multiply the contents of the bins of histogram by the constant scale, i.e. h’_1(i) = h_1(i) * scale.
histogram
) scale) ¶Multiply the contents of the bins of histogram by the constant scale, i.e. h’_1(i) = h_1(i) * scale.
histogram2d
) (histogram2 histogram2d
)) ¶Multiply the contents of the bins of histogram1 by the contents of the corresponding bins in histogram2 i.e. h’_1(i) = h_1(i) * h_2(i). The two histograms must have identical bin ranges.
histogram
) (histogram2 histogram
)) ¶Multiply the contents of the bins of histogram1 by the contents of the corresponding bins in histogram2 i.e. h’_1(i) = h_1(i) * h_2(i). The two histograms must have identical bin ranges.
float
) (a foreign-array
)) ¶matrix-complex-double-float
) (x complex
)) ¶matrix-complex-single-float
) (x complex
)) ¶vector-complex-double-float
) (x complex
)) ¶vector-complex-single-float
) (x complex
)) ¶matrix-unsigned-byte-64
) (x float
)) ¶matrix-signed-byte-64
) (x float
)) ¶matrix-unsigned-byte-32
) (x float
)) ¶matrix-signed-byte-32
) (x float
)) ¶matrix-unsigned-byte-16
) (x float
)) ¶matrix-signed-byte-16
) (x float
)) ¶matrix-unsigned-byte-8
) (x float
)) ¶matrix-signed-byte-8
) (x float
)) ¶matrix-double-float
) (x float
)) ¶matrix-single-float
) (x float
)) ¶vector-unsigned-byte-64
) (x float
)) ¶vector-signed-byte-64
) (x float
)) ¶vector-unsigned-byte-32
) (x float
)) ¶vector-signed-byte-32
) (x float
)) ¶vector-unsigned-byte-16
) (x float
)) ¶vector-signed-byte-16
) (x float
)) ¶vector-unsigned-byte-8
) (x float
)) ¶vector-signed-byte-8
) (x float
)) ¶vector-double-float
) (x float
)) ¶vector-single-float
) (x float
)) ¶matrix-unsigned-byte-64
) (b matrix-unsigned-byte-64
)) ¶matrix-signed-byte-64
) (b matrix-signed-byte-64
)) ¶matrix-unsigned-byte-32
) (b matrix-unsigned-byte-32
)) ¶matrix-signed-byte-32
) (b matrix-signed-byte-32
)) ¶matrix-unsigned-byte-16
) (b matrix-unsigned-byte-16
)) ¶matrix-signed-byte-16
) (b matrix-signed-byte-16
)) ¶matrix-unsigned-byte-8
) (b matrix-unsigned-byte-8
)) ¶matrix-signed-byte-8
) (b matrix-signed-byte-8
)) ¶matrix-double-float
) (b matrix-double-float
)) ¶matrix-single-float
) (b matrix-single-float
)) ¶vector-single-float
) (b vector-single-float
)) ¶vector-double-float
) (b vector-double-float
)) ¶vector-complex-single-float
) (b vector-complex-single-float
)) ¶vector-complex-double-float
) (b vector-complex-double-float
)) ¶vector-signed-byte-8
) (b vector-signed-byte-8
)) ¶vector-unsigned-byte-8
) (b vector-unsigned-byte-8
)) ¶vector-signed-byte-16
) (b vector-signed-byte-16
)) ¶vector-unsigned-byte-16
) (b vector-unsigned-byte-16
)) ¶vector-signed-byte-32
) (b vector-signed-byte-32
)) ¶vector-unsigned-byte-32
) (b vector-unsigned-byte-32
)) ¶vector-signed-byte-64
) (b vector-signed-byte-64
)) ¶vector-unsigned-byte-64
) (b vector-unsigned-byte-64
)) ¶Add the elements of b to the elements of vector a The two must have the same dimensions.
gsll
.
histogram2d
) (histogram2 histogram2d
)) ¶Add the contents of the bins in histogram2 to the
corresponding bins of histogram1 i.e. h’_1(i) =
h_1(i) + h_2(i). The two histograms must have identical bin
ranges.
histogram
) (histogram2 histogram
)) ¶Add the contents of the bins in histogram2 to the
corresponding bins of histogram1 i.e. h’_1(i) =
h_1(i) + h_2(i). The two histograms must have identical bin
ranges.
float
) (a foreign-array
)) ¶matrix-complex-double-float
) (x complex
)) ¶matrix-complex-single-float
) (x complex
)) ¶vector-complex-double-float
) (x complex
)) ¶vector-complex-single-float
) (x complex
)) ¶matrix-unsigned-byte-64
) (x float
)) ¶matrix-signed-byte-64
) (x float
)) ¶matrix-unsigned-byte-32
) (x float
)) ¶matrix-signed-byte-32
) (x float
)) ¶matrix-unsigned-byte-16
) (x float
)) ¶matrix-signed-byte-16
) (x float
)) ¶matrix-unsigned-byte-8
) (x float
)) ¶matrix-signed-byte-8
) (x float
)) ¶matrix-double-float
) (x float
)) ¶matrix-single-float
) (x float
)) ¶vector-unsigned-byte-64
) (x float
)) ¶vector-signed-byte-64
) (x float
)) ¶vector-unsigned-byte-32
) (x float
)) ¶vector-signed-byte-32
) (x float
)) ¶vector-unsigned-byte-16
) (x float
)) ¶vector-signed-byte-16
) (x float
)) ¶vector-unsigned-byte-8
) (x float
)) ¶vector-signed-byte-8
) (x float
)) ¶vector-double-float
) (x float
)) ¶vector-single-float
) (x float
)) ¶vector-single-float
) (b vector-single-float
)) ¶vector-double-float
) (b vector-double-float
)) ¶vector-complex-single-float
) (b vector-complex-single-float
)) ¶vector-complex-double-float
) (b vector-complex-double-float
)) ¶vector-signed-byte-8
) (b vector-signed-byte-8
)) ¶vector-unsigned-byte-8
) (b vector-unsigned-byte-8
)) ¶vector-signed-byte-16
) (b vector-signed-byte-16
)) ¶vector-unsigned-byte-16
) (b vector-unsigned-byte-16
)) ¶vector-signed-byte-32
) (b vector-signed-byte-32
)) ¶vector-unsigned-byte-32
) (b vector-unsigned-byte-32
)) ¶vector-signed-byte-64
) (b vector-signed-byte-64
)) ¶vector-unsigned-byte-64
) (b vector-unsigned-byte-64
)) ¶matrix-single-float
) (b matrix-single-float
)) ¶matrix-double-float
) (b matrix-double-float
)) ¶matrix-complex-single-float
) (b matrix-complex-single-float
)) ¶matrix-complex-double-float
) (b matrix-complex-double-float
)) ¶matrix-signed-byte-8
) (b matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
) (b matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
) (b matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
) (b matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
) (b matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
) (b matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
) (b matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
) (b matrix-unsigned-byte-64
)) ¶Subtract the elements of b from the elements of a. The two must have the same dimensions.
gsll
.
histogram2d
) (histogram2 histogram2d
)) ¶Subtract the contents of the bins in histogram2 from the corresponding bins of histogram1 i.e. h’_1(i) = h_1(i) - h_2(i). The two histograms must have identical bin ranges.
histogram
) (histogram2 histogram
)) ¶Subtract the contents of the bins in histogram2 from the corresponding bins of histogram1 i.e. h’_1(i) = h_1(i) - h_2(i). The two histograms must have identical bin ranges.
foreign-array
) (x float
)) ¶vector-single-float
) (b vector-single-float
)) ¶vector-double-float
) (b vector-double-float
)) ¶vector-complex-single-float
) (b vector-complex-single-float
)) ¶vector-complex-double-float
) (b vector-complex-double-float
)) ¶vector-signed-byte-8
) (b vector-signed-byte-8
)) ¶vector-unsigned-byte-8
) (b vector-unsigned-byte-8
)) ¶vector-signed-byte-16
) (b vector-signed-byte-16
)) ¶vector-unsigned-byte-16
) (b vector-unsigned-byte-16
)) ¶vector-signed-byte-32
) (b vector-signed-byte-32
)) ¶vector-unsigned-byte-32
) (b vector-unsigned-byte-32
)) ¶vector-signed-byte-64
) (b vector-signed-byte-64
)) ¶vector-unsigned-byte-64
) (b vector-unsigned-byte-64
)) ¶matrix-single-float
) (b matrix-single-float
)) ¶matrix-double-float
) (b matrix-double-float
)) ¶matrix-complex-single-float
) (b matrix-complex-single-float
)) ¶matrix-complex-double-float
) (b matrix-complex-double-float
)) ¶matrix-signed-byte-8
) (b matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
) (b matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
) (b matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
) (b matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
) (b matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
) (b matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
) (b matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
) (b matrix-unsigned-byte-64
)) ¶Divide the elements of a by the elements of b. The two must have the same dimensions.
gsll
.
histogram2d
) (histogram2 histogram2d
)) ¶Divide the contents of the bins of histogram1 by the contents of the corresponding bins in histogram2 i.e. h’_1(i) = h_1(i) / h_2(i). The two histograms must have identical bin ranges.
histogram
) (histogram2 histogram
)) ¶Divide the contents of the bins of histogram1 by the contents of the corresponding bins in histogram2 i.e. h’_1(i) = h_1(i) / h_2(i). The two histograms must have identical bin ranges.
foreign-array
) (x number
)) ¶matrix-unsigned-byte-64
) (b matrix-unsigned-byte-64
)) ¶matrix-signed-byte-64
) (b matrix-signed-byte-64
)) ¶matrix-unsigned-byte-32
) (b matrix-unsigned-byte-32
)) ¶matrix-signed-byte-32
) (b matrix-signed-byte-32
)) ¶matrix-unsigned-byte-16
) (b matrix-unsigned-byte-16
)) ¶matrix-signed-byte-16
) (b matrix-signed-byte-16
)) ¶matrix-unsigned-byte-8
) (b matrix-unsigned-byte-8
)) ¶matrix-signed-byte-8
) (b matrix-signed-byte-8
)) ¶matrix-double-float
) (b matrix-double-float
)) ¶matrix-single-float
) (b matrix-single-float
)) ¶vector-single-float
) (b vector-single-float
)) ¶vector-double-float
) (b vector-double-float
)) ¶vector-complex-single-float
) (b vector-complex-single-float
)) ¶vector-complex-double-float
) (b vector-complex-double-float
)) ¶vector-signed-byte-8
) (b vector-signed-byte-8
)) ¶vector-unsigned-byte-8
) (b vector-unsigned-byte-8
)) ¶vector-signed-byte-16
) (b vector-signed-byte-16
)) ¶vector-unsigned-byte-16
) (b vector-unsigned-byte-16
)) ¶vector-signed-byte-32
) (b vector-signed-byte-32
)) ¶vector-unsigned-byte-32
) (b vector-unsigned-byte-32
)) ¶vector-signed-byte-64
) (b vector-signed-byte-64
)) ¶vector-unsigned-byte-64
) (b vector-unsigned-byte-64
)) ¶Are all of the individual bin ranges of the two histograms are identical?
gsll
.
histogram2d
) (histogram2 histogram2d
)) ¶The Euclidean norm ||x||_2 = sqrt {sum x_i^2} of the vector x.
Evaluate the GSL object.
gsll
.
basis-spline
) x &key b) ¶Evaluate all B-spline basis functions at the position x and store
them in the GSL vector B, so that the ith element of B is B_i(x).
B must be of length n = nbreak + k - 2. This value is
also stored in the workspace. It is far more
efficient to compute all of the basis functions at once than to
compute them individually, due to the nature of the defining
recurrence relation.
chebyshev
) x &key order) ¶Evaluate the Chebyshev series at a point x. If order is supplied, evaluate to at most the given order.
interpolation
) x &key xa ya acceleration) ¶Find the interpolated value of y for a given
point x, using the interpolation object interpolation, data arrays
xa and ya and the accelerator acceleration.
vector-complex-double-float
) (x complex
) &key) ¶Evaluate the polyonomial with coefficients at the complex value x.
vector-double-float
) (x complex
) &key) ¶Evaluate the polyonomial with coefficients at the complex value x.
vector-double-float
) (x float
) &key divided-difference) ¶Evaluate the polyonomial with coefficients at the point x.
Find the derivative of an interpolated function for a given point x, using the interpolation object interpolation, data arrays xa and ya and the accelerator acceleration.
gsll
.
interpolation
) x &key xa ya acceleration) ¶Find the numerical integral of an interpolated function over the range [low, high], using the interpolation object interpolation, data arrays xa and ya and the accelerator ’acceleration.
gsll
.
interpolation
) low high &key xa ya acceleration) ¶Find the second derivative of an interpolated function for a given point
x, using the interpolation object interpolation, data arrays
xa and ya and the accelerator acceleration.
gsll
.
interpolation
) x &key xa ya acceleration) ¶Forward discrete Fourier transform provided to check the FFT routines.
The current value of the function that solves this object.
gsll
.
nonlinear-fdffit
)) ¶multi-dimensional-minimizer-fdf
)) ¶The current best estimate of the value of the minimum.
multi-dimensional-minimizer-f
)) ¶The current best estimate of the value of the minimum.
multi-dimensional-root-solver-fdf
)) ¶The function value f(x) at the current estimate x of the root for the solver.
multi-dimensional-root-solver-f
)) ¶The function value f(x) at the current estimate x of the root for the solver.
one-dimensional-minimizer
)) ¶The value of the function at the current estimate of the minimum for the minimizer.
These functions compute a Givens rotation (c,s) to the vector (x,y),
[ c s ] [ x ] = [ r ]
[ -s c ] [ y ] [ 0 ]
The variables x and y are overwritten by the routine.
These functions compute a Givens rotation (c,s) to the vector (x,y),
[ c s ] [ x ] = [ r ]
[ -s c ] [ y ] [ 0 ]
The variables x and y are overwritten by the routine.
The cosine function cos(x).
The natural logarithm of x, log(x), for x > 0.
The sine function sin(x).
If the first argument is a vector,
compute the hermitian rank-1 update A = alpha x x^H + A of the
hermitian matrix A. Since the matrix A is hermitian only its upper
half or lower half need to be stored. When Uplo is :upper then the
upper triangle and diagonal of A are used, and when Uplo is
:lower then the lower triangle and diagonal of A are used. The
imaginary elements of the diagonal are automatically set to zero.
If the first argument is a matrix, compute a rank-k update of the
hermitian matrix C, C = alpha A A^H + beta C when Trans is
:notrans and C = alpha A^H A + beta C when Trans is
:trans. Since the matrix C is hermitian only its upper half or
lower half need to be stored. When Uplo is :upper then the upper
triangle and diagonal of C are used, and when Uplo is :lower
then the lower triangle and diagonal of C are used. The imaginary
elements of the diagonal are automatically set to zero.
gsll
.
matrix-complex-double-float
) (c matrix-complex-double-float
) &optional alpha beta uplo trans) ¶matrix-complex-single-float
) (c matrix-complex-single-float
) &optional alpha beta uplo trans) ¶vector-complex-single-float
) (a matrix-complex-single-float
) &optional alpha beta uplo trans) ¶vector-complex-double-float
) (a matrix-complex-double-float
) &optional alpha beta uplo trans) ¶If the first two arguments are vectors, compute the
hermitian rank-2 update A = alpha x y^H + alpha^* y x^H A of
the hermitian matrix A. Since the matrix A is hermitian only its
upper half or lower half need to be stored. When uplo is :upper
then the upper triangle and diagonal of A are used, and when uplo is
:lower then the lower triangle and diagonal of A are used. The
imaginary elements of the diagonal are automatically set to zero.
If the first two arguments are matrices, compute a rank-2k update of
the hermitian matrix C, C = alpha A B^H + alpha^* B A^H + beta C
when Trans is :notrans and C = alpha A^H B + alpha^* B^H A +
beta C when Trans is :conjtrans. Since the matrix C is
hermitian only its upper half or lower half need to be stored. When
Uplo is :upper then the upper triangle and diagonal of C are
used, and when Uplo is :lower then the lower triangle and
diagonal of C are used. The imaginary elements of the diagonal are
automatically set to zero.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) (c matrix-complex-double-float
) &optional alpha beta uplo trans) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) (c matrix-complex-single-float
) &optional alpha beta uplo trans) ¶vector-complex-single-float
) (y vector-complex-single-float
) (a matrix-complex-single-float
) &optional alpha beta uplo trans) ¶vector-complex-double-float
) (y vector-complex-double-float
) (a matrix-complex-double-float
) &optional alpha beta uplo trans) ¶The confluent hypergeometric function 1F1(m,n,x) = M(m,n,x).
gsll
.
float
) (b float
) x) ¶The confluent hypergeometric function
1F1(a,b,x) = M(a,b,x) for general parameters a, b.
integer
) (n integer
) x) ¶The confluent hypergeometric function 1F1(m,n,x) = M(m,n,x) for integer parameters m, n.
The confluent hypergeometric function U(m,n,x).
The confluent hypergeometric function
U(m,n,x) that returns a result with extended range.
gsll
.
float
) (b float
) x) ¶The confluent hypergeometric function
U(a,b,x) using that returns a result with extended range.
integer
) (n integer
) x) ¶The confluent hypergeometric function
U(m,n,x) for integer parameters m, n that returns a
result with extended range.
Update the histogram by adding the weight
(which defaults to 1.0) to the
bin whose range contains the coordinate x.
If x lies in the valid range of the histogram then the function
returns zero to indicate success. If x is less than the lower
limit of the histogram then the function issues a warning input-domain, and
none of bins are modified. Similarly, if the value of x is greater
than or equal to the upper limit of the histogram then the function
issues a warning input-domain, and none of the bins are modified. The error
handler is not called, however, since it is often necessary to compute
histograms for a small range of a larger dataset, ignoring the values
outside the range of interest.
gsll
.
histogram2d
) values &optional weight) ¶The index of the largest element of the vector
x. The largest element is determined by its absolute magnitude for
real vectors and by the sum of the magnitudes of the real and
imaginary parts |Re(x_i)| + |Im(x_i)| for complex vectors. If the
largest value occurs several times then the index of the first
occurrence is returned.
Inverse discrete Fourier transform provided to check the FFT routines.
If the second argument is a vector, compute
inv(op(A)) x for x, where op(A) = A, A^T, A^H for
TransA = :NoTrans, :Trans, :ConjTrans. When Uplo is
:Upper then the upper triangle of A is used, and when Uplo is
:Lower then the lower triangle of A is used. If Diag is
:NonUnit then the diagonal of the matrix is used, but if Diag
is :Unit then the diagonal elements of the matrix A are taken
as unity and are not referenced.
If the second argument is a matrix, compute
the inverse-matrix matrix product B = alpha op(inv(A))B if
Side is :Left and B = alpha B op(inv(A)) if Side is
:Right. The matrix A is triangular and op(A) = A, A^T, A^H
for TransA = :NoTrans, :Trans, :ConjTrans When
Uplo is :Upper then the upper triangle of A is used, and
when Uplo is :Lower then the lower triangle of A is
used. If Diag is :NonUnit then the diagonal of A is used,
but if Diag is :Unit then the diagonal elements of the
matrix A are taken as unity and are not referenced.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) &optional alpha uplo transa diag side) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) &optional alpha uplo transa diag side) ¶matrix-double-float
) (b matrix-double-float
) &optional alpha uplo transa diag side) ¶matrix-single-float
) (b matrix-single-float
) &optional alpha uplo transa diag side) ¶matrix-single-float
) (x vector-single-float
) &optional alpha uplo transa diag side) ¶matrix-double-float
) (x vector-double-float
) &optional alpha uplo transa diag side) ¶matrix-complex-single-float
) (x vector-complex-single-float
) &optional alpha uplo transa diag side) ¶matrix-complex-double-float
) (x vector-complex-double-float
) &optional alpha uplo transa diag side) ¶Take the next iteration step for this object.
gsll
.
nonlinear-fdffit
)) ¶Perform a single iteration of the solver. The solver maintains a current estimate of the best-fit parameters at all times.
nonlinear-ffit
)) ¶Perform a single iteration of the solver. The solver maintains a current estimate of the best-fit parameters at all times.
multi-dimensional-minimizer-fdf
)) ¶Perform a single iteration of the minimizer. If the iteration encounters an unexpected problem then an error code will be returned.
multi-dimensional-minimizer-f
)) ¶Perform a single iteration of the minimizer. If the iteration encounters an unexpected problem then an error code will be returned.
multi-dimensional-root-solver-fdf
)) ¶Perform a single iteration of the solver. The following errors may be signalled: ’bad-function-supplied, the iteration encountered a singular point where the function or its derivative evaluated to infinity or NaN, or ’gsl-division-by-zero, the derivative of the function vanished at the iteration point, preventing the algorithm from continuing without a division by zero.
multi-dimensional-root-solver-f
)) ¶Perform a single iteration of the solver. The following errors may be signalled: ’bad-function-supplied, the iteration encountered a singular point where the function or its derivative evaluated to infinity or NaN, or ’gsl-division-by-zero, the derivative of the function vanished at the iteration point, preventing the algorithm from continuing without a division by zero.
one-dimensional-minimizer
)) ¶Perform a single iteration of the minimizer. The following
errors may be signalled: ’bad-function-supplied,
the iteration encountered a singular point where the function or its
derivative evaluated to infinity or NaN, or
:FAILURE, the algorithm could not improve the current best approximation or
bounding interval.
one-dimensional-root-solver-fdf
)) ¶Perform a single iteration of the solver. The following errors may be signalled: ’bad-function-supplied, the iteration encountered a singular point where the function or its derivative evaluated to infinity or NaN, or ’gsl-division-by-zero, the derivative of the function vanished at the iteration point, preventing the algorithm from continuing without a division by zero.
one-dimensional-root-solver-f
)) ¶Perform a single iteration of the solver. The following errors may be signalled: ’bad-function-supplied, the iteration encountered a singular point where the function or its derivative evaluated to infinity or NaN, or ’gsl-division-by-zero, the derivative of the function vanished at the iteration point, preventing the algorithm from continuing without a division by zero.
The kurtosis of data defined as
kurtosis = ((1/N) sum ((x_i - Hatmu)/Hatsigma)^4) - 3
The kurtosis measures how sharply peaked a distribution is,
relative to its width. The kurtosis is normalized to zero
for a gaussian distribution.
gsll
.
vector-single-float
) &optional mean standard-deviation) ¶vector-double-float
) &optional mean standard-deviation) ¶vector-signed-byte-8
) &optional mean standard-deviation) ¶vector-unsigned-byte-8
) &optional mean standard-deviation) ¶vector-signed-byte-16
) &optional mean standard-deviation) ¶vector-unsigned-byte-16
) &optional mean standard-deviation) ¶vector-signed-byte-32
) &optional mean standard-deviation) ¶vector-unsigned-byte-32
) &optional mean standard-deviation) ¶vector-signed-byte-64
) &optional mean standard-deviation) ¶vector-unsigned-byte-64
) &optional mean standard-deviation) ¶The last step dx taken by the solver.
gsll
.
nonlinear-fdffit
)) ¶multi-dimensional-root-solver-fdf
)) ¶The last step dx taken by the solver.
multi-dimensional-root-solver-f
)) ¶The last step dx taken by the solver.
Factorize the square matrix A into the LU decomposition PA = LU,
and return the sign of the permutation. On output the diagonal and
upper triangular part of the input matrix A contain the matrix U.
The lower triangular part of the input matrix (excluding the
diagonal) contains L. The diagonal elements of L are unity, and are
not stored.
The permutation matrix P is encoded in the permutation supplied as
the second argument and returned as the second value. The j-th
column of the matrix P is given by the k-th column of the identity
matrix, where k = p_j the j-th element of the permutation
vector. The sign of the permutation is returned as the second value;
it is the value (-1)^n, where n is the number of interchanges in the
permutation.
The algorithm used in the decomposition is Gaussian Elimination with partial pivoting (Golub & Van Loan, Matrix Computations, Algorithm 3.4.1).
Compute the determinant of a matrix from its LU
decomposition, LU. The determinant is computed as the product of the
diagonal elements of U and the sign of the row permutation signum.
Compute the inverse of a matrix A from its LU
decomposition (LU,p), storing the result in the matrix inverse. The
inverse is computed by solving the system A x = b for each column of
the identity matrix. It is preferable to avoid direct use of the
inverse whenever possible, as the linear solver functions can obtain
the same result more efficiently and reliably (consult any
introductory textbook on numerical linear algebra for details).
The logarithm of the absolute value of the
determinant of a matrix A, ln|det(A)|, from its LU decomposition,
LU. This function may be useful if the direct computation of the
determinant would overflow or underflow.
Apply an iterative improvement to x, the solution of
A x = b, using the LU decomposition of A into (LU,p). The initial
residual r = A x - b is also computed and stored in residual.
Compute the sign or phase factor of the determinant of a matrix A, det(A)/|det(A)|, from its LU decomposition, LU.
Solve the square system A x = b using the LU
decomposition of A into (LU, p) given by LU-decomp.
If x-spec is nil, the solution will be computed in-place replacing b,
if it is T, an appropriate vector will be created and the solution
will be computed there. Otherwise it should be a supplied vector.
If the second and third arguments are vectors, compute
the matrix-vector product and sum
y = alpha op(A) x + beta y, where op(A) = A, A^T, A^H
for TransA = :notrans, :trans, :conjtrans.
If the second and third arguments are matrices, compute
the matrix-matrix product and sum C = alpha
op(A) op(B) + beta C where op(A) = A, A^T, A^H for TransA =
:notrans, :trans, :conjtrans and similarly for the
parameter TransB.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) &optional c alpha beta transa transb) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) &optional c alpha beta transa transb) ¶matrix-double-float
) (b matrix-double-float
) &optional c alpha beta transa transb) ¶matrix-single-float
) (b matrix-single-float
) &optional c alpha beta transa transb) ¶matrix-single-float
) (x vector-single-float
) &optional y alpha beta transa transb) ¶matrix-double-float
) (x vector-double-float
) &optional y alpha beta transa transb) ¶matrix-complex-single-float
) (x vector-complex-single-float
) &optional y alpha beta transa transb) ¶matrix-complex-double-float
) (x vector-complex-double-float
) &optional y alpha beta transa transb) ¶If the second and third arguments are vectors, compute the
matrix-vector product and sum y = alpha A x + beta y for the
hermitian matrix A. Since the matrix A is hermitian only its upper
half or lower half need to be stored. When Uplo is :upper then
the upper triangle and diagonal of A are used, and when Uplo is
:lower then the lower triangle and diagonal of A are used. The
imaginary elements of the diagonal are automatically assumed to be
zero and are not referenced. If the second and third arguments are
matrices, compute the matrix-matrix product and sum C = alpha A B +
beta C if Side is :left and C = alpha B A + beta C if Side
is :right, where the matrix A is hermitian. When Uplo is
:upper then the upper triangle and diagonal of A are used, and
when Uplo is :lower then the lower triangle and diagonal of A
are used. The imaginary elements of the diagonal are automatically
set to zero.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) &optional c alpha beta uplo side) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) &optional c alpha beta uplo side) ¶matrix-complex-single-float
) (x vector-complex-single-float
) &optional y alpha beta uplo side) ¶matrix-complex-double-float
) (x vector-complex-double-float
) &optional y alpha beta uplo side) ¶If the second and third arguments are vectors, compute
the matrix-vector product and sum y = alpha A
x + beta y for the symmetric matrix A. Since the matrix A is
symmetric only its upper half or lower half need to be
stored. When Uplo is :Upper then the upper triangle and
diagonal of A are used, and when Uplo is :Lower then the
lower triangle and diagonal of A are used.
If the second and third arguments are matrices, compute
the matrix-matrix product and sum C = alpha A
B + beta C for Side is :Left and C = alpha B A + beta C
for Side is :Right, where the matrix A is symmetric. When
Uplo is :Upper then the upper triangle and diagonal of A
are used, and when Uplo is :Lower then the lower triangle
and diagonal of A are used.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) &optional c alpha beta uplo side) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) &optional c alpha beta uplo side) ¶matrix-double-float
) (b matrix-double-float
) &optional c alpha beta uplo side) ¶matrix-single-float
) (b matrix-single-float
) &optional c alpha beta uplo side) ¶matrix-single-float
) (x vector-single-float
) &optional y alpha beta uplo side) ¶matrix-double-float
) (x vector-double-float
) &optional y alpha beta uplo side) ¶If the second argument is a vector, compute
the matrix-vector product x = op(A) x
for the triangular matrix A, where op(A) = A, A^T, A^H for
TransA = :NoTrans, :Trans, :ConjTrans. When Uplo
is :Upper then the upper triangle of A is used, and when
Uplo is :Lower then the lower triangle of A is used. If
Diag is :NonUnit then the diagonal of the matrix is used,
but if Diag is :Unit then the diagonal elements of the
matrix A are taken as unity and are not referenced.
If the second argument is a matrix, compute
the matrix-matrix product B = alpha op(A) B
if Side is :Left and B = alpha B op(A) if Side is
:Right. The matrix A is triangular and op(A) = A, A^T, A^H
for TransA = :NoTrans, :Trans, :ConjTrans When Uplo
is :Upper then the upper triangle of A is used, and when
Uplo is :Lower then the lower triangle of A is used. If
Diag is :NonUnit then the diagonal of A is used, but if
Diag is :Unit then the diagonal elements of the matrix A
are taken as unity and are not referenced.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) &optional alpha uplo transa diag side) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) &optional alpha uplo transa diag side) ¶matrix-double-float
) (b matrix-double-float
) &optional alpha uplo transa diag side) ¶matrix-single-float
) (b matrix-single-float
) &optional alpha uplo transa diag side) ¶matrix-single-float
) (x vector-single-float
) &optional alpha uplo transa diag side) ¶matrix-double-float
) (x vector-double-float
) &optional alpha uplo transa diag side) ¶matrix-complex-single-float
) (x vector-complex-single-float
) &optional alpha uplo transa diag side) ¶matrix-complex-double-float
) (x vector-complex-double-float
) &optional alpha uplo transa diag side) ¶Make the destination matrix the transpose of the source matrix by copying the elements. The dimensions of the destination matrix must match the transposed dimensions of the source.
gsll
.
matrix-single-float
) &optional destination) ¶matrix-double-float
) &optional destination) ¶matrix-complex-single-float
) &optional destination) ¶matrix-complex-double-float
) &optional destination) ¶matrix-signed-byte-8
) &optional destination) ¶matrix-unsigned-byte-8
) &optional destination) ¶matrix-signed-byte-16
) &optional destination) ¶matrix-unsigned-byte-16
) &optional destination) ¶matrix-signed-byte-32
) &optional destination) ¶matrix-unsigned-byte-32
) &optional destination) ¶matrix-signed-byte-64
) &optional destination) ¶matrix-unsigned-byte-64
) &optional destination) ¶Replace the matrix by its transpose by copying the elements of the matrix in-place. The matrix must be square for this operation to be possible.
gsll
.
matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The index of the maximum value in a. When there are several equal maximum elements, then the lowest index is returned.
gsll
.
histogram2d
)) ¶The indices of the bin containing the maximum value. In the case where several bins contain the same maximum value the first bin found is returned.
histogram
)) ¶The index of the bin containing the maximum value. In the case where several bins contain the same maximum value the smallest index is returned.
matrix-unsigned-byte-64
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-8
)) ¶matrix-double-float
)) ¶matrix-single-float
)) ¶vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The maximum upper range limit(s) of the histogram.
gsll
.
histogram2d
)) ¶The arithmetic mean of the array.
The arithmetic mean, or sample mean, is denoted by
Hatmu and defined as Hatmu = (1/N) sum x_i. Returns a double-float.
gsll
.
histogram2d
)) ¶histogram
)) ¶The mean of the histogrammed variable, where the histogram is regarded as a probability distribution. Negative bin values are ignored for the purposes of this calculation. The resolution of the result is limited by the bin width.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The median value of sorted-data. The elements of the array
must be in ascending numerical order. There are no checks to see
whether the data are sorted, so the function #’sort should
always be used first.
When the dataset has an odd number of elements the median is the value
of element (n-1)/2. When the dataset has an even number of
elements the median is the mean of the two nearest middle values,
elements (n-1)/2 and n/2. Since the algorithm for
computing the median involves interpolation this function always returns
a floating-point number, even for integer data types.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The index of the minimum value in a. When there are several equal minimum elements, then the lowest index is returned.
gsll
.
histogram2d
)) ¶The indices of the bin containing the minimum value. In the case where several bins contain the same minimum value the first bin found is returned.
histogram
)) ¶The index of the bin containing the minimum value. In the case where several bins contain the same minimum value the smallest index is returned.
matrix-unsigned-byte-64
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-8
)) ¶matrix-double-float
)) ¶matrix-single-float
)) ¶vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The minimum lower range limit(s) of the histogram.
gsll
.
histogram2d
)) ¶The minimum number of points required by the interpolation. For example, Akima spline interpolation requires a minimum of 5 points.
gsll
.
interpolation
)) ¶The minimum and maximum values in a.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The indices of the minimum and maximum values in a.
When there are several equal minimum elements then the lowest index is
returned. Returned indices are minimum, maximum; for matrices
imin, jmin, imax, jmax.
gsll
.
matrix-unsigned-byte-64
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-8
)) ¶matrix-double-float
)) ¶matrix-single-float
)) ¶vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The maximum value in a.
gsll
.
histogram2d
)) ¶The maximum value contained in the histogram bins.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The minimum value in a.
gsll
.
histogram2d
)) ¶The minimum value contained in the histogram bins.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶All elements of a are negative.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-complex-single-float
)) ¶vector-complex-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶Not explained
gsll
.
vector-single-float
) (d2 vector-single-float
) (b1 vector-single-float
) b2 (p vector-single-float
)) ¶vector-double-float
) (d2 vector-double-float
) (b1 vector-double-float
) b2 (p vector-double-float
)) ¶Not explained
All elements of a are positive.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-complex-single-float
)) ¶vector-complex-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶Sort the n elements of the array data with stride stride into ascending numerical order.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶All elements of a are zero.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-complex-single-float
)) ¶vector-complex-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The name given to the GSL object.
gsll
.
nonlinear-fdffit
)) ¶The name of the solver type.
nonlinear-ffit
)) ¶The name of the solver type.
multi-dimensional-minimizer-fdf
)) ¶The name of the minimizer.
multi-dimensional-minimizer-f
)) ¶The name of the minimizer.
multi-dimensional-root-solver-fdf
)) ¶The name of the solver.
multi-dimensional-root-solver-f
)) ¶The name of the solver.
one-dimensional-minimizer
)) ¶The name of the minimizer.
one-dimensional-root-solver-fdf
)) ¶The name of the solver.
one-dimensional-root-solver-f
)) ¶The name of the solver.
interpolation
)) ¶The name of the interpolation type.
ode-control
)) ¶The name of the control function.
ode-stepper
)) ¶The name of the stepping function.
quasi-random-number-generator
)) ¶random-number-generator
)) ¶obsolete-gsl-version
)) ¶name
.
All elements of a are non-negative.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-complex-single-float
)) ¶vector-complex-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The order of the GSL object.
gsll
.
basis-spline
)) ¶Get the value of the GSL parameter from the GSL object.
gsll
.
monte-carlo-vegas
) parameter) ¶monte-carlo-miser
) parameter) ¶Set the value of the GSL parameter from the GSL object.
gsll
.
monte-carlo-vegas
) parameter) ¶monte-carlo-miser
) parameter) ¶Apply the permutation p to the elements of the
vector v considered as a row-vector acted on by a permutation
matrix from the right, v’ = v P. The jth column of the
permutation matrix P is given by the p_j-th column of the
identity matrix. The permutation p and the vector v must
have the same length.
gsll
.
system-area-pointer
) &optional size stride) ¶Apply the permutation p to the array data of size n with stride stride.
permutation
) (v vector-single-float
) &optional size stride) ¶permutation
) (v vector-double-float
) &optional size stride) ¶permutation
) (v vector-complex-single-float
) &optional size stride) ¶permutation
) (v vector-complex-double-float
) &optional size stride) ¶permutation
) (v vector-signed-byte-8
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-8
) &optional size stride) ¶permutation
) (v vector-signed-byte-16
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-16
) &optional size stride) ¶permutation
) (v vector-signed-byte-32
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-32
) &optional size stride) ¶permutation
) (v vector-signed-byte-64
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-64
) &optional size stride) ¶Apply the permutation p to the elements of the vector v considered as a row-vector acted on by a permutation matrix from the right, v’ = v P. The jth column of the permutation matrix P is given by the p_j-th column of the identity matrix. The permutation p and the vector v must have the same length.
gsll
.
system-area-pointer
) &optional size stride) ¶Apply the inverse of the permutation p to the array data of size n with stride.
permutation
) (v vector-single-float
) &optional size stride) ¶permutation
) (v vector-double-float
) &optional size stride) ¶permutation
) (v vector-complex-single-float
) &optional size stride) ¶permutation
) (v vector-complex-double-float
) &optional size stride) ¶permutation
) (v vector-signed-byte-8
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-8
) &optional size stride) ¶permutation
) (v vector-signed-byte-16
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-16
) &optional size stride) ¶permutation
) (v vector-signed-byte-32
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-32
) &optional size stride) ¶permutation
) (v vector-signed-byte-64
) &optional size stride) ¶permutation
) (v vector-unsigned-byte-64
) &optional size stride) ¶The psi, or digamma, function.
The Trigamma function.
A quantile value of sorted-data. The
elements of the array must be in ascending numerical order. The
quantile is determined by a fraction between 0 and 1. For
example, to compute the value of the 75th percentile
’fraction should have the value 0.75.
There are no checks to see whether the data are sorted, so the function
#’sort should always be used first.
hbox{quantile} = (1 - delta) x_i + delta x_{i+1}
where i is floor((n - 1)f) and delta is (n-1)f - i.
Thus the minimum value of the array (data[0*stride]) is given by
’fraction equal to zero, the maximum value (data[(n-1)*stride]) is
given by ’fraction equal to one and the median value is given by ’fraction
equal to 0.5. Since the algorithm for computing quantiles involves
interpolation this function always returns a floating-point number, even
for integer data types.
gsll
.
vector-single-float
) fraction) ¶vector-double-float
) fraction) ¶vector-signed-byte-8
) fraction) ¶vector-unsigned-byte-8
) fraction) ¶vector-signed-byte-16
) fraction) ¶vector-unsigned-byte-16
) fraction) ¶vector-signed-byte-32
) fraction) ¶vector-unsigned-byte-32
) fraction) ¶vector-signed-byte-64
) fraction) ¶vector-unsigned-byte-64
) fraction) ¶Find the upper and lower range limits of the i-th
bin of the histogram. If the index i is valid then the
corresponding range limits are stored in lower and upper.
The lower limit is inclusive (i.e. events with this coordinate are
included in the bin) and the upper limit is exclusive (i.e. events with
the coordinate of the upper limit are excluded and fall in the
neighboring higher bin, if it exists).
If i lies outside the valid range of indices for
the histogram, then the error input-domain is signalled.
gsll
.
histogram2d
) i) ¶The rank-1 update A = alpha x y^T + A of the matrix A.
gsll
.
vector-single-float
) (y vector-single-float
) (a matrix-single-float
)) ¶vector-double-float
) (y vector-double-float
) (a matrix-double-float
)) ¶vector-complex-single-float
) (y vector-complex-single-float
) (a matrix-complex-single-float
)) ¶vector-complex-double-float
) (y vector-complex-double-float
) (a matrix-complex-double-float
)) ¶A pointer to the state of generator.
gsll
.
quasi-random-number-generator
)) ¶random-number-generator
)) ¶Copy the elements of the ith row of the matrix
into the vector. The length of the vector must be the
same as the length of the row.
gsll
.
matrix-single-float
) i &optional vector) ¶matrix-double-float
) i &optional vector) ¶matrix-complex-single-float
) i &optional vector) ¶matrix-complex-double-float
) i &optional vector) ¶matrix-signed-byte-8
) i &optional vector) ¶matrix-unsigned-byte-8
) i &optional vector) ¶matrix-signed-byte-16
) i &optional vector) ¶matrix-unsigned-byte-16
) i &optional vector) ¶matrix-signed-byte-32
) i &optional vector) ¶matrix-unsigned-byte-32
) i &optional vector) ¶matrix-signed-byte-64
) i &optional vector) ¶matrix-unsigned-byte-64
) i &optional vector) ¶Copy the elements of the vector into the jth row of the matrix. The length of the vector must be the same as the length of the row.
gsll
.
matrix-single-float
) i) ¶matrix-double-float
) i) ¶matrix-complex-single-float
) i) ¶matrix-complex-double-float
) i) ¶matrix-signed-byte-8
) i) ¶matrix-unsigned-byte-8
) i) ¶matrix-signed-byte-16
) i) ¶matrix-unsigned-byte-16
) i) ¶matrix-signed-byte-32
) i) ¶matrix-unsigned-byte-32
) i) ¶matrix-signed-byte-64
) i) ¶matrix-unsigned-byte-64
) i) ¶Sample from the probability distribution.
gsll
.
random-number-generator
) (pdf histogram2d-pdf
) &key) ¶random-number-generator
) (pdf histogram-pdf
) &key) ¶number
) (pdf histogram2d-pdf
) &key) ¶number
) (pdf histogram-pdf
) &key) ¶Given a uniform random number (source) between zero and one,
compute a single random sample from the probability distribution
’pdf. The algorithm used to compute the sample s is given by
s = range[i] + delta * (range[i+1] - range[i])
where i is the index which satisfies
sum[i] <= value < sum[i+1] and delta is
(value - sum[i])/(sum[i+1] - sum[i]).
random-number-generator
) (type (eql :random-sample)
) &key src dest) ¶Like :choose-random, but samples k items from the original array of n items src with replacement, so the same object can appear more than once in the output sequence dest. There is no requirement that k be less than n in this case.
random-number-generator
) (type (eql :choose-random)
) &key src dest) ¶Fill the array destarr[k] with k objects taken randomly from the n
elements of the array src[0...n-1]. The output of the random
number generator r is used to make the selection. The algorithm
ensures all possible samples are equally likely, assuming a perfect
source of randomness.
The objects are sampled without replacement, thus each object can
only appear once in destarr[k]. It is required that k be less
than or equal to n. The objects in destarr will be in the
same relative order as those in src. You will need to call
with :shuffle if you want to randomize the order.
random-number-generator
) (type (eql :shuffle)
) &key base) ¶Randomly shuffle the order of n objects, each of
size size, stored in the array base[0...n-1]. The
output of the random number generator r is used to produce the
permutation. The algorithm generates all possible n!
permutations with equal probability, assuming a perfect source of random
numbers.
random-number-generator
) (type (eql :logarithmic)
) &key probability) ¶A random integer from the logarithmic distribution.
The probability distribution for logarithmic random variates
is p(k) = {-1 over log(1-p)} {left( p^k over k right)}
for k >= 1.
random-number-generator
) (type (eql :hypergeometric)
) &key n1 n2 tt) ¶A random integer from the hypergeometric
distribution. The probability distribution for hypergeometric
random variates is
p(k) = C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t)
where C(a,b) = a!/(b!(a-b)!) and
t <= n_1 + n_2. The domain of k is
max(0,t-n_2), ..., min(t,n_1).
If a population contains n_1 elements of “type 1” and
n_2 elements of “type 2” then the hypergeometric
distribution gives the probability of obtaining k elements of
“type 1” in t samples from the population without
replacement.
random-number-generator
) (type (eql :geometric)
) &key probability) ¶A random integer from the geometric distribution,
the number of independent trials with probability p until the
first success. The probability distribution for geometric variates
is p(k) = p (1-p)^{k-1} for k >= 1.
Note that the distribution begins with k=1 with this
definition. There is another convention in which the exponent k-1
is replaced by k.
random-number-generator
) (type (eql :pascal)
) &key probability n) ¶A random integer from the Pascal distribution. The
Pascal distribution is simply a negative binomial distribution with an
integer value of n.
p(k) = {(n + k - 1)! over k! (n - 1)! } p^n (1-p)^k
k >= 0.
random-number-generator
) (type (eql :negative-binomial)
) &key probability n) ¶A random integer from the negative binomial
distribution, the number of failures occurring before n successes
in independent trials with probability of success. The
probability distribution for negative binomial variates is
given by probability (p):
p(k) = {Gamma(n + k) over Gamma(k+1) Gamma(n) } p^n (1-p)^k
Note that n is not required to be an integer.
random-number-generator
) (type (eql :multinomial)
) &key sum probabilities n) ¶Returns an array n of (dim0 probabilities) random variates from a
multinomial distribution. The sum of the array n is specified
by sum. The distribution function is
P(n_1, n_2, ..., n_K) =
(N!/(n_1! n_2! ... n_K!)) p_1^n_1 p_2^n_2 ... p_K^n_K
where (n_1, n_2, ..., n_K) are nonnegative integers with
sum_{k=1}^K n_k = N, and (p_1, p_2, ..., p_K)
is a probability distribution with sum p_i = 1.
If the array p[K] is not normalized then its entries will be
treated as weights and normalized appropriately.
Random variates are generated using the conditional binomial method (see
C.S. David, "The computer generation of multinomial random
variates," Comp. Stat. Data Anal. 16 (1993) 205–217 for details).
random-number-generator
) (type (eql :bernoulli)
) &key probability) ¶Returns either 0 or 1, the result of a Bernoulli trial
with probability p. The probability distribution for
a Bernoulli trial is
p(0) = 1 - p
p(1) = p.
random-number-generator
) (type (eql :poisson)
) &key mu) ¶A random integer from the Poisson distribution with mean mu.
The probability distribution for Poisson variates is
p(k) = {mu^k over k!} exp(-mu)
k >= 0.
random-number-generator
) (type (eql :discrete)
) &key table) ¶Generate discrete random numbers.
random-number-generator
) (type (eql :dirichlet)
) &key alpha theta) ¶An array of K=(length alpha) random variates from a Dirichlet
distribution of order K-1. The distribution function is
p(theta_1,ldots,theta_K) , dtheta_1 cdots dtheta_K =
{1 over Z} prod_{i=1}^{K} theta_i^{alpha_i - 1}
; delta(1 -sum_{i=1}^K theta_i) dtheta_1 cdots dtheta_K
theta_i >= 0 and alpha_i >= 0.
The delta function ensures that sum theta_i = 1.
The normalization factor Z is
Z = {prod_{i=1}^K Gamma(alpha_i) over Gamma( sum_{i=1}^K alpha_i)}
The random variates are generated by sampling K values
from gamma distributions with parameters a=alpha_i, b=1,
and renormalizing.
See A.M. Law, W.D. Kelton, "Simulation Modeling and Analysis"
(1991).
random-number-generator
) (type (eql :gumbel2)
) &key a b) ¶A random variate from the Type-2 Gumbel
distribution, p(x) dx = a b x^{-a-1} exp(-b x^{-a}) dx
for 0 < x < infty.
random-number-generator
) (type (eql :gumbel1)
) &key a b) ¶A random variate from the Type-1 Gumbel
distribution,
p(x) dx = a b exp(-(b exp(-ax) + ax)) dx
for -infty < x < infty.
random-number-generator
) (type (eql :weibull)
) &key a b) ¶A random variate from the Weibull distribution. The distribution function is
p(x) dx = {b over a^b} x^{b-1} exp(-(x/a)^b) dx
for x >= 0.
random-number-generator
) (type (eql :direction-nd)
) &key vector) ¶A random direction vector v = (x_1,x_2,...,x_n) in n dimensions,
where n is the length of the vector x passed in. The vector is normalized such that
|v|^2 = x_1^2 + x_2^2 + ... + x_n^2 = 1. The method
uses the fact that a multivariate gaussian distribution is spherically
symmetric. Each component is generated to have a gaussian distribution,
and then the components are normalized. The method is described by
Knuth, v2, 3rd ed, p135–136, and attributed to G. W. Brown, Modern
Mathematics for the Engineer (1956).
random-number-generator
) (type (eql :direction-3d)
) &key) ¶A random direction vector v =
(x,y,z) in three dimensions. The vector is normalized
such that |v|^2 = x^2 + y^2 + z^2 = 1. The method employed is
due to Robert E. Knop (CACM 13, 326 (1970)), and explained in Knuth, v2,
3rd ed, p136. It uses the surprising fact that the distribution
projected along any axis is actually uniform (this is only true for 3
dimensions).
random-number-generator
) (type (eql :direction-2d-trig-method)
) &key) ¶A random direction vector v = (x,y) in
two dimensions. The vector is normalized such that
|v|^2 = x^2 + y^2 = 1. Uses trigonometric functions.
random-number-generator
) (type (eql :direction-2d)
) &key) ¶A random direction vector v = (x,y) in
two dimensions. The vector is normalized such that
|v|^2 = x^2 + y^2 = 1.
random-number-generator
) (type (eql :pareto)
) &key a b) ¶A random variate from the Pareto distribution of order a.
The distribution function is
p(x) dx = (a/b) / (x/b)^{a+1} dx
x >= b.
random-number-generator
) (type (eql :logistic)
) &key a) ¶A random variate from the logistic distribution. The distribution function is
p(x) dx = { exp(-x/a) over a (1 + exp(-x/a))^2 } dx
for -infty < x < +infty.
random-number-generator
) (type (eql :beta)
) &key a b) ¶A random variate from the beta distribution. The distribution function is p(x) dx = {Gamma(a+b) over Gamma(a) Gamma(b)} x^{a-1} (1-x)^{b-1} dx 0 <= x <= 1.
random-number-generator
) (type (eql :tdist)
) &key nu) ¶A random variate from the Student t-distribution. The
distribution function is,
p(x) dx = {Gamma((nu + 1)/2) over sqrt{pi nu} Gamma(nu/2)}
(1 + x^2/nu)^{-(nu + 1)/2} dx
for -infty < x < +infty.
random-number-generator
) (type (eql :fdist)
) &key nu1 nu2) ¶A random variate from the F-distribution with degrees of freedom nu1
and nu2. The distribution function is
p(x) dx =
{ Gamma((nu_1 + nu_2)/2)
over Gamma(nu_1/2) Gamma(nu_2/2) }
nu_1^{nu_1/2} nu_2^{nu_2/2}
x^{nu_1/2 - 1} (nu_2 + nu_1 x)^{-nu_1/2 -nu_2/2}
for x >= 0.
random-number-generator
) (type (eql :chi-squared)
) &key nu) ¶A random variate from the chi-squared distribution
with nu degrees of freedom. The distribution function is
p(x) dx = {1 over 2 Gamma(nu/2) } (x/2)^{nu/2 - 1} exp(-x/2) dx
x >= 0.
random-number-generator
) (type (eql :lognormal)
) &key zeta sigma) ¶A random variate from the lognormal distribution.
The distribution function is
p(x) dx = {1 over x sqrt{2 pi sigma^2}} exp(-(ln(x) - zeta)^2/2 sigma^2) dx
for x > 0.
random-number-generator
) (type (eql :flat)
) &key a b) ¶A random variate from the flat (uniform)
distribution from a to b. The distribution is
p(x) dx = {1 over (b-a)} dx
if a <= x < b, and 0 otherwise.
random-number-generator
) (type (eql :gamma-mt)
) &key a b) ¶A gamma variate using the Marsaglia-Tsang fast gamma method.
random-number-generator
) (type (eql :gamma)
) &key a b) ¶A random variate from the gamma distribution.
The distribution function is
p(x) dx = {1 over Gamma(a) b^a} x^{a-1} e^{-x/b} dx
for x > 0. The gamma distribution with an integer parameter a
is known as the Erlang distribution. The variates are computed using
the algorithms from Knuth (vol 2).
random-number-generator
) (type (eql :levy-skew)
) &key c alpha beta) ¶A random variate from the Levy skew stable
distribution with scale c exponent alpha and skewness
parameter beta. The skewness parameter must lie in the range
[-1,1]. The Levy skew stable probability distribution is defined
by a fourier transform,
p(x) = {1 over 2 pi} int_{-infty}^{+infty} dt
exp(-it x - |c t|^alpha (1-i beta sign(t) tan(pialpha/2)))
When alpha = 1 the term tan(pi alpha/2) is replaced by
-(2/pi)log|t|. There is no explicit solution for the form of
p(x)} and the library does not define a corresponding pdf
function. For alpha = 2 the distribution reduces to a Gaussian
distribution with sigma = sqrt{2} c and the skewness parameter
has no effect. For alpha < 1 the tails of the distribution
become extremely wide. The symmetric distribution corresponds to beta = 0.
The algorithm only works for 0 < alpha le 2.
random-number-generator
) (type (eql :levy)
) &key c alpha) ¶A random variate from the Levy symmetric stable
distribution with scale c and exponent alpha. The symmetric
stable probability distribution is defined by a fourier transform,
p(x) = {1 over 2 pi} int_{-infty}^{+infty} dt exp(-it x - |c t|^alpha)
There is no explicit solution for the form of p(x) and the
library does not define a corresponding pdf function. For
alpha = 1 the distribution reduces to the Cauchy distribution. For
alpha = 2 it is a Gaussian distribution with sigma = sqrt{2} c
For alpha < 1 the tails of the distribution become extremely wide.
The algorithm only works for 0 < alpha <= 2.
random-number-generator
) (type (eql :landau)
) &key) ¶A random variate from the Landau distribution. The
probability distribution for Landau random variates is defined
analytically by the complex integral,
{1 over {2 pi i}} int_{c-iinfty}^{c+iinfty} ds, exp(s log(s) + x s)
For numerical purposes it is more convenient to use the following
equivalent form of the integral,
p(x) = (1/pi) int_0^infty dt exp(-t log(t) - x t) sin(pi t).
random-number-generator
) (type (eql :rayleigh-tail)
) &key a sigma) ¶A random variate from the tail of the Rayleigh
distribution with scale parameter sigma and a lower limit of
a. The distribution is
p(x) dx = {x over sigma^2} exp ((a^2 - x^2) /(2 sigma^2)) dx
for x > a.
random-number-generator
) (type (eql :rayleigh)
) &key sigma) ¶A random variate from the Rayleigh distribution with
scale parameter sigma. The distribution is
p(x) dx = {x over sigma^2} exp(- x^2/(2 sigma^2)) dx
for x > 0.
random-number-generator
) (type (eql :cauchy)
) &key a) ¶A random variate from the Cauchy distribution with
scale parameter a. The probability distribution for Cauchy
random variates is,
p(x) dx = {1 over api (1 + (x/a)^2) } dx
for x in the range -infty to +infty. The Cauchy
distribution is also known as the Lorentz distribution.
random-number-generator
) (type (eql :exponential-power)
) &key a b) ¶A random variate from the exponential power distribution with scale parameter a and exponent b. The distribution is p(x) dx = {1 over 2 a Gamma(1+1/b)} exp(-|x/a|^b) dx for x >= 0. For b = 1 this reduces to the Laplace distribution. For b = 2 it has the same form as a gaussian distribution, but with a = sqrt{2} sigma.
random-number-generator
) (type (eql :laplace)
) &key a) ¶A random variate from the Laplace distribution with width a.
The distribution is
p(x) dx = {1 over 2 a} exp(-|x/a|) dx
for -infty < x < infty.
random-number-generator
) (type (eql :exponential)
) &key mu) ¶A random variate from the exponential distribution
with mean mu. The distribution is
p(x) dx = {1 over mu} exp(-x/mu) dx
x >= 0.
random-number-generator
) (type (eql :bivariate-gaussian)
) &key sigma-x sigma-y rho) ¶Generate a pair of correlated Gaussian variates, with
mean zero, correlation coefficient rho and standard deviations
sigma_x and sigma_y in the x and y directions.
The probability distribution for bivariate Gaussian random variates is,
p(x,y) dx dy
= {1 over 2 pi sigma_x sigma_y sqrt{1-rho^2}}
exp left(-{(x^2/sigma_x^2 + y^2/sigma_y^2 - 2 rho x y/(sigma_xsigma_y))
over 2(1-rho^2)}right) dx dy
for x,y in the range -infty to +infty. The
correlation coefficient rho should lie between 1 and -1.
random-number-generator
) (type (eql :ugaussian-tail)
) &key a) ¶Equivalent to gaussian-tail with sigma=1.
random-number-generator
) (type (eql :gaussian-tail)
) &key a sigma) ¶Random variates from the upper tail of a Gaussian
distribution with standard deviation sigma. The values returned
are larger than the lower limit a, which must be positive. The
method is based on Marsaglia’s famous rectangle-wedge-tail algorithm (Ann.
Math. Stat. 32, 894–899 (1961)), with this aspect explained in Knuth, v2,
3rd ed, p139,586 (exercise 11).
The probability distribution for Gaussian tail random variates is,
p(x) dx = {1 over N(a;sigma) sqrt{2 pi sigma^2}}
exp (- x^2 / 2sigma^2) dx
for x > a where N(a;sigma) is the normalization constant,
N(a;sigma) = (1/2) erfc(a / sqrt(2 sigma^2)).
random-number-generator
) (type (eql :ugaussian-ratio-method)
) &key) ¶Compute results for the unit Gaussian distribution,
equivalent to the #’sample :gaussian-ration-method with a standard
deviation of one, sigma = 1.
random-number-generator
) (type (eql :ugaussian)
) &key) ¶Compute results for the unit Gaussian distribution,
equivalent to the #’sample :gaussian with a standard deviation of
one, sigma = 1.
random-number-generator
) (type (eql :gaussian-ratio-method)
) &key sigma) ¶Compute a Gaussian random variate using the Kinderman-Monahan-Leva ratio method.
random-number-generator
) (type (eql :gaussian-ziggurat)
) &key sigma) ¶Compute a Gaussian random variate using the alternative Marsaglia-Tsang ziggurat method. The Ziggurat algorithm is the fastest available algorithm in most cases.
random-number-generator
) (type (eql :gaussian)
) &key sigma) ¶A Gaussian random variate, with mean zero and
standard deviation sigma. The probability distribution for
Gaussian random variates is
p(x) dx = {1 over sqrt{2 pi sigma^2}} exp (-x^2 / 2sigma^2) dx
for x in the range -infty to +infty. Use the
transformation z = mu + x on the numbers returned by
this function to obtain a Gaussian distribution with mean
mu. This function uses the Box-Mueller algorithm which requires two
calls to the random number generator r.
random-number-generator
) (type (eql :uniform-fixnum)
) &key upperbound) ¶Generate a random integer from 0 to upperbound-1 inclusive.
All integers in the range are equally likely, regardless
of the generator used. An offset correction is applied so that zero is
always returned with the correct probability, for any minimum value of
the underlying generator. If upperbound is larger than the range
of the generator then the function signals an error.
random-number-generator
) (type (eql :uniform>0)
) &key) ¶Return a positive double precision floating point number uniformly distributed in the range (0,1), excluding both 0.0 and 1.0. The number is obtained by sampling the generator with the algorithm for type ’uniform until a non-zero value is obtained. You can use this function if you need to avoid a singularity at 0.0.
random-number-generator
) (type (eql :uniform)
) &key) ¶A double precision floating point number uniformly
distributed in the range [0,1). The range includes 0.0 but excludes 1.0.
The value is typically obtained by dividing the result of
#’get-random-number by (+ (rng-max generator) 1.0) in double
precision. Some generators compute this ratio internally so that they
can provide floating point numbers with more than 32 bits of randomness
(the maximum number of bits that can be portably represented in a single
:ulong.
Rescale the vector x by the multiplicative factor alpha.
gsll
.
float
) (x vector-complex-double-float
)) ¶float
) (x vector-complex-single-float
)) ¶float
) (x vector-single-float
)) ¶float
) (x vector-double-float
)) ¶complex
) (x vector-complex-single-float
)) ¶complex
) (x vector-complex-double-float
)) ¶Set all elements to the value.
gsll
.
vector-single-float
) value) ¶vector-double-float
) value) ¶vector-complex-single-float
) value) ¶vector-complex-double-float
) value) ¶vector-signed-byte-8
) value) ¶vector-unsigned-byte-8
) value) ¶vector-signed-byte-16
) value) ¶vector-unsigned-byte-16
) value) ¶vector-signed-byte-32
) value) ¶vector-unsigned-byte-32
) value) ¶vector-signed-byte-64
) value) ¶vector-unsigned-byte-64
) value) ¶matrix-single-float
) value) ¶matrix-double-float
) value) ¶matrix-complex-single-float
) value) ¶matrix-complex-double-float
) value) ¶matrix-signed-byte-8
) value) ¶matrix-unsigned-byte-8
) value) ¶matrix-signed-byte-16
) value) ¶matrix-unsigned-byte-16
) value) ¶matrix-signed-byte-32
) value) ¶matrix-unsigned-byte-32
) value) ¶matrix-signed-byte-64
) value) ¶matrix-unsigned-byte-64
) value) ¶Set the index element to 1, and the rest to 0.
gsll
.
vector-single-float
) index) ¶vector-double-float
) index) ¶vector-complex-single-float
) index) ¶vector-complex-double-float
) index) ¶vector-signed-byte-8
) index) ¶vector-unsigned-byte-8
) index) ¶vector-signed-byte-16
) index) ¶vector-unsigned-byte-16
) index) ¶vector-signed-byte-32
) index) ¶vector-unsigned-byte-32
) index) ¶vector-signed-byte-64
) index) ¶vector-unsigned-byte-64
) index) ¶Set the elements of the matrix to the
corresponding elements of the identity matrix, m(i,j) =
delta(i,j), i.e. a unit diagonal with all off-diagonal elements zero.
This applies to both square and rectangular matrices.
gsll
.
permutation
)) ¶Initialize the permutation p to the identity, i.e. (0,1,2,...,n-1).
matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶Set the ranges of the existing histogram h to cover
the range xmin to xmax uniformly. The values of the
histogram bins are reset to zero. The bin ranges are shown in the table
below,
bin[0] corresponds to xmin <= x < xmin + d
bin[1] corresponds to xmin + d <= x < xmin + 2 d
......
bin[n-1] corresponds to xmin + (n-1)d <= x < xmax
where d is the bin spacing, d = (xmax-xmin)/n.
gsll
.
histogram2d
) x-minimum x-maximum &optional y-minimum y-maximum) ¶Set all elements to 0.
gsll
.
histogram2d
)) ¶Reset all the bins in the histogram to zero.
vector-single-float
)) ¶vector-double-float
)) ¶vector-complex-single-float
)) ¶vector-complex-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-complex-single-float
)) ¶matrix-complex-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶Shift the contents of the bins of histogram h by the constant offset, i.e. h’_1(i) = h_1(i) + offset.
gsll
.
histogram2d
) offset) ¶The standard deviation of the histogrammed variable, where the histogram is regarded as a probability distribution. Negative bin values are ignored for the purposes of this calculation. The resolution of the result is limited by the bin width. For 2d histograms, the sigmas are returned as multiple values.
gsll
.
histogram2d
)) ¶The size of the GSL object.
gsll
.
multi-dimensional-minimizer-f
)) ¶A minimizer-specific characteristic size for the minimizer.
quasi-random-number-generator
)) ¶random-number-generator
)) ¶combination
)) ¶The number of elements (k) in the combination c.
permutation
)) ¶The size of the permutation p.
array
)) ¶foreign-array
)) ¶The skewness of data, defined as skew = (1/N) sum ((x_i -
Hatmu)/Hatsigma)^3 where x_i are the elements of the dataset
data. The skewness measures the asymmetry of the tails of a
distribution. If mean and standard deviation are supplied, compute
skewness of the dataset data using the given values skew = (1/N)
sum ((x_i - mean)/sd)^3. This is useful if you have
already computed the mean and standard deviation of data and want to
avoid recomputing them.
gsll
.
vector-single-float
) &optional mean standard-deviation) ¶vector-double-float
) &optional mean standard-deviation) ¶vector-signed-byte-8
) &optional mean standard-deviation) ¶vector-unsigned-byte-8
) &optional mean standard-deviation) ¶vector-signed-byte-16
) &optional mean standard-deviation) ¶vector-unsigned-byte-16
) &optional mean standard-deviation) ¶vector-signed-byte-32
) &optional mean standard-deviation) ¶vector-unsigned-byte-32
) &optional mean standard-deviation) ¶vector-signed-byte-64
) &optional mean standard-deviation) ¶vector-unsigned-byte-64
) &optional mean standard-deviation) ¶The current value of the independent variable(s) that solves this object.
gsll
.
nonlinear-fdffit
)) ¶The current best-fit parameters.
nonlinear-ffit
)) ¶The current best-fit parameters.
multi-dimensional-minimizer-fdf
)) ¶The current best estimate of the location of the minimum.
multi-dimensional-minimizer-f
)) ¶The current best estimate of the location of the minimum.
multi-dimensional-root-solver-fdf
)) ¶The current estimate of the root for the solver.
multi-dimensional-root-solver-f
)) ¶The current estimate of the root for the solver.
one-dimensional-minimizer
)) ¶The current estimate of the position of the minimum for the minimizer.
one-dimensional-root-solver-fdf
)) ¶The current estimate of the root for the solver.
one-dimensional-root-solver-f
)) ¶The current estimate of the root for the solver.
Simultaneously sort the eigenvalues stored in the vector
eigenvalues and the corresponding real eigenvectors stored in the columns
of the matrix eigenvectors into ascending or descending order according to
the value of the parameter sort-type: :value-ascending,
:value-descending, :absolute-ascending, :absolute-descending.
Indirectly sort the n elements of the array vector with stride stride
into ascending order, storing the resulting permutation. The latter
must be created with the same size as the vector.
The elements of permutation give the index of the
array element which would have been stored in that position if the
array had been sorted in place. The array data is not changed.
gsll
.
permutation
) (vector vector-single-float
)) ¶permutation
) (vector vector-double-float
)) ¶permutation
) (vector vector-signed-byte-8
)) ¶permutation
) (vector vector-unsigned-byte-8
)) ¶permutation
) (vector vector-signed-byte-16
)) ¶permutation
) (vector vector-unsigned-byte-16
)) ¶permutation
) (vector vector-signed-byte-32
)) ¶permutation
) (vector vector-unsigned-byte-32
)) ¶permutation
) (vector vector-signed-byte-64
)) ¶permutation
) (vector vector-unsigned-byte-64
)) ¶Find the largest elements of the vector v and put them into dest, which must be shorter than v.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The indices of the largest elements of the vector. If size-or-array is an integer, it is the number of smallest elements. If it is an array of sizet elements, it is filled.
gsll
.
vector-single-float
) &optional size-or-array) ¶vector-double-float
) &optional size-or-array) ¶vector-signed-byte-8
) &optional size-or-array) ¶vector-unsigned-byte-8
) &optional size-or-array) ¶vector-signed-byte-16
) &optional size-or-array) ¶vector-unsigned-byte-16
) &optional size-or-array) ¶vector-signed-byte-32
) &optional size-or-array) ¶vector-unsigned-byte-32
) &optional size-or-array) ¶vector-signed-byte-64
) &optional size-or-array) ¶vector-unsigned-byte-64
) &optional size-or-array) ¶Find the smallest elements of the vector v and put them into dest, which must be shorter than v.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶matrix-single-float
)) ¶matrix-double-float
)) ¶matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
)) ¶The indices of the smallest elements of the vector. If size-or-array is an integer, it is the number of smallest elements. If it is an array of :sizet elements, it is filled.
gsll
.
vector-single-float
) &optional size-or-array) ¶vector-double-float
) &optional size-or-array) ¶vector-signed-byte-8
) &optional size-or-array) ¶vector-unsigned-byte-8
) &optional size-or-array) ¶vector-signed-byte-16
) &optional size-or-array) ¶vector-unsigned-byte-16
) &optional size-or-array) ¶vector-signed-byte-32
) &optional size-or-array) ¶vector-unsigned-byte-32
) &optional size-or-array) ¶vector-signed-byte-64
) &optional size-or-array) ¶vector-unsigned-byte-64
) &optional size-or-array) ¶Sort the elements of the vector v into ascending numerical order.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶Indirectly sort the elements of the vector v into
ascending order, storing the resulting permutation in p. The
elements of p give the index of the vector element which would
have been stored in that position if the vector had been sorted in
place. The first element of p gives the index of the least element
in v and the last element of p gives the index of the
greatest element in v. The vector v is not changed.
gsll
.
permutation
) (vector vector-single-float
)) ¶permutation
) (vector vector-double-float
)) ¶permutation
) (vector vector-signed-byte-8
)) ¶permutation
) (vector vector-unsigned-byte-8
)) ¶permutation
) (vector vector-signed-byte-16
)) ¶permutation
) (vector vector-unsigned-byte-16
)) ¶permutation
) (vector vector-signed-byte-32
)) ¶permutation
) (vector vector-unsigned-byte-32
)) ¶permutation
) (vector vector-signed-byte-64
)) ¶permutation
) (vector vector-unsigned-byte-64
)) ¶Find the largest elements of the vector v and put them into dest, which must be shorter than v.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The indices of the largest elements of the vector stored,
returned as a CL vector of element type fixnum. If
indices is a positive initeger, a vector will be
allocated and returned. If it is a CL vector,
it will be filled with the indices.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶Find the smallest elements of the vector v and put them into dest, which must be shorter than v.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The indices of the smallest elements of the vector stored,
returned as a CL vector of element type fixnum. If
indices is a positive initeger, a vector will be
allocated and returned. If it is a CL vector,
it will be filled with the indices.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The standard deviation, square root of the variance.
If the mean value is known, it may be supplied which will use more
efficient routines to compute the variance.
gsll
.
vector-single-float
) &optional mean) ¶vector-double-float
) &optional mean) ¶vector-signed-byte-8
) &optional mean) ¶vector-unsigned-byte-8
) &optional mean) ¶vector-signed-byte-16
) &optional mean) ¶vector-unsigned-byte-16
) &optional mean) ¶vector-signed-byte-32
) &optional mean) ¶vector-unsigned-byte-32
) &optional mean) ¶vector-signed-byte-64
) &optional mean) ¶vector-unsigned-byte-64
) &optional mean) ¶matrix-single-float
) &optional mean) ¶matrix-double-float
) &optional mean) ¶matrix-signed-byte-8
) &optional mean) ¶matrix-unsigned-byte-8
) &optional mean) ¶matrix-signed-byte-16
) &optional mean) ¶matrix-unsigned-byte-16
) &optional mean) ¶matrix-signed-byte-32
) &optional mean) ¶matrix-unsigned-byte-32
) &optional mean) ¶matrix-signed-byte-64
) &optional mean) ¶matrix-unsigned-byte-64
) &optional mean) ¶The standard deviation of data for a fixed population mean. The result is the square root of the corresponding variance function.
gsll
.
vector-single-float
) mean) ¶vector-double-float
) mean) ¶vector-signed-byte-8
) mean) ¶vector-unsigned-byte-8
) mean) ¶vector-signed-byte-16
) mean) ¶vector-unsigned-byte-16
) mean) ¶vector-signed-byte-32
) mean) ¶vector-unsigned-byte-32
) mean) ¶vector-signed-byte-64
) mean) ¶vector-unsigned-byte-64
) mean) ¶matrix-single-float
) mean) ¶matrix-double-float
) mean) ¶matrix-signed-byte-8
) mean) ¶matrix-unsigned-byte-8
) mean) ¶matrix-signed-byte-16
) mean) ¶matrix-unsigned-byte-16
) mean) ¶matrix-signed-byte-32
) mean) ¶matrix-unsigned-byte-32
) mean) ¶matrix-signed-byte-64
) mean) ¶matrix-unsigned-byte-64
) mean) ¶The sum of all bin values. Negative bin values are included in the sum.
gsll
.
histogram2d
)) ¶Exchange the elements of a and b
by copying. The two must have the same dimensions.
gsll
.
vector-single-float
) (b vector-single-float
)) ¶vector-double-float
) (b vector-double-float
)) ¶vector-complex-single-float
) (b vector-complex-single-float
)) ¶vector-complex-double-float
) (b vector-complex-double-float
)) ¶vector-signed-byte-8
) (b vector-signed-byte-8
)) ¶vector-unsigned-byte-8
) (b vector-unsigned-byte-8
)) ¶vector-signed-byte-16
) (b vector-signed-byte-16
)) ¶vector-unsigned-byte-16
) (b vector-unsigned-byte-16
)) ¶vector-signed-byte-32
) (b vector-signed-byte-32
)) ¶vector-unsigned-byte-32
) (b vector-unsigned-byte-32
)) ¶vector-signed-byte-64
) (b vector-signed-byte-64
)) ¶vector-unsigned-byte-64
) (b vector-unsigned-byte-64
)) ¶matrix-single-float
) (b matrix-single-float
)) ¶matrix-double-float
) (b matrix-double-float
)) ¶matrix-complex-single-float
) (b matrix-complex-single-float
)) ¶matrix-complex-double-float
) (b matrix-complex-double-float
)) ¶matrix-signed-byte-8
) (b matrix-signed-byte-8
)) ¶matrix-unsigned-byte-8
) (b matrix-unsigned-byte-8
)) ¶matrix-signed-byte-16
) (b matrix-signed-byte-16
)) ¶matrix-unsigned-byte-16
) (b matrix-unsigned-byte-16
)) ¶matrix-signed-byte-32
) (b matrix-signed-byte-32
)) ¶matrix-unsigned-byte-32
) (b matrix-unsigned-byte-32
)) ¶matrix-signed-byte-64
) (b matrix-signed-byte-64
)) ¶matrix-unsigned-byte-64
) (b matrix-unsigned-byte-64
)) ¶Exchange the ith and jth columns of the matrix in-place.
gsll
.
matrix-single-float
) i j) ¶matrix-double-float
) i j) ¶matrix-complex-single-float
) i j) ¶matrix-complex-double-float
) i j) ¶matrix-signed-byte-8
) i j) ¶matrix-unsigned-byte-8
) i j) ¶matrix-signed-byte-16
) i j) ¶matrix-unsigned-byte-16
) i j) ¶matrix-signed-byte-32
) i j) ¶matrix-unsigned-byte-32
) i j) ¶matrix-signed-byte-64
) i j) ¶matrix-unsigned-byte-64
) i j) ¶Exchange the i-th and j-th elements of the vector vec in-place.
gsll
.
permutation
) i j) ¶Exchanges the ith and jth elements of the permutation p.
vector-single-float
) i j) ¶vector-double-float
) i j) ¶vector-complex-single-float
) i j) ¶vector-complex-double-float
) i j) ¶vector-signed-byte-8
) i j) ¶vector-unsigned-byte-8
) i j) ¶vector-signed-byte-16
) i j) ¶vector-unsigned-byte-16
) i j) ¶vector-signed-byte-32
) i j) ¶vector-unsigned-byte-32
) i j) ¶vector-signed-byte-64
) i j) ¶vector-unsigned-byte-64
) i j) ¶Exchange the ith row and jth column of the
matrix in-place. The matrix must be square for this operation to
be possible.
gsll
.
matrix-single-float
) i j) ¶matrix-double-float
) i j) ¶matrix-complex-single-float
) i j) ¶matrix-complex-double-float
) i j) ¶matrix-signed-byte-8
) i j) ¶matrix-unsigned-byte-8
) i j) ¶matrix-signed-byte-16
) i j) ¶matrix-unsigned-byte-16
) i j) ¶matrix-signed-byte-32
) i j) ¶matrix-unsigned-byte-32
) i j) ¶matrix-signed-byte-64
) i j) ¶matrix-unsigned-byte-64
) i j) ¶Exchange the ith and jth rows of the matrix in-place.
gsll
.
matrix-single-float
) i j) ¶matrix-double-float
) i j) ¶matrix-complex-single-float
) i j) ¶matrix-complex-double-float
) i j) ¶matrix-signed-byte-8
) i j) ¶matrix-unsigned-byte-8
) i j) ¶matrix-signed-byte-16
) i j) ¶matrix-unsigned-byte-16
) i j) ¶matrix-signed-byte-32
) i j) ¶matrix-unsigned-byte-32
) i j) ¶matrix-signed-byte-64
) i j) ¶matrix-unsigned-byte-64
) i j) ¶If the first argument is a vector,
the symmetric rank-1 update A = alpha x x^T + A of the symmetric
matrix A. Since the matrix A is symmetric only its upper half or
lower half need to be stored. When Uplo is :Upper then the upper
triangle and diagonal of A are used, and when Uplo is :Lower then
the lower triangle and diagonal of A are used. If the first
argument is a matrix, a rank-k update of the symmetric matrix C, C =
alpha A A^T + beta C when Trans is CblasNoTrans and C = alpha A^T
A + beta C when Trans is CblasTrans. Since the matrix C is
symmetric only its upper half or lower half need to be stored. When
Uplo is CblasUpper then the upper triangle and diagonal of C are
used, and when Uplo is CblasLower then the lower triangle and
diagonal of C are used.
gsll
.
matrix-complex-double-float
) (c matrix-complex-double-float
) &optional alpha beta uplo trans) ¶matrix-complex-single-float
) (c matrix-complex-single-float
) &optional alpha beta uplo trans) ¶matrix-double-float
) (c matrix-double-float
) &optional alpha beta uplo trans) ¶matrix-single-float
) (c matrix-single-float
) &optional alpha beta uplo trans) ¶vector-single-float
) (a matrix-single-float
) &optional alpha beta uplo trans) ¶vector-double-float
) (a matrix-double-float
) &optional alpha beta uplo trans) ¶If the first two arguments are vectors, compute
the symmetric rank-2 update A = alpha x y^T + alpha y x^T + A of the
symmetric matrix A. Since the matrix A is symmetric only its upper
half or lower half need to be stored. When Uplo is :upper then the
upper triangle and diagonal of A are used, and when Uplo is :lower
then the lower triangle and diagonal of A are used. If the first
two arguments are matrices, compute a rank-2k update of the
symmetric matrix C, C = alpha A B^T + alpha B A^T + beta C when
Trans is :notrans and C = alpha A^T B + alpha B^T A + beta C
when Trans is :trans. Since the matrix C is symmetric only its
upper half or lower half need to be stored. When Uplo is :upper
then the upper triangle and diagonal of C are used, and when Uplo is
:lower then the lower triangle and diagonal of C are used.
gsll
.
matrix-complex-double-float
) (b matrix-complex-double-float
) (c matrix-complex-double-float
) &optional alpha beta uplo trans) ¶matrix-complex-single-float
) (b matrix-complex-single-float
) (c matrix-complex-single-float
) &optional alpha beta uplo trans) ¶matrix-double-float
) (b matrix-double-float
) (c matrix-double-float
) &optional alpha beta uplo trans) ¶matrix-single-float
) (b matrix-single-float
) (c matrix-single-float
) &optional alpha beta uplo trans) ¶vector-single-float
) (y vector-single-float
) (a matrix-single-float
) &optional alpha beta uplo trans) ¶vector-double-float
) (y vector-double-float
) (a matrix-double-float
) &optional alpha beta uplo trans) ¶Factorizes the symmetric square matrix or hermitian matrix A into the
symmetric tridiagonal decomposition Q T Q^T. On output the
diagonal and subdiagonal part of the input matrix A contain the
tridiagonal matrix T. The remaining lower triangular part of the
input matrix contains the Householder vectors which, together with the
Householder coefficients tau, encode the orthogonal matrix
Q. This storage scheme is the same as used by lapack. The
upper triangular part of A is not referenced.
Unpacks the encoded symmetric tridiagonal decomposition
(A, tau) obtained from #’tridiagonal-decomposition into the
orthogonal or unitary matrix Q, the vector of diagonal elements diag
and the real vector of subdiagonal elements subdiag.
Unpack the diagonal and subdiagonal of the encoded symmetric tridiagonal decomposition (A, tau) obtained from #’tridiagonal-decomposition into the real vectors diag and subdiag.
Check that the object p is valid.
gsll
.
combination
)) ¶Check that the combination is valid. The k
elements should lie in the range 0 to n-1, with each
value occurring once at most and in increasing order.
permutation
)) ¶Check that the permutation p is valid. The n
elements should contain each of the numbers 0 to n-1 once and only
once.
The estimated, or sample, variance of data. The
estimated variance is denoted by Hatsigma^2 and is defined by
Hatsigma^2 = (1/(N-1)) sum (x_i - Hatmu)^2
where x_i are the elements of the dataset data. Note that
the normalization factor of 1/(N-1) results from the derivation
of Hatsigma^2 as an unbiased estimator of the population
variance sigma^2. For samples drawn from a gaussian distribution
the variance of Hatsigma^2 itself is 2 sigma^4 / N.
If the mean value is known, it may be supplied which will use more
efficient routines to compute the variance.
gsll
.
vector-single-float
) &optional mean) ¶vector-double-float
) &optional mean) ¶vector-signed-byte-8
) &optional mean) ¶vector-unsigned-byte-8
) &optional mean) ¶vector-signed-byte-16
) &optional mean) ¶vector-unsigned-byte-16
) &optional mean) ¶vector-signed-byte-32
) &optional mean) ¶vector-unsigned-byte-32
) &optional mean) ¶vector-signed-byte-64
) &optional mean) ¶vector-unsigned-byte-64
) &optional mean) ¶matrix-single-float
) &optional mean) ¶matrix-double-float
) &optional mean) ¶matrix-signed-byte-8
) &optional mean) ¶matrix-unsigned-byte-8
) &optional mean) ¶matrix-signed-byte-16
) &optional mean) ¶matrix-unsigned-byte-16
) &optional mean) ¶matrix-signed-byte-32
) &optional mean) ¶matrix-unsigned-byte-32
) &optional mean) ¶matrix-signed-byte-64
) &optional mean) ¶matrix-unsigned-byte-64
) &optional mean) ¶An unbiased estimate of the variance of
data when the population mean of the underlying
distribution is known a priori. In this case the estimator for
the variance uses the factor 1/N and the sample mean
Hatmu is replaced by the known population mean mu,
Hatsigma^2 = (1/N) sum (x_i - mu)^2.
gsll
.
vector-single-float
) mean) ¶vector-double-float
) mean) ¶vector-signed-byte-8
) mean) ¶vector-unsigned-byte-8
) mean) ¶vector-signed-byte-16
) mean) ¶vector-unsigned-byte-16
) mean) ¶vector-signed-byte-32
) mean) ¶vector-unsigned-byte-32
) mean) ¶vector-signed-byte-64
) mean) ¶vector-unsigned-byte-64
) mean) ¶matrix-single-float
) mean) ¶matrix-double-float
) mean) ¶matrix-signed-byte-8
) mean) ¶matrix-unsigned-byte-8
) mean) ¶matrix-signed-byte-16
) mean) ¶matrix-unsigned-byte-16
) mean) ¶matrix-signed-byte-32
) mean) ¶matrix-unsigned-byte-32
) mean) ¶matrix-signed-byte-64
) mean) ¶matrix-unsigned-byte-64
) mean) ¶Reverse the order of the elements of the vector vec.
gsll
.
vector-single-float
)) ¶vector-double-float
)) ¶vector-complex-single-float
)) ¶vector-complex-double-float
)) ¶vector-signed-byte-8
)) ¶vector-unsigned-byte-8
)) ¶vector-signed-byte-16
)) ¶vector-unsigned-byte-16
)) ¶vector-signed-byte-32
)) ¶vector-unsigned-byte-32
)) ¶vector-signed-byte-64
)) ¶vector-unsigned-byte-64
)) ¶The weighted absolute deviation from the weighted
mean, defined as
absdev = (sum w_i |x_i - Hatmu|) / (sum w_i).
The weighted kurtosis of the dataset.
kurtosis = ((sum w_i ((x_i - xbar)/sigma)^4) / (sum w_i)) - 3.
The weighted mean of the dataset, using the set of weights
The weighted mean is defined as
Hatmu = (sum w_i x_i) / (sum w_i).
gsll
.
vector-single-float
) (weights vector-single-float
)) ¶vector-double-float
) (weights vector-double-float
)) ¶matrix-single-float
) (weights matrix-single-float
)) ¶matrix-double-float
) (weights matrix-double-float
)) ¶The weighted skewness of the dataset.
skew = (sum w_i ((x_i - xbar)/sigma)^3) / (sum w_i).
The weighted standard deviation, square root of the variance.
If the mean value is known, it may be supplied which will use more
efficient routines to compute the variance.
gsll
.
vector-single-float
) (weights vector-single-float
) &optional mean) ¶vector-double-float
) (weights vector-double-float
) &optional mean) ¶matrix-single-float
) (weights matrix-single-float
) &optional mean) ¶matrix-double-float
) (weights matrix-double-float
) &optional mean) ¶The square root of the corresponding variance function #’weighted-variance-with-fixed-mean.
gsll
.
vector-single-float
) (weights vector-single-float
) mean) ¶vector-double-float
) (weights vector-double-float
) mean) ¶matrix-single-float
) (weights matrix-single-float
) mean) ¶matrix-double-float
) (weights matrix-double-float
) mean) ¶The estimated variance of a weighted dataset is defined as
Hatsigma^2 = ((sum w_i)/((sum w_i)^2 - sum (w_i^2)))
sum w_i (x_i - Hatmu)^2
Note that this expression reduces to an unweighted variance with the
familiar 1/(N-1) factor when there are N equal non-zero weights.
If the mean value is known, it may be supplied which will use more
efficient routines to compute the variance.
gsll
.
vector-single-float
) (weights vector-single-float
) &optional mean) ¶vector-double-float
) (weights vector-double-float
) &optional mean) ¶matrix-single-float
) (weights matrix-single-float
) &optional mean) ¶matrix-double-float
) (weights matrix-double-float
) &optional mean) ¶An unbiased estimate of the variance of weighted
dataset when the population mean of the underlying
distribution is known a priori. In this case the estimator for
the variance replaces the sample mean Hatmu by the known
population mean mu,
Hatsigma^2 = (sum w_i (x_i - mu)^2) / (sum w_i).
gsll
.
vector-single-float
) (weights vector-single-float
) mean) ¶vector-double-float
) (weights vector-double-float
) mean) ¶matrix-single-float
) (weights matrix-single-float
) mean) ¶matrix-double-float
) (weights matrix-double-float
) mean) ¶The Riemann zeta function zeta(n).
zeta - 1.
histogram
) &rest indices) ¶Return the contents of the i-th bin of the histogram. If i lies outside the valid range of index for the histogram then an error (input-domain) is signalled.
grid
.
histogram2d
) &rest indices) ¶Return the contents of the i-th, j-th bin of the 2D histogram. If either index lies outside the valid range of index for the histogram then an error (input-domain) is signalled.
grid
.
permutation
) &rest indices) ¶grid
.
random-number-generator
) &key destination &allow-other-keys) ¶grid
.
quasi-random-number-generator
) &key destination &allow-other-keys) ¶grid
.
histogram2d
) &key destination &allow-other-keys) ¶grid
.
permutation
) &key grid-type destination &allow-other-keys) ¶grid
.
combination
) &key grid-type destination &allow-other-keys) ¶grid
.
histogram
)) ¶The number of bins in the histogram.
grid
.
histogram2d
)) ¶grid
.
permutation
)) ¶grid
.
callback-included
)) ¶automatically generated reader method
grid
.
interpolation
) &key mpointer size type xa ya) ¶monte-carlo-plain
) &key mpointer dim) ¶eigen-genherm
) &key mpointer n) ¶histogram-pdf
) &key mpointer number-of-bins histogram) ¶random-number-generator
) &key mpointer rng-type value) ¶eigen-symmv
) &key mpointer n) ¶eigen-nonsymm
) &key mpointer n) ¶multi-dimensional-root-solver-f
) &key mpointer dimensions type functions initial) ¶yp-control
) &key mpointer dydt-scaling y-scaling absolute-error relative-error) ¶basis-spline
) &key mpointer order number-of-breakpoints) ¶fit-workspace
) &key mpointer number-of-observations number-of-parameters) ¶qawo-table
) &key mpointer n omega l trig) ¶multi-dimensional-root-solver-fdf
) &key mpointer dimensions type functions initial) ¶acceleration
) &key mpointer) ¶discrete-random
) &key mpointer probabilities) ¶one-dimensional-root-solver-fdf
) &key mpointer root-guess functions type) ¶eigen-nonsymmv
) &key mpointer n) ¶polynomial-complex-workspace
) &key mpointer n) ¶multi-dimensional-minimizer-fdf
) &key mpointer tolerance step-size initial functions type dimensions) ¶nonlinear-fdffit
) &key mpointer dimensions solver-type functions initial-guess) ¶multi-dimensional-minimizer-f
) &key mpointer step-size initial functions type dimensions) ¶histogram
) &key mpointer number-of-bins ranges) ¶eigen-gensymmv
) &key mpointer n) ¶wavelet-workspace
) &key mpointer size) ¶eigen-genv
) &key mpointer n) ¶one-dimensional-root-solver-f
) &key mpointer upper lower functions type) ¶qaws-table
) &key mpointer alpha beta mu nu) ¶integration-workspace
) &key mpointer size) ¶scaled-control
) &key mpointer dimension absolute-scale absolute-error relative-error y-scaling dydt-scaling) ¶quasi-random-number-generator
) &key mpointer rng-type dimension) ¶eigen-symm
) &key mpointer n) ¶histogram2d
) &key mpointer number-of-bins-y number-of-bins-x x-ranges y-ranges) ¶ode-stepper
) &key mpointer type dimensions) ¶one-dimensional-minimizer
) &key mpointer f-upper x-upper f-lower x-lower f-minimum x-minimum functions type) ¶eigen-herm
) &key mpointer n) ¶eigen-genhermv
) &key mpointer n) ¶monte-carlo-miser
) &key mpointer dim) ¶chebyshev
) &key mpointer upper-limit lower-limit functions order) ¶ode-evolution
) &key mpointer dimensions) ¶eigen-hermv
) &key mpointer n) ¶nonlinear-ffit
) &key mpointer dimensions solver-type functions initial-guess) ¶standard-control
) &key mpointer absolute-error relative-error y-scaling dydt-scaling) ¶eigen-gensymm
) &key mpointer n) ¶monte-carlo-vegas
) &key mpointer dim) ¶histogram2d-pdf
) &key mpointer number-of-bins-y number-of-bins-x histogram) ¶y-control
) &key mpointer dydt-scaling y-scaling absolute-error relative-error) ¶levin-truncated
) &key mpointer order) ¶permutation
) &key mpointer size) ¶combination
) &key range dimensions &allow-other-keys) ¶fft-half-complex-wavetable-double-float
) &key mpointer n) ¶fft-real-workspace-double-float
) &key mpointer n) ¶fft-complex-wavetable-single-float
) &key mpointer n) ¶fft-complex-workspace-double-float
) &key mpointer n) ¶fft-complex-wavetable-double-float
) &key mpointer n) ¶fft-half-complex-wavetable-single-float
) &key mpointer n) ¶fft-real-workspace-single-float
) &key mpointer n) ¶fft-real-wavetable-single-float
) &key mpointer n) ¶fft-complex-workspace-single-float
) &key mpointer n) ¶fft-real-wavetable-double-float
) &key mpointer n) ¶random-number-generator
) stream) ¶permutation
) stream) ¶combination
) stream) ¶callback-included
) stream) ¶interpolation
) &key xa ya) ¶monte-carlo-plain
) &key) ¶histogram-pdf
) &key histogram) ¶random-number-generator
) &key value) ¶multi-dimensional-root-solver-f
) &key functions initial) ¶yp-control
) &key absolute-error relative-error y-scaling dydt-scaling) ¶qawo-table
) &key omega l trig) ¶multi-dimensional-root-solver-fdf
) &key functions initial) ¶one-dimensional-root-solver-fdf
) &key functions root-guess) ¶multi-dimensional-minimizer-fdf
) &key functions initial step-size tolerance) ¶nonlinear-fdffit
) &key functions initial-guess) ¶multi-dimensional-minimizer-f
) &key functions initial step-size) ¶one-dimensional-root-solver-f
) &key functions lower upper) ¶qaws-table
) &key alpha beta mu nu) ¶scaled-control
) &key absolute-error relative-error y-scaling dydt-scaling) ¶quasi-random-number-generator
) &key) ¶histogram2d
) &key x-ranges y-ranges) ¶ode-stepper
) &key) ¶one-dimensional-minimizer
) &key functions x-minimum f-minimum x-lower f-lower x-upper f-upper) ¶monte-carlo-miser
) &key) ¶chebyshev
) &key functions lower-limit upper-limit) ¶ode-evolution
) &key) ¶nonlinear-ffit
) &key functions initial-guess) ¶standard-control
) &key absolute-error relative-error y-scaling dydt-scaling) ¶monte-carlo-vegas
) &key) ¶histogram2d-pdf
) &key histogram) ¶y-control
) &key absolute-error relative-error y-scaling dydt-scaling) ¶permutation
) &key) ¶The condition BAD-FUNCTION-SUPPLIED, ‘Problem with user-supplied function,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+ebadfunc+)
:error-number
This slot is read-only.
:class
(quote "problem with user-supplied function")
:error-text
This slot is read-only.
The condition CACHE-LIMIT-EXCEEDED, ‘Cache limit exceeded,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+ecache+)
:error-number
This slot is read-only.
:class
(quote "cache limit exceeded")
:error-text
This slot is read-only.
The condition DIVERGENCE, ‘Integral or series is divergent,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+ediverge+)
:error-number
This slot is read-only.
:class
(quote "integral or series is divergent")
:error-text
This slot is read-only.
The condition EXCEEDED-MAXIMUM-ITERATIONS, ‘Exceeded max number of iterations,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+emaxiter+)
:error-number
This slot is read-only.
:class
(quote "exceeded max number of iterations")
:error-text
This slot is read-only.
The condition FACTORIZATION-FAILURE, ‘Factorization failed,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+efactor+)
:error-number
This slot is read-only.
:class
(quote "factorization failed")
:error-text
This slot is read-only.
The condition FAILURE-TO-REACH-TOLERANCE, ‘Failed to reach the specified tolerance,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+etol+)
:error-number
This slot is read-only.
:class
(quote "failed to reach the specified tolerance")
:error-text
This slot is read-only.
The condition FAILURE-TO-REACH-TOLERANCE-F, ‘Cannot reach the specified tolerance in F,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+etolf+)
:error-number
This slot is read-only.
:class
(quote "cannot reach the specified tolerance in f")
:error-text
This slot is read-only.
The condition FAILURE-TO-REACH-TOLERANCE-G, ‘Cannot reach the specified tolerance in gradient,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+etolg+)
:error-number
This slot is read-only.
:class
(quote "cannot reach the specified tolerance in gradient")
:error-text
This slot is read-only.
The condition FAILURE-TO-REACH-TOLERANCE-X, ‘Cannot reach the specified tolerance in X,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+etolx+)
:error-number
This slot is read-only.
:class
(quote "cannot reach the specified tolerance in x")
:error-text
This slot is read-only.
The condition GENERIC-FAILURE-1, ‘Generic failure,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+efailed+)
:error-number
This slot is read-only.
:class
(quote "generic failure")
:error-text
This slot is read-only.
The condition GENERIC-FAILURE-2, ‘Generic failure,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+failure+)
:error-number
This slot is read-only.
:class
(quote "generic failure")
:error-text
This slot is read-only.
A condition that has been signalled by the GNU Scientific Library.
gsll
.
arithmetic-error
.
warning
.
bad-function-supplied
.
cache-limit-exceeded
.
divergence
.
exceeded-maximum-iterations
.
factorization-failure
.
failure-to-reach-tolerance
.
failure-to-reach-tolerance-f
.
failure-to-reach-tolerance-g
.
failure-to-reach-tolerance-x
.
generic-failure-1
.
generic-failure-2
.
gsl-division-by-zero
.
input-domain
.
input-range
.
invalid-argument
.
invalid-pointer
.
invalid-tolerance
.
jacobian-not-improving
.
loss-of-accuracy
.
memory-allocation-failure
.
no-progress
.
nonconformant-dimensions
.
nonsquare-matrix
.
overflow
.
roundoff-failure
.
runaway-iteration
.
sanity-check-failure
.
singularity
.
table-limit-exceeded
.
underflow
.
unimplemented-feature
.
unspecified-errno
.
unsupported-feature
.
:error-number
This slot is read-only.
:error-text
This slot is read-only.
:explanation
This slot is read-only.
(quote nil)
:source-file
This slot is read-only.
(quote 0)
:line-number
This slot is read-only.
The condition GSL-DIVISION-BY-ZERO, ‘Tried to divide by zero,’ signalled by the GNU Scientific Library.
gsll
.
division-by-zero
.
gsl-condition
.
:class
(quote gsll::+ezerodiv+)
:error-number
This slot is read-only.
:class
(quote "tried to divide by zero")
:error-text
This slot is read-only.
The condition GSL-EOF, ‘End of file,’ signalled by the GNU Scientific Library.
The condition INPUT-DOMAIN, ‘Input domain error,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+edom+)
:error-number
This slot is read-only.
:class
(quote "input domain error")
:error-text
This slot is read-only.
The condition INPUT-RANGE, ‘Output range error,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+erange+)
:error-number
This slot is read-only.
:class
(quote "output range error")
:error-text
This slot is read-only.
The condition INVALID-ARGUMENT, ‘Invalid argument,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+einval+)
:error-number
This slot is read-only.
:class
(quote "invalid argument")
:error-text
This slot is read-only.
The condition INVALID-POINTER, ‘Invalid pointer,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+efault+)
:error-number
This slot is read-only.
:class
(quote "invalid pointer")
:error-text
This slot is read-only.
The condition INVALID-TOLERANCE, ‘User specified an invalid tolerance,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+ebadtol+)
:error-number
This slot is read-only.
:class
(quote "user specified an invalid tolerance")
:error-text
This slot is read-only.
The condition JACOBIAN-NOT-IMPROVING, ‘Jacobian evaluations are not improving the solution,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+enoprogj+)
:error-number
This slot is read-only.
:class
(quote "jacobian evaluations are not improving the solution")
:error-text
This slot is read-only.
The condition LOSS-OF-ACCURACY, ‘Loss of accuracy,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+eloss+)
:error-number
This slot is read-only.
:class
(quote "loss of accuracy")
:error-text
This slot is read-only.
The condition MEMORY-ALLOCATION-FAILURE, ‘Malloc failed,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+enomem+)
:error-number
This slot is read-only.
:class
(quote "malloc failed")
:error-text
This slot is read-only.
The condition NO-PROGRESS, ‘Iteration is not making progress towards solution,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+enoprog+)
:error-number
This slot is read-only.
:class
(quote "iteration is not making progress towards solution")
:error-text
This slot is read-only.
The condition NONCONFORMANT-DIMENSIONS, ‘Matrix, vector lengths are not conformant,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+ebadlen+)
:error-number
This slot is read-only.
:class
(quote "matrix, vector lengths are not conformant")
:error-text
This slot is read-only.
The condition NONSQUARE-MATRIX, ‘Matrix not square,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+enotsqr+)
:error-number
This slot is read-only.
:class
(quote "matrix not square")
:error-text
This slot is read-only.
The condition OVERFLOW, ‘Overflow,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+eovrflw+)
:error-number
This slot is read-only.
:class
(quote "overflow")
:error-text
This slot is read-only.
The condition ROUNDOFF-FAILURE, ‘Failed because of roundoff error,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+eround+)
:error-number
This slot is read-only.
:class
(quote "failed because of roundoff error")
:error-text
This slot is read-only.
The condition RUNAWAY-ITERATION, ‘Iterative process is out of control,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+erunaway+)
:error-number
This slot is read-only.
:class
(quote "iterative process is out of control")
:error-text
This slot is read-only.
The condition SANITY-CHECK-FAILURE, ‘Sanity check failed - shouldn’t happen,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+esanity+)
:error-number
This slot is read-only.
:class
(quote "sanity check failed - shouldn't happen")
:error-text
This slot is read-only.
The condition SINGULARITY, ‘Apparent singularity detected,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+esing+)
:error-number
This slot is read-only.
:class
(quote "apparent singularity detected")
:error-text
This slot is read-only.
The condition TABLE-LIMIT-EXCEEDED, ‘Table limit exceeded,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+etable+)
:error-number
This slot is read-only.
:class
(quote "table limit exceeded")
:error-text
This slot is read-only.
The condition UNDERFLOW, ‘Underflow,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+eundrflw+)
:error-number
This slot is read-only.
:class
(quote "underflow")
:error-text
This slot is read-only.
The condition UNIMPLEMENTED-FEATURE, ‘Requested feature not (yet) implemented,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+eunimpl+)
:error-number
This slot is read-only.
:class
(quote "requested feature not (yet) implemented")
:error-text
This slot is read-only.
The condition UNSUPPORTED-FEATURE, ‘Requested feature is not supported by the hardware,’ signalled by the GNU Scientific Library.
gsll
.
:class
(quote gsll::+eunsup+)
:error-number
This slot is read-only.
:class
(quote "requested feature is not supported by the hardware")
:error-text
This slot is read-only.
The GSL representation of the acceleration for interpolation.
gsll
.
The GSL representation of the basis spline.
gsll
.
The GSL representation of the Chebyshev series.
The GSL representation of the lookup table for the discrete random number generator.
gsll
.
The GSL representation of the generalized nonsymmetric eigenvalue workspace.
gsll
.
The GSL representation of the hermitian generalized eigenvalue workspace.
gsll
.
The GSL representation of the hermitian generalized eigensystem workspace.
gsll
.
The GSL representation of the symmetric generalized eigenvalue workspace.
gsll
.
The GSL representation of the symmetric generalized eigensystem workspace.
gsll
.
The GSL representation of the generalized nonsymmetric eigenvector and eigenvalue workspace.
gsll
.
The GSL representation of the Hermitian eigenvalue workspace.
gsll
.
The GSL representation of the Hermitian eigensystem workspace.
gsll
.
The GSL representation of the non-symmetric eigenvalue workspace.
gsll
.
The GSL representation of the non-symmetric eigenvector and eigenvalue workspace.
gsll
.
The GSL representation of the symmetric eigenvalue workspace.
gsll
.
The GSL representation of the symmetric eigensystem workspace.
gsll
.
The GSL representation of the multi-dimensional root solver with function only.
gsll
.
The GSL representation of the discrete Hankel Transform.
gsll
.
The GSL representation of the one-dimensional histogram, including bin boundaries and bin contents.
gsll
.
The GSL representation of the one-dimensional histogram PDF.
gsll
.
The GSL representation of the two-dimensional histogram, including bin boundaries and bin contents..
gsll
.
The GSL representation of the two-dimensional histogram PDF.
gsll
.
The GSL representation of the integration workspace.
gsll
.
The GSL representation of the interpolation.
gsll
.
The GSL representation of the Levin u-transform.
gsll
.
The GSL representation of the truncated Levin u-transform.
gsll
.
The GSL representation of the workspace for Mathieu functions.
gsll
.
The GSL representation of the miser Monte Carlo integration.
gsll
.
The GSL representation of the plain Monte Carlo integration.
gsll
.
The GSL representation of the vegas Monte Carlo integration.
gsll
.
The GSL representation of the multi-dimensional minimizer with function only.
The GSL representation of the multi-dimensional minimizer with function and derivative.
The GSL representation of the multi-dimensional root solver with function only.
The GSL representation of the multi-dimensional root solver with function and derivative.
The GSL representation of the nonlinear least squares fit with function and derivative.
The GSL representation of the nonlinear least squares fit with function only.
The GSL representation of the evolution for ordinary differential equations.
gsll
.
The GSL representation of the stepper for ordinary differential equations.
The GSL representation of the one-dimensional minimizer.
The GSL representation of the one-dimensional root solver with function only.
The GSL representation of the one-dimensional root solver with function and derivative.
The GSL representation of the permutation.
gsll
.
allocate
.
aref
.
copy
.
dimensions
.
initialize-instance
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
permute-inverse
.
print-object
.
reinitialize-instance
.
set-identity
.
size
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
sort-vector-index
.
swap-elements
.
validp
.
The GSL representation of the complex workspace for polynomials.
gsll
.
The GSL representation of the table for QAWO numerical integration method.
gsll
.
The GSL representation of the table for QAWS numerical integration method.
gsll
.
The GSL representation of the quasi random number generator.
gsll
.
The GSL representation of the random number generator.
gsll
.
allocate
.
copy
.
initialize-instance
.
name
.
print-object
.
reinitialize-instance
.
rng-state
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
sample
.
size
.
The GSL representation of the scaled control for ordinary differential equations.
gsll
.
The GSL representation of the spline.
gsll
.
The GSL representation of the standard control for ordinary differential equations.
gsll
.
The GSL representation of the wavelet.
gsll
.
The GSL representation of the wavelet workspace.
gsll
.
The GSL representation of the y control for ordinary differential equations.
gsll
.
The GSL representation of the yp control for ordinary differential equations.
gsll
.
The list of floating point types that can be spliced into BLAS function names.
gsll
.
A table of :callbacks arguments for each class.
gsll
.
Mapping the C standard types to the BLAS splice name.
gsll
.
Mapping the C standard types to the GSL splice name.
gsll
.
The default size to make an array returned from a special function.
gsll
.
A sequence of random double floats ranging between -100.0d0 and +100.0d0.
gsll
.
The list of floating point types that can be spliced into function names.
gsll
.
The list of integer types that can be spliced into function names.
gsll
.
The full path string of the ntuple example data file. This can be created with the function #’make-ntuple-example-data.
gsll
.
An arbitrary offset for the generated pointers; non-negative fixnum value is irrelevant and changed for debugging purposes only.
gsll
.
A sequence of random integers ranging between -255 and 255.
gsll
.
A sequence of random integers ranging between 0 and 255.
gsll
.
Data for example wavelet transform from doc/examples/ecg.dat.
gsll
.
gsll
.
gsll
.
gsll
.
Define the random number generator type.
gsll
.
Definition of a GSL function.
gsll
.
Define the class, the allocate, initialize-instance and reinitialize-instance methods, and the make-* function for the GSL object.
gsll
.
Define a library variable pointer.
gsll
.
T if all FFT tests pass.
gsll
.
T if all FFT tests pass.
gsll
.
Execute this form only if the pointer is of grid:+foreign-pointer-type+; otherwise call the next method.
gsll
.
gsll
.
Bind defmfun’s key arguments.
gsll
.
Create a form to access the GSL array value from the mpointer. If value is not nil, set the value; otherwise, get the value.
Replace the declared proto-type with an actual GSL struct type in the GSL function name.
gsll
.
From the category (’vector, ’grid:matrix, or ’both) and element type, find the class name.
gsll
.
Replace the prototype arglist with an actual arglist.
gsll
.
Replace the generic element type :element-c-type with the actual element type.
gsll
.
Create the GSL or BLAS function name for data from the base name and the CL type.
gsll
.
The portion of the arglist from the first llk on.
gsll
.
Create a function that returns dimensions for argspecs that are arrays for the specified direction.
gsll
.
Get arglist without classes and a list of categories.
gsll
.
Make an array of the current type and initialize from the pool.
gsll
.
A list of forms reference each array element in succession.
If there is no argspec for the argument, just reference the variable itself.
gsll
.
Update the fixnum vectors count and edge with sample random values from the distribution, and return the mean.
gsll
.
Expand the body (computational part) of the defmfun.
gsll
.
Wrap necessary array-handling forms around the expanded unswitched body form.
gsll
.
Create the body of a defmfun with &optional in its arglist, where the presence or absence of the optional argument(s) selects one of two GSL functions.
gsll
.
The arguments passed by GSL to the callback function.
gsll
.
Remove from the list the symbol representing the foreign callback argument.
gsll
.
Replace in the list the symbol representing the foreign callback argument.
gsll
.
Make a form to set the dynamic variable defining callbacks.
gsll
.
Create the multiple-value-bind form in the callback to set the return C arrays.
gsll
.
Set the slots in the foreign callback struct.
gsll
.
Generate the form to set each of the dynamic (special) variables to (function scalarsp dimensions...) in the body of the demfun for each of the callback functions.
gsll
.
Find the category (class) for the given argument.
gsll
.
Check the return status code from a GSL function and signal a warning if it is not :SUCCESS.
gsll
.
Create CL argument and types from the C arguments.
gsll
.
Generate a form that calls the appropriate converter from C/GSL to CL.
gsll
.
The GSL splice string from the CL type.
gsll
.
Copy the elements of the combination source into the
combination destination. The two combinations must have the same size.
gsll
.
A complete definition form, starting with defun, :method, or defmethod.
gsll
.
Return two complex numbers, the value and the error.
gsll
.
Copy a vector and initialize it.
gsll
.
Make Hilbert matrix used to test linear algebra functions.
gsll
.
Make a matrix or vector of the specified dimensions, with contents based on a function of the element indices i, j.
gsll
.
Make Van der Monde matrix used to test linear algebra functions.
gsll
.
The symbol-type of the return from the C function.
gsll
.
The significand (mantissa), exponent, and sign of the IEEE 754
representation of a floating point number, given as integers. It does
not matter whether the actual representation follows IEEE.
Values returned are significand, exponent, sign, bits in significand,
bits in exponent.
gsll
.
When defining :method in a defgeneric, (nil foo) is used for the name, and foo will be returned from this function.
gsll
.
Generate the return computation expression for defmfun.
gsll
.
Compute the CDF for a bin from the PDF.
gsll
.
Find the actual form to use as the default based on the list in form.
gsll
.
If this argument has an eql specializer, return the specialization category; otherwise nil.
gsll
.
Evaluate integral of sin(x) in interval 0-pi. sin(x) is tabulated over a 0-2pi interval and interpolated with +periodic-cubic-spline-interpolation+
gsll
.
gsll
.
Define methods for all kinds of arrays.
gsll
.
Define a generic function and methods for all kinds of arrays.
gsll
.
Create a specific method for a previously-defined generic function.
gsll
.
Expand defmfun where there is an optional argument
present, giving the choice between two different GSL functions.
gsll
.
gsll
.
Compute the negative of the residuals with the exponential model for the nonlinear least squares example.
gsll
.
Compute the partial derivatives of the negative of the
residuals with the exponential model
for the nonlinear least squares example.
gsll
.
Compute the function and partial derivatives of the negative of the
residuals with the exponential model
for the nonlinear least squares example.
gsll
.
Make the form that turns the mpointer into a foreign-array.
gsll
.
Return the index where the highest frequency component is located in a vector of the given size, after applying an FFT. The second value that is returned, is the most negative frequency divided by the sample frequency step.
gsll
.
Return the frequency step for the FFT of a vector with the given size and assuming the given sample spacing.
gsll
.
Return the highest frequency for the FFT of a vector with the given size and assuming the given sample spacing.
gsll
.
Generate all the permutations of n objects.
gsll
.
Generate all the permutations of n objects.
gsll
.
Create all the methods for a generic function.
gsll
.
Create the data used in the nonlinear least squares fit example.
gsll
.
Get all parameters, as a foreign struct, for the MISER method.
gsll
.
Get all parameters, as a foreign struct, for the VEGAS method.
gsll
.
The GSL version currently running is at least the version wanted, specified as (major minor).
gsll
.
Copy the histogram source into the pre-existing
histogram destination, making the latter into
an exact copy of the former.
The two histograms must be of the same size.
gsll
.
Copy the histogram source into the pre-existing
histogram destination, making the latter into
an exact copy of the former.
The two histograms must be of the same size.
gsll
.
The bytespec to access the sign bit in the IEEE754 specification.
gsll
.
The specified initialize-suffix indicates that there are two foreign functions that can be called; which one is called is dependent on the presence or absense of certain arguments.
gsll
.
Integrate the van der Pol oscillator as given in Section 25.5 of the GSL manual. To reproduce that example, (integrate-vanderpol 100.0d0).
gsll
.
Returns nil if finite and within limits.
gsll
.
Second example in Section 36.5 of the GSL manual. Returns the coefficients of x^0, x^1, x^2 for the best fit, and the chi squared.
gsll
.
First example in Section 36.5 of the GSL manual.
gsll
.
Compute the best-fit parameters c of the weighted or unweighted
model y = X c for the observations y and optional weights
and the model matrix X. The covariance matrix of
the model parameters is computed with the given weights. The
weighted sum of squares of the residuals from the best-fit,
chi^2, is returned as the last value.
The best-fit is found by singular value decomposition of the matrix model using the preallocated workspace provided. The modified Golub-Reinsch SVD algorithm is used for the unweighted solution, with column scaling to improve the accuracy of the singular values. Any components which have zero singular value (to machine precision) are discarded from the fit.
gsll
.
Compute the best-fit parameters c of the weighted or unweighted model y = X c for the observations y and weights and the model matrix X. The covariance matrix of the model parameters is computed with the given weights. The weighted or unweighted sum of squares of the residuals from the best-fit, chi^2, is returned as the first value.
The best-fit is found by singular value decomposition of the matrix model using the preallocated workspace provided. The modified Golub-Reinsch SVD algorithm is used, with column scaling to improve the accuracy of the singular values (unweighted). Any components which have zero singular value (to machine precision) are discarded from the fit. In the second form of the function the components are discarded if the ratio of singular values s_i/s_0 falls below the user-specified tolerance, and the effective rank is returned as the second value.
gsll
.
Make a vector of the given element type and size. If init-offset is given, it is assumed to be a valid number, with which the vector is initialised; each element is set to a unique, predetermined value. See also test.c in GSL’s fft directory.
gsll
.
Make the callback structure.
gsll
.
Make the callback structure based on the mobject definition.
gsll
.
Create the GSL object representing a structure that holds the factorization and trigonometric lookup tables for
the mixed radix complex fft algorithm (class FFT-COMPLEX-WAVETABLE-DOUBLE-FLOAT).
This function prepares a trigonometric lookup table for a complex FFT of
length n. The function returns a pointer to the newly allocated
gsl_fft_complex_wavetable if no errors were detected, and a null pointer in
the case of error. The length n is factorized into a product of
subtransforms, and the factors and their trigonometric coefficients are
stored in the wavetable. The trigonometric coefficients are computed using
direct calls to sin and cos, for accuracy. Recursion relations could be used
to compute the lookup table faster, but if an application performs many FFTs
of the same length then this computation is a one-off overhead which does
not affect the final throughput.
The wavetable structure can be used repeatedly for any transform of the same
length. The table is not modified by calls to any of the other FFT
functions. The same wavetable can be used for both forward and backward (or
inverse) transforms of a given length.
gsll
.
Create the GSL object representing a structure that holds the factorization and trigonometric lookup tables for
the mixed radix complex float fft algorithm (class FFT-COMPLEX-WAVETABLE-SINGLE-FLOAT).
This function prepares a trigonometric lookup table for a complex float FFT
of length n. The function returns a pointer to the newly allocated
gsl_fft_complex_wavetable if no errors were detected, and a null pointer in
the case of error. The length n is factorized into a product of
subtransforms, and the factors and their trigonometric coefficients are
stored in the wavetable. The trigonometric coefficients are computed using
direct calls to sin and cos, for accuracy. Recursion relations could be used
to compute the lookup table faster, but if an application performs many FFTs
of the same length then this computation is a one-off overhead which does
not affect the final throughput.
The wavetable structure can be used repeatedly for any transform of the same
length. The table is not modified by calls to any of the other FFT
functions. The same wavetable can be used for both forward and backward (or
inverse) transforms of a given length.
gsll
.
Create the GSL object representing a Structure that holds the additional working space required for the intermediate steps of the mixed radix complex fft algoritms (class FFT-COMPLEX-WORKSPACE-DOUBLE-FLOAT). This function allocates a workspace for a complex transform of length n.
gsll
.
Create the GSL object representing a Structure that holds the additional working space required for the
intermediate steps of the mixed radix complex float fft algoritms (class FFT-COMPLEX-WORKSPACE-SINGLE-FLOAT).
This function allocates a workspace for a complex float transform of length
n.
gsll
.
Create the GSL object representing a structure that holds the factorization and trigonometric lookup tables for
the mixed radix halfcomplex fft algorithm (class FFT-HALF-COMPLEX-WAVETABLE-DOUBLE-FLOAT).
These functions prepare trigonometric lookup tables for an FFT of size n
real elements. The functions return a pointer to the newly allocated struct
if no errors were detected, and a null pointer in the case of error. The
length n is factorized into a product of subtransforms, and the factors and
their trigonometric coefficients are stored in the wavetable. The
trigonometric coefficients are computed using direct calls to sin and cos,
for accuracy. Recursion relations could be used to compute the lookup table
faster, but if an application performs many FFTs of the same length then
computing the wavetable is a one-off overhead which does not affect the
final throughput.
The wavetable structure can be used repeatedly for any transform of the same
length. The table is not modified by calls to any of the other FFT
functions. The appropriate type of wavetable must be used for forward real
or inverse half-complex transforms.
gsll
.
Create the GSL object representing a structure that holds the factorization and trigonometric lookup tables for
the mixed radix real float fft algorithm (class FFT-HALF-COMPLEX-WAVETABLE-SINGLE-FLOAT).
These functions prepare trigonometric lookup tables for an FFT of size n
real float elements. The functions return a pointer to the newly allocated
struct if no errors were detected, and a null pointer in the case of error.
The length n is factorized into a product of subtransforms, and the factors
and their trigonometric coefficients are stored in the wavetable. The
trigonometric coefficients are computed using direct calls to sin and cos,
for accuracy. Recursion relations could be used to compute the lookup table
faster, but if an application performs many FFTs of the same length then
computing the wavetable is a one-off overhead which does not affect the
final throughput.
The wavetable structure can be used repeatedly for any transform of the same
length. The table is not modified by calls to any of the other FFT
functions. The appropriate type of wavetable must be used for forward real
or inverse half-complex transforms.
gsll
.
Create the GSL object representing a structure that holds the factorization and trigonometric lookup tables for
the mixed radix real fft algorithm (class FFT-REAL-WAVETABLE-DOUBLE-FLOAT).
These functions prepare trigonometric lookup tables for an FFT of size n
real elements. The functions return a pointer to the newly allocated struct
if no errors were detected, and a null pointer in the case of error. The
length n is factorized into a product of subtransforms, and the factors and
their trigonometric coefficients are stored in the wavetable. The
trigonometric coefficients are computed using direct calls to sin and cos,
for accuracy. Recursion relations could be used to compute the lookup table
faster, but if an application performs many FFTs of the same length then
computing the wavetable is a one-off overhead which does not affect the
final throughput.
The wavetable structure can be used repeatedly for any transform of the same
length. The table is not modified by calls to any of the other FFT
functions. The appropriate type of wavetable must be used for forward real
or inverse half-complex transforms.
gsll
.
Create the GSL object representing a structure that holds the factorization and trigonometric lookup tables for
the mixed radix real float fft algorithm (class FFT-REAL-WAVETABLE-SINGLE-FLOAT).
These functions prepare trigonometric lookup tables for an FFT of size n
real float elements. The functions return a pointer to the newly allocated
struct if no errors were detected, and a null pointer in the case of error.
The length n is factorized into a product of subtransforms, and the factors
and their trigonometric coefficients are stored in the wavetable. The
trigonometric coefficients are computed using direct calls to sin and cos,
for accuracy. Recursion relations could be used to compute the lookup table
faster, but if an application performs many FFTs of the same length then
computing the wavetable is a one-off overhead which does not affect the
final throughput.
The wavetable structure can be used repeatedly for any transform of the same
length. The table is not modified by calls to any of the other FFT
functions. The appropriate type of wavetable must be used for forward real
or inverse half-complex transforms.
gsll
.
Create the GSL object representing a Structure that holds the additional working space required for the intermediate steps of the mixed radix real fft algoritms (class FFT-REAL-WORKSPACE-DOUBLE-FLOAT). This function allocates a workspace for a real transform of length n.
gsll
.
Create the GSL object representing a Structure that holds the additional working space required for the
intermediate steps of the mixed radix real float fft algoritms (class FFT-REAL-WORKSPACE-SINGLE-FLOAT).
This function allocates a workspace for a real float transform of length
n.
gsll
.
Make the foreign array when a GSL pointer to a gsl-vector-c or gsl-matrix-c is given.
gsll
.
Define a wrapper function to interface GSL with the user’s function. scalarsp will be either T or NIL, depending on whether the user function expects and returns scalars, and dimension-values should be a list of number(s), (dim0) or (dim0 dim1), or NIL.
gsll
.
Make compiled functions for the object that can be funcalled in the callback.
gsll
.
Make the necessary GSL metadata (mpointer and block-pointer) for the given foreign array, and return the mpointer. This should only be called by #’mpointer the first time it is called on a particular foreign-array.
gsll
.
gsll
.
Make a list for :initial-contents of the specified element type and length using the pool data for the type and starting at the specified point in the pool.
gsll
.
Make the defmcallback forms needed to define the callbacks associated with mobject that includes callback functions.
gsll
.
Make a new simulated annealing state.
Pass any arguments to user-state-maker-function.
gsll
.
Expand the reinitialize-instance form.
gsll
.
Make a vector with random elements.
gsll
.
maps elements in list and finally appends all resulted lists.
gsll
.
Example function for Monte Carlo used in random walk studies.
gsll
.
The mean of the histogrammed x variable, where the histogram is regarded as a probability distribution. Negative bin values are ignored for the purposes of this calculation.
gsll
.
The mean of the histogrammed y variable, where the histogram is regarded as a probability distribution. Negative bin values are ignored for the purposes of this calculation.
gsll
.
Solving a minimum, the example given in Sec. 33.8 of the GSL manual.
gsll
.
Make the defun form that makes the mobject.
gsll
.
This is an example solving the multidimensional minimization problem of a paraboloid using the derivative. The callback functions paraboloid-vector and paraboloid-derivative expect vectors. Contrast this with multimin-example-derivative-scalars, which expects and returns the scalar components.
gsll
.
This is an example solving the multidimensional minimization problem
of a paraboloid using the derivative. The callback functions
paraboloid-scalar and paraboloid-derivative-scalar expect scalars.
Contrast this with multimin-example-derivative, which
expects and returns vectors.
gsll
.
Generate data for second example in Section 36.5 of the GSL manual.
gsll
.
gsll
.
Create an ntuple historgram example data file, and read it.
gsll
.
The presence/absence of optional arguments will switch between the first and second listed GSL function names.
gsll
.
gsll
.
A paraboloid function of two arguments, given in GSL manual Sec. 35.4. This version takes scalar arguments.
gsll
.
A paraboloid function of two arguments, given in GSL manual Sec. 35.4. This version takes a vector-double-float argument.
gsll
.
From the :callbacks argument, parse a single argument of a single function specification.
gsll
.
From the :callbacks argument, parse a single function specification.
gsll
.
Get the information component from the callbacks list.
gsll
.
Copy the elements of the permutation source into the
permutation destination. The two permutations must have the same size.
gsll
.
Copy the quasi-random sequence generator src into the pre-existing generator dest, making dest into an exact copy of src. The two generators must be of the same type.
gsll
.
The real vector consisting of the real part of the complex vector.
gsll
.
Create the form to reference the element of a foreign array, or a scalar, for getting or setting.
gsll
.
Copy the random number generator source into the
pre-existing generator destination,
making destination into an exact copy
of source. The two generators must be of the same type.
gsll
.
A pointer to an array of all the available generator types, terminated by a null pointer. The function should be called once at the start of the program, if needed. Users should call all-random-number-generators.
gsll
.
Solving Rosenbrock with derivatives, the example given in Sec. 34.8 of the GSL manual.
gsll
.
Solving Rosenbrock, the example given in Sec. 34.8 of the GSL manual.
gsll
.
Solving a quadratic, the example given in Sec. 32.10 of the GSL manual.
gsll
.
Solving a quadratic, the example given in Sec. 32.10 of the GSL manual.
gsll
.
The partial derivatives of the Rosenbrock functions.
gsll
.
Make a scalar of the current type from the pool. For complex types, setting float-type will select a real of the corresponding component float type.
gsll
.
Make the slots in the foreign callback structure.
gsll
.
Set the parameter for the MISER method.
gsll
.
Set the parameters slot to null.
gsll
.
gsll
.
gsll
.
Set the slot in the cbstruct to the callback corresponding to gsl-function. If gsl-function is nil, set to the null-pointer.
gsll
.
gsll
.
Check the results of multiple returns where each value may have an error estimate returned as well.
gsll
.
Check the result of a single value as in test_sf_check_result in specfunc/test_sf.c.
gsll
.
Signal an error from the GSL library.
gsll
.
Signal a warning from the GSL library.
gsll
.
gsll
.
In the form, replace the plural symbol with the singular symbol given.
gsll
.
Return the size of a vector while taking the stride into account.
gsll
.
Solution differential equation
y=1 with boundary conditions y(0)=(n-1)^2, y(n-1)=0.
The solution is the sequence: (n-1)^2, (n-2)^2, ... 9, 4, 2, 1, 0
Desicretization of y leads to a tridiagonal system of equations
(y_(i-1)-2_i+y_(i+1))/2 = 1 for 1 < i < (n - 2)
The boundary conditions are implemented as
y(0)=(n-1)^2
y(n-1)=0
gsll
.
The first example in Sec. 26.7 of the GSL manual.
gsll
.
Walk the form and if the first symbol of the list is a member of eval-list, evaluate it and use the result. Otherwise use the result as-is.
gsll
.
This will work with the simplest s-expression forms only to find variables used.
gsll
.
If status is +success+, return T, otherwise return NIL.
gsll
.
If status is either +success+ or +continue+, return T; otherwise, return NIL.
gsll
.
Make a list of key symbol, listifying if singular.
gsll
.
Decompose using Cholesky and then multiply.
gsll
.
Invert using Cholesky decomposition
gsll
.
Solve the linear equation using Cholesky with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
gsll
.
Test forward, inverse and backward FFT for a complex vector and return all three results.
gsll
.
A test of real forward and complex forward, reverse, and inverse FFT
on random noise. Returns the result of the DFT forward Fourier transformation
and the forward FFT, which should be the same, and the original vector and the
inverse FFT, which should also be the same. In addition,
the backward Fourier transform is returned for complex vectors, which
should be the same as the last two.
gsll
.
Solve the linear equation using Householder with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
gsll
.
Solve the linear equation using LU with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
Solve the QR decomposition with the supplied
matrix and a right-hand side vector which is the reciprocal of one
more than the index.
Solve the linear equation using QR least squares with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index. Returns the solution and the residual.
Solve the linear equation using QR with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
Solve the linear equation using QR with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
Test QR rank-1 update; this should return a matrix with all elements near zero.
Solve the QRPT decomposition with the supplied
matrix and a right-hand side vector which is the reciprocal of one
more than the index.
Solve the linear equation using QRPT with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
Solve the linear equation using QRPT with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
Test forward and inverse FFT for a real vector, and return both results in unpacked form.
gsll
.
Solve the linear equation using SVD with the supplied matrix and a right-hand side vector which is the reciprocal of one more than the index.
Test the probability density function in the same way that GSL does. If everything is functioning correctly, this will return T.
gsll
.
Return argspec ’dimensions with numerical sizes for dimensions substituted for dim0, dim1. If total = T, then return the product of those dimensions. The list dimensions-values is a list of one or two numerical values, (dim0-value dim1-value) or (dim0-value).
gsll
.
Return numbers as values and errors.
gsll
.
Find the arguments passed to the C function. This is a poor quality code walker, but is sufficient for actual usage of defmfun.
gsll
.
A view of the histogram bin counts as a foreign array. The two objects point to the same foreign data.
gsll
.
A view of the histogram range as a foreign array. This vector has one more element than the number of bins; the first element is the lower bound of the first bin, and the last element is the upper bound of the last bin. The two objects point to the same foreign data.
gsll
.
Find the specs for all variables, or all array variables, with the specified direction.
gsll
.
Demonstrates the use of the one-dimensional wavelet transform functions. It computes an approximation to an input signal (of length 256) using the 20 largest components of the wavelet transform, while setting the others to zero. See GSL manual Section 30.4.
gsll
.
Simpler example, with only a Daubechies wavelet forward transformation.
gsll
.
Wrap the expanded-body with index and export if requested. Use a progn if needed.
gsll
.
Allocate memory for the GSL struct given a block pointer.
gsll
.
matrix-unsigned-byte-64
) blockptr) ¶matrix-signed-byte-64
) blockptr) ¶matrix-unsigned-byte-32
) blockptr) ¶matrix-signed-byte-32
) blockptr) ¶matrix-unsigned-byte-16
) blockptr) ¶matrix-signed-byte-16
) blockptr) ¶matrix-unsigned-byte-8
) blockptr) ¶matrix-signed-byte-8
) blockptr) ¶matrix-complex-double-float
) blockptr) ¶matrix-complex-single-float
) blockptr) ¶matrix-double-float
) blockptr) ¶matrix-single-float
) blockptr) ¶vector-single-float
) blockptr) ¶vector-double-float
) blockptr) ¶vector-complex-single-float
) blockptr) ¶vector-complex-double-float
) blockptr) ¶vector-signed-byte-8
) blockptr) ¶vector-unsigned-byte-8
) blockptr) ¶vector-signed-byte-16
) blockptr) ¶vector-unsigned-byte-16
) blockptr) ¶vector-signed-byte-32
) blockptr) ¶vector-unsigned-byte-32
) blockptr) ¶vector-signed-byte-64
) blockptr) ¶vector-unsigned-byte-64
) blockptr) ¶Use GSL to allocate memory. Returns pointer but does not bind mpointer slot.
gsll
.
basis-spline
) &key order number-of-breakpoints) ¶nonlinear-fdffit
) &key solver-type dimensions) ¶nonlinear-ffit
) &key solver-type dimensions) ¶fit-workspace
) &key number-of-observations number-of-parameters) ¶multi-dimensional-minimizer-fdf
) &key type dimensions) ¶multi-dimensional-minimizer-f
) &key type dimensions) ¶multi-dimensional-root-solver-fdf
) &key type dimensions) ¶multi-dimensional-root-solver-f
) &key type dimensions) ¶one-dimensional-minimizer
) &key type) ¶one-dimensional-root-solver-fdf
) &key type) ¶one-dimensional-root-solver-f
) &key type) ¶wavelet-workspace
) &key size) ¶levin-truncated
) &key order) ¶acceleration
) &key) ¶interpolation
) &key type size) ¶ode-evolution
) &key dimensions) ¶scaled-control
) &key absolute-error relative-error y-scaling dydt-scaling absolute-scale dimension) ¶yp-control
) &key absolute-error relative-error) ¶standard-control
) &key absolute-error relative-error y-scaling dydt-scaling) ¶ode-stepper
) &key type dimensions) ¶monte-carlo-vegas
) &key dim) ¶monte-carlo-miser
) &key dim) ¶monte-carlo-plain
) &key dim) ¶qawo-table
) &key omega l trig n) ¶qaws-table
) &key alpha beta mu nu) ¶integration-workspace
) &key size) ¶histogram2d-pdf
) &key number-of-bins-x number-of-bins-y) ¶histogram-pdf
) &key number-of-bins) ¶histogram2d
) &key number-of-bins-x number-of-bins-y) ¶discrete-random
) &key probabilities) ¶quasi-random-number-generator
) &key rng-type dimension) ¶random-number-generator
) &key rng-type) ¶fft-half-complex-wavetable-single-float
) &key n) ¶fft-half-complex-wavetable-double-float
) &key n) ¶fft-complex-workspace-single-float
) &key n) ¶fft-complex-workspace-double-float
) &key n) ¶fft-complex-wavetable-single-float
) &key n) ¶fft-complex-wavetable-double-float
) &key n) ¶fft-real-workspace-single-float
) &key n) ¶fft-real-workspace-double-float
) &key n) ¶fft-real-wavetable-single-float
) &key n) ¶fft-real-wavetable-double-float
) &key n) ¶eigen-genv
) &key n) ¶eigen-genhermv
) &key n) ¶eigen-genherm
) &key n) ¶eigen-gensymmv
) &key n) ¶eigen-gensymm
) &key n) ¶eigen-nonsymmv
) &key n) ¶eigen-nonsymm
) &key n) ¶eigen-hermv
) &key n) ¶eigen-herm
) &key n) ¶eigen-symmv
) &key n) ¶eigen-symm
) &key n) ¶polynomial-complex-workspace
) &key n) ¶permutation
) &key size) ¶Backward decimation-in-frequency FFT on a vector for which (floor length stride) is a power of 2.
Backward FFT on a vector for which (floor length stride) is not a power of 2, in half complex form.
Backward FFT on a vector for which (floor length stride) is a power of 2, in half complex form.
Backward FFT on a complex vector for which (floor length stride) is not a power of 2.
Backward FFT on a vector for which (floor length stride) is a power of 2.
gsll
.
callback-included-cl
)) ¶automatically generated reader method
gsll
.
callback-included
)) ¶The specification form for static callback information.
gsll
.
callback-included
)) ¶The names in the GSL struct for dimensions.
gsll
.
failure-to-reach-tolerance-g
)) ¶failure-to-reach-tolerance-x
)) ¶failure-to-reach-tolerance-f
)) ¶jacobian-not-improving
)) ¶no-progress
)) ¶table-limit-exceeded
)) ¶cache-limit-exceeded
)) ¶unimplemented-feature
)) ¶unsupported-feature
)) ¶divergence
)) ¶singularity
)) ¶nonsquare-matrix
)) ¶nonconformant-dimensions
)) ¶roundoff-failure
)) ¶loss-of-accuracy
)) ¶failure-to-reach-tolerance
)) ¶invalid-tolerance
)) ¶gsl-division-by-zero
)) ¶exceeded-maximum-iterations
)) ¶runaway-iteration
)) ¶bad-function-supplied
)) ¶memory-allocation-failure
)) ¶sanity-check-failure
)) ¶factorization-failure
)) ¶generic-failure-2
)) ¶generic-failure-1
)) ¶invalid-argument
)) ¶invalid-pointer
)) ¶input-range
)) ¶input-domain
)) ¶gsl-condition
)) ¶gsll
.
failure-to-reach-tolerance-g
)) ¶failure-to-reach-tolerance-x
)) ¶failure-to-reach-tolerance-f
)) ¶jacobian-not-improving
)) ¶no-progress
)) ¶table-limit-exceeded
)) ¶cache-limit-exceeded
)) ¶unimplemented-feature
)) ¶unsupported-feature
)) ¶divergence
)) ¶singularity
)) ¶nonsquare-matrix
)) ¶nonconformant-dimensions
)) ¶roundoff-failure
)) ¶loss-of-accuracy
)) ¶failure-to-reach-tolerance
)) ¶invalid-tolerance
)) ¶gsl-division-by-zero
)) ¶exceeded-maximum-iterations
)) ¶runaway-iteration
)) ¶bad-function-supplied
)) ¶memory-allocation-failure
)) ¶sanity-check-failure
)) ¶factorization-failure
)) ¶generic-failure-2
)) ¶generic-failure-1
)) ¶invalid-argument
)) ¶invalid-pointer
)) ¶input-range
)) ¶input-domain
)) ¶unspecified-errno
)) ¶gsl-condition
)) ¶gsll
.
gsl-condition
)) ¶Convert an array of half-complex coefficients as returned by real-fft-radix2-transform, into an ordinary complex array.
This function converts an array of half-complex coefficients as returned by fft-real-transform, into an ordinary complex array. It fills in the complex array using the symmetry z_k = z_{n-k}^* to reconstruct the redundant elements.
This function converts a single real array into an equivalent complex array (with imaginary part set to zero), suitable for fft-complex routines.
Forward decimation-in-frequency FFT on a vector for which (floor length stride) is a power of 2.
Forward FFT on a vector for which (floor length stride) is not a power of 2, in half complex form.
Forward FFT on a vector for which (floor length stride) is a power of 2, in half complex form.
Forward FFT on a vector for which (floor length stride) is not a power of 2.
gsll
.
vector-single-float
) &key stride wavetable workspace) ¶vector-double-float
) &key stride wavetable workspace) ¶vector-complex-single-float
) &key stride wavetable workspace) ¶vector-complex-double-float
) &key stride wavetable workspace) ¶Forward FFT on a vector for which (floor length stride) is a power of 2.
gsll
.
vector-single-float
) &key stride) ¶vector-double-float
) &key stride) ¶vector-complex-single-float
) &key stride) ¶vector-complex-double-float
) &key stride) ¶Decimation-in-frequency version of the FFT in the given direction for a complex radix-2 vector
FFT in the given direction for a complex radix-2 vector
gsll
.
callback-included
)) ¶The function objects that will be called by the callbacks.
gsll
.
callback-included
)) ¶The user functions as function designators.
These should correspond in order to the structure-slot-name list.
gsll
.
obsolete-gsl-version
)) ¶gsll
.
obsolete-gsl-version
)) ¶Inverse decimation-in-frequency FFT on a vector for which (floor length stride) is a power of 2.
Inverse FFT on a vector for which (floor length stride) is not a power of 2, in half complex form.
Inverse FFT on a vector for which (floor length stride) is a power of 2, in half complex form.
Inverse FFT on a complex vector for which (floor length stride) is not a power of 2.
Inverse FFT on a vector for which (floor length stride) is a power of 2.
gsll
.
gsl-condition
)) ¶gsll
.
callback-included
)) ¶Whether the function expect to be passed and return scalars or arrays.
gsll
.
gsl-condition
)) ¶An error indicating that the currently loaded version of the GSL libary does not have the function defined.
Errno value from GNU Scientific Library not recognized.
A mobject that includes a callback function or functions to GSL.
gsll
.
The specification form for static callback information.
:cbinfo
This slot is read-only.
The names in the GSL struct for dimensions.
:dimension-names
This slot is read-only.
The user functions as function designators.
These should correspond in order to the structure-slot-name list.
:functions
This slot is read-only.
The function objects that will be called by the callbacks.
:funcallables
This slot is read-only.
Whether the function expect to be passed and return scalars or arrays.
t
:scalarsp
This slot is read-only.
grid
.
:dimensions
This slot is read-only.
A mobject that includes a callback function or functions, in which the pointer to the callback structure is stored in a CL class slot.
GSL combinations.
gsll
.
vector-unsigned-byte-64
.
The GSL representation of the structure that holds the factorization and trigonometric lookup tables for the mixed radix complex fft algorithm.
gsll
.
The GSL representation of the structure that holds the factorization and trigonometric lookup tables for the mixed radix complex float fft algorithm.
gsll
.
The GSL representation of the Structure that holds the additional working space required for the intermediate steps of the mixed radix complex fft algoritms.
gsll
.
The GSL representation of the Structure that holds the additional working space required for the intermediate steps of the mixed radix complex float fft algoritms.
gsll
.
The GSL representation of the structure that holds the factorization and trigonometric lookup tables for the mixed radix halfcomplex fft algorithm.
gsll
.
The GSL representation of the structure that holds the factorization and trigonometric lookup tables for the mixed radix real float fft algorithm.
gsll
.
The GSL representation of the structure that holds the factorization and trigonometric lookup tables for the mixed radix real fft algorithm.
gsll
.
The GSL representation of the structure that holds the factorization and trigonometric lookup tables for the mixed radix real float fft algorithm.
gsll
.
The GSL representation of the Structure that holds the additional working space required for the intermediate steps of the mixed radix real fft algoritms.
gsll
.
The GSL representation of the Structure that holds the additional working space required for the intermediate steps of the mixed radix real float fft algoritms.
gsll
.
gsll
.
foreign-struct-type
.
translatable-foreign-type
.
gsll
.
acceleration
.
basis-spline
.
callback-included
.
discrete-random
.
eigen-gen
.
eigen-genherm
.
eigen-genhermv
.
eigen-gensymm
.
eigen-gensymmv
.
eigen-genv
.
eigen-herm
.
eigen-hermv
.
eigen-nonsymm
.
eigen-nonsymmv
.
eigen-symm
.
eigen-symmv
.
fft-complex-wavetable-double-float
.
fft-complex-wavetable-single-float
.
fft-complex-workspace-double-float
.
fft-complex-workspace-single-float
.
fft-half-complex-wavetable-double-float
.
fft-half-complex-wavetable-single-float
.
fft-real-wavetable-double-float
.
fft-real-wavetable-single-float
.
fft-real-workspace-double-float
.
fft-real-workspace-single-float
.
fit-workspace
.
hankel
.
histogram
.
histogram-pdf
.
histogram2d
.
histogram2d-pdf
.
integration-workspace
.
interpolation
.
levin
.
levin-truncated
.
mathieu
.
monte-carlo-miser
.
monte-carlo-plain
.
monte-carlo-vegas
.
ode-control
.
ode-evolution
.
permutation
.
polynomial-complex-workspace
.
qawo-table
.
qaws-table
.
quasi-random-number-generator
.
random-number-generator
.
spline
.
wavelet
.
wavelet-workspace
.
gsll
.
foreign-struct-type
.
translatable-foreign-type
.
Objects used for control of ordinary differential equation integration.
gsll
.
foreign-struct-type
.
translatable-foreign-type
.
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