The num-utils Reference Manual

Parent

num-utils (system)

Location

elementwise.lisp

Exported Definitions

e* (function)
e+ (function)
e- (function)
e/ (function)
e1- (generic function)
e1- (method)
e1- (method)
e1/ (generic function)
e1/ (method)
e1/ (method)
e1log (generic function)
e1log (method)
e1log (method)
e2* (generic function)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2+ (generic function)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2- (generic function)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2/ (generic function)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2log (generic function)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
eceiling (generic function)
eceiling (method)
eceiling (method)
econjugate (generic function)
econjugate (method)
econjugate (method)
eexp (generic function)
eexp (method)
eexp (method)
eexpt (generic function)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
efloor (generic function)
efloor (method)
efloor (method)
elementwise-float-contagion (function)
elog (function)
emax (function)
emin (function)
emod (generic function)
emod (method)
emod (method)
emod (method)
emod (method)
emod (method)
emod (method)
emod (method)
ereduce (generic function)
ereduce (method)
ereduce (method)
ereduce (method)
esqrt (generic function)
esqrt (method)
esqrt (method)

Internal Definitions

define-e& (macro)
define-e1 (macro)
define-e2 (macro)
define-elementwise-reduction (macro)
esquare (generic function)
esquare (method)
esquare (method)
mapping-array (macro)

3.1.7 `num-utils/extended-real.lisp`

Dependency

Parent

num-utils (system)

Location

extended-real.lisp

Exported Definitions

< (function)
<= (function)
= (function)
> (function)
>= (function)
extended-real (type)
infinite? (function)
lambda-template (macro)
with-template (macro)

Internal Definitions

define-comparison (macro)
extend-pairwise-comparison (function)
infinite (type)

3.1.8 `num-utils/interval.lisp`

Dependency

extended-real.lisp (file)

Parent

num-utils (system)

Location

interval.lisp

Exported Definitions

&interval (macro)
extend-interval (generic function)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extendf-interval (macro)
finite-interval (class)
grid-in (function)
in-interval? (function)
interval (function)
interval (class)
interval-hull (function)
interval-length (function)
interval-midpoint (function)
left (generic function)
left (method)
left (method)
minusinf-interval (class)
num= (method)
num= (method)
open-left? (generic function)
open-left? (method)
open-left? (method)
open-right? (generic function)
open-right? (method)
open-right? (method)
plusinf-interval (class)
plusminus-interval (function)
real-line (class)
relative (function)
relative (structure)
right (generic function)
right (method)
right (method)
shift-interval (generic function)
shift-interval (method)
shrink-interval (function)
spacer (function)
spacer (structure)
split-interval (function)
subintervals-in (function)

Internal Definitions

copy-relative (function)
copy-spacer (function)
interval/finite-left (class)
interval/finite-right (class)
interval/infinite-left (class)
interval/infinite-right (class)
print-left-endpoint (generic function)
print-left-endpoint (method)
print-left-endpoint (method)
print-right-endpoint (generic function)
print-right-endpoint (method)
print-right-endpoint (method)
relative-fraction (function)
relative-p (function)
spacer-p (function)
spacer-weight (function)

3.1.9 `num-utils/print-matrix.lisp`

Dependency

interval.lisp (file)

Parent

num-utils (system)

Location

print-matrix.lisp

Exported Definitions

*print-matrix-precision* (special variable)
print-length-truncate (function)
print-matrix (function)

Internal Definitions

print-matrix-formatter (function)

3.1.10 `num-utils/matrix.lisp`

Dependency

print-matrix.lisp (file)

Parent

num-utils (system)

Location

matrix.lisp

Exported Definitions

diagonal-matrix (function)
diagonal-matrix (structure)
diagonal-matrix-elements (function)
(setf diagonal-matrix-elements) (function)
diagonal-vector (generic function)
diagonal-vector (method)
diagonal-vector (method)
(setf diagonal-vector) (generic function)
e1- (method)
e1- (method)
e1- (method)
e1- (method)
e1/ (method)
e1/ (method)
e1/ (method)
e1/ (method)
e1log (method)
e1log (method)
e1log (method)
e1log (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
eexp (method)
eexp (method)
eexp (method)
eexp (method)
esqrt (method)
esqrt (method)
esqrt (method)
esqrt (method)
hermitian-matrix (function)
hermitian-matrix (structure)
lower-triangular-matrix (function)
lower-triangular-matrix (structure)
map-array (method)
num= (method)
num= (method)
transpose (generic function)
transpose (method)
transpose (method)
transpose (method)
transpose (method)
transpose (method)
triangular-matrix (type)
upper-triangular-matrix (function)
upper-triangular-matrix (structure)
wrapped-matrix (structure)
wrapped-matrix-elements (function)

Internal Definitions

&diagonal-matrix (macro)
&diagonal-matrix-r/o (macro)
above-diagonal? (function)
below-diagonal? (function)
copy-diagonal-matrix (function)
copy-hermitian-matrix (function)
copy-lower-triangular-matrix (function)
copy-upper-triangular-matrix (function)
copy-wrapped-matrix (function)
define-elementwise-as-array (macro)
define-elementwise-same-class (macro)
define-elementwise-univariate (macro)
define-elementwise-with-constant (macro)
define-wrapped-matrix (macro)
diagonal-matrix-p (function)
ensure-valid-elements (function)
hermitian-matrix-elements (function)
hermitian-matrix-p (function)
lower-triangular-matrix-elements (function)
lower-triangular-matrix-p (function)
make-diagonal-matrix (function)
make-hermitian-matrix (function)
make-lower-triangular-matrix (function)
make-upper-triangular-matrix (function)
make-wrapped-matrix (function)
upper-triangular-matrix-elements (function)
upper-triangular-matrix-p (function)
valid-sparse-type? (function)
wrapped-matrix-p (function)
zero-like (function)

3.1.11 `num-utils/matrix-shorthand.lisp`

Dependency

matrix.lisp (file)

Parent

num-utils (system)

Location

matrix-shorthand.lisp

Exported Definitions

diagonal-mx (function)
hermitian-mx (macro)
lower-triangular-mx (macro)
mx (macro)
upper-triangular-mx (macro)
vec (function)

Internal Definitions

pad-left-expansion (function)

3.1.12 `num-utils/statistics.lisp`

Dependency

matrix-shorthand.lisp (file)

Parent

num-utils (system)

Location

statistics.lisp

Exported Definitions

*central-sample-moments-default-degree* (special variable)
add (generic function)
add (method)
add (method)
add (method)
add (method)
as-alist (method)
central-m2 (generic function)
central-m2 (method)
central-m2 (method)
central-m3 (generic function)
central-m3 (method)
central-m3 (method)
central-m4 (generic function)
central-m4 (method)
central-m4 (method)
central-sample-moments (generic function)
central-sample-moments (method)
central-sample-moments (method)
central-sample-moments (method)
central-sample-moments (structure)
central-sample-moments-degree (function)
cross-tabulate (function)
empirical-quantile (function)
empirical-quantile-probabilities (function)
empty-accumulator (condition)
ensure-sorted-reals (generic function)
ensure-sorted-reals (method)
ensure-sorted-reals (method)
ensure-sorted-reals (method)
ensure-sorted-vector (function)
information-not-collected-in-accumulator (condition)
kurtosis (generic function)
kurtosis (method)
kurtosis (method)
make-sparse-counter (function)
mean (generic function)
mean (method)
mean (method)
median (generic function)
median (method)
median (method)
not-enough-elements-in-accumulator (condition)
num= (method)
pool (function)
quantile (generic function)
quantile (method)
quantile (method)
quantiles (generic function)
quantiles (method)
quantiles (method)
sd (generic function)
sd (method)
skewness (generic function)
skewness (method)
skewness (method)
sorted-reals (structure)
sorted-reals-elements (function)
sparse-counter (structure)
sparse-counter-count (function)
sparse-counter-table (function)
tabulate (function)
tally (generic function)
tally (method)
tally (method)
variance (generic function)
variance (method)
variance (method)
weighted-quantiles (function)

Internal Definitions

&sorted-reals (macro)
&sorted-reals-r/o (macro)
central-sample-moments-m (function)
(setf central-sample-moments-m) (function)
central-sample-moments-p (function)
central-sample-moments-s2 (function)
(setf central-sample-moments-s2) (function)
central-sample-moments-s3 (function)
(setf central-sample-moments-s3) (function)
central-sample-moments-s4 (function)
(setf central-sample-moments-s4) (function)
central-sample-moments-w (function)
(setf central-sample-moments-w) (function)
copy-central-sample-moments (function)
copy-sorted-reals (function)
copy-sparse-counter (function)
copy-tally-mixin (function)
define-central-sample-moment (macro)
make-central-sample-moments (function)
make-sorted-reals (function)
make-sparse-counter% (function)
make-tally-mixin (function)
pool2 (generic function)
pool2 (method)
sort-reals (function)
sorted-reals-ordered-elements (function)
(setf sorted-reals-ordered-elements) (function)
sorted-reals-p (function)
sorted-reals-unordered-elements (function)
(setf sorted-reals-unordered-elements) (function)
sparse-counter-p (function)
tally-mixin (structure)
tally-mixin-p (function)
tally-mixin-w (function)
(setf tally-mixin-w) (function)
weighted-empirical-quantile (function)
weighted-quantile-p-table (function)

3.1.13 `num-utils/chebyshev.lisp`

Dependency

Parent

num-utils (system)

Location

chebyshev.lisp

Exported Definitions

chebyshev-approximate (function)
chebyshev-regression (function)
chebyshev-root (function)
chebyshev-roots (function)
evaluate-chebyshev (function)

Internal Definitions

ab-to-cd-intercept-slope (function)
ab-to-cinf (function)
chebyshev-approximate-implementation (generic function)
chebyshev-approximate-implementation (method)
chebyshev-approximate-implementation (method)
chebyshev-recursion (function)
cinf-to-ab (function)

3.1.14 `num-utils/polynomial.lisp`

Dependency: chebyshev.lisp (file)
Parent: num-utils (system)
Location: polynomial.lisp
Exported Definitions: evaluate-polynomial (function)

3.1.15 `num-utils/rootfinding.lisp`

Dependency

polynomial.lisp (file)

Parent

num-utils (system)

Location

rootfinding.lisp

Exported Definitions

*rootfinding-delta-relative* (special variable)
*rootfinding-epsilon* (special variable)
root-bisection (function)

Internal Definitions

narrow-bracket? (function)
near-root? (function)
opposite-sign? (function)
rootfinding-delta (function)
univariate-rootfinder-loop% (macro)

3.1.16 `num-utils/quadrature.lisp`

Dependency

rootfinding.lisp (file)

Parent

num-utils (system)

Location

quadrature.lisp

Exported Definitions

romberg-quadrature (function)

Internal Definitions

copy-iterative-quadrature (function)
copy-midpoint-quadrature (function)
copy-richardson-extrapolation (function)
copy-trapezoidal-quadrature (function)
iterative-quadrature (structure)
iterative-quadrature-a (function)
(setf iterative-quadrature-a) (function)
iterative-quadrature-b (function)
(setf iterative-quadrature-b) (function)
iterative-quadrature-f (function)
(setf iterative-quadrature-f) (function)
iterative-quadrature-h (function)
(setf iterative-quadrature-h) (function)
iterative-quadrature-n (function)
(setf iterative-quadrature-n) (function)
iterative-quadrature-p (function)
iterative-quadrature-sum (function)
(setf iterative-quadrature-sum) (function)
make-iterative-quadrature (function)
midpoint-quadrature (function)
midpoint-quadrature (structure)
midpoint-quadrature% (function)
midpoint-quadrature-a (function)
(setf midpoint-quadrature-a) (function)
midpoint-quadrature-b (function)
(setf midpoint-quadrature-b) (function)
midpoint-quadrature-f (function)
(setf midpoint-quadrature-f) (function)
midpoint-quadrature-h (function)
(setf midpoint-quadrature-h) (function)
midpoint-quadrature-n (function)
(setf midpoint-quadrature-n) (function)
midpoint-quadrature-p (function)
midpoint-quadrature-sum (function)
(setf midpoint-quadrature-sum) (function)
refine-quadrature (generic function)
refine-quadrature (method)
refine-quadrature (method)
richardson-coefficient (generic function)
richardson-coefficient (method)
richardson-coefficient (method)
richardson-extrapolation (function)
richardson-extrapolation (structure)
richardson-extrapolation-coefficient (function)
(setf richardson-extrapolation-coefficient) (function)
richardson-extrapolation-diagonal (function)
(setf richardson-extrapolation-diagonal) (function)
richardson-extrapolation-n (function)
(setf richardson-extrapolation-n) (function)
richardson-extrapolation-p (function)
richardson-iteration (function)
romberg-quadrature% (function)
transformed-quadrature (generic function)
transformed-quadrature (method)
transformed-quadrature (method)
trapezoidal-quadrature (function)
trapezoidal-quadrature (structure)
trapezoidal-quadrature% (function)
trapezoidal-quadrature-a (function)
(setf trapezoidal-quadrature-a) (function)
trapezoidal-quadrature-b (function)
(setf trapezoidal-quadrature-b) (function)
trapezoidal-quadrature-f (function)
(setf trapezoidal-quadrature-f) (function)
trapezoidal-quadrature-h (function)
(setf trapezoidal-quadrature-h) (function)
trapezoidal-quadrature-n (function)
(setf trapezoidal-quadrature-n) (function)
trapezoidal-quadrature-p (function)
trapezoidal-quadrature-sum (function)
(setf trapezoidal-quadrature-sum) (function)

3.1.17 `num-utils/log-exp.lisp`

Dependency

Parent

num-utils (system)

Location

log-exp.lisp

Exported Definitions

exp-1 (function)
exp-1/x (function)
expt-1 (function)
hypot (function)
log1+ (function)
log1+/x (function)
log1+exp (function)
log1- (function)
log1-exp (function)
log1pmx (function)
log2-exp (function)
logexp-1 (function)

3.1.18 `num-utils/test-utilities.lisp`

Dependency

log-exp.lisp (file)

Parent

num-utils (system)

Location

test-utilities.lisp

Exported Definitions

compare-fns (function)
compare-vectors (function)
max-error (function)
(setf max-error) (function)
mean-error (function)
(setf mean-error) (function)
min-error (function)
(setf min-error) (function)
rms (function)
(setf rms) (function)
test-count (function)
(setf test-count) (function)
test-fn (function)
test-results (structure)
variance0 (function)
(setf variance0) (function)
variance1 (function)
(setf variance1) (function)
worst-case (function)
(setf worst-case) (function)

Internal Definitions

copy-test-results (function)
make-test-results (function)
test-results-p (function)

3.1.19 `num-utils/common-package.lisp`

Dependency: test-utilities.lisp (file)
Parent: num-utils (system)
Location: common-package.lisp
Packages: num-utils

4 Packages

Packages are listed by definition order.

4.1 `num-utils.polynomial`

Source

packages.lisp (file)

Nickname

poly

Use List

num-utils.utilities
alexandria
common-lisp

Exported Definitions

evaluate-polynomial (function)

4.2 `num-utils.interval`

Source

packages.lisp (file)

Use List

let-plus
num-utils.utilities
num-utils.num=
anaphora
alexandria
common-lisp

Used By List

num-utils.rootfinding
num-utils.quadrature
num-utils.chebyshev

Exported Definitions

&interval (macro)
extend-interval (generic function)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extend-interval (method)
extendf-interval (macro)
finite-interval (class)
grid-in (function)
in-interval? (function)
interval (function)
interval (class)
interval-hull (function)
interval-length (function)
interval-midpoint (function)
left (generic function)
left (method)
left (method)
minusinf-interval (class)
open-left? (generic function)
open-left? (method)
open-left? (method)
open-right? (generic function)
open-right? (method)
open-right? (method)
plusinf-interval (class)
plusminus-interval (function)
real-line (class)
relative (function)
relative (structure)
right (generic function)
right (method)
right (method)
shift-interval (generic function)
shift-interval (method)
shrink-interval (function)
spacer (function)
spacer (structure)
split-interval (function)
subintervals-in (function)

Internal Definitions

copy-relative (function)
copy-spacer (function)
interval/finite-left (class)
interval/finite-right (class)
interval/infinite-left (class)
interval/infinite-right (class)
print-left-endpoint (generic function)
print-left-endpoint (method)
print-left-endpoint (method)
print-right-endpoint (generic function)
print-right-endpoint (method)
print-right-endpoint (method)
relative-fraction (function)
relative-p (function)
spacer-p (function)
spacer-weight (function)

4.3 `num-utils.print-matrix`

Source

packages.lisp (file)

Use List

let-plus
anaphora
alexandria
common-lisp

Used By List

Exported Definitions

*print-matrix-precision* (special variable)
print-length-truncate (function)
print-matrix (function)

Internal Definitions

print-matrix-formatter (function)

4.4 `num-utils.utilities`

Source

packages.lisp (file)

Use List

let-plus
anaphora
alexandria
common-lisp

Used By List

num-utils.statistics
num-utils.rootfinding
num-utils.quadrature
num-utils.matrix-shorthand
num-utils.matrix
num-utils.elementwise
num-utils.polynomial
num-utils.chebyshev
num-utils.interval
num-utils.arithmetic

Exported Definitions

as-alist (generic function)
as-alist (method)
as-double-float (function)
as-plist (generic function)
as-plist (method)
as-simple-fixnum-vector (function)
bic (function)
binary-search (function)
check-types (macro)
curry* (macro)
define-with-multiple-bindings (macro)
expanding (macro)
fixnum? (function)
generate-sequence (function)
gethash* (macro)
make-vector (compiler macro)
make-vector (function)
sequencep (function)
simple-double-float-vector (type)
simple-fixnum-vector (type)
simple-single-float-vector (type)
splice-awhen (macro)
splice-when (macro)
unlessf (macro)
with-double-floats (macro)
within? (function)

4.5 `num-utils.arithmetic`

Source

packages.lisp (file)

Use List

let-plus
num-utils.utilities
anaphora
alexandria-2
common-lisp

Used By List

num-utils.statistics
num-utils.quadrature
num-utils.elementwise

Exported Definitions

1c (function)
abs-diff (function)
absolute-square (function)
as-integer (function)
ceiling* (function)
cube (function)
cumulative-product (function)
cumulative-sum (function)
divides? (function)
floor* (function)
ivec (function)
l2norm (function)
l2norm-square (generic function)
l2norm-square (method)
log10 (function)
log2 (function)
multf (macro)
normalize-probabilities (function)
numseq (function)
product (generic function)
product (method)
product (method)
round* (function)
same-sign-p (function)
sequence-maximum (function)
sequence-minimum (function)
square (function)
sum (generic function)
sum (method)
sum (method)
truncate* (function)

Internal Definitions

define-rounding-with-offset (macro)
ln (function)
similar-element-type (function)
similar-sequence-type (function)

4.6 `num-utils.matrix-shorthand`

Source

packages.lisp (file)

Nickname

nu.mx

Use List

let-plus
num-utils.utilities
num-utils.matrix
anaphora
alexandria
common-lisp

Exported Definitions

diagonal-mx (function)
hermitian-mx (macro)
lower-triangular-mx (macro)
mx (macro)
upper-triangular-mx (macro)
vec (function)

Internal Definitions

pad-left-expansion (function)

4.7 `num-utils.num=`

Source

packages.lisp (file)

Use List

let-plus
anaphora
alexandria
common-lisp

Used By List

num-utils.statistics
num-utils.matrix
num-utils.interval

Exported Definitions

*num=-tolerance* (special variable)
define-num=-with-accessors (macro)
define-structure-num= (macro)
num-delta (function)
num= (generic function)
num= (method)
num= (method)
num= (method)
num= (method)
num= (method)
num= (method)
num= (method)
num= (method)
num= (method)
num= (method)
num=-function (function)

4.8 `num-utils.test-utilities`

Source

packages.lisp (file)

Use List

common-lisp

Exported Definitions

compare-fns (function)
compare-vectors (function)
max-error (function)
(setf max-error) (function)
mean-error (function)
(setf mean-error) (function)
min-error (function)
(setf min-error) (function)
rms (function)
(setf rms) (function)
test-count (function)
(setf test-count) (function)
test-fn (function)
test-results (structure)
variance0 (function)
(setf variance0) (function)
variance1 (function)
(setf variance1) (function)
worst-case (function)
(setf worst-case) (function)

Internal Definitions

copy-test-results (function)
make-test-results (function)
test-results-p (function)

4.9 `num-utils.extended-real`

Source

packages.lisp (file)

Nickname

xreal

Use List

alexandria
common-lisp

Exported Definitions

< (function)
<= (function)
= (function)
> (function)
>= (function)
extended-real (type)
infinite? (function)
lambda-template (macro)
with-template (macro)

Internal Definitions

define-comparison (macro)
extend-pairwise-comparison (function)
infinite (type)

4.10 `num-utils.quadrature`

Source

packages.lisp (file)

Use List

let-plus
num-utils.utilities
num-utils.interval
num-utils.arithmetic
anaphora
alexandria
common-lisp

Exported Definitions

romberg-quadrature (function)

Internal Definitions

copy-iterative-quadrature (function)
copy-midpoint-quadrature (function)
copy-richardson-extrapolation (function)
copy-trapezoidal-quadrature (function)
iterative-quadrature (structure)
iterative-quadrature-a (function)
(setf iterative-quadrature-a) (function)
iterative-quadrature-b (function)
(setf iterative-quadrature-b) (function)
iterative-quadrature-f (function)
(setf iterative-quadrature-f) (function)
iterative-quadrature-h (function)
(setf iterative-quadrature-h) (function)
iterative-quadrature-n (function)
(setf iterative-quadrature-n) (function)
iterative-quadrature-p (function)
iterative-quadrature-sum (function)
(setf iterative-quadrature-sum) (function)
make-iterative-quadrature (function)
midpoint-quadrature (function)
midpoint-quadrature (structure)
midpoint-quadrature% (function)
midpoint-quadrature-a (function)
(setf midpoint-quadrature-a) (function)
midpoint-quadrature-b (function)
(setf midpoint-quadrature-b) (function)
midpoint-quadrature-f (function)
(setf midpoint-quadrature-f) (function)
midpoint-quadrature-h (function)
(setf midpoint-quadrature-h) (function)
midpoint-quadrature-n (function)
(setf midpoint-quadrature-n) (function)
midpoint-quadrature-p (function)
midpoint-quadrature-sum (function)
(setf midpoint-quadrature-sum) (function)
refine-quadrature (generic function)
refine-quadrature (method)
refine-quadrature (method)
richardson-coefficient (generic function)
richardson-coefficient (method)
richardson-coefficient (method)
richardson-extrapolation (function)
richardson-extrapolation (structure)
richardson-extrapolation-coefficient (function)
(setf richardson-extrapolation-coefficient) (function)
richardson-extrapolation-diagonal (function)
(setf richardson-extrapolation-diagonal) (function)
richardson-extrapolation-n (function)
(setf richardson-extrapolation-n) (function)
richardson-extrapolation-p (function)
richardson-iteration (function)
romberg-quadrature% (function)
transformed-quadrature (generic function)
transformed-quadrature (method)
transformed-quadrature (method)
trapezoidal-quadrature (function)
trapezoidal-quadrature (structure)
trapezoidal-quadrature% (function)
trapezoidal-quadrature-a (function)
(setf trapezoidal-quadrature-a) (function)
trapezoidal-quadrature-b (function)
(setf trapezoidal-quadrature-b) (function)
trapezoidal-quadrature-f (function)
(setf trapezoidal-quadrature-f) (function)
trapezoidal-quadrature-h (function)
(setf trapezoidal-quadrature-h) (function)
trapezoidal-quadrature-n (function)
(setf trapezoidal-quadrature-n) (function)
trapezoidal-quadrature-p (function)
trapezoidal-quadrature-sum (function)
(setf trapezoidal-quadrature-sum) (function)

4.11 `num-utils.statistics`

Source

packages.lisp (file)

Nickname

nu.stats

Use List

let-plus
num-utils.utilities
num-utils.num=
num-utils.arithmetic
alexandria
anaphora
common-lisp

Exported Definitions

*central-sample-moments-default-degree* (special variable)
add (generic function)
add (method)
add (method)
add (method)
add (method)
central-m2 (generic function)
central-m2 (method)
central-m2 (method)
central-m3 (generic function)
central-m3 (method)
central-m3 (method)
central-m4 (generic function)
central-m4 (method)
central-m4 (method)
central-sample-moments (generic function)
central-sample-moments (method)
central-sample-moments (method)
central-sample-moments (method)
central-sample-moments (structure)
central-sample-moments-degree (function)
cross-tabulate (function)
empirical-quantile (function)
empirical-quantile-probabilities (function)
empty-accumulator (condition)
ensure-sorted-reals (generic function)
ensure-sorted-reals (method)
ensure-sorted-reals (method)
ensure-sorted-reals (method)
ensure-sorted-vector (function)
information-not-collected-in-accumulator (condition)
kurtosis (generic function)
kurtosis (method)
kurtosis (method)
make-sparse-counter (function)
mean (generic function)
mean (method)
mean (method)
median (generic function)
median (method)
median (method)
not-enough-elements-in-accumulator (condition)
pool (function)
quantile (generic function)
quantile (method)
quantile (method)
quantiles (generic function)
quantiles (method)
quantiles (method)
sd (generic function)
sd (method)
skewness (generic function)
skewness (method)
skewness (method)
sorted-reals (structure)
sorted-reals-elements (function)
sparse-counter (structure)
sparse-counter-count (function)
sparse-counter-table (function)
tabulate (function)
tally (generic function)
tally (method)
tally (method)
variance (generic function)
variance (method)
variance (method)
weighted-quantiles (function)

Internal Definitions

&sorted-reals (macro)
&sorted-reals-r/o (macro)
central-sample-moments-m (function)
(setf central-sample-moments-m) (function)
central-sample-moments-p (function)
central-sample-moments-s2 (function)
(setf central-sample-moments-s2) (function)
central-sample-moments-s3 (function)
(setf central-sample-moments-s3) (function)
central-sample-moments-s4 (function)
(setf central-sample-moments-s4) (function)
central-sample-moments-w (function)
(setf central-sample-moments-w) (function)
copy-central-sample-moments (function)
copy-sorted-reals (function)
copy-sparse-counter (function)
copy-tally-mixin (function)
define-central-sample-moment (macro)
make-central-sample-moments (function)
make-sorted-reals (function)
make-sparse-counter% (function)
make-tally-mixin (function)
pool2 (generic function)
pool2 (method)
sort-reals (function)
sorted-reals-ordered-elements (function)
(setf sorted-reals-ordered-elements) (function)
sorted-reals-p (function)
sorted-reals-unordered-elements (function)
(setf sorted-reals-unordered-elements) (function)
sparse-counter-p (function)
tally-mixin (structure)
tally-mixin-p (function)
tally-mixin-w (function)
(setf tally-mixin-w) (function)
weighted-empirical-quantile (function)
weighted-quantile-p-table (function)

4.12 `num-utils.rootfinding`

Source

packages.lisp (file)

Use List

let-plus
num-utils.utilities
num-utils.interval
alexandria
common-lisp

Exported Definitions

*rootfinding-delta-relative* (special variable)
*rootfinding-epsilon* (special variable)
root-bisection (function)

Internal Definitions

narrow-bracket? (function)
near-root? (function)
opposite-sign? (function)
rootfinding-delta (function)
univariate-rootfinder-loop% (macro)

4.13 `num-utils.elementwise`

Source

packages.lisp (file)

Nickname

elmt

Use List

let-plus
num-utils.utilities
num-utils.arithmetic
alexandria
common-lisp

Used By List

num-utils.matrix-shorthand

Exported Definitions

e* (function)
e+ (function)
e- (function)
e/ (function)
e1- (generic function)
e1- (method)
e1- (method)
e1- (method)
e1- (method)
e1- (method)
e1- (method)
e1/ (generic function)
e1/ (method)
e1/ (method)
e1/ (method)
e1/ (method)
e1/ (method)
e1/ (method)
e1log (generic function)
e1log (method)
e1log (method)
e1log (method)
e1log (method)
e1log (method)
e1log (method)
e2* (generic function)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2* (method)
e2+ (generic function)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2+ (method)
e2- (generic function)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2- (method)
e2/ (generic function)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2/ (method)
e2log (generic function)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
e2log (method)
eceiling (generic function)
eceiling (method)
eceiling (method)
econjugate (generic function)
econjugate (method)
econjugate (method)
eexp (generic function)
eexp (method)
eexp (method)
eexp (method)
eexp (method)
eexp (method)
eexp (method)
eexpt (generic function)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
eexpt (method)
efloor (generic function)
efloor (method)
efloor (method)
elementwise-float-contagion (function)
elog (function)
emax (function)
emin (function)
emod (generic function)
emod (method)
emod (method)
emod (method)
emod (method)
emod (method)
emod (method)
emod (method)
ereduce (generic function)
ereduce (method)
ereduce (method)
ereduce (method)
esqrt (generic function)
esqrt (method)
esqrt (method)
esqrt (method)
esqrt (method)
esqrt (method)
esqrt (method)

Internal Definitions

define-e& (macro)
define-e1 (macro)
define-e2 (macro)
define-elementwise-reduction (macro)
esquare (generic function)
esquare (method)
esquare (method)
mapping-array (macro)

4.14 `num-utils.chebyshev`

Source

packages.lisp (file)

Use List

let-plus
num-utils.utilities
num-utils.interval
anaphora
alexandria
common-lisp

Exported Definitions

chebyshev-approximate (function)
chebyshev-regression (function)
chebyshev-root (function)
chebyshev-roots (function)
evaluate-chebyshev (function)

Internal Definitions

ab-to-cd-intercept-slope (function)
ab-to-cinf (function)
chebyshev-approximate-implementation (generic function)
chebyshev-approximate-implementation (method)
chebyshev-approximate-implementation (method)
chebyshev-recursion (function)
cinf-to-ab (function)

4.15 `num-utils.log-exp`

Source

packages.lisp (file)

Use List

let-plus
common-lisp

Exported Definitions

exp-1 (function)
exp-1/x (function)
expt-1 (function)
hypot (function)
log1+ (function)
log1+/x (function)
log1+exp (function)
log1- (function)
log1-exp (function)
log1pmx (function)
log2-exp (function)
logexp-1 (function)

4.16 `num-utils.matrix`

Source

packages.lisp (file)

Use List

let-plus
select
num-utils.utilities
num-utils.print-matrix
num-utils.num=
num-utils.elementwise
anaphora
alexandria
common-lisp

Used By List

Exported Definitions

diagonal-matrix (function)
diagonal-matrix (structure)
diagonal-matrix-elements (function)
(setf diagonal-matrix-elements) (function)
diagonal-vector (generic function)
diagonal-vector (method)
diagonal-vector (method)
(setf diagonal-vector) (generic function)
hermitian-matrix (function)
hermitian-matrix (structure)
lower-triangular-matrix (function)
lower-triangular-matrix (structure)
map-array (generic function)
map-array (method)
transpose (generic function)
transpose (method)
transpose (method)
transpose (method)
transpose (method)
transpose (method)
triangular-matrix (type)
upper-triangular-matrix (function)
upper-triangular-matrix (structure)
wrapped-matrix (structure)
wrapped-matrix-elements (function)

Internal Definitions

&diagonal-matrix (macro)
&diagonal-matrix-r/o (macro)
above-diagonal? (function)
below-diagonal? (function)
copy-diagonal-matrix (function)
copy-hermitian-matrix (function)
copy-lower-triangular-matrix (function)
copy-upper-triangular-matrix (function)
copy-wrapped-matrix (function)
define-elementwise-as-array (macro)
define-elementwise-same-class (macro)
define-elementwise-univariate (macro)
define-elementwise-with-constant (macro)
define-wrapped-matrix (macro)
diagonal-matrix-p (function)
ensure-valid-elements (function)
hermitian-matrix-elements (function)
hermitian-matrix-p (function)
lower-triangular-matrix-elements (function)
lower-triangular-matrix-p (function)
make-diagonal-matrix (function)
make-hermitian-matrix (function)
make-lower-triangular-matrix (function)
make-upper-triangular-matrix (function)
make-wrapped-matrix (function)
upper-triangular-matrix-elements (function)
upper-triangular-matrix-p (function)
valid-sparse-type? (function)
wrapped-matrix-p (function)
zero-like (function)

4.17 `num-utils`

Source: common-package.lisp (file)
Nickname: nu
Use List: common-lisp

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

5.1 Exported definitions

5.1.1 Special variables

Special Variable: *central-sample-moments-default-degree*

Default degree for (weighted) central sample moments.

Package: num-utils.statistics
Source: statistics.lisp (file)

Special Variable: *num=-tolerance*

Default tolerance for NUM=.

Package: num-utils.num=
Source: num=.lisp (file)

Special Variable: *print-matrix-precision*

Number of digits after the decimal point when printing numeric matrices.

Package: num-utils.print-matrix
Source: print-matrix.lisp (file)

Special Variable: *rootfinding-delta-relative*

Default relative interval width for rootfinding.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

Special Variable: *rootfinding-epsilon*

Default maximum for the absolute value of the function, used for rootfinding.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

5.1.2 Macros

Macro: &interval LEFT RIGHT

LET+ expansion for interval endpoints. If given a list of two values, the second value is an indicator for whether the endpoint is open.

Package: num-utils.interval
Source: interval.lisp (file)

Macro: check-types (&rest ARGUMENTS) TYPE

CHECK-TYPE for multiple places of the same type. Each argument is either a place, or a list of a place and a type-string.

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: curry* FUNCTION &rest ARGUMENTS

Currying in all variables that are not *. Note that this is a macro, so * should not be quoted, and FUNCTION will be used as is, ie it can be a LAMBDA form.

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: define-num=-with-accessors CLASS ACCESSORS

Define a method for NUM=, specialized to the given class, comparing values obtained with accessors.

Package: num-utils.num=
Source: num=.lisp (file)

Macro: define-structure-num= STRUCTURE &rest SLOTS

Define a NUM= method for the given structure, comparing the given slots.

Package: num-utils.num=
Source: num=.lisp (file)

Macro: define-with-multiple-bindings MACRO &key PLURAL DOCSTRING

Define a version of MACRO with multiple arguments, given as a list. Application of MACRO will be nested. The new name is the plural of the old one (generated using format by default).

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: expanding &body BODY

Expand BODY. Useful for generating code programmatically.

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: extendf-interval PLACE OBJECT

Apply EXTEND-INTERVAL on PLACE using OBJECT.

Package: num-utils.interval
Source: interval.lisp (file)

Macro: gethash* KEY HASH-TABLE &optional DATUM &rest ARGUMENTS

Like GETHASH, but checking that KEY is present and raising the given error if not.

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: hermitian-mx ELEMENT-TYPE &body ROWS

Macro for creating a lower triangular matrix. ROWS should be a list of lists, elements are evaluated. Masked elements (above the diagonal) are ignored at the expansion, rows which don’t have enough elements are padded with zeros.

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Macro: lambda-template (PREFIX &rest VARIABLES) &body BODY

LAMBDA with WITH-TEMPLATE in its BODY.

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Macro: lower-triangular-mx ELEMENT-TYPE &body ROWS

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Macro: multf PLACE COEFFICIENT

Multiply place by COEFFICIENT.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Macro: mx ELEMENT-TYPE &body ROWS

Macro for creating a (dense) matrix (ie a rank 2 array). ROWS should be a list of lists (or atoms, which are treated as lists), elements are evaluated.

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Macro: splice-awhen TEST &body FORMS

Similar to splice-when, but binds IT to test.

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: splice-when TEST &body FORMS

Similar to when, but wraps the result in list.

Example: ‘(,foo ,@(splice-when add-bar? bar))

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: unlessf PLACE VALUE-FORM

When PLACE is NIL, evaluate VALUE-FORM and save it there.

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: upper-triangular-mx ELEMENT-TYPE &body ROWS

Macro for creating an upper triangular matrix. ROWS should be a list of lists, elements are evaluated. Masked elements (below the diagonal) are ignored at the expansion.

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Macro: with-double-floats BINDINGS &body BODY

For each binding = (variable value), coerce VALUE to DOUBLE-FLOAT and bind it to VARIABLE for BODY. When VALUE is omitted, VARIABLE is used instead. When BINDING is an atom, it is used for both the value and the variable.

Example:
(with-double-floats (a
(b)
(c 1))
...)

Package: num-utils.utilities
Source: utilities.lisp (file)

Macro: with-template (PREFIX &rest VARIABLES) &body BODY

Define the function (PREFIX &rest VARIABLES) which can be used to match variables using :PLUSINF, :MINUSINF, REAL, or T.

Package: num-utils.extended-real
Source: extended-real.lisp (file)

5.1.3 Compiler macros

Compiler Macro: make-vector ELEMENT-TYPE &rest INITIAL-CONTENTS

Package: num-utils.utilities
Source: utilities.lisp (file)

5.1.4 Functions

Function: 1c NUMBER

Return 1-number. The mnemonic is "1 complement", 1- is already a CL library function.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: < NUMBER &rest MORE-NUMBERS

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: <= NUMBER &rest MORE-NUMBERS

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: = NUMBER &rest MORE-NUMBERS

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: > NUMBER &rest MORE-NUMBERS

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: >= NUMBER &rest MORE-NUMBERS

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: abs-diff A B

Absolute difference of A and B.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: absolute-square NUMBER

Number multiplied by its complex conjugate.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: as-double-float V

Convert argument to DOUBLE-FLOAT.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: as-integer NUMBER

If NUMBER represents an integer (as an integer, complex, or float, etc), return it as an integer, otherwise signal an error. Floats are converted with RATIONALIZE.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: as-simple-fixnum-vector SEQUENCE &optional COPY?

Convert SEQUENCE to a SIMPLE-FIXNUM-VECTOR. When COPY?, make sure that the they don’t share structure.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: bic A B

Biconditional. Returns A <=> B.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: binary-search SORTED-REALS VALUE

Return INDEX such that

(WITHIN? (AREF SORTED-REALS INDEX) VALUE (AREF SORTED-REALS (1+ INDEX)).

SORTED-REALS is assumed to be reals sorted in ascending order (not checked, if this does not hold the result may be nonsensical, though the algorithm will terminate).

If value is below (or above) the first (last) break, NIL (T) is returned.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: ceiling* NUMBER &optional DIVISOR OFFSET

Find the lowest A=I*DIVISOR+OFFSET >= NUMBER, return (values A (- A NUMBER).

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: central-sample-moments-degree CENTRAL-SAMPLE-MOMENTS

Return the degree of CENTRAL-SAMPLE-MOMENTS.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: chebyshev-approximate F INTERVAL N-POLYNOMIALS &key N-POINTS

Return a closure approximating F on the given INTERVAL (may be infinite on either end) using the given number of Chebyshev polynomials.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: chebyshev-regression F N-POLYNOMIALS &optional N-POINTS

Chebyshev polynomial regression using the given number of polynomials and points (zeroes of the corresponding Chebyshev polynomial).

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: chebyshev-root M I

Return the iTH root of the Mth Chebyshev polynomial as double-float.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: chebyshev-roots M

Return the roots of the Mth Chebyshev polynomial as a vector of double-floats.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: compare-fns FN-1 FN-2 &rest FN-PARAMS

Compare the values returned by two functions

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: compare-vectors REFERENCE-VALUES COMPUTED-VALUES

Compare two vectors containing the results of previous computations

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: cross-tabulate SEQUENCE1 SEQUENCE2 &key TEST

Cross-tabulate two sequences (using a SPARSE-COUNTER with the given TEST). TEST is used to compare conses.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: cube NUMBER

Cube of number.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: cumulative-product SEQUENCE &key RESULT-TYPE

Cumulative product of sequence. Return a sequence of the same kind and length; last element is the total product. The latter is also returned as the second value.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: cumulative-sum SEQUENCE &key RESULT-TYPE

Cumulative sum of sequence. Return a sequence of the same kind and length; last element is the total. The latter is returned as the second value.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: diagonal-matrix ELEMENTS

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: diagonal-matrix-elements INSTANCE

Function: (setf diagonal-matrix-elements) VALUE INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: diagonal-mx ELEMENT-TYPE &rest ELEMENTS

Return a DIAGONAL-MATRIX with elements coerced to ELEMENT-TYPE.

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Function: divides? NUMBER DIVISOR

Test if DIVISOR divides NUMBER without remainder, and if so, return the quotient. Works generally, but makes most sense for rationals.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: e* ARGUMENT &rest MORE-ARGUMENTS

Elementwise *.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: e+ ARGUMENT &rest MORE-ARGUMENTS

Elementwise +.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: e- ARGUMENT &rest MORE-ARGUMENTS

Elementwise -.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: e/ ARGUMENT &rest MORE-ARGUMENTS

Elementwise /.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: elementwise-float-contagion &rest OBJECTS

Return the resulting float type when objects (or their elements) are combined using arithmetic operations.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: elog A &optional BASE

Elementwise logarithm.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: emax OBJECT

Elementwise MAX.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: emin OBJECT

Elementwise MIN.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Function: empirical-quantile SORTED-VECTOR Q

Return the empirical quantile of a vector of real numbers, sorted in ascending order (not checked). Uses a 0.5 correction.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: empirical-quantile-probabilities N

Probabilities that correspond to the empirical quantiles of a vector of length N. That is to say,

(== (quantiles sample (empirical-quantile-probabilities (length sample)))
sample)

for any vector SAMPLE.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: ensure-sorted-vector OBJECT

Return the elements of OBJECT as a vector (or reals) sorted in ascending order.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: evaluate-chebyshev COEFFICIENTS X

Return the sum of Chebyshev polynomials, weighted by COEFFICIENTS, at X.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: evaluate-polynomial COEFFICIENTS X

Return the sum of polynomials, weighted by COEFFICIENTS, at X. COFFICIENTS are ordered from the highest degree down to the constant term. X must be of the same type as COEFFICIENTS.

Package: num-utils.polynomial
Source: polynomial.lisp (file)

Function: exp-1 X

Compute (- (exp x) 1) stably even when X is near 0

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: exp-1/x X

Compute (/ (- (exp x) 1) x) stably even when X is near zero.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: expt-1 A Z

Compute (a^z)-1 stably even when A is close to 1 or Z is close to zero.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: fixnum? OBJECT

Check of type of OBJECT is fixnum.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: floor* NUMBER &optional DIVISOR OFFSET

Find the highest A=I*DIVISOR+OFFSET <= NUMBER, return (values A (- A NUMBER).

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: generate-sequence RESULT-TYPE SIZE FUNCTION

Like MAKE-SEQUENCE, but using a function to fill the result.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: grid-in INTERVAL SIZE &optional SEQUENCE-TYPE

Return an arithmetic sequence of the given size (length) between the endpoints of the interval. The endpoints of the sequence coincide with the respective endpoint of the interval iff it is closed. RESULT-TYPE determines the result type (eg list), if not given it is a simple-array (of rank 1), narrowing to the appropriate float type or fixnum if possible.

Package: num-utils.interval
Source: interval.lisp (file)

Function: hermitian-matrix ELEMENTS

Create a lower-triangular-matrix.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: hypot X Y

Compute the hypotenuse of X and Y without danger of floating-point overflow or underflow.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: in-interval? INTERVAL NUMBER

Test if NUMBER is in INTERVAL (which can be NIL, designating the empty set).

Package: num-utils.interval
Source: interval.lisp (file)

Function: infinite? OBJECT

Test if an object represents positive or negative infinity.

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: interval LEFT RIGHT &key OPEN-LEFT? OPEN-RIGHT?

Create an INTERVAL.

Package: num-utils.interval
Source: interval.lisp (file)

Function: interval-hull OBJECT

Return the smallest connected interval that contains (elements in) OBJECT.

Package: num-utils.interval
Source: interval.lisp (file)

Function: interval-length INTERVAL

Difference between left and right.

Package: num-utils.interval
Source: interval.lisp (file)

Function: interval-midpoint INTERVAL &optional ALPHA

Convex combination of left and right, with alpha (defaults to 0.5) weight on right.

Package: num-utils.interval
Source: interval.lisp (file)

Function: ivec END-OR-START &optional END BY STRICT-DIRECTION?

Return a vector of fixnums.

(ivec end) => #(0 ... end-1) (or #(0 ... end+1) when end is negative).

(ivec start end) => #(start ... end-1) or to end+1 when end is negative.

When BY is given it determines the increment, adjusted to match the direction unless STRICT-DIRECTION, in which case an error is signalled.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: l2norm OBJECT

$L_2$ norm of OBJECT.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: log1+ X

Compute (log (1+ x)) stably even when X is near 0.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: log1+/x X

Compute (/ (log (+ 1 x)) x) stably even when X is near zero.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: log1+exp A

Accurately compute log(1+exp(x)) even when A is near zero.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: log1- X

Compute (log (- 1 x)) stably even when X is near zero.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: log1-exp A

Compute log(1-exp(x)) stably even when A is near zero.
This is sometimes known as the E_3, the third Einstein function.
See Mächler 2008 for notes on accurate calculation. https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: log10 NUMBER

Abbreviation for decimal logarithm.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: log1pmx X

Compute (- (log (1+ x)) x)
Accuracy within ~2ulps for -0.227 < x < 0.315

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: log2 NUMBER

Abbreviation for binary logarithm.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: log2-exp X

Compute log(2-exp(x)) stably even when X is near zero.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: logexp-1 A

Compute log(exp(a)-1) stably even when A is small.

Package: num-utils.log-exp
Source: log-exp.lisp (file)

Function: lower-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: make-sparse-counter &key TEST

Create a sparse counter. Elements are compared with TEST (should be accepted by HASH-TABLE).

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: make-vector ELEMENT-TYPE &rest INITIAL-CONTENTS

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: max-error INSTANCE

Function: (setf max-error) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: mean-error INSTANCE

Function: (setf mean-error) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: min-error INSTANCE

Function: (setf min-error) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: normalize-probabilities VECTOR &key ELEMENT-TYPE RESULT

Verify that each element of VECTOR is nonnegative and return a vector multiplied so that they sum to 1. ELEMENT-TYPE can be used to specify the element-type of the result. When RESULT is given, the result is placed there. When RESULT is NIL, VECTOR is modified instead.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: num-delta A B

|a-b|/max(1,|a|,|b|). Useful for comparing numbers.

Package: num-utils.num=
Source: num=.lisp (file)

Function: num=-function TOLERANCE

Curried version of num=, with given tolerance.

Package: num-utils.num=
Source: num=.lisp (file)

Function: numseq FROM TO &key LENGTH BY TYPE

Return a sequence between FROM and TO, progressing by BY, of the given LENGTH. Only 3 of these a parameters should be given, the missing one (NIL) should be inferred automatically. The sign of BY is adjusted if necessary. If TYPE is LIST, the result is a list, otherwise it determines the element type of the resulting simple array. If TYPE is nil, it as autodetected from the arguments (as a FIXNUM, a RATIONAL, or some subtype of FLOAT). Note that the implementation may upgrade the element type.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: plusminus-interval CENTER HALF-WIDTH &key OPEN-LEFT? OPEN-RIGHT?

A symmetric interval around CENTER.

Package: num-utils.interval
Source: interval.lisp (file)

Function: pool &rest ACCUMULATORS

Pool ACCUMULATORS.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: print-length-truncate DIMENSION

Return values (min dimension *print-length*) and whether the constraint is binding.

Package: num-utils.print-matrix
Source: print-matrix.lisp (file)

Function: print-matrix MATRIX STREAM &key FORMATTER MASKED-FN ALIGNED? PADDING INDENT

Format and print the elements of MATRIX (a 2d array) to STREAM, using PADDING between columns.

MASKED-FN is called on row and column indices. If it returns nil, the corresponding element is formatted using FORMATTER and printed. Otherwise, it should return a string, which is printed as is. INDENT is printed before each row.

If ALIGNED?, columns will be right-aligned. At most *PRINT-LENGTH* rows and columns are printed, more is indicated with ellipses (...).

Package: num-utils.print-matrix
Source: print-matrix.lisp (file)

Function: relative FRACTION

Package: num-utils.interval
Source: interval.lisp (file)

Function: rms INSTANCE

Function: (setf rms) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: romberg-quadrature F INTERVAL &key EPSILON MIN-ITER MAX-ITER TRANSFORMATION

Romberg quadrature of F on the interval. The iteration stops if the relative change is below EPSILON, but only after MIN-ITER refinements (to avoid spurious premature convergence). An error occurs when MAX-ITER iterations are reached without convergence.

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: root-bisection F BRACKET &key DELTA EPSILON

Find the root of f bracketed between a and b using bisection.
The algorithm stops when either the root is bracketed in an interval of length TOLERANCE (relative to the initial |a-b|), or root is found such that abs(f(root)) <= epsilon.

Return five values: the root, the value of the function at the root, and a boolean which is true iff abs(f(root)) <= epsilon. If the third value is true, the fourth and fifth values are the endpoints of the bracketing interval, otherwise they are undefined.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

Function: round* NUMBER &optional DIVISOR OFFSET

Find A=I*DIVISOR+OFFSET that minimizes |A-NUMBER|, return (values A (- A NUMBER). When NUMBER is exactly in between two possible A’s, the rounding rule of ROUND is used on NUMBER-OFFSET.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: same-sign-p &rest ARGUMENTS

Test whether all arguments have the same sign (ie all are positive, negative, or zero).

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: sequence-maximum X

Return the maximum value in the sequence X

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: sequence-minimum X

Return the minimum value in the sequence X

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: sequencep X

Return T if X is type SEQUENCE.

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: shrink-interval INTERVAL LEFT &optional RIGHT CHECK-FLIP?

Shrink interval by given magnitudes (which may be REAL or RELATIVE). When check-flip?, the result is checked for endpoints being in a different order than the original. Negative LEFT and RIGHT extend the interval.

Package: num-utils.interval
Source: interval.lisp (file)

Function: sorted-reals-elements SORTED-REALS

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: spacer &optional WEIGHT

Package: num-utils.interval
Source: interval.lisp (file)

Function: sparse-counter-count SPARSE-COUNTER OBJECT

Return the count for OBJECT.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: sparse-counter-table INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: split-interval INTERVAL DIVISIONS

Return a vector of subintervals (same length as DIVISIONS), splitting the interval using the sequence DIVISIONS, which can be nonnegative real numbers (or RELATIVE specifications) and SPACERs which divide the leftover proportionally. If there are no spacers and the divisions don’t fill up the interval, and error is signalled.

Package: num-utils.interval
Source: interval.lisp (file)

Function: square NUMBER

Square of number.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: subintervals-in INTERVAL COUNT &optional MID-OPEN-RIGHT?

Return INTERVAL evenly divided into COUNT subintervals as a vector. When MID-OPEN-RIGHT?, subintervals in the middle are open on the right and closed on the left, otherwise the opposite; openness of endpoints on the edge follows INTERVAL.

Package: num-utils.interval
Source: interval.lisp (file)

Function: tabulate SEQUENCE &key TEST

Tabulate a sequence (using a SPARSE-COUNTER with the given TEST).

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: test-count INSTANCE

Function: (setf test-count) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: test-fn EXPECTED-COLUMN FN &rest FN-PARAM-COLUMNS

Test the differences between expected values and the given function

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: truncate* NUMBER &optional DIVISOR OFFSET

Find A=I*DIVISOR+OFFSET that maximizes |A|<=|NUMBER| with the same sign, return (values A (- A NUMBER).

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: upper-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: variance0 INSTANCE

Function: (setf variance0) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: variance1 INSTANCE

Function: (setf variance1) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: vec ELEMENT-TYPE &rest ELEMENTS

Return a vector with elements coerced to ELEMENT-TYPE.

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Function: weighted-quantiles VALUES WEIGHTS QS

Calculate quantiles QS of weighted observations. Uses a 0.5 correction.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: within? LEFT VALUE RIGHT

Return non-nil iff value is in [left,right).

Package: num-utils.utilities
Source: utilities.lisp (file)

Function: worst-case INSTANCE

Function: (setf worst-case) VALUE INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: wrapped-matrix-elements INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

5.1.5 Generic functions

Generic Function: add ACCUMULATOR OBJECT &key WEIGHT

Add OBJECT to ACCUMULATOR. Return OBJECT. NILs are ignored by the accumulator, unless a specialized method decides otherwise. Keywords may be used to specify additional information (eg weight).

Package

Source

Methods

Method: add (ACCUMULATOR sparse-counter) OBJECT &key WEIGHT: Increments the count of OBJECT in SPARSE-COUNTER, optionally with a weight

Method: add (ACCUMULATOR sorted-reals) OBJECT &key

Method: add (MOMENTS central-sample-moments) (Y real) &key WEIGHT

Method: add ACCUMULATOR (OBJECT null) &key

Generic Function: as-alist OBJECT

Return OBJECT as an ALIST. Semantics depends on OBJECT.

Package

num-utils.utilities

Source

utilities.lisp (file)

Methods

Method: as-alist (OBJECT sparse-counter)

Return (OBJECT . COUNT) pairs as an alist.

Source: statistics.lisp (file)

Generic Function: as-plist OBJECT

Return OBJECT as a PLIST. Semantics depends on OBJECT. The default method uses AS-ALIST.

Package

num-utils.utilities

Source

utilities.lisp (file)

Methods

Method: as-plist OBJECT

Generic Function: central-m2 OBJECT &key WEIGHTS

Second central moment. For samples, normalized by the total weight (and thus not the unbiased estimator, see VARIANCE).

Package

Source

Methods

Method: central-m2 OBJECT &key WEIGHTS

Method: central-m2 (OBJECT central-sample-moments) &key WEIGHTS

Generic Function: central-m3 OBJECT &key WEIGHTS

Third central moment.

Package

Source

Methods

Method: central-m3 OBJECT &key WEIGHTS

Method: central-m3 (OBJECT central-sample-moments) &key WEIGHTS

Generic Function: central-m4 OBJECT &key WEIGHTS

Fourth central moment.

Package

Source

Methods

Method: central-m4 OBJECT &key WEIGHTS

Method: central-m4 (OBJECT central-sample-moments) &key WEIGHTS

Generic Function: central-sample-moments OBJECT &key DEGREE WEIGHTS

Return a CENTRAL-SAMPLE-MOMENTS object that allows the
calculation of the central sample moments of OBJECT up to the given DEGREE.

When WEIGHTS are given, they need to be a sequence of matching length.

Package

Source

Methods

Method: central-sample-moments (OBJECT null) &key DEGREE WEIGHTS

Method: central-sample-moments (MOMENTS central-sample-moments) &key DEGREE WEIGHTS

Method: central-sample-moments (SEQUENCE sequence) &key DEGREE WEIGHTS

Generic Function: diagonal-vector MATRIX

Return the diagonal elements of MATRIX as a vector.

Package

Source

matrix.lisp (file)

Writer

(setf diagonal-vector) (generic function)

Methods

Method: diagonal-vector (MATRIX array)

Method: diagonal-vector MATRIX

Generic Function: (setf diagonal-vector) VECTOR MATRIX

Set the diagonal elements of MATRIX using VECTOR.

Package: num-utils.matrix
Source: matrix.lisp (file)
Reader: diagonal-vector (generic function)

Generic Function: e1- A

Univariate elementwise -.

Package

Source

Methods

Method: e1- (A diagonal-matrix)

Source: matrix.lisp (file)

Method: e1- (A hermitian-matrix)

Source: matrix.lisp (file)

Method: e1- (A upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e1- (A lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e1- (A number)

Method: e1- (A array)

Generic Function: e1/ A

Univariate elementwise /.

Package

Source

Methods

Method: e1/ (A diagonal-matrix)

Source: matrix.lisp (file)

Method: e1/ (A hermitian-matrix)

Source: matrix.lisp (file)

Method: e1/ (A upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e1/ (A lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e1/ (A number)

Method: e1/ (A array)

Generic Function: e1log A

Univariate elementwise LOG.

Package

Source

Methods

Method: e1log (A diagonal-matrix)

Source: matrix.lisp (file)

Method: e1log (A hermitian-matrix)

Source: matrix.lisp (file)

Method: e1log (A upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e1log (A lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e1log (A number)

Method: e1log (A array)

Generic Function: e2* A B

Bivariate elementwise *.

Package

Source

Methods

Method: e2* (A diagonal-matrix) (B diagonal-matrix)

Source: matrix.lisp (file)

Method: e2* (A hermitian-matrix) (B hermitian-matrix)

Source: matrix.lisp (file)

Method: e2* (A upper-triangular-matrix) (B upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e2* (A lower-triangular-matrix) (B lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e2* (A number) (B diagonal-matrix)

Source: matrix.lisp (file)

Method: e2* (A diagonal-matrix) (B number)

Source: matrix.lisp (file)

Method: e2* (A number) (B hermitian-matrix)

Source: matrix.lisp (file)

Method: e2* (A hermitian-matrix) (B number)

Source: matrix.lisp (file)

Method: e2* (A number) (B upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e2* (A upper-triangular-matrix) (B number)

Source: matrix.lisp (file)

Method: e2* (A number) (B lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e2* (A lower-triangular-matrix) (B number)

Source: matrix.lisp (file)

Method: e2* A (B wrapped-matrix)

Source: matrix.lisp (file)

Method: e2* (A wrapped-matrix) B

Source: matrix.lisp (file)

Method: e2* (A number) (B number)

Method: e2* (A vector) (B number)

Method: e2* (A number) (B vector)

Method: e2* (A vector) (B vector)

Method: e2* (A array) (B number)

Method: e2* (A number) (B array)

Method: e2* (A array) (B array)

Generic Function: e2+ A B

Bivariate elementwise +.

Package

Source

Methods

Method: e2+ (A diagonal-matrix) (B diagonal-matrix)

Source: matrix.lisp (file)

Method: e2+ (A hermitian-matrix) (B hermitian-matrix)

Source: matrix.lisp (file)

Method: e2+ (A upper-triangular-matrix) (B upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e2+ (A lower-triangular-matrix) (B lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e2+ A (B wrapped-matrix)

Source: matrix.lisp (file)

Method: e2+ (A wrapped-matrix) B

Source: matrix.lisp (file)

Method: e2+ (A number) (B number)

Method: e2+ (A vector) (B number)

Method: e2+ (A number) (B vector)

Method: e2+ (A vector) (B vector)

Method: e2+ (A array) (B number)

Method: e2+ (A number) (B array)

Method: e2+ (A array) (B array)

Generic Function: e2- A B

Bivariate elementwise -.

Package

Source

Methods

Method: e2- (A diagonal-matrix) (B diagonal-matrix)

Source: matrix.lisp (file)

Method: e2- (A hermitian-matrix) (B hermitian-matrix)

Source: matrix.lisp (file)

Method: e2- (A upper-triangular-matrix) (B upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e2- (A lower-triangular-matrix) (B lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e2- A (B wrapped-matrix)

Source: matrix.lisp (file)

Method: e2- (A wrapped-matrix) B

Source: matrix.lisp (file)

Method: e2- (A number) (B number)

Method: e2- (A vector) (B number)

Method: e2- (A number) (B vector)

Method: e2- (A vector) (B vector)

Method: e2- (A array) (B number)

Method: e2- (A number) (B array)

Method: e2- (A array) (B array)

Generic Function: e2/ A B

Bivariate elementwise /.

Package

Source

Methods

Method: e2/ (A number) (B diagonal-matrix)

Source: matrix.lisp (file)

Method: e2/ (A diagonal-matrix) (B number)

Source: matrix.lisp (file)

Method: e2/ (A number) (B hermitian-matrix)

Source: matrix.lisp (file)

Method: e2/ (A hermitian-matrix) (B number)

Source: matrix.lisp (file)

Method: e2/ (A number) (B upper-triangular-matrix)

Source: matrix.lisp (file)

Method: e2/ (A upper-triangular-matrix) (B number)

Source: matrix.lisp (file)

Method: e2/ (A number) (B lower-triangular-matrix)

Source: matrix.lisp (file)

Method: e2/ (A lower-triangular-matrix) (B number)

Source: matrix.lisp (file)

Method: e2/ (A number) (B number)

Method: e2/ (A vector) (B number)

Method: e2/ (A number) (B vector)

Method: e2/ (A vector) (B vector)

Method: e2/ (A array) (B number)

Method: e2/ (A number) (B array)

Method: e2/ (A array) (B array)

Generic Function: e2log A B

Bivariate elementwise LOG.

Package

Source

Methods

Method: e2log (A number) (B number)

Method: e2log (A vector) (B number)

Method: e2log (A number) (B vector)

Method: e2log (A vector) (B vector)

Method: e2log (A array) (B number)

Method: e2log (A number) (B array)

Method: e2log (A array) (B array)

Generic Function: eceiling A

Univariate elementwise CEILING.

Package

Source

Methods

Method: eceiling (A number)

Method: eceiling (A array)

Generic Function: econjugate A

Univariate elementwise CONJUGATE.

Package

Source

Methods

Method: econjugate (A number)

Method: econjugate (A array)

Generic Function: eexp A

Univariate elementwise EXP.

Package

Source

Methods

Method: eexp (A diagonal-matrix)

Source: matrix.lisp (file)

Method: eexp (A hermitian-matrix)

Source: matrix.lisp (file)

Method: eexp (A upper-triangular-matrix)

Source: matrix.lisp (file)

Method: eexp (A lower-triangular-matrix)

Source: matrix.lisp (file)

Method: eexp (A number)

Method: eexp (A array)

Generic Function: eexpt A B

Bivariate elementwise EXPT.

Package

Source

Methods

Method: eexpt (A number) (B number)

Method: eexpt (A vector) (B number)

Method: eexpt (A number) (B vector)

Method: eexpt (A vector) (B vector)

Method: eexpt (A array) (B number)

Method: eexpt (A number) (B array)

Method: eexpt (A array) (B array)

Generic Function: efloor A

Univariate elementwise FLOOR.

Package

Source

Methods

Method: efloor (A number)

Method: efloor (A array)

Generic Function: emod A B

Bivariate elementwise MOD.

Package

Source

Methods

Method: emod (A number) (B number)

Method: emod (A vector) (B number)

Method: emod (A number) (B vector)

Method: emod (A vector) (B vector)

Method: emod (A array) (B number)

Method: emod (A number) (B array)

Method: emod (A array) (B array)

Generic Function: ensure-sorted-reals OBJECT

Return the contents of OBJECT as a SORTED-REALS.

Package

Source

Methods

Method: ensure-sorted-reals (SORTED-REALS sorted-reals)

Method: ensure-sorted-reals (ARRAY array)

Method: ensure-sorted-reals (LIST list)

Generic Function: ereduce FUNCTION OBJECT &key KEY

Elementwise reduce, traversing in row-major order.

Package

Source

Methods

Method: ereduce FUNCTION (ARRAY array) &key KEY

Method: ereduce FUNCTION (SEQUENCE sequence) &key KEY

Method: ereduce FUNCTION OBJECT &key KEY

Generic Function: esqrt A

Univariate elementwise SQRT.

Package

Source

Methods

Method: esqrt (A diagonal-matrix)

Source: matrix.lisp (file)

Method: esqrt (A hermitian-matrix)

Source: matrix.lisp (file)

Method: esqrt (A upper-triangular-matrix)

Source: matrix.lisp (file)

Method: esqrt (A lower-triangular-matrix)

Source: matrix.lisp (file)

Method: esqrt (A number)

Method: esqrt (A array)

Generic Function: extend-interval INTERVAL OBJECT

Return an interval that includes INTERVAL and OBJECT. NIL stands for the empty set.

Package

Source

interval.lisp (file)

Methods

Method: extend-interval (INTERVAL null) (OBJECT null)

Method: extend-interval (INTERVAL null) (NUMBER real)

Method: extend-interval (INTERVAL interval) (NUMBER real)

Method: extend-interval INTERVAL (OBJECT interval)

Method: extend-interval INTERVAL (LIST list)

Method: extend-interval INTERVAL (ARRAY array)

Generic Function: kurtosis OBJECT &key WEIGHTS

Kurtosis FIXME talk about bias, maybe implement unbiased?

Package

Source

Methods

Method: kurtosis OBJECT &key WEIGHTS

Method: kurtosis (OBJECT central-sample-moments) &key WEIGHTS

Generic Function: l2norm-square OBJECT

Square of the $L_2$ norm of OBJECT.

Package

num-utils.arithmetic

Source

Methods

Method: l2norm-square (SEQUENCE sequence)

Generic Function: left INTERVAL

Left endpoint of interval.

Package

Source

interval.lisp (file)

Methods

Method: left (INTERVAL interval/infinite-left)

Method: left (INTERVAL/FINITE-LEFT interval/finite-left): automatically generated reader method

Generic Function: map-array ARRAY FUNCTION &optional RETVAL

Package

Methods

Method: map-array ARRAY FUNCTION &optional RETVAL

Apply FUNCTION to each element of ARRAY
Return a new array, or write into the optional 3rd argument.

Source: matrix.lisp (file)

Generic Function: mean OBJECT &key WEIGHTS

The mean of elements in OBJECT.

Package

Source

Methods

Method: mean OBJECT &key WEIGHTS

Method: mean (OBJECT central-sample-moments) &key WEIGHTS

Generic Function: median OBJECT

Median of OBJECT.

Package

Source

Methods

Method: median (SAMPLE sequence): Returns median of SAMPLE. SAMPLE must be a sequence of real numbers.

Method: median OBJECT

Generic Function: num= A B &optional TOLERANCE

Compare A and B for approximate equality, checking corresponding elements when applicable (using TOLERANCE).

Two numbers A and B are NUM= iff |a-b|/max(1,|a|,|b|) <= tolerance.

Unless a method is defined for them, two objects are compared with EQUALP.

Generally, methods should be defined so that two objects are NUM= if they the same class, same dimensions, and all their elements are NUM=.

Package

num-utils.num=

Source

num=.lisp (file)

Methods

Method: num= (A central-sample-moments) (B central-sample-moments) &optional TOLERANCE

Source: statistics.lisp (file)

Method: num= (A diagonal-matrix) (B diagonal-matrix) &optional TOLERANCE

Source: matrix.lisp (file)

Method: num= (A wrapped-matrix) (B wrapped-matrix) &optional TOLERANCE

Source: matrix.lisp (file)

Method: num= (A finite-interval) (B finite-interval) &optional TOLERANCE

Source: interval.lisp (file)

Method: num= (A real-line) (B real-line) &optional TOLERANCE

Source: interval.lisp (file)

Method: num= A B &optional TOLERANCE

Method: num= (A number) (B number) &optional TOLERANCE

Method: num= (A array) (B array) &optional TOLERANCE

Method: num= (A cons) (B cons) &optional TOLERANCE

Method: num= (A null) (B null) &optional TOLERANCE

Generic Function: open-left? INTERVAL

True iff the left endpoint of the interval is open.

Package

Source

interval.lisp (file)

Methods

Method: open-left? (INTERVAL interval/infinite-left)

Method: open-left? (INTERVAL/FINITE-LEFT interval/finite-left): automatically generated reader method

Generic Function: open-right? INTERVAL

True iff the right endpoint of the interval is open.

Package

Source

interval.lisp (file)

Methods

Method: open-right? (INTERVAL interval/infinite-right)

Method: open-right? (INTERVAL/FINITE-RIGHT interval/finite-right): automatically generated reader method

Generic Function: product OBJECT

Product of elements in object.

Package

num-utils.arithmetic

Source

Methods

Method: product (SEQUENCE sequence)

Method: product (ARRAY array)

Generic Function: quantile OBJECT Q

Return an element at quantile Q. May be an interpolation or an approximation, depending on OBJECT and Q. NOTE: Extensions should define methods for QUANTILES, not QUANTILE.

Package

Source

Methods

Method: quantile (OBJECT sequence) Q

Method: quantile OBJECT Q

Generic Function: quantiles OBJECT QS

Multiple quantiles (see QUANTILE). NOTE: Extensions should define methods for QUANTILES, not QUANTILE.

Package

Source

Methods

Method: quantiles (OBJECT sequence) QS

Method: quantiles (ACCUMULATOR sorted-reals) Q

Generic Function: right INTERVAL

Right endpoint of interval.

Package

Source

interval.lisp (file)

Methods

Method: right (INTERVAL interval/infinite-right)

Method: right (INTERVAL/FINITE-RIGHT interval/finite-right): automatically generated reader method

Generic Function: sd OBJECT &key WEIGHTS

Standard deviation. For samples, the square root of the unbiased estimator (see VARIANCE).

Package

Source

Methods

Method: sd OBJECT &key WEIGHTS

Generic Function: shift-interval INTERVAL OFFSET

Package

Source

interval.lisp (file)

Methods

Method: shift-interval (INTERVAL finite-interval) (OFFSET real)

Generic Function: skewness OBJECT &key WEIGHTS

Skewness FIXME talk about bias, maybe implement unbiased?

Package

Source

Methods

Method: skewness OBJECT &key WEIGHTS

Method: skewness (OBJECT central-sample-moments) &key WEIGHTS

Generic Function: sum OBJECT &key KEY

Sum of elements in object. KEY is applied to each element.

Package

num-utils.arithmetic

Source

Methods

Method: sum (SEQUENCE sequence) &key KEY

Method: sum (ARRAY array) &key KEY

Generic Function: tally ACCUMULATOR

The total weight of elements in ACCUMULATOR.

Package

Source

Methods

Method: tally (ACCUMULATOR sparse-counter): Return the total ’weight’ of the accumulator

Method: tally (ACCUMULATOR tally-mixin)

Generic Function: transpose ARRAY

Transpose.

Package

Source

matrix.lisp (file)

Methods

Method: transpose (ARRAY array)

Method: transpose (MATRIX lower-triangular-matrix)

Method: transpose (MATRIX upper-triangular-matrix)

Method: transpose (MATRIX hermitian-matrix)

Method: transpose (DIAGONAL diagonal-matrix)

Generic Function: variance OBJECT &key WEIGHTS

Variance of OBJECT. For samples, normalized by the weight-1 (and thus unbiased if certain assumptions hold, eg weights that count frequencies).

Package

Source

Methods

Method: variance OBJECT &key WEIGHTS

Method: variance (OBJECT central-sample-moments) &key WEIGHTS

5.1.6 Conditions

Condition: empty-accumulator ()

Package: num-utils.statistics
Source: statistics.lisp (file)
Direct superclasses: error (condition)

Condition: information-not-collected-in-accumulator ()

Package: num-utils.statistics
Source: statistics.lisp (file)
Direct superclasses: error (condition)

Condition: not-enough-elements-in-accumulator ()

Package: num-utils.statistics
Source: statistics.lisp (file)
Direct superclasses: error (condition)

5.1.7 Structures

Structure: central-sample-moments ()

Central sample moments calculated on-line/single-pass.

M weighted mean
S2 weighted sum of squared deviations from the mean, not calculated when NIL S3 weighted sum of cubed deviations from the mean, not calculated when NIL S4 weighted sum of 4th power deviations from the mean, not calculated when NIL

Allows on-line, numerically stable calculation of moments. See cite{bennett2009numerically} and cite{pebay2008formulas} for the description of the algorithm. M_2, ..., M_4 in the paper are s2, ..., s4 in the code.

Package

Source

Direct superclasses

tally-mixin (structure)

Direct methods

kurtosis (method)
skewness (method)
central-m4 (method)
central-m3 (method)
central-m2 (method)
variance (method)
mean (method)
central-sample-moments (method)
pool2 (method)
add (method)
num= (method)

Direct slots

Slot: m

Type: real
Initform: 0.0d0
Readers: central-sample-moments-m (function)
Writers: (setf central-sample-moments-m) (function)

Slot: s2

Type: (or (real 0) null)
Initform: 0.0d0
Readers: central-sample-moments-s2 (function)
Writers: (setf central-sample-moments-s2) (function)

Slot: s3

Type: (or real null)
Initform: 0.0d0
Readers: central-sample-moments-s3 (function)
Writers: (setf central-sample-moments-s3) (function)

Slot: s4

Type: (or (real 0) null)
Initform: 0.0d0
Readers: central-sample-moments-s4 (function)
Writers: (setf central-sample-moments-s4) (function)

Structure: diagonal-matrix ()

Diagonal matrix. The elements in the diagonal are stored in a vector.

Package

Source

matrix.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods

transpose (method)
num= (method)
esqrt (method)
e1log (method)
eexp (method)
e1/ (method)
e1- (method)
e2* (method)
e2- (method)
e2+ (method)
e2/ (method)
e2/ (method)
e2* (method)
e2* (method)
dims (method)
element-type (method)
as-array (method)

Direct slots

Slot: elements

Type: vector
Readers: diagonal-matrix-elements (function)
Writers: (setf diagonal-matrix-elements) (function)

Structure: hermitian-matrix ()

Hermitian/symmetric matrix, with elements stored in the _lower_ triangle.

Implements _both_ real symmetric and complex Hermitian matrices — as technically, real symmetric matrices are also Hermitian. Complex symmetric matrices are _not_ implemented as a special matrix type, as they don’t have any special properties (eg real eigenvalues, etc).

Package

Source

matrix.lisp (file)

Direct superclasses

wrapped-matrix (structure)

Direct methods

transpose (method)
esqrt (method)
e1log (method)
eexp (method)
e1/ (method)
e1- (method)
e2* (method)
e2- (method)
e2+ (method)
e2/ (method)
e2/ (method)
e2* (method)
e2* (method)
select (method)
print-object (method)
as-array (method)

Structure: lower-triangular-matrix ()

Lower triangular matrix. ELEMENTS in the upper triangle are treated as zero.

Package

Source

matrix.lisp (file)

Direct superclasses

wrapped-matrix (structure)

Direct methods

transpose (method)
esqrt (method)
e1log (method)
eexp (method)
e1/ (method)
e1- (method)
e2* (method)
e2- (method)
e2+ (method)
e2/ (method)
e2/ (method)
e2* (method)
e2* (method)
select (method)
print-object (method)
as-array (method)

Structure: relative ()

Relative sizes are in terms of width.

Package

Source

interval.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: fraction

Type: (real 0)
Readers: relative-fraction (function)
Writers: (setf relative-fraction) (function)

Structure: sorted-reals ()

Accumulator which sorts elements. ELEMENTS return the sorted elements.

Package

Source

Direct superclasses

structure-object (structure)

Direct methods

quantiles (method)
ensure-sorted-reals (method)
print-object (method)
add (method)

Direct slots

Slot: ordered-elements

Type: vector
Initform: #()
Readers: sorted-reals-ordered-elements (function)
Writers: (setf sorted-reals-ordered-elements) (function)

Slot: unordered-elements

Type: list
Readers: sorted-reals-unordered-elements (function)
Writers: (setf sorted-reals-unordered-elements) (function)

Structure: spacer ()

Spacers divide the leftover portion of an interval.

Package

Source

interval.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: weight

Type: (real 0)
Initform: 1
Readers: spacer-weight (function)
Writers: (setf spacer-weight) (function)

Structure: sparse-counter ()

Package

Source

num-utils.test-utilities

Direct superclasses

structure-object (structure)

Direct methods

print-object (method)
as-alist (method)
tally (method)
add (method)

Direct slots

Slot: table

Type: hash-table
Readers: sparse-counter-table (function)
Writers: (setf sparse-counter-table) (function)

Structure: test-results ()

Differences between reference values and computed values

Package

Source

test-utilities.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: worst-case

Type: integer
Initform: 0
Readers: worst-case (function)
Writers: (setf worst-case) (function)

Slot: min-error

Type: double-float
Initform: 0.0d0
Readers: min-error (function)
Writers: (setf min-error) (function)

Slot: max-error

Type: double-float
Initform: 0.0d0
Readers: max-error (function)
Writers: (setf max-error) (function)

Slot: mean-error

Type: double-float
Initform: 0.0d0
Readers: mean-error (function)
Writers: (setf mean-error) (function)

Slot: test-count

Type: integer
Initform: 0
Readers: test-count (function)
Writers: (setf test-count) (function)

Slot: variance0

Type: double-float
Initform: 0.0d0
Readers: variance0 (function)
Writers: (setf variance0) (function)

Slot: variance1

Type: double-float
Initform: 0.0d0
Readers: variance1 (function)
Writers: (setf variance1) (function)

Slot: rms

Type: double-float
Initform: 0.0d0
Readers: rms (function)
Writers: (setf rms) (function)

Structure: upper-triangular-matrix ()

Upper triangular matrix. ELEMENTS in the lower triangle are treated as zero.

Package

Source

matrix.lisp (file)

Direct superclasses

wrapped-matrix (structure)

Direct methods

transpose (method)
esqrt (method)
e1log (method)
eexp (method)
e1/ (method)
e1- (method)
e2* (method)
e2- (method)
e2+ (method)
e2/ (method)
e2/ (method)
e2* (method)
e2* (method)
select (method)
print-object (method)
as-array (method)

Structure: wrapped-matrix ()

A matrix that has some special structure (eg triangular, symmetric/hermitian). ELEMENTS is always a matrix. Not used directly, not exported.

Package

Source

matrix.lisp (file)

Direct superclasses

structure-object (structure)

Direct subclasses

lower-triangular-matrix (structure)
upper-triangular-matrix (structure)
hermitian-matrix (structure)

Direct methods

num= (method)
e2* (method)
e2* (method)
e2- (method)
e2- (method)
e2+ (method)
e2+ (method)
dims (method)
element-type (method)

Direct slots

Slot: elements

Type: (array * (* *))
Readers: wrapped-matrix-elements (function)
Writers: (setf wrapped-matrix-elements) (function)

5.1.8 Classes

Class: finite-interval ()

Interval with finite endpoints.

Package

Source

interval.lisp (file)

Direct superclasses

interval/finite-right (class)
interval/finite-left (class)
interval (class)

Direct methods

transformed-quadrature (method)
chebyshev-approximate-implementation (method)
shift-interval (method)
num= (method)
initialize-instance (method)

Class: interval ()

Abstract superclass for all intervals.

Package

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

finite-interval (class)
plusinf-interval (class)
minusinf-interval (class)
real-line (class)

Direct methods

extend-interval (method)
extend-interval (method)
print-object (method)

Class: minusinf-interval ()

Interval from -∞ to RIGHT.

Package

Source

interval.lisp (file)

Direct superclasses

interval/finite-right (class)
interval/infinite-left (class)
interval (class)

Class: plusinf-interval ()

Interval from LEFT to ∞.

Package

Source

interval.lisp (file)

Direct superclasses

interval/infinite-right (class)
interval/finite-left (class)
interval (class)

Direct methods

transformed-quadrature (method)
chebyshev-approximate-implementation (method)

Class: real-line ()

Representing the real line (-∞,∞).

Package

Source

interval.lisp (file)

Direct superclasses

interval/infinite-right (class)
interval/infinite-left (class)
interval (class)

Direct methods

num= (method)

5.1.9 Types

Type: extended-real &optional BASE

Extended real number.

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Type: simple-double-float-vector &optional LENGTH

Simple vector of double-float elements.

Package: num-utils.utilities
Source: utilities.lisp (file)

Type: simple-fixnum-vector ()

Simple vector or fixnum elements.

Package: num-utils.utilities
Source: utilities.lisp (file)

Type: simple-single-float-vector &optional LENGTH

Simple vector of single-float elements.

Package: num-utils.utilities
Source: utilities.lisp (file)

Type: triangular-matrix ()

Triangular matrix (either lower or upper).

Package: num-utils.matrix
Source: matrix.lisp (file)

5.2 Internal definitions

5.2.1 Macros

Macro: &diagonal-matrix ELEMENTS

LET+ form for slots of the structure DIAGONAL-MATRIX.

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: &diagonal-matrix-r/o ELEMENTS

LET+ form for slots of the structure DIAGONAL-MATRIX. Read-only.

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: &sorted-reals ORDERED-ELEMENTS UNORDERED-ELEMENTS

LET+ form for slots of the structure SORTED-REALS.

Package: num-utils.statistics
Source: statistics.lisp (file)

Macro: &sorted-reals-r/o ORDERED-ELEMENTS UNORDERED-ELEMENTS

LET+ form for slots of the structure SORTED-REALS. Read-only.

Package: num-utils.statistics
Source: statistics.lisp (file)

Macro: define-central-sample-moment FUNCTION (VARIABLE DEGREE) &body BODY

FIXME documentation, factor out general part

Package: num-utils.statistics
Source: statistics.lisp (file)

Macro: define-comparison NAME TEST

Define a comparison, extendeding a pairwise comparison to an arbitrary number of arguments.

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Macro: define-e& OPERATION &key FUNCTION BIVARIATE UNIVARIATE DOCSTRING

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Macro: define-e1 OPERATION &key FUNCTION DOCSTRING

Define an univariate elementwise operation.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Macro: define-e2 OPERATION &key FUNCTION DOCSTRING

Define a bivariate elementwise operation.

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Macro: define-elementwise-as-array TYPE &key FUNCTIONS

Define binary elementwise operations for FUNCTION, implemented by converting them to arrays.

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: define-elementwise-reduction NAME FUNCTION &optional DOCSTRING

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Macro: define-elementwise-same-class TYPE &key FUNCTIONS ELEMENTS-ACCESSOR

Define binary elementwise operations for FUNCTION for two arguments of the same class.

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: define-elementwise-univariate TYPE &key FUNCTIONS ELEMENTS-ACCESSOR

Define unary elementwise operations for FUNCTION for all subclasses of wrapped-elements.

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: define-elementwise-with-constant TYPE &key FUNCTIONS ELEMENTS-ACCESSOR

Define binary elementwise operations for FUNCTION for all subclasses of wrapped-elements.

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: define-rounding-with-offset NAME FUNCTION DOCSTRING

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Macro: define-wrapped-matrix TYPE ELEMENTS STRUCT-DOCSTRING (MASKED-TEST MASKED-STRING) CHECK-AND-CONVERT-ELEMENTS REGULARIZE-ELEMENTS

Package: num-utils.matrix
Source: matrix.lisp (file)

Macro: mapping-array (REF ARRAY &rest OTHER) FORM

Package: num-utils.elementwise
Source: elementwise.lisp (file)

Macro: univariate-rootfinder-loop% ((F A B FA FB) (F-TESTED TEST-BRACKET DELTA EPSILON)) &body BODY

Common parts for univariate rootfinder functions.

Sets up the following:

- function OPPOSITE-SIGN-P for checking that two numbers are on the opposite side of 0

- function EVALUATE-AND-RETURN-IF-WITHIN-EPSILON which checks that |f(x)| <= EPSILON, if so, returns from the block with (VALUES X FX T), otherwise simply returns the value

- function RETURN-IF-WITHIN-TOLERANCE checks if the interval [A,B] bracketing X is small enough (smaller than TOLERANCE) and if so, returns (X FX NIL (INTERVAL A B))

- variables FA and FB to hold function values at A and B

Initially, it checks for either $f(a)$ or $f(b)$ being a root, and establishes $a leq b$ by exchanging $a,f(a)$ and $b,f(b)$ if necessary. Also checks that $f(a)$ and $f(b)$ are of opposite sign. Checks that both tolerance and epsilon are nonnegative.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

5.2.2 Functions

Function: ab-to-cd-intercept-slope A B C D

Return (values INTERCEPT SLOPE) for linear mapping x:-> intercept+slope*x from [a,b] to [c,d].

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: ab-to-cinf Z A B C

Inverse of cinf-to-ab.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: above-diagonal? ROW COL

Test if element with indexes row and col is (strictly) above the diagonal.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: below-diagonal? ROW COL

Test if element with indexes row and col is (strictly) below the diagonal.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: central-sample-moments-m INSTANCE

Function: (setf central-sample-moments-m) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: central-sample-moments-p OBJECT

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: central-sample-moments-s2 INSTANCE

Function: (setf central-sample-moments-s2) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: central-sample-moments-s3 INSTANCE

Function: (setf central-sample-moments-s3) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: central-sample-moments-s4 INSTANCE

Function: (setf central-sample-moments-s4) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: central-sample-moments-w INSTANCE

Function: (setf central-sample-moments-w) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: chebyshev-recursion X VALUE PREVIOUS-VALUE

Chebyshev polynomial recursion formula.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: cinf-to-ab X A B C

Map x in [c,plus-infinity) to z in [a,b] using x -> (x-c)/(1+x-c)+(b-a)+a.

Package: num-utils.chebyshev
Source: chebyshev.lisp (file)

Function: copy-central-sample-moments INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: copy-diagonal-matrix INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: copy-hermitian-matrix INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: copy-iterative-quadrature INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: copy-lower-triangular-matrix INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: copy-midpoint-quadrature INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: copy-relative INSTANCE

Package: num-utils.interval
Source: interval.lisp (file)

Function: copy-richardson-extrapolation INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: copy-sorted-reals INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: copy-spacer INSTANCE

Package: num-utils.interval
Source: interval.lisp (file)

Function: copy-sparse-counter INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: copy-tally-mixin INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: copy-test-results INSTANCE

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: copy-trapezoidal-quadrature INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: copy-upper-triangular-matrix INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: copy-wrapped-matrix INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: diagonal-matrix-p OBJECT

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: ensure-valid-elements ARRAY RANK &rest PREDICATES

Convert OBJECT to an array, check that it

1. has the required rank,

2. has a valid sparse element type, and

3. that it satisfies PREDICATES.

Return the array.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: extend-pairwise-comparison TEST FIRST REST

Extend TEST (a pairwise comparison) to an arbitrary number of arguments (but at least one, FIRST).

Package: num-utils.extended-real
Source: extended-real.lisp (file)

Function: hermitian-matrix-elements INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: hermitian-matrix-p OBJECT

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: iterative-quadrature-a INSTANCE

Function: (setf iterative-quadrature-a) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: iterative-quadrature-b INSTANCE

Function: (setf iterative-quadrature-b) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: iterative-quadrature-f INSTANCE

Function: (setf iterative-quadrature-f) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: iterative-quadrature-h INSTANCE

Function: (setf iterative-quadrature-h) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: iterative-quadrature-n INSTANCE

Function: (setf iterative-quadrature-n) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: iterative-quadrature-p OBJECT

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: iterative-quadrature-sum INSTANCE

Function: (setf iterative-quadrature-sum) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: ln N

Natural logarithm.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: lower-triangular-matrix-elements INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: lower-triangular-matrix-p OBJECT

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: make-central-sample-moments &key (W W) (M M) (S2 S2) (S3 S3) (S4 S4)

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: make-diagonal-matrix &key (ELEMENTS ELEMENTS)

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: make-hermitian-matrix &key (ELEMENTS ELEMENTS)

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: make-iterative-quadrature &key (F F) (A A) (B B) (H H) (N N) (SUM SUM)

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: make-lower-triangular-matrix &key (ELEMENTS ELEMENTS)

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: make-sorted-reals &key (ORDERED-ELEMENTS ORDERED-ELEMENTS) (UNORDERED-ELEMENTS UNORDERED-ELEMENTS)

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: make-sparse-counter% &key (TABLE TABLE)

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: make-tally-mixin &key (W W)

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: make-test-results &key (WORST-CASE WORST-CASE) (MIN-ERROR MIN-ERROR) (MAX-ERROR MAX-ERROR) (MEAN-ERROR MEAN-ERROR) (TEST-COUNT TEST-COUNT) (VARIANCE0 VARIANCE0) (VARIANCE1 VARIANCE1) (RMS RMS)

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: make-upper-triangular-matrix &key (ELEMENTS ELEMENTS)

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: make-wrapped-matrix &key (ELEMENTS ELEMENTS)

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: midpoint-quadrature F A B

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature% &key (F F) (A A) (B B) (H H) (N N) (SUM SUM)

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-a INSTANCE

Function: (setf midpoint-quadrature-a) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-b INSTANCE

Function: (setf midpoint-quadrature-b) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-f INSTANCE

Function: (setf midpoint-quadrature-f) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-h INSTANCE

Function: (setf midpoint-quadrature-h) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-n INSTANCE

Function: (setf midpoint-quadrature-n) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-p OBJECT

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: midpoint-quadrature-sum INSTANCE

Function: (setf midpoint-quadrature-sum) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: narrow-bracket? A B DELTA

Return true iff $|a-b| < \delta$.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

Function: near-root? F EPSILON

Return true iff $|f| < \epsilon$.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

Function: opposite-sign? A B

Return true iff A and B are on opposite sides of 0.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

Function: pad-left-expansion ROWS NCOL

Pad ragged-right rows. Used internally to implement ragged right matrix specifications.

Package: num-utils.matrix-shorthand
Source: matrix-shorthand.lisp (file)

Function: print-matrix-formatter X

Standard formatter for matrix printing. Respects *print-precision*, and formats complex numbers as a+bi, eg 0.0+1.0i.

Package: num-utils.print-matrix
Source: print-matrix.lisp (file)

Function: relative-fraction INSTANCE

Package: num-utils.interval
Source: interval.lisp (file)

Function: relative-p OBJECT

Package: num-utils.interval
Source: interval.lisp (file)

Function: richardson-extrapolation COEFFICIENT ITERATIONS &aux DIAGONAL

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: richardson-extrapolation-coefficient INSTANCE

Function: (setf richardson-extrapolation-coefficient) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: richardson-extrapolation-diagonal INSTANCE

Function: (setf richardson-extrapolation-diagonal) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: richardson-extrapolation-n INSTANCE

Function: (setf richardson-extrapolation-n) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: richardson-extrapolation-p OBJECT

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: richardson-iteration EXTRAPOLATION STEP

Add STEP (= $A(h q^{-k}$) to an existing Richardson EXTRAPOLATION. See the documentation of RICHARDSON-EXTRAPOLATION for details.

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: romberg-quadrature% QUADRATURE EPSILON MIN-ITER MAX-ITER

Internal function implementing Romberg quadrature. Requires an iterative quadrature instance, a relative EPSILON and MIN-ITER for the stopping criterion, and the maximum number of iterations allowed. Works on finite intervals.

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: rootfinding-delta INTERVAL &optional DELTA-RELATIVE

Default DELTA for rootfinding methods, uses bracket width.

Package: num-utils.rootfinding
Source: rootfinding.lisp (file)

Function: similar-element-type ELEMENT-TYPE

Return a type that is a supertype of ELEMENT-TYPE and is closed under arithmetic operations. May not be the narrowest.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: similar-sequence-type SEQUENCE

Return type that sequence can be mapped to using arithmetic operations.

Package: num-utils.arithmetic
Source: arithmetic.lisp (file)

Function: sort-reals SEQUENCE

Return a SORTED-REALS structure.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: sorted-reals-ordered-elements INSTANCE

Function: (setf sorted-reals-ordered-elements) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: sorted-reals-p OBJECT

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: sorted-reals-unordered-elements INSTANCE

Function: (setf sorted-reals-unordered-elements) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: spacer-p OBJECT

Package: num-utils.interval
Source: interval.lisp (file)

Function: spacer-weight INSTANCE

Package: num-utils.interval
Source: interval.lisp (file)

Function: sparse-counter-p OBJECT

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: tally-mixin-p OBJECT

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: tally-mixin-w INSTANCE

Function: (setf tally-mixin-w) VALUE INSTANCE

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: test-results-p OBJECT

Package: num-utils.test-utilities
Source: test-utilities.lisp (file)

Function: trapezoidal-quadrature F A B

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature% &key (F F) (A A) (B B) (H H) (N N) (SUM SUM)

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-a INSTANCE

Function: (setf trapezoidal-quadrature-a) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-b INSTANCE

Function: (setf trapezoidal-quadrature-b) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-f INSTANCE

Function: (setf trapezoidal-quadrature-f) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-h INSTANCE

Function: (setf trapezoidal-quadrature-h) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-n INSTANCE

Function: (setf trapezoidal-quadrature-n) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-p OBJECT

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: trapezoidal-quadrature-sum INSTANCE

Function: (setf trapezoidal-quadrature-sum) VALUE INSTANCE

Package: num-utils.quadrature
Source: quadrature.lisp (file)

Function: upper-triangular-matrix-elements INSTANCE

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: upper-triangular-matrix-p OBJECT

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: valid-sparse-type? TYPE

Check if TYPE is a valid type for sparse matrices. Only supertypes and subtypes of NUMBER are allowed.

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: weighted-empirical-quantile SORTED-REALS P-TABLE Q

Return the empirical quantile of a vector of real numbers, sorted in ascending order (not checked). Uses a 0.5 correction.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: weighted-quantile-p-table WEIGHTS

Return table of probability brackets for weighted quantile calculations., built from the weights (which should be positive reals, not checked). Uses a 0.5 correction.

Package: num-utils.statistics
Source: statistics.lisp (file)

Function: wrapped-matrix-p OBJECT

Package: num-utils.matrix
Source: matrix.lisp (file)

Function: zero-like ARRAY

Return 0 coerced to the element type of ARRAY. It is assumed that the latter satisfies VALID-SPARSE-TYPE?.

Package: num-utils.matrix
Source: matrix.lisp (file)

5.2.3 Generic functions

Generic Function: chebyshev-approximate-implementation F INTERVAL N-POLYNOMIALS N-POINTS

Implementation of CHEBYSHEV-APPROXIMATE.

Package

num-utils.chebyshev

Source

chebyshev.lisp (file)

Methods

Method: chebyshev-approximate-implementation F (INTERVAL plusinf-interval) N-POLYNOMIALS N-POINTS

Method: chebyshev-approximate-implementation F (INTERVAL finite-interval) N-POLYNOMIALS N-POINTS

Generic Function: esquare A

Univariate elementwise SQUARE.

Package

Source

Methods

Method: esquare (A number)

Method: esquare (A array)

Generic Function: pool2 ACCUMULATOR1 ACCUMULATOR2

Pool two accumulators. When they are of a different type, the resulting accumulator will be downgraded to the level afforded by the information available in the accumulators.

Package

Source

Methods

Method: pool2 (MOMENTS-A central-sample-moments) (MOMENTS-B central-sample-moments)

Generic Function: print-left-endpoint INTERVAL STREAM

Package

Source

interval.lisp (file)

Methods

Method: print-left-endpoint (INTERVAL interval/finite-left) STREAM

Method: print-left-endpoint (INTERVAL interval/infinite-left) STREAM

Generic Function: print-right-endpoint INTERVAL STREAM

Package

Source

interval.lisp (file)

Methods

Method: print-right-endpoint (INTERVAL interval/finite-right) STREAM

Method: print-right-endpoint (INTERVAL interval/infinite-right) STREAM

Generic Function: refine-quadrature QUADRATURE

Refine quadrature with more points. Return the sum for those points.

Package

Source

Methods

Method: refine-quadrature (QUADRATURE midpoint-quadrature)

Method: refine-quadrature (QUADRATURE trapezoidal-quadrature)

Generic Function: richardson-coefficient QUADRATURE

Return the coefficient $q$ for Richardson approximation.

Package

Source

Methods

Method: richardson-coefficient (QUADRATURE midpoint-quadrature)

Method: richardson-coefficient (QUADRATURE trapezoidal-quadrature)

Generic Function: transformed-quadrature FUNCTION INTERVAL TRANSFORMATION

Return a quadrature for integrating FUNCTION on INTERVAL, which may be infinite, in which case FUNCTION will be transformed. TRANSFORMATION can be used to select the transformation when applicable, otherwise it is NIL.

Package

Source

Methods

Method: transformed-quadrature FUNCTION (INTERVAL finite-interval) (TRANSFORMATION null)

Method: transformed-quadrature FUNCTION (INTERVAL plusinf-interval) (TRANSFORMATION null)

5.2.4 Structures

Structure: iterative-quadrature ()

Quadrature building block.

F is the function.

A and B are the endpoints.

H is the stepsize.

Package

Source

Direct superclasses

structure-object (structure)

Direct subclasses

trapezoidal-quadrature (structure)
midpoint-quadrature (structure)

Direct slots

Slot: f

Type: (function (double-float) double-float)
Readers: iterative-quadrature-f (function)
Writers: (setf iterative-quadrature-f) (function)

Slot: a

Type: double-float
Readers: iterative-quadrature-a (function)
Writers: (setf iterative-quadrature-a) (function)

Slot: b

Type: double-float
Readers: iterative-quadrature-b (function)
Writers: (setf iterative-quadrature-b) (function)

Slot: h

Type: double-float
Readers: iterative-quadrature-h (function)
Writers: (setf iterative-quadrature-h) (function)

Slot: n

Type: fixnum
Initform: 0
Readers: iterative-quadrature-n (function)
Writers: (setf iterative-quadrature-n) (function)

Slot: sum

Type: double-float
Initform: 0.0d0
Readers: iterative-quadrature-sum (function)
Writers: (setf iterative-quadrature-sum) (function)

Structure: midpoint-quadrature ()

Package

Source

Direct superclasses

iterative-quadrature (structure)

Direct methods

richardson-coefficient (method)
refine-quadrature (method)

Structure: richardson-extrapolation ()

Given A(h)=A_0 + sum_{k=1}^infty a_k h^{kp}, calculate approximations for A given A(h q^{-k}), where the latter can be incorporated using RICHARDSON-ITERATION with consecutive values for k=1,...,max_iter, which returns the latest A(0) as the first and the largest relative change, which can be used to test termination.

The algorithm uses Richardson extrapolation, the required coefficient is q^k.

Package

Source

Direct superclasses

structure-object (structure)

Direct slots

Slot: coefficient

Type: double-float
Readers: richardson-extrapolation-coefficient (function)
Writers: (setf richardson-extrapolation-coefficient) (function)

Slot: n

Type: fixnum
Initform: 0
Readers: richardson-extrapolation-n (function)
Writers: (setf richardson-extrapolation-n) (function)

Slot: diagonal

Type: (array double-float (*))
Readers: richardson-extrapolation-diagonal (function)
Writers: (setf richardson-extrapolation-diagonal) (function)

Structure: tally-mixin ()

Mixin structure that contains a tally. Not exported. W is the total weight.

Package

Source

Direct superclasses

structure-object (structure)

Direct subclasses

central-sample-moments (structure)

Direct methods

tally (method)

Direct slots

Slot: w

Type: (real 0)
Initform: 0
Readers: tally-mixin-w (function)
Writers: (setf tally-mixin-w) (function)

Structure: trapezoidal-quadrature ()

Package

Source

Direct superclasses

iterative-quadrature (structure)

Direct methods

richardson-coefficient (method)
refine-quadrature (method)

5.2.5 Classes

Class: interval/finite-left ()

Interval with left endpoint.

Package

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

finite-interval (class)
plusinf-interval (class)

Direct methods

print-left-endpoint (method)
open-left? (method)
left (method)

Direct slots

Slot: left

Type: real
Initargs: :left
Readers: left (generic function)

Slot: open-left?

Type: boolean
Initargs: :open-left?
Readers: open-left? (generic function)

Class: interval/finite-right ()

Interval with right endpoint.

Package

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

finite-interval (class)
minusinf-interval (class)

Direct methods

print-right-endpoint (method)
open-right? (method)
right (method)

Direct slots

Slot: right

Type: real
Initargs: :right
Readers: right (generic function)

Slot: open-right?

Type: boolean
Initargs: :open-right?
Readers: open-right? (generic function)

Class: interval/infinite-left ()

Left endpoint is -∞.

Package

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

minusinf-interval (class)
real-line (class)

Direct methods

print-left-endpoint (method)
open-left? (method)
left (method)

Class: interval/infinite-right ()

Right endpoint is ∞.

Package