3.1.1 num-utils/num-utils.asd

Source

num-utils.asd.

Parent Component

num-utils (system).

ASDF Systems

num-utils.

---

3.1.2 num-utils/packages.lisp

Source

num-utils.asd.

Parent Component

num-utils (system).

Packages

• num-utils.matrix.
• num-utils.log-exp.
• num-utils.chebyshev.
• num-utils.interval.
• num-utils.elementwise.
• num-utils.rootfinding.
• num-utils.statistics.
• num-utils.quadrature.
• num-utils.extended-real.
• num-utils.test-utilities.
• num-utils.num=.
• num-utils.matrix-shorthand.
• num-utils.arithmetic.
• num-utils.utilities.
• num-utils.print-matrix.
• num-utils.polynomial.

---

3.1.3 num-utils/utilities.lisp

Dependency

packages.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

• as-alist (generic function).
• as-double-float (function).
• as-plist (generic function).
• 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).

---

3.1.4 num-utils/num=.lisp

Dependency

utilities.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

---

3.1.5 num-utils/arithmetic.lisp

Dependency

num=.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

• 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).
• log10 (function).
• log2 (function).
• multf (macro).
• normalize-probabilities (function).
• numseq (function).
• product (generic function).
• round* (function).
• same-sign-p (function).
• sequence-maximum (function).
• sequence-minimum (function).
• square (function).
• sum (generic function).
• truncate* (function).

Internals

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

---

3.1.6 num-utils/elementwise.lisp

Dependency

arithmetic.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

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

---

3.1.7 num-utils/extended-real.lisp

Dependency

elementwise.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

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

---

3.1.8 num-utils/interval.lisp

Dependency

extended-real.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

• 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-right-endpoint (generic function).
• relative-fraction (reader).
• relative-p (function).
• spacer-p (function).
• spacer-weight (reader).

---

3.1.9 num-utils/print-matrix.lisp

Dependency

interval.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

print-matrix-formatter (function).

---

3.1.10 num-utils/matrix.lisp

Dependency

print-matrix.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

• as-array (method).
• as-array (method).
• as-array (method).
• as-array (method).
• diagonal-matrix (function).
• diagonal-matrix (structure).
• diagonal-matrix-elements (reader).
• (setf diagonal-matrix-elements) (writer).
• diagonal-vector (generic function).
• (setf diagonal-vector) (generic function).
• dims (method).
• dims (method).
• 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).
• element-type (method).
• element-type (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).
• print-object (method).
• print-object (method).
• print-object (method).
• select (method).
• select (method).
• select (method).
• transpose (generic function).
• triangular-matrix (type).
• upper-triangular-matrix (function).
• upper-triangular-matrix (structure).
• wrapped-matrix (structure).
• wrapped-matrix-elements (reader).

Internals

• &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).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

pad-left-expansion (function).

---

3.1.12 num-utils/statistics.lisp

Dependency

matrix-shorthand.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

• &sorted-reals (macro).
• &sorted-reals-r/o (macro).
• central-sample-moments-m (reader).
• (setf central-sample-moments-m) (writer).
• central-sample-moments-p (function).
• central-sample-moments-s2 (reader).
• (setf central-sample-moments-s2) (writer).
• central-sample-moments-s3 (reader).
• (setf central-sample-moments-s3) (writer).
• central-sample-moments-s4 (reader).
• (setf central-sample-moments-s4) (writer).
• 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).
• sort-reals (function).
• sorted-reals-ordered-elements (reader).
• (setf sorted-reals-ordered-elements) (writer).
• sorted-reals-p (function).
• sorted-reals-unordered-elements (reader).
• (setf sorted-reals-unordered-elements) (writer).
• sparse-counter-p (function).
• tally-mixin (structure).
• tally-mixin-p (function).
• tally-mixin-w (reader).
• (setf tally-mixin-w) (writer).
• weighted-empirical-quantile (function).
• weighted-quantile-p-table (function).

---

3.1.13 num-utils/chebyshev.lisp

Dependency

statistics.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

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

---

3.1.14 num-utils/polynomial.lisp

Dependency

chebyshev.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

evaluate-polynomial (function).

---

3.1.15 num-utils/rootfinding.lisp

Dependency

polynomial.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

• 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).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

romberg-quadrature (function).

Internals

• copy-iterative-quadrature (function).
• copy-midpoint-quadrature (function).
• copy-richardson-extrapolation (function).
• copy-trapezoidal-quadrature (function).
• iterative-quadrature (structure).
• iterative-quadrature-a (reader).
• (setf iterative-quadrature-a) (writer).
• iterative-quadrature-b (reader).
• (setf iterative-quadrature-b) (writer).
• iterative-quadrature-f (reader).
• (setf iterative-quadrature-f) (writer).
• iterative-quadrature-h (reader).
• (setf iterative-quadrature-h) (writer).
• iterative-quadrature-n (reader).
• (setf iterative-quadrature-n) (writer).
• iterative-quadrature-p (function).
• iterative-quadrature-sum (reader).
• (setf iterative-quadrature-sum) (writer).
• 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).
• richardson-coefficient (generic function).
• richardson-extrapolation (function).
• richardson-extrapolation (structure).
• richardson-extrapolation-coefficient (reader).
• (setf richardson-extrapolation-coefficient) (writer).
• richardson-extrapolation-diagonal (reader).
• (setf richardson-extrapolation-diagonal) (writer).
• richardson-extrapolation-n (reader).
• (setf richardson-extrapolation-n) (writer).
• richardson-extrapolation-p (function).
• richardson-iteration (function).
• romberg-quadrature% (function).
• transformed-quadrature (generic function).
• 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

quadrature.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

• 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).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

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

Internals

• 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).

Source

num-utils.asd.

Parent Component

num-utils (system).

Packages

num-utils.

---

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.

Special Variable: *num=-tolerance* ¶

Default tolerance for NUM=.

Package

num-utils.num=.

Source

num=.lisp.

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.

Special Variable: *rootfinding-delta-relative* ¶

Default relative interval width for rootfinding.

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Special Variable: *rootfinding-epsilon* ¶

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

---

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.

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.

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.

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.

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.

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.

Macro: expanding (&body body) ¶

Expand BODY. Useful for generating code programmatically.

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: extendf-interval (place object) ¶

Apply EXTEND-INTERVAL on PLACE using OBJECT.

Package

num-utils.interval.

Source

interval.lisp.

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.

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.

Macro: lambda-template ((prefix &rest variables) &body body) ¶

LAMBDA with WITH-TEMPLATE in its BODY.

Package

num-utils.extended-real.

Source

extended-real.lisp.

Macro: lower-triangular-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.

Macro: multf (place coefficient) ¶

Multiply place by COEFFICIENT.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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.

Macro: splice-awhen (test &body forms) ¶

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

Package

num-utils.utilities.

Source

utilities.lisp.

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.

Macro: unlessf (place value-form) ¶

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

Package

num-utils.utilities.

Source

utilities.lisp.

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.

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.

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.

---

5.1.3 Compiler macros

Compiler Macro: make-vector (element-type &rest initial-contents) ¶

Package

num-utils.utilities.

Source

utilities.lisp.

---

5.1.4 Ordinary 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.

Function: < (number &rest more-numbers) ¶

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: <= (number &rest more-numbers) ¶

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: = (number &rest more-numbers) ¶

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: > (number &rest more-numbers) ¶

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: >= (number &rest more-numbers) ¶

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: abs-diff (a b) ¶

Absolute difference of A and B.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: absolute-square (number) ¶

Number multiplied by its complex conjugate.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: as-double-float (v) ¶

Convert argument to DOUBLE-FLOAT.

Package

num-utils.utilities.

Source

utilities.lisp.

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.

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.

Function: bic (a b) ¶

Biconditional. Returns A <=> B.

Package

num-utils.utilities.

Source

utilities.lisp.

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.

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.

Function: central-sample-moments-degree (central-sample-moments) ¶

Return the degree of CENTRAL-SAMPLE-MOMENTS.

Package

num-utils.statistics.

Source

statistics.lisp.

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.

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.

Function: chebyshev-root (m i) ¶

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

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.

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.

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.

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.

Function: cube (number) ¶

Cube of number.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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.

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.

Function: diagonal-matrix (elements) ¶

Package

num-utils.matrix.

Source

matrix.lisp.

Reader: diagonal-matrix-elements (instance) ¶

Writer: (setf diagonal-matrix-elements) (instance) ¶

Package

num-utils.matrix.

Source

matrix.lisp.

Target Slot

elements.

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.

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.

Function: e* (argument &rest more-arguments) ¶

Elementwise *.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: e+ (argument &rest more-arguments) ¶

Elementwise +.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: e- (argument &rest more-arguments) ¶

Elementwise -.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: e/ (argument &rest more-arguments) ¶

Elementwise /.

Package

num-utils.elementwise.

Source

elementwise.lisp.

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.

Function: elog (a &optional base) ¶

Elementwise logarithm.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: emax (object) ¶

Elementwise MAX.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: emin (object) ¶

Elementwise MIN.

Package

num-utils.elementwise.

Source

elementwise.lisp.

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.

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.

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.

Function: evaluate-chebyshev (coefficients x) ¶

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

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.

Function: exp-1 (x) ¶

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

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.

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.

Function: fixnum? (object) ¶

Check of type of OBJECT is fixnum.

Package

num-utils.utilities.

Source

utilities.lisp.

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.

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.

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.

Function: hermitian-matrix (elements) ¶

Create a lower-triangular-matrix.

Package

num-utils.matrix.

Source

matrix.lisp.

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.

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.

Function: infinite? (object) ¶

Test if an object represents positive or negative infinity.

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: interval (left right &key open-left? open-right?) ¶

Create an INTERVAL.

Package

num-utils.interval.

Source

interval.lisp.

Function: interval-hull (object) ¶

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

Package

num-utils.interval.

Source

interval.lisp.

Function: interval-length (interval) ¶

Difference between left and right.

Package

num-utils.interval.

Source

interval.lisp.

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.

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.

Function: l2norm (object) ¶

$L_2$ norm of OBJECT.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: log1+ (x) ¶

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

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.

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.

Function: log1- (x) ¶

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

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.

Function: log10 (number) ¶

Abbreviation for decimal logarithm.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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.

Function: log2 (number) ¶

Abbreviation for binary logarithm.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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.

Function: logexp-1 (a) ¶

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: lower-triangular-matrix (elements) ¶

Create a lower-triangular-matrix.

Package

num-utils.matrix.

Source

matrix.lisp.

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.

Function: make-vector (element-type &rest initial-contents) ¶

Package

num-utils.utilities.

Source

utilities.lisp.

Reader: max-error (instance) ¶

Writer: (setf max-error) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

max-error.

Reader: mean-error (instance) ¶

Writer: (setf mean-error) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

mean-error.

Reader: min-error (instance) ¶

Writer: (setf min-error) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

min-error.

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.

Function: num-delta (a b) ¶

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

Package

num-utils.num=.

Source

num=.lisp.

Function: num=-function (tolerance) ¶

Curried version of num=, with given tolerance.

Package

num-utils.num=.

Source

num=.lisp.

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.

Function: plusminus-interval (center half-width &key open-left? open-right?) ¶

A symmetric interval around CENTER.

Package

num-utils.interval.

Source

interval.lisp.

Function: pool (&rest accumulators) ¶

Pool ACCUMULATORS.

Package

num-utils.statistics.

Source

statistics.lisp.

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.

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.

Function: relative (fraction) ¶

Package

num-utils.interval.

Source

interval.lisp.

Reader: rms (instance) ¶

Writer: (setf rms) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

rms.

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.

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.

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.

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.

Function: sequence-maximum (x) ¶

Return the maximum value in the sequence X

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: sequence-minimum (x) ¶

Return the minimum value in the sequence X

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: sequencep (x) ¶

Return T if X is type SEQUENCE.

Package

num-utils.utilities.

Source

utilities.lisp.

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.

Function: sorted-reals-elements (sorted-reals) ¶

Package

num-utils.statistics.

Source

statistics.lisp.

Function: spacer (&optional weight) ¶

Package

num-utils.interval.

Source

interval.lisp.

Function: sparse-counter-count (sparse-counter object) ¶

Return the count for OBJECT.

Package

num-utils.statistics.

Source

statistics.lisp.

Reader: sparse-counter-table (instance) ¶

Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

table.

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.

Function: square (number) ¶

Square of number.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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.

Function: tabulate (sequence &key test) ¶

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

Package

num-utils.statistics.

Source

statistics.lisp.

Reader: test-count (instance) ¶

Writer: (setf test-count) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

test-count.

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.

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.

Function: upper-triangular-matrix (elements) ¶

Create a lower-triangular-matrix.

Package

num-utils.matrix.

Source

matrix.lisp.

Reader: variance0 (instance) ¶

Writer: (setf variance0) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

variance0.

Reader: variance1 (instance) ¶

Writer: (setf variance1) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

variance1.

Function: vec (element-type &rest elements) ¶

Return a vector with elements coerced to ELEMENT-TYPE.

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Function: weighted-quantiles (values weights qs) ¶

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: within? (left value right) ¶

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

Package

num-utils.utilities.

Source

utilities.lisp.

Reader: worst-case (instance) ¶

Writer: (setf worst-case) (instance) ¶

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

worst-case.

Reader: wrapped-matrix-elements (instance) ¶

Package

num-utils.matrix.

Source

matrix.lisp.

Target Slot

elements.

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