The cl-num-utils Reference Manual

Table of Contents

The cl-num-utils Reference Manual

This is the cl-num-utils Reference Manual, version 0.1, generated automatically by Declt version 3.0 "Montgomery Scott" on Wed Feb 19 19:54:56 2020 GMT+0.

1 Introduction

* cl-num-utils

This library implements simple numerical functions for Common Lisp, including

- =num==, a comparison operator for floats
- simple arithmeric functions, like =sum= and =l2norm=
- elementwise operations for arrays
- intervals
- special matrices and shorthand for their input
- sample statistics
- Chebyshev polynomials
- univariate rootfinding

See the sources and the docstring for more details.

All the functionality has corresponding unit tests.

** Symbol conflicts with =alexandria=

When you import both =cl-num-utils= and =alexandria=, you get symbol conflicts.  There are two solutions for this: either import only parts of =cl-num-utils= (see the packages named in each file), or shadow some symbols, eg
#+BEGIN_SRC lisp
  (cl:defpackage #:my-package
    (:use #:cl
          #:alexandria
          #:cl-num-utils)
    (:shadowing-import-from #:alexandria #:mean #:variance #:median))
#+END_SRC

** Reporting bugs

   Bugs are tracked on Github, please [[https://github.com/tpapp/cl-num-utils/issues][open an issue]] if you find one.

** Tasks
*** TODO finish histogram code, write tests
*** TODO decide whether recursive indexes are practical
code is still there, but commented out

2 Systems

The main system appears first, followed by any subsystem dependency.

2.1 cl-num-utils

Author

Tamas K Papp <tkpapp@gmail.com>

License

Boost Software License - Version 1.0

Description

Numerical utilities for Common Lisp

Version

0.1

Dependencies

• anaphora
• alexandria
• array-operations
• cl-slice
• let-plus

Source

cl-num-utils.asd (file)

Components

• utilities.lisp (file)
• num=.lisp (file)
• arithmetic.lisp (file)
• elementwise.lisp (file)
• extended-real.lisp (file)
• interval.lisp (file)
• print-matrix.lisp (file)
• matrix.lisp (file)
• matrix-shorthand.lisp (file)
• statistics.lisp (file)
• chebyshev.lisp (file)
• rootfinding.lisp (file)
• quadrature.lisp (file)
• common-package.lisp (file)

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

3.1 Lisp

3.1.1 cl-num-utils.asd

Location

/home/quickref/quicklisp/dists/quicklisp/software/cl-num-utils-20131211-git/cl-num-utils.asd

Systems

cl-num-utils (system)

3.1.2 cl-num-utils/utilities.lisp

Parent

cl-num-utils (system)

Location

utilities.lisp

Packages

cl-num-utils.utilities

Exported Definitions

• as-alist (generic function)
• 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)
• simple-double-float-vector (type)
• simple-fixnum-vector (type)
• splice-awhen (macro)
• splice-when (macro)
• unlessf (macro)
• with-double-floats (macro)
• within? (function)

3.1.3 cl-num-utils/num=.lisp

Dependency

utilities.lisp (file)

Parent

cl-num-utils (system)

Location

num=.lisp

Packages

cl-num-utils.num=

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=-function (function)

3.1.4 cl-num-utils/arithmetic.lisp

Dependency

num=.lisp (file)

Parent

cl-num-utils (system)

Location

arithmetic.lisp

Packages

cl-num-utils.arithmetic

Exported Definitions

• 1c (function)
• abs-diff (function)
• absolute-square (function)
• as-integer (function)
• ceiling* (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? (function)
• square (function)
• sum (generic function)
• sum (method)
• sum (method)
• truncate* (function)

Internal Definitions

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

3.1.5 cl-num-utils/elementwise.lisp

Dependency

arithmetic.lisp (file)

Parent

cl-num-utils (system)

Location

elementwise.lisp

Packages

cl-num-utils.elementwise

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+ (generic function)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2- (generic function)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2/ (generic function)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2log (generic function)
• e2log (method)
• e2log (method)
• e2log (method)
• e2log (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)
• elementwise-float-contagion (function)
• elog (function)
• emax (function)
• emin (function)
• 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)

3.1.6 cl-num-utils/extended-real.lisp

Dependency

elementwise.lisp (file)

Parent

cl-num-utils (system)

Location

extended-real.lisp

Packages

cl-num-utils.extended-real

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)

3.1.7 cl-num-utils/interval.lisp

Dependency

extended-real.lisp (file)

Parent

cl-num-utils (system)

Location

interval.lisp

Packages

cl-num-utils.interval

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)

3.1.8 cl-num-utils/print-matrix.lisp

Dependency

interval.lisp (file)

Parent

cl-num-utils (system)

Location

print-matrix.lisp

Packages

cl-num-utils.print-matrix

Exported Definitions

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

Internal Definitions

print-matrix-formatter (function)

3.1.9 cl-num-utils/matrix.lisp

Dependency

print-matrix.lisp (file)

Parent

cl-num-utils (system)

Location

matrix.lisp

Packages

cl-num-utils.matrix

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)
• 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)

3.1.10 cl-num-utils/matrix-shorthand.lisp

Dependency

matrix.lisp (file)

Parent

cl-num-utils (system)

Location

matrix-shorthand.lisp

Packages

cl-num-utils.matrix-shorthand

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)

3.1.11 cl-num-utils/statistics.lisp

Dependency

matrix-shorthand.lisp (file)

Parent

cl-num-utils (system)

Location

statistics.lisp

Packages

cl-num-utils.statistics

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)

3.1.12 cl-num-utils/chebyshev.lisp

Dependency

statistics.lisp (file)

Parent

cl-num-utils (system)

Location

chebyshev.lisp

Packages

cl-num-utils.chebyshev

Exported Definitions

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

3.1.13 cl-num-utils/rootfinding.lisp

Dependency

chebyshev.lisp (file)

Parent

cl-num-utils (system)

Location

rootfinding.lisp

Packages

cl-num-utils.rootfinding

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)

3.1.14 cl-num-utils/quadrature.lisp

Dependency

rootfinding.lisp (file)

Parent

cl-num-utils (system)

Location

quadrature.lisp

Packages

cl-num-utils.quadrature

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)

3.1.15 cl-num-utils/common-package.lisp

Dependency

quadrature.lisp (file)

Parent

cl-num-utils (system)

Location

common-package.lisp

Packages

cl-num-utils

4 Packages

Packages are listed by definition order.

4.1 cl-num-utils.utilities

Source

utilities.lisp (file)

Use List

• let-plus
• anaphora
• alexandria.1.0.0
• common-lisp

Used By List

• cl-num-utils.quadrature
• cl-num-utils.rootfinding
• cl-num-utils.chebyshev
• cl-num-utils.statistics
• cl-num-utils.matrix-shorthand
• cl-num-utils.matrix
• cl-num-utils.interval
• cl-num-utils.elementwise
• cl-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)
• simple-double-float-vector (type)
• simple-fixnum-vector (type)
• splice-awhen (macro)
• splice-when (macro)
• unlessf (macro)
• with-double-floats (macro)
• within? (function)

4.2 cl-num-utils.num=

Source

num=.lisp (file)

Use List

• let-plus
• anaphora
• alexandria.1.0.0
• common-lisp

Used By List

• cl-num-utils.statistics
• cl-num-utils.matrix
• cl-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)

4.3 cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Use List

• let-plus
• cl-num-utils.utilities
• anaphora
• alexandria.1.0.0
• common-lisp

Used By List

• cl-num-utils.quadrature
• cl-num-utils.statistics
• cl-num-utils.elementwise

Exported Definitions

• 1c (function)
• abs-diff (function)
• absolute-square (function)
• as-integer (function)
• ceiling* (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? (function)
• square (function)
• sum (generic function)
• sum (method)
• sum (method)
• truncate* (function)

Internal Definitions

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

4.4 cl-num-utils.elementwise

Source

elementwise.lisp (file)

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.arithmetic
• alexandria.1.0.0
• common-lisp

Used By List

cl-num-utils.matrix

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+ (generic function)
• 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/ (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)
• e2log (generic function)
• e2log (method)
• e2log (method)
• e2log (method)
• e2log (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)
• elementwise-float-contagion (function)
• elog (function)
• emax (function)
• emin (function)
• 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)

4.5 cl-num-utils.extended-real

Source

extended-real.lisp (file)

Nickname

xreal

Use List

• alexandria.1.0.0
• 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)

4.6 cl-num-utils.interval

Source

interval.lisp (file)

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.num=
• anaphora
• alexandria.1.0.0
• common-lisp

Used By List

• cl-num-utils.quadrature
• cl-num-utils.rootfinding
• cl-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)

4.7 cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Use List

• let-plus
• anaphora
• alexandria.1.0.0
• common-lisp

Used By List

cl-num-utils.matrix

Exported Definitions

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

Internal Definitions

print-matrix-formatter (function)

4.8 cl-num-utils.matrix

Source

matrix.lisp (file)

Use List

• let-plus
• cl-slice
• cl-num-utils.utilities
• cl-num-utils.print-matrix
• cl-num-utils.num=
• cl-num-utils.elementwise
• anaphora
• alexandria.1.0.0
• common-lisp

Used By List

cl-num-utils.matrix-shorthand

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)
• 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)

4.9 cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Nickname

clnu.mx

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.matrix
• anaphora
• alexandria.1.0.0
• 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)

4.10 cl-num-utils.statistics

Source

statistics.lisp (file)

Nickname

clnu.stats

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.num=
• cl-num-utils.arithmetic
• alexandria.1.0.0
• 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)

4.11 cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.interval
• anaphora
• alexandria.1.0.0
• common-lisp

Exported Definitions

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

4.12 cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.interval
• alexandria.1.0.0
• 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 cl-num-utils.quadrature

Source

quadrature.lisp (file)

Use List

• let-plus
• cl-num-utils.utilities
• cl-num-utils.interval
• cl-num-utils.arithmetic
• anaphora
• alexandria.1.0.0
• 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)

4.14 cl-num-utils

Source

common-package.lisp (file)

Nickname

clnu

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Special Variable: *num=-tolerance*

Default tolerance for NUM=.

Package

cl-num-utils.num=

Source

num=.lisp (file)

Special Variable: *print-matrix-precision*

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

Package

cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Special Variable: *rootfinding-delta-relative*

Default relative interval width for rootfinding.

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Special Variable: *rootfinding-epsilon*

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

Package

cl-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

cl-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

cl-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

cl-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

cl-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

cl-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

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: expanding &body BODY

Expand BODY. Useful for generating code programmatically.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: extendf-interval PLACE OBJECT

Apply EXTEND-INTERVAL on PLACE using OBJECT.

Package

cl-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

cl-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

cl-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

cl-num-utils.extended-real

Source

extended-real.lisp (file)

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

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: multf PLACE COEFFICIENT

Multiply place by COEFFICIENT.

Package

cl-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

cl-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

cl-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

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: unlessf PLACE VALUE-FORM

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

Package

cl-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

cl-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

cl-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

cl-num-utils.extended-real

Source

extended-real.lisp (file)

5.1.3 Functions

Function: 1c NUMBER

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: < NUMBER &rest MORE-NUMBERS

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: <= NUMBER &rest MORE-NUMBERS

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: = NUMBER &rest MORE-NUMBERS

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: > NUMBER &rest MORE-NUMBERS

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: >= NUMBER &rest MORE-NUMBERS

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: abs-diff A B

Absolute difference of A and B.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: absolute-square NUMBER

Number multiplied by its complex conjugate.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: as-double-float V

Convert argument to DOUBLE-FLOAT.

Package

cl-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

cl-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

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: bic A B

Biconditional. Returns A <=> B.

Package

cl-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

cl-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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

Return the degree of CENTRAL-SAMPLE-MOMENTS.

Package

cl-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

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: chebyshev-evaluate COEFFICIENTS X

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

Package

cl-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

cl-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

cl-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

cl-num-utils.chebyshev

Source

chebyshev.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

cl-num-utils.statistics

Source

statistics.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

cl-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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: diagonal-matrix ELEMENTS

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: diagonal-matrix-elements INSTANCE

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

Package

cl-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

cl-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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: e* ARGUMENT &rest MORE-ARGUMENTS

Elementwise *.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: e+ ARGUMENT &rest MORE-ARGUMENTS

Elementwise +.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: e- ARGUMENT &rest MORE-ARGUMENTS

Elementwise -.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: e/ ARGUMENT &rest MORE-ARGUMENTS

Elementwise /.

Package

cl-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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: elog A &optional BASE

Elementwise logarithm.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: emax OBJECT

Elementwise MAX.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: emin OBJECT

Elementwise MIN.

Package

cl-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

cl-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

cl-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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: fixnum? OBJECT

Check of type of OBJECT is fixnum.

Package

cl-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

cl-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

cl-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

cl-num-utils.interval

Source

interval.lisp (file)

Function: hermitian-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: in-interval? INTERVAL NUMBER

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: infinite? OBJECT

Test if an object represents positive or negative infinity.

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

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

Create an INTERVAL.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: interval-hull OBJECT

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: interval-length INTERVAL

Difference between left and right.

Package

cl-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

cl-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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: l2norm OBJECT

$L_2$ norm of OBJECT.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: log10 NUMBER

Abbreviation for decimal logarithm.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: log2 NUMBER

Abbreviation for binary logarithm.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: lower-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

cl-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

cl-num-utils.statistics

Source

statistics.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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: num-delta A B

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

Package

cl-num-utils.num=

Source

num=.lisp (file)

Function: num=-function TOLERANCE

Curried version of num=, with given tolerance.

Package

cl-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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

A symmetric interval around CENTER.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: pool &rest ACCUMULATORS

Pool ACCUMULATORS.

Package

cl-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

cl-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

cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Function: relative FRACTION

Package

cl-num-utils.interval

Source

interval.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

cl-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

cl-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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: same-sign? &rest ARGUMENTS

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

Package

cl-num-utils.arithmetic

Source

arithmetic.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

cl-num-utils.interval

Source

interval.lisp (file)

Function: sorted-reals-elements SORTED-REALS

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: spacer &optional WEIGHT

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: sparse-counter-count SPARSE-COUNTER OBJECT

Return the count for OBJECT.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: sparse-counter-table INSTANCE

Package

cl-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

cl-num-utils.interval

Source

interval.lisp (file)

Function: square NUMBER

Square of number.

Package

cl-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

cl-num-utils.interval

Source

interval.lisp (file)

Function: tabulate SEQUENCE &key TEST

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

Package

cl-num-utils.statistics

Source

statistics.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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: upper-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: vec ELEMENT-TYPE &rest ELEMENTS

Return a vector with elements coerced to ELEMENT-TYPE.

Package

cl-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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: within? LEFT VALUE RIGHT

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: wrapped-matrix-elements INSTANCE

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

5.1.4 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

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods

Method: add (ACCUMULATOR sparse-counter) OBJECT &key 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

cl-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

cl-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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.matrix

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

cl-num-utils.matrix

Source

matrix.lisp (file)

Reader

diagonal-vector (generic function)

Generic Function: e1- A

Univariate elementwise -.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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)