The num-utils Reference Manual

Table of Contents

The num-utils Reference Manual

This is the num-utils Reference Manual, version 0.0.2, generated automatically by Declt version 3.0 "Montgomery Scott" on Mon Dec 02 10:59:19 2019 GMT+0.

1 Introduction

* Numerical Utilities Library, version 0.0.2

- =num==, a comparison operator for floats
- simple arithmetic functions, like =sum= and =l2norm=
- element-wise operations for arrays
- intervals
- special matrices and shorthand for their input
- sample statistics
- Chebyshev polynomials
- quadratures
- univariate root finding

* Origin
This library is a maintenance fork of [[https://github.com/tpapp/cl-num-utils][cl-num-utils]]. Changes include:

1. Make work with Genera
2. Convert to [[https://github.com/sionescu/fiveam][fiveam]] for unit tests ([[https://github.com/tgutu/clunit][clunit]] seems abandoned)
3. Restore quadrature tests
4. Fix SBCL compiler warnings

Although the project has been renamed to distinguish it from the
original, the package names are the same and should work as a drop-in
replacement.

* Status
It appears that this library was in the midst of a reorganization when
released. As near as I can tell from the [[https://github.com/tpapp/cl-num-utils/commit/a0f522b44b465fc071623f9662bdde0163be6467][github history]], all the files
in cl-num-utils were moved to src/old/, and then selectively moved
into src/ as they were cleaned up and unit tests written. Some, such
as data-frame, were moved by Papp into separate projects. Several of
the files in old/ could be dusted off and moved into src/ to be
used. Check in data-frames project first because I think some were
moved there without being removed from cl-num-utils.

There was a fair amount of code commented out by the original
author. Where we have commented code, we use the block comment syntax
#| ... |#, and noted the person performing the removal. We have also
added comments throughout the code to make it more readable, or to
include our research notes.

* Known Issues
** Test Failures
[[https://github.com/Symbolics/num-utils/issues/1][Issue 1]] describes a problem with the wrapped-bivariate-to-array test
in tests/matrix.lisp. This fails under fiveam, but passes on clunit. I
believe there to be a bug, either in fiveam or num-utils (or,
possibly, clunit). The [[https://common-lisp.net/project/fiveam/docs/api/macro_005FIT.BESE.FIVEAM_003A_003AIS.html][fiveam reason-arg]] is misleading, it will print
the two values, and they are equal. However this only happens after
the /second/ call. For example, given this code
#+BEGIN_SRC lisp
  (is (num= (funcall op a b)
  	    (funcall op (funcall convert a) b));)
      "Expected ~A to be equal to ~A" (funcall op a b) (funcall op (funcall convert a) b))
#+END_SRC
The sequence
#+BEGIN_SRC lisp
(funcall op a b)
(funcall op (funcall convert a) b)
#+END_SRC
is called twice, once as part of the test and once as part of the
reason-args output. The /first/ time, the results are different. The
/second/ time they are the same, making it appear that the result is a
false negative. It is not.

This test needs to be looked into further. The test code will not win
any 'most readable code of the year' award, and the answer is buried
below several layers of macro expansions, funcalls and currying.

Until this is resolved, use this function with caution.

** Implementation Support
Development is primarily done with SBCL on MS Windows, with occasional
testing on CCL. [[https://github.com/tpapp/cl-num-utils/issues/15][papp15]] reports that generic function definitions may
not work on other implementations. Please report any such problems on
the [[https://github.com/Symbolics/num-utils/issues][Github issue tracker]].

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

* Reporting Bugs and Contributing
We welcom participants and contributors. When contributing to this
repository, please first discuss major changes to the existing code
you wish to make via a github issue. Minor changes and major additions
are welcome as long as they are released under the Boost License.

** Pull Request Process

1. Ensure any install or build dependencies are removed, e.g. .gitignore
2. Update the README.org with details of changes to the interface.
3. Increase the version numbers in any examples files and the ASDF file.
4. Update README.org to the new version that this Pull Request would
   represent. The versioning scheme we use is [[https://semver.org/][SemVer]].

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

* TODO
** Tasks (by Nunez)
- Refactor/rename packages, e.g. consolidate all the matrix utilities into num-util/mops (matrix operations), num-utils/elementwise, num-utils/arithmetic, etc. This way the library can be loaded piecemeal.
- Silence SBCL compiler warnings for tests where we are expecting to signal an error
- More CCL testing
- Test for more specific conditions with fiveam:signal test (now is generic error)
- Investigate unit test failure in wrapped-bivariate-to-array
- Restore old/arithmetic-types.lisp and write tests
** Tasks (by Papp)
- Finish histogram code and tests
- Decide whether recursive indexes are practical.

The code for both is present, but commented out.

2 Systems

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

2.1 num-utils

Author

Steven Nunez <steve.nunez@symbolics.com.sg

License

Boost Software License - Version 1.0

Description

Numerical utilities for Common Lisp

Version

0.0.2

Dependencies

• anaphora
• alexandria
• array-operations
• select
• let-plus

Source

num-utils.asd (file)

Components

• packages.lisp (file)
• 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)
• polynomial.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 num-utils.asd

Location

/home/quickref/quicklisp/dists/quicklisp/software/num-utils-20191130-git/num-utils.asd

Systems

num-utils (system)

3.1.2 num-utils/packages.lisp

Parent

num-utils (system)

Location

packages.lisp

Packages

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

3.1.3 num-utils/utilities.lisp

Dependency

packages.lisp (file)

Parent

num-utils (system)

Location

utilities.lisp

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)
• 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)

Parent

num-utils (system)

Location

num=.lisp

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)

3.1.5 num-utils/arithmetic.lisp

Dependency

num=.lisp (file)

Parent

num-utils (system)

Location

arithmetic.lisp

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)

3.1.6 num-utils/elementwise.lisp

Dependency

arithmetic.lisp (file)

Parent

num-utils (system)

Location

elementwise.lisp

Exported Definitions

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

Internal Definitions

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

3.1.7 num-utils/extended-real.lisp

Dependency

elementwise.lisp (file)

Parent

num-utils (system)

Location

extended-real.lisp

Exported Definitions

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

Internal Definitions

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

3.1.8 num-utils/interval.lisp

Dependency

extended-real.lisp (file)

Parent

num-utils (system)

Location

interval.lisp

Exported Definitions

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

Internal Definitions

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

3.1.9 num-utils/print-matrix.lisp

Dependency

interval.lisp (file)

Parent

num-utils (system)

Location

print-matrix.lisp

Exported Definitions

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

Internal Definitions

print-matrix-formatter (function)

3.1.10 num-utils/matrix.lisp

Dependency

print-matrix.lisp (file)

Parent

num-utils (system)

Location

matrix.lisp

Exported Definitions

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

Internal Definitions

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

3.1.11 num-utils/matrix-shorthand.lisp

Dependency

matrix.lisp (file)

Parent

num-utils (system)

Location

matrix-shorthand.lisp

Exported Definitions

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

Internal Definitions

pad-left-expansion (function)

3.1.12 num-utils/statistics.lisp

Dependency

matrix-shorthand.lisp (file)

Parent

num-utils (system)

Location

statistics.lisp

Exported Definitions

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

Internal Definitions

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

3.1.13 num-utils/chebyshev.lisp

Dependency

statistics.lisp (file)

Parent

num-utils (system)

Location

chebyshev.lisp

Exported Definitions

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

Internal Definitions

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

3.1.14 num-utils/polynomial.lisp

Dependency

chebyshev.lisp (file)

Parent

num-utils (system)

Location

polynomial.lisp

Exported Definitions

evaluate-polynomial (function)

3.1.15 num-utils/rootfinding.lisp

Dependency

polynomial.lisp (file)

Parent

num-utils (system)

Location

rootfinding.lisp

Exported Definitions

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

Internal Definitions

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

3.1.16 num-utils/quadrature.lisp

Dependency

rootfinding.lisp (file)

Parent

num-utils (system)

Location

quadrature.lisp

Exported Definitions

romberg-quadrature (function)

Internal Definitions

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

3.1.17 num-utils/common-package.lisp

Dependency

quadrature.lisp (file)

Parent

num-utils (system)

Location

common-package.lisp

Packages

num-utils

4 Packages

Packages are listed by definition order.

4.1 num-utils.polynomial

Source

packages.lisp (file)

Nickname

poly

Use List

• num-utils.utilities
• alexandria.1.0.0
• common-lisp

Exported Definitions

evaluate-polynomial (function)

4.2 num-utils.interval

Source

packages.lisp (file)

Use List

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

Used By List

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

Exported Definitions

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

Internal Definitions

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

4.3 num-utils.print-matrix

Source

packages.lisp (file)

Use List

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

Used By List

num-utils.matrix

Exported Definitions

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

Internal Definitions

print-matrix-formatter (function)

4.4 num-utils.utilities

Source

packages.lisp (file)

Use List

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

Used By List

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

Exported Definitions

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

4.5 num-utils.arithmetic

Source

packages.lisp (file)

Use List

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

Used By List

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

Exported Definitions

• 1c (function)
• abs-diff (function)
• absolute-square (function)
• as-integer (function)
• ceiling* (function)
• 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)

4.6 num-utils.matrix-shorthand

Source

packages.lisp (file)

Nickname

clnu.mx

Use List

• let-plus
• num-utils.utilities
• 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)

4.7 num-utils.num=

Source

packages.lisp (file)

Use List

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

Used By List

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

Exported Definitions

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

4.8 num-utils.extended-real

Source

packages.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)

4.9 num-utils.quadrature

Source

packages.lisp (file)

Use List

• let-plus
• num-utils.utilities
• num-utils.interval
• 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)

4.10 num-utils.statistics

Source

packages.lisp (file)

Nickname

clnu.stats

Use List

• let-plus
• num-utils.utilities
• num-utils.num=
• 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 num-utils.rootfinding

Source

packages.lisp (file)

Use List

• let-plus
• num-utils.utilities
• 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)

4.12 num-utils.elementwise

Source

packages.lisp (file)

Nickname

nuem

Use List

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

Used By List

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* (method)
• e2* (method)
• e2* (method)
• e2+ (generic function)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2+ (method)
• e2- (generic function)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2- (method)
• e2/ (generic function)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2/ (method)
• e2log (generic function)
• e2log (method)
• e2log (method)
• e2log (method)
• e2log (method)
• e2log (method)
• e2log (method)
• e2log (method)
• eceiling (generic function)
• eceiling (method)
• eceiling (method)
• econjugate (generic function)
• econjugate (method)
• econjugate (method)
• eexp (generic function)
• eexp (method)
• eexp (method)
• eexp (method)
• eexp (method)
• eexp (method)
• eexp (method)
• eexpt (generic function)
• eexpt (method)
• eexpt (method)
• eexpt (method)
• eexpt (method)
• eexpt (method)
• eexpt (method)
• eexpt (method)
• efloor (generic function)
• efloor (method)
• efloor (method)
• elementwise-float-contagion (function)
• elog (function)
• emax (function)
• emin (function)
• 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)

4.13 num-utils.chebyshev

Source

packages.lisp (file)

Use List

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

Exported Definitions

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

Internal Definitions

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

4.14 num-utils.matrix

Source

packages.lisp (file)

Use List

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

Used By List

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)

4.15 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

num-utils.statistics

Source

statistics.lisp (file)

Special Variable: *num=-tolerance*

Default tolerance for NUM=.

Package

num-utils.num=

Source

num=.lisp (file)

Special Variable: *print-matrix-precision*

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

Package

num-utils.print-matrix

Source

print-matrix.lisp (file)

Special Variable: *rootfinding-delta-relative*

Default relative interval width for rootfinding.

Package

num-utils.rootfinding

Source

rootfinding.lisp (file)

Special Variable: *rootfinding-epsilon*

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

Package

num-utils.rootfinding

Source

rootfinding.lisp (file)

5.1.2 Macros

Macro: &interval LEFT RIGHT

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

Package

num-utils.interval

Source

interval.lisp (file)

Macro: check-types (&rest ARGUMENTS) TYPE

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Macro: curry* FUNCTION &rest ARGUMENTS

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

Package

num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

num-utils.num=

Source

num=.lisp (file)

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

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

Package

num-utils.num=

Source

num=.lisp (file)

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

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Macro: expanding &body BODY

Expand BODY. Useful for generating code programmatically.

Package

num-utils.utilities

Source

utilities.lisp (file)

Macro: extendf-interval PLACE OBJECT

Apply EXTEND-INTERVAL on PLACE using OBJECT.

Package

num-utils.interval

Source

interval.lisp (file)

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

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Macro: hermitian-mx ELEMENT-TYPE &body ROWS

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

Package

num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

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

LAMBDA with WITH-TEMPLATE in its BODY.

Package

num-utils.extended-real

Source

extended-real.lisp (file)

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

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

Package

num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: multf PLACE COEFFICIENT

Multiply place by COEFFICIENT.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Macro: mx ELEMENT-TYPE &body ROWS

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

Package

num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: splice-awhen TEST &body FORMS

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Macro: splice-when TEST &body FORMS

Similar to when, but wraps the result in list.

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Macro: unlessf PLACE VALUE-FORM

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

Package

num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: with-double-floats BINDINGS &body BODY

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

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

Package

num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

num-utils.extended-real

Source

extended-real.lisp (file)

5.1.3 Compiler macros

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

Package

num-utils.utilities

Source

utilities.lisp (file)

5.1.4 Functions

Function: 1c NUMBER

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: < NUMBER &rest MORE-NUMBERS

Package

num-utils.extended-real

Source

extended-real.lisp (file)

Function: <= NUMBER &rest MORE-NUMBERS

Package

num-utils.extended-real

Source

extended-real.lisp (file)

Function: = NUMBER &rest MORE-NUMBERS

Package

num-utils.extended-real

Source

extended-real.lisp (file)

Function: > NUMBER &rest MORE-NUMBERS

Package

num-utils.extended-real

Source

extended-real.lisp (file)

Function: >= NUMBER &rest MORE-NUMBERS

Package

num-utils.extended-real

Source

extended-real.lisp (file)

Function: abs-diff A B

Absolute difference of A and B.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: absolute-square NUMBER

Number multiplied by its complex conjugate.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: as-double-float V

Convert argument to DOUBLE-FLOAT.

Package

num-utils.utilities

Source

utilities.lisp (file)

Function: as-integer NUMBER

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

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

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Function: bic A B

Biconditional. Returns A <=> B.

Package

num-utils.utilities

Source

utilities.lisp (file)

Function: binary-search SORTED-REALS VALUE

Return INDEX such that

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

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

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Function: ceiling* NUMBER &optional DIVISOR OFFSET

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

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

Return the degree of CENTRAL-SAMPLE-MOMENTS.

Package

num-utils.statistics

Source

statistics.lisp (file)

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

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

Package

num-utils.chebyshev

Source

chebyshev.lisp (file)

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

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

Package

num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: chebyshev-root M I

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

Package

num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: chebyshev-roots M

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

Package

num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: cross-tabulate SEQUENCE1 SEQUENCE2 &key TEST

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

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: cumulative-product SEQUENCE &key RESULT-TYPE

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: cumulative-sum SEQUENCE &key RESULT-TYPE

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: diagonal-matrix ELEMENTS

Package

num-utils.matrix

Source

matrix.lisp (file)

Function: diagonal-matrix-elements INSTANCE

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

Package

num-utils.matrix

Source

matrix.lisp (file)

Function: diagonal-mx ELEMENT-TYPE &rest ELEMENTS

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

Package

num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Function: divides? NUMBER DIVISOR

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: e* ARGUMENT &rest MORE-ARGUMENTS

Elementwise *.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: e+ ARGUMENT &rest MORE-ARGUMENTS

Elementwise +.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: e- ARGUMENT &rest MORE-ARGUMENTS

Elementwise -.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: e/ ARGUMENT &rest MORE-ARGUMENTS

Elementwise /.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: elementwise-float-contagion &rest OBJECTS

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

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: elog A &optional BASE

Elementwise logarithm.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: emax OBJECT

Elementwise MAX.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: emin OBJECT

Elementwise MIN.

Package

num-utils.elementwise

Source

elementwise.lisp (file)

Function: empirical-quantile SORTED-VECTOR Q

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

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: empirical-quantile-probabilities N

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

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

for any vector SAMPLE.

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: ensure-sorted-vector OBJECT

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

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: evaluate-chebyshev COEFFICIENTS X

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

Package

num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: evaluate-polynomial COEFFICIENTS X

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

Package

num-utils.polynomial

Source

polynomial.lisp (file)

Function: fixnum? OBJECT

Check of type of OBJECT is fixnum.

Package

num-utils.utilities

Source

utilities.lisp (file)

Function: floor* NUMBER &optional DIVISOR OFFSET

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: generate-sequence RESULT-TYPE SIZE FUNCTION

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

Package

num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

num-utils.interval

Source

interval.lisp (file)

Function: hermitian-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

num-utils.matrix

Source

matrix.lisp (file)

Function: in-interval? INTERVAL NUMBER

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

Package

num-utils.interval

Source

interval.lisp (file)

Function: infinite? OBJECT

Test if an object represents positive or negative infinity.

Package

num-utils.extended-real

Source

extended-real.lisp (file)

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

Create an INTERVAL.

Package

num-utils.interval

Source

interval.lisp (file)

Function: interval-hull OBJECT

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

Package

num-utils.interval

Source

interval.lisp (file)

Function: interval-length INTERVAL

Difference between left and right.

Package

num-utils.interval

Source

interval.lisp (file)

Function: interval-midpoint INTERVAL &optional ALPHA

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

Package

num-utils.interval

Source

interval.lisp (file)

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

Return a vector of fixnums.

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

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

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: l2norm OBJECT

$L_2$ norm of OBJECT.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: log10 NUMBER

Abbreviation for decimal logarithm.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: log2 NUMBER

Abbreviation for binary logarithm.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: lower-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

num-utils.matrix

Source

matrix.lisp (file)

Function: make-sparse-counter &key TEST

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

Package

num-utils.statistics

Source

statistics.lisp (file)

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

Package

num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: num-delta A B

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

Package

num-utils.num=

Source

num=.lisp (file)

Function: num=-function TOLERANCE

Curried version of num=, with given tolerance.

Package

num-utils.num=

Source

num=.lisp (file)

Function: numseq FROM TO &key LENGTH BY TYPE

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

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

A symmetric interval around CENTER.

Package

num-utils.interval

Source

interval.lisp (file)

Function: pool &rest ACCUMULATORS

Pool ACCUMULATORS.

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: print-length-truncate DIMENSION

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

Package

num-utils.print-matrix

Source

print-matrix.lisp (file)

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

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

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

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

Package

num-utils.print-matrix

Source

print-matrix.lisp (file)

Function: relative FRACTION

Package

num-utils.interval

Source

interval.lisp (file)

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

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

Package

num-utils.quadrature

Source

quadrature.lisp (file)

Function: root-bisection F BRACKET &key DELTA EPSILON

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

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

Package

num-utils.rootfinding

Source

rootfinding.lisp (file)

Function: round* NUMBER &optional DIVISOR OFFSET

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: same-sign? &rest ARGUMENTS

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: sequencep X

Return T if X is type SEQUENCE.

Package

num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

num-utils.interval

Source

interval.lisp (file)

Function: sorted-reals-elements SORTED-REALS

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: spacer &optional WEIGHT

Package

num-utils.interval

Source

interval.lisp (file)

Function: sparse-counter-count SPARSE-COUNTER OBJECT

Return the count for OBJECT.

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: sparse-counter-table INSTANCE

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: split-interval INTERVAL DIVISIONS

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

Package

num-utils.interval

Source

interval.lisp (file)

Function: square NUMBER

Square of number.

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

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

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

Package

num-utils.interval

Source

interval.lisp (file)

Function: tabulate SEQUENCE &key TEST

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

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: truncate* NUMBER &optional DIVISOR OFFSET

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

Package

num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: upper-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

num-utils.matrix

Source

matrix.lisp (file)

Function: vec ELEMENT-TYPE &rest ELEMENTS

Return a vector with elements coerced to ELEMENT-TYPE.

Package

num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Function: weighted-quantiles VALUES WEIGHTS QS

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

Package

num-utils.statistics

Source

statistics.lisp (file)

Function: within? LEFT VALUE RIGHT

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Function: wrapped-matrix-elements INSTANCE

Package

num-utils.matrix

Source

matrix.lisp (file)

5.1.5 Generic functions

Generic Function: add ACCUMULATOR OBJECT &key WEIGHT

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

Package

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

num-utils.utilities

Source

utilities.lisp (file)

Methods

Method: as-alist (OBJECT sparse-counter)

Return (OBJECT . COUNT) pairs as an alist.

Source

statistics.lisp (file)

Generic Function: as-plist OBJECT

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

Package

num-utils.utilities

Source

utilities.lisp (file)

Methods

Method: as-plist OBJECT

Generic Function: central-m2 OBJECT &key WEIGHTS

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

Package

num-utils.statistics

Source

statistics.lisp (file)

Methods

Method: central-m2 OBJECT &key WEIGHTS

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