The num-utils Reference Manual

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The num-utils Reference Manual

This is the num-utils Reference Manual, version 1.1, generated automatically by Declt version 4.0 beta 2 "William Riker" on Thu Sep 15 05:45:21 2022 GMT+0.

Table of Contents


1 Introduction

Contributors Forks Stargazers Issues MS-PL License LinkedIn

About the Project

This library is a collection of packages useful in numerical applications, each big enough to be its own package, but too small to split out into a separate ASDF system. Included are:

Built With

Getting Started

To get a local copy up and running follow these steps:

Prerequisites

An ANSI Common Lisp implementation. Developed and tested with SBCL ~~and CCL~~.

Installation

To make the system accessible to ASDF (a build facility, similar to make in the C world), clone the repository in a directory ASDF knows about. By default the common-lisp directory in your home directory is known. Create this if it doesn't already exist and then:

  1. Clone the repositories
cd ~/common-lisp && \
git clone https://github.com/Lisp-Stat/numerical-utilities.git && \
git clone https://gitlab.common-lisp.net/alexandria/alexandria.git && \
git clone https://github.com/tokenrove/anaphora.git && \
git clone https://github.com/Lisp-Stat/array-operations.git && \
git clone https://github.com/Lisp-Stat/select && \
git clone https://github.com/sharplispers/let-plus.git
  1. From the REPL reset the ASDF source-registry to find the new systems:
    (asdf:clear-source-registry)
    
  2. Load the system
    (asdf:load-system :num-utils)
    

If you have installed the slime ASDF extensions, you can invoke this with a comma (',') from the slime REPL.

Getting dependencies

To get the third party systems that these system may depend on, you can use a dependency manager, such as Quicklisp or CLPM Once installed, get the dependencies with either of:

(clpm-client:sync :sources "clpi") ;sources may vary
(ql:quickload :num-utils)

You need do this only once. After obtaining the dependencies, you can load the system with ASDF as described above without first syncing sources.

Documentation

The API documentation is in the docs/ directory and is available in emacs info format, PDF and HTML. You can also view the documentation online.

Usage

(nu:median '(1 2 3 4 5 6 7 8 9 10)) ; -> 11/2

Note a ratio is returned. This is a feature and Lisp-Stat leverages the Common Lisp numerical tower.

For more examples, please refer to the Reference Manual

Roadmap

See the open issues for a list of proposed features (and known issues).

Origin

This library is a fork of cl-num-utils. Changes include:

  1. Make work with Genera
  2. Convert to fiveam for unit tests (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 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

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 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

(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))

The sequence

(funcall op a b)
(funcall op (funcall convert a) b)

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' awards, and the answer is buried below several layers of macro expansions, funcalls and currying.

Until this is resolved, use this function with caution.

Papp's issue #16 is no longer a problem. The functionality was moved to SELECT (Papp's CL-SLICE). It should have been closed but was not before Papp abandoned the library.

Implementation Support

Development is primarily done with SBCL and CCL on MS Windows. Issue papp15 reports that generic function definitions may not work on other implementations. Please report any such problems on the 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.

(cl:defpackage #:my-package
  (:use #:cl
    #:alexandria
    #:num-utils)
  (:shadowing-import-from #:alexandria #:mean #:variance #:median))

This is what the top-level ls-user package does.

Resources

This system is part of the Lisp-Stat project; that should be your first stop for information. Also see the resources and community pages for more information.

Contributing

Contributions are what make the open source community such an amazing place to be learn, inspire, and create. Any contributions you make are greatly appreciated. Please see CONTRIBUTING.md for details on our code of conduct, and the process for submitting pull requests.

License

Distributed under the MS-PL License. See LICENSE for more information.

Contact

Project Link: https://github.com/lisp-stat/numerical-utilities


2 Systems

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


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2.1 num-utils

Numerical utilities for Common Lisp

Author

Steven Nunez <steve@symbolics.tech>

License

MS-PL

Version

1.1

Dependencies
  • anaphora (system).
  • alexandria (system).
  • array-operations (system).
  • select (system).
  • let-plus (system).
Source

num-utils.asd.

Child Components

3 Files

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


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3.1 Lisp


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3.1.1 num-utils/num-utils.asd

Source

num-utils.asd.

Parent Component

num-utils (system).

ASDF Systems

num-utils.


3.1.3 num-utils/utilities.lisp

Dependency

packages.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

3.1.4 num-utils/num=.lisp

Dependency

utilities.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

3.1.5 num-utils/arithmetic.lisp

Dependency

num=.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.6 num-utils/elementwise.lisp

Dependency

arithmetic.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.7 num-utils/extended-real.lisp

Dependency

elementwise.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.8 num-utils/interval.lisp

Dependency

extended-real.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.9 num-utils/print-matrix.lisp

Dependency

interval.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

print-matrix-formatter (function).


3.1.10 num-utils/matrix.lisp

Dependency

print-matrix.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.11 num-utils/matrix-shorthand.lisp

Dependency

matrix.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

pad-left-expansion (function).


3.1.12 num-utils/statistics.lisp

Dependency

matrix-shorthand.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.13 num-utils/chebyshev.lisp

Dependency

statistics.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.14 num-utils/polynomial.lisp

Dependency

chebyshev.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

evaluate-polynomial (function).


3.1.15 num-utils/rootfinding.lisp

Dependency

polynomial.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.16 num-utils/quadrature.lisp

Dependency

rootfinding.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

romberg-quadrature (function).

Internals

3.1.17 num-utils/log-exp.lisp

Dependency

quadrature.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface

3.1.18 num-utils/test-utilities.lisp

Dependency

log-exp.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Public Interface
Internals

3.1.19 num-utils/common-package.lisp

Dependency

test-utilities.lisp (file).

Source

num-utils.asd.

Parent Component

num-utils (system).

Packages

num-utils.


4 Packages

Packages are listed by definition order.


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4.1 num-utils.matrix

Source

packages.lisp.

Use List
Used By List

num-utils.matrix-shorthand.

Public Interface
Internals

4.2 num-utils.log-exp

Source

packages.lisp.

Use List
  • common-lisp.
  • let-plus.
Public Interface

4.3 num-utils.chebyshev

Source

packages.lisp.

Use List
Public Interface
Internals

4.4 num-utils.interval

Source

packages.lisp.

Use List
Used By List
Public Interface
Internals

4.5 num-utils.elementwise

Source

packages.lisp.

Nickname

elmt

Use List
Used By List

num-utils.matrix.

Public Interface
Internals

4.6 num-utils.rootfinding

Source

packages.lisp.

Use List
Public Interface
Internals

4.7 num-utils.statistics

Source

packages.lisp.

Nickname

nu.stats

Use List
Public Interface
Internals

4.8 num-utils.quadrature

Source

packages.lisp.

Use List
Public Interface

romberg-quadrature (function).

Internals

4.9 num-utils.extended-real

Source

packages.lisp.

Nickname

xreal

Use List
  • alexandria.
  • common-lisp.
Public Interface
Internals

4.10 num-utils.test-utilities

Source

packages.lisp.

Use List

common-lisp.

Public Interface
Internals

4.11 num-utils.num=

Source

packages.lisp.

Use List
  • alexandria.
  • anaphora.
  • common-lisp.
  • let-plus.
Used By List
Public Interface

4.12 num-utils.matrix-shorthand

Source

packages.lisp.

Nickname

nu.mx

Use List
Public Interface
Internals

pad-left-expansion (function).


4.13 num-utils.arithmetic

Source

packages.lisp.

Use List
Used By List
Public Interface
Internals

4.14 num-utils.utilities

Source

packages.lisp.

Use List
  • alexandria.
  • anaphora.
  • common-lisp.
  • let-plus.
Used By List
Public Interface

Next: , Previous: , Up: Packages   [Contents][Index]

4.15 num-utils.print-matrix

Source

packages.lisp.

Use List
  • alexandria.
  • anaphora.
  • common-lisp.
  • let-plus.
Used By List

num-utils.matrix.

Public Interface
Internals

print-matrix-formatter (function).


4.16 num-utils

Source

common-package.lisp.

Nickname

nu

Use List

common-lisp.


Previous: , Up: Packages   [Contents][Index]

4.17 num-utils.polynomial

Source

packages.lisp.

Nickname

poly

Use List
Public Interface

evaluate-polynomial (function).


5 Definitions

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


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5.1 Public Interface


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5.1.1 Special variables

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

Default degree for (weighted) central sample moments.

Package

num-utils.statistics.

Source

statistics.lisp.

Special Variable: *num=-tolerance*

Default tolerance for NUM=.

Package

num-utils.num=.

Source

num=.lisp.

Special Variable: *print-matrix-precision*

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

Package

num-utils.print-matrix.

Source

print-matrix.lisp.

Special Variable: *rootfinding-delta-relative*

Default relative interval width for rootfinding.

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Special Variable: *rootfinding-epsilon*

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.


5.1.2 Macros

Macro: &interval (left right)

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

Package

num-utils.interval.

Source

interval.lisp.

Macro: check-types ((&rest arguments) type)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: curry* (function &rest arguments)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: define-num=-with-accessors (class accessors)

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

Package

num-utils.num=.

Source

num=.lisp.

Macro: define-structure-num= (structure &rest slots)

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

Package

num-utils.num=.

Source

num=.lisp.

Macro: define-with-multiple-bindings (macro &key plural docstring)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: expanding (&body body)

Expand BODY. Useful for generating code programmatically.

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: extendf-interval (place object)

Apply EXTEND-INTERVAL on PLACE using OBJECT.

Package

num-utils.interval.

Source

interval.lisp.

Macro: gethash* (key hash-table &optional datum &rest arguments)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: hermitian-mx (element-type &body rows)

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

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

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

LAMBDA with WITH-TEMPLATE in its BODY.

Package

num-utils.extended-real.

Source

extended-real.lisp.

Macro: lower-triangular-mx (element-type &body rows)

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

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Macro: multf (place coefficient)

Multiply place by COEFFICIENT.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Macro: mx (element-type &body rows)

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

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Macro: splice-awhen (test &body forms)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: splice-when (test &body forms)

Similar to when, but wraps the result in list.

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: unlessf (place value-form)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: upper-triangular-mx (element-type &body rows)

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

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Macro: with-double-floats (bindings &body body)

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

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

Package

num-utils.utilities.

Source

utilities.lisp.

Macro: with-template ((prefix &rest variables) &body body)

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

Package

num-utils.extended-real.

Source

extended-real.lisp.


5.1.3 Compiler macros

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

num-utils.utilities.

Source

utilities.lisp.


5.1.4 Ordinary functions

Function: 1c (number)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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

num-utils.extended-real.

Source

extended-real.lisp.

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

num-utils.extended-real.

Source

extended-real.lisp.

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

num-utils.extended-real.

Source

extended-real.lisp.

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

num-utils.extended-real.

Source

extended-real.lisp.

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

num-utils.extended-real.

Source

extended-real.lisp.

Function: abs-diff (a b)

Absolute difference of A and B.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: absolute-square (number)

Number multiplied by its complex conjugate.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: as-double-float (v)

Convert argument to DOUBLE-FLOAT.

Package

num-utils.utilities.

Source

utilities.lisp.

Function: as-integer (number)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: as-simple-fixnum-vector (sequence &optional copy?)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Function: bic (a b)

Biconditional. Returns A <=> B.

Package

num-utils.utilities.

Source

utilities.lisp.

Function: binary-search (sorted-reals value)

Return INDEX such that

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

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

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

Package

num-utils.utilities.

Source

utilities.lisp.

Function: ceiling* (number &optional divisor offset)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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

Return the degree of CENTRAL-SAMPLE-MOMENTS.

Package

num-utils.statistics.

Source

statistics.lisp.

Function: chebyshev-approximate (f interval n-polynomials &key n-points)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: chebyshev-regression (f n-polynomials &optional n-points)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: chebyshev-root (m i)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: chebyshev-roots (m)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: compare-fns (fn-1 fn-2 &rest fn-params)

Compare the values returned by two functions

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Function: compare-vectors (reference-values computed-values)

Compare two vectors containing the results of previous computations

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Function: cross-tabulate (sequence1 sequence2 &key test)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: cube (number)

Cube of number.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: cumulative-product (sequence &key result-type)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: cumulative-sum (sequence &key result-type)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: diagonal-matrix (elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Reader: diagonal-matrix-elements (instance)
Writer: (setf diagonal-matrix-elements) (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Target Slot

elements.

Function: diagonal-mx (element-type &rest elements)

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

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Function: divides? (number divisor)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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

Elementwise *.

Package

num-utils.elementwise.

Source

elementwise.lisp.

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

Elementwise +.

Package

num-utils.elementwise.

Source

elementwise.lisp.

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

Elementwise -.

Package

num-utils.elementwise.

Source

elementwise.lisp.

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

Elementwise /.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: elementwise-float-contagion (&rest objects)

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

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: elog (a &optional base)

Elementwise logarithm.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: emax (object)

Elementwise MAX.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: emin (object)

Elementwise MIN.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Function: empirical-quantile (sorted-vector q)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: empirical-quantile-probabilities (n)

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

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

for any vector SAMPLE.

Package

num-utils.statistics.

Source

statistics.lisp.

Function: ensure-sorted-vector (object)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: evaluate-chebyshev (coefficients x)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: evaluate-polynomial (coefficients x)

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

Package

num-utils.polynomial.

Source

polynomial.lisp.

Function: exp-1 (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: exp-1/x (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: expt-1 (a z)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: fixnum? (object)

Check of type of OBJECT is fixnum.

Package

num-utils.utilities.

Source

utilities.lisp.

Function: floor* (number &optional divisor offset)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: generate-sequence (result-type size function)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Function: grid-in (interval size &optional sequence-type)

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

Package

num-utils.interval.

Source

interval.lisp.

Function: hermitian-matrix (elements)

Create a lower-triangular-matrix.

Package

num-utils.matrix.

Source

matrix.lisp.

Function: hypot (x y)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: in-interval? (interval number)

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

Package

num-utils.interval.

Source

interval.lisp.

Function: infinite? (object)

Test if an object represents positive or negative infinity.

Package

num-utils.extended-real.

Source

extended-real.lisp.

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

Create an INTERVAL.

Package

num-utils.interval.

Source

interval.lisp.

Function: interval-hull (object)

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

Package

num-utils.interval.

Source

interval.lisp.

Function: interval-length (interval)

Difference between left and right.

Package

num-utils.interval.

Source

interval.lisp.

Function: interval-midpoint (interval &optional alpha)

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

Package

num-utils.interval.

Source

interval.lisp.

Function: ivec (end-or-start &optional end by strict-direction?)

Return a vector of fixnums.

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

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

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: l2norm (object)

$L_2$ norm of OBJECT.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: log1+ (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: log1+/x (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: log1+exp (a)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: log1- (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: log1-exp (a)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: log10 (number)

Abbreviation for decimal logarithm.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: log1pmx (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: log2 (number)

Abbreviation for binary logarithm.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: log2-exp (x)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: logexp-1 (a)

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

Package

num-utils.log-exp.

Source

log-exp.lisp.

Function: lower-triangular-matrix (elements)

Create a lower-triangular-matrix.

Package

num-utils.matrix.

Source

matrix.lisp.

Function: make-sparse-counter (&key test)

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

Package

num-utils.statistics.

Source

statistics.lisp.

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

num-utils.utilities.

Source

utilities.lisp.

Reader: max-error (instance)
Writer: (setf max-error) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

max-error.

Reader: mean-error (instance)
Writer: (setf mean-error) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

mean-error.

Reader: min-error (instance)
Writer: (setf min-error) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

min-error.

Function: normalize-probabilities (vector &key element-type result)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: num-delta (a b)

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

Package

num-utils.num=.

Source

num=.lisp.

Function: num=-function (tolerance)

Curried version of num=, with given tolerance.

Package

num-utils.num=.

Source

num=.lisp.

Function: numseq (from to &key length by type)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

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

A symmetric interval around CENTER.

Package

num-utils.interval.

Source

interval.lisp.

Function: pool (&rest accumulators)

Pool ACCUMULATORS.

Package

num-utils.statistics.

Source

statistics.lisp.

Function: print-length-truncate (dimension)

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

Package

num-utils.print-matrix.

Source

print-matrix.lisp.

Function: print-matrix (matrix stream &key formatter masked-fn aligned? padding indent)

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

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

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

Package

num-utils.print-matrix.

Source

print-matrix.lisp.

Function: relative (fraction)
Package

num-utils.interval.

Source

interval.lisp.

Reader: rms (instance)
Writer: (setf rms) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

rms.

Function: romberg-quadrature (f interval &key epsilon min-iter max-iter transformation)

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

Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: root-bisection (f bracket &key delta epsilon)

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

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Function: round* (number &optional divisor offset)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: same-sign-p (&rest arguments)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: sequence-maximum (x)

Return the maximum value in the sequence X

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: sequence-minimum (x)

Return the minimum value in the sequence X

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: sequencep (x)

Return T if X is type SEQUENCE.

Package

num-utils.utilities.

Source

utilities.lisp.

Function: shrink-interval (interval left &optional right check-flip?)

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

Package

num-utils.interval.

Source

interval.lisp.

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

num-utils.statistics.

Source

statistics.lisp.

Function: spacer (&optional weight)
Package

num-utils.interval.

Source

interval.lisp.

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

Return the count for OBJECT.

Package

num-utils.statistics.

Source

statistics.lisp.

Reader: sparse-counter-table (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

table.

Function: split-interval (interval divisions)

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

Package

num-utils.interval.

Source

interval.lisp.

Function: square (number)

Square of number.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: subintervals-in (interval count &optional mid-open-right?)

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

Package

num-utils.interval.

Source

interval.lisp.

Function: tabulate (sequence &key test)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Reader: test-count (instance)
Writer: (setf test-count) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

test-count.

Function: test-fn (expected-column fn &rest fn-param-columns)

Test the differences between expected values and the given function

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Function: truncate* (number &optional divisor offset)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: upper-triangular-matrix (elements)

Create a lower-triangular-matrix.

Package

num-utils.matrix.

Source

matrix.lisp.

Reader: variance0 (instance)
Writer: (setf variance0) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

variance0.

Reader: variance1 (instance)
Writer: (setf variance1) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

variance1.

Function: vec (element-type &rest elements)

Return a vector with elements coerced to ELEMENT-TYPE.

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Function: weighted-quantiles (values weights qs)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: within? (left value right)

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

Package

num-utils.utilities.

Source

utilities.lisp.

Reader: worst-case (instance)
Writer: (setf worst-case) (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Target Slot

worst-case.

Reader: wrapped-matrix-elements (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Target Slot

elements.


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.

Methods
Method: add ((accumulator sparse-counter) object &key weight)

Increments the count of OBJECT in SPARSE-COUNTER, optionally with a weight

Method: add ((accumulator sorted-reals) object &key)
Method: add ((moments central-sample-moments) (y real) &key weight)
Method: add (accumulator (object null) &key)
Generic Function: as-alist (object)

Return OBJECT as an ALIST. Semantics depends on OBJECT.

Package

num-utils.utilities.

Source

utilities.lisp.

Methods
Method: as-alist ((object sparse-counter))

Return (OBJECT . COUNT) pairs as an alist.

Source

statistics.lisp.

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.

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.

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

num-utils.statistics.

Source

statistics.lisp.

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

num-utils.statistics.

Source

statistics.lisp.

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

num-utils.statistics.

Source

statistics.lisp.

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

num-utils.matrix.

Source

matrix.lisp.

Methods
Method: diagonal-vector ((matrix array))
Method: diagonal-vector (matrix)
Generic Function: (setf diagonal-vector) (matrix)

Set the diagonal elements of MATRIX using VECTOR.

Package

num-utils.matrix.

Source

matrix.lisp.

Methods
Method: (setf diagonal-vector) ((matrix array))
Generic Function: e1- (a)

Univariate elementwise -.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e1- ((a diagonal-matrix))
Source

matrix.lisp.

Method: e1- ((a hermitian-matrix))
Source

matrix.lisp.

Method: e1- ((a upper-triangular-matrix))
Source

matrix.lisp.

Method: e1- ((a lower-triangular-matrix))
Source

matrix.lisp.

Method: e1- ((a number))
Method: e1- ((a array))
Generic Function: e1/ (a)

Univariate elementwise /.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e1/ ((a diagonal-matrix))
Source

matrix.lisp.

Method: e1/ ((a hermitian-matrix))
Source

matrix.lisp.

Method: e1/ ((a upper-triangular-matrix))
Source

matrix.lisp.

Method: e1/ ((a lower-triangular-matrix))
Source

matrix.lisp.

Method: e1/ ((a number))
Method: e1/ ((a array))
Generic Function: e1log (a)

Univariate elementwise LOG.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e1log ((a diagonal-matrix))
Source

matrix.lisp.

Method: e1log ((a hermitian-matrix))
Source

matrix.lisp.

Method: e1log ((a upper-triangular-matrix))
Source

matrix.lisp.

Method: e1log ((a lower-triangular-matrix))
Source

matrix.lisp.

Method: e1log ((a number))
Method: e1log ((a array))
Generic Function: e2* (a b)

Bivariate elementwise *.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e2* ((a diagonal-matrix) (b diagonal-matrix))
Source

matrix.lisp.

Method: e2* ((a hermitian-matrix) (b hermitian-matrix))
Source

matrix.lisp.

Method: e2* ((a upper-triangular-matrix) (b upper-triangular-matrix))
Source

matrix.lisp.

Method: e2* ((a lower-triangular-matrix) (b lower-triangular-matrix))
Source

matrix.lisp.

Method: e2* ((a number) (b diagonal-matrix))
Source

matrix.lisp.

Method: e2* ((a diagonal-matrix) (b number))
Source

matrix.lisp.

Method: e2* ((a number) (b hermitian-matrix))
Source

matrix.lisp.

Method: e2* ((a hermitian-matrix) (b number))
Source

matrix.lisp.

Method: e2* ((a number) (b upper-triangular-matrix))
Source

matrix.lisp.

Method: e2* ((a upper-triangular-matrix) (b number))
Source

matrix.lisp.

Method: e2* ((a number) (b lower-triangular-matrix))
Source

matrix.lisp.

Method: e2* ((a lower-triangular-matrix) (b number))
Source

matrix.lisp.

Method: e2* (a (b wrapped-matrix))
Source

matrix.lisp.

Method: e2* ((a wrapped-matrix) b)
Source

matrix.lisp.

Method: e2* ((a number) (b number))
Method: e2* ((a vector) (b number))
Method: e2* ((a number) (b vector))
Method: e2* ((a vector) (b vector))
Method: e2* ((a array) (b number))
Method: e2* ((a number) (b array))
Method: e2* ((a array) (b array))
Generic Function: e2+ (a b)

Bivariate elementwise +.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e2+ ((a diagonal-matrix) (b diagonal-matrix))
Source

matrix.lisp.

Method: e2+ ((a hermitian-matrix) (b hermitian-matrix))
Source

matrix.lisp.

Method: e2+ ((a upper-triangular-matrix) (b upper-triangular-matrix))
Source

matrix.lisp.

Method: e2+ ((a lower-triangular-matrix) (b lower-triangular-matrix))
Source

matrix.lisp.

Method: e2+ (a (b wrapped-matrix))
Source

matrix.lisp.

Method: e2+ ((a wrapped-matrix) b)
Source

matrix.lisp.

Method: e2+ ((a number) (b number))
Method: e2+ ((a vector) (b number))
Method: e2+ ((a number) (b vector))
Method: e2+ ((a vector) (b vector))
Method: e2+ ((a array) (b number))
Method: e2+ ((a number) (b array))
Method: e2+ ((a array) (b array))
Generic Function: e2- (a b)

Bivariate elementwise -.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e2- ((a diagonal-matrix) (b diagonal-matrix))
Source

matrix.lisp.

Method: e2- ((a hermitian-matrix) (b hermitian-matrix))
Source

matrix.lisp.

Method: e2- ((a upper-triangular-matrix) (b upper-triangular-matrix))
Source

matrix.lisp.

Method: e2- ((a lower-triangular-matrix) (b lower-triangular-matrix))
Source

matrix.lisp.

Method: e2- (a (b wrapped-matrix))
Source

matrix.lisp.

Method: e2- ((a wrapped-matrix) b)
Source

matrix.lisp.

Method: e2- ((a number) (b number))
Method: e2- ((a vector) (b number))
Method: e2- ((a number) (b vector))
Method: e2- ((a vector) (b vector))
Method: e2- ((a array) (b number))
Method: e2- ((a number) (b array))
Method: e2- ((a array) (b array))
Generic Function: e2/ (a b)

Bivariate elementwise /.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e2/ ((a number) (b diagonal-matrix))
Source

matrix.lisp.

Method: e2/ ((a diagonal-matrix) (b number))
Source

matrix.lisp.

Method: e2/ ((a number) (b hermitian-matrix))
Source

matrix.lisp.

Method: e2/ ((a hermitian-matrix) (b number))
Source

matrix.lisp.

Method: e2/ ((a number) (b upper-triangular-matrix))
Source

matrix.lisp.

Method: e2/ ((a upper-triangular-matrix) (b number))
Source

matrix.lisp.

Method: e2/ ((a number) (b lower-triangular-matrix))
Source

matrix.lisp.

Method: e2/ ((a lower-triangular-matrix) (b number))
Source

matrix.lisp.

Method: e2/ ((a number) (b number))
Method: e2/ ((a vector) (b number))
Method: e2/ ((a number) (b vector))
Method: e2/ ((a vector) (b vector))
Method: e2/ ((a array) (b number))
Method: e2/ ((a number) (b array))
Method: e2/ ((a array) (b array))
Generic Function: e2log (a b)

Bivariate elementwise LOG.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: e2log ((a number) (b number))
Method: e2log ((a vector) (b number))
Method: e2log ((a number) (b vector))
Method: e2log ((a vector) (b vector))
Method: e2log ((a array) (b number))
Method: e2log ((a number) (b array))
Method: e2log ((a array) (b array))
Generic Function: eceiling (a)

Univariate elementwise CEILING.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: eceiling ((a number))
Method: eceiling ((a array))
Generic Function: econjugate (a)

Univariate elementwise CONJUGATE.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: econjugate ((a number))
Method: econjugate ((a array))
Generic Function: eexp (a)

Univariate elementwise EXP.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: eexp ((a diagonal-matrix))
Source

matrix.lisp.

Method: eexp ((a hermitian-matrix))
Source

matrix.lisp.

Method: eexp ((a upper-triangular-matrix))
Source

matrix.lisp.

Method: eexp ((a lower-triangular-matrix))
Source

matrix.lisp.

Method: eexp ((a number))
Method: eexp ((a array))
Generic Function: eexpt (a b)

Bivariate elementwise EXPT.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: eexpt ((a number) (b number))
Method: eexpt ((a vector) (b number))
Method: eexpt ((a number) (b vector))
Method: eexpt ((a vector) (b vector))
Method: eexpt ((a array) (b number))
Method: eexpt ((a number) (b array))
Method: eexpt ((a array) (b array))
Generic Function: efloor (a)

Univariate elementwise FLOOR.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: efloor ((a number))
Method: efloor ((a array))
Generic Function: emod (a b)

Bivariate elementwise MOD.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: emod ((a number) (b number))
Method: emod ((a vector) (b number))
Method: emod ((a number) (b vector))
Method: emod ((a vector) (b vector))
Method: emod ((a array) (b number))
Method: emod ((a number) (b array))
Method: emod ((a array) (b array))
Generic Function: ensure-sorted-reals (object)

Return the contents of OBJECT as a SORTED-REALS.

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: ensure-sorted-reals ((sorted-reals sorted-reals))
Method: ensure-sorted-reals ((array array))
Method: ensure-sorted-reals ((list list))
Generic Function: ereduce (function object &key key)

Elementwise reduce, traversing in row-major order.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: ereduce (function (array array) &key key)
Method: ereduce (function (sequence sequence) &key key)
Method: ereduce (function object &key key)
Generic Function: esqrt (a)

Univariate elementwise SQRT.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: esqrt ((a diagonal-matrix))
Source

matrix.lisp.

Method: esqrt ((a hermitian-matrix))
Source

matrix.lisp.

Method: esqrt ((a upper-triangular-matrix))
Source

matrix.lisp.

Method: esqrt ((a lower-triangular-matrix))
Source

matrix.lisp.

Method: esqrt ((a number))
Method: esqrt ((a array))
Generic Function: extend-interval (interval object)

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

Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: extend-interval ((interval null) (object null))
Method: extend-interval ((interval null) (number real))
Method: extend-interval ((interval interval) (number real))
Method: extend-interval (interval (object interval))
Method: extend-interval (interval (list list))
Method: extend-interval (interval (array array))
Generic Function: kurtosis (object &key weights)

Kurtosis FIXME talk about bias, maybe implement unbiased?

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: kurtosis (object &key weights)
Method: kurtosis ((object central-sample-moments) &key weights)
Generic Function: l2norm-square (object)

Square of the $L_2$ norm of OBJECT.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Methods
Method: l2norm-square ((sequence sequence))
Generic Function: left (interval)

Left endpoint of interval.

Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: left ((interval interval/infinite-left))
Reader Method: left ((interval/finite-left interval/finite-left))

automatically generated reader method

Target Slot

left.

Generic Function: map-array (array function &optional retval)
Package

num-utils.matrix.

Methods
Method: map-array (array function &optional retval)

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

Source

matrix.lisp.

Generic Function: mean (object &key weights)

The mean of elements in OBJECT.

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: mean (object &key weights)
Method: mean ((object central-sample-moments) &key weights)
Generic Function: median (object)

Median of OBJECT.

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: median ((sample sequence))

Returns median of SAMPLE. SAMPLE must be a sequence of real numbers.

Method: median (object)
Generic Function: num= (a b &optional tolerance)

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

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

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

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

Package

num-utils.num=.

Source

num=.lisp.

Methods
Method: num= ((a central-sample-moments) (b central-sample-moments) &optional tolerance)
Source

statistics.lisp.

Method: num= ((a diagonal-matrix) (b diagonal-matrix) &optional tolerance)
Source

matrix.lisp.

Method: num= ((a wrapped-matrix) (b wrapped-matrix) &optional tolerance)
Source

matrix.lisp.

Method: num= ((a finite-interval) (b finite-interval) &optional tolerance)
Source

interval.lisp.

Method: num= ((a real-line) (b real-line) &optional tolerance)
Source

interval.lisp.

Method: num= (a b &optional tolerance)
Method: num= ((a number) (b number) &optional tolerance)
Method: num= ((a array) (b array) &optional tolerance)
Method: num= ((a cons) (b cons) &optional tolerance)
Method: num= ((a null) (b null) &optional tolerance)
Generic Function: open-left? (interval)

True iff the left endpoint of the interval is open.

Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: open-left? ((interval interval/infinite-left))
Reader Method: open-left? ((interval/finite-left interval/finite-left))

automatically generated reader method

Target Slot

open-left?.

Generic Function: open-right? (interval)

True iff the right endpoint of the interval is open.

Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: open-right? ((interval interval/infinite-right))
Reader Method: open-right? ((interval/finite-right interval/finite-right))

automatically generated reader method

Target Slot

open-right?.

Generic Function: product (object)

Product of elements in object.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Methods
Method: product ((sequence sequence))
Method: product ((array array))
Generic Function: quantile (object q)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: quantile ((object sequence) q)
Method: quantile (object q)
Generic Function: quantiles (object qs)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: quantiles ((object sequence) qs)
Method: quantiles ((accumulator sorted-reals) q)
Generic Function: right (interval)

Right endpoint of interval.

Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: right ((interval interval/infinite-right))
Reader Method: right ((interval/finite-right interval/finite-right))

automatically generated reader method

Target Slot

right.

Generic Function: sd (object &key weights)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: sd (object &key weights)
Generic Function: shift-interval (interval offset)
Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: shift-interval ((interval finite-interval) (offset real))
Generic Function: skewness (object &key weights)

Skewness FIXME talk about bias, maybe implement unbiased?

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: skewness (object &key weights)
Method: skewness ((object central-sample-moments) &key weights)
Generic Function: sum (object &key key)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Methods
Method: sum ((sequence sequence) &key key)
Method: sum ((array array) &key key)
Generic Function: tally (accumulator)

The total weight of elements in ACCUMULATOR.

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: tally ((accumulator sparse-counter))

Return the total ’weight’ of the accumulator

Method: tally ((accumulator tally-mixin))
Generic Function: transpose (array)

Transpose.

Package

num-utils.matrix.

Source

matrix.lisp.

Methods
Method: transpose ((array array))
Method: transpose ((matrix lower-triangular-matrix))
Method: transpose ((matrix upper-triangular-matrix))
Method: transpose ((matrix hermitian-matrix))
Method: transpose ((diagonal diagonal-matrix))
Generic Function: variance (object &key weights)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: variance (object &key weights)
Method: variance ((object central-sample-moments) &key weights)

5.1.6 Standalone methods

Method: as-array ((matrix0 upper-triangular-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: as-array ((matrix0 hermitian-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: as-array ((matrix0 lower-triangular-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: as-array ((diagonal-matrix diagonal-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: dims ((wrapped-matrix wrapped-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: dims ((diagonal-matrix diagonal-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: element-type ((wrapped-matrix wrapped-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: element-type ((diagonal-matrix diagonal-matrix))
Package

array-operations/generic.

Source

matrix.lisp.

Method: initialize-instance :after ((interval finite-interval) &key &allow-other-keys)
Source

interval.lisp.

Method: print-object ((matrix0 upper-triangular-matrix) stream1)
Source

matrix.lisp.

Method: print-object ((matrix0 hermitian-matrix) stream1)
Source

matrix.lisp.

Method: print-object ((matrix0 lower-triangular-matrix) stream1)
Source

matrix.lisp.

Method: print-object ((interval interval) stream)
Source

interval.lisp.

Method: print-object ((acc sorted-reals) stream)
Source

statistics.lisp.

Method: print-object ((sparse-counter sparse-counter) stream)
Source

statistics.lisp.

Method: select ((matrix0 upper-triangular-matrix) &rest slices)
Package

select.

Source

matrix.lisp.

Method: select ((matrix0 hermitian-matrix) &rest slices)
Package

select.

Source

matrix.lisp.

Method: select ((matrix0 lower-triangular-matrix) &rest slices)
Package

select.

Source

matrix.lisp.


5.1.7 Conditions

Condition: empty-accumulator
Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

error.

Condition: information-not-collected-in-accumulator
Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

error.

Condition: not-enough-elements-in-accumulator
Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

error.


Next: , Previous: , Up: Public Interface   [Contents][Index]

5.1.8 Structures

Structure: central-sample-moments

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

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

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

Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

tally-mixin.

Direct methods
Direct slots
Slot: m
Type

real

Initform

0.0d0

Readers

central-sample-moments-m.

Writers

(setf central-sample-moments-m).

Slot: s2
Type

(or (real 0) null)

Initform

0.0d0

Readers

central-sample-moments-s2.

Writers

(setf central-sample-moments-s2).

Slot: s3
Type

(or real null)

Initform

0.0d0

Readers

central-sample-moments-s3.

Writers

(setf central-sample-moments-s3).

Slot: s4
Type

(or (real 0) null)

Initform

0.0d0

Readers

central-sample-moments-s4.

Writers

(setf central-sample-moments-s4).

Structure: diagonal-matrix

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

Package

num-utils.matrix.

Source

matrix.lisp.

Direct superclasses

structure-object.

Direct methods
Direct slots
Slot: elements
Type

vector

Readers

diagonal-matrix-elements.

Writers

(setf diagonal-matrix-elements).

Structure: hermitian-matrix

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

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

Package

num-utils.matrix.

Source

matrix.lisp.

Direct superclasses

wrapped-matrix.

Direct methods
Structure: lower-triangular-matrix

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

Package

num-utils.matrix.

Source

matrix.lisp.

Direct superclasses

wrapped-matrix.

Direct methods
Structure: relative

Relative sizes are in terms of width.

Package

num-utils.interval.

Source

interval.lisp.

Direct superclasses

structure-object.

Direct slots
Slot: fraction
Type

(real 0)

Readers

relative-fraction.

Writers

This slot is read-only.

Structure: sorted-reals

Accumulator which sorts elements. ELEMENTS return the sorted elements.

Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

structure-object.

Direct methods
Direct slots
Slot: ordered-elements
Type

vector

Initform

#()

Readers

sorted-reals-ordered-elements.

Writers

(setf sorted-reals-ordered-elements).

Slot: unordered-elements
Type

list

Readers

sorted-reals-unordered-elements.

Writers

(setf sorted-reals-unordered-elements).

Structure: spacer

Spacers divide the leftover portion of an interval.

Package

num-utils.interval.

Source

interval.lisp.

Direct superclasses

structure-object.

Direct slots
Slot: weight
Type

(real 0)

Initform

1

Readers

spacer-weight.

Writers

This slot is read-only.

Structure: sparse-counter
Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

structure-object.

Direct methods
Direct slots
Slot: table
Type

hash-table

Readers

sparse-counter-table.

Writers

This slot is read-only.

Structure: test-results

Differences between reference values and computed values

Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Direct superclasses

structure-object.

Direct slots
Slot: worst-case
Type

integer

Initform

0

Readers

worst-case.

Writers

(setf worst-case).

Slot: min-error
Type

double-float

Initform

0.0d0

Readers

min-error.

Writers

(setf min-error).

Slot: max-error
Type

double-float

Initform

0.0d0

Readers

max-error.

Writers

(setf max-error).

Slot: mean-error
Type

double-float

Initform

0.0d0

Readers

mean-error.

Writers

(setf mean-error).

Slot: test-count
Type

integer

Initform

0

Readers

test-count.

Writers

(setf test-count).

Slot: variance0
Type

double-float

Initform

0.0d0

Readers

variance0.

Writers

(setf variance0).

Slot: variance1
Type

double-float

Initform

0.0d0

Readers

variance1.

Writers

(setf variance1).

Slot: rms
Type

double-float

Initform

0.0d0

Readers

rms.

Writers

(setf rms).

Structure: upper-triangular-matrix

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

Package

num-utils.matrix.

Source

matrix.lisp.

Direct superclasses

wrapped-matrix.

Direct methods
Structure: wrapped-matrix

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

Package

num-utils.matrix.

Source

matrix.lisp.

Direct superclasses

structure-object.

Direct subclasses
Direct methods
Direct slots
Slot: elements
Type

(array * (* *))

Readers

wrapped-matrix-elements.

Writers

This slot is read-only.


Next: , Previous: , Up: Public Interface   [Contents][Index]

5.1.9 Classes

Class: finite-interval

Interval with finite endpoints.

Package

num-utils.interval.

Source

interval.lisp.

Direct superclasses
Direct methods
Class: interval

Abstract superclass for all intervals.

Package

num-utils.interval.

Source

interval.lisp.

Direct subclasses
Direct methods
Class: minusinf-interval

Interval from -∞ to RIGHT.

Package

num-utils.interval.

Source

interval.lisp.

Direct superclasses
Class: plusinf-interval

Interval from LEFT to ∞.

Package

num-utils.interval.

Source

interval.lisp.

Direct superclasses
Direct methods
Class: real-line

Representing the real line (-∞,∞).

Package

num-utils.interval.

Source

interval.lisp.

Direct superclasses
Direct methods

num=.


Previous: , Up: Public Interface   [Contents][Index]

5.1.10 Types

Type: extended-real (&optional base)

Extended real number.

Package

num-utils.extended-real.

Source

extended-real.lisp.

Type: simple-double-float-vector (&optional length)

Simple vector of double-float elements.

Package

num-utils.utilities.

Source

utilities.lisp.

Type: simple-fixnum-vector ()

Simple vector or fixnum elements.

Package

num-utils.utilities.

Source

utilities.lisp.

Type: simple-single-float-vector (&optional length)

Simple vector of single-float elements.

Package

num-utils.utilities.

Source

utilities.lisp.

Type: triangular-matrix ()

Triangular matrix (either lower or upper).

Package

num-utils.matrix.

Source

matrix.lisp.


5.2 Internals


Next: , Previous: , Up: Internals   [Contents][Index]

5.2.1 Macros

Macro: &diagonal-matrix (elements)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Macro: &diagonal-matrix-r/o (elements)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Macro: &sorted-reals (ordered-elements unordered-elements)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Macro: &sorted-reals-r/o (ordered-elements unordered-elements)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Macro: define-central-sample-moment (function (variable degree) &body body)

FIXME documentation, factor out general part

Package

num-utils.statistics.

Source

statistics.lisp.

Macro: define-comparison (name test)

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

Package

num-utils.extended-real.

Source

extended-real.lisp.

Macro: define-e& (operation &key function bivariate univariate docstring)
Package

num-utils.elementwise.

Source

elementwise.lisp.

Macro: define-e1 (operation &key function docstring)

Define an univariate elementwise operation.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Macro: define-e2 (operation &key function docstring)

Define a bivariate elementwise operation.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Macro: define-elementwise-as-array (type &key functions)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Macro: define-elementwise-reduction (name function &optional docstring)
Package

num-utils.elementwise.

Source

elementwise.lisp.

Macro: define-elementwise-same-class (type &key functions elements-accessor)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Macro: define-elementwise-univariate (type &key functions elements-accessor)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Macro: define-elementwise-with-constant (type &key functions elements-accessor)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Macro: define-rounding-with-offset (name function docstring)
Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Macro: define-wrapped-matrix (type elements struct-docstring (masked-test masked-string) check-and-convert-elements regularize-elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Macro: mapping-array ((ref array &rest other) form)
Package

num-utils.elementwise.

Source

elementwise.lisp.

Macro: univariate-rootfinder-loop% (((f a b fa fb) (f-tested test-bracket delta epsilon)) &body body)

Common parts for univariate rootfinder functions.

Sets up the following:

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

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

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

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

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.


Next: , Previous: , Up: Internals   [Contents][Index]

5.2.2 Ordinary functions

Function: ab-to-cd-intercept-slope (a b c d)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: ab-to-cinf (z a b c)

Inverse of cinf-to-ab.

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: above-diagonal? (row col)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Function: below-diagonal? (row col)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Reader: central-sample-moments-m (instance)
Writer: (setf central-sample-moments-m) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

m.

Function: central-sample-moments-p (object)
Package

num-utils.statistics.

Source

statistics.lisp.

Reader: central-sample-moments-s2 (instance)
Writer: (setf central-sample-moments-s2) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

s2.

Reader: central-sample-moments-s3 (instance)
Writer: (setf central-sample-moments-s3) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

s3.

Reader: central-sample-moments-s4 (instance)
Writer: (setf central-sample-moments-s4) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

s4.

Function: central-sample-moments-w (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: (setf central-sample-moments-w) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: chebyshev-recursion (x value previous-value)

Chebyshev polynomial recursion formula.

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: cinf-to-ab (x a b c)

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

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Function: copy-central-sample-moments (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: copy-diagonal-matrix (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: copy-hermitian-matrix (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: copy-iterative-quadrature (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: copy-lower-triangular-matrix (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: copy-midpoint-quadrature (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: copy-relative (instance)
Package

num-utils.interval.

Source

interval.lisp.

Function: copy-richardson-extrapolation (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: copy-sorted-reals (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: copy-spacer (instance)
Package

num-utils.interval.

Source

interval.lisp.

Function: copy-sparse-counter (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: copy-tally-mixin (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: copy-test-results (instance)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Function: copy-trapezoidal-quadrature (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: copy-upper-triangular-matrix (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: copy-wrapped-matrix (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: diagonal-matrix-p (object)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: ensure-valid-elements (array rank &rest predicates)

Convert OBJECT to an array, check that it

1. has the required rank,

2. has a valid sparse element type, and

3. that it satisfies PREDICATES.

Return the array.

Package

num-utils.matrix.

Source

matrix.lisp.

Function: extend-pairwise-comparison (test first rest)

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

Package

num-utils.extended-real.

Source

extended-real.lisp.

Function: hermitian-matrix-elements (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: hermitian-matrix-p (object)
Package

num-utils.matrix.

Source

matrix.lisp.

Reader: iterative-quadrature-a (instance)
Writer: (setf iterative-quadrature-a) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

a.

Reader: iterative-quadrature-b (instance)
Writer: (setf iterative-quadrature-b) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

b.

Reader: iterative-quadrature-f (instance)
Writer: (setf iterative-quadrature-f) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

f.

Reader: iterative-quadrature-h (instance)
Writer: (setf iterative-quadrature-h) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

h.

Reader: iterative-quadrature-n (instance)
Writer: (setf iterative-quadrature-n) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

n.

Function: iterative-quadrature-p (object)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Reader: iterative-quadrature-sum (instance)
Writer: (setf iterative-quadrature-sum) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

sum.

Function: ln (n)

Natural logarithm.

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: lower-triangular-matrix-elements (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: lower-triangular-matrix-p (object)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: make-central-sample-moments (&key w m s2 s3 s4)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: make-diagonal-matrix (&key elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: make-hermitian-matrix (&key elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: make-iterative-quadrature (&key f a b h n sum)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: make-lower-triangular-matrix (&key elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: make-sorted-reals (&key ordered-elements unordered-elements)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: make-sparse-counter% (&key table)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: make-tally-mixin (&key w)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: make-test-results (&key worst-case min-error max-error mean-error test-count variance0 variance1 rms)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Function: make-upper-triangular-matrix (&key elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: make-wrapped-matrix (&key elements)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: midpoint-quadrature (f a b)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature% (&key f a b h n sum)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-a (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf midpoint-quadrature-a) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-b (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf midpoint-quadrature-b) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-f (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf midpoint-quadrature-f) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-h (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf midpoint-quadrature-h) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-n (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf midpoint-quadrature-n) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-p (object)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: midpoint-quadrature-sum (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf midpoint-quadrature-sum) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: narrow-bracket? (a b delta)

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Function: near-root? (f epsilon)

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Function: opposite-sign? (a b)

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

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Function: pad-left-expansion (rows ncol)

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

Package

num-utils.matrix-shorthand.

Source

matrix-shorthand.lisp.

Function: print-matrix-formatter (x)

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

Package

num-utils.print-matrix.

Source

print-matrix.lisp.

Reader: relative-fraction (instance)
Package

num-utils.interval.

Source

interval.lisp.

Target Slot

fraction.

Function: relative-p (object)
Package

num-utils.interval.

Source

interval.lisp.

Function: richardson-extrapolation (coefficient iterations)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Reader: richardson-extrapolation-coefficient (instance)
Writer: (setf richardson-extrapolation-coefficient) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

coefficient.

Reader: richardson-extrapolation-diagonal (instance)
Writer: (setf richardson-extrapolation-diagonal) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

diagonal.

Reader: richardson-extrapolation-n (instance)
Writer: (setf richardson-extrapolation-n) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Target Slot

n.

Function: richardson-extrapolation-p (object)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: richardson-iteration (extrapolation step)

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

Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: romberg-quadrature% (quadrature epsilon min-iter max-iter)

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

Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: rootfinding-delta (interval &optional delta-relative)

Default DELTA for rootfinding methods, uses bracket width.

Package

num-utils.rootfinding.

Source

rootfinding.lisp.

Function: similar-element-type (element-type)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: similar-sequence-type (sequence)

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

Package

num-utils.arithmetic.

Source

arithmetic.lisp.

Function: sort-reals (sequence)

Return a SORTED-REALS structure.

Package

num-utils.statistics.

Source

statistics.lisp.

Reader: sorted-reals-ordered-elements (instance)
Writer: (setf sorted-reals-ordered-elements) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

ordered-elements.

Function: sorted-reals-p (object)
Package

num-utils.statistics.

Source

statistics.lisp.

Reader: sorted-reals-unordered-elements (instance)
Writer: (setf sorted-reals-unordered-elements) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

unordered-elements.

Function: spacer-p (object)
Package

num-utils.interval.

Source

interval.lisp.

Reader: spacer-weight (instance)
Package

num-utils.interval.

Source

interval.lisp.

Target Slot

weight.

Function: sparse-counter-p (object)
Package

num-utils.statistics.

Source

statistics.lisp.

Function: tally-mixin-p (object)
Package

num-utils.statistics.

Source

statistics.lisp.

Reader: tally-mixin-w (instance)
Writer: (setf tally-mixin-w) (instance)
Package

num-utils.statistics.

Source

statistics.lisp.

Target Slot

w.

Function: test-results-p (object)
Package

num-utils.test-utilities.

Source

test-utilities.lisp.

Function: trapezoidal-quadrature (f a b)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature% (&key f a b h n sum)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-a (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf trapezoidal-quadrature-a) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-b (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf trapezoidal-quadrature-b) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-f (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf trapezoidal-quadrature-f) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-h (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf trapezoidal-quadrature-h) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-n (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf trapezoidal-quadrature-n) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-p (object)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: trapezoidal-quadrature-sum (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: (setf trapezoidal-quadrature-sum) (instance)
Package

num-utils.quadrature.

Source

quadrature.lisp.

Function: upper-triangular-matrix-elements (instance)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: upper-triangular-matrix-p (object)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: valid-sparse-type? (type)

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

Package

num-utils.matrix.

Source

matrix.lisp.

Function: weighted-empirical-quantile (sorted-reals p-table q)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: weighted-quantile-p-table (weights)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Function: wrapped-matrix-p (object)
Package

num-utils.matrix.

Source

matrix.lisp.

Function: zero-like (array)

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

Package

num-utils.matrix.

Source

matrix.lisp.


Next: , Previous: , Up: Internals   [Contents][Index]

5.2.3 Generic functions

Generic Function: chebyshev-approximate-implementation (f interval n-polynomials n-points)

Implementation of CHEBYSHEV-APPROXIMATE.

Package

num-utils.chebyshev.

Source

chebyshev.lisp.

Methods
Method: chebyshev-approximate-implementation (f (interval plusinf-interval) n-polynomials n-points)
Method: chebyshev-approximate-implementation (f (interval finite-interval) n-polynomials n-points)
Generic Function: esquare (a)

Univariate elementwise SQUARE.

Package

num-utils.elementwise.

Source

elementwise.lisp.

Methods
Method: esquare ((a number))
Method: esquare ((a array))
Generic Function: pool2 (accumulator1 accumulator2)

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

Package

num-utils.statistics.

Source

statistics.lisp.

Methods
Method: pool2 ((moments-a central-sample-moments) (moments-b central-sample-moments))
Generic Function: print-left-endpoint (interval stream)
Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: print-left-endpoint ((interval interval/finite-left) stream)
Method: print-left-endpoint ((interval interval/infinite-left) stream)
Generic Function: print-right-endpoint (interval stream)
Package

num-utils.interval.

Source

interval.lisp.

Methods
Method: print-right-endpoint ((interval interval/finite-right) stream)
Method: print-right-endpoint ((interval interval/infinite-right) stream)
Generic Function: refine-quadrature (quadrature)

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

Package

num-utils.quadrature.

Source

quadrature.lisp.

Methods
Method: refine-quadrature ((quadrature midpoint-quadrature))
Method: refine-quadrature ((quadrature trapezoidal-quadrature))
Generic Function: richardson-coefficient (quadrature)

Return the coefficient $q$ for Richardson approximation.

Package

num-utils.quadrature.

Source

quadrature.lisp.

Methods
Method: richardson-coefficient ((quadrature midpoint-quadrature))
Method: richardson-coefficient ((quadrature trapezoidal-quadrature))
Generic Function: transformed-quadrature (function interval transformation)

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

Package

num-utils.quadrature.

Source

quadrature.lisp.

Methods
Method: transformed-quadrature (function (interval finite-interval) (transformation null))
Method: transformed-quadrature (function (interval plusinf-interval) (transformation null))

Next: , Previous: , Up: Internals   [Contents][Index]

5.2.4 Structures

Structure: iterative-quadrature

Quadrature building block.

F is the function.

A and B are the endpoints.

H is the stepsize.

Package

num-utils.quadrature.

Source

quadrature.lisp.

Direct superclasses

structure-object.

Direct subclasses
Direct slots
Slot: f
Type

(function (double-float) double-float)

Readers

iterative-quadrature-f.

Writers

(setf iterative-quadrature-f).

Slot: a
Type

double-float

Readers

iterative-quadrature-a.

Writers

(setf iterative-quadrature-a).

Slot: b
Type

double-float

Readers

iterative-quadrature-b.

Writers

(setf iterative-quadrature-b).

Slot: h
Type

double-float

Readers

iterative-quadrature-h.

Writers

(setf iterative-quadrature-h).

Slot: n
Type

fixnum

Initform

0

Readers

iterative-quadrature-n.

Writers

(setf iterative-quadrature-n).

Slot: sum
Package

num-utils.arithmetic.

Type

double-float

Initform

0.0d0

Readers

iterative-quadrature-sum.

Writers

(setf iterative-quadrature-sum).

Structure: midpoint-quadrature
Package

num-utils.quadrature.

Source

quadrature.lisp.

Direct superclasses

iterative-quadrature.

Direct methods
Structure: richardson-extrapolation

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

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

Package

num-utils.quadrature.

Source

quadrature.lisp.

Direct superclasses

structure-object.

Direct slots
Slot: coefficient
Type

double-float

Readers

richardson-extrapolation-coefficient.

Writers

(setf richardson-extrapolation-coefficient).

Slot: n
Type

fixnum

Initform

0

Readers

richardson-extrapolation-n.

Writers

(setf richardson-extrapolation-n).

Slot: diagonal
Type

(array double-float (*))

Readers

richardson-extrapolation-diagonal.

Writers

(setf richardson-extrapolation-diagonal).

Structure: tally-mixin

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

Package

num-utils.statistics.

Source

statistics.lisp.

Direct superclasses

structure-object.

Direct subclasses

central-sample-moments.

Direct methods

tally.

Direct slots
Slot: w
Type

(real 0)

Initform

0

Readers

tally-mixin-w.

Writers

(setf tally-mixin-w).

Structure: trapezoidal-quadrature
Package

num-utils.quadrature.

Source

quadrature.lisp.

Direct superclasses

iterative-quadrature.

Direct methods

Next: , Previous: , Up: Internals   [Contents][Index]

5.2.5 Classes

Class: interval/finite-left

Interval with left endpoint.

Package

num-utils.interval.

Source

interval.lisp.

Direct subclasses
Direct methods
Direct slots
Slot: left
Type

real

Initargs

:left

Readers

left.

Writers

This slot is read-only.

Slot: open-left?
Type

boolean

Initargs

:open-left?

Readers

open-left?.

Writers

This slot is read-only.

Class: interval/finite-right

Interval with right endpoint.

Package

num-utils.interval.

Source

interval.lisp.

Direct subclasses
Direct methods
Direct slots
Slot: right
Type

real

Initargs

:right

Readers

right.

Writers

This slot is read-only.

Slot: open-right?
Type

boolean

Initargs

:open-right?

Readers

open-right?.

Writers

This slot is read-only.

Class: interval/infinite-left

Left endpoint is -∞.

Package

num-utils.interval.

Source

interval.lisp.

Direct subclasses
Direct methods
Class: interval/infinite-right

Right endpoint is ∞.

Package

num-utils.interval.

Source

interval.lisp.

Direct subclasses
Direct methods

Previous: , Up: Internals   [Contents][Index]

5.2.6 Types

Type: infinite ()

Representing infinity (extending the real line).

Package

num-utils.extended-real.

Source

extended-real.lisp.


Appendix A Indexes


Next: , Previous: , Up: Indexes   [Contents][Index]

A.1 Concepts


Next: , Previous: , Up: Indexes   [Contents][Index]

A.2 Functions

Jump to:   &   (   1   <   =   >  
A   B   C   D   E   F   G   H   I   K   L   M   N   O   P   Q   R   S   T   U   V   W   Z  
Index Entry  Section

&
&diagonal-matrix: Private macros
&diagonal-matrix-r/o: Private macros
&interval: Public macros
&sorted-reals: Private macros
&sorted-reals-r/o: Private macros

(
(setf central-sample-moments-m): Private ordinary functions
(setf central-sample-moments-s2): Private ordinary functions
(setf central-sample-moments-s3): Private ordinary functions
(setf central-sample-moments-s4): Private ordinary functions
(setf central-sample-moments-w): Private ordinary functions
(setf diagonal-matrix-elements): Public ordinary functions
(setf diagonal-vector): Public generic functions
(setf diagonal-vector): Public generic functions
(setf iterative-quadrature-a): Private ordinary functions
(setf iterative-quadrature-b): Private ordinary functions
(setf iterative-quadrature-f): Private ordinary functions
(setf iterative-quadrature-h): Private ordinary functions
(setf iterative-quadrature-n): Private ordinary functions
(setf iterative-quadrature-sum): Private ordinary functions
(setf max-error): Public ordinary functions
(setf mean-error): Public ordinary functions
(setf midpoint-quadrature-a): Private ordinary functions
(setf midpoint-quadrature-b): Private ordinary functions
(setf midpoint-quadrature-f): Private ordinary functions
(setf midpoint-quadrature-h): Private ordinary functions
(setf midpoint-quadrature-n): Private ordinary functions
(setf midpoint-quadrature-sum): Private ordinary functions
(setf min-error): Public ordinary functions
(setf richardson-extrapolation-coefficient): Private ordinary functions
(setf richardson-extrapolation-diagonal): Private ordinary functions
(setf richardson-extrapolation-n): Private ordinary functions
(setf rms): Public ordinary functions
(setf sorted-reals-ordered-elements): Private ordinary functions
(setf sorted-reals-unordered-elements): Private ordinary functions
(setf tally-mixin-w): Private ordinary functions
(setf test-count): Public ordinary functions
(setf trapezoidal-quadrature-a): Private ordinary functions
(setf trapezoidal-quadrature-b): Private ordinary functions
(setf trapezoidal-quadrature-f): Private ordinary functions
(setf trapezoidal-quadrature-h): Private ordinary functions
(setf trapezoidal-quadrature-n): Private ordinary functions
(setf trapezoidal-quadrature-sum): Private ordinary functions
(setf variance0): Public ordinary functions
(setf variance1): Public ordinary functions
(setf worst-case): Public ordinary functions

1
1c: Public ordinary functions

<
<: Public ordinary functions
<=: Public ordinary functions

=
=: Public ordinary functions

>
>: Public ordinary functions
>=: Public ordinary functions

A
ab-to-cd-intercept-slope: Private ordinary functions
ab-to-cinf: Private ordinary functions
above-diagonal?: Private ordinary functions
abs-diff: Public ordinary functions
absolute-square: Public ordinary functions
add: Public generic functions
add: Public generic functions
add: Public generic functions
add: Public generic functions
add: Public generic functions
as-alist: Public generic functions
as-alist: Public generic functions
as-array: Public standalone methods
as-array: Public standalone methods
as-array: Public standalone methods
as-array: Public standalone methods
as-double-float: Public ordinary functions
as-integer: Public ordinary functions
as-plist: Public generic functions
as-plist: Public generic functions
as-simple-fixnum-vector: Public ordinary functions

B
below-diagonal?: Private ordinary functions
bic: Public ordinary functions
binary-search: Public ordinary functions

C
ceiling*: Public ordinary functions
central-m2: Public generic functions
central-m2: Public generic functions
central-m2: Public generic functions
central-m3: Public generic functions
central-m3: Public generic functions
central-m3: Public generic functions
central-m4: Public generic functions
central-m4: Public generic functions
central-m4: Public generic functions
central-sample-moments: Public generic functions
central-sample-moments: Public generic functions
central-sample-moments: Public generic functions
central-sample-moments: Public generic functions
central-sample-moments-degree: Public ordinary functions
central-sample-moments-m: Private ordinary functions
central-sample-moments-p: Private ordinary functions
central-sample-moments-s2: Private ordinary functions
central-sample-moments-s3: Private ordinary functions
central-sample-moments-s4: Private ordinary functions
central-sample-moments-w: Private ordinary functions
chebyshev-approximate: Public ordinary functions
chebyshev-approximate-implementation: Private generic functions
chebyshev-approximate-implementation: Private generic functions
chebyshev-approximate-implementation: Private generic functions
chebyshev-recursion: Private ordinary functions
chebyshev-regression: Public ordinary functions
chebyshev-root: Public ordinary functions
chebyshev-roots: Public ordinary functions
check-types: Public macros
cinf-to-ab: Private ordinary functions
compare-fns: Public ordinary functions
compare-vectors: Public ordinary functions
Compiler Macro, make-vector: Public compiler macros
copy-central-sample-moments: Private ordinary functions
copy-diagonal-matrix: Private ordinary functions
copy-hermitian-matrix: Private ordinary functions
copy-iterative-quadrature: Private ordinary functions
copy-lower-triangular-matrix: Private ordinary functions
copy-midpoint-quadrature: Private ordinary functions
copy-relative: Private ordinary functions
copy-richardson-extrapolation: Private ordinary functions
copy-sorted-reals: Private ordinary functions
copy-spacer: Private ordinary functions
copy-sparse-counter: Private ordinary functions
copy-tally-mixin: Private ordinary functions
copy-test-results: Private ordinary functions
copy-trapezoidal-quadrature: Private ordinary functions
copy-upper-triangular-matrix: Private ordinary functions
copy-wrapped-matrix: Private ordinary functions
cross-tabulate: Public ordinary functions
cube: Public ordinary functions
cumulative-product: Public ordinary functions
cumulative-sum: Public ordinary functions
curry*: Public macros

D
define-central-sample-moment: Private macros
define-comparison: Private macros
define-e&: Private macros
define-e1: Private macros
define-e2: Private macros
define-elementwise-as-array: Private macros
define-elementwise-reduction: Private macros
define-elementwise-same-class: Private macros
define-elementwise-univariate: Private macros
define-elementwise-with-constant: Private macros
define-num=-with-accessors: Public macros
define-rounding-with-offset: Private macros
define-structure-num=: Public macros
define-with-multiple-bindings: Public macros
define-wrapped-matrix: Private macros
diagonal-matrix: Public ordinary functions
diagonal-matrix-elements: Public ordinary functions
diagonal-matrix-p: Private ordinary functions
diagonal-mx: Public ordinary functions
diagonal-vector: Public generic functions
diagonal-vector: Public generic functions
diagonal-vector: Public generic functions
dims: Public standalone methods
dims: Public standalone methods
divides?: Public ordinary functions

E
e*: Public ordinary functions
e+: Public ordinary functions
e-: Public ordinary functions
e/: Public ordinary functions
e1-: Public generic functions
e1-: Public generic functions
e1-: Public generic functions
e1-: Public generic functions
e1-: Public generic functions
e1-: Public generic functions
e1-: Public generic functions
e1/: Public generic functions
e1/: Public generic functions
e1/: Public generic functions
e1/: Public generic functions
e1/: Public generic functions
e1/: Public generic functions
e1/: Public generic functions
e1log: Public generic functions
e1log: Public generic functions
e1log: Public generic functions
e1log: Public generic functions
e1log: Public generic functions
e1log: Public generic functions
e1log: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2*: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2+: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2-: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2/: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
e2log: Public generic functions
eceiling: Public generic functions
eceiling: Public generic functions
eceiling: Public generic functions
econjugate: Public generic functions
econjugate: Public generic functions
econjugate: Public generic functions
eexp: Public generic functions
eexp: Public generic functions
eexp: Public generic functions
eexp: Public generic functions
eexp: Public generic functions
eexp: Public generic functions
eexp: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
eexpt: Public generic functions
efloor: Public generic functions
efloor: Public generic functions
efloor: Public generic functions
element-type: Public standalone methods
element-type: Public standalone methods
elementwise-float-contagion: Public ordinary functions
elog: Public ordinary functions
emax: Public ordinary functions
emin: Public ordinary functions
emod: Public generic functions
emod: Public generic functions
emod: Public generic functions
emod: Public generic functions
emod: Public generic functions
emod: Public generic functions
emod: Public generic functions
emod: Public generic functions
empirical-quantile: Public ordinary functions
empirical-quantile-probabilities: Public ordinary functions
ensure-sorted-reals: Public generic functions
ensure-sorted-reals: Public generic functions
ensure-sorted-reals: Public generic functions
ensure-sorted-reals: Public generic functions
ensure-sorted-vector: Public ordinary functions
ensure-valid-elements: Private ordinary functions
ereduce: Public generic functions
ereduce: Public generic functions
ereduce: Public generic functions
ereduce: Public generic functions
esqrt: Public generic functions
esqrt: Public generic functions
esqrt: Public generic functions
esqrt: Public generic functions
esqrt: Public generic functions
esqrt: Public generic functions
esqrt: Public generic functions
esquare: Private generic functions
esquare: Private generic functions
esquare: Private generic functions
evaluate-chebyshev: Public ordinary functions
evaluate-polynomial: Public ordinary functions
exp-1: Public ordinary functions
exp-1/x: Public ordinary functions
expanding: Public macros
expt-1: Public ordinary functions
extend-interval: Public generic functions
extend-interval: Public generic functions
extend-interval: Public generic functions
extend-interval: Public generic functions
extend-interval: Public generic functions
extend-interval: Public generic functions
extend-interval: Public generic functions
extend-pairwise-comparison: Private ordinary functions
extendf-interval: Public macros

F
fixnum?: Public ordinary functions
floor*: Public ordinary functions
Function, (setf central-sample-moments-m): Private ordinary functions
Function, (setf central-sample-moments-s2): Private ordinary functions
Function, (setf central-sample-moments-s3): Private ordinary functions
Function, (setf central-sample-moments-s4): Private ordinary functions
Function, (setf central-sample-moments-w): Private ordinary functions
Function, (setf diagonal-matrix-elements): Public ordinary functions
Function, (setf iterative-quadrature-a): Private ordinary functions
Function, (setf iterative-quadrature-b): Private ordinary functions
Function, (setf iterative-quadrature-f): Private ordinary functions
Function, (setf iterative-quadrature-h): Private ordinary functions
Function, (setf iterative-quadrature-n): Private ordinary functions
Function, (setf iterative-quadrature-sum): Private ordinary functions
Function, (setf max-error): Public ordinary functions
Function, (setf mean-error): Public ordinary functions
Function, (setf midpoint-quadrature-a): Private ordinary functions
Function, (setf midpoint-quadrature-b): Private ordinary functions
Function, (setf midpoint-quadrature-f): Private ordinary functions
Function, (setf midpoint-quadrature-h): Private ordinary functions
Function, (setf midpoint-quadrature-n): Private ordinary functions
Function, (setf midpoint-quadrature-sum): Private ordinary functions
Function, (setf min-error): Public ordinary functions
Function, (setf richardson-extrapolation-coefficient): Private ordinary functions
Function, (setf richardson-extrapolation-diagonal): Private ordinary functions
Function, (setf richardson-extrapolation-n): Private ordinary functions
Function, (setf rms): Public ordinary functions
Function, (setf sorted-reals-ordered-elements): Private ordinary functions
Function, (setf sorted-reals-unordered-elements): Private ordinary functions
Function, (setf tally-mixin-w): Private ordinary functions
Function, (setf test-count): Public ordinary functions
Function, (setf trapezoidal-quadrature-a): Private ordinary functions
Function, (setf trapezoidal-quadrature-b): Private ordinary functions
Function, (setf trapezoidal-quadrature-f): Private ordinary functions
Function, (setf trapezoidal-quadrature-h): Private ordinary functions
Function, (setf trapezoidal-quadrature-n): Private ordinary functions
Function, (setf trapezoidal-quadrature-sum): Private ordinary functions
Function, (setf variance0): Public ordinary functions
Function, (setf variance1): Public ordinary functions
Function, (setf worst-case): Public ordinary functions
Function, 1c: Public ordinary functions
Function, <: Public ordinary functions
Function, <=: Public ordinary functions
Function, =: Public ordinary functions
Function, >: Public ordinary functions
Function, >=: Public ordinary functions
Function, ab-to-cd-intercept-slope: Private ordinary functions
Function, ab-to-cinf: Private ordinary functions
Function, above-diagonal?: Private ordinary functions
Function, abs-diff: Public ordinary functions
Function, absolute-square: Public ordinary functions
Function, as-double-float: Public ordinary functions
Function, as-integer: Public ordinary functions
Function, as-simple-fixnum-vector: Public ordinary functions
Function, below-diagonal?: Private ordinary functions
Function, bic: Public ordinary functions
Function, binary-search: Public ordinary functions
Function, ceiling*: Public ordinary functions
Function, central-sample-moments-degree: Public ordinary functions
Function, central-sample-moments-m: Private ordinary functions
Function, central-sample-moments-p: Private ordinary functions
Function, central-sample-moments-s2: Private ordinary functions
Function, central-sample-moments-s3: Private ordinary functions
Function, central-sample-moments-s4: Private ordinary functions
Function, central-sample-moments-w: Private ordinary functions
Function, chebyshev-approximate: Public ordinary functions
Function, chebyshev-recursion: Private ordinary functions
Function, chebyshev-regression: Public ordinary functions
Function, chebyshev-root: Public ordinary functions
Function, chebyshev-roots: Public ordinary functions
Function, cinf-to-ab: Private ordinary functions
Function, compare-fns: Public ordinary functions
Function, compare-vectors: Public ordinary functions
Function, copy-central-sample-moments: Private ordinary functions
Function, copy-diagonal-matrix: Private ordinary functions
Function, copy-hermitian-matrix: Private ordinary functions
Function, copy-iterative-quadrature: Private ordinary functions
Function, copy-lower-triangular-matrix: Private ordinary functions
Function, copy-midpoint-quadrature: Private ordinary functions
Function, copy-relative: Private ordinary functions
Function, copy-richardson-extrapolation: Private ordinary functions
Function, copy-sorted-reals: Private ordinary functions
Function, copy-spacer: Private ordinary functions
Function, copy-sparse-counter: Private ordinary functions
Function, copy-tally-mixin: Private ordinary functions
Function, copy-test-results: Private ordinary functions
Function, copy-trapezoidal-quadrature: Private ordinary functions
Function, copy-upper-triangular-matrix: Private ordinary functions
Function, copy-wrapped-matrix: Private ordinary functions
Function, cross-tabulate: Public ordinary functions
Function, cube: Public ordinary functions
Function, cumulative-product: Public ordinary functions
Function, cumulative-sum: Public ordinary functions
Function, diagonal-matrix: Public ordinary functions
Function, diagonal-matrix-elements: Public ordinary functions
Function, diagonal-matrix-p: Private ordinary functions
Function, diagonal-mx: Public ordinary functions
Function, divides?: Public ordinary functions
Function, e*: Public ordinary functions
Function, e+: Public ordinary functions
Function, e-: Public ordinary functions
Function, e/: Public ordinary functions
Function, elementwise-float-contagion: Public ordinary functions
Function, elog: Public ordinary functions
Function, emax: Public ordinary functions
Function, emin: Public ordinary functions
Function, empirical-quantile: Public ordinary functions
Function, empirical-quantile-probabilities: Public ordinary functions
Function, ensure-sorted-vector: Public ordinary functions
Function, ensure-valid-elements: Private ordinary functions
Function, evaluate-chebyshev: Public ordinary functions
Function, evaluate-polynomial: Public ordinary functions
Function, exp-1: Public ordinary functions
Function, exp-1/x: Public ordinary functions
Function, expt-1: Public ordinary functions
Function, extend-pairwise-comparison: Private ordinary functions
Function, fixnum?: Public ordinary functions
Function, floor*: Public ordinary functions
Function, generate-sequence: Public ordinary functions
Function, grid-in: Public ordinary functions
Function, hermitian-matrix: Public ordinary functions
Function, hermitian-matrix-elements: Private ordinary functions
Function, hermitian-matrix-p: Private ordinary functions
Function, hypot: Public ordinary functions
Function, in-interval?: Public ordinary functions
Function, infinite?: Public ordinary functions
Function, interval: Public ordinary functions
Function, interval-hull: Public ordinary functions
Function, interval-length: Public ordinary functions
Function, interval-midpoint: Public ordinary functions
Function, iterative-quadrature-a: Private ordinary functions
Function, iterative-quadrature-b: Private ordinary functions
Function, iterative-quadrature-f: Private ordinary functions
Function, iterative-quadrature-h: Private ordinary functions
Function, iterative-quadrature-n: Private ordinary functions
Function, iterative-quadrature-p: Private ordinary functions
Function, iterative-quadrature-sum: Private ordinary functions
Function, ivec: Public ordinary functions
Function, l2norm: Public ordinary functions
Function, ln: Private ordinary functions
Function, log1+: Public ordinary functions
Function, log1+/x: Public ordinary functions
Function, log1+exp: Public ordinary functions
Function, log1-: Public ordinary functions
Function, log1-exp: Public ordinary functions
Function, log10: Public ordinary functions
Function, log1pmx: Public ordinary functions
Function, log2: Public ordinary functions
Function, log2-exp: Public ordinary functions
Function, logexp-1: Public ordinary functions
Function, lower-triangular-matrix: Public ordinary functions
Function, lower-triangular-matrix-elements: Private ordinary functions
Function, lower-triangular-matrix-p: Private ordinary functions
Function, make-central-sample-moments: Private ordinary functions
Function, make-diagonal-matrix: Private ordinary functions
Function, make-hermitian-matrix: Private ordinary functions
Function, make-iterative-quadrature: Private ordinary functions
Function, make-lower-triangular-matrix: Private ordinary functions
Function, make-sorted-reals: Private ordinary functions
Function, make-sparse-counter: Public ordinary functions
Function, make-sparse-counter%: Private ordinary functions
Function, make-tally-mixin: Private ordinary functions
Function, make-test-results: Private ordinary functions
Function, make-upper-triangular-matrix: Private ordinary functions
Function, make-vector: Public ordinary functions
Function, make-wrapped-matrix: Private ordinary functions
Function, max-error: Public ordinary functions
Function, mean-error: Public ordinary functions
Function, midpoint-quadrature: Private ordinary functions
Function, midpoint-quadrature%: Private ordinary functions
Function, midpoint-quadrature-a: Private ordinary functions
Function, midpoint-quadrature-b: Private ordinary functions
Function, midpoint-quadrature-f: Private ordinary functions
Function, midpoint-quadrature-h: Private ordinary functions
Function, midpoint-quadrature-n: Private ordinary functions
Function, midpoint-quadrature-p: Private ordinary functions
Function, midpoint-quadrature-sum: Private ordinary functions
Function, min-error: Public ordinary functions
Function, narrow-bracket?: Private ordinary functions
Function, near-root?: Private ordinary functions
Function, normalize-probabilities: Public ordinary functions
Function, num-delta: Public ordinary functions
Function, num=-function: Public ordinary functions
Function, numseq: Public ordinary functions
Function, opposite-sign?: Private ordinary functions
Function, pad-left-expansion: Private ordinary functions
Function, plusminus-interval: Public ordinary functions
Function, pool: Public ordinary functions
Function, print-length-truncate: Public ordinary functions
Function, print-matrix: Public ordinary functions
Function, print-matrix-formatter: Private ordinary functions
Function, relative: Public ordinary functions
Function, relative-fraction: Private ordinary functions
Function, relative-p: Private ordinary functions
Function, richardson-extrapolation: Private ordinary functions
Function, richardson-extrapolation-coefficient: Private ordinary functions
Function, richardson-extrapolation-diagonal: Private ordinary functions
Function, richardson-extrapolation-n: Private ordinary functions
Function, richardson-extrapolation-p: Private ordinary functions
Function, richardson-iteration: Private ordinary functions
Function, rms: Public ordinary functions
Function, romberg-quadrature: Public ordinary functions
Function, romberg-quadrature%: Private ordinary functions
Function, root-bisection: Public ordinary functions
Function, rootfinding-delta: Private ordinary functions
Function, round*: Public ordinary functions
Function, same-sign-p: Public ordinary functions
Function, sequence-maximum: Public ordinary functions
Function, sequence-minimum: Public ordinary functions
Function, sequencep: Public ordinary functions
Function, shrink-interval: Public ordinary functions
Function, similar-element-type: Private ordinary functions
Function, similar-sequence-type: Private ordinary functions
Function, sort-reals: Private ordinary functions
Function, sorted-reals-elements: Public ordinary functions
Function, sorted-reals-ordered-elements: Private ordinary functions
Function, sorted-reals-p: Private ordinary functions
Function, sorted-reals-unordered-elements: Private ordinary functions
Function, spacer: Public ordinary functions
Function, spacer-p: Private ordinary functions
Function, spacer-weight: Private ordinary functions
Function, sparse-counter-count: Public ordinary functions
Function, sparse-counter-p: Private ordinary functions
Function, sparse-counter-table: Public ordinary functions
Function, split-interval: Public ordinary functions
Function, square: Public ordinary functions
Function, subintervals-in: Public ordinary functions
Function, tabulate: Public ordinary functions
Function, tally-mixin-p: Private ordinary functions
Function, tally-mixin-w: Private ordinary functions
Function, test-count: Public ordinary functions
Function, test-fn: Public ordinary functions
Function, test-results-p: Private ordinary functions
Function, trapezoidal-quadrature: Private ordinary functions
Function, trapezoidal-quadrature%: Private ordinary functions
Function, trapezoidal-quadrature-a: Private ordinary functions
Function, trapezoidal-quadrature-b: Private ordinary functions
Function, trapezoidal-quadrature-f: Private ordinary functions
Function, trapezoidal-quadrature-h: Private ordinary functions
Function, trapezoidal-quadrature-n: Private ordinary functions
Function, trapezoidal-quadrature-p: Private ordinary functions
Function, trapezoidal-quadrature-sum: Private ordinary functions
Function, truncate*: Public ordinary functions
Function, upper-triangular-matrix: Public ordinary functions
Function, upper-triangular-matrix-elements: Private ordinary functions
Function, upper-triangular-matrix-p: Private ordinary functions
Function, valid-sparse-type?: Private ordinary functions
Function, variance0: Public ordinary functions
Function, variance1: Public ordinary functions
Function, vec: Public ordinary functions
Function, weighted-empirical-quantile: Private ordinary functions
Function, weighted-quantile-p-table: Private ordinary functions
Function, weighted-quantiles: Public ordinary functions
Function, within?: Public ordinary functions
Function, worst-case: Public ordinary functions
Function, wrapped-matrix-elements: Public ordinary functions
Function, wrapped-matrix-p: Private ordinary functions
Function, zero-like: Private ordinary functions

G
generate-sequence: Public ordinary functions
Generic Function, (setf diagonal-vector): Public generic functions
Generic Function, add: Public generic functions
Generic Function, as-alist: Public generic functions
Generic Function, as-plist: Public generic functions
Generic Function, central-m2: Public generic functions
Generic Function, central-m3: Public generic functions
Generic Function, central-m4: Public generic functions
Generic Function, central-sample-moments: Public generic functions
Generic Function, chebyshev-approximate-implementation: Private generic functions
Generic Function, diagonal-vector: Public generic functions
Generic Function, e1-: Public generic functions
Generic Function, e1/: Public generic functions
Generic Function, e1log: Public generic functions
Generic Function, e2*: Public generic functions
Generic Function, e2+: Public generic functions
Generic Function, e2-: Public generic functions
Generic Function, e2/: Public generic functions
Generic Function, e2log: Public generic functions
Generic Function, eceiling: Public generic functions
Generic Function, econjugate: Public generic functions
Generic Function, eexp: Public generic functions
Generic Function, eexpt: Public generic functions
Generic Function, efloor: Public generic functions
Generic Function, emod: Public generic functions
Generic Function, ensure-sorted-reals: Public generic functions
Generic Function, ereduce: Public generic functions
Generic Function, esqrt: Public generic functions
Generic Function, esquare: Private generic functions
Generic Function, extend-interval: Public generic functions
Generic Function, kurtosis: Public generic functions
Generic Function, l2norm-square: Public generic functions
Generic Function, left: Public generic functions
Generic Function, map-array: Public generic functions
Generic Function, mean: Public generic functions
Generic Function, median: Public generic functions
Generic Function, num=: Public generic functions
Generic Function, open-left?: Public generic functions
Generic Function, open-right?: Public generic functions
Generic Function, pool2: Private generic functions
Generic Function, print-left-endpoint: Private generic functions
Generic Function, print-right-endpoint: Private generic functions
Generic Function, product: Public generic functions
Generic Function, quantile: Public generic functions
Generic Function, quantiles: Public generic functions
Generic Function, refine-quadrature: Private generic functions
Generic Function, richardson-coefficient: Private generic functions
Generic Function, right: Public generic functions
Generic Function, sd: Public generic functions
Generic Function, shift-interval: Public generic functions
Generic Function, skewness: Public generic functions
Generic Function, sum: Public generic functions
Generic Function, tally: Public generic functions
Generic Function, transformed-quadrature: Private generic functions
Generic Function, transpose: Public generic functions
Generic Function, variance: Public generic functions
gethash*: Public macros
grid-in: Public ordinary functions

H
hermitian-matrix: Public ordinary functions
hermitian-matrix-elements: Private ordinary functions
hermitian-matrix-p: Private ordinary functions
hermitian-mx: Public macros
hypot: Public ordinary functions

I
in-interval?: Public ordinary functions
infinite?: Public ordinary functions
initialize-instance: Public standalone methods
interval: Public ordinary functions
interval-hull: Public ordinary functions
interval-length: Public ordinary functions
interval-midpoint: Public ordinary functions
iterative-quadrature-a: Private ordinary functions
iterative-quadrature-b: Private ordinary functions
iterative-quadrature-f: Private ordinary functions
iterative-quadrature-h: Private ordinary functions
iterative-quadrature-n: Private ordinary functions
iterative-quadrature-p: Private ordinary functions
iterative-quadrature-sum: Private ordinary functions
ivec: Public ordinary functions

K
kurtosis: Public generic functions
kurtosis: Public generic functions
kurtosis: Public generic functions

L
l2norm: Public ordinary functions
l2norm-square: Public generic functions
l2norm-square: Public generic functions
lambda-template: Public macros
left: Public generic functions
left: Public generic functions
left: Public generic functions
ln: Private ordinary functions
log1+: Public ordinary functions
log1+/x: Public ordinary functions
log1+exp: Public ordinary functions
log1-: Public ordinary functions
log1-exp: Public ordinary functions
log10: Public ordinary functions
log1pmx: Public ordinary functions
log2: Public ordinary functions
log2-exp: Public ordinary functions
logexp-1: Public ordinary functions
lower-triangular-matrix: Public ordinary functions
lower-triangular-matrix-elements: Private ordinary functions
lower-triangular-matrix-p: Private ordinary functions
lower-triangular-mx: Public macros

M
Macro, &diagonal-matrix: Private macros
Macro, &diagonal-matrix-r/o: Private macros
Macro, &interval: Public macros
Macro, &sorted-reals: Private macros
Macro, &sorted-reals-r/o: Private macros
Macro, check-types: Public macros
Macro, curry*: Public macros
Macro, define-central-sample-moment: Private macros
Macro, define-comparison: Private macros
Macro, define-e&: Private macros
Macro, define-e1: Private macros
Macro, define-e2: Private macros
Macro, define-elementwise-as-array: Private macros
Macro, define-elementwise-reduction: Private macros
Macro, define-elementwise-same-class: Private macros
Macro, define-elementwise-univariate: Private macros
Macro, define-elementwise-with-constant: Private macros
Macro, define-num=-with-accessors: Public macros
Macro, define-rounding-with-offset: Private macros
Macro, define-structure-num=: Public macros
Macro, define-with-multiple-bindings: Public macros
Macro, define-wrapped-matrix: Private macros
Macro, expanding: Public macros
Macro, extendf-interval: Public macros
Macro, gethash*: Public macros
Macro, hermitian-mx: Public macros
Macro, lambda-template: Public macros
Macro, lower-triangular-mx: Public macros
Macro, mapping-array: Private macros
Macro, multf: Public macros
Macro, mx: Public macros
Macro, splice-awhen: Public macros
Macro, splice-when: Public macros
Macro, univariate-rootfinder-loop%: Private macros
Macro, unlessf: Public macros
Macro, upper-triangular-mx: Public macros
Macro, with-double-floats: Public macros
Macro, with-template: Public macros
make-central-sample-moments: Private ordinary functions
make-diagonal-matrix: Private ordinary functions
make-hermitian-matrix: Private ordinary functions
make-iterative-quadrature: Private ordinary functions
make-lower-triangular-matrix: Private ordinary functions
make-sorted-reals: Private ordinary functions
make-sparse-counter: Public ordinary functions
make-sparse-counter%: Private ordinary functions
make-tally-mixin: Private ordinary functions
make-test-results: Private ordinary functions
make-upper-triangular-matrix: Private ordinary functions
make-vector: Public compiler macros
make-vector: Public ordinary functions
make-wrapped-matrix: Private ordinary functions
map-array: Public generic functions
map-array: Public generic functions
mapping-array: Private macros
max-error: Public ordinary functions
mean: Public generic functions
mean: Public generic functions
mean: Public generic functions
mean-error: Public ordinary functions
median: Public generic functions
median: Public generic functions
median: Public generic functions
Method, (setf diagonal-vector): Public generic functions
Method, add: Public generic functions
Method, add: Public generic functions
Method, add: Public generic functions
Method, add: Public generic functions
Method, as-alist: Public generic functions
Method, as-array: Public standalone methods
Method, as-array: Public standalone methods
Method, as-array: Public standalone methods
Method, as-array: Public standalone methods
Method, as-plist: Public generic functions
Method, central-m2: Public generic functions
Method, central-m2: Public generic functions
Method, central-m3: Public generic functions
Method, central-m3: Public generic functions
Method, central-m4: Public generic functions
Method, central-m4: Public generic functions
Method, central-sample-moments: Public generic functions
Method, central-sample-moments: Public generic functions
Method, central-sample-moments: Public generic functions
Method, chebyshev-approximate-implementation: Private generic functions
Method, chebyshev-approximate-implementation: Private generic functions
Method, diagonal-vector: Public generic functions
Method, diagonal-vector: Public generic functions
Method, dims: Public standalone methods
Method, dims: Public standalone methods
Method, e1-: Public generic functions
Method, e1-: Public generic functions
Method, e1-: Public generic functions
Method, e1-: Public generic functions
Method, e1-: Public generic functions
Method, e1-: Public generic functions
Method, e1/: Public generic functions
Method, e1/: Public generic functions
Method, e1/: Public generic functions
Method, e1/: Public generic functions
Method, e1/: Public generic functions
Method, e1/: Public generic functions
Method, e1log: Public generic functions
Method, e1log: Public generic functions
Method, e1log: Public generic functions
Method, e1log: Public generic functions
Method, e1log: Public generic functions
Method, e1log: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2*: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2+: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2-: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2/: Public generic functions
Method, e2log: Public generic functions
Method, e2log: Public generic functions
Method, e2log: Public generic functions
Method, e2log: Public generic functions
Method, e2log: Public generic functions
Method, e2log: Public generic functions
Method, e2log: Public generic functions
Method, eceiling: Public generic functions
Method, eceiling: Public generic functions
Method, econjugate: Public generic functions
Method, econjugate: Public generic functions
Method, eexp: Public generic functions
Method, eexp: Public generic functions
Method, eexp: Public generic functions
Method, eexp: Public generic functions
Method, eexp: Public generic functions
Method, eexp: Public generic functions
Method, eexpt: Public generic functions
Method, eexpt: Public generic functions
Method, eexpt: Public generic functions
Method, eexpt: Public generic functions
Method, eexpt: Public generic functions
Method, eexpt: Public generic functions
Method, eexpt: Public generic functions
Method, efloor: Public generic functions
Method, efloor: Public generic functions
Method, element-type: Public standalone methods
Method, element-type: Public standalone methods
Method, emod: Public generic functions
Method, emod: Public generic functions
Method, emod: Public generic functions
Method, emod: Public generic functions
Method, emod: Public generic functions
Method, emod: Public generic functions
Method, emod: Public generic functions
Method, ensure-sorted-reals: Public generic functions
Method, ensure-sorted-reals: Public generic functions
Method, ensure-sorted-reals: Public generic functions
Method, ereduce: Public generic functions
Method, ereduce: Public generic functions
Method, ereduce: Public generic functions
Method, esqrt: Public generic functions
Method, esqrt: Public generic functions
Method, esqrt: Public generic functions
Method, esqrt: Public generic functions
Method, esqrt: Public generic functions
Method, esqrt: Public generic functions
Method, esquare: Private generic functions
Method, esquare: Private generic functions
Method, extend-interval: Public generic functions
Method, extend-interval: Public generic functions
Method, extend-interval: Public generic functions
Method, extend-interval: Public generic functions
Method, extend-interval: Public generic functions
Method, extend-interval: Public generic functions
Method, initialize-instance: Public standalone methods
Method, kurtosis: Public generic functions
Method, kurtosis: Public generic functions
Method, l2norm-square: Public generic functions
Method, left: Public generic functions
Method, left: Public generic functions
Method, map-array: Public generic functions
Method, mean: Public generic functions
Method, mean: Public generic functions
Method, median: Public generic functions
Method, median: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, num=: Public generic functions
Method, open-left?: Public generic functions
Method, open-left?: Public generic functions
Method, open-right?: Public generic functions
Method, open-right?: Public generic functions
Method, pool2: Private generic functions
Method, print-left-endpoint: Private generic functions
Method, print-left-endpoint: Private generic functions
Method, print-object: Public standalone methods
Method, print-object: Public standalone methods
Method, print-object: Public standalone methods
Method, print-object: Public standalone methods
Method, print-object: Public standalone methods
Method, print-object: Public standalone methods
Method, print-right-endpoint: Private generic functions
Method, print-right-endpoint: Private generic functions
Method, product: Public generic functions
Method, product: Public generic functions
Method, quantile: Public generic functions
Method, quantile: Public generic functions
Method, quantiles: Public generic functions
Method, quantiles: Public generic functions
Method, refine-quadrature: Private generic functions
Method, refine-quadrature: Private generic functions
Method, richardson-coefficient: Private generic functions
Method, richardson-coefficient: Private generic functions
Method, right: Public generic functions
Method, right: Public generic functions
Method, sd: Public generic functions
Method, select: Public standalone methods
Method, select: Public standalone methods
Method, select: Public standalone methods
Method, shift-interval: Public generic functions
Method, skewness: Public generic functions
Method, skewness: Public generic functions
Method, sum: Public generic functions
Method, sum: Public generic functions
Method, tally: Public generic functions
Method, tally: Public generic functions
Method, transformed-quadrature: Private generic functions
Method, transformed-quadrature: Private generic functions
Method, transpose: Public generic functions
Method, transpose: Public generic functions
Method, transpose: Public generic functions
Method, transpose: Public generic functions
Method, transpose: Public generic functions
Method, variance: Public generic functions
Method, variance: Public generic functions
midpoint-quadrature: Private ordinary functions
midpoint-quadrature%: Private ordinary functions
midpoint-quadrature-a: Private ordinary functions
midpoint-quadrature-b: Private ordinary functions
midpoint-quadrature-f: Private ordinary functions
midpoint-quadrature-h: Private ordinary functions
midpoint-quadrature-n: Private ordinary functions
midpoint-quadrature-p: Private ordinary functions
midpoint-quadrature-sum: Private ordinary functions
min-error: Public ordinary functions
multf: Public macros
mx: Public macros

N
narrow-bracket?: Private ordinary functions
near-root?: Private ordinary functions
normalize-probabilities: Public ordinary functions
num-delta: Public ordinary functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=: Public generic functions
num=-function: Public ordinary functions
numseq: Public ordinary functions

O
open-left?: Public generic functions
open-left?: Public generic functions
open-left?: Public generic functions
open-right?: Public generic functions
open-right?: Public generic functions
open-right?: Public generic functions
opposite-sign?: Private ordinary functions

P
pad-left-expansion: Private ordinary functions
plusminus-interval: Public ordinary functions
pool: Public ordinary functions
pool2: Private generic functions
pool2: Private generic functions
print-left-endpoint: Private generic functions
print-left-endpoint: Private generic functions
print-left-endpoint: Private generic functions
print-length-truncate: Public ordinary functions
print-matrix: Public ordinary functions
print-matrix-formatter: Private ordinary functions
print-object: Public standalone methods
print-object: Public standalone methods
print-object: Public standalone methods
print-object: Public standalone methods
print-object: Public standalone methods
print-object: Public standalone methods
print-right-endpoint: Private generic functions
print-right-endpoint: Private generic functions
print-right-endpoint: Private generic functions
product: Public generic functions
product: Public generic functions
product: Public generic functions

Q
quantile: Public generic functions
quantile: Public generic functions
quantile: Public generic functions
quantiles: Public generic functions
quantiles: Public generic functions
quantiles: Public generic functions

R
refine-quadrature: Private generic functions
refine-quadrature: Private generic functions
refine-quadrature: Private generic functions
relative: Public ordinary functions
relative-fraction: Private ordinary functions
relative-p: Private ordinary functions
richardson-coefficient: Private generic functions
richardson-coefficient: Private generic functions
richardson-coefficient: Private generic functions
richardson-extrapolation: Private ordinary functions
richardson-extrapolation-coefficient: Private ordinary functions
richardson-extrapolation-diagonal: Private ordinary functions
richardson-extrapolation-n: Private ordinary functions
richardson-extrapolation-p: Private ordinary functions
richardson-iteration: Private ordinary functions
right: Public generic functions
right: Public generic functions
right: Public generic functions
rms: Public ordinary functions
romberg-quadrature: Public ordinary functions
romberg-quadrature%: Private ordinary functions
root-bisection: Public ordinary functions
rootfinding-delta: Private ordinary functions
round*: Public ordinary functions

S
same-sign-p: Public ordinary functions
sd: Public generic functions
sd: Public generic functions
select: Public standalone methods
select: Public standalone methods
select: Public standalone methods
sequence-maximum: Public ordinary functions
sequence-minimum: Public ordinary functions
sequencep: Public ordinary functions
shift-interval: Public generic functions
shift-interval: Public generic functions
shrink-interval: Public ordinary functions
similar-element-type: Private ordinary functions
similar-sequence-type: Private ordinary functions
skewness: Public generic functions
skewness: Public generic functions
skewness: Public generic functions
sort-reals: Private ordinary functions
sorted-reals-elements: Public ordinary functions
sorted-reals-ordered-elements: Private ordinary functions
sorted-reals-p: Private ordinary functions
sorted-reals-unordered-elements: Private ordinary functions
spacer: Public ordinary functions
spacer-p: Private ordinary functions
spacer-weight: Private ordinary functions
sparse-counter-count: Public ordinary functions
sparse-counter-p: Private ordinary functions
sparse-counter-table: Public ordinary functions
splice-awhen: Public macros
splice-when: Public macros
split-interval: Public ordinary functions
square: Public ordinary functions
subintervals-in: Public ordinary functions
sum: Public generic functions
sum: Public generic functions
sum: Public generic functions

T
tabulate: Public ordinary functions
tally: Public generic functions
tally: Public generic functions
tally: Public generic functions
tally-mixin-p: Private ordinary functions
tally-mixin-w: Private ordinary functions
test-count: Public ordinary functions
test-fn: Public ordinary functions
test-results-p: Private ordinary functions
transformed-quadrature: Private generic functions
transformed-quadrature: Private generic functions
transformed-quadrature: Private generic functions
transpose: Public generic functions
transpose: Public generic functions
transpose: Public generic functions
transpose: Public generic functions
transpose: Public generic functions
transpose: Public generic functions
trapezoidal-quadrature: Private ordinary functions
trapezoidal-quadrature%: Private ordinary functions
trapezoidal-quadrature-a: Private ordinary functions
trapezoidal-quadrature-b: Private ordinary functions
trapezoidal-quadrature-f: Private ordinary functions
trapezoidal-quadrature-h: Private ordinary functions
trapezoidal-quadrature-n: Private ordinary functions
trapezoidal-quadrature-p: Private ordinary functions
trapezoidal-quadrature-sum: Private ordinary functions
truncate*: Public ordinary functions

U
univariate-rootfinder-loop%: Private macros
unlessf: Public macros
upper-triangular-matrix: Public ordinary functions
upper-triangular-matrix-elements: Private ordinary functions
upper-triangular-matrix-p: Private ordinary functions
upper-triangular-mx: Public macros

V
valid-sparse-type?: Private ordinary functions
variance: Public generic functions
variance: Public generic functions
variance: Public generic functions
variance0: Public ordinary functions
variance1: Public ordinary functions
vec: Public ordinary functions

W
weighted-empirical-quantile: Private ordinary functions
weighted-quantile-p-table: Private ordinary functions
weighted-quantiles: Public ordinary functions
with-double-floats: Public macros
with-template: Public macros
within?: Public ordinary functions
worst-case: Public ordinary functions
wrapped-matrix-elements: Public ordinary functions
wrapped-matrix-p: Private ordinary functions

Z
zero-like: Private ordinary functions

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A.3 Variables

Jump to:   *  
A   B   C   D   E   F   H   L   M   N   O   R   S   T   U   V   W  
Index Entry  Section

*
*central-sample-moments-default-degree*: Public special variables
*num=-tolerance*: Public special variables
*print-matrix-precision*: Public special variables
*rootfinding-delta-relative*: Public special variables
*rootfinding-epsilon*: Public special variables

A
a: Private structures

B
b: Private structures

C
coefficient: Private structures

D
diagonal: Private structures

E
elements: Public structures
elements: Public structures

F
f: Private structures
fraction: Public structures

H
h: Private structures

L
left: Private classes

M
m: Public structures
max-error: Public structures
mean-error: Public structures
min-error: Public structures

N
n: Private structures
n: Private structures

O
open-left?: Private classes
open-right?: Private classes
ordered-elements: Public structures

R
right: Private classes
rms: Public structures

S
s2: Public structures
s3: Public structures
s4: Public structures
Slot, a: Private structures
Slot, b: Private structures
Slot, coefficient: Private structures
Slot, diagonal: Private structures
Slot, elements: Public structures
Slot, elements: Public structures
Slot, f: Private structures
Slot, fraction: Public structures
Slot, h: Private structures
Slot, left: Private classes
Slot, m: Public structures
Slot, max-error: Public structures
Slot, mean-error: Public structures
Slot, min-error: Public structures
Slot, n: Private structures
Slot, n: Private structures
Slot, open-left?: Private classes
Slot, open-right?: Private classes
Slot, ordered-elements: Public structures
Slot, right: Private classes
Slot, rms: Public structures
Slot, s2: Public structures
Slot, s3: Public structures
Slot, s4: Public structures
Slot, sum: Private structures
Slot, table: Public structures
Slot, test-count: Public structures
Slot, unordered-elements: Public structures
Slot, variance0: Public structures
Slot, variance1: Public structures
Slot, w: Private structures
Slot, weight: Public structures
Slot, worst-case: Public structures
Special Variable, *central-sample-moments-default-degree*: Public special variables
Special Variable, *num=-tolerance*: Public special variables
Special Variable, *print-matrix-precision*: Public special variables
Special Variable, *rootfinding-delta-relative*: Public special variables
Special Variable, *rootfinding-epsilon*: Public special variables
sum: Private structures

T
table: Public structures
test-count: Public structures

U
unordered-elements: Public structures

V
variance0: Public structures
variance1: Public structures

W
w: Private structures
weight: Public structures
worst-case: Public structures

Jump to:   *  
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Previous: , Up: Indexes   [Contents][Index]

A.4 Data types

Jump to:   A   C   D   E   F   H   I   L   M   N   P   Q   R   S   T   U   W  
Index Entry  Section

A
arithmetic.lisp: The num-utils/arithmetic․lisp file

C
central-sample-moments: Public structures
chebyshev.lisp: The num-utils/chebyshev․lisp file
Class, finite-interval: Public classes
Class, interval: Public classes
Class, interval/finite-left: Private classes
Class, interval/finite-right: Private classes
Class, interval/infinite-left: Private classes
Class, interval/infinite-right: Private classes
Class, minusinf-interval: Public classes
Class, plusinf-interval: Public classes
Class, real-line: Public classes
common-package.lisp: The num-utils/common-package․lisp file
Condition, empty-accumulator: Public conditions
Condition, information-not-collected-in-accumulator: Public conditions
Condition, not-enough-elements-in-accumulator: Public conditions

D
diagonal-matrix: Public structures

E
elementwise.lisp: The num-utils/elementwise․lisp file
empty-accumulator: Public conditions
extended-real: Public types
extended-real.lisp: The num-utils/extended-real․lisp file

F
File, arithmetic.lisp: The num-utils/arithmetic․lisp file
File, chebyshev.lisp: The num-utils/chebyshev․lisp file
File, common-package.lisp: The num-utils/common-package․lisp file
File, elementwise.lisp: The num-utils/elementwise․lisp file
File, extended-real.lisp: The num-utils/extended-real․lisp file
File, interval.lisp: The num-utils/interval․lisp file
File, log-exp.lisp: The num-utils/log-exp․lisp file
File, matrix-shorthand.lisp: The num-utils/matrix-shorthand․lisp file
File, matrix.lisp: The num-utils/matrix․lisp file
File, num-utils.asd: The num-utils/num-utils․asd file
File, num=.lisp: The num-utils/num=․lisp file
File, packages.lisp: The num-utils/packages․lisp file
File, polynomial.lisp: The num-utils/polynomial․lisp file
File, print-matrix.lisp: The num-utils/print-matrix․lisp file
File, quadrature.lisp: The num-utils/quadrature․lisp file
File, rootfinding.lisp: The num-utils/rootfinding․lisp file
File, statistics.lisp: The num-utils/statistics․lisp file
File, test-utilities.lisp: The num-utils/test-utilities․lisp file
File, utilities.lisp: The num-utils/utilities․lisp file
finite-interval: Public classes

H
hermitian-matrix: Public structures

I
infinite: Private types
information-not-collected-in-accumulator: Public conditions
interval: Public classes
interval.lisp: The num-utils/interval․lisp file
interval/finite-left: Private classes
interval/finite-right: Private classes
interval/infinite-left: Private classes
interval/infinite-right: Private classes
iterative-quadrature: Private structures

L
log-exp.lisp: The num-utils/log-exp․lisp file
lower-triangular-matrix: Public structures

M
matrix-shorthand.lisp: The num-utils/matrix-shorthand․lisp file
matrix.lisp: The num-utils/matrix․lisp file
midpoint-quadrature: Private structures
minusinf-interval: Public classes

N
not-enough-elements-in-accumulator: Public conditions
num-utils: The num-utils system
num-utils: The num-utils package
num-utils.arithmetic: The num-utils․arithmetic package
num-utils.asd: The num-utils/num-utils․asd file
num-utils.chebyshev: The num-utils․chebyshev package
num-utils.elementwise: The num-utils․elementwise package
num-utils.extended-real: The num-utils․extended-real package
num-utils.interval: The num-utils․interval package
num-utils.log-exp: The num-utils․log-exp package
num-utils.matrix: The num-utils․matrix package
num-utils.matrix-shorthand: The num-utils․matrix-shorthand package
num-utils.num=: The num-utils․num= package
num-utils.polynomial: The num-utils․polynomial package
num-utils.print-matrix: The num-utils․print-matrix package
num-utils.quadrature: The num-utils․quadrature package
num-utils.rootfinding: The num-utils․rootfinding package
num-utils.statistics: The num-utils․statistics package
num-utils.test-utilities: The num-utils․test-utilities package
num-utils.utilities: The num-utils․utilities package
num=.lisp: The num-utils/num=․lisp file

P
Package, num-utils: The num-utils package
Package, num-utils.arithmetic: The num-utils․arithmetic package
Package, num-utils.chebyshev: The num-utils․chebyshev package
Package, num-utils.elementwise: The num-utils․elementwise package
Package, num-utils.extended-real: The num-utils․extended-real package
Package, num-utils.interval: The num-utils․interval package
Package, num-utils.log-exp: The num-utils․log-exp package
Package, num-utils.matrix: The num-utils․matrix package
Package, num-utils.matrix-shorthand: The num-utils․matrix-shorthand package
Package, num-utils.num=: The num-utils․num= package
Package, num-utils.polynomial: The num-utils․polynomial package
Package, num-utils.print-matrix: The num-utils․print-matrix package
Package, num-utils.quadrature: The num-utils․quadrature package
Package, num-utils.rootfinding: The num-utils․rootfinding package
Package, num-utils.statistics: The num-utils․statistics package
Package, num-utils.test-utilities: The num-utils․test-utilities package
Package, num-utils.utilities: The num-utils․utilities package
packages.lisp: The num-utils/packages․lisp file
plusinf-interval: Public classes
polynomial.lisp: The num-utils/polynomial․lisp file
print-matrix.lisp: The num-utils/print-matrix․lisp file

Q
quadrature.lisp: The num-utils/quadrature․lisp file

R
real-line: Public classes
relative: Public structures
richardson-extrapolation: Private structures
rootfinding.lisp: The num-utils/rootfinding․lisp file

S
simple-double-float-vector: Public types
simple-fixnum-vector: Public types
simple-single-float-vector: Public types
sorted-reals: Public structures
spacer: Public structures
sparse-counter: Public structures
statistics.lisp: The num-utils/statistics․lisp file
Structure, central-sample-moments: Public structures
Structure, diagonal-matrix: Public structures
Structure, hermitian-matrix: Public structures
Structure, iterative-quadrature: Private structures
Structure, lower-triangular-matrix: Public structures
Structure, midpoint-quadrature: Private structures
Structure, relative: Public structures
Structure, richardson-extrapolation: Private structures
Structure, sorted-reals: Public structures
Structure, spacer: Public structures
Structure, sparse-counter: Public structures
Structure, tally-mixin: Private structures
Structure, test-results: Public structures
Structure, trapezoidal-quadrature: Private structures
Structure, upper-triangular-matrix: Public structures
Structure, wrapped-matrix: Public structures
System, num-utils: The num-utils system

T
tally-mixin: Private structures
test-results: Public structures
test-utilities.lisp: The num-utils/test-utilities․lisp file
trapezoidal-quadrature: Private structures
triangular-matrix: Public types
Type, extended-real: Public types
Type, infinite: Private types
Type, simple-double-float-vector: Public types
Type, simple-fixnum-vector: Public types
Type, simple-single-float-vector: Public types
Type, triangular-matrix: Public types

U
upper-triangular-matrix: Public structures
utilities.lisp: The num-utils/utilities․lisp file

W
wrapped-matrix: Public structures

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