The cl-num-utils Reference Manual

Table of Contents

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The cl-num-utils Reference Manual

This is the cl-num-utils Reference Manual, version 0.1, generated automatically by Declt version 2.4 "Will Decker" on Wed Jun 20 11:16:38 2018 GMT+0.


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1 Introduction

* cl-num-utils

This library implements simple numerical functions for Common Lisp, including

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

See the sources and the docstring for more details.

All the functionality has corresponding unit tests.

** Symbol conflicts with =alexandria=

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

** Reporting bugs

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

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


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2 Systems

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


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2.1 cl-num-utils

Author

Tamas K Papp <tkpapp@gmail.com>

License

Boost Software License - Version 1.0

Description

Numerical utilities for Common Lisp

Version

0.1

Dependencies
Source

cl-num-utils.asd (file)

Components

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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 cl-num-utils.asd

Location

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

Systems

cl-num-utils (system)


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3.1.2 cl-num-utils/utilities.lisp

Parent

cl-num-utils (system)

Location

utilities.lisp

Packages

cl-num-utils.utilities

Exported Definitions

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3.1.3 cl-num-utils/num=.lisp

Dependency

utilities.lisp (file)

Parent

cl-num-utils (system)

Location

num=.lisp

Packages

cl-num-utils.num=

Exported Definitions

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3.1.4 cl-num-utils/arithmetic.lisp

Dependency

num=.lisp (file)

Parent

cl-num-utils (system)

Location

arithmetic.lisp

Packages

cl-num-utils.arithmetic

Exported Definitions
Internal Definitions

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3.1.5 cl-num-utils/elementwise.lisp

Dependency

arithmetic.lisp (file)

Parent

cl-num-utils (system)

Location

elementwise.lisp

Packages

cl-num-utils.elementwise

Exported Definitions
Internal Definitions

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

Dependency

elementwise.lisp (file)

Parent

cl-num-utils (system)

Location

extended-real.lisp

Packages

cl-num-utils.extended-real

Exported Definitions
Internal Definitions

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3.1.7 cl-num-utils/interval.lisp

Dependency

extended-real.lisp (file)

Parent

cl-num-utils (system)

Location

interval.lisp

Packages

cl-num-utils.interval

Exported Definitions
Internal Definitions

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

Dependency

interval.lisp (file)

Parent

cl-num-utils (system)

Location

print-matrix.lisp

Packages

cl-num-utils.print-matrix

Exported Definitions
Internal Definitions

print-matrix-formatter (function)


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3.1.9 cl-num-utils/matrix.lisp

Dependency

print-matrix.lisp (file)

Parent

cl-num-utils (system)

Location

matrix.lisp

Packages

cl-num-utils.matrix

Exported Definitions
Internal Definitions

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

Dependency

matrix.lisp (file)

Parent

cl-num-utils (system)

Location

matrix-shorthand.lisp

Packages

cl-num-utils.matrix-shorthand

Exported Definitions
Internal Definitions

pad-left-expansion (function)


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3.1.11 cl-num-utils/statistics.lisp

Dependency

matrix-shorthand.lisp (file)

Parent

cl-num-utils (system)

Location

statistics.lisp

Packages

cl-num-utils.statistics

Exported Definitions
Internal Definitions

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3.1.12 cl-num-utils/chebyshev.lisp

Dependency

statistics.lisp (file)

Parent

cl-num-utils (system)

Location

chebyshev.lisp

Packages

cl-num-utils.chebyshev

Exported Definitions
Internal Definitions

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3.1.13 cl-num-utils/rootfinding.lisp

Dependency

chebyshev.lisp (file)

Parent

cl-num-utils (system)

Location

rootfinding.lisp

Packages

cl-num-utils.rootfinding

Exported Definitions
Internal Definitions

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3.1.14 cl-num-utils/quadrature.lisp

Dependency

rootfinding.lisp (file)

Parent

cl-num-utils (system)

Location

quadrature.lisp

Packages

cl-num-utils.quadrature

Exported Definitions

romberg-quadrature (function)

Internal Definitions

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

Dependency

quadrature.lisp (file)

Parent

cl-num-utils (system)

Location

common-package.lisp

Packages

cl-num-utils


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4 Packages

Packages are listed by definition order.


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4.1 cl-num-utils.utilities

Source

utilities.lisp (file)

Use List
Used By List
Exported Definitions

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4.2 cl-num-utils.num=

Source

num=.lisp (file)

Use List
Used By List
Exported Definitions

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4.3 cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Use List
Used By List
Exported Definitions
Internal Definitions

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4.4 cl-num-utils.elementwise

Source

elementwise.lisp (file)

Use List
Used By List

cl-num-utils.matrix

Exported Definitions
Internal Definitions

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4.5 cl-num-utils.extended-real

Source

extended-real.lisp (file)

Nickname

xreal

Use List
Exported Definitions
Internal Definitions

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4.6 cl-num-utils.interval

Source

interval.lisp (file)

Use List
Used By List
Exported Definitions
Internal Definitions

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4.7 cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Use List
Used By List

cl-num-utils.matrix

Exported Definitions
Internal Definitions

print-matrix-formatter (function)


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4.8 cl-num-utils.matrix

Source

matrix.lisp (file)

Use List
Used By List

cl-num-utils.matrix-shorthand

Exported Definitions
Internal Definitions

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4.9 cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Nickname

clnu.mx

Use List
Exported Definitions
Internal Definitions

pad-left-expansion (function)


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4.10 cl-num-utils.statistics

Source

statistics.lisp (file)

Nickname

clnu.stats

Use List
Exported Definitions
Internal Definitions

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4.11 cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Use List
Exported Definitions
Internal Definitions

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4.12 cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Use List
Exported Definitions
Internal Definitions

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4.13 cl-num-utils.quadrature

Source

quadrature.lisp (file)

Use List
Exported Definitions

romberg-quadrature (function)

Internal Definitions

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4.14 cl-num-utils

Source

common-package.lisp (file)

Nickname

clnu

Use List

common-lisp


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5 Definitions

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


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5.1 Exported definitions


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5.1.1 Special variables

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

Default degree for (weighted) central sample moments.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Special Variable: *num=-tolerance*

Default tolerance for NUM=.

Package

cl-num-utils.num=

Source

num=.lisp (file)

Special Variable: *print-matrix-precision*

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

Package

cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Special Variable: *rootfinding-delta-relative*

Default relative interval width for rootfinding.

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Special Variable: *rootfinding-epsilon*

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

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)


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5.1.2 Macros

Macro: &interval LEFT RIGHT

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Macro: check-types (&rest ARGUMENTS) TYPE

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: curry* FUNCTION &rest ARGUMENTS

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

cl-num-utils.num=

Source

num=.lisp (file)

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

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

Package

cl-num-utils.num=

Source

num=.lisp (file)

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

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: expanding &body BODY

Expand BODY. Useful for generating code programmatically.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: extendf-interval PLACE OBJECT

Apply EXTEND-INTERVAL on PLACE using OBJECT.

Package

cl-num-utils.interval

Source

interval.lisp (file)

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

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: hermitian-mx ELEMENT-TYPE &body ROWS

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

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

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

LAMBDA with WITH-TEMPLATE in its BODY.

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

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

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

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: multf PLACE COEFFICIENT

Multiply place by COEFFICIENT.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Macro: mx ELEMENT-TYPE &body ROWS

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

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: splice-awhen TEST &body FORMS

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: splice-when TEST &body FORMS

Similar to when, but wraps the result in list.

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Macro: unlessf PLACE VALUE-FORM

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Macro: with-double-floats BINDINGS &body BODY

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

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)


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5.1.3 Functions

Function: 1c NUMBER

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: < NUMBER &rest MORE-NUMBERS
Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: <= NUMBER &rest MORE-NUMBERS
Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: = NUMBER &rest MORE-NUMBERS
Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: > NUMBER &rest MORE-NUMBERS
Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: >= NUMBER &rest MORE-NUMBERS
Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: abs-diff A B

Absolute difference of A and B.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: absolute-square NUMBER

Number multiplied by its complex conjugate.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: as-double-float V

Convert argument to DOUBLE-FLOAT.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: as-integer NUMBER

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: bic A B

Biconditional. Returns A <=> B.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: binary-search SORTED-REALS VALUE

Return INDEX such that

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

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

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: ceiling* NUMBER &optional DIVISOR OFFSET

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

Return the degree of CENTRAL-SAMPLE-MOMENTS.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: chebyshev-evaluate COEFFICIENTS X

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

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

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: chebyshev-root M I

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: chebyshev-roots M

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: cross-tabulate SEQUENCE1 SEQUENCE2 &key TEST

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: cumulative-product SEQUENCE &key RESULT-TYPE

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: cumulative-sum SEQUENCE &key RESULT-TYPE

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: diagonal-matrix ELEMENTS
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: diagonal-mx ELEMENT-TYPE &rest ELEMENTS

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

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Function: divides? NUMBER DIVISOR

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: e* ARGUMENT &rest MORE-ARGUMENTS

Elementwise *.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: e+ ARGUMENT &rest MORE-ARGUMENTS

Elementwise +.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: e- ARGUMENT &rest MORE-ARGUMENTS

Elementwise -.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: e/ ARGUMENT &rest MORE-ARGUMENTS

Elementwise /.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: elementwise-float-contagion &rest OBJECTS

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

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: elog A &optional BASE

Elementwise logarithm.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: emax OBJECT

Elementwise MAX.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: emin OBJECT

Elementwise MIN.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Function: empirical-quantile SORTED-VECTOR Q

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: empirical-quantile-probabilities N

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

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

for any vector SAMPLE.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: ensure-sorted-vector OBJECT

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: fixnum? OBJECT

Check of type of OBJECT is fixnum.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: floor* NUMBER &optional DIVISOR OFFSET

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: generate-sequence RESULT-TYPE SIZE FUNCTION

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

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

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: hermitian-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: in-interval? INTERVAL NUMBER

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: infinite? OBJECT

Test if an object represents positive or negative infinity.

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

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

Create an INTERVAL.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: interval-hull OBJECT

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: interval-length INTERVAL

Difference between left and right.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: interval-midpoint INTERVAL &optional ALPHA

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

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

Return a vector of fixnums.

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

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

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: l2norm OBJECT

$L_2$ norm of OBJECT.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: log10 NUMBER

Abbreviation for decimal logarithm.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: log2 NUMBER

Abbreviation for binary logarithm.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: lower-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: make-sparse-counter &key TEST

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: num-delta A B

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

Package

cl-num-utils.num=

Source

num=.lisp (file)

Function: num=-function TOLERANCE

Curried version of num=, with given tolerance.

Package

cl-num-utils.num=

Source

num=.lisp (file)

Function: numseq FROM TO &key LENGTH BY TYPE

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

A symmetric interval around CENTER.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: pool &rest ACCUMULATORS

Pool ACCUMULATORS.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: print-length-truncate DIMENSION

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

Package

cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

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

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

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

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

Package

cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Function: relative FRACTION
Package

cl-num-utils.interval

Source

interval.lisp (file)

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

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

Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: root-bisection F BRACKET &key DELTA EPSILON

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

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

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Function: round* NUMBER &optional DIVISOR OFFSET

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: same-sign? &rest ARGUMENTS

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: sorted-reals-elements SORTED-REALS
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: spacer &optional WEIGHT
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: sparse-counter-count SPARSE-COUNTER OBJECT

Return the count for OBJECT.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: sparse-counter-table INSTANCE
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: split-interval INTERVAL DIVISIONS

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: square NUMBER

Square of number.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: tabulate SEQUENCE &key TEST

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: truncate* NUMBER &optional DIVISOR OFFSET

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: upper-triangular-matrix ELEMENTS

Create a lower-triangular-matrix.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: vec ELEMENT-TYPE &rest ELEMENTS

Return a vector with elements coerced to ELEMENT-TYPE.

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Function: weighted-quantiles VALUES WEIGHTS QS

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: within? LEFT VALUE RIGHT

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Function: wrapped-matrix-elements INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)


Next: , Previous: , Up: Exported definitions   [Contents][Index]

5.1.4 Generic functions

Generic Function: add ACCUMULATOR OBJECT &key WEIGHT

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: add (ACCUMULATOR sparse-counter) OBJECT &key WEIGHT
Method: add (ACCUMULATOR sorted-reals) OBJECT &key
Method: add (MOMENTS central-sample-moments) (Y real) &key WEIGHT
Method: add ACCUMULATOR (OBJECT null) &key
Generic Function: as-alist OBJECT

Return OBJECT as an ALIST. Semantics depends on OBJECT.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

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

Return (OBJECT . COUNT) pairs as an alist.

Source

statistics.lisp (file)

Generic Function: as-plist OBJECT

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

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Methods
Method: as-plist OBJECT
Generic Function: central-m2 OBJECT &key WEIGHTS

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: central-m2 OBJECT &key WEIGHTS
Method: central-m2 (OBJECT central-sample-moments) &key WEIGHTS
Generic Function: central-m3 OBJECT &key WEIGHTS

Third central moment.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: central-m3 OBJECT &key WEIGHTS
Method: central-m3 (OBJECT central-sample-moments) &key WEIGHTS
Generic Function: central-m4 OBJECT &key WEIGHTS

Fourth central moment.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: central-m4 OBJECT &key WEIGHTS
Method: central-m4 (OBJECT central-sample-moments) &key WEIGHTS
Generic Function: central-sample-moments OBJECT &key DEGREE WEIGHTS

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

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: central-sample-moments (OBJECT null) &key DEGREE WEIGHTS
Method: central-sample-moments (MOMENTS central-sample-moments) &key DEGREE WEIGHTS
Method: central-sample-moments (SEQUENCE sequence) &key DEGREE WEIGHTS
Generic Function: diagonal-vector MATRIX

Return the diagonal elements of MATRIX as a vector.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Writer

(setf diagonal-vector) (generic function)

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

Set the diagonal elements of MATRIX using VECTOR.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Reader

diagonal-vector (generic function)

Generic Function: e1- A

Univariate elementwise -.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

matrix.lisp (file)

Method: e1- (A hermitian-matrix)
Source

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

Univariate elementwise /.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

matrix.lisp (file)

Method: e1/ (A hermitian-matrix)
Source

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

Univariate elementwise LOG.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Methods
Method: e1log (A diagonal-matrix)
Source

matrix.lisp (file)

Method: e1log (A hermitian-matrix)
Source

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: e1log (A number)
Method: e1log (A array)
Generic Function: e2* A B

Bivariate elementwise *.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: e2* A (B wrapped-matrix)
Source

matrix.lisp (file)

Method: e2* (A wrapped-matrix) B
Source

matrix.lisp (file)

Method: e2* (A number) (B number)
Method: e2* (A array) (B number)
Method: e2* (A number) (B array)
Method: e2* (A array) (B array)
Generic Function: e2+ A B

Bivariate elementwise +.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: e2+ A (B wrapped-matrix)
Source

matrix.lisp (file)

Method: e2+ (A wrapped-matrix) B
Source

matrix.lisp (file)

Method: e2+ (A number) (B number)
Method: e2+ (A array) (B number)
Method: e2+ (A number) (B array)
Method: e2+ (A array) (B array)
Generic Function: e2- A B

Bivariate elementwise -.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: e2- A (B wrapped-matrix)
Source

matrix.lisp (file)

Method: e2- (A wrapped-matrix) B
Source

matrix.lisp (file)

Method: e2- (A number) (B number)
Method: e2- (A array) (B number)
Method: e2- (A number) (B array)
Method: e2- (A array) (B array)
Generic Function: e2/ A B

Bivariate elementwise /.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: e2/ (A number) (B number)
Method: e2/ (A array) (B number)
Method: e2/ (A number) (B array)
Method: e2/ (A array) (B array)
Generic Function: e2log A B

Bivariate elementwise LOG.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Methods
Method: e2log (A number) (B number)
Method: e2log (A array) (B number)
Method: e2log (A number) (B array)
Method: e2log (A array) (B array)
Generic Function: econjugate A

Univariate elementwise CONJUGATE.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

Univariate elementwise EXP.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Methods
Method: eexp (A diagonal-matrix)
Source

matrix.lisp (file)

Method: eexp (A hermitian-matrix)
Source

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: eexp (A number)
Method: eexp (A array)
Generic Function: eexpt A B

Bivariate elementwise EXPT.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Methods
Method: eexpt (A number) (B number)
Method: eexpt (A array) (B number)
Method: eexpt (A number) (B array)
Method: eexpt (A array) (B array)
Generic Function: ensure-sorted-reals OBJECT

Return the contents of OBJECT as a SORTED-REALS.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Methods
Method: esqrt (A diagonal-matrix)
Source

matrix.lisp (file)

Method: esqrt (A hermitian-matrix)
Source

matrix.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

Method: esqrt (A number)
Method: esqrt (A array)
Generic Function: extend-interval INTERVAL OBJECT

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

Package

cl-num-utils.interval

Source

interval.lisp (file)

Methods
Method: extend-interval (INTERVAL null) (OBJECT null)
Method: extend-interval (INTERVAL null) (NUMBER real)
Method: extend-interval (INTERVAL interval) (NUMBER real)
Method: extend-interval INTERVAL (OBJECT interval)
Method: extend-interval INTERVAL (LIST list)
Method: extend-interval INTERVAL (ARRAY array)
Generic Function: kurtosis OBJECT &key WEIGHTS

Kurtosis FIXME talk about bias, maybe implement unbiased?

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

Left endpoint of interval.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Methods
Method: left (INTERVAL interval/infinite-left)
Method: left (INTERVAL/FINITE-LEFT interval/finite-left)

automatically generated reader method

Generic Function: mean OBJECT &key WEIGHTS

The mean of elements in OBJECT.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: mean OBJECT &key WEIGHTS
Method: mean (OBJECT central-sample-moments) &key WEIGHTS
Generic Function: median OBJECT

Median of OBJECT.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: median (OBJECT sequence)
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

cl-num-utils.num=

Source

num=.lisp (file)

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

statistics.lisp (file)

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

matrix.lisp (file)

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

matrix.lisp (file)

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

interval.lisp (file)

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

interval.lisp (file)

Method: num= A B &optional TOLERANCE
Method: num= (A number) (B number) &optional TOLERANCE
Method: num= (A array) (B array) &optional TOLERANCE
Method: num= (A cons) (B cons) &optional TOLERANCE
Method: num= (A null) (B null) &optional TOLERANCE
Generic Function: open-left? INTERVAL

True iff the left endpoint of the interval is open.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Methods
Method: open-left? (INTERVAL interval/infinite-left)
Method: open-left? (INTERVAL/FINITE-LEFT interval/finite-left)

automatically generated reader method

Generic Function: open-right? INTERVAL

True iff the right endpoint of the interval is open.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Methods
Method: open-right? (INTERVAL interval/infinite-right)
Method: open-right? (INTERVAL/FINITE-RIGHT interval/finite-right)

automatically generated reader method

Generic Function: product OBJECT

Product of elements in object.

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: quantiles (OBJECT sequence) QS
Method: quantiles (ACCUMULATOR sorted-reals) Q
Generic Function: right INTERVAL

Right endpoint of interval.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Methods
Method: right (INTERVAL interval/infinite-right)
Method: right (INTERVAL/FINITE-RIGHT interval/finite-right)

automatically generated reader method

Generic Function: sd OBJECT &key WEIGHTS

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: sd OBJECT &key WEIGHTS
Generic Function: shift-interval INTERVAL OFFSET
Package

cl-num-utils.interval

Source

interval.lisp (file)

Methods
Method: shift-interval (INTERVAL finite-interval) (OFFSET real)
Generic Function: skewness OBJECT &key WEIGHTS

Skewness FIXME talk about bias, maybe implement unbiased?

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: tally (ACCUMULATOR sparse-counter)
Method: tally (ACCUMULATOR tally-mixin)
Generic Function: transpose ARRAY

Transpose.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Methods
Method: transpose (ARRAY array)
Method: transpose (MATRIX lower-triangular-matrix)
Method: transpose (MATRIX upper-triangular-matrix)
Method: transpose (MATRIX hermitian-matrix)
Method: transpose (DIAGONAL diagonal-matrix)
Generic Function: variance OBJECT &key WEIGHTS

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

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5.1.5 Conditions

Condition: empty-accumulator ()
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

error (condition)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

error (condition)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

error (condition)


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5.1.6 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

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

tally-mixin (structure)

Direct methods
Direct slots
Slot: m
Type

real

Initform

0.0d0

Readers

central-sample-moments-m (function)

Writers

(setf central-sample-moments-m) (function)

Slot: s2
Type

(or (real 0) null)

Initform

0.0d0

Readers

central-sample-moments-s2 (function)

Writers

(setf central-sample-moments-s2) (function)

Slot: s3
Type

(or real null)

Initform

0.0d0

Readers

central-sample-moments-s3 (function)

Writers

(setf central-sample-moments-s3) (function)

Slot: s4
Type

(or (real 0) null)

Initform

0.0d0

Readers

central-sample-moments-s4 (function)

Writers

(setf central-sample-moments-s4) (function)

Structure: diagonal-matrix ()

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods
Direct slots
Slot: elements
Type

vector

Readers

diagonal-matrix-elements (function)

Writers

(setf diagonal-matrix-elements) (function)

Structure: hermitian-matrix ()

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

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Direct superclasses

wrapped-matrix (structure)

Direct methods
Structure: lower-triangular-matrix ()

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Direct superclasses

wrapped-matrix (structure)

Direct methods
Structure: relative ()

Relative sizes are in terms of width.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots
Slot: fraction
Type

(real 0)

Readers

relative-fraction (function)

Writers

(setf relative-fraction) (function)

Structure: sorted-reals ()

Accumulator which sorts elements. ELEMENTS return the sorted elements.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods
Direct slots
Slot: ordered-elements
Type

vector

Initform

#()

Readers

sorted-reals-ordered-elements (function)

Writers

(setf sorted-reals-ordered-elements) (function)

Slot: unordered-elements
Type

list

Readers

sorted-reals-unordered-elements (function)

Writers

(setf sorted-reals-unordered-elements) (function)

Structure: spacer ()

Spacers divide the leftover portion of an interval.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots
Slot: weight
Type

(real 0)

Initform

1

Readers

spacer-weight (function)

Writers

(setf spacer-weight) (function)

Structure: sparse-counter ()
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

structure-object (structure)

Direct methods
Direct slots
Slot: table
Type

hash-table

Readers

sparse-counter-table (function)

Writers

(setf sparse-counter-table) (function)

Structure: upper-triangular-matrix ()

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Direct superclasses

wrapped-matrix (structure)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

Direct superclasses

structure-object (structure)

Direct subclasses
Direct methods
  • num= (method)
  • e2* (method)
  • e2* (method)
  • e2- (method)
  • e2- (method)
  • e2+ (method)
  • e2+ (method)
  • dims (method)
  • element-type (method)
Direct slots
Slot: elements
Type

(array * (* *))

Readers

wrapped-matrix-elements (function)

Writers

(setf wrapped-matrix-elements) (function)


Next: , Previous: , Up: Exported definitions   [Contents][Index]

5.1.7 Classes

Class: finite-interval ()

Interval with finite endpoints.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses
Direct methods
Class: interval ()

Abstract superclass for all intervals.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses
Direct methods
Class: minusinf-interval ()

Interval from -∞ to RIGHT.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses
Class: plusinf-interval ()

Interval from LEFT to ∞.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses
Direct methods
Class: real-line ()

Representing the real line (-∞,∞).

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses
Direct methods

num= (method)


Previous: , Up: Exported definitions   [Contents][Index]

5.1.8 Types

Type: extended-real &optional BASE

Extended real number.

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

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

Simple vector of double-float elements.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Type: simple-fixnum-vector ()

Simple vector or fixnum elements.

Package

cl-num-utils.utilities

Source

utilities.lisp (file)

Type: triangular-matrix ()

Triangular matrix (either lower or upper).

Package

cl-num-utils.matrix

Source

matrix.lisp (file)


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

5.2 Internal definitions


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.1 Macros

Macro: &diagonal-matrix ELEMENTS

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Macro: &diagonal-matrix-r/o ELEMENTS

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

FIXME documentation, factor our general part

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Macro: define-comparison NAME TEST

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

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Macro: define-e1 OPERATION &key FUNCTION DOCSTRING

Define an univariate elementwise operation.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

Macro: define-e2 OPERATION &key FUNCTION DOCSTRING

Define an univariate elementwise operation.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

Common parts for univariate rootfinder functions.

Sets up the following:

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

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

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

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

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

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.2 Functions

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

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: ab-to-cinf Z A B C

Inverse of cinf-to-ab.

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: above-diagonal? ROW COL

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: below-diagonal? ROW COL

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: central-sample-moments-p OBJECT
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: chebyshev-recursion X VALUE PREVIOUS-VALUE

Chebyshev polynomial recursion formula.

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: cinf-to-ab X A B C

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

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Function: copy-central-sample-moments INSTANCE
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: copy-diagonal-matrix INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: copy-hermitian-matrix INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: copy-iterative-quadrature INSTANCE
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: copy-lower-triangular-matrix INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: copy-midpoint-quadrature INSTANCE
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: copy-relative INSTANCE
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: copy-richardson-extrapolation INSTANCE
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: copy-sorted-reals INSTANCE
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: copy-spacer INSTANCE
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: copy-sparse-counter INSTANCE
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: copy-tally-mixin INSTANCE
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: copy-trapezoidal-quadrature INSTANCE
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: copy-upper-triangular-matrix INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: copy-wrapped-matrix INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: diagonal-matrix-p OBJECT
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

Convert OBJECT to an array, check that it

1. has the required rank,

2. has a valid sparse element type, and

3. that it satisfies PREDICATES.

Return the array.

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: extend-pairwise-comparison TEST FIRST REST

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

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)

Function: hermitian-matrix-elements INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: hermitian-matrix-p OBJECT
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: iterative-quadrature-p OBJECT
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: lower-triangular-matrix-elements INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: lower-triangular-matrix-p OBJECT
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

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

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: midpoint-quadrature F A B
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: midpoint-quadrature-p OBJECT
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: narrow-bracket? A B DELTA

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

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Function: near-root? F EPSILON

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

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Function: opposite-sign? A B

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

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Function: pad-left-expansion ROWS NCOL

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

Package

cl-num-utils.matrix-shorthand

Source

matrix-shorthand.lisp (file)

Function: print-matrix-formatter X

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

Package

cl-num-utils.print-matrix

Source

print-matrix.lisp (file)

Function: relative-fraction INSTANCE
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: relative-p OBJECT
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: richardson-extrapolation COEFFICIENT ITERATIONS &aux DIAGONAL
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: richardson-extrapolation-p OBJECT
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: richardson-iteration EXTRAPOLATION STEP

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

Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

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

Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: rootfinding-delta INTERVAL &optional DELTA-RELATIVE

Default DELTA for rootfinding methods, uses bracket width.

Package

cl-num-utils.rootfinding

Source

rootfinding.lisp (file)

Function: similar-element-type ELEMENT-TYPE

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: similar-sequence-type SEQUENCE

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

Package

cl-num-utils.arithmetic

Source

arithmetic.lisp (file)

Function: sort-reals SEQUENCE

Return a SORTED-REALS structure.

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: sorted-reals-p OBJECT
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: spacer-p OBJECT
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: spacer-weight INSTANCE
Package

cl-num-utils.interval

Source

interval.lisp (file)

Function: sparse-counter-p OBJECT
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: tally-mixin-p OBJECT
Package

cl-num-utils.statistics

Source

statistics.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: trapezoidal-quadrature F A B
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: trapezoidal-quadrature-p OBJECT
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Function: upper-triangular-matrix-elements INSTANCE
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: upper-triangular-matrix-p OBJECT
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: valid-sparse-type? TYPE

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)

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

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: weighted-quantile-p-table WEIGHTS

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Function: wrapped-matrix-p OBJECT
Package

cl-num-utils.matrix

Source

matrix.lisp (file)

Function: zero-like ARRAY

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

Package

cl-num-utils.matrix

Source

matrix.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.3 Generic functions

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

Implementation of CHEBYSHEV-APPROXIMATE.

Package

cl-num-utils.chebyshev

Source

chebyshev.lisp (file)

Methods
Method: chebyshev-approximate-implementation F (INTERVAL plusinf-interval) N-POLYNOMIALS N-POINTS
Method: chebyshev-approximate-implementation F (INTERVAL finite-interval) N-POLYNOMIALS N-POINTS
Generic Function: esquare A

Univariate elementwise SQUARE.

Package

cl-num-utils.elementwise

Source

elementwise.lisp (file)

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

cl-num-utils.statistics

Source

statistics.lisp (file)

Methods
Method: pool2 (MOMENTS-A central-sample-moments) (MOMENTS-B central-sample-moments)
Generic Function: print-left-endpoint INTERVAL STREAM
Package

cl-num-utils.interval

Source

interval.lisp (file)

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

cl-num-utils.interval

Source

interval.lisp (file)

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

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

Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

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

Next: , Previous: , Up: Internal definitions   [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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Direct superclasses

structure-object (structure)

Direct subclasses
Direct slots
Slot: f
Type

(function (double-float) double-float)

Readers

iterative-quadrature-f (function)

Writers

(setf iterative-quadrature-f) (function)

Slot: a
Type

double-float

Readers

iterative-quadrature-a (function)

Writers

(setf iterative-quadrature-a) (function)

Slot: b
Type

double-float

Readers

iterative-quadrature-b (function)

Writers

(setf iterative-quadrature-b) (function)

Slot: h
Type

double-float

Readers

iterative-quadrature-h (function)

Writers

(setf iterative-quadrature-h) (function)

Slot: n
Type

fixnum

Initform

0

Readers

iterative-quadrature-n (function)

Writers

(setf iterative-quadrature-n) (function)

Slot: sum
Type

double-float

Initform

0.0d0

Readers

iterative-quadrature-sum (function)

Writers

(setf iterative-quadrature-sum) (function)

Structure: midpoint-quadrature ()
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Direct superclasses

iterative-quadrature (structure)

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

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots
Slot: coefficient
Type

double-float

Readers

richardson-extrapolation-coefficient (function)

Writers

(setf richardson-extrapolation-coefficient) (function)

Slot: n
Type

fixnum

Initform

0

Readers

richardson-extrapolation-n (function)

Writers

(setf richardson-extrapolation-n) (function)

Slot: diagonal
Type

(array double-float (*))

Readers

richardson-extrapolation-diagonal (function)

Writers

(setf richardson-extrapolation-diagonal) (function)

Structure: tally-mixin ()

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

Package

cl-num-utils.statistics

Source

statistics.lisp (file)

Direct superclasses

structure-object (structure)

Direct subclasses

central-sample-moments (structure)

Direct methods

tally (method)

Direct slots
Slot: w
Type

(real 0)

Initform

0

Readers

tally-mixin-w (function)

Writers

(setf tally-mixin-w) (function)

Structure: trapezoidal-quadrature ()
Package

cl-num-utils.quadrature

Source

quadrature.lisp (file)

Direct superclasses

iterative-quadrature (structure)

Direct methods

Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.5 Classes

Class: interval/finite-left ()

Interval with left endpoint.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses
Direct methods
Direct slots
Slot: left
Type

real

Initargs

:left

Readers

left (generic function)

Slot: open-left?
Type

boolean

Initargs

:open-left?

Readers

open-left? (generic function)

Class: interval/finite-right ()

Interval with right endpoint.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses
Direct methods
Direct slots
Slot: right
Type

real

Initargs

:right

Readers

right (generic function)

Slot: open-right?
Type

boolean

Initargs

:open-right?

Readers

open-right? (generic function)

Class: interval/infinite-left ()

Left endpoint is -∞.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses
Direct methods
Class: interval/infinite-right ()

Right endpoint is ∞.

Package

cl-num-utils.interval

Source

interval.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses
Direct methods

Previous: , Up: Internal definitions   [Contents][Index]

5.2.6 Types

Type: infinite ()

Representing infinity (extending the real line).

Package

cl-num-utils.extended-real

Source

extended-real.lisp (file)


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

Appendix A Indexes


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

A.1 Concepts

Jump to:   C   F   L  
Index Entry  Section

C
cl-num-utils.asd: The cl-num-utils<dot>asd file
cl-num-utils/arithmetic.lisp: The cl-num-utils/arithmetic<dot>lisp file
cl-num-utils/chebyshev.lisp: The cl-num-utils/chebyshev<dot>lisp file
cl-num-utils/common-package.lisp: The cl-num-utils/common-package<dot>lisp file
cl-num-utils/elementwise.lisp: The cl-num-utils/elementwise<dot>lisp file
cl-num-utils/extended-real.lisp: The cl-num-utils/extended-real<dot>lisp file
cl-num-utils/interval.lisp: The cl-num-utils/interval<dot>lisp file
cl-num-utils/matrix-shorthand.lisp: The cl-num-utils/matrix-shorthand<dot>lisp file
cl-num-utils/matrix.lisp: The cl-num-utils/matrix<dot>lisp file
cl-num-utils/num=.lisp: The cl-num-utils/num=<dot>lisp file
cl-num-utils/print-matrix.lisp: The cl-num-utils/print-matrix<dot>lisp file
cl-num-utils/quadrature.lisp: The cl-num-utils/quadrature<dot>lisp file
cl-num-utils/rootfinding.lisp: The cl-num-utils/rootfinding<dot>lisp file
cl-num-utils/statistics.lisp: The cl-num-utils/statistics<dot>lisp file
cl-num-utils/utilities.lisp: The cl-num-utils/utilities<dot>lisp file

F
File, Lisp, cl-num-utils.asd: The cl-num-utils<dot>asd file
File, Lisp, cl-num-utils/arithmetic.lisp: The cl-num-utils/arithmetic<dot>lisp file
File, Lisp, cl-num-utils/chebyshev.lisp: The cl-num-utils/chebyshev<dot>lisp file
File, Lisp, cl-num-utils/common-package.lisp: The cl-num-utils/common-package<dot>lisp file
File, Lisp, cl-num-utils/elementwise.lisp: The cl-num-utils/elementwise<dot>lisp file
File, Lisp, cl-num-utils/extended-real.lisp: The cl-num-utils/extended-real<dot>lisp file
File, Lisp, cl-num-utils/interval.lisp: The cl-num-utils/interval<dot>lisp file
File, Lisp, cl-num-utils/matrix-shorthand.lisp: The cl-num-utils/matrix-shorthand<dot>lisp file
File, Lisp, cl-num-utils/matrix.lisp: The cl-num-utils/matrix<dot>lisp file
File, Lisp, cl-num-utils/num=.lisp: The cl-num-utils/num=<dot>lisp file
File, Lisp, cl-num-utils/print-matrix.lisp: The cl-num-utils/print-matrix<dot>lisp file
File, Lisp, cl-num-utils/quadrature.lisp: The cl-num-utils/quadrature<dot>lisp file
File, Lisp, cl-num-utils/rootfinding.lisp: The cl-num-utils/rootfinding<dot>lisp file
File, Lisp, cl-num-utils/statistics.lisp: The cl-num-utils/statistics<dot>lisp file
File, Lisp, cl-num-utils/utilities.lisp: The cl-num-utils/utilities<dot>lisp file

L
Lisp File, cl-num-utils.asd: The cl-num-utils<dot>asd file
Lisp File, cl-num-utils/arithmetic.lisp: The cl-num-utils/arithmetic<dot>lisp file
Lisp File, cl-num-utils/chebyshev.lisp: The cl-num-utils/chebyshev<dot>lisp file
Lisp File, cl-num-utils/common-package.lisp: The cl-num-utils/common-package<dot>lisp file
Lisp File, cl-num-utils/elementwise.lisp: The cl-num-utils/elementwise<dot>lisp file
Lisp File, cl-num-utils/extended-real.lisp: The cl-num-utils/extended-real<dot>lisp file
Lisp File, cl-num-utils/interval.lisp: The cl-num-utils/interval<dot>lisp file
Lisp File, cl-num-utils/matrix-shorthand.lisp: The cl-num-utils/matrix-shorthand<dot>lisp file
Lisp File, cl-num-utils/matrix.lisp: The cl-num-utils/matrix<dot>lisp file
Lisp File, cl-num-utils/num=.lisp: The cl-num-utils/num=<dot>lisp file
Lisp File, cl-num-utils/print-matrix.lisp: The cl-num-utils/print-matrix<dot>lisp file
Lisp File, cl-num-utils/quadrature.lisp: The cl-num-utils/quadrature<dot>lisp file
Lisp File, cl-num-utils/rootfinding.lisp: The cl-num-utils/rootfinding<dot>lisp file
Lisp File, cl-num-utils/statistics.lisp: The cl-num-utils/statistics<dot>lisp file
Lisp File, cl-num-utils/utilities.lisp: The cl-num-utils/utilities<dot>lisp file

Jump to:   C   F   L  

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: Internal macros
&diagonal-matrix-r/o: Internal macros
&interval: Exported macros
&sorted-reals: Internal macros
&sorted-reals-r/o: Internal macros

(
(setf central-sample-moments-m): Internal functions
(setf central-sample-moments-s2): Internal functions
(setf central-sample-moments-s3): Internal functions
(setf central-sample-moments-s4): Internal functions
(setf central-sample-moments-w): Internal functions
(setf diagonal-matrix-elements): Exported functions
(setf diagonal-vector): Exported generic functions
(setf iterative-quadrature-a): Internal functions
(setf iterative-quadrature-b): Internal functions
(setf iterative-quadrature-f): Internal functions
(setf iterative-quadrature-h): Internal functions
(setf iterative-quadrature-n): Internal functions
(setf iterative-quadrature-sum): Internal functions
(setf midpoint-quadrature-a): Internal functions
(setf midpoint-quadrature-b): Internal functions
(setf midpoint-quadrature-f): Internal functions
(setf midpoint-quadrature-h): Internal functions
(setf midpoint-quadrature-n): Internal functions
(setf midpoint-quadrature-sum): Internal functions
(setf richardson-extrapolation-coefficient): Internal functions
(setf richardson-extrapolation-diagonal): Internal functions
(setf richardson-extrapolation-n): Internal functions
(setf sorted-reals-ordered-elements): Internal functions
(setf sorted-reals-unordered-elements): Internal functions
(setf tally-mixin-w): Internal functions
(setf trapezoidal-quadrature-a): Internal functions
(setf trapezoidal-quadrature-b): Internal functions
(setf trapezoidal-quadrature-f): Internal functions
(setf trapezoidal-quadrature-h): Internal functions
(setf trapezoidal-quadrature-n): Internal functions
(setf trapezoidal-quadrature-sum): Internal functions

1
1c: Exported functions

<
<: Exported functions
<=: Exported functions

=
=: Exported functions

>
>: Exported functions
>=: Exported functions

A
ab-to-cd-intercept-slope: Internal functions
ab-to-cinf: Internal functions
above-diagonal?: Internal functions
abs-diff: Exported functions
absolute-square: Exported functions
add: Exported generic functions
add: Exported generic functions
add: Exported generic functions
add: Exported generic functions
add: Exported generic functions
as-alist: Exported generic functions
as-alist: Exported generic functions
as-double-float: Exported functions
as-integer: Exported functions
as-plist: Exported generic functions
as-plist: Exported generic functions
as-simple-fixnum-vector: Exported functions

B
below-diagonal?: Internal functions
bic: Exported functions
binary-search: Exported functions

C
ceiling*: Exported functions
central-m2: Exported generic functions
central-m2: Exported generic functions
central-m2: Exported generic functions
central-m3: Exported generic functions
central-m3: Exported generic functions
central-m3: Exported generic functions
central-m4: Exported generic functions
central-m4: Exported generic functions
central-m4: Exported generic functions
central-sample-moments: Exported generic functions
central-sample-moments: Exported generic functions
central-sample-moments: Exported generic functions
central-sample-moments: Exported generic functions
central-sample-moments-degree: Exported functions
central-sample-moments-m: Internal functions
central-sample-moments-p: Internal functions
central-sample-moments-s2: Internal functions
central-sample-moments-s3: Internal functions
central-sample-moments-s4: Internal functions
central-sample-moments-w: Internal functions
chebyshev-approximate: Exported functions
chebyshev-approximate-implementation: Internal generic functions
chebyshev-approximate-implementation: Internal generic functions
chebyshev-approximate-implementation: Internal generic functions
chebyshev-evaluate: Exported functions
chebyshev-recursion: Internal functions
chebyshev-regression: Exported functions
chebyshev-root: Exported functions
chebyshev-roots: Exported functions
check-types: Exported macros
cinf-to-ab: Internal functions
copy-central-sample-moments: Internal functions
copy-diagonal-matrix: Internal functions
copy-hermitian-matrix: Internal functions
copy-iterative-quadrature: Internal functions
copy-lower-triangular-matrix: Internal functions
copy-midpoint-quadrature: Internal functions
copy-relative: Internal functions
copy-richardson-extrapolation: Internal functions
copy-sorted-reals: Internal functions
copy-spacer: Internal functions
copy-sparse-counter: Internal functions
copy-tally-mixin: Internal functions
copy-trapezoidal-quadrature: Internal functions
copy-upper-triangular-matrix: Internal functions
copy-wrapped-matrix: Internal functions
cross-tabulate: Exported functions
cumulative-product: Exported functions
cumulative-sum: Exported functions
curry*: Exported macros

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

E
e*: Exported functions
e+: Exported functions
e-: Exported functions
e/: Exported functions
e1-: Exported generic functions
e1-: Exported generic functions
e1-: Exported generic functions
e1-: Exported generic functions
e1-: Exported generic functions
e1-: Exported generic functions
e1-: Exported generic functions
e1/: Exported generic functions
e1/: Exported generic functions
e1/: Exported generic functions
e1/: Exported generic functions
e1/: Exported generic functions
e1/: Exported generic functions
e1/: Exported generic functions
e1log: Exported generic functions
e1log: Exported generic functions
e1log: Exported generic functions
e1log: Exported generic functions
e1log: Exported generic functions
e1log: Exported generic functions
e1log: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2*: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2+: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2-: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2/: Exported generic functions
e2log: Exported generic functions
e2log: Exported generic functions
e2log: Exported generic functions
e2log: Exported generic functions
e2log: Exported generic functions
econjugate: Exported generic functions
econjugate: Exported generic functions
econjugate: Exported generic functions
eexp: Exported generic functions
eexp: Exported generic functions
eexp: Exported generic functions
eexp: Exported generic functions
eexp: Exported generic functions
eexp: Exported generic functions
eexp: Exported generic functions
eexpt: Exported generic functions
eexpt: Exported generic functions
eexpt: Exported generic functions
eexpt: Exported generic functions
eexpt: Exported generic functions
elementwise-float-contagion: Exported functions
elog: Exported functions
emax: Exported functions
emin: Exported functions
empirical-quantile: Exported functions
empirical-quantile-probabilities: Exported functions
ensure-sorted-reals: Exported generic functions
ensure-sorted-reals: Exported generic functions
ensure-sorted-reals: Exported generic functions
ensure-sorted-reals: Exported generic functions
ensure-sorted-vector: Exported functions
ensure-valid-elements: Internal functions
ereduce: Exported generic functions
ereduce: Exported generic functions
ereduce: Exported generic functions
ereduce: Exported generic functions
esqrt: Exported generic functions
esqrt: Exported generic functions
esqrt: Exported generic functions
esqrt: Exported generic functions
esqrt: Exported generic functions
esqrt: Exported generic functions
esqrt: Exported generic functions
esquare: Internal generic functions
esquare: Internal generic functions
esquare: Internal generic functions
expanding: Exported macros
extend-interval: Exported generic functions
extend-interval: Exported generic functions
extend-interval: Exported generic functions
extend-interval: Exported generic functions
extend-interval: Exported generic functions
extend-interval: Exported generic functions
extend-interval: Exported generic functions
extend-pairwise-comparison: Internal functions
extendf-interval: Exported macros

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

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

H
hermitian-matrix: Exported functions
hermitian-matrix-elements: Internal functions
hermitian-matrix-p: Internal functions
hermitian-mx: Exported macros

I
in-interval?: Exported functions
infinite?: Exported functions
interval: Exported functions
interval-hull: Exported functions
interval-length: Exported functions
interval-midpoint: Exported functions
iterative-quadrature-a: Internal functions
iterative-quadrature-b: Internal functions
iterative-quadrature-f: Internal functions
iterative-quadrature-h: Internal functions
iterative-quadrature-n: Internal functions
iterative-quadrature-p: Internal functions
iterative-quadrature-sum: Internal functions
ivec: Exported functions

K
kurtosis: Exported generic functions
kurtosis: Exported generic functions
kurtosis: Exported generic functions

L
l2norm: Exported functions
l2norm-square: Exported generic functions
l2norm-square: Exported generic functions
lambda-template: Exported macros
left: Exported generic functions
left: Exported generic functions
left: Exported generic functions
log10: Exported functions
log2: Exported functions
lower-triangular-matrix: Exported functions
lower-triangular-matrix-elements: Internal functions
lower-triangular-matrix-p: Internal functions
lower-triangular-mx: Exported macros

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

N
narrow-bracket?: Internal functions
near-root?: Internal functions
normalize-probabilities: Exported functions
num-delta: Exported functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=: Exported generic functions
num=-function: Exported functions
numseq: Exported functions

O
open-left?: Exported generic functions
open-left?: Exported generic functions
open-left?: Exported generic functions
open-right?: Exported generic functions
open-right?: Exported generic functions
open-right?: Exported generic functions
opposite-sign?: Internal functions

P
pad-left-expansion: Internal functions
plusminus-interval: Exported functions
pool: Exported functions
pool2: Internal generic functions
pool2: Internal generic functions
print-left-endpoint: Internal generic functions
print-left-endpoint: Internal generic functions
print-left-endpoint: Internal generic functions
print-length-truncate: Exported functions
print-matrix: Exported functions
print-matrix-formatter: Internal functions
print-right-endpoint: Internal generic functions
print-right-endpoint: Internal generic functions
print-right-endpoint: Internal generic functions
product: Exported generic functions
product: Exported generic functions
product: Exported generic functions

Q
quantile: Exported generic functions
quantile: Exported generic functions
quantile: Exported generic functions
quantiles: Exported generic functions
quantiles: Exported generic functions
quantiles: Exported generic functions

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

S
same-sign?: Exported functions
sd: Exported generic functions
sd: Exported generic functions
shift-interval: Exported generic functions
shift-interval: Exported generic functions
shrink-interval: Exported functions
similar-element-type: Internal functions
similar-sequence-type: Internal functions
skewness: Exported generic functions
skewness: Exported generic functions
skewness: Exported generic functions
sort-reals: Internal functions
sorted-reals-elements: Exported functions
sorted-reals-ordered-elements: Internal functions
sorted-reals-p: Internal functions
sorted-reals-unordered-elements: Internal functions
spacer: Exported functions
spacer-p: Internal functions
spacer-weight: Internal functions
sparse-counter-count: Exported functions
sparse-counter-p: Internal functions
sparse-counter-table: Exported functions
splice-awhen: Exported macros
splice-when: Exported macros
split-interval: Exported functions
square: Exported functions
subintervals-in: Exported functions
sum: Exported generic functions
sum: Exported generic functions
sum: Exported generic functions

T
tabulate: Exported functions
tally: Exported generic functions
tally: Exported generic functions
tally: Exported generic functions
tally-mixin-p: Internal functions
tally-mixin-w: Internal functions
transformed-quadrature: Internal generic functions
transformed-quadrature: Internal generic functions
transformed-quadrature: Internal generic functions
transpose: Exported generic functions
transpose: Exported generic functions
transpose: Exported generic functions
transpose: Exported generic functions
transpose: Exported generic functions
transpose: Exported generic functions
trapezoidal-quadrature: Internal functions
trapezoidal-quadrature%: Internal functions
trapezoidal-quadrature-a: Internal functions
trapezoidal-quadrature-b: Internal functions
trapezoidal-quadrature-f: Internal functions
trapezoidal-quadrature-h: Internal functions
trapezoidal-quadrature-n: Internal functions
trapezoidal-quadrature-p: Internal functions
trapezoidal-quadrature-sum: Internal functions
truncate*: Exported functions

U
univariate-rootfinder-loop%: Internal macros
unlessf: Exported macros
upper-triangular-matrix: Exported functions
upper-triangular-matrix-elements: Internal functions
upper-triangular-matrix-p: Internal functions
upper-triangular-mx: Exported macros

V
valid-sparse-type?: Internal functions
variance: Exported generic functions
variance: Exported generic functions
variance: Exported generic functions
vec: Exported functions

W
weighted-empirical-quantile: Internal functions
weighted-quantile-p-table: Internal functions
weighted-quantiles: Exported functions
with-double-floats: Exported macros
with-template: Exported macros
within?: Exported functions
wrapped-matrix-elements: Exported functions
wrapped-matrix-p: Internal functions

Z
zero-like: Internal functions

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A.3 Variables

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Index Entry  Section

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

A
a: Internal structures

B
b: Internal structures

C
coefficient: Internal structures

D
diagonal: Internal structures

E
elements: Exported structures
elements: Exported structures

F
f: Internal structures
fraction: Exported structures

H
h: Internal structures

L
left: Internal classes

M
m: Exported structures

N
n: Internal structures
n: Internal structures

O
open-left?: Internal classes
open-right?: Internal classes
ordered-elements: Exported structures

R
right: Internal classes

S
s2: Exported structures
s3: Exported structures
s4: Exported structures
Slot, a: Internal structures
Slot, b: Internal structures
Slot, coefficient: Internal structures
Slot, diagonal: Internal structures
Slot, elements: Exported structures
Slot, elements: Exported structures
Slot, f: Internal structures
Slot, fraction: Exported structures
Slot, h: Internal structures
Slot, left: Internal classes
Slot, m: Exported structures
Slot, n: Internal structures
Slot, n: Internal structures
Slot, open-left?: Internal classes
Slot, open-right?: Internal classes
Slot, ordered-elements: Exported structures
Slot, right: Internal classes
Slot, s2: Exported structures
Slot, s3: Exported structures
Slot, s4: Exported structures
Slot, sum: Internal structures
Slot, table: Exported structures
Slot, unordered-elements: Exported structures
Slot, w: Internal structures
Slot, weight: Exported structures
Special Variable, *central-sample-moments-default-degree*: Exported special variables
Special Variable, *num=-tolerance*: Exported special variables
Special Variable, *print-matrix-precision*: Exported special variables
Special Variable, *rootfinding-delta-relative*: Exported special variables
Special Variable, *rootfinding-epsilon*: Exported special variables
sum: Internal structures

T
table: Exported structures

U
unordered-elements: Exported structures

W
w: Internal structures
weight: Exported structures

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

A.4 Data types

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Index Entry  Section

C
central-sample-moments: Exported structures
cl-num-utils: The cl-num-utils system
cl-num-utils: The cl-num-utils package
cl-num-utils.arithmetic: The cl-num-utils<dot>arithmetic package
cl-num-utils.chebyshev: The cl-num-utils<dot>chebyshev package
cl-num-utils.elementwise: The cl-num-utils<dot>elementwise package
cl-num-utils.extended-real: The cl-num-utils<dot>extended-real package
cl-num-utils.interval: The cl-num-utils<dot>interval package
cl-num-utils.matrix: The cl-num-utils<dot>matrix package
cl-num-utils.matrix-shorthand: The cl-num-utils<dot>matrix-shorthand package
cl-num-utils.num=: The cl-num-utils<dot>num= package
cl-num-utils.print-matrix: The cl-num-utils<dot>print-matrix package
cl-num-utils.quadrature: The cl-num-utils<dot>quadrature package
cl-num-utils.rootfinding: The cl-num-utils<dot>rootfinding package
cl-num-utils.statistics: The cl-num-utils<dot>statistics package
cl-num-utils.utilities: The cl-num-utils<dot>utilities package
Class, finite-interval: Exported classes
Class, interval: Exported classes
Class, interval/finite-left: Internal classes
Class, interval/finite-right: Internal classes
Class, interval/infinite-left: Internal classes
Class, interval/infinite-right: Internal classes
Class, minusinf-interval: Exported classes
Class, plusinf-interval: Exported classes
Class, real-line: Exported classes
Condition, empty-accumulator: Exported conditions
Condition, information-not-collected-in-accumulator: Exported conditions
Condition, not-enough-elements-in-accumulator: Exported conditions

D
diagonal-matrix: Exported structures

E
empty-accumulator: Exported conditions
extended-real: Exported types

F
finite-interval: Exported classes

H
hermitian-matrix: Exported structures

I
infinite: Internal types
information-not-collected-in-accumulator: Exported conditions
interval: Exported classes
interval/finite-left: Internal classes
interval/finite-right: Internal classes
interval/infinite-left: Internal classes
interval/infinite-right: Internal classes
iterative-quadrature: Internal structures

L
lower-triangular-matrix: Exported structures

M
midpoint-quadrature: Internal structures
minusinf-interval: Exported classes

N
not-enough-elements-in-accumulator: Exported conditions

P
Package, cl-num-utils: The cl-num-utils package
Package, cl-num-utils.arithmetic: The cl-num-utils<dot>arithmetic package
Package, cl-num-utils.chebyshev: The cl-num-utils<dot>chebyshev package
Package, cl-num-utils.elementwise: The cl-num-utils<dot>elementwise package
Package, cl-num-utils.extended-real: The cl-num-utils<dot>extended-real package
Package, cl-num-utils.interval: The cl-num-utils<dot>interval package
Package, cl-num-utils.matrix: The cl-num-utils<dot>matrix package
Package, cl-num-utils.matrix-shorthand: The cl-num-utils<dot>matrix-shorthand package
Package, cl-num-utils.num=: The cl-num-utils<dot>num= package
Package, cl-num-utils.print-matrix: The cl-num-utils<dot>print-matrix package
Package, cl-num-utils.quadrature: The cl-num-utils<dot>quadrature package
Package, cl-num-utils.rootfinding: The cl-num-utils<dot>rootfinding package
Package, cl-num-utils.statistics: The cl-num-utils<dot>statistics package
Package, cl-num-utils.utilities: The cl-num-utils<dot>utilities package
plusinf-interval: Exported classes

R
real-line: Exported classes
relative: Exported structures
richardson-extrapolation: Internal structures

S
simple-double-float-vector: Exported types
simple-fixnum-vector: Exported types
sorted-reals: Exported structures
spacer: Exported structures
sparse-counter: Exported structures
Structure, central-sample-moments: Exported structures
Structure, diagonal-matrix: Exported structures
Structure, hermitian-matrix: Exported structures
Structure, iterative-quadrature: Internal structures
Structure, lower-triangular-matrix: Exported structures
Structure, midpoint-quadrature: Internal structures
Structure, relative: Exported structures
Structure, richardson-extrapolation: Internal structures
Structure, sorted-reals: Exported structures
Structure, spacer: Exported structures
Structure, sparse-counter: Exported structures
Structure, tally-mixin: Internal structures
Structure, trapezoidal-quadrature: Internal structures
Structure, upper-triangular-matrix: Exported structures
Structure, wrapped-matrix: Exported structures
System, cl-num-utils: The cl-num-utils system

T
tally-mixin: Internal structures
trapezoidal-quadrature: Internal structures
triangular-matrix: Exported types
Type, extended-real: Exported types
Type, infinite: Internal types
Type, simple-double-float-vector: Exported types
Type, simple-fixnum-vector: Exported types
Type, triangular-matrix: Exported types

U
upper-triangular-matrix: Exported structures

W
wrapped-matrix: Exported structures

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