Math Library
Math Library
Constants and Elementary Functions
Flonums
Special Functions
Number Theory
Arbitrary-
Precision Floating-
Point Numbers (
Bigfloats
Arrays
Matrices and Linear Algebra
Statistics Functions
Probability Distributions
10
Stuff That Doesn’t Belong Anywhere Else
On this page:
Math Library
9.1
Racket
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Math Library
Neil Toronto <
ntoronto@racket-lang.org
Jens Axel Søgaard <
jensaxel@soegaard.net
require
math
package:
math-lib
The
math
library provides functions and data structures useful
for working with numbers and collections of numbers. These include
math/base
: Constants and elementary functions
math/flonum
: Flonum functions, including high-accuracy support
math/special-functions
: Special (i.e. non-elementary) functions
math/bigfloat
: Arbitrary-precision floating-point functions
math/number-theory
: Number-theoretic functions
math/array
: Functional arrays for operating on large rectangular data sets
math/matrix
: Linear algebra functions for arrays
math/distributions
: Probability distributions
math/statistics
: Statistical functions
With this library, we hope to support a wide variety of applied mathematics in
Racket, including simulation, statistical inference, signal processing, and
combinatorics. If you find it lacking for your variety of mathematics, please
Visit the
Math Library Features wiki page
to see what is planned.
Contact us or post to one of the
mailing lists
to
make suggestions or submit patches.
This is a Typed Racket library.
It is most efficient to use it in Typed
Racket, so that contracts are checked statically. However, almost all of it can
be used in untyped Racket. Exceptions and performance warnings are in
bold text
Constants and Elementary Functions
1.1
Constants
1.2
Functions
1.3
Random Number Generation
1.4
Measuring Error
Flonums
2.1
Additional Flonum Functions
2.2
Log-Space Arithmetic
2.3
Debugging Flonum Functions
2.3.1
Measuring Floating-Point Error
2.3.2
Flonum Constants
2.3.3
Low-Level Flonum Operations
2.4
Double-Double Operations
2.4.1
Debugging Double-Double Functions
2.4.2
Low-Level Double-Double Operations
2.5
Additional Flonum Vector Functions
Special Functions
3.1
Real Functions
3.2
Flonum Functions
Number Theory
4.1
Congruences and Modular Arithmetic
4.1.1
Parameterized Modular Arithmetic
4.2
Primes
4.3
Roots
4.4
Powers
4.5
Multiplicative and Arithmetic Functions
4.6
Number Sequences
4.7
Combinatorics
4.8
Special Numbers
4.8.1
Polygonal Numbers
4.9
Fractions
4.10
The Quadratic Equation
4.11
The group Zn and Primitive Roots
Arbitrary-Precision Floating-Point Numbers (
Bigfloats
5.1
Quick Start
5.2
Fictionally Asked Questions
5.3
Type and Constructors
5.4
Accessors and Conversion Functions
5.5
Parameters
5.6
Constants
5.7
Predicates
5.8
Rounding
5.9
Mathematical Operations
5.10
Low-level Functions
Arrays
6.1
Quick Start
6.2
Definitions
6.3
Broadcasting
6.3.1
Broadcasting Rules
6.3.2
Broadcasting Control
6.4
Slicing
6.4.1
Sequenceof
Integer
: pick rows
6.4.2
Slice
: pick rows in a length-aware way
6.4.3
Slice-Dots
: preserve remaining axes
6.4.4
Integer
: remove an axis
6.4.5
Slice-New-Axis
: add an axis
6.5
Nonstrict Arrays
6.5.1
Caching Nonstrict Elements
6.5.2
Performance Considerations
6.6
Types, Predicates and Accessors
6.7
Construction
6.8
Conversion
6.8.1
Printing
6.9
Comprehensions and Sequences
6.10
Pointwise Operations
6.10.1
Broadcasting
6.11
Indexing and Slicing
6.12
Transformations
6.13
Folds, Reductions and Expansions
6.13.1
Axis Folds
6.13.2
Whole-Array Folds
6.13.3
General Reductions and Expansions
6.14
Other Array Operations
6.14.1
Fast Fourier Transform
6.15
Subtypes
6.15.1
Flonum Arrays
6.15.2
Float-Complex Arrays
6.16
Strictness
Matrices and Linear Algebra
7.1
Introduction
7.1.1
Function Types
7.1.2
Failure Arguments
7.1.3
Broadcasting
7.1.4
Strictness
7.2
Types, Predicates and Accessors
7.3
Construction
7.4
Conversion
7.5
Entrywise Operations and Arithmetic
7.6
Polymorphic Operations
7.7
Basic Operations
7.8
Inner Product Space Operations
7.9
Solving Systems of Equations
7.10
Row-Based Algorithms
7.11
Orthogonal Algorithms
7.12
Operator Norms and Comparing Matrices
Statistics Functions
8.1
Expected Values
8.2
Running Expected Values
8.3
Correlation
8.4
Counting and Binning
8.5
Order Statistics
8.6
Simulations
Probability Distributions
9.1
Distribution Objects
9.2
Distribution Types and Operations
9.3
Finite Distribution Families
9.3.1
Unordered Discrete Distributions
9.4
Integer Distribution Families
9.4.1
Bernoulli Distributions
9.4.2
Binomial Distributions
9.4.3
Geometric Distributions
9.4.4
Poisson Distributions
9.5
Real Distribution Families
9.5.1
Beta Distributions
9.5.2
Cauchy Distributions
9.5.3
Delta Distributions
9.5.4
Exponential Distributions
9.5.5
Gamma Distributions
9.5.6
Weibull Distributions
9.5.7
Logistic Distributions
9.5.8
Normal Distributions
9.5.9
Student-t Distributions
9.5.10
Triangular Distributions
9.5.11
Truncated Distributions
9.5.12
Uniform Distributions
9.6
Low-Level Distribution Functions
9.6.1
Integer Distribution Functions
9.6.2
Real Distribution Functions
10
Stuff That Doesn’t Belong Anywhere Else
10.1
Parallelization
10.2
Discrete Fourier Transform Conventions
10.3
Floating-Point Compliance Testing
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