You are looking at historical revision 43216 of this page. It may differ significantly from its current revision.

math-utils

Documentation

Miscellaneous Math Functions

Usage

 
(import math-utils)

number->sign

[procedure] (number->sign N) -> fixnum

Returns -1, 0, or +1 to represent the sign of the number N.

log-with-base

log/base

[procedure] (log-with-base B) -> (real -> real)
[procedure] (log/base B) -> (real -> real)

Returns a function for the base B logarithm.

coprime?

[procedure] (coprime? M [N0 ...]) -> boolean

Are the integers M N0 ... coprime?

pairwise-coprime?

[procedure] (pairwise-coprime? M [N0 ...]) -> boolean

Are the pairs of integers in M N0 ... coprime?

fxcoprime?

[procedure] (fxcoprime? M N) -> boolean

Are the fixnums M N coprime?

(import (only (srfi 1) filter iota))
(import (only (math-utils) fxcoprime?))

(define (coprimes n)
  (filter (cut fxcoprime? n <>) (iota (- n 1) 1)) )
(import (only (streams derived) stream-range stream-filter))
(import (only (math-utils) fxcoprime?))

(define (coprime-numbers-stream n)
  (stream-filter (cut fxcoprime? n <>) (stream-range 1 n)) )

simple-interest

[procedure] (simple-interest RATE TIME [PRIN]) -> number

The accumulation function, the principle is assumed 1. Returns the simple interest for the RATE over TIME.

RATE ; number ; interest rate
TIME ; number ; time period to cover
PRIN ; number ; principle, default 1

compound-interest

[procedure] (compound-interest RATE FREQ TIME [PRIN]) -> number

The accumulation function, the principle is assumed 1. Returns the compound interest for the RATE, applied with FREQ, over TIME.

RATE ; number ; interest rate
FREQ ; number ; compounding frequency
TIME ; number ; time period to cover
PRIN ; number ; principle, default 1
(compound-interest 0.043 4 6 1500)
;=> 1938.84 ;rounded to 2 places

fibonacci

[procedure] (fibonacci N) -> number

Returns fibonacci of N.

fibonacci*

[procedure] (fibonacci* N) -> number

Returns an approximate fibonacci of N.

binomial

[procedure] (binomial N1 N2) -> integer

Returns the Binomial in N1 to N2.

N1 ; integer
N2 ; integer

cross-ratio

[procedure] (cross-ratio N1 N2 N3 N4) -> number

Returns the Cross-ratio of N1, N2 and N3, N4.

N1 ; number
N2 ; number
N3 ; number
N4 ; number

square

[procedure] (square N) -> number

cube

[procedure] (cube N) -> number

average

[procedure] (average N1 N2 ...) -> number
[procedure] (average NUMS) -> number
N1 ; number
N1 ; number
NUMS ; (list-of number)

least-squares

[procedure] (least-squares PNTS) -> number number

Returns b & e such that y ~= b * x + e.

PNTS ; (list-of (pair number number))
list of x,y pairs

trapezoid

[procedure] (trapezoid F N1 N2) -> (fixnum -> number)

Returns a function to calculate the area under F between N1 & N2 using the Trapezoid Rule. The function takes the number of estimations as an argument, larger for a "better" result.

F ; (number -> number)
N1 ; number
N2 ; number

factorial

factorial-

factorial+

[procedure] (factorial N) -> number
[procedure] (factorial- N1 FALL) -> number
[procedure] (factorial+ N1 RISE) -> number
N ; integer
FALL
number : falling factorial
RISE
number : rising factorial

harmonic

[procedure] (harmonic N) -> number

Result of Harmonic series expansion to N terms.

N ; integer

big-pi

[syntax] (big-pi F N1 N2) -> number

Product of F in N1 to N2.

F
(number -> number) ;
N1
number ;
N2
number ;

big-sigma

[syntax] (big-sigma F N1 N2) -> number

Sum of F in N1 to N2.

F
(number -> number) ;
N1
number ;
N2
number ;

Miscellaneous Vector Math Functions

Usage

 
(import (math-utils vector))

absolute-magnitude

[procedure] (absolute-magnitude NUMVEC) -> number
NUMVEC ; (vector-of number)
.

cosine-similarity

[procedure] (cosine-similarity NUMVEC1 NUMVEC2) -> number
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

vector-compare

[procedure] (vector-compare NUMVEC...) -> number

Result is negative, zero, or positive. Comparison by length when unequal & element-wise when equal.

NUMVEC ; (vector-of number)
.

dot-product

[procedure] (dot-product NUMVEC1 NUMVEC2) -> number
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

cross-product

[procedure] (cross-product NUMVEC1 NUMVEC2) -> (or number (vector-of number))
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

Only defined for a vector-length of (0 1 2), returning a number, and (3 4 8), returning a (vector-of number). All others generate an error.

vector-mul

vector-sum

vector-div

vector-dif

vector-min

vector-max

vector-lcm

vector-gcd

[procedure] (vector-mul NUMVEC...) -> (vector-of number)
[procedure] (vector-sum NUMVEC...) -> (vector-of number)
[procedure] (vector-div NUMVEC...) -> (vector-of number)
[procedure] (vector-dif NUMVEC...) -> (vector-of number)
[procedure] (vector-min NUMVEC...) -> (vector-of number)
[procedure] (vector-max NUMVEC...) -> (vector-of number)
[procedure] (vector-lcm NUMVEC...) -> (vector-of number)
[procedure] (vector-gcd NUMVEC...) -> (vector-of number)
NUMVEC ; (vector-of number)
.

Must be same vector-length.

vector-apply

[procedure] (vector-apply FUNC VEC1 VEC2 [VEC...]) -> vector
FUNC ; (* * !#rest * -> *)
.
VEC# ; vector
.

Must be same vector-length.

Requirements

mathh

test test-utils vector-lib

Author

Kon Lovett

Repository

This egg is hosted on the CHICKEN Subversion repository:

https://anonymous@code.call-cc.org/svn/chicken-eggs/release/5/math-utils

If you want to check out the source code repository of this egg and you are not familiar with Subversion, see this page.

Version history
1.0.4
Add fxcoprime?.
1.0.3
*coprime? too slow.
1.0.2
Fix mathh dependency.
1.0.1
Add vector-compare.
1.0.0
From mathh:4.6.5.

License

This code is in the public domain.