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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?

*coprime?

[procedure] (coprime? M N) -> boolean
[procedure] (*coprime? M N) -> boolean

Are the integers M > N coprime?

*coprime? assumes the assertion, whereas coprime? will ensure.

(import (only (srfi 1) filter iota))
(import (only (misc-math-utils *coprime?))

(define (coprimes n #!optional (cnt (- n 1)))
  (filter (cut *coprime? n <>) (iota cnt 1 (quotient n cnt))) )

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.

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 NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-sum NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-div NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-dif NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-min NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-max NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-lcm NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
[procedure] (vector-gcd NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of number)
NUMVEC#
(vector-of number) ; .

Must be same vector-length.

vector<?

vector=?

vector>?

vector<=?

vector>=?

[procedure] (vector<? NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of boolean)
[procedure] (vector=? NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of boolean)
[procedure] (vector>? NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of boolean)
[procedure] (vector<=? NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of boolean)
[procedure] (vector>=? NUMVEC1 NUMVEC2 [NUMVEC...]) -> (vector-of boolean)
NUMVEC#
(vector-of number) ; .

Must be same vector-length.

vector-compare

[procedure] (vector-compare NUMVEC1 NUMVEC2 -> (vector-of number)

Result is (vector-dif NUMVEC2 NUMVEC1).

NUMVEC1
(vector-of number) ; .
NUMVEC2
(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

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
1.0.0
From mathh:4.6.5.

License

This code is in the public domain.