chickadee » math-utils

math-utils

Documentation

Miscellaneous Math Functions

Usage

(import math-utils)

number->sign

number->sign Nprocedure

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

log-with-base

log/base

log-with-base Bprocedure
log/base Bprocedure

Returns a function for the base B logarithm.

coprime?

(coprime? M [N0 ...]) -> booleanprocedure

Are the integers M N0 ... coprime?

pairwise-coprime?

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

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

fxcoprime?

fxcoprime? M Nprocedure

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

simple-interest RATE TIME #!optional PRINprocedure

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

compound-interest RATE FREQ TIME #!optional PRINprocedure

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

fibonacci Nprocedure

Returns fibonacci of N.

fibonacci*

fibonacci* Nprocedure

Returns an approximate fibonacci of N.

binomial

binomial N1 N2procedure

Returns the Binomial in N1 to N2.

N1 ; integer
N2 ; integer

cross-ratio

cross-ratio N1 N2 N3 N4procedure

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

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

square

square Nprocedure

cube

cube Nprocedure

average

average N1 N2 ...procedure
average NUMSprocedure
N1 ; number
N1 ; number
NUMS ; (list-of number)

least-squares

least-squares PNTSprocedure

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

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

trapezoid

trapezoid F N1 N2procedure

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+

factorial Nprocedure
factorial- N1 FALLprocedure
factorial+ N1 RISEprocedure
N ; integer
FALL
number : falling factorial
RISE
number : rising factorial

harmonic

harmonic Nprocedure

Result of Harmonic series expansion to N terms.

N ; integer

big-pi

(big-pi F N1 N2) -> numbersyntax

Product of F in N1 to N2.

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

big-sigma

(big-sigma F N1 N2) -> numbersyntax

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

absolute-magnitude NUMVECprocedure
NUMVEC ; (vector-of number)
.

cosine-similarity

cosine-similarity NUMVEC1 NUMVEC2procedure
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

vector-compare

vector-compare NUMVEC...procedure

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

NUMVEC ; (vector-of number)
.

dot-product

dot-product NUMVEC1 NUMVEC2procedure
NUMVEC1 ; (vector-of number)
.
NUMVEC2 ; (vector-of number)
.

Must be same vector-length.

cross-product

cross-product NUMVEC1 NUMVEC2procedure
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

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

Must be same vector-length.

vector-apply

vector-apply FUNC VEC1 VEC2 #!optional VEC...procedure
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

1.0.6
Remove mathh dependency since include is unreliable.
1.0.5
Use gcd based algorithm.
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.

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