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math-utils

Documentation

Miscellaneous Math Functions

Usage

 
(import math-utils)

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) -> integer

Returns fibonacci of integer N.

*fibonacci

[procedure] (*fibonacci N) -> real

Returns an approximate fibonacci of integer N, with an error of > 1 at N ~= 70.

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 [N0 ...]) -> number
N0
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

[procedure] (factorial N) -> number

factorial-

factorial+

[procedure] (factorial- N FALL) -> real
[procedure] (factorial+ N RISE) -> real
N
real :
FALL
real : falling factorial
RISE
real : rising factorial

harmonic

[procedure] (harmonic N) -> real

Result of Harmonic series expansion to N terms.

N
real :

Allow real even though defined over integer normally.

euclidian-distance

[procedure] (euclidian-distance X1 Y1 X2 Y2) -> number

Distance between X1,Y1 and X2,Y2.

X1 Y1
number number ; from point
X2 Y2
number number ; to point

manhattan-distance

[procedure] (manhattan-distance X1 Y1 X2 Y2) -> number

Distance between X1,Y1 and X2,Y2.

X1 Y1
number number ; from point
X2 Y2
number number ; to point

to-places

[syntax] (to-places PREC (FUNC EXPR))

Truncate the result of (FUNC EXPR) to PREC decimal places.

PREC
fixnum ; precision
FUNC
symbol ; clip operation, i.e. round, floor, etc.
EXPR
* ; value to clip

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

vector-compare2

[procedure] (vector-compare NUMVEC ...) -> number
[procedure] (vector-compare2 NUMVEC 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))

Only defined for a vector-length of (0 1 2 3 4 8). All others generate an error. Must be same vector-length.

NUMVEC1
(vector-of number) : .
NUMVEC2
(vector-of number) : .

vector-sum

[procedure] (vector-sum NUMVEC) -> number

softmax

[procedure] (softmax NUMVEC) -> (vector-of number)

Returns the softmax of the vector elements.

vector-mul

vector-add

vector-div

vector-dif

vector-min

vector-max

vector-lcm

vector-gcd

[procedure] (vector-mul NUMVEC...) -> (vector-of number)
[procedure] (vector-add 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

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
1.4.0
Add softmax. Allow real arguments to factorial+, factorial-, harmonic. Add euclidian-distance & manhattan-distance.
1.3.2
Fix cross-product return.
1.3.1
Fix average signature.
1.3.0
cross-product returns number-vector. Add vector-compare2. Rename fibonacci*. Drop deprecated.
1.2.0
Add to-places. Deprecate with-places.
1.1.0
Add with-places.
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.