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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) -> 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 :

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

[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

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

1.2.0

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.