math-utils

Documentation

Miscellaneous Math Functions

Usage

(import math-utils)

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 :

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 :

euclidian-distance

euclidian-distance X1 Y1 X2 Y2procedure

Distance between X1,Y1 and X2,Y2.

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

manhattan-distance

manhattan-distance X1 Y1 X2 Y2procedure

Distance between X1,Y1 and X2,Y2.

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

to-places

(to-places PREC (FUNC EXPR))syntax

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

(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

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.