math_util.h File Reference

Header file for general utilities. More...

#include <stdlib.h>
#include <cmath>
#include "Bstring.h"
#include "utilities.h"

Functions
double	bfloor (double value, int places)
	Truncates a value to a specified number of decimal places. More...
double	bround (double value, int places)
	Rounds a value to a specified number of decimal places. More...
double	sinc (double d)
	Returns the normalized cardinal sine. More...
double	factorial (int n)
	Calculates the factorial of n. More...
double	number_of_combinations (int n, int r)
	Calculates the number of combinations of size r in set of size n. More...
int	partition (vector< double > &a, int n, int k)
	Determines the index k'th value in the array. More...
int	partition (double *a, int n, int k)
long *	prime_factors (long number, long &n)
	Finds all the prime factor for the input number. More...
long	smallest_prime (long number)
	Finds the smallest prime number factor of the input number. More...
int	next_permutation (Bstring &s)
	Produces the next permutation in lexical order. More...
double	fishers_z_transform (double value)
	Calculates Fisher's z-transform. More...
double	betacf (double a, double b, double x)
	Evaluates the continued fraction for the incomplete beta function. More...
double	betai (double a, double b, double x)
	Calculates the incomplete beta function Ix(a,b). More...
double	kmeans_threshold (long n, double *v)
	Finds a threshold that partitions an array into foreground and background clusters. More...

Detailed Description

Header file for general utilities.

Author

Bernard Heymann

Date

Created: 19990722

Modified: 20220524

Function Documentation

betacf()

double betacf	(	double	a,
		double	b,
		double	x
	)

Evaluates the continued fraction for the incomplete beta function.

Parameters

a	first parameter.
b	second parameter.
x	domain variable [0,1].

Returns

double

Lentz's method.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

betai()

double betai	(	double	a,
		double	b,
		double	x
	)

Calculates the incomplete beta function Ix(a,b).

Parameters

a	first parameter.
b	second parameter.
x	domain variable [0,1].

Returns

double

Limiting values: I0(a,b) = 0, I1(a,b) = 1.
Symmetry relation: Ix(a,b) = 1 - I1-x(b,a).

Reference: Press W.H. et al (1992) Numerical Recipes in C.

bfloor()

double bfloor	(	double	value,
		int	places
	)

Truncates a value to a specified number of decimal places.

Parameters

value	value to be truncated.
places	number of decimal places.

Returns

int 0.

bround()

double bround	(	double	value,
		int	places
	)

Rounds a value to a specified number of decimal places.

Parameters

value	value to be rounded.
places	number of decimal places.

Returns

double rounded value.

factorial()

double factorial

(

int

n

)

Calculates the factorial of n.

Parameters

n

integer.

Returns

double factorial of n, <0 on error.

All values of n less than 1 returns 1.
An exact calculation is done for 1 < n <= 50.
The Lancos approximation is used for n > 50.
Factorials of integers larger than 170 exceeds the capacity of a 
double and causes program termination.
The largest relative error is for 170: 1.22378e-13.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

fishers_z_transform()

double fishers_z_transform

(

double

value

)

Calculates Fisher's z-transform.

Parameters

value

a value.

Returns

double z value.

Fisher's z-transform is given by:
    z = 0.5*log((1+v)/(1-v))

Reference: Press W.H. et al (1992) Numerical Recipes in C.

kmeans_threshold()

double kmeans_threshold	(	long	n,
		double *	v
	)

Finds a threshold that partitions an array into foreground and background clusters.

Parameters

n	number of array elements.
v	array.

Returns

double threshold.

Limiting values: I0(a,b) = 0, I1(a,b) = 1.
Symmetry relation: Ix(a,b) = 1 - I1-x(b,a).

Reference: Press W.H. et al (1992) Numerical Recipes in C.

next_permutation()

int next_permutation

(

Bstring &

s

)

Produces the next permutation in lexical order.

Parameters

&s	string of symbols to permute.

Returns

int 1 = success, 0 = no next permutation.

To get all permutations, the first string needs
to be ordered in ascending order.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

number_of_combinations()

double number_of_combinations	(	int	n,
		int	r
	)

Calculates the number of combinations of size r in set of size n.

Parameters

n	number in set.
r	number in subset.

Returns

double number of combinations, <0 on error.

All values of n less than 1 returns 1.
An exact calculation is done for 1 < n <= 50.
The Lancos approximation is used for n > 50.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

partition() [1/2]

int partition	(	double *	a,
		int	n,
		int	k
	)

partition() [2/2]

int partition	(	vector< double > &	a,
		int	n,
		int	k
	)

Determines the index k'th value in the array.

Parameters

*a	array.
n	number of array elements.
k	rank index to look for.

Returns

0

The array is partioned into 2 sides, with the left side lower or equal 
to and the right side higher or equal to the k'th element.
This is useful to determine the median without full sorting.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

prime_factors()

long * prime_factors	(	long	number,
		long &	n
	)

Finds all the prime factor for the input number.

Parameters

number	integer.
&n	number of prime factors.

Returns

long* array of prime factors (can be NULL).

Calculates the prime factors from the smallest to the largest.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

sinc()

double sinc

(

double

d

)

Returns the normalized cardinal sine.

Parameters

d

value.

Returns

double sinc value.

smallest_prime()

long smallest_prime

(

long

number

)

Finds the smallest prime number factor of the input number.

Parameters

number

integer.

Returns

long smallest prime factor.

Tries to divide the given positive integer number by 
primes from 2 to the square root of the integer.
Returns the first prime divisor found, which may be the 
input number if it is prime.

Reference: Press W.H. et al (1992) Numerical Recipes in C.