random_numbers.cpp File Reference

Functions for generating random sequences. More...

#include "Vector3.h"
#include "utilities.h"

Functions
int	randseed (0)
long	get_rand_max ()
	Finds the maximum random number for a system. More...
double	irm (1.0L/get_rand_max())
long	random_seed ()
	Gets a random seed and sets the flag. More...
int	random_array_uniform_chunk (float *r, long start, long end, double min, double range)
float *	random_array_uniform (long n, double min, double max)
	Generates a series with a uniform random distribution. More...
double	random_gaussian (double avg, double stdev)
	Generates a value with a gaussian random distribution. More...
int	random_array_gaussian_chunk (float *r, long start, long end, double avg, double stdev)
float *	random_array_gaussian (long n, double avg, double stdev)
	Generates a series with a gaussian random distribution of values. More...
double	random_poisson (double avg)
	Generates a value deviating from the average based on a poisson distribution. More...
int	random_array_poisson_chunk (float *r, long start, long end, double avg)
float *	random_array_poisson (int n, double avg)
	Generates a series with a poisson random distribution of values. More...
double	random_logistical (double avg, double stdev)
	Generates a value with a logistical random distribution. More...
int	random_array_logistical_chunk (float *r, long start, long end, double avg, double stdev)
float *	random_array_logistical (long n, double avg, double stdev)
	Generates an array with a logistical random distribution. More...
Vector3< double >	vector3_random_unit_sphere ()
	Generates a random vector on the unit sphere. More...
Vector3< double >	vector3_random (const double min, const double max)
	Generates a random vector within a defined cube. More...
Vector3< double >	vector3_random (Vector3< double > min, Vector3< double > max)
	Generates a random vector within a defined cube. More...
Vector3< double >	vector3_random (const double length)
	Generates a random vector within a defined sphere. More...
Vector3< double >	vector3_random_gaussian (double avg, double stdev)
	Generates a random vector within a random gaussian-distributed length. More...
Vector3< double >	vector3_xy_random_gaussian (double avg, double stdev)
	Generates a random vector within a random gaussian-distributed length in the xy plane. More...
double	halton_number (long i, long b)
double *	halton_sequence (long n, long b)
	Generates a Halton sequence. More...

Variables
int	verbose

Detailed Description

Functions for generating random sequences.

Author

Bernard Heymann

Date

Created: 19990703

Modified: 20151113

Function Documentation

get_rand_max()

long get_rand_max

(

)

Finds the maximum random number for a system.

Returns

long the maximum random number.

Loops through random numbers to determine if the maximum is 2 or 4 bytes.

halton_number()

double halton_number	(	long	i,
		long	b
	)

halton_sequence()

double * halton_sequence	(	long	n,
		long	b
	)

Generates a Halton sequence.

Parameters

n	length of sequence.
b	base.

Returns

double* sequence.

The Halton sequence is a pseudo-random array.

irm()

double irm

(

1.0L/

get_rand_max()

)

random_array_gaussian()

float * random_array_gaussian	(	long	n,
		double	avg,
		double	stdev
	)

Generates a series with a gaussian random distribution of values.

Parameters

n	number of values.
avg	average.
stdev	standard deviation.

Returns

float* the array of values.

An array of floating point numbers is generated with a gaussian 
distribution with a given average and standard deviation:
    value = average + std_dev*sqrt(-2*log(random_value))*
                    cos(2*PI*random_value);
where random_value is between 0 and 1.

random_array_gaussian_chunk()

int random_array_gaussian_chunk	(	float *	r,
		long	start,
		long	end,
		double	avg,
		double	stdev
	)

random_array_logistical()

float * random_array_logistical	(	long	n,
		double	avg,
		double	stdev
	)

Generates an array with a logistical random distribution.

Parameters

n	number of values.
avg	average.
stdev	standard deviation.

Returns

float* array of values.

An array of floating point numbers is generated with a logistical 
differential distribution with a given average and standard deviation:
    value = average + (std_dev/golden)*ln(1/random_value - 1)
where random_value is between 0 and 1 and:
    golden  = (sqrt(5) + 1)/2

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

random_array_logistical_chunk()

int random_array_logistical_chunk	(	float *	r,
		long	start,
		long	end,
		double	avg,
		double	stdev
	)

random_array_poisson()

float * random_array_poisson	(	int	n,
		double	avg
	)

Generates a series with a poisson random distribution of values.

Parameters

n	number of values.
avg	average.

Returns

float* the array of values.

The poisson distribution is given for j = 0,1,... by:
            avg^j * exp(-avg)
    P(j) = -----------------
                   j!
Note that only positive integer values are defined for j and sum(P(j)) = 1.
An array of floating point numbers is generated with a poisson 
distribution with a given average. The standard deviation is:
    std = sqrt(avg)
If the average <= 0, the return array contains only zeroes.

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

random_array_poisson_chunk()

int random_array_poisson_chunk	(	float *	r,
		long	start,
		long	end,
		double	avg
	)

random_array_uniform()

float * random_array_uniform	(	long	n,
		double	min,
		double	max
	)

Generates a series with a uniform random distribution.

Parameters

n	number of values.
min	minimum value.
max	maximum value.

Returns

float* array with uniform random numbers.

An array of floating point numbers is generated distributed uniformly 
in the range of the given minimum and maximum:
    value = random_value*(max - min) + min
where random_value is between 0 and 1.
The average and standard deviation are:
    average = (max + min)/2
    standard deviation = 0.5*sqrt(1/3)*(max - min).

random_array_uniform_chunk()

int random_array_uniform_chunk	(	float *	r,
		long	start,
		long	end,
		double	min,
		double	range
	)

random_gaussian()

double random_gaussian	(	double	avg,
		double	stdev
	)

Generates a value with a gaussian random distribution.

Parameters

avg	average.
stdev	standard deviation.

Returns

double the random value.

A floating point number is generated with a gaussian 
distribution with a given average and standard deviation:
    value = average + std_dev*sqrt(-2*log(random_value))*
                    cos(2*PI*random_value);
where random_value is between 0 and 1.

random_logistical()

double random_logistical	(	double	avg,
		double	stdev
	)

Generates a value with a logistical random distribution.

Parameters

avg	average.
stdev	standard deviation.

Returns

double the random value.

A floating point number is generated with a logistical 
differential distribution with a given average and standard deviation:
    value = average + (std_dev/golden)*ln(1/random_value - 1)
where random_value is between 0 and 1 and:
    golden  = (sqrt(5) + 1)/2

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

random_poisson()

double random_poisson

(

double

avg

)

Generates a value deviating from the average based on a poisson distribution.

Parameters

avg

average.

Returns

double value.

The poisson distribution is given for j = 0,1,... by:
            avg^j * exp(-avg)
    P(j) = -----------------
                   j!
Note that only positive integer values are defined for j and sum(P(j)) = 1.
A value is generated with a poisson distribution with a given average.
If the average <= 0, the return value is zero.

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

random_seed()

long random_seed

(

)

Gets a random seed and sets the flag.

Returns

int flag.

The random seed is obtained using the program pid.
A flag is set to prevent the seed from being generated multiple times.

randseed()

int randseed

(

0

)

vector3_random() [1/3]

Vector3< double > vector3_random

(

const double

length

)

Generates a random vector within a defined sphere.

Parameters

length

maximum vector length.

Returns

Vector3<double> vector.

A random vector is generated, normalized and multiplied with
a random value smaller than the given length.

vector3_random() [2/3]

Vector3< double > vector3_random	(	const double	min,
		const double	max
	)

Generates a random vector within a defined cube.

Parameters

min	minimum.
max	maximum.

Returns

Vector3<double> vector.

Each vector element is set to a random value between the given minimum and maximum.

vector3_random() [3/3]

Vector3< double > vector3_random	(	Vector3< double >	min,
		Vector3< double >	max
	)

Generates a random vector within a defined cube.

Parameters

min	minimum vector.
max	maximum vector.

Returns

Vector3<double> vector.

Each vector element is set to a random value between the given 
minimum and maximum vectors.

vector3_random_gaussian()

Vector3< double > vector3_random_gaussian	(	double	avg,
		double	stdev
	)

Generates a random vector within a random gaussian-distributed length.

Parameters

avg	average of gaussian distribution.
stdev	standard deviation of gaussian distribution.

Returns

Vector3<double> vector.

A random vector is generated, normalized and multiplied with
a random value derived from a gaussian distribution.

vector3_random_unit_sphere()

Vector3< double > vector3_random_unit_sphere

(

)

Generates a random vector on the unit sphere.

Returns

Vector3<double> vector.

A random vector is generated with a uniform distribution on the unit sphere.

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

vector3_xy_random_gaussian()

Vector3< double > vector3_xy_random_gaussian	(	double	avg,
		double	stdev
	)

Generates a random vector within a random gaussian-distributed length in the xy plane.

Parameters

avg	average of gaussian distribution.
stdev	standard deviation of gaussian distribution.

Returns

Vector3<double> vector.

A random vector is generated, the z-component set to zero, normalized 
and multiplied with a random value derived from a gaussian distribution.

Variable Documentation

verbose

int verbose

extern