【算法分析】随机数的生成：均匀分布、正态、泊松 、瑞利_随机数分析

均匀分布：线性同余法

正态分布：sum-of-12 method

其他分布：逆变换法

/*****************************************  
Copyright (c) 2015 Jingshuang Hu  
  
@filename:demo.c  
@datetime:2015.10.18  
@author:HJS  
@e-mail:eleftheria@163.com  
@blog:http://blog.csdn.net/hujingshuang  
*****************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/**********************************************************************************************/
void menu(void);
double *Uniform_Distribution(unsigned int length, unsigned int num);
void Demo_Gaussian(void);
double *Gaussian_Distribution(double miu, double sigma, int length);
void Demo_Rayleigh(void);
double *Rayleigh_Distribution(double sigma, int length);
void Demo_Poisson(void);
int *Poisson_Distribution(double lamda,unsigned int length);
/**********************************************************************************************/
int main()
{
	menu();
	return 0;
}
/**********************************************************************************************/
void menu(void)
{
	int num = 0, flag = 0;
	while(!flag)
	{
		printf("---------random variates---------\n");
		printf("1.gaussian distribution\n2.rayleigh distribution\n3.poisson distribution\n4.exit\n");
		printf("---------------------------------\nyour choice<1,2,3,4>:");
		scanf("%d", &num);
		switch(num)
		{
			case 1:	Demo_Gaussian();break;
			case 2:	Demo_Rayleigh();break;
			case 3:	Demo_Poisson();	break;
			case 4:	flag = 1;		break;
			default:				break;
		}
		printf("Save success,press any key to continue.\n");
		getchar();getchar();
		fflush(stdin);
		system("cls");
	}
}
/**********************************************************************************************/
//uniform
double *Uniform_Distribution(unsigned int length, unsigned int num)
{
	unsigned int i = 0;
	unsigned int xn = (unsigned int)pow(2, 31);
	unsigned int lamda = (unsigned int)pow(7, 5);
	unsigned int base = (unsigned int)pow(2, 31) - 1;
	double *uniform = (double *)malloc(length * sizeof(double));
	for (i = 0; i < num; i++)
	{
		xn = (lamda * xn) % base;
	}
	for (i = 0; i < length; i++)
	{
		xn = (lamda * xn) % base;
		uniform[i] = (double)xn / (double)base;
	}
	return uniform;
}
/**********************************************************************************************/
/**********************************************************************************************/
//demo gaussian
void Demo_Gaussian(void)
{
	int i = 0, length = 0;
	double miu = 0, sigma = 1.0, *gaussian;
	char filename[50];
	FILE *fp;
	printf("length=");	scanf("%d", &length);	//length
	printf("miu=");		scanf("%lf", &miu);		//miu
	printf("sigma=");	scanf("%lf", &sigma);	//sigma
	sprintf(filename, "Gaussian_%d_%d_%d.txt", (int)(miu * 100), (int)(sigma * 100), length);
	gaussian = Gaussian_Distribution(miu, sigma, length);
	fp = fopen(filename,"w"); 
	for (i = 0; i < length; i++)
	{
		fprintf(fp, "%lf\n", gaussian[i]);//fscanf(fp, "%lf", &gaussian[i]);//read data
	}
	fclose(fp);
}
/*********************************************/
//Sum-of-12 Method
double *Gaussian_Distribution_Standard(int length)
{
	int i = 0, j = 0;
	double *gaussian = (double *)malloc(length * sizeof(double));
	double *(uniform[12]);
	for (i = 0; i < length; i++)
	{
		uniform[i] = Uniform_Distribution(length, (i + 1) * length);
	}
	for (j = 0; j < length; j++)
	{
		for (i = 0; i < 12; i++)
		{
			gaussian[j] = gaussian[j] + uniform[i][j];
		}
		gaussian[j] = gaussian[j] - 6.0;
	}
	return gaussian;
}
//N(miu,sigma)
double *Gaussian_Distribution(double miu, double sigma, int length)
{
	int i = 0;
	double *gaussian_standard = Gaussian_Distribution_Standard(length);
	double *gaussian = (double *)malloc(length * sizeof(double));
	for (i = 0; i < length; i++)
	{
		gaussian[i] = gaussian_standard[i] * sqrt(sigma) + miu;
	}
	return gaussian;
}
/**********************************************************************************************/
/**********************************************************************************************/
void Demo_Rayleigh(void)
{
	int i = 0, length = 0;
	char filename[50];//filename
	double sigma = 1.0, *rayleigh;
	FILE *fp;
	printf("length=");		scanf("%d", &length);
	printf("sigma=");		scanf("%lf", &sigma);
	sprintf(filename, "Rayleigh_%d_%d.txt", (int)(sigma * 100), length);
	rayleigh = Rayleigh_Distribution(sigma, length);
	fp = fopen(filename,"w"); 
	for (i = 0; i < length; i++)
	{
		fprintf(fp, "%lf\n", rayleigh[i]);
	}
	fclose(fp);
 
}
//rayleigh
double *Rayleigh_Distribution(double sigma, int length)
{
	int i = 0;
	double *uniform = Uniform_Distribution(length, length);
	double *rayleigh = (double *)malloc(length * sizeof(double));
	for (i = 0; i < length; i++)
	{
		rayleigh[i] = sqrt(-log(pow(uniform[i], 2))) * sigma;
	}
	return rayleigh;
}
/**********************************************************************************************/
/**********************************************************************************************/
//demo poisson
void Demo_Poisson(void)
{
	int i = 0, length = 0;
	char filename[50];
	double lamda = 0;
	int *poisson;
	FILE *fp;
	printf("length=");	scanf("%d", &length);
	printf("lamda=");	scanf("%lf", &lamda);
	sprintf(filename, "Poisson_%d_%d.txt", (int)(lamda * 100), length);
	poisson = Poisson_Distribution(lamda, length);
	fp = fopen(filename,"w"); 
	for (i = 0; i < length; i++)
	{
		fprintf(fp, "%d\n", poisson[i]);
	}
	fclose(fp);
}
//poisson
int *Poisson_Distribution(double lamda,unsigned int length)
{
	unsigned int i = 0, k = 0;
	int *poisson = (int *)malloc(length * sizeof(int));
	double ans = 1.0, temp = exp(-lamda);
	srand((unsigned int)NULL);
	for (i = 0; i < length; i++)
	{
		while(ans >= temp)
		{
			k++;
			ans = ans * rand() / 32767.0;
		}
		poisson[i] = k - 1;
		ans = 1.0;
		k = 0;
	}
	return poisson;
}