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| /*
Truncated Gaussian numbers generator
Usage
-----
y = randnt(m , sigma , [left] , [right] , [n1] , ... , [np]);
Inputs
------
m Mean values (v1 x v2 x ...x vl) or scalar if randnt if called with more than 4 arguments
sigma Variance values (v1 x v2 x ...x vl) or scalar if randnt if called with more than 4 arguments
left Left boundaries (v1 x v2 x ...x vl) or scalar if randnt if called with more than 4 arguments
Right Right boundaries (v1 x v2 x ...x vl) or scalar if randnt if called with more than 4 arguments
ni Size of dimension i
Outputs
------
y Truncated independant samples (v1 x v2 x ... x vl) or (n1 x n2 x .... x np)
Examples
-------
y = randnt(0 , 1 , 0 , 3 , 2 , 3);
y = randnt(0 , 1 , [] , 3 , 2 , 3 , 2);
y = randnt(0 , 1 , [] , [] , 2 , 3 , 2); % <=> randn(2 , 3 , 2)
y = randnt(ones(2,2,3) , ones(2,2,3) , zeros(2,2,3) , ones(2,2,3));
y = randnt(ones(2,2) , ones(2,2)); N(1 , 1)*I_{2,2}
To compile :
------------
mex -DranSHR3 -output randnt.dll randnt.c or mex -DranKISS -output randnt.dll randnt.c (little bit slower)
Myself, I use Intel CPP compiler as :
mex -DranSHR3 -f mexopts_intel10.bat -output randnt.dll randnt.c
Ver 1.0 (03/04/05)
Author : Sébastien PARIS © (sebastien.paris@lsis.org)
-------
*/
#include <math.h>
#include <time.h>
#include "mex.h"
/*---------------- Basic generators definition ------------------- */
#define mix(a , b , c) \
{ \
a -= b; a -= c; a ^= (c>>13); \
b -= c; b -= a; b ^= (a<<8); \
c -= a; c -= b; c ^= (b>>13); \
a -= b; a -= c; a ^= (c>>12); \
b -= c; b -= a; b ^= (a<<16); \
c -= a; c -= b; c ^= (b>>5); \
a -= b; a -= c; a ^= (c>>3); \
b -= c; b -= a; b ^= (a<<10); \
c -= a; c -= b; c ^= (b>>15); \
}
#define znew (z = 36969*(z&65535) + (z>>16) )
#define wnew (w = 18000*(w&65535) + (w>>16) )
#define MWC ((znew<<16) + wnew )
#define SHR3 ( jsr ^= (jsr<<17), jsr ^= (jsr>>13), jsr ^= (jsr<<5) )
#define CONG (jcong = 69069*jcong + 1234567)
#define KISS ((MWC^CONG) + SHR3)
#ifdef ranKISS
#define randint KISS
#define rand() (randint*2.328306e-10)
#endif
#ifdef ranSHR3
#define randint SHR3
#define rand() (0.5 + (signed)randint*2.328306e-10)
#endif
/*--------------------------------------------------------------- */
typedef unsigned long UL;
/*--------------------------------------------------------------- */
static UL jsrseed = 31340134 , jsr;
#ifdef ranKISS
static UL z=362436069, w=521288629, jcong=380116160;
#endif
/*-------------------------------------------------------------------------------------------------*/
void randini(void);
double erf(double );
double icdfn(double );
double randnt(double , double , double , double );
/*-------------------------------------------------------------------------------------------------*/
void mexFunction(int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[])
{
double *a , *b , *left , *right;
double *y;
int *dimsa , *dimsb , *dimsleft , *dimsright ;
int *dimsy;
int proda = 1 , prodb = 1 , prodleft = 1 , prodright = 1;
int numdimsa , numdimsb , numdimsleft , numdimsright;
int numdimsy;
int i , N = 1;
if((nrhs < 2))
{
mexErrMsgTxt("Usage: y = randnt(m , sigma² , [left] , [right] , [n1] , ... , [np]);");
}
/* --- Input 1 ---*/
a = mxGetPr(prhs[0]);
numdimsa = mxGetNumberOfDimensions(prhs[0]);
dimsa = mxGetDimensions(prhs[0]);
/* --- Input 2 ---*/
b = mxGetPr(prhs[1]);
numdimsb = mxGetNumberOfDimensions(prhs[1]);
dimsb = mxGetDimensions(prhs[1]);
if ( numdimsb != numdimsa)
{
mexErrMsgTxt("m and sigma got different size");
}
for (i = 0 ; i < numdimsa ; i++)
{
proda *= dimsa[i];
prodb *= dimsb[i];
}
if ( proda != prodb)
{
mexErrMsgTxt("inner dimensions of m and sigma are different");
}
randini();
/* --- Input 3 ---*/
if((nrhs < 5))
{
if((nrhs > 2))
{
if(mxIsEmpty(prhs[2]))
{
left = (double *)mxMalloc(proda*sizeof(double));
for (i = 0 ; i < proda ; i++)
{
left[i] = a[i] - 5*b[i];
}
}
else
{
left = mxGetPr(prhs[2]);
numdimsleft = mxGetNumberOfDimensions(prhs[2]);
dimsleft = mxGetDimensions(prhs[2]);
if ( numdimsleft != numdimsa)
{
mexErrMsgTxt("left don't have the same size of m and sigma");
}
for (i = 0 ; i < numdimsleft ; i++)
{
prodleft *= dimsleft[i];
}
if ( proda != prodleft)
{
mexErrMsgTxt("inner dimensions of left are not matching with m and sigma");
}
}
}
else
{
left = (double *)mxMalloc(proda*sizeof(double));
for (i = 0 ; i < proda ; i++)
{
left[i] = a[i] - 5*b[i];
}
}
if((nrhs > 3))
{
if(mxIsEmpty(prhs[3]))
{
right = (double *)mxMalloc(proda*sizeof(double));
for (i = 0 ; i < proda ; i++)
{
right[i] = a[i] + 5*b[i];
}
}
else
{
right = mxGetPr(prhs[3]);
numdimsright = mxGetNumberOfDimensions(prhs[3]);
dimsright = mxGetDimensions(prhs[3]);
if ( numdimsright != numdimsa)
{
mexErrMsgTxt("right don't have the same size of m and sigma");
}
for (i = 0 ; i < numdimsright ; i++)
{
prodright *= dimsright[i];
}
if ( proda != prodright)
{
mexErrMsgTxt("inner dimensions of right are not matching with m and sigma");
}
}
}
else
{
right = (double *)mxMalloc(proda*sizeof(double));
for (i = 0 ; i < proda ; i++)
{
right[i] = a[i] + 5*b[i];
}
}
plhs[0] = mxCreateNumericArray(numdimsa, dimsa, mxDOUBLE_CLASS, mxREAL);
y = mxGetPr(plhs[0]);
N = proda;
for (i = 0 ; i < N ; i++)
{
y[i] = randnt(a[i] , b[i] , left[i] , right[i]);
}
if((nrhs > 2))
{
if(mxIsEmpty(prhs[2]))
{
mxFree(left);
}
}
else
{
mxFree(left);
}
if((nrhs > 3))
{
if(mxIsEmpty(prhs[3]))
{
mxFree(right);
}
}
else
{
mxFree(right);
}
}
else
{
if ((dimsa[0] != 1) && (dimsa[1] != 1) && (dimsb[0] != 1) && (dimsb[1] != 1))
{
mexErrMsgTxt("m, sigma² must be scalar if randnt is called with more than 4 inputs argument");
}
if((nrhs > 2))
{
if(mxIsEmpty(prhs[2]))
{
left = (double *)mxMalloc(sizeof(double));
left[0] = a[0] - 10*b[0];
}
else
{
left = mxGetPr(prhs[2]);
numdimsleft = mxGetNumberOfDimensions(prhs[2]);
dimsleft = mxGetDimensions(prhs[2]);
if ( numdimsleft != numdimsa)
{
mexErrMsgTxt("left don't have the same size of m and sigma");
}
for (i = 0 ; i < numdimsleft ; i++)
{
prodleft *= dimsleft[i];
}
if ( proda != prodleft)
{
mexErrMsgTxt("inner dimensions of left are not matching with m and sigma");
}
}
}
if((nrhs > 3))
{
if(mxIsEmpty(prhs[3]))
{
right = (double *)mxMalloc(sizeof(double));
right[0] = a[0] + 10*b[0];
}
else
{
right = mxGetPr(prhs[3]);
numdimsright = mxGetNumberOfDimensions(prhs[3]);
dimsright = mxGetDimensions(prhs[3]);
if ( numdimsright != numdimsa)
{
mexErrMsgTxt("right don't have the same size of m and sigma");
}
for (i = 0 ; i < numdimsright ; i++)
{
prodright *= dimsright[i];
}
if ( proda != prodright)
{
mexErrMsgTxt("inner dimensions of right are not matching with m and sigma");
}
}
}
numdimsy = (nrhs - 4);
dimsy = (int *)mxMalloc(numdimsy*sizeof(int));
for (i = 4 ; i < nrhs ; i++)
{
dimsy[i - 4] = (int) mxGetScalar(prhs[i]);
N *=dimsy[i - 4];
}
plhs[0] = mxCreateNumericArray(numdimsy, dimsy, mxDOUBLE_CLASS, mxREAL);
y = mxGetPr(plhs[0]);
for (i = 0 ; i < N ; i++)
{
y[i] = randnt(a[0] , b[0] , left[0] , right[0]);
}
mxFree(dimsy);
if((nrhs > 3))
{
if(mxIsEmpty(prhs[3]))
{
mxFree(right);
}
}
else
{
mxFree(right);
}
}
}
/*-------------------------------------------------------------------------------------------------*/
double randnt(double a , double b , double left , double right)
{
double std = sqrt(b) , lowerProb , upperProb , u;
lowerProb = 0.5*(1 + erf( ((left - a)/(1.414213562373095*std)) ) );
upperProb = 0.5*(1 + erf( ((right - a)/(1.414213562373095*std)) ) );
u = lowerProb + (upperProb-lowerProb)*rand();
return (a + icdfn(u)*std);
}
/* ----------------------------------------------------------------------- */
double icdfn(double x)
{
/* Coefficients in rational approximations. */
const double a[4] = { 0.886226899, -1.645349621, 0.914624893, -0.140543331};
const double b[4] = {-2.118377725, 1.442710462, -0.329097515, 0.012229801};
const double c[4] = {-1.970840454, -1.624906493, 3.429567803, 1.641345311};
const double d[2] = { 3.543889200, 1.637067800};
int i;
double z, x0;
/* Central range. */
x = 2*x - 1;
x0 = .7;
/* Near end points of range. */
if (x0 < x)
{
z = sqrt(-log((1-x)*0.5));
z = (((c[3]*z+c[2])*z+c[1])*z+c[0]) / ((d[1]*z+d[0])*z+1);
}
else if (x<-x0)
{
z = sqrt(-log((1+x)*0.5));
z = -(((c[3]*z+c[2])*z+c[1])*z+c[0]) / ((d[1]*z+d[0])*z+1);
}
else
{
z = x*x;
z = x*(((a[3]*z+a[2])*z+a[1])*z+a[0]) / ((((b[3]*z+b[2])*z+b[1])*z+b[0])*z+1);
}
/* Newton-Raphson correction to full accuracy.
Without these steps, erfinv() would be about 3 times
faster to compute, but accurate to only about 6 digits. */
for (i = 0 ; i < 2 ; i++)
{
z = z - (erf(z) - x) / (1.128379167095513 * exp(-z*z));
}
x = 1.414213562373095*z;
return(x);
}
/* ----------------------------------------------------------------------- */
double erf(double x)
{
const double p1[5] =
{
3.20937758913846947e03,
3.77485237685302021e02,
1.13864154151050156e02,
3.16112374387056560e00,
1.85777706184603153e-1
};
const double q1[4] =
{
2.84423683343917062e03,
1.28261652607737228e03,
2.44024637934444173e02,
2.36012909523441209e01
};
const double p2[9] =
{
1.23033935479799725e03,
2.05107837782607147e03,
1.71204761263407058e03,
8.81952221241769090e02,
2.98635138197400131e02,
6.61191906371416295e01,
8.88314979438837594e00,
5.64188496988670089e-1,
2.15311535474403846e-8
};
const double q2[8] =
{
1.23033935480374942e03,
3.43936767414372164e03,
4.36261909014324716e03,
3.29079923573345963e03,
1.62138957456669019e03,
5.37181101862009858e02,
1.17693950891312499e02,
1.57449261107098347e01
};
const double p3[6] =
{
6.58749161529837803e-4,
1.60837851487422766e-2,
1.25781726111229246e-1,
3.60344899949804439e-1,
3.05326634961232344e-1,
1.63153871373020978e-2
};
const double q3[5] =
{
2.33520497626869185e-3,
6.05183413124413191e-2,
5.27905102951428412e-1,
1.87295284992346047e00,
2.56852019228982242e00
};
int i;
double xval, xx, p, q;
bool NegativeValue;
xval=x;
if (xval<0)
{
xval = -xval;
NegativeValue = true;
}
else
{
NegativeValue=false;
}
if (xval<=0.46875)
{
xx = xval*xval;
p = p1[4];
q = 1.0;
for (i = 3 ; i>=0 ; i--)
{
p = p*xx + p1[i];
q = q*xx + q1[i];
}
xx=p/q;
return(x*xx);
}
else if (xval<=4)
{
xx = xval;
p = p2[8];
q = 1.0;
for (i=7 ; i>=0 ; i--)
{
p = p*xx + p2[i];
q = q*xx + q2[i];
}
xx = p/q;
xx = exp(-xval*xval)*xx;
if (NegativeValue)
{
return((xx - 0.5)-0.5);
}
else
{
return((0.5 - xx)+0.5);
}
}
else if (xval<10)
{
xx = 1.0/(xval*xval);
p = p3[5];
q = 1.0;
for (i = 4 ; i >= 0 ; i--)
{
p = p*xx+p3[i];
q = q*xx+q3[i];
}
xx = p/q;
xx = exp(-xval*xval)*(0.7071067811865475 - xx)/(xval);
if (mxIsNaN(xx))
{
xx = 0;
}
if (NegativeValue)
{
return((xx - 0.5) - 0.5);
}
else
{
return((0.5 - xx) + 0.5);
}
}
else
{
if (NegativeValue)
{
return(-1);
}
else
{
return(1);
}
}
}
/* ----------------------------------------------------------------------- */
void randini(void)
{
/* SHR3 Seed initialization */
jsrseed = (UL) time( NULL );
jsr ^= jsrseed;
/* KISS Seed initialization */
#ifdef ranKISS
z = (UL) time( NULL );
w = (UL) time( NULL );
jcong = (UL) time( NULL );
mix(z , w , jcong);
#endif
} |
