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/*
* Project: The SPD Image correction and azimuthal regrouping
* http://forge.epn-campus.eu/projects/show/azimuthal
*
* Copyright (C) 2005-2010 European Synchrotron Radiation Facility
* Grenoble, France
*
* Principal authors: P. Boesecke (boesecke@esrf.fr)
* R. Wilcke (wilcke@esrf.fr)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* and the GNU Lesser General Public License along with this program.
* If not, see <http://www.gnu.org/licenses/>.
*/
# define GAUSS_VERSION "gauss : V1.2 Peter Boesecke 2007-04-23"
/*+++------------------------------------------------------------------------
NAME
gauss --- routines for gaussian distributions
SYNOPSIS
# include gauss.h
HISTORY
2000-11-17 V1.0 Peter Boesecke creation
2007-02-21 V1.1 PB SaxsDefinition.h is not needed any more
2007-03-23 V1.2 PB GaussInit() -> GaussInit( void )
----------------------------------------------------------------------------*/
# define GAUSS_LEN 201 /* number of interpolation points */
# define GAUSS_RANGE 8 /* range of LUT in multiples of sigma */
# include "gauss.h"
static int GaussDebugMode = 0;
static double GaussLut_X[GAUSS_LEN];
static double GaussLut_Y[GAUSS_LEN];
static int GaussLutInit = 0;
static double GaussS2Pi = 2.506628274631; // sqrt(2.0*SAXS_PI);
void GaussDebug( int mode )
{ GaussDebugMode = mode; }
double GaussPhi( double X )
{ return( exp ( - X*X*0.5 ) );
} /* GausPhi */
/* initializes GaussLut with the integrated values Y of a Gaussian
GaussPhi( X ) = exp(-Y^2/2), Y = Integral(0,X,GaussPhi(X) */
void GaussInit( void )
{ const int N = GAUSS_LEN-1;
int i;
double X1, X2;
double Y1, Y2;
double range = GAUSS_RANGE;
double step;
double value;
step = range/N;
X2 = 0.0; Y2 = GaussPhi( X2 );
value = 0.0;
GaussLut_X[0] = X2;
GaussLut_Y[0] = value;
for (i=1;i<=N;i++) {
X1 = X2; Y1 = Y2;
X2 = X2 + step; Y2 = GaussPhi( X2 );
value += (Y1+Y2)*0.5*step;
GaussLut_X[i] = X2;
GaussLut_Y[i] = value;
}
GaussLutInit = 1;
} /* GaussInit */
void GaussPrintLut( FILE * out, double X[], double Y[] )
{ const int N=GAUSS_LEN-1;
int i;
fprintf( out, "\n%s\n\n", GAUSS_VERSION );
for (i=0;i<=N;i++) {
fprintf(out,"X[%u] = %10.5g, Y[%u] = %10.5g\n",
i, GaussLut_X[i],i,GaussLut_Y[i]);
}
} /* GaussPrintLut */
/* returns the interpolated values of the LUT
Xn = XX[n]; Yn = YY[n];
Monoton increasing values are required:
X1<X2 <=> Y1<Y2
X < X0 -> Y = Y0
Xn <= X < Xn+1 -> Y = Yn + (Yn+1-Yn)/(Xn+1-Xn) * (X-Xn)
XN <= X -> Y = YN */
double Ipol_LUT2( double XX[], double YY[], double X )
{ double Y;
int i, N = GAUSS_LEN-1;
if ( X < XX[0] ) Y = YY[0];
else if ( XX[N] <= X ) Y = YY[N];
else { for (i=1; i<=N; i++) {
if (X < XX[i]) break;
}
Y = YY[i-1] + (YY[i]-YY[i-1])/(XX[i]-XX[i-1]) * (X-XX[i-1]);
}
return( Y );
} /* Ipol_LUT2 */
/* Gauss(x) = 1.0/(sqrt(2*pi)*sigma) * exp(- x^2/(2*sigma^2) */
double Gauss( double x, double sigma )
{ return( (GaussS2Pi/sigma) * GaussPhi( x/sigma ) );
} /* Gauss */
/* IntGauss(x,sigma)=1.0/(sqrt(2*pi)*sigma)*Integral(-Inf,x,Gauss(x,sigma)) */
double IntGauss ( double x, double sigma )
{ double value;
if (!GaussLutInit) {
GaussInit();
if (GaussDebugMode) GaussPrintLut( stdout , GaussLut_X , GaussLut_Y );
}
if (x<0) value = 0.5-(Ipol_LUT2(GaussLut_X, GaussLut_Y, -x/sigma))/GaussS2Pi;
else value = 0.5+(Ipol_LUT2(GaussLut_X, GaussLut_Y, x/sigma))/GaussS2Pi;
return( value );
} /* IntGauss */
/* InvIntGauss(y,sigma) = Inverted IntGauss */
double InvIntGauss ( double y, double sigma )
{ double value;
if (!GaussLutInit) {
GaussInit();
if (GaussDebugMode) GaussPrintLut( stdout , GaussLut_X , GaussLut_Y );
}
if (y<0.5) value=(-Ipol_LUT2(GaussLut_Y,GaussLut_X,(0.5-y)*GaussS2Pi))*sigma;
else value=(Ipol_LUT2(GaussLut_Y,GaussLut_X,(y-0.5)*GaussS2Pi))*sigma;
return( value );
} /* InvIntGauss */
/* set random number seed */
void GaussNoiseSeed( unsigned int seed )
{ srand( seed );
} /* GaussNoiseSeed */
/* create gaussian distributed noise */
double GaussNoise( double sigma )
{
int rannum = rand();
double p;
double value;
/* create random numbers between 0 and 1 */
p = rannum/(RAND_MAX+1.0);
/* project the range 0 to 1 to the x-range of the gauss distribution */
value = InvIntGauss ( p, sigma );
return ( value );
} /* GaussNoise */
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