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*
* Author: "Sjors H.W. Scheres"
* MRC Laboratory of Molecular Biology
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 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 General Public License for more details.
*
* This complete copyright notice must be included in any revised version of the
* source code. Additional authorship citations may be added, but existing
* author citations must be preserved.
***************************************************************************/
/***************************************************************************
*
* Authors: Carlos Oscar S. Sorzano (coss@cnb.csic.es)
*
* Unidad de Bioinformatica of Centro Nacional de Biotecnologia , CSIC
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
* 02111-1307 USA
*
* All comments concerning this program package may be sent to the
* e-mail address 'xmipp@cnb.csic.es'
***************************************************************************/
#ifndef _NUMERICAL_HH
# define _NUMERICAL_HH
#include <math.h>
#include "src/memory.h"
#include "src/macros.h"
#include "src/error.h"
/*****************************************************************************/
/* Variable and prototype definitions for the Numerical Core */
/*****************************************************************************/
//@defgroup NumericalRecipes Functions from the Numerical Recipes
//@ingroup DataLibrary
//@{
// Utilities --------------------------------------------------------------
void nrerror(const char error_text[]);
// Bessel functions --------------------------------------------------------
DOUBLE bessj0(DOUBLE x);
DOUBLE bessj3_5(DOUBLE x);
DOUBLE bessj1_5(DOUBLE x);
DOUBLE bessi0(DOUBLE x);
DOUBLE bessi1(DOUBLE x);
DOUBLE bessi0_5(DOUBLE x);
DOUBLE bessi1_5(DOUBLE x);
DOUBLE bessi2(DOUBLE x);
DOUBLE bessi3(DOUBLE x);
DOUBLE bessi2_5(DOUBLE x);
DOUBLE bessi3_5(DOUBLE x);
DOUBLE bessi4(DOUBLE x);
// Special functions -------------------------------------------------------
DOUBLE gammln(DOUBLE xx);
DOUBLE gammp(DOUBLE a, DOUBLE x);
DOUBLE betacf(DOUBLE a, DOUBLE b, DOUBLE x);
DOUBLE betai(DOUBLE a, DOUBLE b, DOUBLE x);
// Singular value descomposition of matrix a (numerical recipes, chapter 2-6 for details)
void svdcmp(DOUBLE *a, int m, int n, DOUBLE *w, DOUBLE *v);
void svbksb(DOUBLE *u, DOUBLE *w, DOUBLE *v, int m, int n, DOUBLE *b, DOUBLE *x);
// Optimization ------------------------------------------------------------
void powell(DOUBLE *p, DOUBLE *xi, int n, DOUBLE ftol, int &iter,
DOUBLE &fret, DOUBLE(*func)(DOUBLE *, void *), void *prm,
bool show);
// Working with matrices ---------------------------------------------------
// LU decomposition
#define TINY 1.0e-20;
/* Chapter 2 Section 3: LU DECOMPOSITION */
template <class T>
void ludcmp(T *a, int n, int *indx, T *d)
{
int i, imax, j, k;
T big, dum, sum, temp;
T *vv;
ask_Tvector(vv, 1, n);
*d = (T)1.0;
for (i = 1;i <= n;i++)
{
big = (T)0.0;
for (j = 1;j <= n;j++)
if ((temp = (T)fabs((DOUBLE)a[i*n+j])) > big)
big = temp;
if (big == (T)0.0)
nrerror("Singular matrix in routine LUDCMP");
vv[i] = (T)1.0 / big;
}
for (j = 1;j <= n;j++)
{
for (i = 1;i < j;i++)
{
sum = a[i*n+j];
for (k = 1;k < i;k++)
sum -= a[i*n+k] * a[k*n+j];
a[i*n+j] = sum;
}
big = (T)0.0;
for (i = j;i <= n;i++)
{
sum = a[i*n+j];
for (k = 1;k < j;k++)
sum -= a[i*n+k] * a[k*n+j];
a[i*n+j] = sum;
if ((dum = vv[i] * (T)fabs((DOUBLE)sum)) >= big)
{
big = dum;
imax = i;
}
}
if (j != imax)
{
for (k = 1;k <= n;k++)
{
dum = a[imax*n+k];
a[imax*n+k] = a[j*n+k];
a[j*n+k] = dum;
}
*d = -(*d);
vv[imax] = vv[j];
}
indx[j] = imax;
if (a[j*n+j] == 0.0)
a[j*n+j] = (T) TINY;
if (j != n)
{
dum = (T)1.0 / (a[j*n+j]);
for (i = j + 1;i <= n;i++)
a[i*n+j] *= dum;
}
}
free_Tvector(vv, 1, n);
}
#undef TINY
// Solve Ax=b
/* Chapter 2 Section 3: LU BACKWARD-FORWARD SUBSTITUTION */
template <class T>
void lubksb(T *a, int n, int *indx, T b[])
{
int i, ii = 0, ip, j;
T sum;
for (i = 1;i <= n;i++)
{
ip = indx[i];
sum = b[ip];
b[ip] = b[i];
if (ii)
for (j = ii;j <= i - 1;j++)
sum -= a[i*n+j] * b[j];
else if (sum)
ii = i;
b[i] = sum;
}
for (i = n;i >= 1;i--)
{
sum = b[i];
for (j = i + 1;j <= n;j++)
sum -= a[i*n+j] * b[j];
b[i] = sum / a[i*n+i];
}
}
/* Chapter 2, Section 1. Gauss-Jordan equation system resolution ----------- */
// Solve Ax=b (b=matrix)
template <class T>
void gaussj(T *a, int n, T *b, int m)
{
T temp;
int *indxc, *indxr, *ipiv;
int i, icol, irow, j, k, l, ll;
T big, dum;
DOUBLE pivinv;
ask_Tvector(indxc, 1, n);
ask_Tvector(indxr, 1, n);
ask_Tvector(ipiv, 1, n);
for (j = 1;j <= n;j++)
ipiv[j] = 0;
for (i = 1;i <= n;i++)
{
big = (T)0;
for (j = 1;j <= n;j++)
if (ipiv[j] != 1)
for (k = 1;k <= n;k++)
{
if (ipiv[k] == 0)
{
if (fabs((DOUBLE)a[j*n+k]) >= (DOUBLE) big)
{
big = ABS(a[j*n+k]);
irow = j;
icol = k;
}
}
else if (ipiv[k] > 1)
nrerror("GAUSSJ: Singular Matrix-1");
}
++(ipiv[icol]);
if (irow != icol)
{
for (l = 1;l <= n;l++)
SWAP(a[irow*n+l], a[icol*n+l], temp)
for (l = 1;l <= m;l++)
SWAP(b[irow*n+l], b[icol*n+l], temp)
}
indxr[i] = irow;
indxc[i] = icol;
if (a[icol*n+icol] == 0.0)
nrerror("GAUSSJ: Singular Matrix-2");
pivinv = 1.0f / a[icol*n+icol];
a[icol*n+icol] = (T)1;
for (l = 1;l <= n;l++)
a[icol*n+l] = (T)(pivinv * a[icol*n+l]);
for (l = 1;l <= m;l++)
b[icol*n+l] = (T)(pivinv * b[icol*n+l]);
for (ll = 1;ll <= n;ll++)
if (ll != icol)
{
dum = a[ll*n+icol];
a[ll*n+icol] = (T)0;
for (l = 1;l <= n;l++)
a[ll*n+l] -= a[icol*n+l] * dum;
for (l = 1;l <= m;l++)
b[ll*n+l] -= b[icol*n+l] * dum;
}
}
for (l = n;l >= 1;l--)
{
if (indxr[l] != indxc[l])
for (k = 1;k <= n;k++)
SWAP(a[k*n+indxr[l]], a[k*n+indxc[l]], temp);
}
free_Tvector(ipiv, 1, n);
free_Tvector(indxr, 1, n);
free_Tvector(indxc, 1, n);
}
#endif
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