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git-svn-id: svn://svn.icculus.org/gtkradiant/GtkRadiant/branches/ZeroRadiant.ab@184 8a3a26a2-13c4-0310-b231-cf6edde360e5
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TTimo
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#ifndef __APPLE__
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#include <malloc.h>
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#else
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#include <stdlib.h>
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#endif
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#include <limits.h>
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#include <float.h>
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#include "mathlib.h"
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#define TINY FLT_MIN
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void lubksb(float **a, int n, int *indx, float b[])
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// Solves the set of n linear equations A.X=B. Here a[n][n] is input, not as the matrix
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// A but rather as its LU decomposition determined by the routine ludcmp. indx[n] is input
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// as the permutation vector returned by ludcmp. b[n] is input as the right-hand side vector
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// B, and returns with the solution vector X. a, n and indx are not modified by this routine
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// and can be left in place for successive calls with different right-hand sides b. This routine takes
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// into account the possibility that b will begin with many zero elements, so it is efficient for use
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// in matrix inversion
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{
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int i,ii=-1,ip,j;
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float sum;
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for (i=0;i<n;i++) {
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ip=indx[i];
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sum=b[ip];
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b[ip]=b[i];
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if (ii>=0)
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for (j=ii;j<i;j++) sum -= a[i][j]*b[j];
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else if (sum) ii=i;
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b[i]=sum;
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}
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for (i=n-1;i>=0;i--) {
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sum=b[i];
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for (j=i+1;j<n;j++) sum -= a[i][j]*b[j];
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b[i]=sum/a[i][i];
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}
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}
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/* (C) Copr. 1986-92 Numerical Recipes Software */
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int ludcmp(float **a, int n, int *indx, float *d)
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// given a matrix a[n][n] this routine replaces it with the LU decomposition of a rowwise
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// permutation of itself. a and n are input. a is output, arranged as in above equation;
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// indx[n] is an output vector that records the row permutation effected by the partial
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// pivoting; d is output as +/-1 depending on whether the number of row interchanges was even
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// or odd, respectively. This routine is used in combination with lubksb to solve linear
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// equations or invert a matrix.
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{
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int i,imax,j,k;
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float big,dum,sum,temp;
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float *vv;
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vv=(float*)malloc(sizeof(float)*n);
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*d=1.0;
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for (i=0;i<n;i++) {
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big=0.0;
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for (j=0;j<n;j++)
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if ((temp=(float)fabs(a[i][j])) > big) big=temp;
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if (big == 0.0) return 1;
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vv[i]=1.0f/big;
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}
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for (j=0;j<n;j++) {
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for (i=0;i<j;i++) {
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sum=a[i][j];
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for (k=0;k<i;k++) sum -= a[i][k]*a[k][j];
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a[i][j]=sum;
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}
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big=0.0;
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for (i=j;i<n;i++) {
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sum=a[i][j];
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for (k=0;k<j;k++)
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sum -= a[i][k]*a[k][j];
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a[i][j]=sum;
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if ( (dum=vv[i]*(float)fabs(sum)) >= big) {
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big=dum;
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imax=i;
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}
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}
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if (j != imax) {
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for (k=0;k<n;k++) {
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dum=a[imax][k];
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a[imax][k]=a[j][k];
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a[j][k]=dum;
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}
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*d = -(*d);
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vv[imax]=vv[j];
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}
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indx[j]=imax;
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if (a[j][j] == 0.0) a[j][j]=TINY;
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if (j != n) {
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dum=1.0f/(a[j][j]);
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for (i=j+1;i<n;i++) a[i][j] *= dum;
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}
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}
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free(vv);
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return 0;
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}
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/* (C) Copr. 1986-92 Numerical Recipes Software */
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#ifndef __APPLE__
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#include <malloc.h>
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#else
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#include <stdlib.h>
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#endif
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#include <limits.h>
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#include <float.h>
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#include "mathlib.h"
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#define TINY FLT_MIN
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void lubksb(float **a, int n, int *indx, float b[])
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// Solves the set of n linear equations A.X=B. Here a[n][n] is input, not as the matrix
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// A but rather as its LU decomposition determined by the routine ludcmp. indx[n] is input
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// as the permutation vector returned by ludcmp. b[n] is input as the right-hand side vector
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// B, and returns with the solution vector X. a, n and indx are not modified by this routine
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// and can be left in place for successive calls with different right-hand sides b. This routine takes
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// into account the possibility that b will begin with many zero elements, so it is efficient for use
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// in matrix inversion
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{
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int i,ii=-1,ip,j;
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float sum;
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for (i=0;i<n;i++) {
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ip=indx[i];
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sum=b[ip];
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b[ip]=b[i];
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if (ii>=0)
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for (j=ii;j<i;j++) sum -= a[i][j]*b[j];
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else if (sum) ii=i;
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b[i]=sum;
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}
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for (i=n-1;i>=0;i--) {
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sum=b[i];
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for (j=i+1;j<n;j++) sum -= a[i][j]*b[j];
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b[i]=sum/a[i][i];
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}
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}
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/* (C) Copr. 1986-92 Numerical Recipes Software */
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int ludcmp(float **a, int n, int *indx, float *d)
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// given a matrix a[n][n] this routine replaces it with the LU decomposition of a rowwise
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// permutation of itself. a and n are input. a is output, arranged as in above equation;
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// indx[n] is an output vector that records the row permutation effected by the partial
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// pivoting; d is output as +/-1 depending on whether the number of row interchanges was even
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// or odd, respectively. This routine is used in combination with lubksb to solve linear
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// equations or invert a matrix.
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{
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int i,imax,j,k;
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float big,dum,sum,temp;
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float *vv;
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vv=(float*)malloc(sizeof(float)*n);
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*d=1.0;
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for (i=0;i<n;i++) {
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big=0.0;
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for (j=0;j<n;j++)
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if ((temp=(float)fabs(a[i][j])) > big) big=temp;
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if (big == 0.0) return 1;
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vv[i]=1.0f/big;
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}
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for (j=0;j<n;j++) {
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for (i=0;i<j;i++) {
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sum=a[i][j];
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for (k=0;k<i;k++) sum -= a[i][k]*a[k][j];
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a[i][j]=sum;
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}
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big=0.0;
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for (i=j;i<n;i++) {
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sum=a[i][j];
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for (k=0;k<j;k++)
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sum -= a[i][k]*a[k][j];
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a[i][j]=sum;
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if ( (dum=vv[i]*(float)fabs(sum)) >= big) {
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big=dum;
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imax=i;
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}
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}
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if (j != imax) {
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for (k=0;k<n;k++) {
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dum=a[imax][k];
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a[imax][k]=a[j][k];
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a[j][k]=dum;
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}
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*d = -(*d);
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vv[imax]=vv[j];
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}
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indx[j]=imax;
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if (a[j][j] == 0.0) a[j][j]=TINY;
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if (j != n) {
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dum=1.0f/(a[j][j]);
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for (i=j+1;i<n;i++) a[i][j] *= dum;
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}
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}
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free(vv);
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return 0;
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}
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/* (C) Copr. 1986-92 Numerical Recipes Software */
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