C++求矩阵的逆程序代码

C++求矩阵的逆程序代码

C inverse.c

C Source Code for "GRPP, A Scientific Programming Language

C Processor Designed for Lex and Yacc."

C Author: James Kent Blackburn

C Goddard Space Flight Center, Code 664.0, Greenbelt, MD. 20771

C Computers in Physics, Journal Section, Jan/Feb 1994

/*

Matrix Inversion using

LU Decomposition from

Numerical Recipes in C

Chapter 2

*/

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#define TINY 1.0e-20

void inverse(double**,int);

void ludcmp(double**, int, int*, double*);

void lubksb(double**, int, int*, double*);

double **matrix(int,int,int,int);

double *vector(int,int);

void free_matrix(double**,int,int,int,int);

void free_vector(double*,int,int);

void inverse(double **mat, int dim)

{

int i,j,*indx;

double **y,d,*col;

y = matrix(0,dim-1,0,dim-1);

indx = (int *)malloc((unsigned)(dim*sizeof(int)));

col = vector(0,dim-1);

ludcmp(mat,dim,indx,&d);

for (j=0;j<dim;j++)

{

for (i=0;i<dim;i++) col[i] = 0.0;

col[j] = 1.0;

lubksb(mat,dim,indx,col);

C++求矩阵的逆程序代码

for (i=0;i<dim;i++) y[i][j] = col[i];

}

for (i=0;i<dim;i++)

for (j=0;j<dim;j++)

mat[i][j] = y[i][j];

free_matrix(y,0,dim-1,0,dim-1);

free_vector(col,0,dim-1);

free(indx);

}

void ludcmp(double **a, int n, int *indx, double *d)

{

int i,imax,j,k;

double big,dum,sum,temp;

double *vv;

vv = (double*)malloc((unsigned)(n*sizeof(double))); if (!vv)

{

fprintf(stderr,"Error Allocating Vector Memory\n"); exit(1);

}

*d = 1.0;

for (i=0;i<n;i++)

{

big = 0.0;

for (j=0;j<n;j++)

{

if ((temp=fabs(a[i][j])) > big) big = temp;

}

if (big == 0.0)

{

fprintf(stderr,"Singular Matrix in Routine LUDCMP\n"); for (j=0;j<n;j++) printf(" %f ",a[i][j]); printf("/n"); exit(1);

}

vv[i] = 1.0/big;

}

for (j=0;j<n;j++)

{

for (i=0;i<j;i++)

{

sum = a[i][j];

for (k=0;k<i;k++) sum -= a[i][k] * a[k][j];

C++求矩阵的逆程序代码

}

big = 0.0;

for (i=j;i<n;i++)

{

sum = a[i][j];

for (k=0;k<j;k++) sum -= a[i][k] * a[k][j]; a[i][j] = sum;

if ((dum=vv[i]*fabs(sum)) >= big) {

big = dum;

imax = i;

}

}

if (j != imax)

{

for (k=0;k<n;k++)

{

dum = a[imax][k];

a[imax][k] = a[j][k];

a[j][k] = dum;

}

*d = -(*d);

vv[imax] = vv[j];

}

indx[j] = imax;

if (a[j][j] == 0.0) a[j][j] = TINY;

if (j != n-1)

{

dum = 1.0 / a[j][j];

for (i=j+1;i<n;i++) a[i][j] *= dum; }

}

free(vv);

}

void lubksb(double **a, int n, int *indx, double *b) {

int i,ip,j,ii=-1;

double sum;

for (i=0;i<n;i++)

{

ip = indx[i];

C++求矩阵的逆程序代码

b[ip] = b[i];

if (ii>=0)

for (j=ii;j<i;j++) sum -= a[i][j] * b[j]; else if (sum) ii = i;

b[i] = sum;

}

for (i=n-1;i>=0;i--)

{

sum = b[i];

for (j=i+1;j<n;j++) sum -= a[i][j] * b[j]; b[i] = sum / a[i][i];

}

}

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