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/* @(#)inverse.c 2.1 6/26/87 */
#include <math.h>
#include "libtrans.h"
#define EPSILON 1.0e-16
/* DIM_matrix is defined in "libtrans.h" */
#define N DIM_matrix
/*
* inverse: invert a square matrix (puts pivot elements on main diagonal).
* returns arg2 as the inverse of arg1.
*
* This routine is based on a routine found in Andrei Rogers, "Matrix
* Methods in Urban and Regional Analysis", (1971), pp. 143-153.
*/
int inverse (double m[N][N])
{
int i, j, k, l, ir=0, ic=0 ;
int ipivot[N], itemp[N][2];
double pivot[N], t;
double fabs();
if (isnull (m))
return (-1) ;
/* initialization */
for (i = 0; i < N; i++)
ipivot[i] = 0;
for (i = 0; i < N; i++)
{
t = 0.0; /* search for pivot element */
for (j = 0; j < N; j++)
{
if (ipivot[j] == 1) /* found pivot */
continue;
for (k = 0; k < N; k++)
switch (ipivot[k]-1)
{
case 0:
break;
case -1:
if (fabs (t) < fabs (m[j][k]))
{
ir = j;
ic = k;
t = m[j][k];
}
break;
case 1:
return (-1);
break;
default: /* shouldn't get here */
return (-1);
break;
}
}
ipivot[ic] += 1;
if (ipivot[ic] > 1) /* check for dependency */
{
return (-1);
}
/* interchange rows to put pivot element on diagonal */
if (ir != ic)
for (l = 0; l < N; l++)
{
t = m[ir][l];
m[ir][l] = m[ic][l];
m[ic][l] = t;
}
itemp[i][0] = ir;
itemp[i][1] = ic;
pivot[i] = m[ic][ic];
/* check for zero pivot */
if (fabs (pivot[i]) < EPSILON)
{
return (-1);
}
/* divide pivot row by pivot element */
m[ic][ic] = 1.0;
for (j = 0; j < N; j++)
m[ic][j] /= pivot[i];
/* reduce nonpivot rows */
for (k = 0; k < N; k++)
if (k != ic)
{
t = m[k][ic];
m[k][ic] = 0.0;
for (l = 0; l < N; l++)
m[k][l] -= (m[ic][l] * t);
}
}
/* interchange columns */
for (i = 0; i < N; i++)
{
l = N - i - 1;
if (itemp[l][0] == itemp[l][1])
continue;
ir = itemp[l][0];
ic = itemp[l][1];
for (k = 0; k < N; k++)
{
t = m[k][ir];
m[k][ir] = m[k][ic];
m[k][ic] = t;
}
}
return 1;
}
#define ZERO 1.0e-8
/*
* isnull: returns 1 if matrix is null, else 0.
*/
int isnull (double a[N][N])
{
register int i, j;
double fabs();
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
if ((fabs (a[i][j]) - ZERO) > ZERO)
return 0;
return 1;
}
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