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MATSOLVE.C
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1992-05-24
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/*
*-----------------------------------------------------------------------------
* file: matsolve.c
* desc: solve linear equations
* by: ko shu pui, patrick
* date: 24 nov 91 v0.1
* revi: 14 may 92 v0.2
* ref:
* [1] Mary L.Boas, "Mathematical Methods in the Physical Sciene,"
* John Wiley & Sons, 2nd Ed., 1983. Chap 3.
*
* [2] Kendall E.Atkinson, "An Introduction to Numberical Analysis,"
* John Wiley & Sons, 1978.
*
*-----------------------------------------------------------------------------
*/
#include <stdio.h>
#include <math.h>
#ifdef __TURBOC__
#include <alloc.h>
#else
#include <malloc.h>
#endif
#include "matrix.h"
/*
*-----------------------------------------------------------------------------
* funct: mat_lu
* desct: in-place LU decomposition with partial pivoting
* given: !! A = square matrix (n x n) !ATTENTION! see commen
* P = permutation vector (n x 1)
* retrn: number of permutation performed
* -1 means suspected singular matrix
* comen: A will be overwritten to be a LU-composite matrix
*
* note: the LU decomposed may NOT be equal to the LU of
* the orignal matrix a. But equal to the LU of the
* rows interchanged matrix.
*-----------------------------------------------------------------------------
*/
int mat_lu( A, P )
MATRIX A;
MATRIX P;
{
int i, j, k, n;
int maxi, tmp;
double c, c1;
int p;
n = MatCol(A);
for (p=0,i=0; i<n; i++)
{
P[i][0] = i;
}
for (k=0; k<n; k++)
{
/*
* --- partial pivoting ---
*/
for (i=k, maxi=k, c=0.0; i<n; i++)
{
c1 = fabs( A[P[i][0]][k] );
if (c1 > c)
{
c = c1;
maxi = i;
}
}
/*
* row exchange, update permutation vector
*/
if (k != maxi)
{
p++;
tmp = P[k][0];
P[k][0] = P[maxi][0];
P[maxi][0] = tmp;
}
/*
* suspected singular matrix
*/
if ( A[P[k][0]][k] == 0.0 )
return (-1);
for (i=k+1; i<n; i++)
{
/*
* --- calculate m(i,j) ---
*/
A[P[i][0]][k] = A[P[i][0]][k] / A[P[k][0]][k];
/*
* --- elimination ---
*/
for (j=k+1; j<n; j++)
{
A[P[i][0]][j] -= A[P[i][0]][k] * A[P[k][0]][j];
}
}
}
return (p);
}
/*
*-----------------------------------------------------------------------------
* funct: mat_backsubs1
* desct: back substitution
* given: A = square matrix A (LU composite)
* !! B = column matrix B (attention!, see comen)
* !! X = place to put the result of X
* P = Permutation vector (after calling mat_lu)
* xcol = column of x to put the result
* retrn: column matrix X (of AX = B)
* comen: B will be overwritten
*-----------------------------------------------------------------------------
*/
MATRIX mat_backsubs1( A, B, X, P, xcol )
MATRIX A, B, X, P;
int xcol;
{
int i, j, k, n;
double sum;
n = MatCol(A);
for (k=0; k<n; k++)
{
for (i=k+1; i<n; i++)
B[P[i][0]][0] -= A[P[i][0]][k] * B[P[k][0]][0];
}
X[n-1][xcol] = B[P[n-1][0]][0] / A[P[n-1][0]][n-1];
for (k=n-2; k>=0; k--)
{
sum = 0.0;
for (j=k+1; j<n; j++)
{
sum += A[P[k][0]][j] * X[j][xcol];
}
X[k][xcol] = (B[P[k][0]][0] - sum) / A[P[k][0]][k];
}
return (X);
}
/*
*-----------------------------------------------------------------------------
* funct: mat_lsolve
* desct: solve linear equations
* given: a = square matrix A
* b = column matrix B
* retrn: column matrix X (of AX = B)
*-----------------------------------------------------------------------------
*/
MATRIX mat_lsolve( a, b )
MATRIX a, b;
{
MATRIX A, B, X, P;
int i, n;
double temp;
n = MatCol(a);
A = mat_copy(a);
B = mat_copy(b);
X = mat_creat(n, 1, ZERO_MATRIX);
P = mat_creat(n, 1, UNDEFINED);
mat_lu( A, P );
mat_backsubs1( A, B, X, P, 0 );
mat_free(A);
mat_free(B);
mat_free(P);
return (X);
}