Developer Reference

ID 766877
Date 3/22/2024
Public

## DGESV Example Program in C

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/*
DGESV Example.
==============

The program computes the solution to the system of linear
equations with a square matrix A and multiple
right-hand sides B, where A is the coefficient matrix:

6.80  -6.05  -0.45   8.32  -9.67
-2.11  -3.30   2.58   2.71  -5.14
5.66   5.36  -2.70   4.35  -7.26
5.97  -4.44   0.27  -7.17   6.08
8.23   1.08   9.04   2.14  -6.87

and B is the right-hand side matrix:

4.02  -1.56   9.81
6.19   4.00  -4.09
-8.22  -8.67  -4.57
-7.57   1.75  -8.61
-3.03   2.86   8.99

Description.
============

The routine solves for X the system of linear equations A*X = B,
where A is an n-by-n matrix, the columns of matrix B are individual
right-hand sides, and the columns of X are the corresponding
solutions.

The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = P*L*U, where P is a permutation matrix, L
is unit lower triangular, and U is upper triangular. The factored
form of A is then used to solve the system of equations A*X = B.

Example Program Results.
========================

DGESV Example Program Results

Solution
-0.80  -0.39   0.96
-0.70  -0.55   0.22
0.59   0.84   1.90
1.32  -0.10   5.36
0.57   0.11   4.04

Details of LU factorization
8.23   1.08   9.04   2.14  -6.87
0.83  -6.94  -7.92   6.55  -3.99
0.69  -0.67 -14.18   7.24  -5.19
0.73   0.75   0.02 -13.82  14.19
-0.26   0.44  -0.59  -0.34  -3.43

Pivot indices
5      5      3      4      5
*/
#include <stdlib.h>
#include <stdio.h>

/* DGESV prototype */
extern void dgesv( int* n, int* nrhs, double* a, int* lda, int* ipiv,
double* b, int* ldb, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, double* a, int lda );
extern void print_int_vector( char* desc, int n, int* a );

/* Parameters */
#define N 5
#define NRHS 3
#define LDA N
#define LDB N

/* Main program */
int main() {
/* Locals */
int n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
/* Local arrays */
int ipiv[N];
double a[LDA*N] = {
6.80, -2.11,  5.66,  5.97,  8.23,
-6.05, -3.30,  5.36, -4.44,  1.08,
-0.45,  2.58, -2.70,  0.27,  9.04,
8.32,  2.71,  4.35, -7.17,  2.14,
-9.67, -5.14, -7.26,  6.08, -6.87
};
double b[LDB*NRHS] = {
4.02,  6.19, -8.22, -7.57, -3.03,
-1.56,  4.00, -8.67,  1.75,  2.86,
9.81, -4.09, -4.57, -8.61,  8.99
};
/* Executable statements */
printf( " DGESV Example Program Results\n" );
/* Solve the equations A*X = B */
dgesv( &n, &nrhs, a, &lda, ipiv, b, &ldb, &info );
/* Check for the exact singularity */
if( info > 0 ) {
printf( "The diagonal element of the triangular factor of A,\n" );
printf( "U(%i,%i) is zero, so that A is singular;\n", info, info );
printf( "the solution could not be computed.\n" );
exit( 1 );
}
/* Print solution */
print_matrix( "Solution", n, nrhs, b, ldb );
/* Print details of LU factorization */
print_matrix( "Details of LU factorization", n, n, a, lda );
/* Print pivot indices */
print_int_vector( "Pivot indices", n, ipiv );
exit( 0 );
} /* End of DGESV Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, double* a, int lda ) {
int i, j;
printf( "\n %s\n", desc );
for( i = 0; i < m; i++ ) {
for( j = 0; j < n; j++ ) printf( " %6.2f", a[i+j*lda] );
printf( "\n" );
}
}

/* Auxiliary routine: printing a vector of integers */
void print_int_vector( char* desc, int n, int* a ) {
int j;
printf( "\n %s\n", desc );
for( j = 0; j < n; j++ ) printf( " %6i", a[j] );
printf( "\n" );
}