Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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## DSYSV Example Program in C

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/*
DSYSV Example.
==============

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

-5.86   3.99  -5.93  -2.82   7.69
3.99   4.46   2.58   4.42   4.61
-5.93   2.58  -8.52   8.57   7.69
-2.82   4.42   8.57   3.72   8.07
7.69   4.61   7.69   8.07   9.83

and B is the right-hand side matrix:

1.32  -6.33  -8.77
2.22   1.69  -8.33
0.12  -1.56   9.54
-6.41  -9.49   9.56
6.33  -3.67   7.48

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

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

The diagonal pivoting method is used to factor A as A = U*D*UT or
A = L*D*LT , where U (or L) is a product of permutation and unit upper
(lower) triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.

The factored form of A is then used to solve the system of equations A*X = B.

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

DSYSV Example Program Results

Solution
1.17   0.52  -0.86
-0.71   1.05  -4.90
-0.63  -0.52   0.99
-0.33   0.43   1.22
0.83  -1.22   1.96

Details of factorization
-5.86   0.00   0.00   0.00   0.00
-0.68   7.18   0.00   0.00   0.00
1.01  -0.20  -2.82   0.00   0.00
0.48   0.35  11.93   4.21   0.00
-1.31   1.37   0.02   0.16   6.22

Pivot indices
1      2     -4     -4      5
*/
#include <stdlib.h>
#include <stdio.h>

/* DSYSV prototype */
extern void dsysv( char* uplo, int* n, int* nrhs, double* a, int* lda,
int* ipiv, double* b, int* ldb, double* work, int* lwork, 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, lwork;
double wkopt;
double* work;
/* Local arrays */
int ipiv[N];
double a[LDA*N] = {
-5.86,  3.99, -5.93, -2.82,  7.69,
0.00,  4.46,  2.58,  4.42,  4.61,
0.00,  0.00, -8.52,  8.57,  7.69,
0.00,  0.00,  0.00,  3.72,  8.07,
0.00,  0.00,  0.00,  0.00,  9.83
};
double b[LDB*NRHS] = {
1.32,  2.22,  0.12, -6.41,  6.33,
-6.33,  1.69, -1.56, -9.49, -3.67,
-8.77, -8.33,  9.54,  9.56,  7.48
};
/* Executable statements */
printf( " DSYSV Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
dsysv( "Lower", &n, &nrhs, a, &lda, ipiv, b, &ldb, &wkopt, &lwork, &info );
lwork = (int)wkopt;
work = (double*)malloc( lwork*sizeof(double) );
/* Solve the equations A*X = B */
dsysv( "Lower", &n, &nrhs, a, &lda, ipiv, b, &ldb, work, &lwork, &info );
/* Check for the exact singularity */
if( info > 0 ) {
printf( "The element of the diagonal factor " );
printf( "D(%i,%i) is zero, so that D 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 factorization */
print_matrix( "Details of factorization", n, n, a, lda );
/* Print pivot indices */
print_int_vector( "Pivot indices", n, ipiv );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of DSYSV 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" );
}