## Developer Reference

• 2022.1
• 12/20/2021
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Contents

# CHESV Example Program in C

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/*
CHESV Example.
==============

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

( -2.90,  0.00) (  0.31,  4.46) (  9.66, -5.66) ( -2.28,  2.14)
(  0.31, -4.46) ( -7.93,  0.00) (  9.55, -4.62) ( -3.51,  3.11)
(  9.66,  5.66) (  9.55,  4.62) (  0.30,  0.00) (  9.33, -9.66)
( -2.28, -2.14) ( -3.51, -3.11) (  9.33,  9.66) (  2.40,  0.00)

and B is the right-hand side matrix:

( -5.69, -8.21) ( -2.83,  6.46)
( -3.57,  1.99) ( -7.64,  1.10)
(  8.42, -9.83) ( -2.33, -4.23)
( -5.00,  3.85) (  6.48, -3.81)

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

The routine solves for X the complex system of linear equations A*X = B,
where A is an n-by-n Hermitian 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*UH or
A = L*D*LH, where U (or L) is a product of permutation and unit upper
(lower) triangular matrices, and D is Hermitian 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.
========================

CHESV Example Program Results

Solution
(  0.22, -0.95) ( -1.13,  0.18)
( -1.42, -1.30) (  0.70,  1.13)
( -0.65, -0.40) (  0.04,  0.07)
( -0.48,  1.35) (  1.15, -0.27)

Details of factorization
(  3.17,  0.00) (  7.32,  3.28) ( -0.36,  0.06) (  0.20, -0.82)
(  0.00,  0.00) (  0.03,  0.00) ( -0.48,  0.03) (  0.25, -0.76)
(  0.00,  0.00) (  0.00,  0.00) (  0.30,  0.00) (  9.33, -9.66)
(  0.00,  0.00) (  0.00,  0.00) (  0.00,  0.00) (  2.40,  0.00)

Pivot indices
-1     -1     -3     -3
*/
#include <stdlib.h>
#include <stdio.h>

/* Complex datatype */
struct _fcomplex { float re, im; };
typedef struct _fcomplex fcomplex;

/* CHESV prototype */
extern void chesv( char* uplo, int* n, int* nrhs, fcomplex* a, int* lda,
int* ipiv, fcomplex* b, int* ldb, fcomplex* work, int* lwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, fcomplex* a, int lda );
extern void print_int_vector( char* desc, int n, int* a );

/* Parameters */
#define N 4
#define NRHS 2
#define LDA N
#define LDB N

/* Main program */
int main() {
/* Locals */
int n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork;
fcomplex wkopt;
fcomplex* work;
/* Local arrays */
int ipiv[N];
fcomplex a[LDA*N] = {
{-2.90f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f},
{ 0.31f,  4.46f}, {-7.93f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f},
{ 9.66f, -5.66f}, { 9.55f, -4.62f}, { 0.30f,  0.00f}, { 0.00f,  0.00f},
{-2.28f,  2.14f}, {-3.51f,  3.11f}, { 9.33f, -9.66f}, { 2.40f,  0.00f}
};
fcomplex b[LDB*NRHS] = {
{-5.69f, -8.21f}, {-3.57f,  1.99f}, { 8.42f, -9.83f}, {-5.00f,  3.85f},
{-2.83f,  6.46f}, {-7.64f,  1.10f}, {-2.33f, -4.23f}, { 6.48f, -3.81f}
};
/* Executable statements */
printf( " CHESV Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
chesv( "Upper", &n, &nrhs, a, &lda, ipiv, b, &ldb, &wkopt, &lwork, &info );
lwork = (int)wkopt.re;
work = (fcomplex*)malloc( lwork*sizeof(fcomplex) );
/* Solve the equations A*X = B */
chesv( "Upper", &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 CHESV Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, fcomplex* 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,%6.2f)", a[i+j*lda].re, a[i+j*lda].im );
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" );
}``````

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