## Developer Reference

• 2022.1
• 12/20/2021
• Public Content
Contents

# ZPOSV Example Program in C

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/*
ZPOSV Example.
==============

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

(  5.96,  0.00) (  0.40, -1.19) ( -0.83, -0.48) ( -0.57,  0.40)
(  0.40,  1.19) (  7.95,  0.00) (  0.33,  0.09) (  0.22,  0.74)
( -0.83,  0.48) (  0.33, -0.09) (  4.43,  0.00) ( -1.09,  0.32)
( -0.57, -0.40) (  0.22, -0.74) ( -1.09, -0.32) (  3.46,  0.00)

and B is the right-hand side matrix:

( -2.94,  5.79) (  8.44,  3.07)
(  8.12, -9.12) (  1.00, -4.62)
(  9.09, -5.03) (  3.64, -2.33)
(  7.36,  6.77) (  8.04,  2.87)

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

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

The Cholesky decomposition is used to factor A as
A = UH*U, if uplo = 'U' or A = L*LH, if uplo = 'L',
where U is an upper triangular matrix and L is a lower triangular matrix.
The factored form of A is then used to solve the system of equations A*X = B.

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

ZPOSV Example Program Results

Solution
(  0.80,  1.62) (  2.52,  0.61)
(  1.26, -1.78) (  0.01, -1.38)
(  3.38, -0.29) (  2.42, -0.52)
(  3.46,  2.92) (  3.77,  1.37)

Details of Cholesky factorization
(  2.44,  0.00) (  0.00,  0.00) (  0.00,  0.00) (  0.00,  0.00)
(  0.16,  0.49) (  2.77,  0.00) (  0.00,  0.00) (  0.00,  0.00)
( -0.34,  0.20) (  0.10, -0.10) (  2.06,  0.00) (  0.00,  0.00)
( -0.23, -0.16) (  0.12, -0.30) ( -0.57, -0.20) (  1.71,  0.00)
*/
#include <stdlib.h>
#include <stdio.h>

/* Complex datatype */
struct _dcomplex { double re, im; };
typedef struct _dcomplex dcomplex;

/* ZPOSV prototype */
extern void zposv( char* uplo, int* n, int* nrhs, dcomplex* a, int* lda,
dcomplex* b, int* ldb, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda );

/* 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;
/* Local arrays */
dcomplex a[LDA*N] = {
{ 5.96,  0.00}, { 0.40,  1.19}, {-0.83,  0.48}, {-0.57, -0.40},
{ 0.00,  0.00}, { 7.95,  0.00}, { 0.33, -0.09}, { 0.22, -0.74},
{ 0.00,  0.00}, { 0.00,  0.00}, { 4.43,  0.00}, {-1.09, -0.32},
{ 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, { 3.46,  0.00}
};
dcomplex b[LDB*NRHS] = {
{-2.94,  5.79}, { 8.12, -9.12}, { 9.09, -5.03}, { 7.36,  6.77},
{ 8.44,  3.07}, { 1.00, -4.62}, { 3.64, -2.33}, { 8.04,  2.87}
};
/* Executable statements */
printf( " ZPOSV Example Program Results\n" );
/* Solve the equations A*X = B */
zposv( "Lower", &n, &nrhs, a, &lda, b, &ldb, &info );
/* Check for the positive definiteness */
if( info > 0 ) {
printf( "The leading minor of order %i is not positive ", info );
printf( "definite;\nthe solution could not be computed.\n" );
exit( 1 );
}
/* Print solution */
print_matrix( "Solution", n, nrhs, b, ldb );
/* Print details of Cholesky factorization */
print_matrix( "Details of Cholesky factorization", n, n, a, lda );
exit( 0 );
} /* End of ZPOSV Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, dcomplex* 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" );
}
}``````

#### Product and Performance Information

1

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