## Developer Reference

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

# LAPACKE_cposv Example Program in C for Row Major Data Layout

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/*
LAPACKE_cposv 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.
========================

LAPACKE_cposv (row-major, high-level) 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>
#include "mkl_lapacke.h"

/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex8* a, MKL_INT lda );

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

/* Main program */
int main() {
/* Locals */
MKL_INT n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
/* Local arrays */
MKL_Complex8 a[LDA*N] = {
{ 5.96f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f},
{ 0.40f,  1.19f}, { 7.95f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f},
{-0.83f,  0.48f}, { 0.33f, -0.09f}, { 4.43f,  0.00f}, { 0.00f,  0.00f},
{-0.57f, -0.40f}, { 0.22f, -0.74f}, {-1.09f, -0.32f}, { 3.46f,  0.00f}
};
MKL_Complex8 b[LDB*N] = {
{-2.94f,  5.79f}, { 8.44f,  3.07f},
{ 8.12f, -9.12f}, { 1.00f, -4.62f},
{ 9.09f, -5.03f}, { 3.64f, -2.33f},
{ 7.36f,  6.77f}, { 8.04f,  2.87f}
};
/* Executable statements */
printf( "LAPACKE_cposv (row-major, high-level) Example Program Results\n" );
/* Solve the equations A*X = B */
info = LAPACKE_cposv( LAPACK_ROW_MAJOR, 'L', n, nrhs, a, lda, b, ldb );
/* 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 LAPACKE_cposv Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex8* a, MKL_INT lda ) {
MKL_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*lda+j].real, a[i*lda+j].imag );
printf( "\n" );
}
}``````

#### Product and Performance Information

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