Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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## LAPACKE_zgesv Example Program in C for Column Major Data Layout

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/*
LAPACKE_zgesv 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:

(  1.23, -5.50) (  7.91, -5.38) ( -9.80, -4.86) ( -7.32,  7.57)
( -2.14, -1.12) ( -9.92, -0.79) ( -9.18, -1.12) (  1.37,  0.43)
( -4.30, -7.10) ( -6.47,  2.52) ( -6.51, -2.67) ( -5.86,  7.38)
(  1.27,  7.29) (  8.90,  6.92) ( -8.82,  1.25) (  5.41,  5.37)

and B is the right-hand side matrix:

(  8.33, -7.32) ( -6.11, -3.81)
( -6.18, -4.80) (  0.14, -7.71)
( -5.71, -2.80) (  1.41,  3.40)
( -1.60,  3.08) (  8.54, -4.05)

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.
========================

LAPACKE_zgesv (column-major, high-level) Example Program Results

Solution
( -1.09, -0.18) (  1.28,  1.21)
(  0.97,  0.52) ( -0.22, -0.97)
( -0.20,  0.19) (  0.53,  1.36)
( -0.59,  0.92) (  2.22, -1.00)

Details of LU factorization
( -4.30, -7.10) ( -6.47,  2.52) ( -6.51, -2.67) ( -5.86,  7.38)
(  0.49,  0.47) ( 12.26, -3.57) ( -7.87, -0.49) ( -0.98,  6.71)
(  0.25, -0.15) ( -0.60, -0.37) (-11.70, -4.64) ( -1.35,  1.38)
( -0.83, -0.32) (  0.05,  0.58) (  0.93, -0.50) (  2.66,  7.86)

Pivot indices
3      3      3      4
*/
#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_Complex16* a, MKL_INT lda );
extern void print_int_vector( char* desc, MKL_INT n, MKL_INT* a );

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

/* Main program */
int main() {
/* Locals */
MKL_INT n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
/* Local arrays */
MKL_INT ipiv[N];
MKL_Complex16 a[LDA*N] = {
{ 1.23, -5.50}, {-2.14, -1.12}, {-4.30, -7.10}, { 1.27,  7.29},
{ 7.91, -5.38}, {-9.92, -0.79}, {-6.47,  2.52}, { 8.90,  6.92},
{-9.80, -4.86}, {-9.18, -1.12}, {-6.51, -2.67}, {-8.82,  1.25},
{-7.32,  7.57}, { 1.37,  0.43}, {-5.86,  7.38}, { 5.41,  5.37}
};
MKL_Complex16 b[LDB*NRHS] = {
{ 8.33, -7.32}, {-6.18, -4.80}, {-5.71, -2.80}, {-1.60,  3.08},
{-6.11, -3.81}, { 0.14, -7.71}, { 1.41,  3.40}, { 8.54, -4.05}
};
/* Executable statements */
printf( "LAPACKE_zgesv (column-major, high-level) Example Program Results\n" );
/* Solve the equations A*X = B */
info = LAPACKE_zgesv( LAPACK_COL_MAJOR, n, nrhs, a, lda, ipiv, b, ldb );
/* 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 LAPACKE_zgesv Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* 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+j*lda].real, a[i+j*lda].imag );
printf( "\n" );
}
}

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