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• 12/20/2021
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LAPACKE_dposv Example Program in C for Row Major Data Layout

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/*
LAPACKE_dposv Example.
======================

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

3.14   0.17  -0.90   1.65  -0.72
0.17   0.79   0.83  -0.65   0.28
-0.90   0.83   4.53  -3.70   1.60
1.65  -0.65  -3.70   5.32  -1.37
-0.72   0.28   1.60  -1.37   1.98

and B is the right-hand side matrix:

-7.29   6.11   0.59
9.25   2.90   8.88
5.99  -5.05   7.57
-1.94  -3.80   5.57
-8.30   9.66  -1.67

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

The routine solves for X the real system of linear equations
A*X = B, where A is an n-by-n symmetric 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 = UT*U, if uplo = 'U' or A = L*LT, 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_dposv (row-major, high-level) Example Program Results

Solution
-6.02   3.95  -3.14
15.62   4.32  13.05
3.02  -8.25   4.91
3.25  -4.83   6.11
-8.78   9.04  -3.57

Details of Cholesky factorization
1.77   0.10  -0.51   0.93  -0.41
0.00   0.88   0.99  -0.84   0.36
0.00   0.00   1.81  -1.32   0.57
0.00   0.00   0.00   1.42   0.05
0.00   0.00   0.00   0.00   1.16
*/
#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, double* a, MKL_INT lda );

/* Parameters */
#define N 5
#define NRHS 3
#define LDA N
#define LDB NRHS

/* Main program */
int main() {
/* Locals */
MKL_INT n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
/* Local arrays */
double a[LDA*N] = {
3.14,  0.17, -0.90, 1.65, -0.72,
0.00,  0.79,  0.83, -0.65,  0.28,
0.00,  0.00,  4.53, -3.70,  1.60,
0.00,  0.00,  0.00, 5.32, -1.37,
0.00,  0.00,  0.00, 0.00,  1.98
};
double b[LDB*N] = {
-7.29,  6.11,  0.59,
9.25,  2.90,  8.88,
5.99, -5.05,  7.57,
-1.94, -3.80,  5.57,
-8.30,  9.66, -1.67
};
/* Executable statements */
printf( "LAPACKE_dposv (row-major, high-level) Example Program Results\n" );
/* Solve the equations A*X = B */
info = LAPACKE_dposv( LAPACK_ROW_MAJOR, 'U', 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_dposv Example */

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

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