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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
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SPOSV Example Program in C

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/*
   SPOSV 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.
   ========================
 
 SPOSV 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>

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

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

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

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

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