# 9.2 Calling BLAS/LAPACK Routines from MOSEK¶

Sometimes users need to perform linear algebra operations that involve dense matrices and vectors. Also MOSEK extensively uses high-performance linear algebra routines from the BLAS and LAPACK packages and some of these routines are included in the package shipped to the users.

The MOSEK versions of BLAS/LAPACK routines:

• use MOSEK data types and return value conventions,

• preserve the BLAS/LAPACK naming convention.

Therefore the user can leverage on efficient linear algebra routines, with a simplified interface, with no need for additional packages.

List of available routines

Table 9.1 BLAS routines available.

BLAS Name

MOSEK function

Math Expression

AXPY

MSK_axpy

$$y=\alpha x+y$$

DOT

MSK_dot

$$x^T y$$

GEMV

MSK_gemv

$$y=\alpha Ax + \beta y$$

GEMM

MSK_gemm

$$C=\alpha AB+ \beta C$$

SYRK

MSK_syrk

$$C=\alpha AA^T+ \beta C$$

Table 9.2 LAPACK routines available.

LAPACK Name

MOSEK function

Description

POTRF

MSK_potrf

Cholesky factorization of a semidefinite symmetric matrix

SYEVD

MSK_syevd

Eigenvalues and eigenvectors of a symmetric matrix

SYEIG

MSK_syeig

Eigenvalues of a symmetric matrix

Source code examples

In Listing 9.2 we provide a simple working example. It has no practical meaning except showing how to organize the input and call the methods.

Listing 9.2 Calling BLAS and LAPACK routines from Optimizer API for C. Click here to download.
#include "mosek.h"
void print_matrix(MSKrealt* x, MSKint32t r, MSKint32t c)
{
MSKint32t i, j;
for (i = 0; i < r; i++)
{
for (j = 0; j < c; j++)
printf("%f ", x[j * r + i]);

printf("\n");
}

}

int main(int argc, char*  argv[])
{

MSKrescodee r   = MSK_RES_OK;
MSKenv_t    env = NULL;

const MSKint32t n = 3, m = 2, k = 3;

MSKrealt alpha = 2.0, beta = 0.5;
MSKrealt x[]    = {1.0, 1.0, 1.0};
MSKrealt y[]    = {1.0, 2.0, 3.0};
MSKrealt z[]    = {1.0, 1.0};
MSKrealt A[]    = {1.0, 1.0, 2.0, 2.0, 3.0, 3.0};
MSKrealt B[]    = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
MSKrealt C[]    = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0};
MSKrealt D[]    = {1.0, 1.0, 1.0, 1.0};
MSKrealt Q[]    = {1.0, 0.0, 0.0, 2.0};
MSKrealt v[]    = {0.0, 0.0, 0.0};

MSKrealt xy;

/* BLAS routines*/
r = MSK_makeenv(&env, NULL);
printf("n=%d m=%d k=%d\n", m, n, k);
printf("alpha=%f\n", alpha);
printf("beta=%f\n", beta);

r = MSK_dot(env, n, x, y, &xy);
printf("dot results= %f r=%d\n", xy, r);

print_matrix(x, 1, n);
print_matrix(y, 1, n);

r = MSK_axpy(env, n, alpha, x, y);
puts("axpy results is");
print_matrix(y, 1, n);

r = MSK_gemv(env, MSK_TRANSPOSE_NO, m, n, alpha, A, x, beta, z);
printf("gemv results is (r=%d) \n", r);
print_matrix(z, 1, m);

r = MSK_gemm(env, MSK_TRANSPOSE_NO, MSK_TRANSPOSE_NO, m, n, k, alpha, A, B, beta, C);
printf("gemm results is (r=%d) \n", r);
print_matrix(C, m, n);

r = MSK_syrk(env, MSK_UPLO_LO, MSK_TRANSPOSE_NO, m, k, 1., A, beta, D);
printf("syrk results is (r=%d) \n", r);
print_matrix(D, m, m);

/* LAPACK routines*/

r = MSK_potrf(env, MSK_UPLO_LO, m, Q);
printf("potrf results is (r=%d) \n", r);
print_matrix(Q, m, m);

r = MSK_syeig(env, MSK_UPLO_LO, m, Q, v);
printf("syeig results is (r=%d) \n", r);
print_matrix(v, 1, m);

r = MSK_syevd(env, MSK_UPLO_LO, m, Q, v);
printf("syevd results is (r=%d) \n", r);
print_matrix(v, 1, m);
print_matrix(Q, m, m);

/* Delete the environment and the associated data. */
MSK_deleteenv(&env);

return r;
}