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;
}