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 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 10 LAPACK routines available.
LAPACK Name MOSEK function Description
POTRF MSK_potrf Cholesky factorization of a semidefinite symmetric matrix
SYEVD MSK_syevd Eigenvalues of a symmetric matrix
SYEIG MSK_syeig Eigenvalues and eigenvectors of a symmetric matrix

Source code examples

In Listing 25 we provide a simple working example. It has no practical meaning except showing how to organize the input and call the methods.

Listing 25 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]);



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. */

  return r;