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 Env.axpy \(y=\alpha x+y\)
DOT Env.dot \(x^T y\)
GEMV Env.gemv \(y=\alpha Ax + \beta y\)
GEMM Env.gemm \(C=\alpha AB+ \beta C\)
SYRK Env.syrk \(C=\alpha AA^T+ \beta C\)
Table 10 LAPACK routines available.
LAPACK Name MOSEK function Description
POTRF Env.potrf Cholesky factorization of a semidefinite symmetric matrix
SYEVD Env.syevd Eigenvalues of a symmetric matrix
SYEIG Env.syeig Eigenvalues and eigenvectors of a symmetric matrix

Source code examples

In Listing 23 we provide a simple working example. It has no practical meaning except showing how to organize the input and call the methods.

Listing 23 Calling BLAS and LAPACK routines from Optimizer API for Java. Click here to download.
package com.mosek.example;

public class blas_lapack {
  static final int n = 3, m = 2, k = 3;

  public static void main (String[] args) {

    double alpha = 2.0, beta = 0.5;
    double[] x = {1., 1., 1.};
    double[] y = {1., 2., 3.};
    double[] z = {1.0, 1.0};

    /*A has m=2 rows and k=3 cols*/
    double[] A = {1., 1., 2., 2., 3., 3.};
    /*B has k=3 rows and n=3 cols*/
    double[] B = {1., 1., 1., 1., 1., 1., 1., 1., 1.};
    double[] C = { 1., 2., 3., 4., 5., 6.};

    double[] D = {1.0, 1.0, 1.0, 1.0};
    double[] Q = {1.0, 0.0, 0.0, 2.0};
    double[] v = new double[2];

    double[] xy = {0.};

    try (mosek.Env  env = new mosek.Env()) {
      /*  routines*/

      env.dot(n, x, y, xy);

      env.axpy(n, alpha, x, y);

      env.gemv(mosek.transpose.no, m, n, alpha, A, x, beta, z);

      env.gemm(mosek.transpose.no, mosek.transpose.no, m, n, k, alpha, A, B, beta, C);

      env.syrk(mosek.uplo.lo, mosek.transpose.no, m, k, alpha, A, beta, D);

      /* LAPACK routines*/

      env.potrf(mosek.uplo.lo, m, Q);

      env.syeig(mosek.uplo.lo, m, Q, v);

      env.syevd(mosek.uplo.lo, m, Q, v);

    } catch (mosek.Exception e) {
      System.out.println ("An error/warning was encountered");
      System.out.println (e.toString());
    }
  }
}