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 Python. Click here to download.
import mosek

def print_matrix(x, r, c):
    for i in range(r):
        print([x[j * r + i] for j in range(c)])

with mosek.Env() as env:

    n = 3
    m = 2
    k = 3

    alpha = 2.0
    beta = 0.5

    x = [1.0, 1.0, 1.0]
    y = [1.0, 2.0, 3.0]
    z = [1.0, 1.0]
    v = [0.0, 0.0]
    #A has m=2 rows and k=3 cols
    A = [1.0, 1.0, 2.0, 2.0, 3., 3.]
    #B has k=3 rows and n=3 cols
    B = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
    C = [0.0 for i in range(n * m)]
    D = [1.0, 1.0, 1.0, 1.0]
    Q = [1.0, 0.0, 0.0, 2.0]

# BLAS routines

    xy = env.dot(n, x, y)
    print("dot results= %f\n" % xy)

    env.axpy(n, alpha, x, y)
    print("\naxpy results is ")
    print_matrix(y, 1, len(y))

    env.gemv(mosek.transpose.no, m, n, alpha, A, x, beta, z)
    print("\ngemv results is ")
    print_matrix(z, 1, len(z))

    env.gemm(mosek.transpose.no, mosek.transpose.no,
             m, n, k, alpha, A, B, beta, C)
    print("\ngemm results is ")
    print_matrix(C, m, n)

    env.syrk(mosek.uplo.lo, mosek.transpose.no, m, k, alpha, A, beta, D)
    print("\nsyrk results is")
    print_matrix(D, m, m)

# LAPACK routines

    env.potrf(mosek.uplo.lo, m, Q)
    print("\npotrf results is ")
    print_matrix(Q, m, m)

    env.syeig(mosek.uplo.lo, m, Q, v)
    print("\nsyeig results is")
    print_matrix(v, 1, m)

    env.syevd(mosek.uplo.lo, m, Q, v)
    print("\nsyevd results is")
    print('v: ')
    print_matrix(v, 1, m)
    print('Q: ')
    print_matrix(Q, m, m)