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	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 9.2 LAPACK routines available.

LAPACK Name	MOSEK function	Description
POTRF	Env.potrf	Cholesky factorization of a semidefinite symmetric matrix
SYEVD	Env.syevd	Eigenvalues and eigenvectors of a symmetric matrix
SYEIG	Env.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 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)

    print("Exiting...")