Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

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mkl_sparse_?_gv

Computes the largest/smallest eigenvalues and corresponding eigenvectors of a generalized eigenvalue problem

Syntax

stat = mkl_sparse_s_gv (which, pm, A, descrA, B, descrB, k0, k, E, X, res);

stat = mkl_sparse_d_gv (which, pm, A, descrA, B, descrB, k0, k, E, X, res);

Include Files

  • mkl_solvers_ee.f90

Description

The mkl_sparse_?_gv routine computes the largest/smallest eigenvalues and corresponding eigenvectors of a generalized eigenvalue problem.

Ax = lambda Bx

where A is the real symmetric matrix and B is the real symmetric positive definite matrix.

Input Parameters

which

CHARACTER

Indicates eigenvalues for which to search:

  • which = 'L' indicates the largest eigenvalues.

  • which = 'S' indicates the smallest eigenvalues.

pm

C_INT

Array of size 128. This array is used to pass various parameters to Extended Eigensolver routines. See • Extended Eigensolver Input Parameters for Extremal Eigenvalue Problem for a complete description of the parameters and their default values.

A

SPARSE_MATRIX_T

Handle containing sparse matrix in internal data structure.

descrA

MATRIX_DESCR

Structure specifying sparse matrix properties.

sparse_matrix_type_t type

Specifies the type of a sparse matrix:

  • SPARSE_MATRIX_TYPE_GENERAL

    The matrix is processed as-is.

  • SPARSE_MATRIX_TYPE_SYMMETRIC

    The matrix is symmetric (only the requested triangle is processed).

sparse_fill_mode_t mode

Specifies the triangular matrix part for symmetric, Hermitian, triangular, and block-triangular matrices:

  • SPARSE_FILL_MODE_LOWER

    The lower triangular matrix part is processed.

  • SPARSE_FILL_MODE_UPPER

    The upper triangular matrix part is processed.

sparse_diag_type_t diag

Specifies the diagonal type for non-general matrices:

  • SPARSE_DIAG_NON_UNIT

    Diagonal elements might not be equal to one.

  • SPARSE_DIAG_UNIT

    Diagonal elements are equal to one

B

SPARSE_MATRIX_T

Handle containing sparse matrix in internal data structure.

descrB

MATRIX_DESCR

Structure specifying sparse matrix properties.

sparse_matrix_type_t type

Specifies the type of a sparse matrix:

  • SPARSE_MATRIX_TYPE_GENERAL

    The matrix is processed as-is.

  • SPARSE_MATRIX_TYPE_SYMMETRIC

    The matrix is symmetric (only the requested triangle is processed).

sparse_fill_mode_t mode

Specifies the triangular matrix part for symmetric, Hermitian, triangular, and block-triangular matrices:

  • SPARSE_FILL_MODE_LOWER

    The lower triangular matrix part is processed.

  • SPARSE_FILL_MODE_UPPER

    The upper triangular matrix part is processed.

sparse_diag_type_t diag

Specifies the diagonal type for non-general matrices:

  • SPARSE_DIAG_NON_UNIT

    Diagonal elements might not be equal to one.

  • SPARSE_DIAG_UNIT

    Diagonal elements are equal to one

k0

C_INT

The desired number of the largest/smallest eigenvalues to find.

Output Parameters

k

C_INT

Number of eigenvalues found.

E

C_FLOAT for mkl_sparse_s_gv

C_DOUBLE for mkl_sparse_d_gv

Array of size k0. Contains k largest/smallest eigenvalues.

X

C_FLOAT for mkl_sparse_s_gv

C_DOUBLE for mkl_sparse_d_gv

Array of size k0*Number of columns of matrix A. Contains k eigenvectors.

Res

C_FLOAT for mkl_sparse_s_gv

C_DOUBLE for mkl_sparse_d_gv

Array of size k0. Contains k residuals.

Stat

INTEGER

The function returns a value indicating whether the operation was successful or not, and why.

Return Values

SPARSE_STATUS_SUCCESS

The operation was successful.

SPARSE_STATUS_NOT_INITIALIZED

The routine encountered an empty handle or matrix array.

SPARSE_STATUS_ALLOC_FAILED

Internal memory allocation failed.

SPARSE_STATUS_INVALID_VALUE

The input parameters contain an invalid value.

SPARSE_STATUS_EXECUTION_FAILED

Execution failed.

SPARSE_STATUS_INTERNAL_ERROR

An error in algorithm implementation occurred.

SPARSE_STATUS_NOT_SUPPORTED

The requested operation is not supported.