mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/22/2024

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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.

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.

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

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

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.

Parent topic: Extended Eigensolver Interfaces to find largest/smallest eigenvalues

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