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Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 6/24/2024

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?spev

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.

Syntax

lapack_int LAPACKE_sspev (int matrix_layout, char jobz, char uplo, lapack_int n, float* ap, float* w, float* z, lapack_int ldz);

lapack_int LAPACKE_dspev (int matrix_layout, char jobz, char uplo, lapack_int n, double* ap, double* w, double* z, lapack_int ldz);

Include Files

mkl.h

Description

The routine computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

jobz

Must be 'N' or 'V'.

If job = 'N', then only eigenvalues are computed.

If job = 'V', then eigenvalues and eigenvectors are computed.

uplo

Must be 'U' or 'L'.

If uplo = 'U', ap stores the packed upper triangular part of A.

If uplo = 'L', ap stores the packed lower triangular part of A.

n

The order of the matrix A (n≥ 0).

ap

Array ap contains the packed upper or lower triangle of symmetric matrix A, as specified by uplo.

The size of ap must be at least max(1, n*(n+1)/2).

ldz

The leading dimension of the output array z. Constraints:

if jobz = 'N', then ldz≥ 1;

if jobz = 'V', then ldz≥ max(1, n).

Output Parameters

w, z

Arrays:

w, size at least max(1, n).

If info = 0, w contains the eigenvalues of the matrix A in ascending order.

z (size max(1, ldz*n)).

If jobz = 'V', then if info = 0, z contains the orthonormal eigenvectors of the matrix A, with the i-th column of z holding the eigenvector associated with w[i - 1].

If jobz = 'N', then z is not referenced.

ap

On exit, this array is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of A.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

If info = i, then the algorithm failed to converge; i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?spev

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values