?stedc

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?stedc

Computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

Syntax

lapack_int LAPACKE_sstedc( int matrix_layout, char compz, lapack_int n, float* d, float* e, float* z, lapack_int ldz );

lapack_int LAPACKE_dstedc( int matrix_layout, char compz, lapack_int n, double* d, double* e, double* z, lapack_int ldz );

lapack_int LAPACKE_cstedc( int matrix_layout, char compz, lapack_int n, float* d, float* e, lapack_complex_float* z, lapack_int ldz );

lapack_int LAPACKE_zstedc( int matrix_layout, char compz, lapack_int n, double* d, double* e, lapack_complex_double* z, lapack_int ldz );

Include Files

mkl.h

Description

The routine computes all the eigenvalues and (optionally) all the eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band real symmetric or complex Hermitian matrix can also be found if sytrd/hetrd or sptrd/hptrd or sbtrd/hbtrd has been used to reduce this matrix to tridiagonal form.

Input Parameters

matrix_layout

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

compz

Must be 'N' or 'I' or 'V'.

If compz = 'N', the routine computes eigenvalues only.

If compz = 'I', the routine computes the eigenvalues and eigenvectors of the tridiagonal matrix.

If compz = 'V', the routine computes the eigenvalues and eigenvectors of original symmetric/Hermitian matrix. On entry, the array z must contain the orthogonal/unitary matrix used to reduce the original matrix to tridiagonal form.

n

The order of the symmetric tridiagonal matrix (n≥ 0).

d, e

Arrays:

d contains the diagonal elements of the tridiagonal matrix.

The dimension of d must be at least max(1, n).

e contains the subdiagonal elements of the tridiagonal matrix.

The dimension of e must be at least max(1, n-1).

z

Array z is of size max(1, ldz*n).

If compz = 'V', then, on entry, z must contain the orthogonal/unitary matrix used to reduce the original matrix to tridiagonal form.

ldz

The leading dimension of z. Constraints:

ldz≥ 1 if compz = 'N';

ldz≥ max(1, n) if compz = 'V' or 'I'.

Output Parameters

d

The n eigenvalues in ascending order, unless info≠ 0.

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, the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns i/(n+1) through mod(i, n+1).

Parent topic: Symmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?stedc

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values