?spgvd

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?spgvd

Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with matrices in packed storage using a divide and conquer method.

Syntax

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

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

Include Files

mkl.h

Description

The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form

A*x = λ*B*x, A*B*x = λ*x, or B*A*x = λ*x.

Here A and B are assumed to be symmetric, stored in packed format, and B is also positive definite.

If eigenvectors are desired, it uses a divide and conquer algorithm.

Input Parameters

matrix_layout

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

itype

Must be 1 or 2 or 3. Specifies the problem type to be solved:

if itype = 1, the problem type is A*x = lambda*B*x;

if itype = 2, the problem type is A*B*x = lambda*x;

if itype = 3, the problem type is B*A*x = lambda*x.

jobz

Must be 'N' or 'V'.

If jobz = 'N', then compute eigenvalues only.

If jobz = 'V', then compute eigenvalues and eigenvectors.

uplo

Must be 'U' or 'L'.

If uplo = 'U', arrays ap and bp store the upper triangles of A and B;

If uplo = 'L', arrays ap and bp store the lower triangles of A and B.

n

The order of the matrices A and B (n≥ 0).

ap, bp

Arrays:

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

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

bp contains the packed upper or lower triangle of the symmetric matrix B, as specified by uplo.

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

ldz

The leading dimension of the output array z; ldz≥ 1. If jobz = 'V', ldz≥ max(1, n).

Output Parameters

ap

On exit, the contents of ap are overwritten.

bp

On exit, contains the triangular factor U or L from the Cholesky factorization B = U^T*U or B = L*L^T, in the same storage format as B.

w, z

Arrays:

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

If info = 0, contains the eigenvalues in ascending order.

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

If jobz = 'V', then if info = 0, z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:

if itype = 1 or 2, Z^T*B*Z = I;

if itype = 3, Z^T*inv(B)*Z = I;

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

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 > 0, spptrf/dpptrf and sspevd/dspevd returned an error code:

If info = i≤n, sspevd/dspevd failed to converge, and i off-diagonal elements of an intermediate tridiagonal did not converge to zero;

If info = n + i, for 1 ≤i≤n, then the leading minor of order i of B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

Parent topic: Generalized Symmetric Definite Eigenvalue Problems: LAPACK Driver Routines

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