Visible to Intel only — GUID: GUID-65F4BF3F-A175-48B3-9397-2842E09382BF
Visible to Intel only — GUID: GUID-65F4BF3F-A175-48B3-9397-2842E09382BF
?hbevd
Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian band matrix using divide and conquer algorithm.
Syntax
lapack_int LAPACKE_chbevd( int matrix_layout, char jobz, char uplo, lapack_int n, lapack_int kd, lapack_complex_float* ab, lapack_int ldab, float* w, lapack_complex_float* z, lapack_int ldz );
lapack_int LAPACKE_zhbevd( int matrix_layout, char jobz, char uplo, lapack_int n, lapack_int kd, lapack_complex_double* ab, lapack_int ldab, double* w, 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 complex Hermitian band matrix A. In other words, it can compute the spectral factorization of A as: A = Z*Λ*ZH.
Here Λ is a real diagonal matrix whose diagonal elements are the eigenvalues λi, and Z is the (complex) unitary matrix whose columns are the eigenvectors zi. Thus,
A*zi = λi*zi for i = 1, 2, ..., n.
If the eigenvectors are requested, then this routine uses a divide and conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal-Walker-Kahan variant of the QL or QR algorithm.
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 jobz = 'N', then only eigenvalues are computed.
If jobz = 'V', then eigenvalues and eigenvectors are computed.
- uplo
-
Must be 'U' or 'L'.
If uplo = 'U', ab stores the upper triangular part of A.
If uplo = 'L', ab stores the lower triangular part of A.
- n
-
The order of the matrix A (n≥ 0).
- kd
-
The number of super- or sub-diagonals in A
(kd≥ 0).
- ab
-
ab (size at least max(1, ldab*n) for column major layout and at least max(1, ldab*(kd + 1)) for row major layout) is an array containing either upper or lower triangular part of the Hermitian matrix A (as specified by uplo) in band storage format.
- ldab
-
The leading dimension of ab; must be at least kd+1 for column major layout and n for row major layout.
- 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
-
Array, size at least max(1, n).
If info = 0, contains the eigenvalues of the matrix A in ascending order. See also info.
- z
-
Array, size max(1, ldz*n if job = 'V' and at least 1 if job = 'N'.
If jobz = 'V', then this array is overwritten by the unitary matrix Z which contains the eigenvectors of A. The i-th column of Z contains the eigenvector which corresponds to the eigenvalue w[i - 1].
If jobz = 'N', then z is not referenced.
- ab
-
On exit, this array is overwritten by the values generated during the reduction to tridiagonal form.
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.