Visible to Intel only — GUID: GUID-B9E2749F-DADA-43CE-8245-52EF07FCF7B1
Visible to Intel only — GUID: GUID-B9E2749F-DADA-43CE-8245-52EF07FCF7B1
?hbev
Computes all eigenvalues and, optionally, eigenvectors of a Hermitian band matrix.
Syntax
call chbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)
call zhbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)
call hbev(ab, w [,uplo] [,z] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.
Input Parameters
- jobz
-
CHARACTER*1. Must be 'N' or 'V'.
If jobz = 'N', then only eigenvalues are computed.
If jobz = 'V', then eigenvalues and eigenvectors are computed.
- uplo
-
CHARACTER*1. 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
-
INTEGER. The order of the matrix A (n≥ 0).
- kd
-
INTEGER. The number of super- or sub-diagonals in A
(kd≥ 0).
- ab, work
-
COMPLEX for chbev
DOUBLE COMPLEX for zhbev.
Arrays:
ab(lda,*) is an array containing either upper or lower triangular part of the Hermitian matrix A (as specified by uplo) in band storage format.
The second dimension of ab must be at least max(1, n).
work (*) is a workspace array.
The dimension of work must be at least max(1, n).
- ldab
-
INTEGER. The leading dimension of ab; must be at least kd +1.
- ldz
-
INTEGER. The leading dimension of the output array z.
Constraints:
if jobz = 'N', then ldz≥ 1;
if jobz = 'V', then ldz≥ max(1, n) .
- rwork
-
REAL for chbev
DOUBLE PRECISION for zhbev
Workspace array, size at least max(1, 3n-2).
Output Parameters
- w
-
REAL for chbev
DOUBLE PRECISION for zhbev
Array, size at least max(1, n).
If info = 0, contains the eigenvalues in ascending order.
- z
-
COMPLEX for chbev
DOUBLE COMPLEX for zhbev.
Array z(ldz,*).
The second dimension of z must be at least max(1, 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).
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(see the description of hbtrd).
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the ith 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.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine hbev interface are the following:
- ab
-
Holds the array A of size (kd+1,n).
- w
-
Holds the vector with the number of elements n.
- z
-
Holds the matrix Z of size (n, n).
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
- jobz
-
Restored based on the presence of the argument z as follows:
jobz = 'V', if z is present,
jobz = 'N', if z is omitted.