Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian definite eigenproblem with banded matrices.
FORTRAN 77:
call chbgv(jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
call zhbgv(jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
Fortran 95:
call hbgv(ab, bb, w [,uplo] [,z] [,info])
C:
lapack_int LAPACKE_chbgv( int matrix_order, char jobz, char uplo, lapack_int n, lapack_int ka, lapack_int kb, lapack_complex_float* ab, lapack_int ldab, lapack_complex_float* bb, lapack_int ldbb, float* w, lapack_complex_float* z, lapack_int ldz );
lapack_int LAPACKE_zhbgv( int matrix_order, char jobz, char uplo, lapack_int n, lapack_int ka, lapack_int kb, lapack_complex_double* ab, lapack_int ldab, lapack_complex_double* bb, lapack_int ldbb, double* w, lapack_complex_double* z, lapack_int ldz );
The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.
The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x = λ*B*x. Here A and B are Hermitian and banded matrices, and matrix B is also positive definite.
The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
CHARACTER*1. Must be 'N' or 'V'.
If jobz = 'N', then compute eigenvalues only.
If jobz = 'V', then compute eigenvalues and eigenvectors.
CHARACTER*1. Must be 'U' or 'L'.
If uplo = 'U', arrays ab and bb store the upper triangles of A and B;
If uplo = 'L', arrays ab and bb store the lower triangles of A and B.
INTEGER. The order of the matrices A and B (n ≥ 0).
INTEGER. The number of super- or sub-diagonals in A
(ka ≥ 0).
INTEGER. The number of super- or sub-diagonals in B (kb ≥ 0).
COMPLEX for chbgv
DOUBLE COMPLEX for zhbgv
Arrays:
ab (ldab,*) 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 the array ab must be at least max(1, n).
bb(ldbb,*) is an array containing either upper or lower triangular part of the Hermitian matrix B (as specified by uplo) in band storage format.
The second dimension of the array bb must be at least max(1, n).
work(*) is a workspace array, dimension at least max(1, n).
INTEGER. The leading dimension of the array ab; must be at least ka+1.
INTEGER. The leading dimension of the array bb; must be at least kb+1.
INTEGER. The leading dimension of the output array z; ldz ≥ 1. If jobz = 'V', ldz ≥ max(1, n).
REAL for chbgv
DOUBLE PRECISION for zhbgv.
Workspace array, DIMENSION at least max(1, 3n).
On exit, the contents of ab are overwritten.
On exit, contains the factor S from the split Cholesky factorization B = SH*S, as returned by cpbstf/zpbstf.
REAL for chbgv
DOUBLE PRECISION for zhbgv.
Array, DIMENSION at least max(1, n).
If info = 0, contains the eigenvalues in ascending order.
COMPLEX for chbgv
DOUBLE COMPLEX for zhbgv
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 matrix Z of eigenvectors, with the i-th column of z holding the eigenvector associated with w(i). The eigenvectors are normalized so that ZH*B*Z = I.
If jobz = 'N', then z is not referenced.
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th argument had an illegal value.
If info > 0, and
if i ≤ n, the algorithm 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 cpbstf/zpbstf returned info = i and B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.
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 Fortran 95 Interface Conventions.
Specific details for the routine hbgv interface are the following:
Holds the array A of size (ka+1,n).
Holds the array B of size (kb+1,n).
Holds the vector with the number of elements n.
Holds the matrix Z of size (n, n).
Must be 'U' or 'L'. The default value is 'U'.
Restored based on the presence of the argument z as follows:
jobz = 'V', if z is present,
jobz = 'N', if z is omitted.
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