Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?hbgv
Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian positive-definite eigenproblem with banded matrices.
Syntax
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 )
call hbgv ( ab , bb , w [ , uplo ] [ , z ] [ , info ] )
Include Files
mkl.fi , mkl_lapack.f90
Description
chbgv zhbgv hbgv
The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-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.
Input Parameters
jobz
CHARACTER*1 . Must be ‘N’ or ‘V’ .
If jobz = 'N' , then compute eigenvalues only. If jobz = 'V' , then compute eigenvalues and eigenvectors.
uplo
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 .
n
INTEGER . The order of the matrices A and B ( n≥ 0 ).
ka
INTEGER . The number of super- or sub-diagonals in A
( ka≥ 0 ).
kb
INTEGER . The number of super- or sub-diagonals in B ( kb ≥ 0).
- ab , bb , work
-
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 ).
ldab
INTEGER . The leading dimension of the array ab ; must be at least ka +1 .
ldbb
INTEGER . The leading dimension of the array bb ; must be at least kb +1 .
ldz
INTEGER . The leading dimension of the output array z ; ldz≥ 1 . If jobz = 'V' , ldz≥ max(1, n) .
- rwork
-
REAL for chbgv DOUBLE PRECISION for zhbgv . Workspace array, size at least max(1, 3 n ).
Output Parameters
- ab
-
On exit, the contents of ab are overwritten.
- bb
-
On exit, contains the factor S from the split Cholesky factorization B = S:code:`H`*S , as returned by pbstf / pbstf .
- w
-
REAL for chbgv DOUBLE PRECISION for zhbgv . Array, size at least max(1, n ). If info = 0 , contains the eigenvalues in ascending order.
- z
-
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 Z^{H}*B*Z = I . If jobz = 'N' , then z is not referenced.
info
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 pbstf / pbstf returned info = i and B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.
Return Values
No return value, info is an Output Parameter.
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 hbgv interface are the following:
ab
Holds the array A of size ( ka+1,n ).
bb
Holds the array B of size ( kb+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.