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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine zhbgv | ( | character | jobz, |
| character | uplo, | ||
| integer | n, | ||
| integer | ka, | ||
| integer | kb, | ||
| complex*16, dimension( ldab, * ) | ab, | ||
| integer | ldab, | ||
| complex*16, dimension( ldbb, * ) | bb, | ||
| integer | ldbb, | ||
| double precision, dimension( * ) | w, | ||
| complex*16, dimension( ldz, * ) | z, | ||
| integer | ldz, | ||
| complex*16, dimension( * ) | work, | ||
| double precision, dimension( * ) | rwork, | ||
| integer | info | ||
| ) |
ZHBGV
Download ZHBGV + dependencies [TGZ] [ZIP] [TXT]
ZHBGV computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite.
| [in] | JOBZ | JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors. |
| [in] | UPLO | UPLO is CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored. |
| [in] | N | N is INTEGER
The order of the matrices A and B. N >= 0. |
| [in] | KA | KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0. |
| [in] | KB | KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0. |
| [in,out] | AB | AB is COMPLEX*16 array, dimension (LDAB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first ka+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed. |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1. |
| [in,out] | BB | BB is COMPLEX*16 array, dimension (LDBB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix B, stored in the first kb+1 rows of the array. The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization
B = S**H*S, as returned by ZPBSTF. |
| [in] | LDBB | LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1. |
| [out] | W | W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order. |
| [out] | Z | Z is COMPLEX*16 array, dimension (LDZ, 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. |
| [in] | LDZ | LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= N. |
| [out] | WORK | WORK is COMPLEX*16 array, dimension (N) |
| [out] | RWORK | RWORK is DOUBLE PRECISION array, dimension (3*N) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge:
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed. |
Definition at line 181 of file zhbgv.f.
1.9.7