ZHBGV(3F) ZHBGV(3F)
ZHBGV - compute all the eigenvalues, and optionally, the eigenvectors of
a complex generalized Hermitian-definite banded eigenproblem, of the form
A*x=(lambda)*B*x
SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
WORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), Z( LDZ, * )
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.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
KA (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input) INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KB >= 0.
AB (input/output) 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,jka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+ka).
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ZHBGV(3F) ZHBGV(3F)
On exit, the contents of AB are destroyed.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KA+1.
BB (input/output) 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,jkb)<=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.
LDBB (input) INTEGER
The leading dimension of the array BB. LDBB >= KB+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= N.
WORK (workspace) COMPLEX*16 array, dimension (N)
RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
INFO (output) 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.
ZHBGV(3F) ZHBGV(3F)
ZHBGV - compute all the eigenvalues, and optionally, the eigenvectors of
a complex generalized Hermitian-definite banded eigenproblem, of the form
A*x=(lambda)*B*x
SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
WORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), Z( LDZ, * )
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.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
KA (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input) INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KB >= 0.
AB (input/output) 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,jka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+ka).
Page 1
ZHBGV(3F) ZHBGV(3F)
On exit, the contents of AB are destroyed.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KA+1.
BB (input/output) 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,jkb)<=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.
LDBB (input) INTEGER
The leading dimension of the array BB. LDBB >= KB+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= N.
WORK (workspace) COMPLEX*16 array, dimension (N)
RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
INFO (output) 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.
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