Man page - hbgv(3)

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Manual

hbgv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chbgv (character jobz, character uplo, integer n, integer ka,integer kb, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, complex,dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real,dimension( * ) rwork, integer info)
subroutine dsbgv (character jobz, character uplo, integer n, integer ka,integer kb, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( ldbb, * ) bb, integer ldbb, doubleprecision, dimension( * ) w, double precision, dimension( ldz, * ) z,integer ldz, double precision, dimension( * ) work, integer info)
subroutine ssbgv (character jobz, character uplo, integer n, integer ka,integer kb, real, dimension( ldab, * ) ab, integer ldab, real,dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, real,dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integerinfo)
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)
Author

NAME

hbgv - {hb,sb}gv: eig, QR iteration

SYNOPSIS

Functions

subroutine chbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
CHBGV
subroutine dsbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info)
DSBGV
subroutine ssbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info)
SSBGV
subroutine zhbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
ZHBGV

Detailed Description

Function Documentation

subroutine chbgv (character jobz, character uplo, integer n, integer ka,integer kb, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, complex,dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real,dimension( * ) rwork, integer info)

CHBGV

Purpose:

CHBGV 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.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

KA

KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KA >= 0.

KB

KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KB >= 0.

AB

AB is COMPLEX 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 = ā€™Uā€™, AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).

On exit, the contents of AB are destroyed.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1.

BB

BB is COMPLEX 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 = ā€™Uā€™, BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = ā€™Lā€™, 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 CPBSTF.

LDBB

LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is COMPLEX array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, 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 = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= N.

WORK

WORK is COMPLEX array, dimension (N)

RWORK

RWORK is REAL array, dimension (3*N)

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 CPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsbgv (character jobz, character uplo, integer n, integer ka,integer kb, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( ldbb, * ) bb, integer ldbb, doubleprecision, dimension( * ) w, double precision, dimension( ldz, * ) z,integer ldz, double precision, dimension( * ) work, integer info)

DSBGV

Purpose:

DSBGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

KA

KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KA >= 0.

KB

KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KB >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric 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 = ā€™Uā€™, AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).

On exit, the contents of AB are destroyed.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1.

BB

BB is DOUBLE PRECISION array, dimension (LDBB, N)
On entry, the upper or lower triangle of the symmetric 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 = ā€™Uā€™, BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = ā€™Lā€™, 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**T*S, as returned by DPBSTF.

LDBB

LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1.

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, 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**T*B*Z = I.
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= N.

WORK

WORK is DOUBLE PRECISION array, dimension (3*N)

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 DPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssbgv (character jobz, character uplo, integer n, integer ka,integer kb, real, dimension( ldab, * ) ab, integer ldab, real,dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, real,dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integerinfo)

SSBGV

Purpose:

SSBGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

KA

KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KA >= 0.

KB

KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KB >= 0.

AB

AB is REAL array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric 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 = ā€™Uā€™, AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).

On exit, the contents of AB are destroyed.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1.

BB

BB is REAL array, dimension (LDBB, N)
On entry, the upper or lower triangle of the symmetric 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 = ā€™Uā€™, BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = ā€™Lā€™, 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**T*S, as returned by SPBSTF.

LDBB

LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is REAL array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, 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**T*B*Z = I.
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= N.

WORK

WORK is REAL array, dimension (3*N)

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 SPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

Purpose:

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.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

KA

KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KA >= 0.

KB

KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KB >= 0.

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 = ā€™Uā€™, AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).

On exit, the contents of AB are destroyed.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1.

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 = ā€™Uā€™, BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = ā€™Lā€™, 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

LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1.

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, 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 = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= N.

WORK

WORK is COMPLEX*16 array, dimension (N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (3*N)

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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