Man page - hbev(3)

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Manual

hbev

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chbev (character jobz, character uplo, integer n, integer kd,complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w,complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * )work, real, dimension( * ) rwork, integer info)
subroutine dsbev (character jobz, character uplo, integer n, integer kd,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) w, double precision, dimension( ldz, * ) z,integer ldz, double precision, dimension( * ) work, integer info)
subroutine ssbev (character jobz, character uplo, integer n, integer kd,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w,real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,integer info)
subroutine zhbev (character jobz, character uplo, integer n, integer kd,complex*16, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz,complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)
Author

NAME

hbev - {hb,sb}ev: eig, QR iteration

SYNOPSIS

Functions

subroutine chbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)
CHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dsbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info)
DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine ssbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info)
SSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)
ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

subroutine chbev (character jobz, character uplo, integer n, integer kd,complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w,complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * )work, real, dimension( * ) rwork, integer info)

CHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

CHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A.

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 triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 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 orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(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 >= max(1,N).

WORK

WORK is COMPLEX array, dimension (N)

RWORK

RWORK is REAL array, dimension (max(1,3*N-2))

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsbev (character jobz, character uplo, integer n, integer kd,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) w, double precision, dimension( ldz, * ) z,integer ldz, double precision, dimension( * ) work, integer info)

DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

DSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A.

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 triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 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 orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(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 >= max(1,N).

WORK

WORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssbev (character jobz, character uplo, integer n, integer kd,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w,real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,integer info)

SSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

SSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A.

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 triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 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 orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(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 >= max(1,N).

WORK

WORK is REAL array, dimension (max(1,3*N-2))

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zhbev (character jobz, character uplo, integer n, integer kd,complex*16, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz,complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)

ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A.

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 triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 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 orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(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 >= max(1,N).

WORK

WORK is COMPLEX*16 array, dimension (N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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