Man page - hbevd(3)

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Manual

hbevd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chbevd (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, integer lwork, real, dimension( * ) rwork, integer lrwork,integer, dimension( * ) iwork, integer liwork, integer info)
subroutine dsbevd (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 lwork,integer, dimension( * ) iwork, integer liwork, integer info)
subroutine ssbevd (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 lwork, integer, dimension( * ) iwork, integer liwork, integerinfo)
subroutine zhbevd (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, integer lwork, double precision,dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,integer liwork, integer info)
Author

NAME

hbevd - {hb,sb}evd: eig, divide and conquer

SYNOPSIS

Functions

subroutine chbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dsbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, iwork, liwork, info)
DSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine ssbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, iwork, liwork, info)
SSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

subroutine chbevd (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, integer lwork, real, dimension( * ) rwork, integer lrwork,integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A. If eigenvectors are desired, it
uses a divide and conquer algorithm.

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be at least N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is REAL array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

LRWORK is INTEGER
The dimension of array RWORK.
If N <= 1, LRWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK must be at least N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK must be at least 3 + 5*N .

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

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 dsbevd (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 lwork,integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A. If eigenvectors are desired, it uses
a divide and conquer algorithm.

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 (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
IF N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 2, LWORK must be at least 2*N.
If JOBZ = ā€™Vā€™ and N > 2, LWORK must be at least
( 1 + 5*N + 2*N**2 ).

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 2, LIWORK must be at least 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

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 ssbevd (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 lwork, integer, dimension( * ) iwork, integer liwork, integerinfo)

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

Purpose:

SSBEVD computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A. If eigenvectors are desired, it uses
a divide and conquer algorithm.

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 (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
IF N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 2, LWORK must be at least 2*N.
If JOBZ = ā€™Vā€™ and N > 2, LWORK must be at least
( 1 + 5*N + 2*N**2 ).

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 2, LIWORK must be at least 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

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 zhbevd (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, integer lwork, double precision,dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,integer liwork, integer info)

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

Purpose:

ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A. If eigenvectors are desired, it
uses a divide and conquer algorithm.

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be at least N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

LRWORK is INTEGER
The dimension of array RWORK.
If N <= 1, LRWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK must be at least N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK must be at least 3 + 5*N .

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

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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