Man page - hpevd(3)

Packages contains this manual

Manual

hpevd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpevd (character jobz, character uplo, integer n, complex,dimension( * ) ap, 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 dspevd (character jobz, character uplo, integer n, doubleprecision, dimension( * ) ap, double precision, dimension( * ) w,double precision, dimension( ldz, * ) z, integer ldz, double precision,dimension( * ) work, integer lwork, integer, dimension( * ) iwork,integer liwork, integer info)
subroutine sspevd (character jobz, character uplo, integer n, real,dimension( * ) ap, real, dimension( * ) w, real, dimension( ldz, * ) z,integer ldz, real, dimension( * ) work, integer lwork, integer,dimension( * ) iwork, integer liwork, integer info)
subroutine zhpevd (character jobz, character uplo, integer n, complex*16,dimension( * ) ap, 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

hpevd - {hp,sp}evd: eig, divide and conquer

SYNOPSIS

Functions

subroutine chpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dspevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info)
DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine sspevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info)
SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

subroutine chpevd (character jobz, character uplo, integer n, complex,dimension( * ) ap, 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)

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

Purpose:

CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage. 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.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = ā€™Lā€™, the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.

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 required LWORK.

LWORK

LWORK is INTEGER
The dimension of 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.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required 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 (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the required 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 required 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 required 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 required 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 dspevd (character jobz, character uplo, integer n, doubleprecision, dimension( * ) ap, double precision, dimension( * ) w,double precision, dimension( ldz, * ) z, integer ldz, double precision,dimension( * ) work, integer lwork, integer, dimension( * ) iwork,integer liwork, integer info)

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

Purpose:

DSPEVD computes all the eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. 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.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = ā€™Lā€™, the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.

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,LWORK))
On exit, if INFO = 0, WORK(1) returns the required 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 2*N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least
1 + 6*N + N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required 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 required 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 > 1, LIWORK must be at least 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required 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 sspevd (character jobz, character uplo, integer n, real,dimension( * ) ap, real, dimension( * ) w, real, dimension( ldz, * ) z,integer ldz, real, dimension( * ) work, integer lwork, integer,dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

SSPEVD computes all the eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. 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.

AP

AP is REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = ā€™Lā€™, the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.

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,LWORK))
On exit, if INFO = 0, WORK(1) returns the required 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 2*N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least
1 + 6*N + N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required 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 required 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 > 1, LIWORK must be at least 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required 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 zhpevd (character jobz, character uplo, integer n, complex*16,dimension( * ) ap, 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)

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

Purpose:

ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage. 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.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = ā€™Lā€™, the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.

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 required LWORK.

LWORK

LWORK is INTEGER
The dimension of 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.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required 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 (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the required 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 required 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 required 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 required 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

Generated automatically by Doxygen for LAPACK from the source code.