zheevd (3) - Linux Manuals

NAME

zheevd.f -

SYNOPSIS


Functions/Subroutines


subroutine zheevd (JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Function/Subroutine Documentation

subroutine zheevd (characterJOBZ, characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )W, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Purpose: 

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

 The divide and conquer algorithm makes very mild assumptions about
 floating point arithmetic. It will work on machines with a guard
 digit in add/subtract, or on those binary machines without guard
 digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
 Cray-2. It could conceivably fail on hexadecimal or decimal machines
 without guard digits, but we know of none.


 

Parameters:

JOBZ 

          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.


UPLO 

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.


N 

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


A 

          A is COMPLEX*16 array, dimension (LDA, N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the
          leading N-by-N upper triangular part of A contains the
          upper triangular part of the matrix A.  If UPLO = 'L',
          the leading N-by-N lower triangular part of A contains
          the lower triangular part of the matrix A.
          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
          orthonormal eigenvectors of the matrix A.
          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
          or the upper triangle (if UPLO='U') of A, including the
          diagonal, is destroyed.


LDA 

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).


W 

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


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 length of the array WORK.
          If N <= 1,                LWORK must be at least 1.
          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + 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 the array RWORK.
          If N <= 1,                LRWORK must be at least 1.
          If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
          If JOBZ  = 'V' 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 the array IWORK.
          If N <= 1,                LIWORK must be at least 1.
          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
          If JOBZ  = 'V' 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 and JOBZ = 'N', then the algorithm failed
                to converge; i off-diagonal elements of an intermediate
                tridiagonal form did not converge to zero;
                if INFO = i and JOBZ = 'V', then the algorithm failed
                to compute an eigenvalue while working on the submatrix
                lying in rows and columns INFO/(N+1) through
                mod(INFO,N+1).


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

Modified description of INFO. Sven, 16 Feb 05.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 205 of file zheevd.f.

Author

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