zhpevd (3) - Linux Manuals

NAME

zhpevd.f -

SYNOPSIS


Functions/Subroutines


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

Function/Subroutine Documentation

subroutine zhpevd (characterJOBZ, characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

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.

 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.


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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', 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 = 'U', the diagonal
          and first superdiagonal of the tridiagonal matrix T overwrite
          the corresponding elements of A, and if UPLO = 'L', 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 = 'V', 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 = 'N', then Z is not referenced.


LDZ 

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', 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 = 'N' and N > 1, LWORK must be at least N.
          If JOBZ = 'V' 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 (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 = '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 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  = 'N' or 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 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.

Date:

November 2011

Definition at line 201 of file zhpevd.f.

Author

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