zstedc (3) - Linux Manuals

NAME

zstedc.f -

SYNOPSIS


Functions/Subroutines


subroutine zstedc (COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZSTEDC

Function/Subroutine Documentation

subroutine zstedc (characterCOMPZ, integerN, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

ZSTEDC

Purpose: 

 ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer method.
 The eigenvectors of a full or band complex Hermitian matrix can also
 be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
 matrix to tridiagonal form.

 This code 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.  See DLAED3 for details.


 

Parameters:

COMPZ 

          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original Hermitian matrix
                  also.  On entry, Z contains the unitary matrix used
                  to reduce the original matrix to tridiagonal form.


N 

          N is INTEGER
          The dimension of the symmetric tridiagonal matrix.  N >= 0.


D 

          D is DOUBLE PRECISION array, dimension (N)
          On entry, the diagonal elements of the tridiagonal matrix.
          On exit, if INFO = 0, the eigenvalues in ascending order.


E 

          E is DOUBLE PRECISION array, dimension (N-1)
          On entry, the subdiagonal elements of the tridiagonal matrix.
          On exit, E has been destroyed.


Z 

          Z is COMPLEX*16 array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the unitary
          matrix used in the reduction to tridiagonal form.
          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
          orthonormal eigenvectors of the original Hermitian matrix,
          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
          of the symmetric tridiagonal matrix.
          If  COMPZ = 'N', then Z is not referenced.


LDZ 

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1.
          If eigenvectors are desired, then 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 COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
          Note that for COMPZ = 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LWORK need
          only be 1.

          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 COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
          If COMPZ = 'V' and N > 1, LRWORK must be at least
                         1 + 3*N + 2*N*lg N + 4*N**2 ,
                         where lg( N ) = smallest integer k such
                         that 2**k >= N.
          If COMPZ = 'I' and N > 1, LRWORK must be at least
                         1 + 4*N + 2*N**2 .
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LRWORK
          need only be max(1,2*(N-1)).

          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 COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
          If COMPZ = 'V' or N > 1,  LIWORK must be at least
                                    6 + 6*N + 5*N*lg N.
          If COMPZ = 'I' or N > 1,  LIWORK must be at least
                                    3 + 5*N .
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LIWORK
          need only be 1.

          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:  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

Contributors:

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

Definition at line 213 of file zstedc.f.

Author

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