zstedc.f(3)

!>
!> 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.
!>
!> 

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 (MAX(1,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).
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

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