SRC/zstein.f(3)

NAME
SRC/zstein.f

SYNOPSIS

  Functions/Subroutines
subroutine zstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
ZSTEIN

Function/Subroutine Documentation

  subroutine zstein (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer m, double precision, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, complex*16, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

ZSTEIN

Purpose:

    !>
    !> ZSTEIN computes the eigenvectors of a real symmetric tridiagonal
    !> matrix T corresponding to specified eigenvalues, using inverse
    !> iteration.
    !>
    !> The maximum number of iterations allowed for each eigenvector is
    !> specified by an internal parameter MAXITS (currently set to 5).
    !>
    !> Although the eigenvectors are real, they are stored in a complex
    !> array, which may be passed to ZUNMTR or ZUPMTR for back
    !> transformation to the eigenvectors of a complex Hermitian matrix
    !> which was reduced to tridiagonal form.
    !>
    !>

Parameters
    N

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

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix T.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix
    !>          T, stored in elements 1 to N-1.
    !>

    M

    !>          M is INTEGER
    !>          The number of eigenvectors to be found.  0 <= M <= N.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          The first M elements of W contain the eigenvalues for
    !>          which eigenvectors are to be computed.  The eigenvalues
    !>          should be grouped by split-off block and ordered from
    !>          smallest to largest within the block.  ( The output array
    !>          W from DSTEBZ with ORDER = 'B' is expected here. )
    !>

    IBLOCK

    !>          IBLOCK is INTEGER array, dimension (N)
    !>          The submatrix indices associated with the corresponding
    !>          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
    !>          the first submatrix from the top, =2 if W(i) belongs to
    !>          the second submatrix, etc.  ( The output array IBLOCK
    !>          from DSTEBZ is expected here. )
    !>

    ISPLIT

    !>          ISPLIT is INTEGER array, dimension (N)
    !>          The splitting points, at which T breaks up into submatrices.
    !>          The first submatrix consists of rows/columns 1 to
    !>          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
    !>          through ISPLIT( 2 ), etc.
    !>          ( The output array ISPLIT from DSTEBZ is expected here. )
    !>

    Z

    !>          Z is COMPLEX*16 array, dimension (LDZ, M)
    !>          The computed eigenvectors.  The eigenvector associated
    !>          with the eigenvalue W(i) is stored in the i-th column of
    !>          Z.  Any vector which fails to converge is set to its current
    !>          iterate after MAXITS iterations.
    !>          The imaginary parts of the eigenvectors are set to zero.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (5*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    IFAIL

    !>          IFAIL is INTEGER array, dimension (M)
    !>          On normal exit, all elements of IFAIL are zero.
    !>          If one or more eigenvectors fail to converge after
    !>          MAXITS iterations, then their indices are stored in
    !>          array IFAIL.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, then i eigenvectors failed to converge
    !>               in MAXITS iterations.  Their indices are stored in
    !>               array IFAIL.
    !>

Internal Parameters:

    !>  MAXITS  INTEGER, default = 5
    !>          The maximum number of iterations performed.
    !>
    !>  EXTRA   INTEGER, default = 2
    !>          The number of iterations performed after norm growth
    !>          criterion is satisfied, should be at least 1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 180 of file zstein.f.

Author

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