zstein.f(3)

NAME
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.

Date:
    December 2016

Definition at line 184 of file zstein.f.

Author

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