CSTEIN(3)      LAPACK routine of NEC Numeric Library Collection      CSTEIN(3)



NAME
       CSTEIN

SYNOPSIS
       SUBROUTINE CSTEIN (N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
           IFAIL, INFO)



PURPOSE
            CSTEIN 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 CUNMTR or CUPMTR for back
            transformation to the eigenvectors of a complex Hermitian matrix
            which was reduced to tridiagonal form.




ARGUMENTS
           N         (input)
                     N is INTEGER
                     The order of the matrix.  N >= 0.

           D         (input)
                     D is REAL array, dimension (N)
                     The n diagonal elements of the tridiagonal matrix T.

           E         (input)
                     E is REAL array, dimension (N-1)
                     The (n-1) subdiagonal elements of the tridiagonal matrix
                     T, stored in elements 1 to N-1.

           M         (input)
                     M is INTEGER
                     The number of eigenvectors to be found.  0 <= M <= N.

           W         (input)
                     W is REAL 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 SSTEBZ with ORDER = 'B' is expected here. )

           IBLOCK    (input)
                     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 SSTEBZ is expected here. )

           ISPLIT    (input)
                     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 SSTEBZ is expected here. )

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

           WORK      (output)
                     WORK is REAL array, dimension (5*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (N)

           IFAIL     (output)
                     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      (output)
                     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.



LAPACK routine                  31 October 2017                      CSTEIN(3)