CSTEIN man page on IRIX

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CSTEIN(3F)							    CSTEIN(3F)

NAME
     CSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix
     T corresponding to specified eigenvalues, using inverse iteration

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

	 INTEGER	INFO, LDZ, M, N

	 INTEGER	IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )

	 REAL		D( * ), E( * ), W( * ), WORK( * )

	 COMPLEX	Z( LDZ, * )

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) INTEGER
	     The order of the matrix.  N >= 0.

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

     E	     (input) REAL array, dimension (N)
	     The (n-1) subdiagonal elements of the tridiagonal matrix T,
	     stored in elements 1 to N-1; E(N) need not be set.

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

     W	     (input) 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. )

									Page 1

CSTEIN(3F)							    CSTEIN(3F)

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

     WORK    (workspace) REAL array, dimension (5*N)

     IWORK   (workspace) INTEGER array, dimension (N)

     IFAIL   (output) 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) 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.

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.

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