001        SUBROUTINE SSTEIN2( N , D , E , M , W , IBLOCK , ISPLIT , ORFAC , Z , LDZ ,
002       $WORK , IWORK , IFAIL , INFO )
003  
004  *     -- ScaLAPACK routine(version 1.7) --
005  *     University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
006  *     and University of California , Berkeley.
007  *     May 1 , 1997
008  
009  *     .. Scalar Arguments ..
010        INTEGER INFO , LDZ , M , N
011        REAL ORFAC
012  *     ..
013  *     .. Array Arguments ..
014        INTEGER IBLOCK( * ) , IFAIL( * ) , ISPLIT( * ) ,
015       $IWORK( * )
016        REAL D( * ) , E( * ) , W( * ) , WORK( * ) , Z( LDZ , * )
017  *     ..
018  
019  *     Purpose
020  *     === ====
021  
022  *     SSTEIN2 computes the eigenvectors of a real symmetric tridiagonal
023  *     matrix T corresponding to specified eigenvalues , using inverse
024  *     iteration.
025  
026  *     The maximum number of iterations allowed for each eigenvector is
027  *     specified by an internal parameter MAXITS(currently set to 5).
028  
029  *     Arguments
030  *     === ======
031  
032  *     N(input) INTEGER
033  *     The order of the matrix. N >= 0.
034  
035  *     D(input) REAL array , dimension(N)
036  *     The n diagonal elements of the tridiagonal matrix T.
037  
038  *     E(input) REAL array , dimension(N)
039  *     The(n - 1) subdiagonal elements of the tridiagonal matrix
040  *     T , in elements 1 to N - 1. E(N) need not be set.
041  
042  *     M(input) INTEGER
043  *     The number of eigenvectors to be found. 0 <= M <= N.
044  
045  *     W(input) REAL array , dimension(N)
046  *     The first M elements of W contain the eigenvalues for
047  *     which eigenvectors are to be computed. The eigenvalues
048  *     should be grouped by split - off block and ordered from
049  *     smallest to largest within the block.( The output array
050  *     W from SSTEBZ with ORDER = 'B' is expected here. )
051  
052  *     IBLOCK(input) INTEGER array , dimension(N)
053  *     The submatrix indices associated with the corresponding
054  *     eigenvalues in W ; IBLOCK(i) = 1 if eigenvalue W(i) belongs to
055  *     the first submatrix from the top , = 2 if W(i) belongs to
056  *     the second submatrix , etc.( The output array IBLOCK
057  *     from SSTEBZ is expected here. )
058  
059  *     ISPLIT(input) INTEGER array , dimension(N)
060  *     The splitting points , at which T breaks up into submatrices.
061  *     The first submatrix consists of rows / columns 1 to
062  *     ISPLIT( 1 ) , the second of rows / columns ISPLIT( 1 ) + 1
063  *     through ISPLIT( 2 ) , etc.
064  *     ( The output array ISPLIT from SSTEBZ is expected here. )
065  
066  *     ORFAC(input) REAL
067  *     ORFAC specifies which eigenvectors should be
068  *     orthogonalized. Eigenvectors that correspond to eigenvalues
069  *     which are within ORFAC*||T|| of each other are to be
070  *     orthogonalized.
071  
072  *     Z(output) REAL array , dimension(LDZ , M)
073  *     The computed eigenvectors. The eigenvector associated
074  *     with the eigenvalue W(i) is stored in the i - th column of
075  *     Z. Any vector which fails to converge is set to its current
076  *     iterate after MAXITS iterations.
077  
078  *     LDZ(input) INTEGER
079  *     The leading dimension of the array Z. LDZ >= max(1 , N).
080  
081  *     WORK(workspace) REAL array , dimension(5*N)
082  
083  *     IWORK(workspace) INTEGER array , dimension(N)
084  
085  *     IFAIL(output) INTEGER array , dimension(M)
086  *     On normal exit , all elements of IFAIL are zero.
087  *     If one or more eigenvectors fail to converge after
088  *     MAXITS iterations , then their indices are stored in
089  *     array IFAIL.
090  
091  *     INFO(output) INTEGER
092  *     = 0 : successful exit.
093  *     < 0 : if INFO = - i , the i - th argument had an illegal value
094  *     > 0 : if INFO = i , then i eigenvectors failed to converge
095  *     in MAXITS iterations. Their indices are stored in
096  *     array IFAIL.
097  
098  *     Internal Parameters
099  *     === ================
100  
101  *     MAXITS INTEGER , default = 5
102  *     The maximum number of iterations performed.
103  
104  *     EXTRA INTEGER , default = 2
105  *     The number of iterations performed after norm growth
106  *     criterion is satisfied , should be at least 1.
107  
108  *     === ==================================================================
109  
110  *     .. Parameters ..
111        REAL ZERO , ONE , TEN , ODM1
112        PARAMETER( ZERO = 0.0E + 0 , ONE = 1.0E + 0 , TEN = 1.0E + 1 ,
113       $ODM1 = 1.0E - 1 )
114        INTEGER MAXITS , EXTRA
115        PARAMETER( MAXITS = 5 , EXTRA = 2 )
116        END7825