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.

N

          N is INTEGER


          The order of the matrix.  N >= 0.

D

          D is REAL array, dimension (N)


          The n diagonal elements of the tridiagonal matrix T.

E

          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

          M is INTEGER


          The number of eigenvectors to be found.  0 <= M <= N.

W

          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

          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

          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

          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

          LDZ is INTEGER


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

WORK

          WORK is REAL 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.

  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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011