LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
cstein.f File Reference

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## Functions/Subroutines

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

## Function/Subroutine Documentation

 subroutine cstein ( integer N, real, dimension( * ) D, real, dimension( * ) E, integer M, real, dimension( * ) W, integer, dimension( * ) IBLOCK, integer, dimension( * ) ISPLIT, complex, dimension( ldz, * ) Z, integer LDZ, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer, dimension( * ) IFAIL, integer INFO )

CSTEIN

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.```
Parameters:
 [in] N ``` N is INTEGER The order of the matrix. N >= 0.``` [in] D ``` D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix T.``` [in] 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.``` [in] M ``` M is INTEGER The number of eigenvectors to be found. 0 <= M <= N.``` [in] 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. )``` [in] 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. )``` [in] 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. )``` [out] 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.``` [in] LDZ ``` LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,N).``` [out] WORK ` WORK is REAL array, dimension (5*N)` [out] IWORK ` IWORK is INTEGER array, dimension (N)` [out] 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.``` [out] 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.```
Date:
November 2011

Definition at line 182 of file cstein.f.

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