1CSTEIN(1) LAPACK routine (version 3.2) CSTEIN(1)
2
6 CSTEIN - computes the eigenvectors of a real symmetric tridiagonal
7 matrix T corresponding to specified eigenvalues, using inverse itera‐
8 tion
9
11 SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
12 IFAIL, INFO )
13 INTEGER INFO, LDZ, M, N
15 INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )
17 REAL D( * ), E( * ), W( * ), WORK( * )
19 COMPLEX Z( LDZ, * )
21
23 CSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix
24 T corresponding to specified eigenvalues, using inverse iteration. The
25 maximum number of iterations allowed for each eigenvector is specified
26 by an internal parameter MAXITS (currently set to 5). Although the
27 eigenvectors are real, they are stored in a complex array, which may be
28 passed to CUNMTR or CUPMTR for back
29 transformation to the eigenvectors of a complex Hermitian matrix which
30 was reduced to tridiagonal form.
31
33 N (input) INTEGER
34 The order of the matrix. N >= 0.
35 D (input) REAL array, dimension (N)
37 The n diagonal elements of the tridiagonal matrix T.
38 E (input) REAL array, dimension (N-1)
40 The (n-1) subdiagonal elements of the tridiagonal matrix T,
41 stored in elements 1 to N-1.
42 M (input) INTEGER
44 The number of eigenvectors to be found. 0 <= M <= N.
45 W (input) REAL array, dimension (N)
47 The first M elements of W contain the eigenvalues for which
48 eigenvectors are to be computed. The eigenvalues should be
49 grouped by split-off block and ordered from smallest to largest
50 within the block. ( The output array W from SSTEBZ with ORDER
51 = 'B' is expected here. )
52 IBLOCK (input) INTEGER array, dimension (N)
54 The submatrix indices associated with the corresponding eigen‐
55 values in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
56 first submatrix from the top, =2 if W(i) belongs to the second
57 submatrix, etc. ( The output array IBLOCK from SSTEBZ is
58 expected here. )
59 ISPLIT (input) INTEGER array, dimension (N)
61 The splitting points, at which T breaks up into submatrices.
62 The first submatrix consists of rows/columns 1 to ISPLIT( 1 ),
63 the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ),
64 etc. ( The output array ISPLIT from SSTEBZ is expected here. )
65 Z (output) COMPLEX array, dimension (LDZ, M)
67 The computed eigenvectors. The eigenvector associated with the
68 eigenvalue W(i) is stored in the i-th column of Z. Any vector
69 which fails to converge is set to its current iterate after
70 MAXITS iterations. The imaginary parts of the eigenvectors are
71 set to zero.
72 LDZ (input) INTEGER
74 The leading dimension of the array Z. LDZ >= max(1,N).
75 WORK (workspace) REAL array, dimension (5*N)
77 IWORK (workspace) INTEGER array, dimension (N)
79 IFAIL (output) INTEGER array, dimension (M)
81 On normal exit, all elements of IFAIL are zero. If one or more
82 eigenvectors fail to converge after MAXITS iterations, then
83 their indices are stored in array IFAIL.
84 INFO (output) INTEGER
86 = 0: successful exit
87 < 0: if INFO = -i, the i-th argument had an illegal value
88 > 0: if INFO = i, then i eigenvectors failed to converge in
89 MAXITS iterations. Their indices are stored in array IFAIL.
90
92 MAXITS INTEGER, default = 5
93 The maximum number of iterations performed.
94 EXTRA INTEGER, default = 2
96 The number of iterations performed after norm growth criterion
97 is satisfied, should be at least 1.
98 LAPACK routine (version 3.2) November 2008 CSTEIN(1)