1SSTEIN(1) LAPACK routine (version 3.2) SSTEIN(1)
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6 SSTEIN - computes the eigenvectors of a real symmetric tridiagonal
7 matrix T corresponding to specified eigenvalues, using inverse itera‐
8 tion
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11 SUBROUTINE SSTEIN( 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( * ), Z( LDZ, * )
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21 SSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix
22 T corresponding to specified eigenvalues, using inverse iteration. The
23 maximum number of iterations allowed for each eigenvector is specified
24 by an internal parameter MAXITS (currently set to 5).
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27 N (input) INTEGER
28 The order of the matrix. N >= 0.
29 D (input) REAL array, dimension (N)
31 The n diagonal elements of the tridiagonal matrix T.
32 E (input) REAL array, dimension (N-1)
34 The (n-1) subdiagonal elements of the tridiagonal matrix T, in
35 elements 1 to N-1.
36 M (input) INTEGER
38 The number of eigenvectors to be found. 0 <= M <= N.
39 W (input) REAL array, dimension (N)
41 The first M elements of W contain the eigenvalues for which
42 eigenvectors are to be computed. The eigenvalues should be
43 grouped by split-off block and ordered from smallest to largest
44 within the block. ( The output array W from SSTEBZ with ORDER
45 = 'B' is expected here. )
46 IBLOCK (input) INTEGER array, dimension (N)
48 The submatrix indices associated with the corresponding eigen‐
49 values in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
50 first submatrix from the top, =2 if W(i) belongs to the second
51 submatrix, etc. ( The output array IBLOCK from SSTEBZ is
52 expected here. )
53 ISPLIT (input) INTEGER array, dimension (N)
55 The splitting points, at which T breaks up into submatrices.
56 The first submatrix consists of rows/columns 1 to ISPLIT( 1 ),
57 the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ),
58 etc. ( The output array ISPLIT from SSTEBZ is expected here. )
59 Z (output) REAL array, dimension (LDZ, M)
61 The computed eigenvectors. The eigenvector associated with the
62 eigenvalue W(i) is stored in the i-th column of Z. Any vector
63 which fails to converge is set to its current iterate after
64 MAXITS iterations.
65 LDZ (input) INTEGER
67 The leading dimension of the array Z. LDZ >= max(1,N).
68 WORK (workspace) REAL array, dimension (5*N)
70 IWORK (workspace) INTEGER array, dimension (N)
72 IFAIL (output) INTEGER array, dimension (M)
74 On normal exit, all elements of IFAIL are zero. If one or more
75 eigenvectors fail to converge after MAXITS iterations, then
76 their indices are stored in array IFAIL.
77 INFO (output) INTEGER
79 = 0: successful exit.
80 < 0: if INFO = -i, the i-th argument had an illegal value
81 > 0: if INFO = i, then i eigenvectors failed to converge in
82 MAXITS iterations. Their indices are stored in array IFAIL.
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85 MAXITS INTEGER, default = 5
86 The maximum number of iterations performed.
87 EXTRA INTEGER, default = 2
89 The number of iterations performed after norm growth criterion
90 is satisfied, should be at least 1.
91 LAPACK routine (version 3.2) November 2008 SSTEIN(1)