1SSTEIN(1) LAPACK routine (version 3.1) SSTEIN(1)
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6 SSTEIN - the eigenvectors of a real symmetric tridiagonal matrix T cor‐
7 responding to specified eigenvalues, using inverse iteration
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10 SUBROUTINE SSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
11 IFAIL, INFO )
12 INTEGER INFO, LDZ, M, N
14 INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )
16 REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
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20 SSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix
21 T corresponding to specified eigenvalues, using inverse iteration.
22 The maximum number of iterations allowed for each eigenvector is speci‐
24 fied by an internal parameter MAXITS (currently set to 5).
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28 N (input) INTEGER
29 The order of the matrix. N >= 0.
30 D (input) REAL array, dimension (N)
32 The n diagonal elements of the tridiagonal matrix T.
33 E (input) REAL array, dimension (N-1)
35 The (n-1) subdiagonal elements of the tridiagonal matrix T, in
36 elements 1 to N-1.
37 M (input) INTEGER
39 The number of eigenvectors to be found. 0 <= M <= N.
40 W (input) REAL array, dimension (N)
42 The first M elements of W contain the eigenvalues for which
43 eigenvectors are to be computed. The eigenvalues should be
44 grouped by split-off block and ordered from smallest to largest
45 within the block. ( The output array W from SSTEBZ with ORDER
46 = 'B' is expected here. )
47 IBLOCK (input) INTEGER array, dimension (N)
49 The submatrix indices associated with the corresponding eigen‐
50 values in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
51 first submatrix from the top, =2 if W(i) belongs to the second
52 submatrix, etc. ( The output array IBLOCK from SSTEBZ is
53 expected here. )
54 ISPLIT (input) INTEGER array, dimension (N)
56 The splitting points, at which T breaks up into submatrices.
57 The first submatrix consists of rows/columns 1 to ISPLIT( 1 ),
58 the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ),
59 etc. ( The output array ISPLIT from SSTEBZ is expected here. )
60 Z (output) REAL array, dimension (LDZ, M)
62 The computed eigenvectors. The eigenvector associated with the
63 eigenvalue W(i) is stored in the i-th column of Z. Any vector
64 which fails to converge is set to its current iterate after
65 MAXITS iterations.
66 LDZ (input) INTEGER
68 The leading dimension of the array Z. LDZ >= max(1,N).
69 WORK (workspace) REAL array, dimension (5*N)
71 IWORK (workspace) INTEGER array, dimension (N)
73 IFAIL (output) INTEGER array, dimension (M)
75 On normal exit, all elements of IFAIL are zero. If one or more
76 eigenvectors fail to converge after MAXITS iterations, then
77 their indices are stored in array IFAIL.
78 INFO (output) INTEGER
80 = 0: successful exit.
81 < 0: if INFO = -i, the i-th argument had an illegal value
82 > 0: if INFO = i, then i eigenvectors failed to converge in
83 MAXITS iterations. Their indices are stored in array IFAIL.
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86 MAXITS INTEGER, default = 5
87 The maximum number of iterations performed.
88 EXTRA INTEGER, default = 2
90 The number of iterations performed after norm growth criterion
91 is satisfied, should be at least 1.
92 LAPACK routine (version 3.1) November 2006 SSTEIN(1)