1DSTEIN(1) LAPACK routine (version 3.1) DSTEIN(1)
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6 DSTEIN - the eigenvectors of a real symmetric tridiagonal matrix T cor‐
7 responding to specified eigenvalues, using inverse iteration
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10 SUBROUTINE DSTEIN( 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 DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ,
18 * )
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21 DSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix
22 T corresponding to specified eigenvalues, using inverse iteration.
23 The maximum number of iterations allowed for each eigenvector is speci‐
25 fied by an internal parameter MAXITS (currently set to 5).
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29 N (input) INTEGER
30 The order of the matrix. N >= 0.
31 D (input) DOUBLE PRECISION array, dimension (N)
33 The n diagonal elements of the tridiagonal matrix T.
34 E (input) DOUBLE PRECISION array, dimension (N-1)
36 The (n-1) subdiagonal elements of the tridiagonal matrix T, in
37 elements 1 to N-1.
38 M (input) INTEGER
40 The number of eigenvectors to be found. 0 <= M <= N.
41 W (input) DOUBLE PRECISION array, dimension (N)
43 The first M elements of W contain the eigenvalues for which
44 eigenvectors are to be computed. The eigenvalues should be
45 grouped by split-off block and ordered from smallest to largest
46 within the block. ( The output array W from DSTEBZ with ORDER
47 = 'B' is expected here. )
48 IBLOCK (input) INTEGER array, dimension (N)
50 The submatrix indices associated with the corresponding eigen‐
51 values in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
52 first submatrix from the top, =2 if W(i) belongs to the second
53 submatrix, etc. ( The output array IBLOCK from DSTEBZ is
54 expected here. )
55 ISPLIT (input) INTEGER array, dimension (N)
57 The splitting points, at which T breaks up into submatrices.
58 The first submatrix consists of rows/columns 1 to ISPLIT( 1 ),
59 the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ),
60 etc. ( The output array ISPLIT from DSTEBZ is expected here. )
61 Z (output) DOUBLE PRECISION array, dimension (LDZ, M)
63 The computed eigenvectors. The eigenvector associated with the
64 eigenvalue W(i) is stored in the i-th column of Z. Any vector
65 which fails to converge is set to its current iterate after
66 MAXITS iterations.
67 LDZ (input) INTEGER
69 The leading dimension of the array Z. LDZ >= max(1,N).
70 WORK (workspace) DOUBLE PRECISION array, dimension (5*N)
72 IWORK (workspace) INTEGER array, dimension (N)
74 IFAIL (output) INTEGER array, dimension (M)
76 On normal exit, all elements of IFAIL are zero. If one or more
77 eigenvectors fail to converge after MAXITS iterations, then
78 their indices are stored in array IFAIL.
79 INFO (output) INTEGER
81 = 0: successful exit.
82 < 0: if INFO = -i, the i-th argument had an illegal value
83 > 0: if INFO = i, then i eigenvectors failed to converge in
84 MAXITS iterations. Their indices are stored in array IFAIL.
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87 MAXITS INTEGER, default = 5
88 The maximum number of iterations performed.
89 EXTRA INTEGER, default = 2
91 The number of iterations performed after norm growth criterion
92 is satisfied, should be at least 1.
93 LAPACK routine (version 3.1) November 2006 DSTEIN(1)