1SGSVJ0(1)LAPACK routine (version 3.2) SGSVJ0(1)
2
6 SGSVJ0 - is called from SGESVJ as a pre-processor and that is its main
7 purpose
8
10 SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
11 + SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
13 IMPLICIT NONE
15 INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
17 REAL EPS, SFMIN, TOL
19 CHARACTER*1 JOBV
21 REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
23 + WORK( LWORK )
25
27 SGSVJ0 is called from SGESVJ as a pre-processor and that is its main
28 purpose. It applies Jacobi rotations in the same way as SGESVJ does,
29 but it does not check convergence (stopping criterion). Few tuning
30 parameters (marked by [TP]) are available for the implementer. Further
31 Details
32 SGSVJ0 is used just to enable SGESVJ to call a simplified version of
33 itself to work on a submatrix of the original matrix.
34 Contributors
35 ~~~~~~~~~~~~
36 Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
37 Bugs, Examples and Comments
38 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
39 Please report all bugs and send interesting test examples and comments
40 to drmac@math.hr. Thank you.
41
43 JOBV (input) CHARACTER*1
44 Specifies whether the output from this procedure is used to
45 compute the matrix V:
46 = 'V': the product of the Jacobi rotations is accumulated by
47 postmulyiplying the N-by-N array V. (See the description of
48 V.) = 'A': the product of the Jacobi rotations is accumulated
49 by postmulyiplying the MV-by-N array V. (See the descriptions
50 of MV and V.) = 'N': the Jacobi rotations are not accumulated.
51 M (input) INTEGER
53 The number of rows of the input matrix A. M >= 0.
54 N (input) INTEGER
56 The number of columns of the input matrix A. M >= N >= 0.
57 A (input/output) REAL array, dimension (LDA,N)
59 On entry, M-by-N matrix A, such that A*diag(D) represents the
60 input matrix. On exit, A_onexit * D_onexit represents the
61 input matrix A*diag(D) post-multiplied by a sequence of Jacobi
62 rotations, where the rotation threshold and the total number of
63 sweeps are given in TOL and NSWEEP, respectively. (See the
64 descriptions of D, TOL and NSWEEP.)
65 LDA (input) INTEGER
67 The leading dimension of the array A. LDA >= max(1,M).
68 D (input/workspace/output) REAL array, dimension (N)
70 The array D accumulates the scaling factors from the fast
71 scaled Jacobi rotations. On entry, A*diag(D) represents the
72 input matrix. On exit, A_onexit*diag(D_onexit) represents the
73 input matrix post-multiplied by a sequence of Jacobi rotations,
74 where the rotation threshold and the total number of sweeps are
75 given in TOL and NSWEEP, respectively. (See the descriptions
76 of A, TOL and NSWEEP.)
77 SVA (input/workspace/output) REAL array, dimension (N)
79 On entry, SVA contains the Euclidean norms of the columns of
80 the matrix A*diag(D). On exit, SVA contains the Euclidean
81 norms of the columns of the matrix onexit*diag(D_onexit).
82 MV (input) INTEGER
84 If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
85 sequence of Jacobi rotations. If JOBV = 'N', then MV is not
86 referenced.
87 V (input/output) REAL array, dimension (LDV,N)
89 If JOBV .EQ. 'V' then N rows of V are post-multipled by a
90 sequence of Jacobi rotations. If JOBV .EQ. 'A' then MV rows of
91 V are post-multipled by a sequence of Jacobi rotations. If
92 JOBV = 'N', then V is not referenced.
93 LDV (input) INTEGER
95 The leading dimension of the array V, LDV >= 1. If JOBV =
96 'V', LDV .GE. N. If JOBV = 'A', LDV .GE. MV.
97 EPS (input) INTEGER
99 EPS = SLAMCH('Epsilon')
100 SFMIN (input) INTEGER
102 SFMIN = SLAMCH('Safe Minimum')
103 TOL (input) REAL
105 TOL is the threshold for Jacobi rotations. For a pair A(:,p),
106 A(:,q) of pivot columns, the Jacobi rotation is
107 applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
108 NSWEEP (input) INTEGER
110 NSWEEP is the number of sweeps of Jacobi rotations to be per‐
111 formed.
112 WORK (workspace) REAL array, dimension LWORK.
114 LWORK (input) INTEGER
116 LWORK is the dimension of WORK. LWORK .GE. M.
117 INFO (output) INTEGER
119 = 0 : successful exit.
120 < 0 : if INFO = -i, then the i-th argument had an illegal value
121 LAPACK routine (version 3.2) November 2008 SGSVJ0(1)