1DLATDF(1) LAPACK auxiliary routine (version 3.1) DLATDF(1)
2
6 DLATDF - the LU factorization of the n-by-n matrix Z computed by DGETC2
7 and computes a contribution to the reciprocal Dif-estimate by solving Z
8 * x = b for x, and choosing the r.h.s
9
11 SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )
12 INTEGER IJOB, LDZ, N
14 DOUBLE PRECISION RDSCAL, RDSUM
16 INTEGER IPIV( * ), JPIV( * )
18 DOUBLE PRECISION RHS( * ), Z( LDZ, * )
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22 DLATDF uses the LU factorization of the n-by-n matrix Z computed by
23 DGETC2 and computes a contribution to the reciprocal Dif-estimate by
24 solving Z * x = b for x, and choosing the r.h.s. b such that the norm
25 of x is as large as possible. On entry RHS = b holds the contribution
26 from earlier solved sub-systems, and on return RHS = x.
27 The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,
29 where P and Q are permutation matrices. L is lower triangular with unit
30 diagonal elements and U is upper triangular.
31
34 IJOB (input) INTEGER
35 IJOB = 2: First compute an approximative null-vector e of Z
36 using DGECON, e is normalized and solve for Zx = +-e - f with
37 the sign giving the greater value of 2-norm(x). About 5 times
38 as expensive as Default. IJOB .ne. 2: Local look ahead strat‐
39 egy where all entries of the r.h.s. b is choosen as either +1
40 or -1 (Default).
41 N (input) INTEGER
43 The number of columns of the matrix Z.
44 Z (input) DOUBLE PRECISION array, dimension (LDZ, N)
46 On entry, the LU part of the factorization of the n-by-n matrix
47 Z computed by DGETC2: Z = P * L * U * Q
48 LDZ (input) INTEGER
50 The leading dimension of the array Z. LDA >= max(1, N).
51 RHS (input/output) DOUBLE PRECISION array, dimension N.
53 On entry, RHS contains contributions from other subsystems. On
54 exit, RHS contains the solution of the subsystem with entries
55 acoording to the value of IJOB (see above).
56 RDSUM (input/output) DOUBLE PRECISION
58 On entry, the sum of squares of computed contributions to the
59 Dif-estimate under computation by DTGSYL, where the scaling
60 factor RDSCAL (see below) has been factored out. On exit, the
61 corresponding sum of squares updated with the contributions
62 from the current sub-system. If TRANS = 'T' RDSUM is not
63 touched. NOTE: RDSUM only makes sense when DTGSY2 is called by
64 STGSYL.
65 RDSCAL (input/output) DOUBLE PRECISION
67 On entry, scaling factor used to prevent overflow in RDSUM. On
68 exit, RDSCAL is updated w.r.t. the current contributions in
69 RDSUM. If TRANS = 'T', RDSCAL is not touched. NOTE: RDSCAL
70 only makes sense when DTGSY2 is called by DTGSYL.
71 IPIV (input) INTEGER array, dimension (N).
73 The pivot indices; for 1 <= i <= N, row i of the matrix has
74 been interchanged with row IPIV(i).
75 JPIV (input) INTEGER array, dimension (N).
77 The pivot indices; for 1 <= j <= N, column j of the matrix has
78 been interchanged with column JPIV(j).
79
81 Based on contributions by
82 Bo Kagstrom and Peter Poromaa, Department of Computing Science,
83 Umea University, S-901 87 Umea, Sweden.
84 This routine is a further developed implementation of algorithm BSOLVE
86 in [1] using complete pivoting in the LU factorization.
87 [1] Bo Kagstrom and Lars Westin,
89 Generalized Schur Methods with Condition Estimators for
90 Solving the Generalized Sylvester Equation, IEEE Transactions
91 on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
92 [2] Peter Poromaa,
94 On Efficient and Robust Estimators for the Separation
95 between two Regular Matrix Pairs with Applications in
96 Condition Estimation. Report IMINF-95.05, Departement of
97 Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
98 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006 DLATDF(1)