1DLATDF(1) LAPACK auxiliary routine (version 3.2) DLATDF(1)
2
6 DLATDF - uses the LU factorization of the n-by-n matrix Z computed by
7 DGETC2 and computes a contribution to the reciprocal Dif-estimate by
8 solving Z * 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, * )
20
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. The factoriza‐
27 tion of Z returned by DGETC2 has the form Z = P*L*U*Q, where P and Q
28 are permutation matrices. L is lower triangular with unit diagonal ele‐
29 ments and U is upper triangular.
30
32 IJOB (input) INTEGER
33 IJOB = 2: First compute an approximative null-vector e of Z
34 using DGECON, e is normalized and solve for Zx = +-e - f with
35 the sign giving the greater value of 2-norm(x). About 5 times
36 as expensive as Default. IJOB .ne. 2: Local look ahead strat‐
37 egy where all entries of the r.h.s. b is choosen as either +1
38 or -1 (Default).
39 N (input) INTEGER
41 The number of columns of the matrix Z.
42 Z (input) DOUBLE PRECISION array, dimension (LDZ, N)
44 On entry, the LU part of the factorization of the n-by-n matrix
45 Z computed by DGETC2: Z = P * L * U * Q
46 LDZ (input) INTEGER
48 The leading dimension of the array Z. LDA >= max(1, N).
49 RHS (input/output) DOUBLE PRECISION array, dimension N.
51 On entry, RHS contains contributions from other subsystems. On
52 exit, RHS contains the solution of the subsystem with entries
53 acoording to the value of IJOB (see above).
54 RDSUM (input/output) DOUBLE PRECISION
56 On entry, the sum of squares of computed contributions to the
57 Dif-estimate under computation by DTGSYL, where the scaling
58 factor RDSCAL (see below) has been factored out. On exit, the
59 corresponding sum of squares updated with the contributions
60 from the current sub-system. If TRANS = 'T' RDSUM is not
61 touched. NOTE: RDSUM only makes sense when DTGSY2 is called by
62 STGSYL.
63 RDSCAL (input/output) DOUBLE PRECISION
65 On entry, scaling factor used to prevent overflow in RDSUM. On
66 exit, RDSCAL is updated w.r.t. the current contributions in
67 RDSUM. If TRANS = 'T', RDSCAL is not touched. NOTE: RDSCAL
68 only makes sense when DTGSY2 is called by DTGSYL.
69 IPIV (input) INTEGER array, dimension (N).
71 The pivot indices; for 1 <= i <= N, row i of the matrix has
72 been interchanged with row IPIV(i).
73 JPIV (input) INTEGER array, dimension (N).
75 The pivot indices; for 1 <= j <= N, column j of the matrix has
76 been interchanged with column JPIV(j).
77
79 Based on contributions by
80 Bo Kagstrom and Peter Poromaa, Department of Computing Science,
81 Umea University, S-901 87 Umea, Sweden.
82 This routine is a further developed implementation of algorithm BSOLVE
83 in [1] using complete pivoting in the LU factorization. [1] Bo
84 Kagstrom and Lars Westin,
85 Generalized Schur Methods with Condition Estimators for
86 Solving the Generalized Sylvester Equation, IEEE Transactions
87 on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. [2]
88 Peter Poromaa,
89 On Efficient and Robust Estimators for the Separation
90 between two Regular Matrix Pairs with Applications in
91 Condition Estimation. Report IMINF-95.05, Departement of
92 Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
93 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 DLATDF(1)