1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
SUBROUTINE MB02SZ( N, H, LDH, IPIV, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To compute an LU factorization of a complex n-by-n upper
C Hessenberg matrix H using partial pivoting with row interchanges.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C N (input) INTEGER
C The order of the matrix H. N >= 0.
C
C H (input/output) COMPLEX*16 array, dimension (LDH,N)
C On entry, the n-by-n upper Hessenberg matrix to be
C factored.
C On exit, the factors L and U from the factorization
C H = P*L*U; the unit diagonal elements of L are not stored,
C and L is lower bidiagonal.
C
C LDH INTEGER
C The leading dimension of the array H. LDH >= max(1,N).
C
C IPIV (output) INTEGER array, dimension (N)
C The pivot indices; for 1 <= i <= N, row i of the matrix
C was interchanged with row IPIV(i).
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value;
C > 0: if INFO = i, U(i,i) is exactly zero. The
C factorization has been completed, but the factor U
C is exactly singular, and division by zero will occur
C if it is used to solve a system of equations.
C
C METHOD
C
C The factorization has the form
C H = P * L * U
C where P is a permutation matrix, L is lower triangular with unit
C diagonal elements (and one nonzero subdiagonal), and U is upper
C triangular.
C
C This is the right-looking Level 2 BLAS version of the algorithm
C (adapted after ZGETF2).
C
C REFERENCES
C
C -
C
C NUMERICAL ASPECTS
C 2
C The algorithm requires 0( N ) complex operations.
C
C CONTRIBUTOR
C
C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996.
C Supersedes Release 2.0 routine TB01FX by A.J. Laub, University of
C Southern California, United States of America, May 1980.
C
C REVISIONS
C
C V. Sima, Research Institute for Informatics, Bucharest, Oct. 2000,
C Jan. 2005.
C
C KEYWORDS
C
C Frequency response, Hessenberg form, matrix algebra.
C
C ******************************************************************
C
C .. Parameters ..
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
C .. Scalar Arguments ..
INTEGER INFO, LDH, N
C .. Array Arguments ..
INTEGER IPIV(*)
COMPLEX*16 H(LDH,*)
C .. Local Scalars ..
INTEGER J, JP
C .. External Functions ..
DOUBLE PRECISION DCABS1
EXTERNAL DCABS1
C .. External Subroutines ..
EXTERNAL XERBLA, ZAXPY, ZSWAP
C .. Intrinsic Functions ..
INTRINSIC MAX
C ..
C .. Executable Statements ..
C
C Check the scalar input parameters.
C
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( LDH.LT.MAX( 1, N ) ) THEN
INFO = -3
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'MB02SZ', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( N.EQ.0 )
$ RETURN
C
DO 10 J = 1, N
C
C Find pivot and test for singularity.
C
JP = J
IF ( J.LT.N ) THEN
IF ( DCABS1( H( J+1, J ) ).GT.DCABS1( H( J, J ) ) )
$ JP = J + 1
END IF
IPIV( J ) = JP
IF( H( JP, J ).NE.ZERO ) THEN
C
C Apply the interchange to columns J:N.
C
IF( JP.NE.J )
$ CALL ZSWAP( N-J+1, H( J, J ), LDH, H( JP, J ), LDH )
C
C Compute element J+1 of J-th column.
C
IF( J.LT.N )
$ H( J+1, J ) = H( J+1, J )/H( J, J )
C
ELSE IF( INFO.EQ.0 ) THEN
C
INFO = J
END IF
C
IF( J.LT.N ) THEN
C
C Update trailing submatrix.
C
CALL ZAXPY( N-J, -H( J+1, J ), H( J, J+1 ), LDH,
$ H( J+1, J+1 ), LDH )
END IF
10 CONTINUE
RETURN
C *** Last line of MB02SZ ***
END
|
