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
|
<HTML>
<HEAD><TITLE>MB02SZ - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB02SZ">MB02SZ</A></H2>
<H3>
LU factorization of a complex upper Hessenberg matrix H
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To compute an LU factorization of a complex n-by-n upper
Hessenberg matrix H using partial pivoting with row interchanges.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB02SZ( N, H, LDH, IPIV, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDH, N
C .. Array Arguments ..
INTEGER IPIV(*)
COMPLEX*16 H(LDH,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix H. N >= 0.
H (input/output) COMPLEX*16 array, dimension (LDH,N)
On entry, the n-by-n upper Hessenberg matrix to be
factored.
On exit, the factors L and U from the factorization
H = P*L*U; the unit diagonal elements of L are not stored,
and L is lower bidiagonal.
LDH INTEGER
The leading dimension of the array H. LDH >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix
was interchanged with row IPIV(i).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value;
> 0: if INFO = i, U(i,i) is exactly zero. The
factorization has been completed, but the factor U
is exactly singular, and division by zero will occur
if it is used to solve a system of equations.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The factorization has the form
H = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (and one nonzero subdiagonal), and U is upper
triangular.
This is the right-looking Level 2 BLAS version of the algorithm
(adapted after ZGETF2).
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
-
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE> 2
The algorithm requires 0( N ) complex operations.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
<HR>
<p>
<A HREF=..\libindex.html><B>Return to index</B></A></BODY>
</HTML>
|
