control_systems_torbox 0.2.1

Control systems toolbox
Documentation 
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

<HTML>
<HEAD><TITLE>MB01OO - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MB01OO">MB01OO</A></H2>
<H3>
Computation of P or P' with P = op(H) X op(E)' with X symmetric, H upper Hessenberg, and E upper triangular
</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 either P or P', with P defined by the matrix formula

     P = op( H )*X*op( E )',

  where H is an upper Hessenberg matrix, X is a symmetric matrix,
  E is an upper triangular matrix, and op( M ) is one of

     op( M ) = M   or   op( M ) = M'.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB01OO( UPLO, TRANS, N, H, LDH, X, LDX, E, LDE, P, LDP,
     $                   INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, LDE, LDH, LDP, LDX, N
      CHARACTER         TRANS, UPLO
C     .. Array Arguments ..
      DOUBLE PRECISION  E(LDE,*), H(LDH,*), P(LDP,*), X(LDX,*)

</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>

<B>Mode Parameters</B>
<PRE>
  UPLO    CHARACTER*1
          Specifies which triangle of the symmetric matrix X is
          given as follows:
          = 'U':  the upper triangular part is given;
          = 'L':  the lower triangular part is given.

  TRANS   CHARACTER*1
          Specifies the operation to be performed as follows:
          = 'N':         compute P  = H*X*E';
          = 'T' or 'C':  compute P' = E'*X*H.

</PRE>
<B>Input/Output Parameters</B>
<PRE>
  N       (input) INTEGER
          The order of the matrices H, X, E, and P.  N &gt;= 0.

  H       (input) DOUBLE PRECISION array, dimension (LDH,N)
          On entry, the leading N-by-N upper Hessenberg part of this
          array must contain the upper Hessenberg matrix H.
          The remaining part of this array is not referenced.

  LDH     INTEGER
          The leading dimension of the array H.  LDH &gt;= MAX(1,N).

  X       (input) DOUBLE PRECISION array, dimension (LDX,N)
          On entry, if UPLO = 'U', the leading N-by-N upper
          triangular part of this array must contain the upper
          triangular part of the symmetric matrix X and the strictly
          lower triangular part of the array is not referenced.
          On entry, if UPLO = 'L', the leading N-by-N lower
          triangular part of this array must contain the lower
          triangular part of the symmetric matrix X and the strictly
          upper triangular part of the array is not referenced.

  LDX     INTEGER
          The leading dimension of the array X.  LDX &gt;= MAX(1,N).

  E       (input) DOUBLE PRECISION array, dimension (LDE,N)
          On entry, the leading N-by-N upper triangular part of this
          array must contain the upper triangular matrix E.
          The remaining part of this array is not referenced.

  LDE     INTEGER
          The leading dimension of array E.  LDE &gt;= MAX(1,N).

  P       (output) DOUBLE PRECISION array, dimension (LDP,N)
          On exit, the leading N-by-N part of this array contains
          the computed matrix P  = H*X*E', if TRANS = 'N', or
          the computed matrix P' = E'*X*H, if TRANS = 'T'.

  LDP     INTEGER
          The leading dimension of the array P.  LDP &gt;= MAX(1,N).

</PRE>
<B>Error Indicator</B>
<PRE>
  INFO    INTEGER
          = 0:  successful exit;
          &lt; 0:  if INFO = -k, the k-th argument had an illegal
                value.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The matrix expression is efficiently evaluated taking the
  structure into account, and using BLAS and SLICOT routines.
  Let W = H*X, or W = X*H, computed using SLICOT Library routine
  MB01OS. The result is then obtained calling BLAS 3 routine DTRMM.

</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
  The algorithm requires approximately N**3 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>
<A HREF=support.html><B>Return to Supporting Routines index</B></A></BODY>
</HTML>