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<HTML>
<HEAD><TITLE>TF01MX - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="TF01MX">TF01MX</A></H2>
<H3>
Output sequence of a linear time-invariant open-loop system given its system matrix
</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 the output sequence of a linear time-invariant
open-loop system given by its discrete-time state-space model
with an (N+P)-by-(N+M) general system matrix S,
( A B )
S = ( ) .
( C D )
The initial state vector x(1) must be supplied by the user.
The input and output trajectories are stored as in the SLICOT
Library routine TF01MY.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE TF01MX( N, M, P, NY, S, LDS, U, LDU, X, Y, LDY,
$ DWORK, LDWORK, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDS, LDU, LDWORK, LDY, M, N, NY, P
C .. Array Arguments ..
DOUBLE PRECISION DWORK(*), S(LDS,*), U(LDU,*), X(*), Y(LDY,*)
</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 A. N >= 0.
M (input) INTEGER
The number of system inputs. M >= 0.
P (input) INTEGER
The number of system outputs. P >= 0.
NY (input) INTEGER
The number of output vectors y(k) to be computed.
NY >= 0.
S (input) DOUBLE PRECISION array, dimension (LDS,N+M)
The leading (N+P)-by-(N+M) part of this array must contain
the system matrix S.
LDS INTEGER
The leading dimension of array S. LDS >= MAX(1,N+P).
U (input) DOUBLE PRECISION array, dimension (LDU,M)
The leading NY-by-M part of this array must contain the
input vector sequence u(k), for k = 1,2,...,NY.
Specifically, the k-th row of U must contain u(k)'.
LDU INTEGER
The leading dimension of array U. LDU >= MAX(1,NY).
X (input/output) DOUBLE PRECISION array, dimension (N)
On entry, this array must contain the initial state vector
x(1) which consists of the N initial states of the system.
On exit, this array contains the final state vector
x(NY+1) of the N states of the system at instant NY+1.
Y (output) DOUBLE PRECISION array, dimension (LDY,P)
The leading NY-by-P part of this array contains the output
vector sequence y(1),y(2),...,y(NY) such that the k-th
row of Y contains y(k)' (the outputs at instant k),
for k = 1,2,...,NY.
LDY INTEGER
The leading dimension of array Y. LDY >= MAX(1,NY).
</PRE>
<B>Workspace</B>
<PRE>
DWORK DOUBLE PRECISION array, dimension (LDWORK)
LDWORK INTEGER
The length of the array DWORK.
LDWORK >= 0, if MIN(N,P,NY) = 0; otherwise,
LDWORK >= N+P, if M = 0;
LDWORK >= 2*N+M+P, if M > 0.
For better performance, LDWORK should be larger.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
Given an initial state vector x(1), the output vector sequence
y(1), y(2),..., y(NY) is obtained via the formulae
( x(k+1) ) ( x(k) )
( ) = S ( ) ,
( y(k) ) ( u(k) )
where each element y(k) is a vector of length P containing the
outputs at instant k, and k = 1,2,...,NY.
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Luenberger, D.G.
Introduction to Dynamic Systems: Theory, Models and
Applications.
John Wiley & Sons, New York, 1979.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The algorithm requires approximately (N + M) x (N + P) x NY
multiplications and additions.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
The implementation exploits data locality as much as possible,
given the workspace length.
</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>
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