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<HTML>
<HEAD><TITLE>TF01MY - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="TF01MY">TF01MY</A></H2>
<H3>
Output sequence of a linear time-invariant open-loop system (variant)
</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
(A,B,C,D), where A is an N-by-N general matrix.
The initial state vector x(1) must be supplied by the user.
This routine differs from SLICOT Library routine TF01MD in the
way the input and output trajectories are stored.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE TF01MY( N, M, P, NY, A, LDA, B, LDB, C, LDC, D, LDD,
$ U, LDU, X, Y, LDY, DWORK, LDWORK, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDC, LDD, LDU, LDWORK, LDY, M,
$ N, NY, P
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*),
$ DWORK(*), 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.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The leading N-by-N part of this array must contain the
state matrix A of the system.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,N).
B (input) DOUBLE PRECISION array, dimension (LDB,M)
The leading N-by-M part of this array must contain the
input matrix B of the system.
LDB INTEGER
The leading dimension of array B. LDB >= MAX(1,N).
C (input) DOUBLE PRECISION array, dimension (LDC,N)
The leading P-by-N part of this array must contain the
output matrix C of the system.
LDC INTEGER
The leading dimension of array C. LDC >= MAX(1,P).
D (input) DOUBLE PRECISION array, dimension (LDD,M)
The leading P-by-M part of this array must contain the
direct link matrix D of the system.
LDD INTEGER
The leading dimension of array D. LDD >= MAX(1,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)
On exit, if INFO = 0, DWORK(1) returns the optimal LDWORK.
LDWORK INTEGER
The length of the array DWORK. LDWORK >= MAX(1,N).
For better performance, LDWORK should be larger.
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of the
DWORK array, returns this value as the first entry of
the DWORK array, and no error message related to LDWORK
is issued by XERBLA.
</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) = A x(k) + B u(k)
y(k) = C x(k) + D 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 and uses BLAS 3
operations 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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