# Copyright (c) P.J.Gawthrop 1998

###############################################################
## Version control history
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## $Id$
## $Log$
## Revision 1.3  2000/09/11 10:53:54  peterg
## Uses 1st io of mimo to create siso
##
## Revision 1.2  1998/01/22 13:25:22  peterg
## Added END;; to output file.
##
## Revision 1.1  1998/01/22 13:16:43  peterg
## Initial revision
##
###############################################################

rm -f sm2smo_r.log

# Use reduce to accomplish the transformation
reduce >sm2smo_r.log << EOF

in "$1_def.r";
in "$1_sm.r";
in "$1_smc.r";
in "$1_tf.r";

%Read the formatting function
in "$MTTPATH/trans/reduce_matrix.r";


OFF Echo;
OFF Nat;

% Find  observibility matrix.
MATRIX MTTObs(MTTNx,MTTNX);
MTTCA := MTTC;
FOR i := 1:MTTNx DO
  BEGIN
   FOR j := 1:MTTNx DO 
      MTTObs(i,j) := MTTCA(1,j);
   MTTCA := MTTCA*MTTA;
  END;

%Canonical forms:
% This statement makes Gs a scalar transfer function
Gs := MTTtf(1,1);

% Numerator and denominator polynomials
bs := num(gs);
as := den(gs);
%Observable form (dual of controller form)
MTTA_o := tp(MTTA_c);
MTTB_o := tp(MTTC_c);
MTTC_o := tp(MTTB_c);
MTTD_o := MTTD;

% extract coeficients and divide by coeff of s^n
% reverse operator puts list with highest oder coeffs first
ai := reverse(coeff(as,s));
a0 := first(ai);
MTTn := length(ai) - 1;


% Normalised coeficients;
ai := reverse(coeff(as/a0,s));
bi := reverse(coeff(bs/a0,s));
MTTm := length(bi)-1;

% Zap the (unity) first element of ai list;
ai := rest(ai);

% System in observer form
% MTTA_o matrix
matrix MTTA_o(MTTNx,MTTNx);

% First column is ai coefficients
for i := 1:MTTNx do
  MTTA_o(i,1) := -part(ai,i);

% (MTTNx-1)x(MTTNx-1) unit matrix in upper right-hand corner (if n>1)
if MTTNx>1 then
  for i := 1:MTTNx-1 do
    MTTA_o(i,i+1) := 1;

% C_o vector;
matrix MTTC_o(1,MTTNx);
  MTTC_o(1,1) := 1;
MTTC_o;
% B_o vector;
matrix MTTB_o(MTTNx,1);
for i := 1:MTTm+1 do
  MTTB_o(i+MTTNx-MTTm-1,1) := part(bi,i);

% D_o
MTTD_o := MTTD;

%Observability matrix of observer form
MATRIX MTTObs_o(MTTNx,MTTNX);
MTTCA := MTTC_o;
FOR i := 1:MTTNx DO
  BEGIN
   FOR j := 1:MTTNx DO