% CALCDEMO  Demonstration of Basic Functions in the MFD TOOLBOX.

echo off
%       J.M. Boyle  30th August 1987
% Copyright (c) 1987 by GEC Engineering Research Centre & Cambridge Control Ltd
% History:
%       Minor layout changes made, 12.7.93, JMM.
%       MRN0007, MRN0016, MRN0023, MRN0036

if exist('genrdata.mat') ~= 2, % If data file does not exist ...
  disp(' Generating data for demonstration')
  genrprep;                 % ... then generate it.
end
load genrdata
w=ws;
mvfr = mvfrs;
clc
echo on

% Basic Functions in the Multivariable Frequency Domain Toolbox.
% ===============================================================

% This demo introduces some of the basic functions that are 
% available in the Multivariable Frequency Domain Toolbox. 
% All the functions operate on Multi-Variable Frequency Response 
% (MVFR) matrices.

% Ways in which an MVFR matrix can be formed are covered in the demo:
% 'Generating and Displaying an MVFR matrix'.  
% The MVFR matrix generated during that demo is reused here. 
% Remember that the MVFR matrix represents an open loop unstable 
% chemical reactor.

% To refresh your memory, here are the component matrices of the 
% compressed MVFR matrix.

pause   % Strike any key to display MVFR matrix.
clc

fdisp(w,mvfr)

pause   % Strike any key to continue.
clc

% Now let's look at how to pick out parts of a frequency response matrix.

% To pick out a single component matrix we can use FGETF(W,F,INDEX). 
% INDEX is a vector which specifies which component matrices are to 
% be picked out. To return the second component matrix, INDEX = 2:

[f2,w2] = fgetf(w,mvfr,2)

pause   % Strike any key to continue.
clc

% To pick out elements of component matrices we can use FGET(W,F,INDEX).
% INDEX is a two column matrix whose rows specify the elements to be 
% picked out. To pick out the frequency response of the (1,1) element:

f = fget(w,mvfr,[1,1])

pause  % Strike any key to continue.

% If you use FGET to pick out elements of a component matrix and then 
% modify those elements in some way, you can use 
% FPUT(W,F,ELEMENTS,INDEX) to put back the elements.

% The columns of ELEMENTS contain the elements to be 'put' and
% INDEX specifies the positions in the component matrices where
% the elements are to be 'put'.

pause  % Strike any key to continue.
clc

% Let's put the [1,1] element we picked out using FGET back into
% the [2,2] position.

ftemp = fput(w,mvfr,f,[2,2]);

pause % Strike any key to display the resulting MVFR matrix.
clc

fdisp(w,ftemp)

pause   % Strike any key to continue.
clc

% To extract the diagonal elements of component matrices, use
%  FDIAG(W,F).

fd = fdiag(w,ftemp);

% Strike any key to display the diagonal elements.

% These should be the same, because we copied the [1,1] element to 
% the [2,2] position.

pause

fdisp(w,fd)

% FDIAG can also be used to generate diagonal MVFR matrices.
pause  % Strike any key to continue.
clc

% Combining MVFR Matrices.
% ========================

% There is a set of functions that allow MVFR matrices to be combined.

% Addition.
% ---------

% FADD(W,F,C) adds the matrix C to each component matrix of F.

% Firstly, we must make up an arbitrary C matrix.

c = [100 0;0 -100]

ftemp = fadd(w,mvfr,c);

pause % Strike any key to display the resulting matrix.

fdisp(w,ftemp)

pause % Strike any key to continue.
clc

% FADDF(W,F1,F2) adds two MVFR matrices
% In this example we will add one MVFR matrix to itself.

ftemp = faddf(w,mvfr,mvfr);

pause % Strike any key to display the resulting matrix.

fdisp(w,ftemp)

pause % Strike any key to continue.
clc

% Multiplication.
% ---------------

% FMUL(W,F,C) multiplies each component matrix of F by C.

ftemp = fmul(w,mvfr,c);

pause % Strike any key to display the resulting matrix.

fdisp(w,ftemp)

pause % Strike any key to continue.
clc

% FMULF(W,F1,F2) multiplies two MVFR matrices.
% Take care with the order in which you specify F1 and F2.

ftemp = fmulf(w,mvfr,mvfr);

pause % Strike any key to display the resulting matrix.

fdisp(w,ftemp)

pause % Strike any key to continue.
clc

% Basic Mathematical Operations on a MVFR Matrix.
% ===============================================

% We shall now look at some of the mathematical operations which
% may be performed on a MVFR matrix.

% Calculating Eigenvalues.
% ------------------------

% The eigenvalues of an MVFR matrix are calculated using
% FEIG(W,F)

eigval = feig(w,mvfr);

pause  % Strike any key to display the eigenvalues.

fdisp(w,eigval)

pause % Strike any key to continue.
clc

% Calculating Singular Values.
% ----------------------------

% The singular values of an MVFR matrix are calculated using the
% function FSVD(W,F).

sval = fsvd(w,mvfr);

pause % Strike any key to display the singular values.

fdisp(w,sval)

pause  % Strike any key to continue.
clc

% Inverting an MVFR matrix.
% -------------------------

% FINV inverts the component matrices of an MVFR matrix.

ftemp = finv(w,mvfr);
fident = fmulf(w,mvfr,ftemp);

% Strike any key to display results
% of the MVFR matrix multipled by its inverse
pause
clc

fdisp(w,fident)

pause  % Strike any key to continue.
clc


% Complex Conjugate Transpose of a MVFR matrix.
% ---------------------------------------------

% FTRN transposes the component matrices of a MVFR matrix.

mtrn = ftrn(w,mvfr);

pause  % Strike any key to display results.

fdisp(w,mtrn)

pause  % Strike any key to continue.
clc

% In fact, we have developed a function FFUN(W,F,'FUN'), that 
% allows us to execute a function on each component matrix of
% an MVFR matrix. The parameter 'FUN' specifies which function 
% is to be executed. It can be either a resident MATLAB function 
% or one you have written yourself. The function must accept a 
% single matrix argument and return a single result (scalar, 
% vector or matrix). For example, we can call the SRQT function:

msqrt = ffun(w,mvfr,'sqrt');

pause  % Strike any key to display the results.

fdisp(w,msqrt)

pause % Strike any key to return to the Main Menu.
echo off