%-----------------------------------------------------------------------
% Regression of Antoine coefficients by minimizing sse.
% Estimate the Antoine constants of water by fitting the given steam data
% to the equation
%   Psat = exp( A-B/(T+C))
% where Psat is the saturation pressure in psia and T is temperature in øF.
% Programming Note: call fmins (old) or fminsearch; need steamrf.m (which specifies sse)
% Instructor: Nam Sun Wang
%-----------------------------------------------------------------------

% Start fresh
      clear all

% Extend data x and y to external subroutines
      global T P

% Program header -------------------------------------------------------
      disp('Nonlinear regression of Antoine coefficients of water')
      disp('  Psat = exp(A-B/(T+C))')

% Read data from a file ------------------------------------------------
      load steam.dat;
      T = steam(:,1);
      P = steam(:,2);

% Initial guess --------------------------------------------------------
      param(1) =    15.;
      param(2) = 10000.;
      param(3) =   460.;

% Call a routine (fmins or fminsearch) to find the parameters ------------------------
%     param = fmins('steamrf', param); ... obsolete
      param = fminsearch('steamrf', param);

% Print the coefficients -----------------------------------------------
      A = param(1);
      B = param(2);
      C = param(3);
      disp('The coefficients are:')
      disp(['  A = ', num2str(A) ])
      disp(['  B = ', num2str(B) ])
      disp(['  C = ', num2str(C) ])
      disp(['The value of sse is: ', num2str(steamrf(param)) ])

% Generate the fitted function
      Pregress = exp(A-B./(T+C));

% Plot and compare results
      plot(T, P, 'o', T, Pregress, '-')