function [gf] = gfit2(t,y,gFitMeasure,options)
% GFIT2 Computes goodness of fit for regression model
%
% USAGE:
% [gf] = gfit2(t,y)
% [gf] = gfit2(t,y,gFitMeasure)
% [gf] = gfit2(t,y,gFitMeasure,options)
%
% INPUT:
% t: matrix or vector of target values for regression model
% y: matrix or vector of output from regression model.
% gFitMeasure: a string or cell array of string values representing
% different form of goodness of fit measure as follows:
%
% 'all' - calculates all the measures below
% '1' - mean squared error (mse)
% '2' - normalised mean squared error (nmse)
% '3' - root mean squared error (rmse)
% '4' - normalised root mean squared error (nrmse)
% '5' - mean absolute error (mae)
% '6' - mean absolute relative error (mare)
% '7' - coefficient of correlation (r)
% '8' - coefficient of determination (d)
% '9' - coefficient of efficiency (e)
% '10' - maximum absolute error
% '11' - maximum absolute relative error
%
% options: a string containing other output options, currently the only
% option is verbose output.
%
% 'v' - verbose output, posts some text output for the
% chosen measures to the command line
%
% OUTPUT:
% gf: vector of goodness of fit values between model output and target for
% each of the strings in gFitMeasure
%
% EXAMPLES
%
% gf = gfit2(t,y); for all statistics in list returned as vector
%
% gf = gfit2(t,y,'3'); for root mean squared error
%
% gf = gfit2(t,y, {'3'}); for root mean squared error
%
% gf = gfit2(t,y, {'1' '3' '9'}); for mean squared error, root mean
% | squared error, and coefficient of
% \|/ efficiency
% gf = [mse rmse e]
%
% gf = gfit2(t,y,'all','v'); for all statistics in list returned as
% vector with information posted to the command
% line on each statistic
%
% gf = gfit2(t,y, {'1' '3' '9'}, 'v'); for mean squared error, root mean
% squared error, and coefficient of
% efficiency as a vector with
% information on each of these
% also posted to the command line
%
% Modified from gFit 2008/11/07 by Richard Crozier, extended to report multiple
% statistics at once (i.e. can pass in a cell array of strings describing
% desired output), added checking for NaNs, removed superfluous code, added
% max error code and now handles matrices by reshaping them into vectors.
% Also made small improvement to error reporting.
%
% 30 JUN 2009: Added verbose option
% ***********************************************************************
%% INPUT ARGUMENTS CHECK
error(nargchk(2,4,nargin));
% reshape matrices into vectors (order of data is not important)
t = reshape(t,1,[]);
y = reshape(y,1,[]);
if length(t) ~= length(y)
error('Invalid data size: size of t and y must be same')
end
if nargin > 2
% check if gFitMeasure is cell string array or just a string
if ~iscell(gFitMeasure) && ischar(gFitMeasure)
if strcmp(gFitMeasure,'all')
% if the string 'all' is passed in, all the stats are
% required so make the appropriate cell string array
gFitMeasure = {'1' '2' '3' '4' '5' '6' '7' '8' '9' '10' '11'}; % return all measures
else
% otherwise convert string to cell string array of size 1
gFitMeasure = {gFitMeasure};
end
else
% if it is a cell array of strings, check its size
if size(gFitMeasure,2) == 1
% if there is only one element check it is not a request
% for all measures
if strcmp(char(gFitMeasure),'all')
% if the string 'all' is passed in, all the stats are
% required so make the appropriate cell string array
gFitMeasure = {'1' '2' '3' '4' '5' '6' '7' '8' '9' '10' '11'}; % return all measures
end
end
end
else
% return all measures if only two inputs, nothing will be posted to
% the command line
gFitMeasure = {'1' '2' '3' '4' '5' '6' '7' '8' '9' '10' '11'};
end
% remove NaNs from the arrays, avoid modifying them if there are no
% NaNs to prevent reallocation of memory
if sum(isnan(t) | isnan(y))
inds = ~isnan(t) | ~isnan(y);
t = t(inds);
y = y(inds);
end
e = t - y; % Calculate the error
gf = ones(1,size(gFitMeasure,2)); % preallocate array
for i = 1:size(gFitMeasure,2)
switch char(gFitMeasure(i))
case '1' % mean squared error
gf(i) = mean(e.^2); % 0 - perfect match between output and target
if nargin == 4
if options == 'v'
disp(sprintf(['mean squared error (mse): ' num2str(gf(i))]))
end
end
case '2' % normalised mean squared error
gf(i) = mean(e.^2)/var(t); % 0 - perfect match
if nargin == 4
if options == 'v'
disp(['normalised mean squared error (nmse): ' num2str(gf(i))])
end
end
case '3' % root mean squared error
gf(i) = sqrt(mean(e.^2)); % 0 - perfect match
if nargin == 4
if options == 'v'
disp(['root mean squared error (rmse): ' num2str(gf(i))])
end
end
case '4' % normalised root mean squared error
gf(i) = sqrt(mean(e.^2)/var(t)); % 0 - perfect match
if nargin == 4
if options == 'v'
disp(['normalised root mean squared error (nrmse): ' num2str(gf(i))])
end
end
case '5' % mean absolute error
gf(i) = mean(abs(e)); % 0 - perfect match
if nargin == 4
if options == 'v'
disp(['mean absolute error (mae): ' num2str(gf(5))])
end
end
case '6' % mean absolute relative error
gf(i) = mean((abs(e./t))); % 0 - perfect match
if nargin == 4
if options == 'v'
disp(['mean absolute relative error (mare): ' num2str(gf(6))])
end
end
case '7' % coefficient of correlation
cf = corrcoef(t,y); % 1 - perfect match
gf(i) = cf(1,2);
if nargin == 4
if options == 'v'
disp(['coefficient of correlation (r): ' num2str(gf(7))])
end
end
case '8' % coefficient of determination (r-squared)
cf = corrcoef(t,y);
gf(i) = cf(1,2);
gf(i) = gf(i)^2; % 1 - perfect match
if nargin == 4
if options == 'v'
disp(['coefficient of determination (r-squared): ' num2str(gf(8))])
end
end
case '9' % coefficient of efficiency
gf(i) = 1 - sum(e.^2)/sum((t - mean(t)).^2); % 1 - perfect match
if nargin == 4
if options == 'v'
disp(['coefficient of efficiency (e): ' num2str(gf(9))])
end
end
case '10'
gf(i) = max(abs(e)); % maximum absolute error
if nargin == 4
if options == 'v'
disp(['maximum absolute error: ' num2str(gf(10))])
end
end
case '11'
gf(i) = max(abs(e./t)); % maximum absolute relative error
if nargin == 4
if options == 'v'
disp(['maximum absolute relative error: ' num2str(gf(11))])
end
end
otherwise
error('Invalid goodness of fit measure in gFitMeasure(%d):\nIt must be one of the strings {1 2 3 4 5 6 7 8 9 10 11}, but actually contained ''%s''',i,char(gFitMeasure(i)))
end
end
end
%**************************************************************************
