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function [x, e] = LeastSquareSolution(fileNameA, fileNameB, output)
inputData = load(fileNameA);
A = inputData;
inputData = load(fileNameB);
b = inputData;
% singular value decomposition
CI = [];
%testing one sample at a time, using all remaining samples as training data
total_folds = 10;
fold_size = length(b)/total_folds;
total_folds = floor(total_folds)
remainder_of_total_folds = length(b) - total_folds*fold_size
elements_per_fold = fold_size;
solution=[];
for i=0:(total_folds-1)
% debug
file_id_number = num2str((i+1),'%2d');
debug_file = strcat(output, '/');
debug_file = strcat(debug_file, 'Fold_');
debug_file = strcat(debug_file, file_id_number);
debug_file = strcat(debug_file, '.txt');
if (i == (total_folds-1))
elements_per_fold = fold_size + remainder_of_total_folds
end
%select one sample at a time for testing using the rest for training
%if the value is set to 1, that is the sample that will be used for
%training/testing
train = ones(length(b),1); %create a column vector of ones
for k=(i*fold_size+1):((i*fold_size) + elements_per_fold)
train(k) = 0; %set the i-th sample to be the test sample, all others are used for training
end
train = ismember(train, 1); %converts to logical the train set
test = ismember(train, 0); %converts to logical the test set
A_ = A(train,:); % A_ will contain all the data except the test data. This is the train data.
b_ = b(train); % b_ will contain all status except the test status
[m n] = size(A_);
% do the SVD on the test A data
[U,S,V] = svd(A_);
% this value should be equal to A_
U*S*V';
% compute the c from the training b data
c = U'*b_;
% compute y on from the singular values
y=[];
for j=1:n
yj = c(j)/S(j,j);
y = [y; yj];
end
% compute the unknown x values we are trying to find the least
% square approximation of
x = V*y;
% the error estimate on the training data
e = A_*x - b_;
% add the solution to the solution vector
solution = [solution; x']
% compute the ci value of the test data
test_data = A(test,:); % this extract just a row vector
size(test_data)
ci = test_data*x; % compute the ci value for this test sample
%saving the calculated cis
CI = [CI; ci]; % store the ci values
%fid_debug = fopen(debug_file,'w');
%fprintf(fid_debug, '%s\n','Train data');
%fprintf(fid_debug, '%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f', A_);
% fprintf(fid_debug, '%s\n','Test data');
% fprintf(fid_debug, '%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f\t%8.6f', test_data);
fid_debug = fopen(debug_file,'w');
% fprintf(fid_debug, '%s\n\n','Test data');
fprintf(fid_debug, '%s\n\n','new CI');
fprintf(fid_debug, '%8.6f\n', ci);
fprintf(fid_debug, '%s\n\n','actual CI');
actual_ci = b(test,:);
fprintf(fid_debug, '%8.6f\n', actual_ci);
fprintf(fid_debug, '%s\n\n','error');
fprintf(fid_debug, '%8.6f\n', (ci-actual_ci));
% fprintf(fid_debug, '%s\n\n','Train data');
fclose(fid_debug);
dlmwrite(debug_file, A_, 'delimiter', '\t', '-append');
dlmwrite(debug_file, test_data, 'delimiter', '\t', '-append');
end
% write out the ci values
fid_ci = fopen('newCIs.txt','w');
fprintf(fid_ci, '%8.6f\n', CI);
fclose(fid_ci);
%fid_solution_vectors = fopen('Solution_vectors.txt', 'w');
dlmwrite('Solution_vectors.txt', solution, 'delimiter', '\t');
%fclose(fid_solution_vectors);
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