56 lines
No EOL
1.9 KiB
Matlab
56 lines
No EOL
1.9 KiB
Matlab
function [A_aug,h,c_aug] = standardize(type,A,h,c,m,sign)
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% Input arguments:
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% type = 'max' for maximization, 'min' for minimization
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% A = matrix holding the constraints coefficients
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% h = coefficients of the constraints inequalities (rhs vector)
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% c = coefficients of the objective function
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% m = size(A, 1)
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% sign = vector holding information about the constraints if the system
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% needs to be standardized (-1: less or equal, 0: equal, 1: greater or equal)
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% return arguments are:
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% (1) A_aug = augmented matrix A, containing also the surplus and slack variables
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% (2) c_aug = augmented coefficients vector c (check compatibility of dimensions with A)
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% (3) h, right hand side vector (remember to flip the signs when changing the inequalities)
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aug_matrix = eye(m); % matrix corresponding to the slack/surplus variables
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if strcmp(type, 'max')
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for i = 1:m
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if sign(i) == 1
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% Using a surplus instead of a slack variable
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aug_matrix(i,:) = -aug_matrix(i,:);
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end
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end
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elseif strcmp(type, 'min')
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for i = 1:m
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if sign(i) == -1
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% Using a slack instead of a surplus variable
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aug_matrix(i,:) = -aug_matrix(i,:);
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end
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end
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else
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error('Incorrect type specified. Choose either a maximisation (max) or minimisation (min) problem.')
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end
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% Correction on the sign of h for auxiliary problem (we want to
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% ensure that h>=0, but we need to flip all the signs)
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for i = 1:m
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if h(i) < 0
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A(i,:) = -A(i,:);
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h(i,:) = -h(i,:);
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aug_matrix(i,:) = -aug_matrix(i,:);
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end
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end
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c_aug = [c, zeros(1,m)];
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if strcmp(type,'max')
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A_aug = [A aug_matrix];
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% Extend matrix A by adding the slack variables
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elseif strcmp(type,'min')
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A_aug = [A -aug_matrix];
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% Extend matrix A by adding the surplus variables
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else
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error('Incorrect type specified. Choose either a maximisation (max) or minimisation (min) problem.')
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end
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end |