MULTI_SUBTRACTION

Contents

function [RES,I_minu,I_subt] = multi_subtraction(MINUEND,SUBTRAHEND,type)
        

Subtraction of multi-indices

The output is a matrix, containing all columns of $\texttt{MINUEND}$ subtracted by all columns of $\texttt{SUBTRAHEND}$ that do not lead to columns with negative entries. The matrix $\texttt{I\_g}$ contains in position $j$ the column index of $\texttt{SUBTRAHEND}$ corresponding to the column $j$ of $\texttt{RES}$ . The same holds for $\texttt{I\_minu}$ .

Example:

$\texttt{I\_subt(3) = 1}$ , $\texttt{I\_minu(3) = 5}$ implies that $\texttt{RES(:,3)} = \texttt{MINUEND(:,5)} - \texttt{SUBTRAHEND(:,1)}$ .

different functionalities for parametrisation multi indices and forcing multi indices

switch type
    case 'Parametrised'
        minu_sz = size(MINUEND,2);
        subt_sz = size(SUBTRAHEND,2);

        % Index of the subtrahends
        I_subt = reshape(repmat(1:subt_sz,minu_sz,1),1,[]);
        % Index of the minuends
        I_minu = repmat(1:minu_sz,1,subt_sz);
        RES = MINUEND(:,I_minu)-SUBTRAHEND(:,I_subt);


        [~,neg]    = find(RES<0);
        RES(:,neg)   = []; %delete columns with negative entries
        I_subt(:,neg) = [];
        I_minu(:,neg) = [];


    case 'Physical'
        %subtrahend is always identity matrix

        [I_minu,I_subt] = find(MINUEND.');
        RES =  (MINUEND(:,I_minu)-SUBTRAHEND(:,I_subt));
end

% Output indices as row vector
if size(I_minu,1)>1
    I_minu = I_minu.';
end

if size(I_subt,1)>1
    I_subt = I_subt.';
end
        

end
        

Published with MATLAB® R2023a