MULTI_INDEX_2_ORERING

Contents

function [I] = multi_index_2_ordering(m,ordering,lex2conj)
        

Compute index of a multi-index in an ordered set

Given a multi- index array containing multi-indices in its columns this function computes the position of the multi-indices in a ordered set of all multi-index vectors that have the same order as each of the multi-indices. The ordering can be 'lex' for lexicographical or 'antilex' for anti-lexicographical or 'conj' for conjugate ordering, where conjugate pairs of multi-indices are only taken into account once.

if isempty(m)
    I = [];
elseif size(m,1) == 1 % 1D SSM
    sz   = size(m,2);
    I    = ones(1,sz);
else
    l    = size(m,1);
    sz   = size(m,2);
    mabs = sum(m,1);
    I    = ones(1,sz);
    for ij  = 1:sz
        bij = 0;
        if m(1,ij) ~= 0
            for i = 0:m(1,ij)-1
                bij = bij+ nchoosek(mabs(ij)-i+l-1-1,l-1-1);
            end
        end

        for j = 2:(l-1)
            if m(j,ij) ~= 0
                for i  = 0:(m(j,ij)-1)
                    bij = bij+ nchoosek(mabs(ij)-sum(m(1:j-1,ij)) ...
                        -i+l-j-1,l-j-1);
                end
            end
        end
        I(ij) = bij+1;
    end

    %if order is reverse-lexicographical, then the position is
    % the mirrored value about the centre of the array.
    switch ordering
        case 'lex'
            %Ordering is corrects

        case 'revlex'
            if all(mabs == mabs(1))
                I = nchoosek(mabs(1)+l-1,l-1)+1-I;
            else
                for i = 1:sz
                    I(i) = nchoosek(mabs(i)+l-1,l-1)+1-I(i);
                end
            end

    % if order is conjugate, convert to that
        case 'conjugate'
            if all(mabs == mabs(1))
                I = nchoosek(mabs(1)+l-1,l-1)+1-I;
            else
                for i = 1:sz
                    I(i) = nchoosek(mabs(i)+l-1,l-1)+1-I(i);

                end
            end

            for i = 1:sz
                idx = lex2conj{mabs(i)};
                I(i)= find(idx==I(i));
            end
    end
end
        

end
        

Published with MATLAB® R2023a