nnz_internal.m

optimization toolbox

function F = nnz_internal(z,x,direction)

switch direction
    case 0
        [nx,mx] = size(x);
        if issymmetric(x)
            d = binvar(nx,nx);  % d == 1 means x(i,j) can be non-zero
        else
            d = binvar(nx,mx,'full');
        end
        x = reshape(x,nx*mx,1);
        d = reshape(d,nx*mx,1);
        [M,m] = derivebounds(x);
        F = set(m.*d <= x <= M.*d) + set(z == sum(sum(d)));
        F = F + set(0 <=z <= nx*mx);
     
    case 1
        [nx,mx] = size(x);
        if issymmetric(x)
            du = binvar(nx,nx);  % du == 1 means x(i,j) > 0
            dd = binvar(nx,nx);  % dd == 1 means x(i,j) < 0
        else
            du = binvar(nx,mx,'full');
            dd = binvar(nx,mx,'full');
        end
        x = reshape(x,nx*mx,1);
        du = reshape(du,nx*mx,1);
        dd = reshape(dd,nx*mx,1);
        [M,m] = derivebounds(x);
        F = set(m.*(du+dd) <= x <= M.*(du+dd)) + set(sum([du dd],2) <= 1);
        F = F + set(z == ((sum(du) + sum(dd))));
        F = F + set(x > 1+(-1+m).*(1-du));
        F = F + set(x < -1+(1+M).*(1-dd));
        F = F + set(0 <= z <=nx*mx);
    otherwise
end