Check if sum over dimension is 0

I have a matrix A_vk (VxK), and a matrix A_kn (KxN). How to check if A_.k. is 0 or not in which A_.k. = sum (1 to V) sum(1 to N) A_vkn, and A_vk & A_kn are generated form multinational distribution

(A_v1j,A_v2j,...,A_vKj)= mult_rand(X,Phi,Theta)

I generated A_vk and A_kn from here

[A_vk,A_kn]= mult_rand(X,Phi,Theta); Here is mult_rand(X,Phi,Theta)

function [x_pk,x_kn] = mult_rand(X,Phi,Theta)

P = size(X,1); [K,N] = size(Theta);
x_pk = zeros(P,K); x_kn = zeros(K,N);

for n=1:N
inz = find(X(:,n))';
map = bsxfun(@times,Phi(inz,:),Theta(:,n)'); % P x K
map = cumsum(map,2);
x_kp = zeros(K,numel(inz));
for m=1:numel(inz)
    x_kp(:,m) = x_kp(:,m) + mrand(X(inz(m),n),map(m,:));
end

x_kn(:,n) = sum(x_kp,2);
x_pk(inz,:) = x_pk(inz,:)+x_kp';
end

end

mrand function

    function x = mrand(n,cp)

    % cp = cumsum( p );

    x = sum(bsxfun(@gt,rand(n,1)*cp(end),cp),2)+1; 
  x = sparse(x,1,1,numel(cp),1);

    end

Hopefully it is easy to understand

matlab matrix