function [BCoeff] = TransformBack(B, W, P, Q, LatVar);

[MQ, NvarQ] = size(Q);
[MW, NvarW] = size(W);
W = W(:,1:LatVar);
Q = Q(:,1:LatVar);
P = P(:,1:LatVar);
B = B(:,1:LatVar);

BCoeff = zeros(MQ * LatVar, MW);
if MQ == 1
  BCoeff = (W * inv(P'*W) * diag(B))';                                 % ready
else
  Z = (W * inv(P'*W) * diag(B))';
  for lv = 1:LatVar
    ZZ = Z(lv,:);
    BCoeff((lv-1)*MQ+1:lv*MQ,:) = diag(Q(:,lv)) * ZZ(ones(MQ,1),:);    % write out all coefficients
  end
end