// make the jacobian matrix.  J(i,j) is the distnace the i-th ray
// travels in the j-th cell.

function jacobian = makejacobian(nrows,ncols,deltaz,rec)
  
jacobian = zeros(nrows,ncols);
for i = 1:nrows
  ndepth = floor(rec(i)/deltaz);    // ndepth is layer you're in
  eps = rec(i) - ndepth * deltaz;
  for j = 1:ncols
    if(j <= ndepth) 
      jacobian(i,j) = deltaz;
    elseif(j > ndepth)
      jacobian(i,j) = eps;
      break
    end
  end
end