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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def _calc_grad_tiled(self, img, t_grad, tile_size=512):
        '''Compute the value of tensor t_grad over the image in a tiled way.
        Random shifts are applied to the image to blur tile boundaries over 
        multiple iterations.'''
        sz = tile_size
        h, w = img.shape[:2]
        sx, sy = np.random.randint(sz, size=2)
        img_shift = np.roll(np.roll(img, sx, 1), sy, 0)
        grad = np.zeros_like(img)
        for y in range(0, max(h-sz//2, sz),sz):
            for x in range(0, max(w-sz//2, sz),sz):
                sub = img_shift[y:y+sz,x:x+sz]
                g = self._session.run(t_grad, {self._t_input:sub})
                grad[y:y+sz,x:x+sz] = g
        return np.roll(np.roll(grad, -sx, 1), -sy, 0)