def conv_forward_im2col(x, w, b, conv_param):
    '\n  A fast implementation of the forward pass for a convolutional layer\n  based on im2col and col2im.\n  '
    (N, C, H, W) = x.shape
    (num_filters, _, filter_height, filter_width) = w.shape
    (stride, pad) = (conv_param['stride'], conv_param['pad'])
    assert ((((W + (2 * pad)) - filter_width) % stride) == 0), 'width does not work'
    assert ((((H + (2 * pad)) - filter_height) % stride) == 0), 'height does not work'
    out_height = ((((H + (2 * pad)) - filter_height) / stride) + 1)
    out_width = ((((W + (2 * pad)) - filter_width) / stride) + 1)
    out = np.zeros((N, num_filters, out_height, out_width), dtype=x.dtype)
    x_cols = im2col_cython(x, w.shape[2], w.shape[3], pad, stride)
    res = (w.reshape((w.shape[0], (- 1))).dot(x_cols) + b.reshape((- 1), 1))
    out = res.reshape(w.shape[0], out.shape[2], out.shape[3], x.shape[0])
    out = out.transpose(3, 0, 1, 2)
    cache = (x, w, b, conv_param, x_cols)
    return (out, cache)
A fast implementation of the forward pass for a convolutional layer
based on im2col and col2im.
def conv_forward_im2col(x, w, b, conv_param):
    '\n  A fast implementation of the forward pass for a convolutional layer\n  based on im2col and col2im.\n  '
    (N, C, H, W) = x.shape
    (num_filters, _, filter_height, filter_width) = w.shape
    (stride, pad) = (conv_param['stride'], conv_param['pad'])
    assert ((((W + (2 * pad)) - filter_width) % stride) == 0), 'width does not work'
    assert ((((H + (2 * pad)) - filter_height) % stride) == 0), 'height does not work'
    out_height = ((((H + (2 * pad)) - filter_height) / stride) + 1)
    out_width = ((((W + (2 * pad)) - filter_width) / stride) + 1)
    out = np.zeros((N, num_filters, out_height, out_width), dtype=x.dtype)
    x_cols = im2col_cython(x, w.shape[2], w.shape[3], pad, stride)
    res = (w.reshape((w.shape[0], (- 1))).dot(x_cols) + b.reshape((- 1), 1))
    out = res.reshape(w.shape[0], out.shape[2], out.shape[3], x.shape[0])
    out = out.transpose(3, 0, 1, 2)
    cache = (x, w, b, conv_param, x_cols)
    return (out, cache)