Winograd F(2,3)

This tutorial shows how to compute wino_f23:

1. define transform matrix

   G_F23 = np.array([
        [ 1.0,  0.0, 0.0 ],
        [ 0.5,  0.5, 0.5 ],
        [ 0.5, -0.5, 0.5 ],
        [ 0.0,  0.0, 1.0 ]])
    Bt_F23 = np.array([
        [ 1.0,  0.0, -1.0,  0.0 ],
        [ 0.0,  1.0,  1.0,  0.0 ],
        [ 0.0, -1.0,  1.0,  0.0 ],
        [ 0.0,  1.0,  0.0, -1.0 ]])
    At_F23 = np.array([
        [ 1.0, 1.0,  1.0,  0.0 ],
        [ 0.0, 1.0, -1.0, -1.0 ]])

2. compute transformation for input, kernel, output

    def trans_kernel(g):
        return np.dot(np.dot(G_F23,g),G_F23.T)
    def trans_input(d):
        return np.dot(np.dot(Bt_F23,d),Bt_F23.T)
    def trans_output(r):
        return np.dot(np.dot(At_F23,r),At_F23.T)

3. do conv_winof23, conv_direct

    def wino_f23(kernel,input):
        tran_inp = trans_input(input)
        tran_ker = trans_kernel(kernel)
        mid = tran_inp * tran_ker
        out = trans_output(mid)
        return out
   
    def conv_direct(kernel,input):
        out=np.zeros((2,2))
        for h in range(2):
            for w in range(2):
                out[h,w]=np.sum(input[h:h+3,w:w+3]*kernel)
        return out

4. given one test data, test the results

   def test():
       input=np.array([
           [0,1,2,3],
           [4,5,6,7],
           [8,9,10,11],
           [12,13,14,15]
       ])
       kernel=np.array([
       [1,2,1],
       [2,1,0],
       [1,1,2]
       ])
       out_wino = wino_f23(kernel,input)
       print("out_wino:\n",out_wino)
       out_direct= conv_direct(kernel,input)
       print("out_direct:\n",out_direct)
       print("max error: ",np.max(np.abs(out_wino-out_direct)))

run

python3 wino_f23.py

you will get

out_wino:
 [[  54.   65.]
 [  98.  109.]]
out_direct:
 [[  54.   65.]
 [  98.  109.]]
max error:  0.0