simple_fprop_direct.py

import numpy as np

def ceil_div(x, y):
    return -(-x // y)

def out_dim(S, X, padding, strides):
    return ceil_div(X - S + 1 + 2*padding, strides)

def fconv_slice(q, S, X, padding, strides):

    qs = q * strides - padding
    x1 = None
    for s in range(S):
        x = qs + s
        if x1 is None and x >= 0:
            x1 = x
            f1 = s
        if x < X:
            x2 = x
            f2 = s

    return slice(f1, f2+1), slice(x1, x2+1)

def fprop_direct(I, F, O, padding, strides):

    C, H, W, N = I.shape
    C, R, S, K = F.shape
    K, P, Q, N = O.shape

    qSlice = [ fconv_slice(q, S, W, padding[0], strides[0]) for q in range(Q) ]

    for p in range(P):
        sliceR, sliceY = fconv_slice(p, R, H, padding[1], strides[1])

        for q in range(Q):
            sliceS, sliceX = qSlice[q]

            slicedF = F[:,sliceR,sliceS,:].reshape((-1, K))
            slicedI = I[:,sliceY,sliceX,:].reshape((-1, N))

            O[:,p,q,:] = np.dot( slicedF.T,  slicedI )

N    = 1
C, K = 1, 1
H, W = 4, 4
R, S = 3, 3
strides = 1, 1
padding = 1, 1

P = out_dim(R, H, padding[0], strides[0])
Q = out_dim(S, W, padding[1], strides[1])

dimI = (C,H,W,N)
dimF = (C,R,S,K)
dimO = (K,P,Q,N)

I  = np.ones(dimI)
F  = np.ones(dimF)
O  = np.ones(dimO)

fprop_direct(I, F, O, padding, strides)

print O[0,:,:,0]