这是我的第一篇技术博客！

在学习吴恩达老师的深度学习课程中的卷积神经网络的建模部分，我遇到了一个问题，就是在不使用深度学习框架的情况下做CNN的前馈时，搞不清楚循环和各变量的维度之间的关系，比如下面这个过程：

最好的方法其实就是把问题化简，看其最小、最本质的步骤是什么，就是如上图所示的过程，看输出层的单个例子、单个通道的特定一点 $z[i,h,w,c]$是怎么得来的，具体实现代码如下：

def conv_forward(A_prev, W, b, hparameters):
    """
    Implements the forward propagation for a convolution function
    
    Arguments:
    A_prev -- output activations of the previous layer, 
        numpy array of shape (m, n_H_prev, n_W_prev, n_C_prev)
    W -- Weights, numpy array of shape (f, f, n_C_prev, n_C)
    b -- Biases, numpy array of shape (1, 1, 1, n_C)
    hparameters -- python dictionary containing "stride" and "pad"
        
    Returns:
    Z -- conv output, numpy array of shape (m, n_H, n_W, n_C)
    cache -- cache of values needed for the conv_backward() function
    """
    
    ### START CODE HERE ###
    # Retrieve dimensions from A_prev's shape (≈1 line)  
    (m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
    
    # Retrieve dimensions from W's shape (≈1 line)
    (f, f, n_C_prev, n_C) =W.shape
    
    # Retrieve information from "hparameters" (≈2 lines)
    stride = hparameters["stride"]
    pad = hparameters['pad']
    
    # Compute the dimensions of the CONV output volume using the formula given above. 
    # Hint: use int() to apply the 'floor' operation. (≈2 lines)
    n_H = int(np.floor((n_H_prev-f+2*pad)/stride)+1)
    n_W = int(np.floor((n_W_prev-f+2*pad)/stride)+1)
    # Initialize the output volume Z with zeros. (≈1 line)
    Z = np.zeros((m,n_H,n_W,n_C))
    
    # Create A_prev_pad by padding A_prev
    A_prev_pad = zero_pad(A_prev, pad)
    
    for i in range(m):               # loop over the batch of training examples
        a_prev_pad = A_prev_pad[i,:,:,:]               # Select ith training example's padded activation
        for h in range(n_H):           # loop over vertical axis of the output volume
            # Find the vertical start and end of the current "slice" (≈2 lines)
            vert_start = h*stride
            vert_end =vert_start+f
            
            for w in range(n_W):       # loop over horizontal axis of the output volume
                # Find the horizontal start and end of the current "slice" (≈2 lines)
                horiz_start = w*stride
                horiz_end = horiz_start+f
                
                for c in range(n_C):   # loop over channels (= #filters) of the output volume
                                        
                    # Use the corners to define the (3D) slice of a_prev_pad (See Hint above the cell). (≈1 line)
                    a_slice_prev = a_prev_pad[vert_start:vert_end,horiz_start:horiz_end,:]
                    
                    # Convolve the (3D) slice with the correct filter W and bias b, to get back one output neuron. (≈3 line)
                    weights = W[:,:,:,c]
                    biases = b[:,:,:,c]
                    Z[i, h, w, c] = conv_single_step(a_slice_prev, weights,biases)
                                        
    ### END CODE HERE ###
    
    # Making sure your output shape is correct
    assert(Z.shape == (m, n_H, n_W, n_C))
    # Save information in "cache" for the backprop
    cache = (A_prev, W, b, hparameters)
    
    return Z, cache

结束了