二维卷积层

from mxnet import gluon,init
from mxnet.gluon import nn,loss as gloss
from mxnet.gluon import data as gdata
from mxnet import autograd,nd

# 二维互相关运算
def corr2d(X, K):
    h, w = K.shape
    Y = nd.zeros((X.shape[0] - h + 1, X.shape[1] - w + 1))
    for i in range(Y.shape[0]):
        for j in range(Y.shape[1]):
            Y[i, j] = (X[i: i + h, j: j + w] * K).sum()
    return Y

X = nd.array([[0,1,2],[3,4,5],[6,7,8]])
K = nd.array([[0,1],[2,3]])
print(corr2d(X,K))

# 二维卷积层
class Conv2D(nn.Block):
    def __init__(self,kernel_size,**kwargs):
        super(Conv2D,self).__init__(**kwargs)
        self.weight = self.params.get('weight',shape=kernel_size)
        self.bias = self.params.get('bias', shape=(1,))

    def forward(self, x):
        return corr2d(x,self.weight.data()) + self.bias.data()

# 图像物体边缘检测
X = nd.ones((6,8))
X[:,2:6] = 0
print(X)

K = nd.array([[1,-1]])
Y = corr2d(X,K)
print(Y)


# 通过数据学习核数组
conv2d = nn.Conv2D(1,kernel_size=(1,2))
conv2d.initialize()

# 二维卷积层使用4维输入输出，格式为(样本，通道，高，宽)
# 这里样本数，通道数为 1
X = X.reshape((1,1,6,8))
Y = Y.reshape((1,1,6,7))
print(X)
print(Y)

for i in range(20):
    with autograd.record():
        Y_hat = conv2d(X)
        l = (Y_hat - Y)**2
    l.backward()
    # 调整参数
    conv2d.weight.data()[:] -= 3e-2*conv2d.weight.grad()
    print('batch %d,loss %.3f'%(i+1,l.sum().asscalar()))
print(conv2d.weight.data().reshape((1,2)))

# 互相关运算和卷积运算
# 只需将核数组左右翻转，上下翻转，再与输入数组做互相关运算
# 深度学习核数组都是学出来的，卷积层使用互相关还是卷积不影响模型预测时的输出