# 互相关运算
import torch
from torch import nn
from d2l import torch as d2l

def corr2d(X, K):   # X 为输入，K为核矩阵
    """计算二维互相关信息"""
    h, w = K.shape  # 核矩阵的行数和列数
    Y = torch.zeros((X.shape[0] - h + 1, X.shape[1] - w + 1)) # X.shape[0]为输入高    
    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() # 图片的小方块区域与卷积核做点积
    return Y

# 验证上述二维互相关运算的输出
X = torch.tensor([[0.0,1.0,2.0],[3.0,4.0,5.0],[6.0,7.0,8.0]])
K = torch.tensor([[0.0,1.0],[2.0,3.0]])
corr2d(X,K)

# 实现二维卷积层
class Conv2D(nn.Module):
    def __init__(self, kernel_size):
        self.weight = nn.Parameter(torch.rand(kernel_size))
        self.bias = nn.Parameter(torch.zeros(1))
        
    def forward(Self, x):
        return corr2d(x, self.weight) + self.bias
    
# 卷积层的一个简单应用：检测图片中不同颜色的边缘
X = torch.ones((6,8))
X[:,2:6] = 0  # 把中间四列设置为0
print(X)  # 0 与 1 之间进行过渡，表示边缘

K = torch.tensor([[1.0,-1.0]])  # 如果左右原值相等，那么这两原值乘1和-1相加为0，则不是边缘
Y = corr2d(X, K)
print(Y)
print(corr2d(X.t(), K)) # X.t() 为X的转置，而K卷积核只能检测垂直边缘

# 学习由X生成Y的卷积核
conv2d = nn.Conv2d(1, 1, kernel_size=(1,2), bias=False) # 单个矩阵，输入通道为1，黑白图片通道为1，彩色图片通道为3。这里输入通道为1，输出通道为1.   
X = X.reshape((1,1,6,8)) # 通道维：通道数，RGB图3通道，灰度图1通道，批量维就是样本维，就是样本数
Y = Y.reshape((1,1,6,7))
for i in range(10):
    Y_hat = conv2d(X)
    l = (Y_hat - Y) ** 2
    conv2d.zero_grad()
    l.sum().backward()
    conv2d.weight.data[:] -= 3e-2 * conv2d.weight.grad # 3e-2是学习率
    if(i+1) % 2 == 0:
        print(f'batch {i+1},loss {l.sum():.3f}')

# 所学的卷积核的权重张量
print(conv2d.weight.data.reshape((1,2)))