用python写一个rnn代码，要求体现每一步公式，输入为正弦函数的值，预测后续的数据且每一步完成后都输出结果图

好的，我可以帮你写一个简单的RNN代码，但是在代码中不会涉及到绘图的部分。需要使用Matplotlib等库来完成绘图。

首先，我们需要导入相关的库：

import numpy as np
import matplotlib.pyplot as plt

接下来，我们定义一些参数：

# 定义RNN的参数
input_size = 1
hidden_size = 32
output_size = 1

# 定义训练的参数
learning_rate = 0.01
sequence_length = 20
num_epochs = 200

# 定义正弦函数的参数
start = 0
stop = 100
step = 0.1

然后，我们生成正弦函数的数据：

# 生成正弦函数的数据
data = np.sin(np.arange(start, stop, step))

接下来，我们定义RNN的模型：

# 定义RNN的模型
class RNN:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size

        # 初始化参数
        self.Wxh = np.random.randn(hidden_size, input_size) * 0.01
        self.Whh = np.random.randn(hidden_size, hidden_size) * 0.01
        self.Why = np.random.randn(output_size, hidden_size) * 0.01
        self.bh = np.zeros((hidden_size, 1))
        self.by = np.zeros((output_size, 1))

    def forward(self, inputs, h_prev):
        # 前向传播
        self.inputs = inputs
        self.h_prev = h_prev

        self.h = np.tanh(np.dot(self.Wxh, inputs) + np.dot(self.Whh, h_prev) + self.bh)
        self.y = np.dot(self.Why, self.h) + self.by

        return self.y, self.h

    def backward(self, dy, dh_next):
        # 反向传播
        self.dy = dy
        self.dh_next = dh_next

        dWhy = np.dot(dy, self.h.T)
        dby = dy
        dh = np.dot(self.Why.T, dy) + dh_next
        dh_raw = (1 - self.h * self.h) * dh
        dbh = dh_raw
        dWxh = np.dot(dh_raw, self.inputs.T)
        dWhh = np.dot(dh_raw, self.h_prev.T)

        return dWxh, dWhh, dWhy, dbh, dby

    def update(self, dWxh, dWhh, dWhy, dbh, dby):
        # 更新参数
        self.Wxh -= learning_rate * dWxh
        self.Whh -= learning_rate * dWhh
        self.Why -= learning_rate * dWhy
        self.bh -= learning_rate * dbh
        self.by -= learning_rate * dby

    def train(self, inputs, targets, h_prev):
        # 训练模型
        xs, hs, ys, ps = {}, {}, {}, {}
        hs[-1] = np.copy(h_prev)
        loss = 0

        # 前向传播
        for t in range(len(inputs)):
            xs[t] = np.zeros((input_size, 1))
            xs[t][0][0] = inputs[t]
            ys[t], hs[t] = self.forward(xs[t], hs[t - 1])
            loss += (ys[t][0][0] - targets[t]) ** 2

        # 反向传播
        dys, dhs_next = {}, {}
        dWxh, dWhh, dWhy = np.zeros_like(self.Wxh), np.zeros_like(self.Whh), np.zeros_like(self.Why)
        dbh, dby = np.zeros_like(self.bh), np.zeros_like(self.by)
        for t in reversed(range(len(inputs))):
            dys[t] = np.copy(ys[t])
            dys[t][0][0] -= targets[t]
            dWxh_t, dWhh_t, dWhy_t, dbh_t, dby_t = self.backward(dys[t], dhs_next.get(t, np.zeros_like(self.h)))
            dWxh += dWxh_t
            dWhh += dWhh_t
            dWhy += dWhy_t
            dbh += dbh_t
            dby += dby_t
            dhs_next[t - 1] = np.dot(self.Whh.T, (1 - hs[t] * hs[t]) * (np.dot(self.Wxh, xs[t]) + np.dot(self.Whh, hs[t - 1]) + self.bh))

        # 更新参数
        self.update(dWxh, dWhh, dWhy, dbh, dby)

        # 返回损失和最终的隐藏状态
        return loss, hs[len(inputs) - 1]

接下来，我们进行训练并预测：

# 训练模型
rnn = RNN(input_size, hidden_size, output_size)
losses = []
h_prev = np.zeros((hidden_size, 1))
for epoch in range(num_epochs):
    loss = 0
    for i in range(len(data) - sequence_length):
        inputs = data[i:i + sequence_length]
        targets = data[i + 1:i + sequence_length + 1]

        loss_t, h_prev = rnn.train(inputs, targets, h_prev)
        loss += loss_t

    losses.append(loss)

    if epoch % 10 == 0:
        print('Epoch %d Loss: %f' % (epoch, loss))

# 预测模型
predictions = []
h_prev = np.zeros((hidden_size, 1))
for i in range(len(data) - sequence_length):
    inputs = data[i:i + sequence_length]
    targets = data[i + 1:i + sequence_length + 1]

    prediction, h_prev = rnn.forward(inputs, h_prev)
    predictions.append(prediction[0][0])

# 绘制预测结果
plt.plot(data[sequence_length:], label='True Data')
plt.plot(predictions, label='Predictions')
plt.legend()
plt.show()

这里我们使用了一个简单的RNN模型来预测正弦函数的后续数据，并且在训练过程中输出损失值，并在预测结束后绘制了真实数据和预测数据的图像。