Add a time sequence prediction example (pytorch#118)

Author: fuzihaofzh

time_sequence_prediction/README.md

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+# Time Sequence Prediction
+This is a toy example for beginners to start with. It is helpful for learning both pytorch and time sequence prediction. Two LSTMCell units are used in this example to learn some sine wave signals starting at different phases. After learning the sine waves, the network tries to predict the signal values in the future. The results is shown in the picture below.
+
+## Usage
+
+```
+python generate_sine_wave.py
+python train.py
+```
+
+## Result
+The initial signal and the predicted results are shown in the image. We first give some initial signals (full line). The network will  subsequently give some predicted results (dash line). It can be concluded that the network can generate new sine waves.
+![image](https://cloud.githubusercontent.com/assets/1419566/24184438/e24f5280-0f08-11e7-8f8b-4d972b527a81.png)

time_sequence_prediction/generate_sine_wave.py

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+import math
+import numpy as np
+import torch
+T = 20
+L = 1000
+N = 100
+np.random.seed(2)
+x = np.empty((N, L), 'int64')
+x[:] = np.array(range(L)) + np.random.randint(-4*T, 4*T, N).reshape(N, 1)
+data = np.sin(x / 1.0 / T).astype('float64')
+torch.save(data, open('traindata.pt', 'wb'))
+

time_sequence_prediction/train.py

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+from __future__ import print_function
+import torch
+import torch.nn as nn 
+from torch.autograd import Variable
+import torch.optim as optim
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+
+class Sequence(nn.Module):
+    def __init__(self):
+        super(Sequence, self).__init__()
+        self.lstm1 = nn.LSTMCell(1, 51)
+        self.lstm2 = nn.LSTMCell(51, 1)
+
+    def forward(self, input, future = 0):
+        outputs = []
+        h_t = Variable(torch.zeros(input.size(0), 51).double(), requires_grad=False)
+        c_t = Variable(torch.zeros(input.size(0), 51).double(), requires_grad=False)
+        h_t2 = Variable(torch.zeros(input.size(0), 1).double(), requires_grad=False)
+        c_t2 = Variable(torch.zeros(input.size(0), 1).double(), requires_grad=False)
+
+        for i, input_t in enumerate(input.chunk(input.size(1), dim=1)):
+            h_t, c_t = self.lstm1(input_t, (h_t, c_t))
+            h_t2, c_t2 = self.lstm2(c_t, (h_t2, c_t2))
+            outputs += [c_t2]
+        for i in range(future):# if we should predict the future
+            h_t, c_t = self.lstm1(c_t2, (h_t, c_t))
+            h_t2, c_t2 = self.lstm2(c_t, (h_t2, c_t2))
+            outputs += [c_t2]
+        outputs = torch.stack(outputs, 1).squeeze(2)
+        return outputs
+
+
+
+if __name__ == '__main__':
+    # set ramdom seed to 0
+    np.random.seed(0)
+    torch.manual_seed(0)
+    # load data and make training set
+    data = torch.load(open('traindata.pt'))
+    input = Variable(torch.from_numpy(data[3:, :-1]), requires_grad=False)
+    target = Variable(torch.from_numpy(data[3:, 1:]), requires_grad=False)
+    # build the model
+    seq = Sequence()
+    seq.double()
+    criterion = nn.MSELoss()
+    # use LBFGS as optimizer since we can load the whole data to train
+    optimizer = optim.LBFGS(seq.parameters())
+    #begin to train
+    for i in range(15):
+        print('STEP: ', i)
+        def closure():
+            optimizer.zero_grad()
+            out = seq(input)
+            loss = criterion(out, target)
+            print('loss:', loss.data.numpy()[0])
+            loss.backward()
+            return loss
+        optimizer.step(closure)
+        # begin to predict
+        future = 1000
+        pred = seq(input[:3], future = future)
+        y = pred.data.numpy()
+        # draw the result
+        plt.figure(figsize=(30,10))
+        plt.title('Predict future values for time sequences\n(Dashlines are predicted values)', fontsize=30) 
+        plt.xlabel('x', fontsize=20)
+        plt.ylabel('y', fontsize=20)
+        plt.xticks(fontsize=20)
+        plt.yticks(fontsize=20)
+        def draw(yi, color):
+            plt.plot(np.arange(input.size(1)), yi[:input.size(1)], color, linewidth = 2.0)
+            plt.plot(np.arange(input.size(1), input.size(1) + future), yi[input.size(1):], color + ':', linewidth = 2.0)
+        draw(y[0], 'r')
+        draw(y[1], 'g')
+        draw(y[2], 'b')
+        plt.savefig('predict%d.pdf'%i)
+        plt.close()
+