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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements; and to You under the Apache License, Version 2.0. 
Train a multi-layer perceptron (MLP) model
In this notebook, we are going to use PySINGA to train a MLP model for classifying 2-d points into two categories (i.e., positive and negative). We use this example to illustrate the usage of PySINGA's modules. Please refer to the documentation page for the functions of each module.
Step1:  To import PySINGA modules
Step2:  Task is to train a MLP model to classify 2-d points into the positive and negative categories.
Training data generation
The following steps would be conducted to generate the training data.
1. draw a boundary line in the 2-d space 
2. generate data points in the 2-dspace
3. label the data points above the boundary line as positive points, and label other points as negative points.
We draw the boundary line as $y=5x+1$
Step3:  We generate the datapoints by adding a random noise to the data points on the boundary line
Step4:  We label the data points above the boundary line as positive points with label 1 and other data points with label 0 (negative).
Step5:  Create the MLP model
We will create a MLP by with one dense layer (i.e. fully connected layer).
We use the Softmax function to get compute the probability of each category for every data point.
We use the cross-entropy as the loss function.
We initialize the weight matrix following guassian distribution (mean=0, std=0.1), and set the bias to 0.
We creat a SGD updater to update the model parameters.
2 and 3 are combined by the SoftmaxCrossEntropy.
Step6:  Each layer is created with a layer name and other meta data, e.g., the dimension size for the dense layer. The last argument is the shape of a single input sample of this layer.
param_values() returns a list of tensors as the parameter objects of this layer
SGD optimzier is typically created with the weight decay, and momentum specified. The learning rate could be specified at creation or passed in when the optimizer is applied.
Train the model
We run 1000 iterations to train the MLP model. 
1. For each iteration, we compute the gradient of the models parameters and use them to update the model parameters.
2. Periodically, we plot the prediction from the model.
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Python Code:
from __future__ import print_function
from builtins import range
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
Explanation: Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements; and to You under the Apache License, Version 2.0. 
Train a multi-layer perceptron (MLP) model
In this notebook, we are going to use PySINGA to train a MLP model for classifying 2-d points into two categories (i.e., positive and negative). We use this example to illustrate the usage of PySINGA's modules. Please refer to the documentation page for the functions of each module.
End of explanation
from singa import tensor
from singa import optimizer
from singa import loss
from singa import layer
#from singa.proto import model_pb2
Explanation: To import PySINGA modules
End of explanation
# generate the boundary
f = lambda x: (5 * x + 1)
bd_x = np.linspace(-1., 1, 200)
bd_y = f(bd_x)
Explanation: Task is to train a MLP model to classify 2-d points into the positive and negative categories.
Training data generation
The following steps would be conducted to generate the training data.
1. draw a boundary line in the 2-d space 
2. generate data points in the 2-dspace
3. label the data points above the boundary line as positive points, and label other points as negative points.
We draw the boundary line as $y=5x+1$
End of explanation
# generate the training data
x = np.random.uniform(-1, 1, 400)
y = f(x) + 2 * np.random.randn(len(x))
Explanation: We generate the datapoints by adding a random noise to the data points on the boundary line
End of explanation
# convert training data to 2d space
label = np.asarray([5 * a + 1 > b for (a, b) in zip(x, y)])
data = np.array([[a,b] for (a, b) in zip(x, y)], dtype=np.float32)
plt.plot(bd_x, bd_y, 'k', label = 'boundary')
plt.plot(x[label], y[label], 'ro', ms=7)
plt.plot(x[~label], y[~label], 'bo', ms=7)
plt.legend(loc='best')
plt.show()
Explanation: We label the data points above the boundary line as positive points with label 1 and other data points with label 0 (negative).
End of explanation
# create layers
layer.engine = 'singacpp'
dense = layer.Dense('dense', 2, input_sample_shape=(2,))
p = dense.param_values()
print(p[0].shape, p[1].shape)
# init parameters
p[0].gaussian(0, 0.1) # weight matrix
p[1].set_value(0) # bias
# setup optimizer and loss func
opt = optimizer.SGD(lr=0.05)
lossfunc = loss.SoftmaxCrossEntropy()
Explanation: Create the MLP model
We will create a MLP by with one dense layer (i.e. fully connected layer).
We use the Softmax function to get compute the probability of each category for every data point.
We use the cross-entropy as the loss function.
We initialize the weight matrix following guassian distribution (mean=0, std=0.1), and set the bias to 0.
We creat a SGD updater to update the model parameters.
2 and 3 are combined by the SoftmaxCrossEntropy.
End of explanation
tr_data = tensor.from_numpy(data)
tr_label = tensor.from_numpy(label.astype(int))
# plot the classification results using the current model parameters
def plot_status(w, b, title='origin'):
    global bd_x, bd_y, data      
    pr = np.add(np.dot(data, w), b)
    lbl = pr[:, 0] < pr[:, 1]
            
    plt.figure(figsize=(6,3));
    plt.plot(bd_x, bd_y, 'k', label='truth line')    
    plt.plot(data[lbl, 0], data[lbl, 1], 'ro', ms=7)
    plt.plot(data[~lbl, 0], data[~lbl, 1], 'bo', ms=7)
    plt.legend(loc='best')
    plt.title(title)
    plt.xlim(-1, 1);
    plt.ylim(data[:, 1].min()-1, data[:, 1].max()+1)
    
# sgd
for i in range(1000):
    act = dense.forward(True, tr_data)
    lvalue = lossfunc.forward(True, act, tr_label)
    dact = lossfunc.backward()
    dact /= tr_data.shape[0]
    _, dp = dense.backward(True, dact)
    # update the parameters
    opt.apply(i, dp[0], p[0], 'w')
    opt.apply(i, dp[1], p[1], 'b')
    if (i%100 == 0):
        print('training loss =  %f' % lvalue.l1())
        plot_status(tensor.to_numpy(p[0]), tensor.to_numpy(p[1]),title='epoch %d' % i)
#train(dat, label)
Explanation: Each layer is created with a layer name and other meta data, e.g., the dimension size for the dense layer. The last argument is the shape of a single input sample of this layer.
param_values() returns a list of tensors as the parameter objects of this layer
SGD optimzier is typically created with the weight decay, and momentum specified. The learning rate could be specified at creation or passed in when the optimizer is applied.
Train the model
We run 1000 iterations to train the MLP model. 
1. For each iteration, we compute the gradient of the models parameters and use them to update the model parameters.
2. Periodically, we plot the prediction from the model.
End of explanation
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