In this notebook, we are going to use the tensor module from PySINGA to train a linear regression model. We use this example to illustrate the usage of tensor of PySINGA. Please refer the documentation page to for more tensor functions provided by PySINGA.

In [1]:

```
from __future__ import division
from __future__ import print_function
from builtins import range
from past.utils import old_div
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
```

To import the tensor module of PySINGA, run

In [2]:

```
from singa import tensor
```

Our problem is to find a line that fits a set of 2-d data points. We first plot the ground truth line,

In [3]:

```
a, b = 3, 2
f = lambda x: a * x + b
gx = np.linspace(0.,1,100)
gy = [f(x) for x in gx]
plt.plot(gx, gy, label='y=f(x)')
plt.xlabel('x')
plt.ylabel('y')
plt.legend(loc='best')
```

Out[3]:

Then we generate the training data points by adding a random error to sampling points from the ground truth line. 30 data points are generated.

In [4]:

```
nb_points = 30
# generate training data
train_x = np.asarray(np.random.uniform(0., 1., nb_points), np.float32)
train_y = np.asarray(f(train_x) + np.random.rand(30), np.float32)
plt.plot(train_x, train_y, 'bo', ms=7)
```

Out[4]:

Assuming that we know the training data points are sampled from a line, but we don't know the line slope and intercept. The training is then to learn the slop (k) and intercept (b) by minimizing the error, i.e. ||kx+b-y||^2.

- we set the initial values of k and b (could be any values).
- we iteratively update k and b by moving them in the direction of reducing the prediction error, i.e. in the gradient direction. For every iteration, we plot the learned line.

In [5]:

```
def plot(idx, x, y):
global gx, gy, axes
# print the ground truth line
axes[idx//5, idx%5].plot(gx, gy, label='y=f(x)')
# print the learned line
axes[idx//5, idx%5].plot(x, y, label='y=kx+b')
axes[idx//5, idx%5].legend(loc='best')
# set hyper-parameters
max_iter = 15
alpha = 0.05
# init parameters
k, b = 2.,0.
```

SINGA tensor module supports basic linear algebra operations, like `+ - * /`

, and advanced functions including axpy, gemm, gemv, and random function (e.g., Gaussian and Uniform).

SINGA Tensor instances could be created via **tensor.Tensor()** by specifying the shape, and optionally the device and data type. Note that every Tensor instance should be initialized (e.g., via **set_value()** or random functions) before reading data from it. You can also create Tensor instances from numpy arrays,

- numpy array could be converted into SINGA tensor via
**tensor.from_numpy(np_ary)** - SINGA tensor could be converted into numpy array via
**tensor.to_numpy()**; Note that the tensor should be on the host device. tensor instances could be transferred from other devices to host device via**to_host()**

Users cannot read a single cell of the Tensor instance. To read a single cell, users need to convert the Tesnor into a numpy array.

In [6]:

```
# to plot the intermediate results
fig, axes = plt.subplots(3, 5, figsize=(12, 8))
x = tensor.from_numpy(train_x)
y = tensor.from_numpy(train_y)
# sgd
for idx in range(max_iter):
y_ = x * k + b
err = y_ - y
loss = old_div(tensor.sum(err * err), nb_points)
print('loss at iter %d = %f' % (idx, loss))
da1 = old_div(tensor.sum(err * x), nb_points)
db1 = old_div(tensor.sum(err), nb_points)
# update the parameters
k -= da1 * alpha
b -= db1 * alpha
plot(idx, tensor.to_numpy(x), tensor.to_numpy(y_))
```

We can see that the learned line is becoming closer to the ground truth line (in blue color).

In [7]:

```
# to plot the intermediate results
fig, axes = plt.subplots(3, 5, figsize=(12, 8))
x = tensor.from_numpy(train_x)
y = tensor.from_numpy(train_y)
# sgd
for idx in range(max_iter):
y_ = x * k + b
err = y_ - y
loss = old_div(tensor.sum(err * err), nb_points)
print('loss at iter %d = %f' % (idx, loss))
da1 = old_div(tensor.sum(err * x), nb_points)
db1 = old_div(tensor.sum(err), nb_points)
# update the parameters
k -= da1 * alpha
b -= db1 * alpha
plot(idx, tensor.to_numpy(x), tensor.to_numpy(y_))
```