# Baby steps from 
# http://deeplearning.net/software/theano/tutorial/adding.html

import theano.tensor as T
from theano import function

x = T.dscalar('x')
y = T.dscalar('y')
z = x + y
f = function([x, y], z)


f(2,4)

f(16.2, 9.1)


############################################################



import theano
import theano.tensor as T
import numpy as np 

#dtype = theano.config.floatX


#training data
train_x = np.arange(-5., 5., 0.1)

def linear_noisy_y_data(x, a, b, sigma):
    return a + b * x + sigma * np.random.randn(train_x.shape[0])

train_y = linear_noisy_y_data(train_x, 1., 3., 1.2)

#theano symbolic variables
x = T.scalar()
target = T.scalar()

def linear_model(x, p0, p1):
    return  p0 + x * p1  
    
param0 = theano.shared(0.)
param1 = theano.shared(0.)

prediction = linear_model(x, param0, param1)

cost = T.mean(T.sqr(target - prediction))

g_param0 = T.grad(cost=cost, wrt=param0)
g_param1 = T.grad(cost=cost, wrt=param1)

# learning rate 
alpha = 0.0005

updates = [[param0, param0 - alpha * g_param0], [param1, param1 - alpha * g_param1]]

train_func = theano.function(inputs=[x, target], outputs=cost, updates=updates, 
allow_input_downcast=True)
 
cost_over_epochs = np.ndarray([20]) 
for epoch in range(20):
  for a_x, a_y in zip(train_x, train_y):
    c = train_func(a_x, a_y)
  cost_over_epochs[epoch] = c
    
%pylab
#plt.plot(np.arange(20), cost_over_epochs)

plt.plot(train_x, train_y,'.')
p0 = param0.eval()
p1 = param1.eval()
plt.plot(np.array([-5., 5]), np.array([p0-5.*p1, p0+5.*p1]),'-')