import graphlab

"""
Explanation: Regression Week 3: Assessing Fit (polynomial regression)
In this notebook you will compare different regression models in order to assess which model fits best. We will be using polynomial regression as a means to examine this topic. In particular you will:
* Write a function to take an SArray and a degree and return an SFrame where each column is the SArray to a polynomial value up to the total degree e.g. degree = 3 then column 1 is the SArray column 2 is the SArray squared and column 3 is the SArray cubed
* Use matplotlib to visualize polynomial regressions
* Use matplotlib to visualize the same polynomial degree on different subsets of the data
* Use a validation set to select a polynomial degree
* Assess the final fit using test data
We will continue to use the House data from previous notebooks.
Fire up graphlab create
End of explanation
"""


tmp = graphlab.SArray([1., 2., 3.])
tmp_cubed = tmp.apply(lambda x: x**3)
print tmp
print tmp_cubed

"""
Explanation: Next we're going to write a polynomial function that takes an SArray and a maximal degree and returns an SFrame with columns containing the SArray to all the powers up to the maximal degree.
The easiest way to apply a power to an SArray is to use the .apply() and lambda x: functions. 
For example to take the example array and compute the third power we can do as follows: (note running this cell the first time may take longer than expected since it loads graphlab)
End of explanation
"""


ex_sframe = graphlab.SFrame()
ex_sframe['power_1'] = tmp
print ex_sframe

"""
Explanation: We can create an empty SFrame using graphlab.SFrame() and then add any columns to it with ex_sframe['column_name'] = value. For example we create an empty SFrame and make the column 'power_1' to be the first power of tmp (i.e. tmp itself).
End of explanation
"""


def polynomial_sframe(feature, degree):
    # assume that degree >= 1
    # initialize the SFrame:
    poly_sframe = graphlab.SFrame()
    # and set poly_sframe['power_1'] equal to the passed feature

    # first check if degree > 1
    if degree > 1:
        # then loop over the remaining degrees:
        # range usually starts at 0 and stops at the endpoint-1. We want it to start at 2 and stop at degree
        for power in range(2, degree+1): 
            # first we'll give the column a name:
            name = 'power_' + str(power)
            # then assign poly_sframe[name] to the appropriate power of feature

    return poly_sframe

"""
Explanation: Polynomial_sframe function
Using the hints above complete the following function to create an SFrame consisting of the powers of an SArray up to a specific degree:
End of explanation
"""


print polynomial_sframe(tmp, 3)

"""
Explanation: To test your function consider the smaller tmp variable and what you would expect the outcome of the following call:
End of explanation
"""


sales = graphlab.SFrame('kc_house_data.gl/')

"""
Explanation: Visualizing polynomial regression
Let's use matplotlib to visualize what a polynomial regression looks like on some real data.
End of explanation
"""


sales = sales.sort(['sqft_living', 'price'])

"""
Explanation: As in Week 3, we will use the sqft_living variable. For plotting purposes (connecting the dots), you'll need to sort by the values of sqft_living. For houses with identical square footage, we break the tie by their prices.
End of explanation
"""


poly1_data = polynomial_sframe(sales['sqft_living'], 1)
poly1_data['price'] = sales['price'] # add price to the data since it's the target

"""
Explanation: Let's start with a degree 1 polynomial using 'sqft_living' (i.e. a line) to predict 'price' and plot what it looks like.
End of explanation
"""


model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = ['power_1'], validation_set = None)

#let's take a look at the weights before we plot
model1.get("coefficients")

import matplotlib.pyplot as plt
%matplotlib inline

plt.plot(poly1_data['power_1'],poly1_data['price'],'.',
        poly1_data['power_1'], model1.predict(poly1_data),'-')

"""
Explanation: NOTE: for all the models in this notebook use validation_set = None to ensure that all results are consistent across users.
End of explanation
"""


poly2_data = polynomial_sframe(sales['sqft_living'], 2)
my_features = poly2_data.column_names() # get the name of the features
poly2_data['price'] = sales['price'] # add price to the data since it's the target
model2 = graphlab.linear_regression.create(poly2_data, target = 'price', features = my_features, validation_set = None)

model2.get("coefficients")

plt.plot(poly2_data['power_1'],poly2_data['price'],'.',
        poly2_data['power_1'], model2.predict(poly2_data),'-')

"""
Explanation: Let's unpack that plt.plot() command. The first pair of SArrays we passed are the 1st power of sqft and the actual price we then ask it to print these as dots '.'. The next pair we pass is the 1st power of sqft and the predicted values from the linear model. We ask these to be plotted as a line '-'. 
We can see, not surprisingly, that the predicted values all fall on a line, specifically the one with slope 280 and intercept -43579. What if we wanted to plot a second degree polynomial?
End of explanation
"""


