class Interpolator:
    """Provides linear interpolation for functions y=f(x)"""

    def __init__(self,xs,fs):
        """Create an interpolator using the list of anchor points xs
        and their values fs for the interpolation."""
        if len(xs) != len(fs):
            raise Exception('Lists were not the same length.')
        self.data = sorted(zip(xs,fs))
        # '_' can be used to indicate that a tuple value is not used
        self.minX, _ = self.data[0]
        self.maxX, _ = self.data[-1]



    def f(self,x):
        """Return the linearly interpolated value f(x) from the whole
        range spanned by the xs."""
        if x < self.minX or x > self.maxX:
            raise Exception('Cannot extrapolate outside x range %s.'
                            % ((self.minX, self.maxX),))

        ### FIX THIS FUNCTION (Q.3b) ###
        # find enclosing pair of values left=(x0,f0) right=(x1,f1)
        # where x0 < x < x1
        left = self.data[-2]
        right = self.data[-1]

        # linearly interpolate between neighbouring points
        return self.interpolate(x, left, right)



    def interpolate(self,x,left,right):
        """Interpolate the value of f(x) given left=(x0,y0)
        and right=(x1,y1) anchor points."""
        x0, y0 = left
        x1, y1 = right
        ### FIX THIS FUNCTION (Q.3a) ###
        return y0




        
if __name__ == '__main__':
    import numpy, pylab

    # create anchor points from a sin() function
    xs = numpy.arange(-5,5,0.8)
    fs = numpy.sin(xs)

    # create interpolator
    ip = Interpolator(xs,fs)

    # plot the function with steps inbetween the anchor points
    x = numpy.arange(min(xs),max(xs),0.1)
    y = [ ip.f(xx) for xx in x ]
    
    pylab.plot(x,y,'.')
    pylab.show()