from numpy import average,std,polyfit,poly1d
from scipy import interpolate

##############################################################################
# Define utility functions
##############################################################################


def normalise_mean(data):
    return [x/average(data) for x in data]

def interpolate_integrate(x,y,x0,x1):
    assert len(x) == len(y)
    #check strictly increasing x
    assert all(x[idx] < x[idx+1] for idx in xrange(len(x)-1))
    assert x1 >= x0
    assert x1 <= max(x) and x1 >= min(x)
    assert x0 <= max(x) and x0 >= min(x)
    
    if x1 == x0:
        return 0.0
    
    interp_fcn = interpolate.interp1d(x,y)
    
    integral = 0.0    
    
    for idx in xrange(len(x)-1):
        if x[idx] >= x0 and x[idx+1] <= x1:
            #completely within range            
            integral += (x[idx+1]-x[idx])*(y[idx]+y[idx+1])*0.5
        elif x[idx] >= x0 and x[idx] <= x1 and x[idx+1] >= x1:
            #end of integral
            integral += (x1 - x[idx])*(interp_fcn(x1) + y[idx])*0.5
        elif x[idx] <= x0 and x[idx+1] >= x1:
            #integral is all within one step
            integral += (x1 - x0)*(interp_fcn(x0) + interp_fcn(x1))*0.5
        elif x[idx] <= x0 and x[idx+1] > x0 and x[idx+1] <= x1:
            #start of integral
            integral += (x[idx+1] - x0)*(interp_fcn(x0) + interp_fcn(x[idx+1]))*0.5
    
    return integral