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""" function.py
Module containing classes representing piece-wise constant and piece-wise linear
functions.
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
"""
from __future__ import print_function
import numpy as np
class PieceWiseConstFunc:
""" A class representing a piece-wise constant function. """
def __init__(self, x, y):
""" Constructs the piece-wise const function.
Params:
- x: array of length N+1 defining the edges of the intervals of the pwc
function.
- y: array of length N defining the function values at the intervals.
"""
self.x = x
self.y = y
def get_plottable_data(self):
""" Returns two arrays containing x- and y-coordinates for immeditate
plotting of the piece-wise function.
"""
x_plot = np.empty(2*len(self.x)-2)
x_plot[0] = self.x[0]
x_plot[1::2] = self.x[1:]
x_plot[2::2] = self.x[1:-1]
y_plot = np.empty(2*len(self.y))
y_plot[::2] = self.y
y_plot[1::2] = self.y
return x_plot, y_plot
def avrg(self):
""" Computes the average of the piece-wise const function:
a = 1/T int f(x) dx where T is the length of the interval.
Returns:
- the average a.
"""
return np.sum((self.x[1:]-self.x[:-1]) * self.y) / \
(self.x[-1]-self.x[0])
def abs_avrg(self):
""" Computes the average of the abs value of the piece-wise const
function:
a = 1/T int |f(x)| dx where T is the length of the interval.
Returns:
- the average a.
"""
return np.sum((self.x[1:]-self.x[:-1]) * np.abs(self.y)) / \
(self.x[-1]-self.x[0])
def add(self, f):
""" Adds another PieceWiseConst function to this function.
Note: only functions defined on the same interval can be summed.
Params:
- f: PieceWiseConst function to be added.
"""
assert self.x[0] == f.x[0], "The functions have different intervals"
assert self.x[-1] == f.x[-1], "The functions have different intervals"
x_new = np.empty(len(self.x) + len(f.x))
y_new = np.empty_like(x_new)
x_new[0] = self.x[0]
y_new[0] = self.y[0] + f.y[0]
index1 = 1
index2 = 1
index = 1
while (index1+1 < len(self.x)) and (index2+1 < len(f.x)):
if self.x[index1+1] < f.x[index2+1]:
x_new[index] = self.x[index1]
index1 += 1
elif self.x[index1+1] > f.x[index2+1]:
x_new[index] = f.x[index2+1]
index2 += 1
else: # self.x[index1+1] == f.x[index2+1]:
x_new[index] = self.x[index1]
index1 += 1
index2 += 1
index += 1
y_new[index] = self.y[index1] + f.y[index2]
# both indices should have reached the maximum simultaneously
assert (index1+1 == len(self.x)) and (index2+1 == len(f.x))
# only use the data that was actually filled
self.x = x_new[:index+1]
self.y = y_new[:index+1]
class PieceWiseLinFunc:
""" A class representing a piece-wise linear function. """
def __init__(self, x, y1, y2):
""" Constructs the piece-wise linear function.
Params:
- x: array of length N+1 defining the edges of the intervals of the pwc
function.
- y1: array of length N defining the function values at the left of the
intervals.
- y2: array of length N defining the function values at the right of the
intervals.
"""
self.x = x
self.y1 = y1
self.y2 = y2
def get_plottable_data(self):
""" Returns two arrays containing x- and y-coordinates for immeditate
plotting of the piece-wise function.
"""
x_plot = np.empty(2*len(self.x)-2)
x_plot[0] = self.x[0]
x_plot[1::2] = self.x[1:]
x_plot[2::2] = self.x[1:-1]
y_plot = np.empty_like(x_plot)
y_plot[0::2] = self.y1
y_plot[1::2] = self.y2
return x_plot, y_plot
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