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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>
Distributed under the BSD License
"""
from __future__ import print_function
import numpy as np
##############################################################
# PieceWiseConstFunc
##############################################################
class PieceWiseConstFunc:
""" A class representing a piece-wise constant function. """
def __init__(self, x, y):
""" Constructs the piece-wise const function.
Args:
- 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 = np.array(x)
self.y = np.array(y)
def almost_equal(self, other, decimal=14):
""" Checks if the function is equal to another function up to `decimal`
precision.
Args:
- other: another PieceWiseConstFunc object
Returns:
True if the two functions are equal up to `decimal` decimals,
False otherwise
"""
eps = 10.0**(-decimal)
return np.allclose(self.x, other.x, atol=eps, rtol=0.0) and \
np.allclose(self.y, other.y, atol=eps, rtol=0.0)
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 add(self, f):
""" Adds another PieceWiseConst function to this function.
Note: only functions defined on the same interval can be summed.
Args:
- 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"
# python implementation
# from python_backend import add_piece_wise_const_python
# self.x, self.y = add_piece_wise_const_python(self.x, self.y,
# f.x, f.y)
# cython version
from cython_add import add_piece_wise_const_cython
self.x, self.y = add_piece_wise_const_cython(self.x, self.y, f.x, f.y)
def mul_scalar(self, fac):
""" Multiplies the function with a scalar value
Args:
- fac: Value to multiply
"""
self.y *= fac
##############################################################
# PieceWiseLinFunc
##############################################################
class PieceWiseLinFunc:
""" A class representing a piece-wise linear function. """
def __init__(self, x, y1, y2):
""" Constructs the piece-wise linear function.
Args:
- 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 = np.array(x)
self.y1 = np.array(y1)
self.y2 = np.array(y2)
def almost_equal(self, other, decimal=14):
""" Checks if the function is equal to another function up to `decimal`
precision.
Args:
- other: another PieceWiseLinFunc object
Returns:
True if the two functions are equal up to `decimal` decimals,
False otherwise
"""
eps = 10.0**(-decimal)
return np.allclose(self.x, other.x, atol=eps, rtol=0.0) and \
np.allclose(self.y1, other.y1, atol=eps, rtol=0.0) and \
np.allclose(self.y2, other.y2, atol=eps, rtol=0.0)
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
def avrg(self):
""" Computes the average of the piece-wise linear 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]) * 0.5*(self.y1+self.y2)) / \
(self.x[-1]-self.x[0])
def abs_avrg(self):
""" Computes the absolute average of the piece-wise linear 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]) * 0.5 *
(np.abs(self.y1)+np.abs(self.y2)))/(self.x[-1]-self.x[0])
def add(self, f):
""" Adds another PieceWiseLin function to this function.
Note: only functions defined on the same interval can be summed.
Args:
- f: PieceWiseLin 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"
# python implementation
# from python_backend import add_piece_wise_lin_python
# self.x, self.y1, self.y2 = add_piece_wise_lin_python(
# self.x, self.y1, self.y2, f.x, f.y1, f.y2)
# cython version
from cython_add import add_piece_wise_lin_cython
self.x, self.y1, self.y2 = add_piece_wise_lin_cython(
self.x, self.y1, self.y2, f.x, f.y1, f.y2)
def mul_scalar(self, fac):
""" Multiplies the function with a scalar value
Args:
- fac: Value to multiply
"""
self.y1 *= fac
self.y2 *= fac
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