Peace-wise interpolation and lazy evaluation in cython

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License: BSD 3-Clause License

Author: eduardo moguillansky

Requires: Python >=3.8

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Project description

BPF4

wheels

About

bpf4 is a library for curve fitting and break-point functions in python. It is mainly programmed in Cython for efficiency.

Documentation

The documentation is hosted at https://bpf4.readthedocs.io

Example

Find the intersection between two curves

from bpf4 import bpf  # this imports the api
a = bpf.spline((0, 0), (1, 5), (2, 3), (5, 10))  # each point (x, y)
b = bpf.expon((0, -10), (2,15), (5, 3), exp=3)
a.plot() # uses matplotlib
b.plot() 
zeros = (a - b).zeros()
import pylab
pylab.plot(zeros, a.map(zeros), 'o')

1

Features

Many interpolation types besides linear:

  • spline
  • half-cosine
  • exponential
  • fibonacci
  • exponantial half-cosine
  • pchip
  • logarithmic
  • etc.

Interpolation types can be mixed, so that each segment has a different interpolation (with the exception of spline interpolation)
Curves can be combined non-destructively. Following from the example above.

c = (a + b).sin().abs()
c[1.5:4].plot()  # plot only the range (1.5, 4)

2

Syntax support for shifting, scaling and slicing a bpf

a >> 2        # a shifted to the right
(a * 5) ^ 2   # scale the x coord by 2, scale the y coord by 5
a[2:2.5]      # slice only a portion of the bpf
a[::0.01]     # sample the bpf with an interval of 0.01
  • Derivation and Integration: c.derivative().plot() or c.integrated().integrated().plot()
  • Numerical integration: c.integrate_between(2, 4)

Installation

pip install --upgrade bpf4

To install from source:

git clone https://github.com/gesellkammer/bpf4.git
cd bpf4
pip install .

Mathematical operations

Max / Min

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
core.Max((a, b)).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')


a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
core.Min((a, b)).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

+, -, *, /

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
(a*b).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')


a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
(a**b).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')


a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
((a+b)/2).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

Building functions

A bpf can be used to build complex formulas

Fresnel's Integral: ( S(x) = \int_0^x {sin(t^2)} dt )

t = slope(1)
f = (t**2).sin()[0:10:0.001].integrated()
f.plot()

Polar plots

Any kind of matplotlib plot can be used. For example, polar plots are possible by creating an axes with polar=True

Cardiod: (\rho = 1 + sin(-\theta) )

from math import *
theta = slope(1, bounds=(0, 2*pi))
r = 1 + (-theta).sin()

ax = plt.axes(polar=True)
ax.set_rticks([0.5, 1, 1.5, 2]); ax.set_rlabel_position(38)
r.plot(axes=ax)

Flower 5: (\rho = 3 + cos(5 * \theta) )

theta = core.Slope(1, bounds=(0, 2*pi))
r = 3 + (5*theta).cos()

ax = plt.axes(polar=True)
r.plot(axes=ax)

Project details

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License: BSD 3-Clause License

Author: eduardo moguillansky

Requires: Python >=3.8

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