skipi is a library to easily define mathematical functions and apply various transforms on it.
A function always consists of a domain and a map. Usually the domain is ommited since it's clear for the human what the domain is, however, not for the computer.
This library aims to combine the domain and the map into one Function object and offer multiple convenient operations on it.
Supported features are: Addition, Subtraction, Multiplication, Division, Exponentiation, Composition
import numpy as np
from skipi.function import Function
f = Function(np.linspace(0, 10, 100), lambda x: 2+x)
g = Function(f.get_domain(), lambda x: np.sin(x))
h1, h2, h3, h4, h5, h6 = f+g, f-g, f*g, g/f, f.composeWith(g), f**g
A function is plotted using matplotlib calling plot(). If you want to plot multiple functions into one graph, simply use
g.plot() # does not draw the graph yet
f.plot(show=True) # draws it
If you want to re-mesh a function on a different domain/grid, you can use remesh
or vremesh
.
The method remesh
assigns a new mesh, independent of the previous one.
f = Function(np.linspace(0, 10, 10), lambda x: np.sin(x))
f.remesh(np.linspace(0, 20, 1000))
However, if you want to restrict the domain, you can use vremesh
which has a similar syntax as slice
except that instead of indices we use values and it allows multiple slicing:
f = Function(np.linspace(0, 10, 1000), lambda x: np.sin(x))
f.vremesh((np.pi, 2*np.pi)) # domain is now restricted to [pi, 2pi]
f.vremesh((None, 2*np.pi)) # domain is now restricted to [0, 2pi]
f.vremesh((np.pi, None)) # domain is now restricted to [pi, 10]
f.vremesh((0.5, 1.5), (2.0, 2.5)) # domain is now restricted to [0.5, 1.5] union [2.0, 2.5]
If you don't have an analytical formulation of y = f(x)
, but rather have y_i and x_i values, then you can create a function by interpolation. By default, linear interpolation is used.
x_i = np.linspace(0, 10, 100)
y_i = np.sin(x_i)
f = Function.to_function(x_i, y_i)
print(f(0.1234)) # linearly interpolated, not sin(0.1234)!
Calculate the integral function of f(x) = 5x
import numpy as np
from skipi.function import Function, Integral
f = Function(np.linspace(0, 10, 100), lambda x: 5*x)
F = Integral.from_function(f) # Integral function
F.plot(show=True)
Calculate the fourier transform (analytical fourier transform, not fft) of f(x) = exp(-x^2)
from skipi.fourier import FourierTransform, InverseFourierTransform
t_space, freq_space = np.linspace(-5, 5, 100), np.linspace(-10, 10, 100)
f = Function(t_space, lambda x: np.exp(-x**2))
F = FourierTransform.from_function(freq_space, f)
f2 = InverseFourierTransform.from_function(t_space, F)
# f2 should be equal to f
(f-f2).plot(show=True)