Step function in python

scipy.signal.step#

describing the system. The following gives the number of elements in the tuple and the interpretation:

Initial state-vector (default is zero).

T array_like, optional

Time points (computed if not given).

N int, optional

Number of time points to compute if T is not given.

Returns : T 1D ndarray

yout 1D ndarray

If (num, den) is passed in for system , coefficients for both the numerator and denominator should be specified in descending exponent order (e.g. s^2 + 3s + 5 would be represented as [1, 3, 5] ).

>>> from scipy import signal >>> import matplotlib.pyplot as plt >>> lti = signal.lti([1.0], [1.0, 1.0]) >>> t, y = signal.step(lti) >>> plt.plot(t, y) >>> plt.xlabel('Time [s]') >>> plt.ylabel('Amplitude') >>> plt.title('Step response for 1. Order Lowpass') >>> plt.grid() 

Источник

Fit a Step Function in Python

Step functions are methods with graphs that look like a series of steps. They consist of a series of horizontal line segments with intervals in between and can also be referred to as staircase functions.

At any given interval, step functions have a constant value, creating a horizontal line on the graph. The intervals make the jumps in between each line segment.

Step functions are helpful when generating discrete plots and are widely used in vectorized plotting in Python. They can be implemented in Python using numpy .

A simple demonstration of step functions is given in this article.

Fit a Step Function in Python

For this example will be using Python version 3.10.6. Furthermore, we need to install the required libraries, which, in our case, is numpy.

Numpy can be installed by running the following command.

Now we need scipy to optimize and fit the data to the graphs. It can be installed using the command below.

We will generate a simple step function using a dataset for this example. Starting, import numpy and scipy to the environment using the following statements:

import numpy as np import scipy 

We will use the numpy linspace method for this example to generate a small dataset. The following code snippet can generate this dataset:

We need to generate a heaviside function to showcase the staircase plotting. Depending on the use case requirement, it can be either generated using numpy or a custom method.

To create the function, we will use the numpy method heaviside for this example.

This method generates the heaviside value according to the following plot.

 0 if x1  0 heaviside(x1, x2) = x2 if x1 == 0  1 if x1 > 0 

We will use curve_fit from the scipy library to generate the args with optimal data points.

Now that we have cleared up and understood the flow, the final script will look something like this:

import numpy as np from scipy.special import expit from scipy.optimize import curve_fit  x = np.linspace(0, 10, 101) y = np.heaviside((x - 5), 0.)  def sigmoid(x, x0, b):  return expit((x - x0) * b)  args, cov = curve_fit(sigmoid, x, y) print(args) 

We can monitor the results of this plotting using matplotlib . Adding the plotting snippet and the final code will be as below.

import matplotlib.pyplot as plt import numpy as np from scipy.special import expit from scipy.optimize import curve_fit  x = np.linspace(0, 10, 101) y = np.heaviside((x - 5), 0.)  def sigmoid(x, x0, b):  return expit((x - x0) * b)  args, cov = curve_fit(sigmoid, x, y) plt.scatter(x, y) plt.plot(x, sigmoid(x, *args)) plt.show() print(args) 

I am Fariba Laiq from Pakistan. An android app developer, technical content writer, and coding instructor. Writing has always been one of my passions. I love to learn, implement and convey my knowledge to others.

Related Article — Python Function

Источник

Saved searches

Use saved searches to filter your results more quickly

You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window. Reload to refresh your session. You switched accounts on another tab or window. Reload to refresh your session.

Python class representing a step function.

License

terhorst/stepfun

This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?

Sign In Required

Please sign in to use Codespaces.

Launching GitHub Desktop

If nothing happens, download GitHub Desktop and try again.

Launching GitHub Desktop

If nothing happens, download GitHub Desktop and try again.

Launching Xcode

If nothing happens, download Xcode and try again.

Launching Visual Studio Code

Your codespace will open once ready.

There was a problem preparing your codespace, please try again.

Latest commit

Git stats

Files

Failed to load latest commit information.

README.rst

stepfun is a Python class for representing mathematical step functions. It supports simple arithmetic operations (addition, subtraction, multiplication, etc.) as well as vectorized evaluation and integration.

A step function f(z) with K \ge 1 steps is specified by real numbers x_0 < x_1 < \cdots < x_Kand y_1 < \cdots < y_Ksuch that

The function is undefined for x \notin [x_0, x_K). It is fine to set x_0 = -\infty and/or x_K = \infty, allowing f to be supported on the entire real line.

>>> from stepfun import StepFunction >>> inf = float("infinity") >>> s1 = StepFunction(x=[-inf, +inf], y=[1.]) # constant function s1 = 1 >>> s1 StepFunction(x=array([-inf, inf]), y=array([ 1.])) >>> s1.K 1 >>> StepFunction(x=[-inf, +inf], y=[1., 2.]) Traceback (most recent call last): . RuntimeError: len(x) != 1 + len(y)

Step functions are closed under the usual operations of addition, subtraction, multiplication, etc.

>>> s1 + s1 StepFunction(x=array([-inf, inf]), y=array([ 2.])) >>> s2 = StepFunction(x=[-inf, +inf], y=[ 2. ]) >>> s2 - s1 StepFunction(x=array([-inf, inf]), y=array([ 1.])) >>> s2 / s1 == s2 True >>> s1 / s2 StepFunction(x=array([-inf, inf]), y=array([ 0.5]))

Equality testing is supported, and requires that all elements of both \mathbf and \mathbf match exactly.

>> s1 == s1 True >> s1 + s1 == s2 True >> s1 == s2 False >> s1 == StepFunction(x=[-inf, 0., inf], y=[1., 1.]) True # see "Breakpoint compatibility", below

Step functions have a natural partial ordering. Step function s1 is (strictly) greater than s2 if s1 - s2 is everywhere (strictly) positive.

>>> 2 * s1 > s1 True >>> s1 > s1 False >>> s1 >= s1 True

Functions which have different domains of definition cannot be compared.

>>> one = StepFunction(x=[-1., 1.], y=[2.]) >>> one > s1 Traceback (most recent call last): . TypeError: Step functions have different support: [-1. 1.] vs. [-inf inf]

Comparison against objects which are not of type StepFunction falls through to the underlying array of y values.

>>> s1 > 0 True >>> two = StepFunction([-1, 0, 1], [2, 3]) >>> two  [3, 4] True >>> two  [2, 4] False >>> two  [2, 4] True

Unary options such as negation and powers are also supported.

>>> s2**2 StepFunction(x=array([-inf, inf]), y=array([ 4.])) >>> -s1 StepFunction(x=array([-inf, inf]), y=array([-1.])) >>> abs(-s1) StepFunction(x=array([-inf, inf]), y=array([ 1.]))

In the above examples, functions s1 and s2 were defined on the same set of break points, but this is not necessary in general.

>>> s3 = StepFunction(x=[-inf, -1., 1., inf], y=[0, 1., 0]) >>> s4 = StepFunction(x=[-inf, -1., 0.5, 1.0, inf], y=[0, 1., 2., 3.]) >>> s3 + s4 StepFunction(x=array([-inf, -1. , 0.5, inf]), y=array([ 0., 2., 3.]))

Note that the class constructor will automatically eliminate redundant elements of the representation.

>>> s3 - s3 StepFunction(x=array([-inf, inf]), y=array([ 0.])) >>> StepFunction(x=[-inf, 0., inf], y=[0., 0.]) StepFunction(x=array([-inf, inf]), y=array([ 0.]))

It is possible to perform scalar operations on step functions. Any operand which is not recognized as a companion step function is "passed through" to the underlying array of \mathbf values.

>>> s1 * 2 StepFunction(x=array([-inf, inf]), y=array([ 2.])) >>> s1 - 1 == 0 * s1 True >>> s1 * "error" # don't know how to multiply y by string Traceback (most recent call last): . TypeError: .

Step functions may be evaluated using the __call__() syntax.

Vectorized evaluation is also supported.

>>> s1([-1, 1, 2, 10]) array([ 1., 1., 1., 1.]) >>> s3([-1, 0., 1.5, 2]) array([ 1., 1., 0., 0.])

The integral() method returns the Riemann integral of the step function over its domain.

>>> s1.integral() inf >>> impulse = StepFunction(x=[-1, 0, 1], y=[-1, 1]) / 2**.5 >>> impulse.integral() 0.0 >>> (impulse**2).integral() 0.99999999999999978

Источник