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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

By : Cyrille Rossant
4.4 (7)
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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

4.4 (7)
By: Cyrille Rossant

Overview of this book

Python is one of the leading open source platforms for data science and numerical computing. IPython and the associated Jupyter Notebook offer efficient interfaces to Python for data analysis and interactive visualization, and they constitute an ideal gateway to the platform. IPython Interactive Computing and Visualization Cookbook, Second Edition contains many ready-to-use, focused recipes for high-performance scientific computing and data analysis, from the latest IPython/Jupyter features to the most advanced tricks, to help you write better and faster code. You will apply these state-of-the-art methods to various real-world examples, illustrating topics in applied mathematics, scientific modeling, and machine learning. The first part of the book covers programming techniques: code quality and reproducibility, code optimization, high-performance computing through just-in-time compilation, parallel computing, and graphics card programming. The second part tackles data science, statistics, machine learning, signal and image processing, dynamical systems, and pure and applied mathematics.
Table of Contents (17 chapters)
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16
Index

Analyzing real-valued functions

SymPy contains a rich calculus toolbox to analyze real-valued functions: limits, power series, derivatives, integrals, Fourier transforms, and so on. In this recipe, we will show the very basics of these capabilities.

How to do it...

  1. Let's define a few symbols and a function (which is just an expression depending on x):
    >>> from sympy import *
        init_printing()
    >>> var('x z')
    How to do it...
    >>> f = 1 / (1 + x**2)
  2. Let's evaluate this function at 1:
    >>> f.subs(x, 1)
    How to do it...
  3. We can compute the derivative of this function:
    >>> diff(f, x)
    How to do it...
  4. What is How to do it...'s limit to infinity? (Note the double o (oo) for the infinity symbol):
    >>> limit(f, x, oo)
    How to do it...
  5. Here's how to compute a Taylor series (here, around 0, of order 9). The Big O can be removed with the removeO() method.
    >>> series(f, x0=0, n=9)
    How to do it...
  6. We can compute definite integrals (here, over the entire real line):
    >>> integrate(f, (x, -oo, oo))
    How to do it...
  7. SymPy can also compute...

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