Cheat Sheet Jupyter Notebook

Jupyter Notebook has support for many kinds of interactive outputs, including the ipywidgets ecosystem as well as many interactive visualization libraries. These are supported in Jupyter Book, with the right configuration. This page has a few common examples. First off, we’ll download a little bit of data and show its structure. Jupyter Notebook files Notebooks written entirely in Markdown Custom notebook formats and Jupytext reStructuredText files Build your book. # MyST Cheat Sheet. Jupyter Notebook is a web-based interface that helps you to build and exchange documents containing live code, visualizations, informative text, and equations. Also, Jupyter Notebook includes statistical modeling, numerical simulation, machine learning, data cleaning, and transformation. In this cheat sheet you will learn the following techniques.

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7.1. Table of Contents¶

7.2. Numeric¶

7.3. Basic plotting functions¶

7.4. Symbolic manipulation¶

7.4.1. Imports¶

Symbol definitions

Example controller and system

7.4.2. Working with rational functions and polynomials¶

We often want nice rational functions, but sympy doesn’t make expressions rational by default

$$frac{5 K_{c} left(s tau + 1right)}{s tau left(10 s + 1right)^{2}} + 1$$

The cancel function forces this to be a fraction. collect collects terms.

$$frac{5 K_{c} + 100 s^{3} tau + 20 s^{2} tau + s left(5 K_{c} tau + tauright)}{100 s^{3} tau + 20 s^{2} tau + s tau}$$

In some cases we can factor equations:

$$frac{5 K_{c} + 100 s^{3} tau + 20 s^{2} tau + s left(5 K_{c} tau + tauright)}{s tau left(10 s + 1right)^{2}}$$

Obtain the numerator and denominator:

$$left ( 5 K_{c} + 100 s^{3} tau + 20 s^{2} tau + s left(5 K_{c} tau + tauright), quad 100 s^{3} tau + 20 s^{2} tau + s tauright )$$

If you want them both, you can use

$$left ( 5 K_{c} + 100 s^{3} tau + 20 s^{2} tau + s left(5 K_{c} tau + tauright), quad 100 s^{3} tau + 20 s^{2} tau + s tauright )$$

Convert to polynomial in s

Once we have a polynomial, it is easy to obtain coefficients:

$$left [ 100 tau, quad 20 tau, quad 5 K_{c} tau + tau, quad 5 K_{c}right ]$$

Calculate the Routh Array

$$left[begin{matrix}100 tau & 5 K_{c} tau + tau20 tau & 5 K_{c}- 25 K_{c} + tau left(5 K_{c} + 1right) & 05 K_{c} & 0end{matrix}right]$$

To get a function which can be used numerically, use lambdify:

7.4.3. Functions useful for discrete systems¶

Write in terms of positive powers of (z):

Write in terms of negative powers of (z):

Inversion of the (z) transform

$$left [ 0, quad 1, quad 1, quad 1, quad 1, quad 1, quad 1, quad 1, quad 1, quad 1right ]$$

7.5. Equation solving¶

7.5.1. Symbolic¶

$$left { x : - a, quad y : a + 2, quad z : -2right }$$

7.5.2. Numeric sympy¶

$$left[begin{matrix}-2.219107148913752.21910714891375end{matrix}right]$$

7.5.3. Numeric¶

7.6. Matrix math¶

7.6.1. Symbolic¶

Creation

$$left[begin{matrix}G_{11} & G_{12}G_{21} & G_{22}end{matrix}right]$$

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Determinant, inverse, transpose

$$left ( G_{11} G_{22} - G_{12} G_{21}, quad left[begin{matrix}frac{G_{22}}{G_{11} G_{22} - G_{12} G_{21}} & - frac{G_{12}}{G_{11} G_{22} - G_{12} G_{21}}- frac{G_{21}}{G_{11} G_{22} - G_{12} G_{21}} & frac{G_{11}}{G_{11} G_{22} - G_{12} G_{21}}end{matrix}right], quad left[begin{matrix}G_{11} & G_{21}G_{12} & G_{22}end{matrix}right]right )$$

Math operations: Multiplication, addition, elementwise multiplication:

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$$left ( left[begin{matrix}G_{11}^{2} + G_{12} G_{21} & G_{11} G_{12} + G_{12} G_{22}G_{11} G_{21} + G_{21} G_{22} & G_{12} G_{21} + G_{22}^{2}end{matrix}right], quad left[begin{matrix}2 G_{11} & 2 G_{12}2 G_{21} & 2 G_{22}end{matrix}right], quad left[begin{matrix}G_{11}^{2} & G_{12}^{2}G_{21}^{2} & G_{22}^{2}end{matrix}right]right )$$

7.6.2. Numeric¶

Creation

Determinant, inverse, transpose

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Math operations: Multiplication, addition, elementwise multiplication: