Gain insights into Python for scientific computing. Explore arrays, plotting, linear equations, and algorithms using NumPy, Matplotlib, SciPy. Delve into applying tools with practical exercises.

Dockerfile.tar.gz

Python3

If you're a scientist or an engineer interested in learning scientific computing, this is the place to start.

In this course, you'll learn to write your own useful code to perform impactful scientific computations. Along the way, your understanding will be tested with periodic quizzes and exercises.

Topics covered in this course include arrays, plotting, linear equations, symbolic computation, scientific algorithms, and random variables. You’ll also be exposed to popular Python packages like NumPy, Matplotlib, SciPy, and others. In the last part of the course, the application section will test your ability to recall and apply the tools you have studied into newly learned scientific concepts.

At the end of this course, you'll be equipped with the tools necessary for everyday scientific computation.

Python for Scientists and Engineers

# Sparse matrices in Python
The procedure we have used so far to construct the matrix for a is not very efficient. A full matrix is created, which consists mostly of zeros with non-zero values only appearing on diagonals. There are more efficient routines that store what are called **sparse matrices**. In a sparse matrix, only the value and location of non-zero values in a matrix are stored. Functionality for sparse matrices is available in the `scipy` submodule `sparse`. 

> <img src="/api/collection/10370001/6066104977850368/page/4580102618742784/image/6441996354846720" width="35"> We will import the `scipy.sparse` submodule as `sp`.

```python
import scipy.sparse as sp
```

# Dense to sparse
When we create a sparse matrix, we have to choose which format it should be stored in. There are many ways to store a sparse matrix. Two most commonly used are:
1. *compressed sparse column* using the `csc_matrix(A)` method. 
2. *compressed sparse row* using the `csr_matrix(A)` method.

The following matrix is an example of this:



<center>
  <fontsize="size">

$\large \begin{bmatrix}2 & 3 & 0& 0\\1 & 2 & 3 & 0 \\0 & 1 & 2 & 3 \\0 & 0 & 1 & 2  \end{bmatrix}$

</center>

Let's convert this dense matrix to a sparse matrix. In the first example, we will convert it into a compressed sparse column:

In this lesson, we will learn about different sparse matrices in Python and the conversion between sparse and dense matrices. 

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Sparse Matrices

Sparse matrices in Python #