book

Scientific Computing with Python - Second Edition

by Claus Führer, Claus Fuhrer, Jan Erik Solem, Olivier Verdier

July 2021

Intermediate to advanced

392 pages

9h 40m

English

Packt Publishing

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Scientific Computing with Python Second Edition
About the authorsAbout the reviewer
Who this book is forWhat this book coversTo get the most out of this bookDownload the example code filesDownload the color imagesConventions usedGet in touchReviews
1.1 Installation and configuration instructions1.1.1 Installation1.1.2 Anaconda1.1.3 Spyder1.1.4 Configuration1.1.5 Python shell1.1.6 Executing scripts1.1.7 Getting help1.1.8 Jupyter – Python notebook1.2 Program and program flow1.2.1 Comments1.2.2 Line joining1.3 Basic data types in Python1.3.1 Numbers1.3.2 Strings1.3.3 Variables1.3.4 ListsOperations on lists1.3.6 Boolean expressions1.4 Repeating statements with loops1.4.1 Repeating a task1.4.2 break and else1.5 Conditional statements1.6 Encapsulating code with functions1.7 Understanding scripts and modules1.7.1 Simple modules – collecting functions1.7.2 Using modules and namespaces1.8 Python interpreterSummary
2.1 Variables2.2 Numeric types2.2.1 IntegersPlain integers2.2.2 Floating-point numbersFloating-point representationInfinite and not a numberUnderflow – Machine epsilonOther float types in NumPy2.2.3 Complex numbersComplex numbers in mathematicsThe j notationReal and imaginary parts2.3 Booleans2.3.1 Boolean operators2.3.2 Boolean castingAutomatic Boolean casting2.3.3 Return values of and and or2.3.4 Booleans and integers2.4 Strings2.4.1 Escape sequences and raw strings2.4.2 Operations on strings and string methods2.4.3 String formatting2.5 Summary2.6 Exercises
3.1 Lists3.1.1 SlicingStrides3.1.2 Altering lists3.1.3 Belonging to a list3.1.4 List methodsIn-place operations3.1.5 Merging lists – zip3.1.6 List comprehension3.2 A quick glance at the concept of arrays3.3 Tuples3.3.1 Packing and unpacking variables3.4 Dictionaries3.4.1 Creating and altering dictionaries3.4.2 Looping over dictionaries3.5 Sets3.6 Container conversions3.7 Checking the type of a variable3.8 Summary3.9 Exercises
4.1 Overview of the array type4.1.1 Vectors and matrices4.1.2 Indexing and slices4.1.3 Linear algebra operationsSolving a linear system4.2 Mathematical preliminaries4.2.1 Arrays as functions4.2.2 Operations are elementwise4.2.3 Shape and number of dimensions4.2.4 The dot operations4.3 The array type4.3.1 Array properties4.3.2 Creating arrays from listsArray and Python parentheses4.4 Accessing array entries4.4.1 Basic array slicing4.4.2 Altering an array using slices4.5 Functions to construct arrays4.6 Accessing and changing the shape4.6.1 The function shape4.6.2 Number of dimensions4.6.3 ReshapeTranspose4.7 Stacking4.7.1 Stacking vectors4.8 Functions acting on arrays4.8.1 Universal functionsBuilt-in universal functionsCreation of universal functions4.8.2 Array functions4.9 Linear algebra methods in SciPy4.9.1 Solving several linear equation systems with LU4.9.2 Solving a least square problem with SVD4.9.3 More methods4.10 Summary4.11 Exercises
5.1 Array views and copies5.1.1 Array views5.1.2 Slices as views5.1.3 Generating views by transposing and reshaping5.1.4 Array copies5.2 Comparing arrays5.2.1 Boolean arrays5.2.2 Checking for array equality5.2.3 Boolean operations on arrays5.3 Array indexing5.3.1 Indexing with Boolean arrays5.3.2 Using the command where5.4 Performance and vectorization5.4.1 Vectorization5.5 Broadcasting5.5.1 Mathematical viewsConstant functionsFunctions of several variablesGeneral mechanismConventions5.5.2 Broadcasting arraysThe broadcasting problemShape mismatch5.5.3 Typical examplesRescale rowsRescale columnsFunctions of two variables5.6. Sparse matrices5.6.1 Sparse matrix formatsCompressed sparse row format (CSR)Compressed sparse column format (CSC)Row-based linked list format (LIL)Altering and slicing matrices in LIL format5.6.2 Generating sparse matrices5.6.3 Sparse matrix methods5.7 Summary

6.1 Making plots with basic plotting commands6.1.1 Using the plot command and some of its variants6.1.2 Formatting6.1.3 Working with meshgrid and contours6.1.4 Generating images and contours6.2 Working with Matplotlib objects directly6.2.1 Creating axes objects6.2.2 Modifying line properties6.2.3 Making annotations6.2.4 Filling areas between curves 6.2.5 Defining ticks and tick labels6.2.6 Setting spines makes your plot more instructive – a comprehensive example6.3 Making 3D plots6.4 Making movies from plots6.5 Summary6.6 Exercises
7.1 Functions in mathematics and functions in Python7.2 Parameters and arguments7.2.1 Passing arguments – by position and by keyword7.2.2 Changing arguments7.2.3 Access to variables defined outside the local namespace7.2.4 Default argumentsBeware of mutable default arguments7.2.5 Variable number of arguments7.3 Return values7.4 Recursive functions7.5 Function documentation7.6 Functions are objects7.6.1 Partial application7.6.2 Using closures7.7 Anonymous functions – the keyword lambda7.7.1 The lambda construction is always replaceable7.8 Functions as decorators7.9 Summary7.10 Exercises
8.1 Introduction to classes8.1.1 A guiding example: Rational numbers8.1.2 Defining a class and making an instance8.1.3 The __init__ method8.1.4 Attributes and methods8.1.5 Special methodsReverse operationsMethods mimicking function calls and iterables8.2 Attributes that depend on each other8.2.1 The function property8.3 Bound and unbound methods8.4 Class attributes and class methods8.4.1 Class attributes8.4.2 Class methods8.5 Subclasses and inheritance8.6 Encapsulation8.7 Classes as decorators8.8 Summary8.9 Exercises
9.1 The for statement9.2 Controlling the flow inside the loop9.3 Iterable objects9.3.1 Generators9.3.2 Iterators are disposable9.3.3 Iterator tools9.3.4 Generators of recursive sequences9.3.5 Examples for iterators in mathematicsArithmetic geometric meanConvergence acceleration9.4 List-filling patterns9.4.1 List filling with the append method9.4.2 List from iterators9.4.3 Storing generated values9.5 When iterators behave as lists9.5.1 Generator expressions9.5.2 Zipping iterators9.6 Iterator objects9.7 Infinite iterations9.7.1 The while loop9.7.2 Recursion9.8 Summary9.9 Exercises
10. 1 A guiding example: Solar cells10.2 NumPy arrays and pandas dataframes10.2.1 Indexing rules10.3 Creating and modifying dataframes10.3.1 Creating a dataframe from imported data10.3.2 Setting the index10.3.3 Deleting entries10.3.4 Merging dataframes10.3.5 Missing data in a dataframe10.4 Working with dataframes10.4.1 Plotting from dataframes10.4.2 Calculations within dataframes10.4.3 Grouping data10.5 Summary
11.1 A guiding example to widgets11.1.1 Changing a value with a slider barAn example with two sliders11.2 The button widget and mouse events11.2.1 Updating curve parameters with a button11.2.2 Mouse events and textboxes11.3 Summary
12.1 What are exceptions?12.1.1 Basic principlesRaising exceptionsCatching exceptions12.1.2 User-defined exceptions12.1.3 Context managers – the with statement12.2 Finding errors: debugging12.2.1 Bugs12.2.2 The stack12.2.3 The Python debugger12.2.4 Overview – debug commands12.2.5 Debugging in IPython12.3 Summary
13.1 Namespaces13.2 The scope of a variable13.3 Modules13.3.1 Introduction13.3.2 Modules in IPythonThe IPython magic command – run13.3.3 The variable __name__13.3.4 Some useful modules13.4 Summary
14.1 File handling14.1.1 Interacting with files14.1.2 Files are iterables14.1.3 File modes14.2 NumPy methods14.2.1 savetxt14.2.3 loadtxt14.3 Pickling14.4 Shelves14.5 Reading and writing Matlab data files14.6 Reading and writing images14.7 Summary
15.1 Manual testing15.2 Automatic testing15.2.1 Testing the bisection algorithm15.2.2 Using the unittest module15.2.3 Test setUp and tearDown methodsSetting up testdata when a test case is created15.2.4 Parameterizing tests15.2.5 Assertion tools15.2.6 Float comparisons15.2.7 Unit and functional tests15.2.8 Debugging15.2.9 Test discovery15.3 Measuring execution time15.3.1 Timing with a magic function15.3.2 Timing with the Python module timeit15.3.3 Timing with a context manager15.4 Summary15.5 Exercises
16.1 What are symbolic computations?16.1.1 Elaborating an example in SymPy16.2 Basic elements of SymPy16.2.1 Symbols – the basis of all formulas16.2.2 Numbers16.2.3 FunctionsUndefined functions16.2.4 Elementary functions16.2.5 Lambda functions16.3 Symbolic linear algebra16.3.1 Symbolic matrices16.3.2 Examples for linear algebra methods in SymPy16.4 Substitutions16. 5 Evaluating symbolic expressions16.5.1 Example: A study on the convergence order of Newton's method16.5.2 Converting a symbolic expression into a numeric functionA study on the parameter dependency of polynomial coefficients16.6 Summary
17.1 Running a Python program in a Linux shell17.2 The module sys17.2.1 Command-line arguments17.2.2 Input and output streamsRedirecting streamsBuilding a pipe between a Linux command and a Python script17.3 How to execute Linux commands from Python17.3.1 The modules subprocess and shlexA complete process: subprocess.runCreating processes: subprocess.Popen17.4 Summary
18.1 Multicore computers and computer clusters18.2 Message passing interface (MPI)18.2.1 Prerequisites18.3 Distributing tasks to different cores18.3.1 Information exchange between processes18.3.2 Point-to-point communication18.3.3 Sending NumPy arrays18.3.4 Blocking and non-blocking communication18.3.5 One-to-all and all-to-one communicationPreparing the data for communicationThe commands – scatter and gatherA final data reduction operation – the command reduceSending the same message to allBuffered data18.4 Summary
19.1 Polynomials19.1.1 Theoretical background19.1.2 Tasks19.1.3 The polynomial class19.1.4 Usage examples of the polynomial class19.1.5 Newton polynomial19.2 Spectral clustering19.3 Solving initial value problems19.4 Summary19.5 Exercises
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Content preview from Scientific Computing with Python - Second Edition

Classes

In mathematics, when we write , we refer to a mathematical object for which we know many methods from elementary calculus. For example:

We might want to evaluate at , that is, compute , which returns a real number.
We might want to compute its derivative, which gives us another mathematical object, cos.
We might want to compute the first ...