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  • Book Overview & Buying Scientific Computing with Python 3
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Scientific Computing with Python 3

Scientific Computing with Python 3

By : Claus Führer, Claus Fuhrer, Jan Erik Solem, Olivier Verdier
4 (2)
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Scientific Computing with Python 3

Scientific Computing with Python 3

4 (2)
By: Claus Führer, Claus Fuhrer, Jan Erik Solem, Olivier Verdier
Buy this Book

Overview of this book

Python can be used for more than just general-purpose programming. It is a free, open source language and environment that has tremendous potential for use within the domain of scientific computing. This book presents Python in tight connection with mathematical applications and demonstrates how to use various concepts in Python for computing purposes, including examples with the latest version of Python 3. Python is an effective tool to use when coupling scientific computing and mathematics and this book will teach you how to use it for linear algebra, arrays, plotting, iterating, functions, polynomials, and much more.
Table of Contents (17 chapters)
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Preface
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Preface
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What this book covers
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What you need for this book
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Who this book is for
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Other Python literature
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Conventions
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Reader feedback
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Customer support
Lock Free Chapter
1
1. Getting Started
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1. Getting Started
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Installation and configuration instructions
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Program and program flow
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Basic types
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Repeating statements with loops
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Conditional statements
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Encapsulating code with functions
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Scripts and modules
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Interpreter
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Summary
2
2. Variables and Basic Types
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2. Variables and Basic Types
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Variables
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Numeric types
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Booleans
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Strings
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Summary
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Exercises
3
3. Container Types
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3. Container Types
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Lists
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Arrays
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Tuples
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Dictionaries
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Sets
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Container conversions
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Type checking
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Summary
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Exercises
4
4. Linear Algebra – Arrays
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4. Linear Algebra – Arrays
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Overview of the array type
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Mathematical preliminaries
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The array type
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Accessing array entries
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Functions to construct arrays
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Accessing and changing the shape
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Stacking
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Functions acting on arrays
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Linear algebra methods in SciPy
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Summary
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Exercises
5
5. Advanced Array Concepts
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5. Advanced Array Concepts
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Array views and copies
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Comparing arrays
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Boolean operations on arrays
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Array indexing
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Performance and Vectorization
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Broadcasting
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Sparse matrices
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Summary
6
6. Plotting
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6. Plotting
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Basic plotting
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Formatting
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Meshgrid and contours
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Images and contours
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Matplotlib objects
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Making 3D plots
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Making movies from plots
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Summary
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Exercises
7
7. Functions
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7. Functions
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Basics
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Parameters and arguments
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Variable number of arguments
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Return values
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Recursive functions
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Function documentation
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Functions are objects
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Anonymous functions - the  lambda keyword
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Functions as decorators
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Summary
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Exercises
8
8. Classes
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8. Classes
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Introduction to classes
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Attributes and methods
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Attributes that depend on each other
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Bound and unbound methods
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Class attributes
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Class methods
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Subclassing and inheritance
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Encapsulation
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Classes as decorators
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Summary
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Exercises
9
9. Iterating
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9. Iterating
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The for statement
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Controlling the flow inside the loop
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Iterators
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Convergence acceleration
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List filling patterns
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When iterators behave as lists
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Iterator objects
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Infinite iterations
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Summary
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Exercises
10
10. Error Handling
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10. Error Handling
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What are exceptions?
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Finding Errors: Debugging
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Summary
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11. Namespaces, Scopes, and Modules
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11. Namespaces, Scopes, and Modules
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Namespace
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Scope of a variable
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Modules
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Summary
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12. Input and Output
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12. Input and Output
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File handling
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NumPy methods
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Pickling
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Shelves
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Reading and writing Matlab data files
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Reading and writing images
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Summary
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13. Testing
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13. Testing
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Manual testing
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Automatic testing
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Using unittest package
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Parameterizing tests
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Assertion tools
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Float comparisons
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Unit and functional tests
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Debugging
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Test discovery
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Measuring execution time
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Summary
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Exercises
14
14. Comprehensive Examples
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14. Comprehensive Examples
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Polynomials
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The polynomial class
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Newton polynomial
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Spectral clustering
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Solving initial value problems
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Summary
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Exercises
15
15. Symbolic Computations - SymPy
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15. Symbolic Computations - SymPy
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What are symbolic computations?
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Basic elements of SymPy
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Elementary Functions
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Symbolic Linear Algebra
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Examples for Linear Algebra Methods in SymPy
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Substitutions
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Evaluating symbolic expressions
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Converting a symbolic expression into a numeric function
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Summary
16
References
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References

Convergence acceleration

We give an example of application of generators for convergence acceleration. This presentation follows closely the example given by Pramode C.E in Python Generator Tricks (refer [9] for more information).

Note that a generator may take an other generator as an input parameter. For instance, suppose that we have defined a generator that generates the elements of a converging sequence. It is then possible to improve the convergence by an acceleration technique due to Euler and Aitken, often called Aitken’s Δ2-method (Refer [33]). It transforms a sequence si into another by defining 

Convergence acceleration

Both sequences have the same limit, but the sequence Convergence acceleration  converges significantly faster. One possible implementation is as follows:

def Euler_accelerate(sequence):
    """
    Accelerate the iterator in the variable `sequence`.
    """
    s0 = next(sequence) # Si
    ...
CONTINUE READING
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Tech Concepts
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Programming languages
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Scientific Computing with Python 3
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