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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

By : Ivan Idris
2 (1)
Buy this Book
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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

2 (1)
By: Ivan Idris
Buy this Book

Overview of this book

This book is for the scientists, engineers, programmers, or analysts looking for a high-quality, open source mathematical library. Knowledge of Python is assumed. Also, some affinity, or at least interest, in mathematics and statistics is required. However, I have provided brief explanations and pointers to learning resources.
Table of Contents (16 chapters)
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Preface
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Preface
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What is NumPy?
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History
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Why use NumPy?
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Limitations of NumPy
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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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Sections
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Time for action – heading
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Conventions
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Reader feedback
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Customer support
Free Chapter
1
1. NumPy Quick Start
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1. NumPy Quick Start
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Python
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Time for action – installing Python on different operating systems
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The Python help system
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Time for action – using the Python help system
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Basic arithmetic and variable assignment
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Time for action – using Python as a calculator
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Time for action – assigning values to variables
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The print() function
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Time for action – printing with the print() function
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Code comments
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Time for action – commenting code
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The if statement
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Time for action – deciding with the if statement
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The for loop
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Time for action – repeating instructions with loops
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Python functions
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Time for action – defining functions
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Python modules
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Time for action – importing modules
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NumPy on Windows
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Time for action – installing NumPy, matplotlib, SciPy, and IPython on Windows
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NumPy on Linux
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Time for action – installing NumPy, matplotlib, SciPy, and IPython on Linux
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NumPy on Mac OS X
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Time for action – installing NumPy, SciPy, matplotlib, and IPython with MacPorts or Fink
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Building from source
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Arrays
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Time for action – adding vectors
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IPython – an interactive shell
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Online resources and help
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Summary
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2. Beginning with NumPy Fundamentals
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2. Beginning with NumPy Fundamentals
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NumPy array object
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Time for action – creating a multidimensional array
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Time for action – creating a record data type
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One-dimensional slicing and indexing
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Time for action – slicing and indexing multidimensional arrays
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Time for action – manipulating array shapes
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Time for action – stacking arrays
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Time for action – splitting arrays
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Time for action – converting arrays
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Summary
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3. Getting Familiar with Commonly Used Functions
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3. Getting Familiar with Commonly Used Functions
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File I/O
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Time for action – reading and writing files
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Comma-seperated value files
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Time for action – loading from CSV files
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Volume Weighted Average Price
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Time for action – calculating Volume Weighted Average Price
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Value range
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Time for action – finding highest and lowest values
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Statistics
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Time for action – performing simple statistics
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Stock returns
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Time for action – analyzing stock returns
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Dates
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Time for action – dealing with dates
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Time for action – using the datetime64 data type
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Weekly summary
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Time for action – summarizing data
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Average True Range
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Time for action – calculating the Average True Range
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Simple Moving Average
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Time for action – computing the Simple Moving Average
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Exponential Moving Average
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Time for action – calculating the Exponential Moving Average
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Bollinger Bands
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Time for action – enveloping with Bollinger Bands
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Linear model
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Time for action – predicting price with a linear model
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Trend lines
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Time for action – drawing trend lines
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Methods of ndarray
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Time for action – clipping and compressing arrays
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Factorial
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Time for action – calculating the factorial
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Missing values and Jackknife resampling
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Time for action – handling NaNs with the nanmean(), nanvar(), and nanstd() functions
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Summary
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4. Convenience Functions for Your Convenience
chevron up
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4. Convenience Functions for Your Convenience
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Correlation
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Time for action – trading correlated pairs
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Polynomials
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Time for action – fitting to polynomials
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On-balance volume
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Time for action – balancing volume
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Simulation
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Time for action – avoiding loops with vectorize()
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Smoothing
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Time for action – smoothing with the hanning() function
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Initialization
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Time for action – creating value initialized arrays with the full() and full_like() functions
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Summary
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5. Working with Matrices and ufuncs
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5. Working with Matrices and ufuncs
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Matrices
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Time for action – creating matrices
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Creating a matrix from other matrices
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Time for action – creating a matrix from other matrices
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Universal functions
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Time for action – creating universal functions
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Universal function methods
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Time for action – applying the ufunc methods to the add function
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Arithmetic functions
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Time for action – dividing arrays
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Modulo operation
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Time for action – computing the modulo
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Fibonacci numbers
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Time for action – computing Fibonacci numbers
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Lissajous curves
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Time for action – drawing Lissajous curves
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Square waves
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Time for action – drawing a square wave
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Sawtooth and triangle waves
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Time for action – drawing sawtooth and triangle waves
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Bitwise and comparison functions
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Time for action – twiddling bits
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Fancy indexing
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Time for action – fancy indexing in-place for ufuncs with the at() method
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Summary
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6. Moving Further with NumPy Modules
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6. Moving Further with NumPy Modules
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Linear algebra
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Time for action – inverting matrices
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Solving linear systems
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Time for action – solving a linear system
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Finding eigenvalues and eigenvectors
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Time for action – determining eigenvalues and eigenvectors
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Singular value decomposition
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Time for action – decomposing a matrix
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Pseudo inverse
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Time for action – computing the pseudo inverse of a matrix
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Determinants
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Time for action – calculating the determinant of a matrix
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Fast Fourier transform
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Time for action – calculating the Fourier transform
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Shifting
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Time for action – shifting frequencies
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Random numbers
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Time for action – gambling with the binomial
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Hypergeometric distribution
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Time for action – simulating a game show
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Continuous distributions
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Time for action – drawing a normal distribution
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Lognormal distribution
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Time for action – drawing the lognormal distribution
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Bootstrapping in statistics
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Time for action – sampling with numpy.random.choice()
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Summary
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7. Peeking into Special Routines
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7. Peeking into Special Routines
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Sorting
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Time for action – sorting lexically
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Time for action – partial sorting via selection for a fast median with the partition() function
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Complex numbers
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Time for action – sorting complex numbers
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Searching
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Time for action – using searchsorted
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Array elements extraction
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Time for action – extracting elements from an array
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Financial functions
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Time for action – determining the future value
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Present value
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Time for action – getting the present value
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Net present value
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Time for action – calculating the net present value
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Internal rate of return
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Time for action – determining the internal rate of return
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Periodic payments
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Time for action – calculating the periodic payments
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Number of payments
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Time for action – determining the number of periodic payments
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Interest rate
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Time for action – figuring out the rate
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Window functions
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Time for action – plotting the Bartlett window
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Blackman window
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Time for action – smoothing stock prices with the Blackman window
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Hamming window
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Time for action – plotting the Hamming window
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Kaiser window
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Time for action – plotting the Kaiser window
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Special mathematical functions
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Time for action – plotting the modified Bessel function
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sinc
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Time for action – plotting the sinc function
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Summary
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8. Assuring Quality with Testing
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8. Assuring Quality with Testing
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Assert functions
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Time for action – asserting almost equal
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Approximately equal arrays
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Time for action – asserting approximately equal
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Almost equal arrays
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Time for action – asserting arrays almost equal
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Equal arrays
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Time for action – comparing arrays
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Ordering arrays
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Time for action – checking the array order
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Object comparison
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Time for action – comparing objects
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String comparison
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Time for action – comparing strings
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Floating-point comparisons
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Time for action – comparing with assert_array_almost_equal_nulp
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Comparison of floats with more ULPs
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Time for action – comparing using maxulp of 2
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Unit tests
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Time for action – writing a unit test
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Nose test decorators
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Time for action – decorating tests
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Docstrings
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Time for action – executing doctests
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Summary
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9. Plotting with matplotlib
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9. Plotting with matplotlib
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Simple plots
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Time for action – plotting a polynomial function
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Plot format string
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Time for action – plotting a polynomial and its derivatives
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Subplots
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Time for action – plotting a polynomial and its derivatives
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Finance
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Time for action – plotting a year's worth of stock quotes
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Histograms
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Time for action – charting stock price distributions
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Logarithmic plots
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Time for action – plotting stock volume
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Scatter plots
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Time for action – plotting price and volume returns with a scatter plot
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Fill between
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Time for action – shading plot regions based on a condition
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Legend and annotations
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Time for action – using a legend and annotations
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Three-dimensional plots
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Time for action – plotting in three dimensions
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Contour plots
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Time for action – drawing a filled contour plot
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Animation
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Time for action – animating plots
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Summary
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10. When NumPy Is Not Enough – SciPy and Beyond
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10. When NumPy Is Not Enough – SciPy and Beyond
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MATLAB and Octave
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Time for action – saving and loading a .mat file
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Statistics
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Time for action – analyzing random values
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Sample comparison and SciKits
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Time for action – comparing stock log returns
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Signal processing
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Time for action – detecting a trend in QQQ
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Fourier analysis
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Time for action – filtering a detrended signal
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Mathematical optimization
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Time for action – fitting to a sine
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Numerical integration
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Time for action – calculating the Gaussian integral
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Interpolation
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Time for action – interpolating in one dimension
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Image processing
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Time for action – manipulating Lena
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Audio processing
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Time for action – replaying audio clips
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Summary
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11. Playing with Pygame
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11. Playing with Pygame
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Pygame
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Time for action – installing Pygame
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Hello World
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Time for action – creating a simple game
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Animation
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Time for action – animating objects with NumPy and Pygame
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matplotlib
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Time for Action – using matplotlib in Pygame
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Surface pixels
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Time for Action – accessing surface pixel data with NumPy
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Artificial Intelligence
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Time for Action – clustering points
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OpenGL and Pygame
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Time for Action – drawing the Sierpinski gasket
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Simulation game with Pygame
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Time for Action – simulating life
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Summary
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A. Pop Quiz Answers
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Chapter 1, NumPy Quick Start
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Chapter 2, Beginning with NumPy Fundamentals
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Chapter 3, Getting Familiar with Commonly Used Functions
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Chapter 4, Convenience Functions for Your Convenience
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Chapter 5, Working with Matrices and ufuncs
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Chapter 6, Move Further with NumPy Modules
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Chapter 7, Peeking into Special Routines
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Chapter 8, Assuring Quality with Testing
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Chapter 9, Plotting with matplotlib
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Chapter 10, When NumPy Is Not Enough –Scipy and Beyond
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B. Additional Online Resources
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B. Additional Online Resources
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Python
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Mathematics and statistics
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C. NumPy Functions' References
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C. NumPy Functions' References
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Index
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Index

Polynomials

Do you like calculus? Well I love it! One of the ideas in calculus is Taylor expansion, that is, representing a differentiable function as an infinite series (see https://www.khanacademy.org/math/integral-calculus/sequences_series_approx_calc/taylor-series/v/generalized-taylor-series-approximation and http://en.wikipedia.org/wiki/Taylor_series.).

Note

The Taylor series is defined as the following sum:

Polynomials
Polynomials

in this definition is the nth derivative of the function f computed at the point a.

In practice, this means that we can estimate any differentiable, and therefore continuous, function with a polynomial of a high degree. We would then assume that the terms of the higher degrees are negligibly small.

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