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Numpy Beginner's Guide (Update)

By : Ivan Idris

2 (1)

Numpy Beginner's Guide (Update)

2 (1)

By: Ivan Idris

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.

Preface

Preface

What is NumPy?

History

Why use NumPy?

Limitations of NumPy

What this book covers

What you need for this book

Who this book is for

Sections

Time for action – heading

Conventions

Reader feedback

Customer support

Free Chapter

1. NumPy Quick Start

1. NumPy Quick Start

Python

Time for action – installing Python on different operating systems

The Python help system

Time for action – using the Python help system

Basic arithmetic and variable assignment

Time for action – using Python as a calculator

Time for action – assigning values to variables

The print() function

Time for action – printing with the print() function

Code comments

Time for action – commenting code

The if statement

Time for action – deciding with the if statement

The for loop

Time for action – repeating instructions with loops

Python functions

Time for action – defining functions

Python modules

Time for action – importing modules

NumPy on Windows

Time for action – installing NumPy, matplotlib, SciPy, and IPython on Windows

NumPy on Linux

Time for action – installing NumPy, matplotlib, SciPy, and IPython on Linux

NumPy on Mac OS X

Time for action – installing NumPy, SciPy, matplotlib, and IPython with MacPorts or Fink

Building from source

Arrays

Time for action – adding vectors

IPython – an interactive shell

Online resources and help

Summary

2. Beginning with NumPy Fundamentals

2. Beginning with NumPy Fundamentals

NumPy array object

Time for action – creating a multidimensional array

Time for action – creating a record data type

One-dimensional slicing and indexing

Time for action – slicing and indexing multidimensional arrays

Time for action – manipulating array shapes

Time for action – stacking arrays

Time for action – splitting arrays

Time for action – converting arrays

Summary

3. Getting Familiar with Commonly Used Functions

3. Getting Familiar with Commonly Used Functions

File I/O

Time for action – reading and writing files

Comma-seperated value files

Time for action – loading from CSV files

Volume Weighted Average Price

Time for action – calculating Volume Weighted Average Price

Value range

Time for action – finding highest and lowest values

Statistics

Time for action – performing simple statistics

Stock returns

Time for action – analyzing stock returns

Dates

Time for action – dealing with dates

Time for action – using the datetime64 data type

Weekly summary

Time for action – summarizing data

Average True Range

Time for action – calculating the Average True Range

Simple Moving Average

Time for action – computing the Simple Moving Average

Exponential Moving Average

Time for action – calculating the Exponential Moving Average

Bollinger Bands

Time for action – enveloping with Bollinger Bands

Linear model

Time for action – predicting price with a linear model

Trend lines

Time for action – drawing trend lines

Methods of ndarray

Time for action – clipping and compressing arrays

Factorial

Time for action – calculating the factorial

Missing values and Jackknife resampling

Time for action – handling NaNs with the nanmean(), nanvar(), and nanstd() functions

Summary

4. Convenience Functions for Your Convenience

4. Convenience Functions for Your Convenience

Correlation

Time for action – trading correlated pairs

Polynomials

Time for action – fitting to polynomials

On-balance volume

Time for action – balancing volume

Simulation

Time for action – avoiding loops with vectorize()

Smoothing

Time for action – smoothing with the hanning() function

Initialization

Time for action – creating value initialized arrays with the full() and full_like() functions

Summary

5. Working with Matrices and ufuncs

5. Working with Matrices and ufuncs

Matrices

Time for action – creating matrices

Creating a matrix from other matrices

Time for action – creating a matrix from other matrices

Universal functions

Time for action – creating universal functions

Universal function methods

Time for action – applying the ufunc methods to the add function

Arithmetic functions

Time for action – dividing arrays

Modulo operation

Time for action – computing the modulo

Fibonacci numbers

Time for action – computing Fibonacci numbers

Lissajous curves

Time for action – drawing Lissajous curves

Square waves

Time for action – drawing a square wave

Sawtooth and triangle waves

Time for action – drawing sawtooth and triangle waves

Bitwise and comparison functions

Time for action – twiddling bits

Fancy indexing

Time for action – fancy indexing in-place for ufuncs with the at() method

Summary

6. Moving Further with NumPy Modules

6. Moving Further with NumPy Modules

Linear algebra

Time for action – inverting matrices

Solving linear systems

Time for action – solving a linear system

Finding eigenvalues and eigenvectors

Time for action – determining eigenvalues and eigenvectors

Singular value decomposition

Time for action – decomposing a matrix

Pseudo inverse

Time for action – computing the pseudo inverse of a matrix

Determinants

Time for action – calculating the determinant of a matrix

Fast Fourier transform

Time for action – calculating the Fourier transform

Shifting

Time for action – shifting frequencies

Random numbers

Time for action – gambling with the binomial

Hypergeometric distribution

Time for action – simulating a game show

Continuous distributions

Time for action – drawing a normal distribution

Lognormal distribution

Time for action – drawing the lognormal distribution

Bootstrapping in statistics

Time for action – sampling with numpy.random.choice()

Summary

7. Peeking into Special Routines

7. Peeking into Special Routines

Sorting

Time for action – sorting lexically

Time for action – partial sorting via selection for a fast median with the partition() function

Complex numbers

Time for action – sorting complex numbers

Searching

Time for action – using searchsorted

Array elements extraction

Time for action – extracting elements from an array

Financial functions

Time for action – determining the future value

Present value

Time for action – getting the present value

Net present value

Time for action – calculating the net present value

Internal rate of return

Time for action – determining the internal rate of return

Periodic payments

Time for action – calculating the periodic payments

Number of payments

Time for action – determining the number of periodic payments

Interest rate

Time for action – figuring out the rate

Window functions

Time for action – plotting the Bartlett window

Blackman window

Time for action – smoothing stock prices with the Blackman window

Hamming window

Time for action – plotting the Hamming window

Kaiser window

Time for action – plotting the Kaiser window

Special mathematical functions

Time for action – plotting the modified Bessel function

sinc

Time for action – plotting the sinc function

Summary

8. Assuring Quality with Testing

8. Assuring Quality with Testing

Assert functions

Time for action – asserting almost equal

Approximately equal arrays

Time for action – asserting approximately equal

Almost equal arrays

Time for action – asserting arrays almost equal

Equal arrays

Time for action – comparing arrays

Ordering arrays

Time for action – checking the array order

Object comparison

Time for action – comparing objects

String comparison

Time for action – comparing strings

Floating-point comparisons

Time for action – comparing with assert_array_almost_equal_nulp

Comparison of floats with more ULPs

Time for action – comparing using maxulp of 2

Unit tests

Time for action – writing a unit test

Nose test decorators

Time for action – decorating tests

Docstrings

Time for action – executing doctests

Summary

9. Plotting with matplotlib

9. Plotting with matplotlib

Simple plots

Time for action – plotting a polynomial function

Plot format string

Time for action – plotting a polynomial and its derivatives

Subplots

Time for action – plotting a polynomial and its derivatives

Finance

Time for action – plotting a year's worth of stock quotes

Histograms

Time for action – charting stock price distributions

Logarithmic plots

Time for action – plotting stock volume

Scatter plots

Time for action – plotting price and volume returns with a scatter plot

Fill between

Time for action – shading plot regions based on a condition

Legend and annotations

Time for action – using a legend and annotations

Three-dimensional plots

Time for action – plotting in three dimensions

Contour plots

Time for action – drawing a filled contour plot

Animation

Time for action – animating plots

Summary

10. When NumPy Is Not Enough – SciPy and Beyond

10. When NumPy Is Not Enough – SciPy and Beyond

MATLAB and Octave

Time for action – saving and loading a .mat file

Statistics

Time for action – analyzing random values

Sample comparison and SciKits

Time for action – comparing stock log returns

Signal processing

Time for action – detecting a trend in QQQ

Fourier analysis

Time for action – filtering a detrended signal

Mathematical optimization

Time for action – fitting to a sine

Numerical integration

Time for action – calculating the Gaussian integral

Interpolation

Time for action – interpolating in one dimension

Image processing

Time for action – manipulating Lena

Audio processing

Time for action – replaying audio clips

Summary

11. Playing with Pygame

11. Playing with Pygame

Pygame

Time for action – installing Pygame

Hello World

Time for action – creating a simple game

Animation

Time for action – animating objects with NumPy and Pygame

matplotlib

Time for Action – using matplotlib in Pygame

Surface pixels

Time for Action – accessing surface pixel data with NumPy

Artificial Intelligence

Time for Action – clustering points

OpenGL and Pygame

Time for Action – drawing the Sierpinski gasket

Simulation game with Pygame

Time for Action – simulating life

Summary

A. Pop Quiz Answers

Chapter 1, NumPy Quick Start

Chapter 2, Beginning with NumPy Fundamentals

Chapter 3, Getting Familiar with Commonly Used Functions

Chapter 4, Convenience Functions for Your Convenience

Chapter 5, Working with Matrices and ufuncs

Chapter 6, Move Further with NumPy Modules

Chapter 7, Peeking into Special Routines

Chapter 8, Assuring Quality with Testing

Chapter 9, Plotting with matplotlib

Chapter 10, When NumPy Is Not Enough –Scipy and Beyond

B. Additional Online Resources

B. Additional Online Resources

Python

Mathematics and statistics

C. NumPy Functions' References

C. NumPy Functions' References

Index

Index

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Time for action – fitting to a sine

In the previous Time for action section, we created a simple filter for detrended data. Now, let's use a more restrictive filter that will leave us only with the main frequency component. We will fit a sinusoidal pattern to it and plot our results. This model has four parameters—amplitude, frequency, phase, and vertical offset.

Define a residuals function based on a sine wave model:

def residuals(p, y, x):
   A,k,theta,b = p
   err = y-A * np.sin(2* np.pi* k * x + theta) + b
   return err

Transform the filtered signal back to the original domain:
```
filtered = -fftpack.irfft(fftpack.ifftshift(amps))
```
Guess the values of the parameters of which we are trying to estimate a transformation from the time domain into the frequency domain:
```
N = len(qqq)
f = np.linspace(-N/2, N/2, N)
p0 = [filtered.max(), f[amps.argmax()]/(2*N), 0, 0]
print("P0", p0)
```
The initial values appear as follows:
```
P0 [2.6679532410065212, 0.00099598469163686377, 0, 0]
```
Call...

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