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Scipy Tutorial(Scipy教程).pdf
I Getting started with Python for science
Python scientific computing ecosystem
Why Python?
The Scientific Python ecosystem
Before starting: Installing a working environment
The workflow: interactive environments and text editors
The Python language
First steps
Basic types
Control Flow
Defining functions
Reusing code: scripts and modules
Input and Output
Standard Library
Exception handling in Python
Object-oriented programming (OOP)
NumPy: creating and manipulating numerical data
The NumPy array object
Numerical operations on arrays
More elaborate arrays
Advanced operations
Some exercises
Full code examples
Matplotlib: plotting
Introduction
Simple plot
Figures, Subplots, Axes and Ticks
Other Types of Plots: examples and exercises
Beyond this tutorial
Quick references
Full code examples
Scipy : high-level scientific computing
File input/output: scipy.io
Special functions: scipy.special
Linear algebra operations: scipy.linalg
Interpolation: scipy.interpolate
Optimization and fit: scipy.optimize
Statistics and random numbers: scipy.stats
Numerical integration: scipy.integrate
Fast Fourier transforms: scipy.fftpack
Signal processing: scipy.signal
Image manipulation: scipy.ndimage
Summary exercises on scientific computing
Full code examples for the scipy chapter
Getting help and finding documentation
II Advanced topics
Advanced Python Constructs
Iterators, generator expressions and generators
Decorators
Context managers
Advanced NumPy
Life of ndarray
Universal functions
Interoperability features
Array siblings: chararray, maskedarray, matrix
Summary
Contributing to NumPy/Scipy
Debugging code
Avoiding bugs
Debugging workflow
Using the Python debugger
Debugging segmentation faults using gdb
Optimizing code
Optimization workflow
Profiling Python code
Making code go faster
Writing faster numerical code
Sparse Matrices in SciPy
Introduction
Storage Schemes
Linear System Solvers
Other Interesting Packages
Image manipulation and processing using Numpy and Scipy
Opening and writing to image files
Displaying images
Basic manipulations
Image filtering
Feature extraction
Measuring objects properties: ndimage.measurements
Full code examples
Examples for the image processing chapter
Mathematical optimization: finding minima of functions
Knowing your problem
A review of the different optimizers
Full code examples
Examples for the mathematical optimization chapter
Practical guide to optimization with scipy
Special case: non-linear least-squares
Optimization with constraints
Full code examples
Examples for the mathematical optimization chapter
Interfacing with C
Introduction
Python-C-Api
Ctypes
SWIG
Cython
Summary
Further Reading and References
Exercises
III Packages and applications
Statistics in Python
Data representation and interaction
Hypothesis testing: comparing two groups
Linear models, multiple factors, and analysis of variance
More visualization: seaborn for statistical exploration
Testing for interactions
Full code for the figures
Solutions to this chapter’s exercises
Sympy : Symbolic Mathematics in Python
First Steps with SymPy
Algebraic manipulations
Calculus
Equation solving
Linear Algebra
Scikit-image: image processing
Introduction and concepts
Input/output, data types and colorspaces
Image preprocessing / enhancement
Image segmentation
Measuring regions’ properties
Data visualization and interaction
Feature extraction for computer vision
Full code examples
Examples for the scikit-image chapter
Traits: building interactive dialogs
Introduction
Example
What are Traits
3D plotting with Mayavi
Mlab: the scripting interface
Interactive work
Slicing and dicing data: sources, modules and filters
Animating the data
Making interactive dialogs
Putting it together
scikit-learn: machine learning in Python
Introduction: problem settings
Basic principles of machine learning with scikit-learn
Supervised Learning: Classification of Handwritten Digits
Supervised Learning: Regression of Housing Data
Measuring prediction performance
Unsupervised Learning: Dimensionality Reduction and Visualization
The eigenfaces example: chaining PCA and SVMs
Parameter selection, Validation, and Testing
Examples for the scikit-learn chapter
Index
PythonMatplotlibSciKitsNumpySciPyIPythonIP[y]:Cython2017EDITIONEdited byGaël VaroquauxEmmanuelle GouillartOlaf VahtrasScipyLecture Noteswww.scipy-lectures.orgGaël Varoquaux • Emmanuelle Gouillart • Olav VahtrasChristopher Burns • Adrian Chauve • Robert Cimrman • Christophe Combelles Pierre de Buyl • Ralf Gommers • André Espaze • Zbigniew Jędrzejewski-Szmek Valentin Haenel • Gert-Ludwig Ingold • Fabian Pedregosa • Didrik Pinte Nicolas P. Rougier • Pauli Virtanen and many others...
Contents
I Getting started with Python for science
1 Python scientific computing ecosystem
1.1 Why Python?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Scientific Python ecosystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Before starting: Installing a working environment
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 The workflow: interactive environments and text editors . . . . . . . . . . . . . . . . . . . . . . . .
2
4
4
6
8
8
2 The Python language
12
First steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Basic types
2.3 Control Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Defining functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Reusing code: scripts and modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6
Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.7
Standard Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.8 Exception handling in Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.9 Object-oriented programming (OOP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3 NumPy: creating and manipulating numerical data
47
3.1 The NumPy array object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Numerical operations on arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 More elaborate arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Advanced operations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Some exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.5
3.6
Full code examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Matplotlib: plotting
97
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1
Simple plot
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.2
4.3
Figures, Subplots, Axes and Ticks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4 Other Types of Plots: examples and exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.5 Beyond this tutorial
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6 Quick references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.7
Full code examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5 Scipy : high-level scientific computing
184
File input/output: scipy.io . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Special functions: scipy.special . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Linear algebra operations: scipy.linalg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.1
5.2
5.3
i
Interpolation: scipy.interpolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.4
5.5 Optimization and fit: scipy.optimize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Statistics and random numbers: scipy.stats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5.6
5.7 Numerical integration: scipy.integrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Fast Fourier transforms: scipy.fftpack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.8
Signal processing: scipy.signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.9
5.10 Image manipulation: scipy.ndimage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.11 Summary exercises on scientific computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
5.12 Full code examples for the scipy chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
6 Getting help and finding documentation
II Advanced topics
259
262
7 Advanced Python Constructs
264
Iterators, generator expressions and generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
7.1
7.2 Decorators
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
7.3 Context managers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
8 Advanced NumPy
281
8.1
Life of ndarray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8.2 Universal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
8.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
8.4 Array siblings: chararray, maskedarray, matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
8.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
8.6 Contributing to NumPy/Scipy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
Interoperability features
9 Debugging code
314
9.1 Avoiding bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
9.2 Debugging workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
9.3 Using the Python debugger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
9.4 Debugging segmentation faults using gdb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
10 Optimizing code
325
10.1 Optimization workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
10.2 Profiling Python code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
10.3 Making code go faster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
10.4 Writing faster numerical code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
11 Sparse Matrices in SciPy
332
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
11.2 Storage Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
11.3 Linear System Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
11.4 Other Interesting Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
12 Image manipulation and processing using Numpy and Scipy
352
12.1 Opening and writing to image files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
12.2 Displaying images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
12.3 Basic manipulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
12.4 Image filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
12.5 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
12.6 Measuring objects properties: ndimage.measurements . . . . . . . . . . . . . . . . . . . . . . . . 366
12.7 Full code examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
12.8 Examples for the image processing chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
13 Mathematical optimization: finding minima of functions
397
13.1 Knowing your problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
13.2 A review of the different optimizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
13.3 Full code examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
13.4 Examples for the mathematical optimization chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 406
ii
13.5 Practical guide to optimization with scipy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
13.6 Special case: non-linear least-squares
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
13.7 Optimization with constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
13.8 Full code examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
13.9 Examples for the mathematical optimization chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 438
14 Interfacing with C
439
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
14.2 Python-C-Api . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
14.3 Ctypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
14.4 SWIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
14.5 Cython . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
14.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
14.7 Further Reading and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
14.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
III Packages and applications
460
15 Statistics in Python
462
15.1 Data representation and interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
15.2 Hypothesis testing: comparing two groups
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
15.3 Linear models, multiple factors, and analysis of variance . . . . . . . . . . . . . . . . . . . . . . . . 471
15.4 More visualization: seaborn for statistical exploration . . . . . . . . . . . . . . . . . . . . . . . . . . 476
15.5 Testing for interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
15.6 Full code for the figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
15.7 Solutions to this chapter’s exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
16 Sympy : Symbolic Mathematics in Python
505
16.1 First Steps with SymPy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
16.2 Algebraic manipulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
16.3 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
16.4 Equation solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510
16.5 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
17 Scikit-image: image processing
513
17.1 Introduction and concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
17.2 Input/output, data types and colorspaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
17.3 Image preprocessing / enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
17.4 Image segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
17.5 Measuring regions’ properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
17.6 Data visualization and interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
17.7 Feature extraction for computer vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
17.8 Full code examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
17.9 Examples for the scikit-image chapter
18 Traits: building interactive dialogs
538
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
18.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
18.3 What are Traits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
19 3D plotting with Mayavi
557
19.1 Mlab: the scripting interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
19.2 Interactive work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564
19.3 Slicing and dicing data: sources, modules and filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
19.4 Animating the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568
19.5 Making interactive dialogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
19.6 Putting it together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
20 scikit-learn: machine learning in Python
572
iii
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
20.1 Introduction: problem settings
20.2 Basic principles of machine learning with scikit-learn . . . . . . . . . . . . . . . . . . . . . . . . . . 577
20.3 Supervised Learning: Classification of Handwritten Digits . . . . . . . . . . . . . . . . . . . . . . . 582
20.4 Supervised Learning: Regression of Housing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
20.5 Measuring prediction performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589
20.6 Unsupervised Learning: Dimensionality Reduction and Visualization . . . . . . . . . . . . . . . . 594
20.7 The eigenfaces example: chaining PCA and SVMs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 597
20.8 Parameter selection, Validation, and Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603
20.9 Examples for the scikit-learn chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
Index
652
iv
Scipy lecture notes, Edition 2017.1
Contents
1
Part I
Getting started with Python for science
2
This part of the Scipy lecture notes is a self-contained introduction to everything that is needed to use Python
for science, from the language itself, to numerical computing or plotting.
Scipy lecture notes, Edition 2017.1
3
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