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• Scipy lecture notes
• ¶
• One document to learn numerics, science, and data with Python
• PDF, 2 pages per side
• PDF, 1 page per side
• Authors
• What’s new
• License
• Contributing
• 1. Getting started with Python for science
• 1.1. Python scientific computing ecosystem
• 1.1.1. Why Python?
• 1.1.1.1. The scientist’s needs
• 1.1.1.2. Python’s strengths
• 1.1.1.3. How does Python compare to other solutions?
• Compiled languages: C, C++, Fortran…
• Matlab scripting language
• Julia
• Other scripting languages: Scilab, Octave, R, IDL, etc.
• Python
• 1.1.2. The Scientific Python ecosystem
• 1.1.3. Before starting: Installing a working environment
• 1.1.4. The workflow: interactive environments and text editors
• 1.1.4.1. Interactive work
• 1.1.4.2. Elaboration of the work in an editor
• 1.1.4.3. IPython and Jupyter Tips and Tricks
• 1.2. The Python language
• 1.2.1. First steps
• 1.2.2. Basic types
• 1.2.2.1. Numerical types
• 1.2.2.2. Containers
• Lists
• Strings
• Dictionaries
• More container types
• 1.2.2.3. Assignment operator
• 1.2.3. Control Flow
• 1.2.3.1. if/elif/else
• 1.2.3.2. for/range
• 1.2.3.3. while/break/continue
• 1.2.3.4. Conditional Expressions
• 1.2.3.5. Advanced iteration
• Iterate over any
• Keeping track of enumeration number
• Looping over a dictionary
• 1.2.3.6. List Comprehensions
• 1.2.4. Defining functions
• 1.2.4.1. Function definition
• 1.2.4.2. Return statement
• 1.2.4.3. Parameters
• 1.2.4.4. Passing by value
• 1.2.4.5. Global variables
• 1.2.4.6. Variable number of parameters
• 1.2.4.7. Docstrings
• 1.2.4.8. Functions are objects
• 1.2.4.9. Methods
• 1.2.4.10. Exercises
• 1.2.5. Reusing code: scripts and modules
• 1.2.5.1. Scripts
• 1.2.5.2. Importing objects from modules
• 1.2.5.3. Creating modules
• 1.2.5.4. ‘__main__’ and module loading
• 1.2.5.5. Scripts or modules? How to organize your code
• How modules are found and imported
• 1.2.5.6. Packages
• 1.2.5.7. Good practices
• 1.2.6. Input and Output
• 1.2.6.1. Iterating over a file
• File modes
• 1.2.7. Standard Library
• 1.2.7.1.
• Directory and file manipulation
• http://scipy-lectures.org/intro/language/standard_library.html#os-path-path-manipulations
• Running an external command
• Walking a directory
• Environment variables:
• 1.2.7.2.
• 1.2.7.3.
• 1.2.7.4.
• 1.2.7.5.
• 1.2.8. Exception handling in Python
• 1.2.8.1. Exceptions
• 1.2.8.2. Catching exceptions
• try/except
• try/finally
• Easier to ask for forgiveness than for permission
• 1.2.8.3. Raising exceptions
• 1.2.9. Object-oriented programming (OOP)
• 1.3. Python 2 and Python 3
• 1.3.1. A very short summary
• 1.3.2. Breaking changes between Python 2 and Python 3
• 1.3.2.1. Print function
• 1.3.2.2. Division
• 1.3.3. Some new features in Python 3
• 1.4. NumPy: creating and manipulating numerical data
• 1.4.1. The NumPy array object
• 1.4.1.1. What are NumPy and NumPy arrays?
• NumPy arrays
• NumPy Reference documentation
• Import conventions
• 1.4.1.2. Creating arrays
• Manual construction of arrays
• Functions for creating arrays
• 1.4.1.3. Basic data types
• 1.4.1.4. Basic visualization
• 1.4.1.5. Indexing and slicing
• 1.4.1.6. Copies and views
• 1.4.1.7. Fancy indexing
• Using boolean masks
• Indexing with an array of integers
• 1.4.2. Numerical operations on arrays
• 1.4.2.1. Elementwise operations
• Basic operations
• Other operations
• 1.4.2.2. Basic reductions
• Computing sums
• Other reductions
• 1.4.2.3. Broadcasting
• 1.4.2.4. Array shape manipulation
• Flattening
• Reshaping
• Adding a dimension
• Dimension shuffling
• Resizing
• 1.4.2.5. Sorting data
• 1.4.2.6. Summary
• 1.4.3. More elaborate arrays
• 1.4.3.1. More data types
• Casting
• Different data type sizes
• 1.4.3.2. Structured data types
• 1.4.3.3.
• 1.4.4. Advanced operations
• 1.4.4.1. Polynomials
• More polynomials (with more bases)
• 1.4.4.2. Loading data files
• Text files
• Images
• NumPy’s own format
• Well-known (& more obscure) file formats
• 1.4.5. Some exercises
• 1.4.5.1. Array manipulations
• 1.4.5.2. Picture manipulation: Framing a Face
• 1.4.5.3. Data statistics
• 1.4.5.4. Crude integral approximations
• 1.4.5.5. Mandelbrot set
• 1.4.5.6. Markov chain
• 1.4.6. Full code examples
• 1.4.6.1. Full code examples for the numpy chapter
• 1.5. Matplotlib: plotting
• 1.5.1. Introduction
• 1.5.1.1. IPython, Jupyter, and matplotlib modes
• 1.5.1.2. pyplot
• 1.5.2. Simple plot
• 1.5.2.1. Plotting with default settings
• 1.5.2.2. Instantiating defaults
• 1.5.2.3. Changing colors and line widths
• 1.5.2.4. Setting limits
• 1.5.2.5. Setting ticks
• 1.5.2.6. Setting tick labels
• 1.5.2.7. Moving spines
• 1.5.2.8. Adding a legend
• 1.5.2.9. Annotate some points
• 1.5.2.10. Devil is in the details
• 1.5.3. Figures, Subplots, Axes and Ticks
• 1.5.3.1. Figures
• 1.5.3.2. Subplots
• 1.5.3.3. Axes
• 1.5.3.4. Ticks
• Tick Locators
• 1.5.4. Other Types of Plots: examples and exercises
• 1.5.4.1. Regular Plots
• 1.5.4.2. Scatter Plots
• 1.5.4.3. Bar Plots
• 1.5.4.4. Contour Plots
• 1.5.4.5. Imshow
• 1.5.4.6. Pie Charts
• 1.5.4.7. Quiver Plots
• 1.5.4.8. Grids
• 1.5.4.9. Multi Plots
• 1.5.4.10. Polar Axis
• 1.5.4.11. 3D Plots
• 1.5.4.12. Text
• 1.5.5. Beyond this tutorial
• 1.5.5.1. Tutorials
• 1.5.5.2. Matplotlib documentation
• 1.5.5.3. Code documentation
• 1.5.5.4. Galleries
• 1.5.5.5. Mailing lists
• 1.5.6. Quick references
• 1.5.6.1. Line properties
• 1.5.6.2. Line styles
• 1.5.6.3. Markers
• 1.5.6.4. Colormaps
• 1.5.7. Full code examples
• 1.5.7.1. Code samples for Matplotlib
• 1.5.7.2. Code for the chapter’s exercises
• 1.5.7.3. Example demoing choices for an option
• 1.5.7.4. Code generating the summary figures with a title
• 1.6. Scipy : high-level scientific computing
• 1.6.1. File input/output:
• 1.6.2. Special functions:
• 1.6.3. Linear algebra operations:
• 1.6.4. Interpolation:
• 1.6.5. Optimization and fit:
• 1.6.5.1. Curve fitting
• 1.6.5.2. Finding the minimum of a scalar function
• 1.6.5.3. Finding the roots of a scalar function
• 1.6.6. Statistics and random numbers:
• 1.6.6.1. Distributions: histogram and probability density function
• 1.6.6.2. Mean, median and percentiles
• 1.6.6.3. Statistical tests
• 1.6.7. Numerical integration:
• 1.6.7.1. Function integrals
• 1.6.7.2. Integrating differential equations
• 1.6.8. Fast Fourier transforms:
• 1.6.9. Signal processing:
• 1.6.10. Image manipulation:
• 1.6.10.1. Geometrical transformations on images
• 1.6.10.2. Image filtering
• 1.6.10.3. Mathematical morphology
• 1.6.10.4. Connected components and measurements on images
• 1.6.11. Summary exercises on scientific computing
• 1.6.11.1. Maximum wind speed prediction at the Sprogø station
• Statistical approach
• Computing the cumulative probabilities
• Prediction with UnivariateSpline
• Exercise with the Gumbell distribution
• 1.6.11.2. Non linear least squares curve fitting: application to point extraction in topographical lidar data
• Introduction
• Loading and visualization
• Fitting a waveform with a simple Gaussian model
• Model
• Initial solution
• Fit
• Going further
• 1.6.11.3. Image processing application: counting bubbles and unmolten grains
• Statement of the problem
• 1.6.11.4. Example of solution for the image processing exercise: unmolten grains in glass
• 1.6.12. Full code examples for the scipy chapter
• 1.6.12.18. Solutions of the exercises for scipy
• 1.7. Getting help and finding documentation
• 2. Advanced topics
• 2.1. Advanced Python Constructs
• 2.1.1. Iterators, generator expressions and generators
• 2.1.1.1. Iterators
• 2.1.1.2. Generator expressions
• 2.1.1.3. Generators
• 2.1.1.4. Bidirectional communication
• 2.1.1.5. Chaining generators
• 2.1.2. Decorators
• 2.1.2.1. Replacing or tweaking the original object
• 2.1.2.2. Decorators implemented as classes and as functions
• 2.1.2.3. Copying the docstring and other attributes of the original function
• 2.1.2.4. Examples in the standard library
• 2.1.2.5. Deprecation of functions
• 2.1.2.6. A
• 2.1.2.7. A plugin registration system
• 2.1.3. Context managers
• 2.1.3.1. Catching exceptions
• 2.1.3.2. Using generators to define context managers
• 2.2. Advanced NumPy
• 2.2.1. Life of ndarray
• 2.2.1.1. It’s…
• 2.2.1.2. Block of memory
• 2.2.1.3. Data types
• The descriptor
• Example: reading
• Casting and re-interpretation/views
• Casting
• Re-interpretation / viewing
• 2.2.1.4. Indexing scheme: strides
• Main point
• C and Fortran order
• Slicing with integers
• Example: fake dimensions with strides
• Broadcasting
• More tricks: diagonals
• CPU cache effects
• 2.2.1.5. Findings in dissection
• 2.2.2. Universal functions
• 2.2.2.1. What they are?
• Parts of an Ufunc
• Making it easier
• 2.2.2.2. Exercise: building an ufunc from scratch
• 2.2.2.3. Solution: building an ufunc from scratch
• 2.2.2.4. Generalized ufuncs
• 2.2.3. Interoperability features
• 2.2.3.1. Sharing multidimensional, typed data
• 2.2.3.2. The old buffer protocol
• 2.2.3.3. The old buffer protocol
• 2.2.3.4. Array interface protocol
• 2.2.4. Array siblings:
• 2.2.4.1.
• 2.2.4.2.
• The mask
• Domain-aware functions
• 2.2.4.3.
• 2.2.4.4.
• 2.2.5. Summary
• 2.2.6. Contributing to NumPy/Scipy
• 2.2.6.1. Why
• 2.2.6.2. Reporting bugs
• Good bug report
• 2.2.6.3. Contributing to documentation
• 2.2.6.4. Contributing features
• 2.2.6.5. How to help, in general
• 2.3. Debugging code
• 2.3.1. Avoiding bugs
• 2.3.1.1. Coding best practices to avoid getting in trouble
• 2.3.1.2. pyflakes: fast static analysis
• Running pyflakes on the current edited file
• A type-as-go spell-checker like integration
• 2.3.2. Debugging workflow
• 2.3.3. Using the Python debugger
• 2.3.3.1. Invoking the debugger
• Postmortem
• Step-by-step execution
• Other ways of starting a debugger
• 2.3.3.2. Debugger commands and interaction
• Getting help when in the debugger
• 2.3.4. Debugging segmentation faults using gdb
• 2.4. Optimizing code
• 2.4.1. Optimization workflow
• 2.4.2. Profiling Python code
• 2.4.2.1. Timeit
• 2.4.2.2. Profiler
• 2.4.2.3. Line-profiler
• 2.4.3. Making code go faster
• 2.4.3.1. Algorithmic optimization
• Example of the SVD
• 2.4.4. Writing faster numerical code
• 2.4.4.1. Additional Links
• 2.5. Sparse Matrices in SciPy
• 2.5.1. Introduction
• 2.5.1.1. Why Sparse Matrices?
• 2.5.1.2. Sparse Matrices vs. Sparse Matrix Storage Schemes
• 2.5.1.3. Typical Applications
• 2.5.1.4. Prerequisites
• 2.5.1.5. Sparsity Structure Visualization
• 2.5.2. Storage Schemes
• 2.5.2.1. Common Methods
• 2.5.2.2. Sparse Matrix Classes
• Diagonal Format (DIA)
• Examples
• List of Lists Format (LIL)
• Examples
• Dictionary of Keys Format (DOK)
• Examples
• Coordinate Format (COO)
• Examples
• Compressed Sparse Row Format (CSR)
• Examples
• Compressed Sparse Column Format (CSC)
• Examples
• Block Compressed Row Format (BSR)
• Examples
• 2.5.2.3. Summary
• 2.5.3. Linear System Solvers
• 2.5.3.1. Sparse Direct Solvers
• Examples
• 2.5.3.2. Iterative Solvers
• Common Parameters
• LinearOperator Class
• A Few Notes on Preconditioning
• 2.5.3.3. Eigenvalue Problem Solvers
• The
• 2.5.4. Other Interesting Packages
• 2.6. Image manipulation and processing using Numpy and Scipy
• 2.6.1. Opening and writing to image files
• 2.6.2. Displaying images
• 2.6.3. Basic manipulations
• 2.6.3.1. Statistical information
• 2.6.3.2. Geometrical transformations
• 2.6.4. Image filtering
• 2.6.4.1. Blurring/smoothing
• 2.6.4.2. Sharpening
• 2.6.4.3. Denoising
• 2.6.4.4. Mathematical morphology
• 2.6.5. Feature extraction
• 2.6.5.1. Edge detection
• 2.6.5.2. Segmentation
• 2.6.6. Measuring objects properties:
• 2.6.7. Full code examples
• 2.6.8. Examples for the image processing chapter
• 2.7. Mathematical optimization: finding minima of functions
• 2.7.1. Knowing your problem
• 2.7.1.1. Convex versus non-convex optimization
• 2.7.1.2. Smooth and non-smooth problems
• 2.7.1.3. Noisy versus exact cost functions
• 2.7.1.4. Constraints
• 2.7.2. A review of the different optimizers
• 2.7.2.1. Getting started: 1D optimization
• 2.7.2.2. Gradient based methods
• Some intuitions about gradient descent
• Conjugate gradient descent
• 2.7.2.3. Newton and quasi-newton methods
• Newton methods: using the Hessian (2nd differential)
• Quasi-Newton methods: approximating the Hessian on the fly
• 2.7.3. Full code examples
• 2.7.4. Examples for the mathematical optimization chapter
• 2.7.4.12. Gradient-less methods
• A shooting method: the Powell algorithm
• Simplex method: the Nelder-Mead
• 2.7.4.13. Global optimizers
• Brute force: a grid search
• 2.7.5. Practical guide to optimization with scipy
• 2.7.5.1. Choosing a method
• 2.7.5.2. Making your optimizer faster
• 2.7.5.3. Computing gradients
• 2.7.5.4. Synthetic exercices
• 2.7.6. Special case: non-linear least-squares
• 2.7.6.1. Minimizing the norm of a vector function
• 2.7.6.2. Curve fitting
• 2.7.7. Optimization with constraints
• 2.7.7.1. Box bounds
• 2.7.7.2. General constraints
• 2.7.8. Full code examples
• 2.7.9. Examples for the mathematical optimization chapter
• 2.8. Interfacing with C
• 2.8.1. Introduction
• 2.8.2. Python-C-Api
• 2.8.2.1. Example
• 2.8.2.2. Numpy Support
• 2.8.3. Ctypes
• 2.8.3.1. Example
• 2.8.3.2. Numpy Support
• 2.8.4. SWIG
• 2.8.4.1. Example
• 2.8.4.2. Numpy Support
• 2.8.5. Cython
• 2.8.5.1. Example
• 2.8.5.2. Numpy Support
• 2.8.6. Summary
• 2.8.7. Further Reading and References
• 2.8.8. Exercises
• 2.8.8.1. Python-C-API
• 2.8.8.2. Ctypes
• 2.8.8.3. SWIG
• 2.8.8.4. Cython
• 3. Packages and applications
• 3.1. Statistics in Python
• 3.1.1. Data representation and interaction
• 3.1.1.1. Data as a table
• 3.1.1.2. The pandas data-frame
• Creating dataframes: reading data files or converting arrays
• Manipulating data
• Plotting data
• 3.1.2. Hypothesis testing: comparing two groups
• 3.1.2.1. Student’s t-test: the simplest statistical test
• 1-sample t-test: testing the value of a population mean
• 2-sample t-test: testing for difference across populations
• 3.1.2.2. Paired tests: repeated measurements on the same individuals
• 3.1.3. Linear models, multiple factors, and analysis of variance
• 3.1.3.1. “formulas” to specify statistical models in Python
• A simple linear regression
• Categorical variables: comparing groups or multiple categories
• 3.1.3.2. Multiple Regression: including multiple factors
• 3.1.3.3. Post-hoc hypothesis testing: analysis of variance (ANOVA)
• 3.1.4. More visualization: seaborn for statistical exploration
• 3.1.4.1. Pairplot: scatter matrices
• 3.1.4.2. lmplot: plotting a univariate regression
• 3.1.5. Testing for interactions
• 3.1.6. Full code for the figures
• 3.1.7. Solutions to this chapter’s exercises
• 3.2. Sympy : Symbolic Mathematics in Python
• 3.2.1. First Steps with SymPy
• 3.2.1.1. Using SymPy as a calculator
• 3.2.1.2. Symbols
• 3.2.2. Algebraic manipulations
• 3.2.2.1. Expand
• 3.2.2.2. Simplify
• 3.2.3. Calculus
• 3.2.3.1. Limits
• 3.2.3.2. Differentiation
• 3.2.3.3. Series expansion
• 3.2.3.4. Integration
• 3.2.4. Equation solving
• 3.2.5. Linear Algebra
• 3.2.5.1. Matrices
• 3.2.5.2. Differential Equations
• 3.3. Scikit-image: image processing
• 3.3.1. Introduction and concepts
• 3.3.1.1.
• 3.3.1.2. What’s to be found in scikit-image
• 3.3.2. Input/output, data types and colorspaces
• 3.3.2.1. Data types
• 3.3.2.2. Colorspaces
• 3.3.3. Image preprocessing / enhancement
• 3.3.3.1. Local filters
• 3.3.3.2. Non-local filters
• 3.3.3.3. Mathematical morphology
• 3.3.4. Image segmentation
• 3.3.4.1. Binary segmentation: foreground + background
• Histogram-based method:
• Labeling connected components of a discrete image
• 3.3.4.2. Marker based methods
• http://scipy-lectures.org/packages/scikit-image/index.html#watershed-segmentation
• http://scipy-lectures.org/packages/scikit-image/index.html#random-walker-segmentation
• 3.3.5. Measuring regions’ properties
• 3.3.6. Data visualization and interaction
• 3.3.7. Feature extraction for computer vision
• 3.3.8. Full code examples
• 3.3.9. Examples for the scikit-image chapter
• 3.4. Traits: building interactive dialogs
• 3.4.1. Introduction
• 3.4.2. Example
• 3.4.3. What are Traits
• 3.4.3.1. Initialisation
• 3.4.3.2. Validation
• 3.4.3.3. Documentation
• 3.4.3.4. Visualization: opening a dialog
• 3.4.3.5. Deferral
• 3.4.3.6. Notification
• 3.4.3.7. Some more advanced traits
• 3.5. 3D plotting with Mayavi
• 3.5.1. Mlab: the scripting interface
• 3.5.1.1. 3D plotting functions
• Points
• Lines
• Elevation surface
• Arbitrary regular mesh
• Volumetric data
• 3.5.1.2. Figures and decorations
• Figure management
• Changing plot properties
• Decorations
• 3.5.2. Interactive work
• 3.5.2.1. The “pipeline dialog”
• 3.5.2.2. The script recording button
• 3.5.3. Slicing and dicing data: sources, modules and filters
• 3.5.3.1. An example: inspecting magnetic fields
• 3.5.3.2. Different views on data: sources and modules
• Different sources: scatters and fields
• Transforming data: filters
• http://scipy-lectures.org/packages/3d_plotting/index.html#mlab-pipeline-the-scripting-layer
• 3.5.4. Animating the data
• 3.5.5. Making interactive dialogs
• 3.5.5.1. A simple dialog
• 3.5.5.2. Making it interactive
• 3.5.6. Putting it together
• 3.6. scikit-learn: machine learning in Python
• 3.6.1. Introduction: problem settings
• 3.6.1.1. What is machine learning?
• 3.6.1.2. Data in scikit-learn
• The data matrix
• A Simple Example: the Iris Dataset
• The application problem
• Loading the Iris Data with Scikit-learn
• 3.6.2. Basic principles of machine learning with scikit-learn
• 3.6.2.1. Introducing the scikit-learn estimator object
• Fitting on data
• 3.6.2.2. Supervised Learning: Classification and regression
• 3.6.2.3. A recap on Scikit-learn’s estimator interface
• 3.6.2.4. Regularization: what it is and why it is necessary
• Prefering simpler models
• Simple versus complex models for classification
• 3.6.3. Supervised Learning: Classification of Handwritten Digits
• 3.6.3.1. The nature of the data
• 3.6.3.2. Visualizing the Data on its principal components
• 3.6.3.3. Gaussian Naive Bayes Classification
• 3.6.3.4. Quantitative Measurement of Performance
• 3.6.4. Supervised Learning: Regression of Housing Data
• 3.6.4.1. A quick look at the data
• 3.6.4.2. Predicting Home Prices: a Simple Linear Regression
• 3.6.5. Measuring prediction performance
• 3.6.5.1. A quick test on the K-neighbors classifier
• 3.6.5.2. A correct approach: Using a validation set
• 3.6.5.3. Model Selection via Validation
• 3.6.5.4. Cross-validation
• 3.6.5.5. Hyperparameter optimization with cross-validation
• Basic Hyperparameter Optimization
• Automatically Performing Grid Search
• Built-in Hyperparameter Search
• Nested cross-validation
• 3.6.6. Unsupervised Learning: Dimensionality Reduction and Visualization
• 3.6.6.1. Dimensionality Reduction: PCA
• 3.6.6.2. Visualization with a non-linear embedding: tSNE
• 3.6.7. The eigenfaces example: chaining PCA and SVMs
• 3.6.8. The eigenfaces example: chaining PCA and SVMs
• 3.6.8.1. Preprocessing: Principal Component Analysis
• 3.6.8.2. Doing the Learning: Support Vector Machines
• 3.6.8.3. Pipelining
• 3.6.9. Parameter selection, Validation, and Testing
• 3.6.9.1. Hyperparameters, Over-fitting, and Under-fitting
• Bias-variance trade-off: illustration on a simple regression problem
• 3.6.9.2. Visualizing the Bias/Variance Tradeoff
• Validation Curves
• Learning Curves
• 3.6.9.3. Summary on model selection
• High Bias
• High Variance
• 3.6.9.4. A last word of caution: separate validation and test set
• 3.6.10. Examples for the scikit-learn chapter
• http://scipy-lectures.org/_downloads/ScipyLectures.pdf
• http://scipy-lectures.org/_downloads/ScipyLectures-simple.pdf
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