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