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Scipy Lecture Notes — Scipy lecture notes Navigation next Scipy lecture notes ? Collapse document to compact view Edit Improve this page: Edit it on Github. Scipy Lecture Notes? One document to learn numerics, science, and data with Python? ? Download ? PDF, 2 pages per side ? PDF, 1 page per side ? HTML and example files ? Source code (github) Tutorials on the scientific Python ecosystem: a quick introduction to central tools and techniques. The different chapters each correspond to a 1 to 2 hours course with increasing level of expertise, from beginner to expert. About the scipy lecture notes Authors What’s new License Contributing 1. Getting started with Python for science 1.1. Scientific computing with tools and workflow 1.1.1. Why Python? 1.1.1.1. The scientist’s needs 1.1.1.2. Specifications 1.1.1.3. Existing solutions 1.1.2. Scientific Python building blocks 1.1.3. The interactive workflow: IPython and a text editor 1.1.3.1. Command line interaction 1.1.3.2. Elaboration of the algorithm in an editor 1.1.3.3. IPython 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 1.2.2.2.1. Lists 1.2.2.2.2. Strings 1.2.2.2.3. Dictionaries 1.2.2.2.4. 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 1.2.3.5.1. Iterate over any sequence 1.2.3.5.2. Keeping track of enumeration number 1.2.3.5.3. 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 1.2.5.5.1. 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 1.2.6.1.1. File modes 1.2.7. Standard Library 1.2.7.1. os module: operating system functionality 1.2.7.1.1. Directory and file manipulation 1.2.7.1.2. os.path: path manipulations 1.2.7.1.3. Running an external command 1.2.7.1.4. Walking a directory 1.2.7.1.5. Environment variables: 1.2.7.2. shutil: high-level file operations 1.2.7.3. glob: Pattern matching on files 1.2.7.4. sys module: system-specific information 1.2.7.5. pickle: easy persistence 1.2.8. Exception handling in Python 1.2.8.1. Exceptions 1.2.8.2. Catching exceptions 1.2.8.2.1. try/except 1.2.8.2.2. try/finally 1.2.8.2.3. Easier to ask for forgiveness than for permission 1.2.8.3. Raising exceptions 1.2.9. Object-oriented programming (OOP) 1.3. NumPy: creating and manipulating numerical data 1.3.1. The Numpy array object 1.3.1.1. What are Numpy and Numpy arrays? 1.3.1.1.1. Numpy arrays 1.3.1.1.2. Numpy Reference documentation 1.3.1.1.3. Import conventions 1.3.1.2. Creating arrays 1.3.1.2.1. Manual construction of arrays 1.3.1.2.2. Functions for creating arrays 1.3.1.3. Basic data types 1.3.1.4. Basic visualization 1.3.1.5. Indexing and slicing 1.3.1.6. Copies and views 1.3.1.7. Fancy indexing 1.3.1.7.1. Using boolean masks 1.3.1.7.2. Indexing with an array of integers 1.3.2. Numerical operations on arrays 1.3.2.1. Elementwise operations 1.3.2.1.1. Basic operations 1.3.2.1.2. Other operations 1.3.2.2. Basic reductions 1.3.2.2.1. Computing sums 1.3.2.2.2. Other reductions 1.3.2.3. Broadcasting 1.3.2.4. Array shape manipulation 1.3.2.4.1. Flattening 1.3.2.4.2. Reshaping 1.3.2.4.3. Adding a dimension 1.3.2.4.4. Dimension shuffling 1.3.2.4.5. Resizing 1.3.2.5. Sorting data 1.3.2.6. Summary 1.3.3. More elaborate arrays 1.3.3.1. More data types 1.3.3.1.1. Casting 1.3.3.1.2. Different data type sizes 1.3.3.2. Structured data types 1.3.3.3. maskedarray: dealing with (propagation of) missing data 1.3.4. Advanced operations 1.3.4.1. Polynomials 1.3.4.1.1. More polynomials (with more bases) 1.3.4.2. Loading data files 1.3.4.2.1. Text files 1.3.4.2.2. Images 1.3.4.2.3. Numpy’s own format 1.3.4.2.4. Well-known (& more obscure) file formats 1.3.5. Some exercises 1.3.5.1. Array manipulations 1.3.5.2. Picture manipulation: Framing a Face 1.3.5.3. Data statistics 1.3.5.4. Crude integral approximations 1.3.5.5. Mandelbrot set 1.3.5.6. Markov chain 1.4. Matplotlib: plotting 1.4.1. Introduction 1.4.1.1. IPython and the matplotlib mode 1.4.1.2. pyplot 1.4.2. Simple plot 1.4.2.1. Plotting with default settings 1.4.2.2. Instantiating defaults 1.4.2.3. Changing colors and line widths 1.4.2.4. Setting limits 1.4.2.5. Setting ticks 1.4.2.6. Setting tick labels 1.4.2.7. Moving spines 1.4.2.8. Adding a legend 1.4.2.9. Annotate some points 1.4.2.10. Devil is in the details 1.4.3. Figures, Subplots, Axes and Ticks 1.4.3.1. Figures 1.4.3.2. Subplots 1.4.3.3. Axes 1.4.3.4. Ticks 1.4.3.4.1. Tick Locators 1.4.4. Other Types of Plots: examples and exercises 1.4.4.1. Regular Plots 1.4.4.2. Scatter Plots 1.4.4.3. Bar Plots 1.4.4.4. Contour Plots 1.4.4.5. Imshow 1.4.4.6. Pie Charts 1.4.4.7. Quiver Plots 1.4.4.8. Grids 1.4.4.9. Multi Plots 1.4.4.10. Polar Axis 1.4.4.11. 3D Plots 1.4.4.12. Text 1.4.5. Beyond this tutorial 1.4.5.1. Tutorials 1.4.5.2. Matplotlib documentation 1.4.5.3. Code documentation 1.4.5.4. Galleries 1.4.5.5. Mailing lists 1.4.6. Quick references 1.4.6.1. Line properties 1.4.6.2. Line styles 1.4.6.3. Markers 1.4.6.4. Colormaps 1.5. Scipy : high-level scientific computing 1.5.1. File input/output: scipy.io 1.5.2. Special functions: scipy.special 1.5.3. Linear algebra operations: scipy.linalg 1.5.4. Fast Fourier transforms: scipy.fftpack 1.5.5. Optimization and fit: scipy.optimize 1.5.6. Statistics and random numbers: scipy.stats 1.5.6.1. Histogram and probability density function 1.5.6.2. Percentiles 1.5.6.3. Statistical tests 1.5.7. Interpolation: scipy.interpolate 1.5.8. Numerical integration: scipy.integrate 1.5.9. Signal processing: scipy.signal 1.5.10. Image processing: scipy.ndimage 1.5.10.1. Geometrical transformations on images 1.5.10.2. Image filtering 1.5.10.3. Mathematical morphology 1.5.10.4. Measurements on images 1.5.11. Summary exercises on scientific computing 1.5.11.13. Maximum wind speed prediction at the Sprog? station 1.5.11.13.1. Statistical approach 1.5.11.13.2. Computing the cumulative probabilities 1.5.11.13.3. Prediction with UnivariateSpline 1.5.11.13.4. Exercise with the Gumbell distribution 1.5.11.14. Non linear least squares curve fitting: application to point extraction in topographical lidar data 1.5.11.14.1. Introduction 1.5.11.14.2. Loading and visualization 1.5.11.14.3. Fitting a waveform with a simple Gaussian model 1.5.11.14.3.1. Model 1.5.11.14.3.2. Initial solution 1.5.11.14.3.3. Fit 1.5.11.14.4. Going further 1.5.11.15. Image processing application: counting bubbles and unmolten grains 1.5.11.15.1. Statement of the problem 1.5.11.15.2. Proposed solution 1.5.11.16. Example of solution for the image processing exercise: unmolten grains in glass 1.5.11.13. Maximum wind speed prediction at the Sprog? station 1.5.11.13.1. Statistical approach 1.5.11.13.2. Computing the cumulative probabilities 1.5.11.13.3. Prediction with UnivariateSpline 1.5.11.13.4. Exercise with the Gumbell distribution 1.5.11.14. Non linear least squares curve fitting: application to point extraction in topographical lidar data 1.5.11.14.1. Introduction 1.5.11.14.2. Loading and visualization 1.5.11.14.3. Fitting a waveform with a simple Gaussian model 1.5.11.14.3.1. Model 1.5.11.14.3.2. Initial solution 1.5.11.14.3.3. Fit 1.5.11.14.4. Going further 1.5.11.15. Image processing application: counting bubbles and unmolten grains 1.5.11.15.1. Statement of the problem 1.5.11.15.2. Proposed solution 1.5.11.16. Example of solution for the image processing exercise: unmolten grains in glass 1.5.11.13. Maximum wind speed prediction at the Sprog? station 1.5.11.13.1. Statistical approach 1.5.11.13.2. Computing the cumulative probabilities 1.5.11.13.3. Prediction with UnivariateSpline 1.5.11.13.4. Exercise with the Gumbell distribution 1.5.11.14. Non linear least squares curve fitting: application to point extraction in topographical lidar data 1.5.11.14.1. Introduction 1.5.11.14.2. Loading and visualization 1.5.11.14.3. Fitting a waveform with a simple Gaussian model 1.5.11.14.3.1. Model 1.5.11.14.3.2. Initial solution 1.5.11.14.3.3. Fit 1.5.11.14.4. Going further 1.5.11.15. Image processing application: counting bubbles and unmolten grains 1.5.11.15.1. Statement of the problem 1.5.11.15.2. Proposed solution 1.5.11.16. Example of solution for the image processing exercise: unmolten grains in glass 1.6. 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 while-loop removing decorator 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 2.2.1.3.1. The descriptor 2.2.1.3.2. Example: reading .wav files 2.2.1.3.3. Casting and re-interpretation/views 2.2.1.3.3.1. Casting 2.2.1.3.3.2. Re-interpretation / viewing 2.2.1.4. Indexing scheme: strides 2.2.1.4.1. Main point 2.2.1.4.1.1. C and Fortran order 2.2.1.4.1.2. Slicing with integers 2.2.1.4.2. Example: fake dimensions with strides 2.2.1.4.3. Broadcasting 2.2.1.4.4. More tricks: diagonals 2.2.1.4.5. CPU cache effects 2.2.1.4.6. Example: inplace operations (caveat emptor) 2.2.1.5. Findings in dissection 2.2.2. Universal functions 2.2.2.1. What they are? 2.2.2.1.1. Parts of an Ufunc 2.2.2.1.2. 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: chararray, maskedarray, matrix 2.2.4.1. chararray: vectorized string operations 2.2.4.2. masked_array missing data 2.2.4.2.1. The mask 2.2.4.2.2. Domain-aware functions 2.2.4.3. recarray: purely convenience 2.2.4.4. matrix: convenience? 2.2.5. Summary 2.2.6. Contributing to Numpy/Scipy 2.2.6.1. Why 2.2.6.2. Reporting bugs 2.2.6.2.1. 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 2.3.1.2.1. Running pyflakes on the current edited file 2.3.1.2.2. 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 2.3.3.1.1. Postmortem 2.3.3.1.2. Step-by-step execution 2.3.3.1.3. Other ways of starting a debugger 2.3.3.2. Debugger commands and interaction 2.3.3.2.1. 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 2.4.3.1.1. 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 2.5.2.2.1. Diagonal Format (DIA) 2.5.2.2.1.1. Examples 2.5.2.2.2. List of Lists Format (LIL) 2.5.2.2.2.1. Examples 2.5.2.2.3. Dictionary of Keys Format (DOK) 2.5.2.2.3.1. Examples 2.5.2.2.4. Coordinate Format (COO) 2.5.2.2.4.1. Examples 2.5.2.2.5. Compressed Sparse Row Format (CSR) 2.5.2.2.5.1. Examples 2.5.2.2.6. Compressed Sparse Column Format (CSC) 2.5.2.2.6.1. Examples 2.5.2.2.7. Block Compressed Row Format (BSR) 2.5.2.2.7.1. Examples 2.5.2.3. Summary 2.5.3. Linear System Solvers 2.5.3.1. Sparse Direct Solvers 2.5.3.1.1. Examples 2.5.3.2. Iterative Solvers 2.5.3.2.1. Common Parameters 2.5.3.2.2. LinearOperator Class 2.5.3.2.3. A Few Notes on Preconditioning 2.5.3.3. Eigenvalue Problem Solvers 2.5.3.3.1. The eigen module 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: ndimage.measurements 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 2.7.2.2.1. Some intuitions about gradient descent 2.7.2.2.2. Conjugate gradient descent 2.7.2.3. Newton and quasi-newton methods 2.7.2.3.1. Newton methods: using the Hessian (2nd differential) 2.7.2.3.2. Quasi-Newton methods: approximating the Hessian on the fly 2.7.2.4. Gradient-less methods 2.7.2.4.1. A shooting method: the Powell algorithm 2.7.2.4.2. Simplex method: the Nelder-Mead 2.7.2.5. Global optimizers 2.7.2.5.1. Brute force: a grid search 2.7.3. Practical guide to optimization with scipy 2.7.3.1. Choosing a method 2.7.3.2. Making your optimizer faster 2.7.3.3. Computing gradients 2.7.3.4. Synthetic exercices 2.7.4. Special case: non-linear least-squares 2.7.4.1. Minimizing the norm of a vector function 2.7.4.2. Curve fitting 2.7.5. Optimization with constraints 2.7.5.1. Box bounds 2.7.5.2. General constraints 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 panda data-frame 3.1.1.2.1. Creating dataframes: reading data files or converting arrays 3.1.1.2.2. Manipulating data 3.1.1.2.3. Plotting data 3.1.2. Hypothesis testing: comparing two groups 3.1.2.1. Student’s t-test: the simplest statistical test 3.1.2.1.1. 1-sample t-test: testing the value of a population mean 3.1.2.1.2. 2-sample t-test: testing for difference across populations 3.1.2.2. Paired tests: repeated measurements on the same indivuals 3.1.3. Linear models, multiple factors, and analysis of variance 3.1.3.1. “formulas” to specify statistical models in Python 3.1.3.1.1. A simple linear regression 3.1.3.1.2. 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 examples 3.1.6.1. Examples 3.1.6.1.1. Code examples 3.1.6.1.2. Solutions to the exercises of the course 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. Exercises 3.2.1.3. 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 3.2.3.5. Exercises 3.2.4. Equation solving 3.2.4.1. Exercises 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. scikit-image and the SciPy ecosystem 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 3.3.4.1.1. Histogram-based method: Otsu thresholding 3.3.4.1.2. Labeling connected components of a discrete image 3.3.4.2. Marker based methods 3.3.4.2.1. Watershed segmentation 3.3.4.2.2. Random walker segmentation 3.3.5. Measuring regions’ properties 3.3.6. Data visualization and interaction 3.3.7. Feature extraction for computer vision 3.4. 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 3.5.1.1.1. Points 3.5.1.1.2. Lines 3.5.1.1.3. Elevation surface 3.5.1.1.4. Arbitrary regular mesh 3.5.1.1.5. Volumetric data 3.5.1.2. Figures and decorations 3.5.1.2.1. Figure management 3.5.1.2.2. Changing plot properties 3.5.1.2.3. 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 3.5.3.2.1. Different sources: scatters and fields 3.5.3.2.2. Transforming data: filters 3.5.3.2.3. 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. Loading an example dataset 3.6.1.1. Learning and Predicting 3.6.2. Classification 3.6.2.1. k-Nearest neighbors classifier 3.6.2.2. Support vector machines (SVMs) for classification 3.6.2.2.1. Linear Support Vector Machines 3.6.2.2.2. Using kernels 3.6.3. Clustering: grouping observations together 3.6.3.1. K-means clustering 3.6.4. Dimension Reduction with Principal Component Analysis 3.6.5. Putting it all together: face recognition 3.6.6. Linear model: from regression to sparsity 3.6.6.1. Sparse models 3.6.7. Model selection: choosing estimators and their parameters 3.6.7.1. Grid-search and cross-validated estimators 3.6.7.1.1. Grid-search 3.6.7.1.2. Cross-validated estimators ScipyLectures.pdf ScipyLectures-simple.pdf Navigation next Scipy lecture notes ? Collapse document to compact view Edit Improve this page: Edit it on Github. ? Copyright 2012,2013,2015. 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Domain Name: SCIPY-LECTURES.ORG