Anybody that has written numerical code will know that a common source of mistakes is the definition of functions that evaluate a complicated formula. One way around this problem is to use a package for symbolic computations, and we will take advantage of sympy, which is a compact Python symbolic package.
Defining, symbolically, a function operating on arrays
by V Kishore Ayyadevara, Ruben Oliva Ramos, L. Felipe Martins
SciPy Recipes
- Preface
- Getting to Know the Tools
- Introduction
- Installing Anaconda on Windows
- Installing Anaconda on macOS
- Installing Anaconda on Linux
- Checking the Anaconda installation
- Installing SciPy from a binary distribution on Windows
- Installing SciPy from a binary distribution on macOS
- Installing SciPy from source on Linux
- Installing optional packages with conda
- Installing packages with pip
- Setting up a virtual environment with conda
- Creating a virtual environment for development with conda
- Creating a conda environment with a different version of a package
- Using conda environments to run different versions of Python
- Creating virtual environments with venv
- Running SciPy in a script
- Running SciPy in Jupyter
- Running SciPy in Spyder
- Running SciPy in PyCharm
- Getting Started with NumPy
- Introduction
- Creating NumPy arrays
- How to do it…
- Creating an array from a list
- Specifying the data type for elements in an array
- Creating an empty array with a given shape
- Creating arrays of zeros and ones with a single value
- Creating arrays with equally spaced values
- Creating an array by repeating elements
- Creating an array by tiling another array
- Creating an array with the same shape as another array
- Using object arrays to store heterogeneous data
- See also
- How to do it…
- Querying and changing the shape of an array
- Storing and retrieving NumPy arrays
- Indexing
- Operations on arrays
- Using masked arrays to represent invalid data
- Using object arrays to store heterogeneous data
- Defining, symbolically, a function operating on arrays
- Using Matplotlib to Create Graphs
- Introduction
- Creating two-dimensional plots of functions and data
- Generating multiple plots in a single figure
- Setting line styles and markers
- Using different backends to display graphs
- Saving plots to disk
- Annotating graphs
- Generating histograms and box plots
- Creating three-dimensional plots
- Generating interactive displays in the Jupyter Notebook
- Object-oriented graph creation using Artist objects
- Creating a map with cartopy
- Data Wrangling with pandas
- Creating Series objects
- Creating DataFrame objects
- Inserting and deleting columns to a DataFrame
- Inserting and deleting rows to a DataFrame
- Selecting items by row indexes and column labels
- Selecting items by integer location
- Selecting items using mixed indexing
- Accessing, selecting, and modifying data
- Selecting rows using Boolean selection
- Reading and storing data in different formats
- Data displays employing different kinds of visual representation
- How to apply numerical functions and operations to Series and DataFrame objects
- Computing statistical functions on Series and DataFrame objects
- How to sort data in Series and DataFrame objects
- Performing merging, joins, concatenation, and grouping
- Matrices and Linear Algebra
- Introduction
- Matrix operations and functions on two-dimensional arrays
- Solving linear systems using matrices
- Calculating the null space of a matrix
- Calculating the LU decompositions of a matrix
- Calculating the QR decomposition of a matrix
- Calculating the eigenvalue and eigenvector of a matrix
- Diagonalizing a matrix
- Calculating the Jordan form of a matrix
- Calculating the singular value decomposition of a matrix
- Creating a sparse matrix
- Computations on top of a sparse matrix
- Solving Equations and Optimization
- Introduction
- Non-linear equations and systems
- System of equations and how to solve it
- Choosing the solver used to find the solution of equations
- Solving constrained non-linear optimization problems in several variables
- Solving one-dimensional optimization problems
- Solving multidimensional non-linear equations using the Newton-Krylov method
- Solving multidimensional non-linear equations using the Anderson method
- Finding the best linear fit for a set of data
- Doing non-linear regression for a set of data
- Regression
- Constants and Special Functions
- Calculus, Interpolation, and Differential Equations
- Introduction
- Integration
- Computing integrals using a Gaussian quadrature
- Computing integrals with weighting functions
- Computing multiple integrals
- Interpolation
- Computing a polynomial interpolation for a set of data points
- Univariate interpolation
- Finding a cubic spline that interpolates a set of data
- Defining a B-spline for a given set of control points
- Differentiation
- Solving a one-dimensional ordinary differential equation
- Solving a system of ordinary differential equations
- Solving differential equations and systems with parameters
- Using ode and the objected-oriented interface to solve differential equations
- Statistics and Probability
- Introduction
- Computing the probability mass function of a discrete random variable
- Computing the probability density function of a continuous random variable
- Computing the cumulative distribution function for a random variable
- Computing the values of inverse probabilities associated with a random variable
- Computing the average, standard deviation, and higher moments of a distribution
- Computing probabilities associated with the multivariate Gaussian distribution
- Computing the summary statistics of a dataset
- Advanced Computations with SciPy
- Discrete Fourier transforms
- Computing the discrete Fourier transform (DFT) of a data series using the FFT algorithm
- Computing the inverse DFT of a data series
- Computing signal construction
- Getting started with filters
- Computing the DFT for two-dimensional data
- How to find the DFT of the derivative of a function
- Computing the convolution of two functions
- Mathematical imaging
- Computing pairwise distances from a dataset, using different distance metrics
- How to identify neighborhoods and nearest neighbors for a dataset and a given metric
- Nearest neighbors regression
Defining, symbolically, a function operating on arrays
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