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Efficient C++ optimized functions for numerical and symbolic calculus.
The R package calculus implements C++ optimized
functions for numerical and symbolic calculus, such as the Einstein
summing convention, fast computation of the Levi-Civita
symbol and generalized Kronecker
delta, Taylor series
expansion, multivariate Hermite
polynomials, high-order derivatives,
ordinary
differential equations, differential
operators and numerical
integration in arbitrary orthogonal coordinate systems. The library
applies numerical methods when working with functions or
symbolic programming when working with characters or
expressions. The package handles multivariate numerical
calculus in arbitrary dimensions and coordinates and implements the
symbolic counterpart of the numerical methods whenever possible, without
depending on external computer algebra systems. Except for Rcpp, the package has
no strict dependencies in order to provide a stable self-contained
toolbox that invites re-use.
Install the package.
install.packages("calculus")Load the package.
library(calculus)Read or browse the documentation and the vignettes.
The package provides a unified interface to work with mathematical
objects in R. The library applies numerical methods when working with
functions or symbolic programming when working with
characters or expressions. To describe
multidimensional objects such as vectors, matrices, and tensors, the
package uses the class array regardless of the dimension.
This is done to prevent unwanted results due to operations among
different classes such as vector for unidimensional objects
or matrix for bidimensional objects.
The package integrates seamlessly with cubature for efficient numerical integration in C. However, except for Rcpp, the package has no strict dependencies in order to provide a stable self-contained toolbox that invites re-use.
Several unit tests are implemented via the standard framework offered by testthat and run via continuous integration.
Report a bug and star the repository.
Guidotti E (2022). “calculus: High-Dimensional Numerical and Symbolic Calculus in R.” Journal of Statistical Software, 104(5), 1-37. doi:10.18637/jss.v104.i05
A BibTeX entry for LaTeX users is
@Article{calculus,
title = {{calculus}: High-Dimensional Numerical and Symbolic Calculus in {R}},
author = {Emanuele Guidotti},
journal = {Journal of Statistical Software},
year = {2022},
volume = {104},
number = {5},
pages = {1--37},
doi = {10.18637/jss.v104.i05},
}These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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