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Sparse arrays and multivariate polynomials

spray-package.Rd

Functionality for sparse arrays, with emphasis on their interpretation as multivariate polynomials.

Details

Base R has the capability of dealing with arbitrary dimensioned numerical arrays, with the array class.

A sparse array is a type of array in which nonzero elements are stored along with an index vector describing their coordinates. This allows for efficient storage and manipulation as base arrays often require the storing of many zero elements which consume computational and memory resources.

In the package, sparse arrays are represented as objects of class spray. They use the C++ standard template library (STL) map class, with keys being (unsigned) integer vectors, and values floats.

One natural application of sparse arrays, for which the package was written, is multivariate polynomials and the package vignette presents an extended discussion. Note that other interpretations exist: the stokes and weyl packages interpret spray objects as differential forms and elements of a Weyl algebra respectively.

Author

Robin K. S. Hankin

Examples


# define a spray using a matrix of indices and a vector of values:
M <- matrix(sample(0:3,21,replace=TRUE),ncol=3)
a <- spray(M,sample(7))
#> Error in spraymaker(list(M, x), addrepeats = addrepeats): repeated indices; yet argument 'addrepeats' is FALSE

# there are many pre-defined simple sprays:
b <- homog(3,4)

# arithmetic operators work:
a + 2*b
#> Error in eval(expr, envir, enclos): object 'a' not found
a - a*b^2/4
#> Error in eval(expr, envir, enclos): object 'a' not found
a+b
#> Error in eval(expr, envir, enclos): object 'a' not found

#  we can sum over particular dimensions:
asum(a+b,1)
#> Error in eval(expr, envir, enclos): object 'a' not found

# differentiation is supported:
deriv(a^6,2)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'expr' in selecting a method for function 'deriv': object 'a' not found

# extraction and replacement work as expected:

b[1,2,1]
#> +a*b^2*c
b[1,2,1,drop=TRUE]
#> [1] 1

b[diag(3)] <- 3