blowupSpray: Change discrete variable in a polynomial

In CharlotteJana/pdmppoly: Moment Approximation for Polynomial PDMPs

Description

This function takes a polynomial (represented by a spray object), uses polyPdmpModel obj to identify the discrete variable and substitutes this variable in the polynomial by several indicator variables. The number of variables depends on the different possible states that the discrete variable can take. The method is used internally for computing the generator of a polyPdmpModel.

Usage

blowupSpray(obj, spray)

Arguments

obj	object of class polyPdmpModel.
spray	object of class spray. This is the polynomial that shall be modified.

Details

This function is best explained in an example. Lets assume that we have one continous variable f and one discrete variable d and that they are given in order f, d in variable init(obj). Let's have discStates(obj) = list(d = -1:1), so d can take the values -1, 0 or 1, respectively. A polynomial of arity 2 would then be transformed into a polynomial of arity 4, where the second variable (that stands for d) is replaced by three indicator variables d1, d2, d3, that can only take values 0 or 1, depending on the value of the original d. If we take for example the polynomial 5f²d³ + f, method blowupSpray changes it into

5f²⋅(-1)³⋅d1 + 5f²⋅0³⋅d2 + 5f²⋅1³⋅d3 + f = -5f²d1 + 5f²d3 + f.

If the order of f and d are reversed (i.e. init(obj) = c(d = ..., f = ...)), the additional variables d1, d2, d3 would still be added at the end, leaving f to be the first variable.

Note

This method only works for one discrete variable

Examples

# the example discussed in section details:
library(spray)
data("simplePoly") 
blowupSpray(simplePoly, 5*product(2:3) + lone(1, 2))

# with other order in slot init:
init(simplePoly) <- c(d = 1, f = 2)
blowupSpray(simplePoly, 5*product(3:2) + lone(2, 1))  

CharlotteJana/pdmppoly documentation built on Sept. 4, 2019, 4:40 p.m.