Iterate: Iterate a function on an initial condition

In mosaicCalc: R-Language Based Calculus Operations for Teaching

Iterate a function on an initial condition

Description

Iterates a function a specified number of times on an initial condition.

Usage

Iterate(f = NULL, A = NULL, x0 = 0, n = 10, fargs = list())

Arguments

f	a function of one or more state variables which returns a vector containing those same state variables. Parameters to f(), if any, should be named and at the end of the argument list. State variables should not have default values.
A	As an alternative to f you can give a square matrix and iteration will be done on the system ⁠x[n+1] = A x[n]⁠. In lieu of a square matrix you can also give a vector to be rendered into a square matrix rowwise.
x0	a vector with the numerical initial condition. There should be 1 component in x0 for each of the state variables in f().
n	an integer specifying the number of iterations
fargs	list containing values for numerical parameters to the function f()

Details

The function f can take one or more arguments. The first of these should represent the state of the dynamical system, e.g. x, or x and y, etc. At the end of the argument list to f can come named parameters. The length of the initial condition x0 must match the number of state arguments. Numerical values for parameters (if any) must be provided in the ... slot.

Value

A data frame with a column .i listing the iteration number and columns for each component of the initial condition. There will be n+1 rows, the first for the initial condition and the remaining for the n iterations.

Examples

Iterate(function(x, mu=3.5) mu*x*(1-x), x0=.232, n=10, list(mu=4)) # chaos
Iterate(function(x, y) c(x+y, x-y), x0 = c(1,1), n=10)
Iterate(function(x, y) c(x+y, x), x0=c(1,0), n=10) # fibonacci
Iterate(A = cbind(rbind(1, 1), rbind(1, 0)), x0=c(1,0), n=5) # fibonacci described by a matrix

mosaicCalc documentation built on Sept. 11, 2024, 9:10 p.m.