unirootGrid {exact2x2}

Function to find a root by grid search.

Description

Find the root (value where the function equals 0) of a monotonic function, func, using a halving algorithm grid search.

Usage

unirootGrid(func, power2 = 12, step.up = TRUE, pos.side = FALSE, 
    print.steps = FALSE, power2grid = power2gridRatio, ...)

Arguments

func

monotonic function

power2

positive integer, number of grid points is 1+2^power2

step.up

logical, start the search at the lower end of the grid and step up?

pos.side

logical, should the root be on the positive side? In other words, should func(root)>=0

print.steps

logical, should each step that is evaluated be printed?

power2grid

function that returns the grid. Take one argument, power2

...

arguments passed to func

Details

The grid is defined with the power2grid argument that defines a function with an argument power2, and returns a grid with 1+2^power2 elements. The root is found by a halving algorithm on the grid, so func is calculated only power2+1 times. The ‘root’ is the element that is closest to the root, either on the positive side (pos.side=TRUE) or not.

The unirootGrid function calls uniroot.integer and finds roots based on grid search. The functions power2gridRatio and power2gridDifference create grids for searching (0,Inf) and (-1,1) respectively. The power2gridRatio grid is equally spaced on the log scale with about half of the grid between 0.5 and 2. The function power2grid allows more flexibility in defining grids.

Value

A list with elements:

iter

number of iterations

f.root

value of func at root

root

root, element on the grid that is closest to the root on the negative side (if pos.side=FALSE)

bound

interval for the accuracy

Author(s)

Michael P. Fay

See Also

uniroot and uniroot.integer

Examples

# print.steps prints all iterations, 
# with x=rank of grid value (e.g., x=1 is lowest value in grid) 
# f(x) really is f(grid[x]) where grid is from the power2grid function 
unirootGrid(function(x){ x - .37}, power2=10, power2grid=power2gridRatio, 
  print.steps=TRUE, pos.side=TRUE)