frac_pow {genscore}

Evaluate x^(a/b) and |x|^(a/b) with integer a and b with extension to conventional operations.

Description

Evaluate x^(a/b) and |x|^(a/b) with integer a and b with extension to conventional operations (listed under details) that would otherwise result in NaN.

Usage

frac_pow(x, a, b, abs)

Arguments

x

A number or a vector of numbers.

a

An integer.

b

An integer.

abs

TRUE or FALSE.

Details

Replace x by abs(x) below if abs == TRUE. If a == 0 && b == 0, returns log(x). If a != 0 && b == 0, returns exp(a*x). Otherwise, for b != 0, evaluates x^(a/b) with the following extensions. 0^0 evaluates to 1. If x < 0, returns (-1)^a * |x|^(a/b) if b is odd, or NaN otherwise. If x == 0 && a < 0, returns NaN.

Value

A vector of numbers of the same size as x. See details.

Examples

frac_pow(-5:5, 3, 2, TRUE) - abs(-5:5)^(3/2)
frac_pow(-5:5, 5, 3, FALSE) - sign(-5:5)^5*abs(-5:5)^(5/3)
frac_pow(-5:5, 2, 3, FALSE) - ((-5:5)^2)^(1/3)
frac_pow(c(-5:-1,1:5), 0, 0, TRUE) - log(abs(c(-5:-1,1:5)))
frac_pow(-5:5, 0, 1, FALSE) - 1
frac_pow(-5:5, 3, 0, FALSE) - exp(3*-5:5)