Solving a system of nonlinear equations in R

Question

Suppose I have the following system of equations:

a * b = 5
sqrt(a * b^2) = 10

How can I solve these equations for a and b in R ?

I

Answer 1

Use this library.

library("nleqslv")

You need to define the multivariate function you want to solve for.

fn <- function(x) {

  rate <- x[1] * x[2] - 5
  shape <- sqrt(x[1] * x[2]^2) - 10

  return(c(rate, shape))

}

Then you're good to go.

nleqslv(c(1,5), fn)

Always look at the detailed results. Numerical calculations can be tricky. In this case I got this:

Warning message:
In sqrt(x[1] * x[2]^2) : NaNs produced

That just means the procedure searched a region that included x[1] < 0 and then presumably noped the heck back to the right hand side of the plane.