Solving a nonlinear system of equations in Julia

General Usage
2

A couple things to point out

  1. Semi colons are not necessary within functions
  2. In julia, when a function ends in an explamation point ! such as h!, that should signify that it mutates (changes) one of its inputs ( I say should since this is not enforced in the language but is a naming convention)
  3. When showing code on this forum, you should put your code in “backticks” (the key under tilda) for readability: this is enclosed in backticks

Now for the code, the error message you get from nlsolve has to do with point #2. NLsolve expects your function to take the residual vector and simply mutate it as opposed to returning a new vector. Here’s an example that works.

julia> using NLsolve

julia> function h!(theta, resvec, alpha, beta)
       resvec[1] = theta[1]*beta - (theta[1] - alpha)
       resvec[2] = theta[2]*beta - (theta[2] - alpha)
       end

julia> function f!(theta, resvec)
           h!(theta,resvec, 0.3, 0.95)
       end

julia> a01 = [1.0,1.0];

julia> nlsolve(f!,a01)
Results of Nonlinear Solver Algorithm
 * Algorithm: Trust-region with dogleg and autoscaling
 * Starting Point: [1.0,1.0]
 * Zero: [6.0,6.0]
 * Inf-norm of residuals: 0.000000
 * Iterations: 3
 * Convergence: true
   * |x - x'| < 0.0e+00: false
   * |f(x)| < 1.0e-08: true
 * Function Calls (f): 4
 * Jacobian Calls (df/dx): 4

I’m sure there are other ways to handle the alpha and beta parameters besides making another function.

Good reading materials:

https://docs.julialang.org/en/release-0.4/manual/noteworthy-differences/

ETA: And to clarify for your other example, Optim is used to optimize a function, this is different than solving it, the error you get is because you are returning a vector, while optimization is performed on a scalar (cost) quantity). Hope this helps!

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