open Jest
open Expect
open TestHelpers

describe("kl divergence", () => {
  let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
  exception KlFailed
  test("of two uniforms is equal to the analytic expression", () => {
    let lowAnswer = 2.3526e0
    let highAnswer = 8.5382e0
    let lowPrediction = 2.3526e0
    let highPrediction = 1.2345e1
    let answer =
      uniformMakeR(lowAnswer, highAnswer)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
    let prediction =
      uniformMakeR(lowPrediction, highPrediction)->E.R2.errMap(s => DistributionTypes.ArgumentError(
        s,
      ))
    // integral along the support of the answer of answer.pdf(x) times log of prediction.pdf(x) divided by answer.pdf(x) dx
    let analyticalKl = Js.Math.log((highPrediction -. lowPrediction) /. (highAnswer -. lowAnswer))
    let kl = E.R.liftJoin2(klDivergence, prediction, answer)
    switch kl {
    | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
    | Error(err) => {
        Js.Console.log(DistributionTypes.Error.toString(err))
        raise(KlFailed)
      }
    }
  })
  test("of two normals is equal to the formula", () => {
    // This test case comes via Nuño https://github.com/quantified-uncertainty/squiggle/issues/433
    let mean1 = 4.0
    let mean2 = 1.0
    let stdev1 = 1.0
    let stdev2 = 1.0

    let prediction =
      normalMakeR(mean1, stdev1)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
    let answer = normalMakeR(mean2, stdev2)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
    let analyticalKl =
      Js.Math.log(stdev2 /. stdev1) +.
      stdev1 ** 2.0 /. 2.0 /. stdev2 ** 2.0 +.
      (mean1 -. mean2) ** 2.0 /. 2.0 /. stdev2 ** 2.0 -. 0.5
    let kl = E.R.liftJoin2(klDivergence, prediction, answer)
    switch kl {
    | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
    | Error(err) => {
        Js.Console.log(DistributionTypes.Error.toString(err))
        raise(KlFailed)
      }
    }
  })
})