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feat: Worked out kinks of the integral!

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This commit is contained in:
NunoSempere 2022-09-05 12:11:42 +02:00
parent fd7720b045
commit 27ca86e729
1 changed files with 40 additions and 13 deletions
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53
packages/squiggle-lang/src/rescript/FunctionRegistry/Library/FR_Danger.res
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@ -108,8 +108,8 @@ module Internals = {
}
result
}
let xsLength = Js.Math.ceil((max -. min) /. increment)
let xs = Belt.Array.makeBy(xsLength + 1, i => min +. Belt_Float.fromInt(i) *. increment)
let xsLength = Js.Math.floor((max -. min) /. increment) // Note that we are loosing a bit of the tail
let xs = Belt.Array.makeBy(xsLength, i => min +. (Belt_Float.fromInt(i) +. 0.5) *. increment)
// makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
let ysOptions = Belt.Array.map(xs, x => applyFunctionAtFloatToFloatOption(x))
let okYs = E.A.R.filterOk(ysOptions)
@ -149,20 +149,47 @@ module Internals = {
}
result
}
let xsLengthCandidate = Belt.Float.toInt(Js.Math.round(numIntervals))
let xsLength = xsLengthCandidate > 0 ? xsLengthCandidate : 1
let increment = (max -. min) /. Belt.Int.toFloat(xsLength)
let xs = Belt.Array.makeBy(xsLength + 1, i => min +. Belt_Float.fromInt(i) *. increment)
// makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
let ysOptions = Belt.Array.map(xs, x => applyFunctionAtFloatToFloatOption(x))
// worked example in comments below, assuming min=0, max = 10
let numTotalPoints = Belt.Float.toInt(numIntervals)
let numInnerPoints = numTotalPoints - 2
let numOuterPoints = 2
let totalWeight = (max -. min)
let weightForAnInnerPoint = totalWeight/.E.I.toFloat(numTotalPoints-1)
let weightForAnOuterPoint = totalWeight/.E.I.toFloat(numTotalPoints-1)/. 2.0
let innerPointIncrement = (max -. min) /. E.I.toFloat(numTotalPoints -1)
let innerXs = Belt.Array.makeBy(numInnerPoints, i => min +. Belt_Float.fromInt(i + 1) *. innerPointIncrement)
// Note that makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
let ysOptions = Belt.Array.map(innerXs, x => applyFunctionAtFloatToFloatOption(x))
let okYs = E.A.R.filterOk(ysOptions)
// Logging
// assuming min = 0, max = 10, results below:
Js.Console.log2("numTotalPoints", numTotalPoints) // 5
Js.Console.log2("numInnerPoints", numInnerPoints) // 3
Js.Console.log2("numOuterPoints", numOuterPoints) // always 2
Js.Console.log2("totalWeight", totalWeight) // 10 - 0 = 10
Js.Console.log2("weightForAnInnerPoint", weightForAnInnerPoint) // 10/4 = 2.5
Js.Console.log2("weightForAnOuterPoint", weightForAnOuterPoint) // 10/4/2 = 1.25
Js.Console.log2("weightForAnInnerPoint * numInnerPoints + weightForAnOuterPoint * numOuterPoints", weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +. weightForAnOuterPoint *. E.I.toFloat(numOuterPoints)) // should be 10
Js.Console.log2("sum of weights == totalWeight", (weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +. weightForAnOuterPoint *. E.I.toFloat(numOuterPoints)) == totalWeight ) // true
Js.Console.log2("innerPointIncrement", innerPointIncrement) // (10-0)/4 = 2.5
Js.Console.log2("innerXs", innerXs) // 2.5, 5, 7.5
Js.Console.log2("ysOptions", ysOptions)
Js.Console.log2("okYs", okYs)
let result = switch E.A.length(ysOptions) == E.A.length(okYs) {
| true => {
let numericIntermediate = okYs->E.A.reduce(0.0, (a, b) => a +. b)
let numericIntermediate2 = numericIntermediate *. increment
let resultWrapped =
numericIntermediate2->ReducerInterface_InternalExpressionValue.IEvNumber->Ok
resultWrapped
let innerPointsSum = okYs->E.A.reduce(0.0, (a, b) => a +. b)
let resultWithOuterPoints = switch(applyFunctionAtFloatToFloatOption(min), applyFunctionAtFloatToFloatOption(max)){
| (Ok(yMin), Ok(yMax)) => {
let result = ((yMin +. yMax)*.weightForAnOuterPoint +. innerPointsSum*.weightForAnInnerPoint)
let wrappedResult = result -> ReducerInterface_InternalExpressionValue.IEvNumber -> Ok
wrappedResult
}
| (Error(b), _) => Error(b)
| (_, Error(b)) => Error(b)
}
resultWithOuterPoints
}
| false => Error("Integration error in Danger.integrate")
}