feat: Added a slightly better integral function

Slightly better because the handling of bounds is better.
Previously we were integrating at min, min + interval,
min + i*interval, ...
which meanst that sometimes we weren't integrating at
max.

Also a minimal amount of cleanup
This commit is contained in:
NunoSempere 2022-09-05 09:08:53 +02:00
parent abad453523
commit e73ffaa10a

View File

@ -57,10 +57,12 @@ module FunctionToNumberZero = {
}
module Internals = {
// Probability functions
let factorial = Stdlib.Math.factorial
let choose = ((n, k)) => factorial(n) /. (factorial(n -. k) *. factorial(k))
let pow = (base, exp) => Js.Math.pow_float(~base, ~exp)
let binomial = ((n, k, p)) => choose((n, k)) *. pow(p, k) *. pow(1.0 -. p, n -. k)
// Integral helper functions
let applyFunctionAtPoint = (
aLambda,
internalNumber: internalExpressionValue,
@ -74,10 +76,9 @@ module Internals = {
let internalZero = ReducerInterface_InternalExpressionValue.IEvNumber(0.0)
let applyFunctionAtZero = (aLambda, environment, reducer) =>
applyFunctionAtPoint(aLambda, internalZero, environment, reducer)
@dead
let applyFunctionAtFloat = (aLambda, point, environment, reducer) =>
@dead let applyFunctionAtFloat = (aLambda, point, environment, reducer) =>
applyFunctionAtPoint(aLambda, ReducerInterface_InternalExpressionValue.IEvNumber(point))
// simplest integral function
let integrateFunctionBetweenWithIncrement = (
aLambda,
min: float,
@ -86,7 +87,6 @@ module Internals = {
environment,
reducer,
) => {
// Should be easy, but tired today.
let applyFunctionAtFloatToFloatOption = (point: float) => {
let pointAsInternalExpression = ReducerInterface_InternalExpressionValue.IEvNumber(point)
let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
@ -118,6 +118,48 @@ module Internals = {
}
result
}
// slightly better integrate function
let integrateFunctionBetweenWithNumIntervals = (
aLambda,
min: float,
max: float,
numIntervals: float, // cast as int?
environment,
reducer,
) => {
let applyFunctionAtFloatToFloatOption = (point: float) => {
let pointAsInternalExpression = ReducerInterface_InternalExpressionValue.IEvNumber(point)
let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
aLambda,
list{pointAsInternalExpression},
environment,
reducer,
)
let result = switch resultAsInternalExpression {
| Ok(IEvNumber(x)) => Ok(x)
| Error(_) => Error("Integration error in Danger.integrate")
| _ => Error("Integration error in Danger.integrate")
}
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, i => min +. Belt_Float.fromInt(i) *. increment)
let ysOptions = Belt.Array.map(xs, x => applyFunctionAtFloatToFloatOption(x))
let okYs = E.A.R.filterOk(ysOptions)
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
}
| false => Error("Integration error in Danger.integrate")
}
result
}
@dead let getDiminishingMarginalReturnsEquilibrium = "To do"
}
@ -162,6 +204,7 @@ let library = [
~definitions=[ThreeNumbersToNumber.make("binomial", Internals.binomial)],
(),
),
// Helper functions building up to the integral
Function.make(
~name="functionToZero",
~nameSpace,
@ -215,6 +258,7 @@ let library = [
],
(),
),
// simplest integral
Function.make(
~name="integrateFunctionBetweenWithIncrement",
~nameSpace,
@ -254,4 +298,44 @@ let library = [
],
(),
),
// Integral which is a bit more thoughtful
Function.make(
~name="integrateFunctionBetweenWithNumIntervals",
~nameSpace,
~output=EvtArray,
~requiresNamespace=false,
~examples=[`Danger.integrateFunctionBetweenWithNumIntervals({|x| x+1}, 1, 10, 10)`],
// should be [x^2/2 + x]1_10 = (100/2 + 10) - (1/2 + 1) = 60 - 1.5 = 58.5
// https://www.wolframalpha.com/input?i=integrate+x%2B1+from+1+to+10
~definitions=[
FnDefinition.make(
~name="integrateFunctionBetweenWithNumIntervals",
~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
~run=(inputs, _, env, reducer) => {
let result = switch inputs {
| [_, _, _, IEvNumber(0.0)] =>
Error("Integration error in Danger.integrate: Increment can't be 0.")
| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(numIntervals)] =>
Internals.integrateFunctionBetweenWithNumIntervals(
aLambda,
min,
max,
numIntervals,
env,
reducer,
)->E.R2.errMap(_ =>
"Integration error in Danger.integrate. Something went wrong along the way"
)
| _ =>
Error(
"Integration error in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
)
}
result
},
(),
),
],
(),
),
]