cleanup: Move integrals to its own module
This commit is contained in:
parent
8ddd1a166a
commit
edce22050a
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@ -57,6 +57,187 @@ module Combinatorics = {
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}
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}
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module Integration = {
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let Helpers = {
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let integrateFunctionBetweenWithNumIntegrationPoints = (
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aLambda,
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min: float,
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max: float,
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numIntegrationPoints: float, // cast as int?
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environment,
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reducer,
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) => {
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let applyFunctionAtFloatToFloatOption = (point: float) => {
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// Defined here so that it has access to environment, reducer
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let pointAsInternalExpression = FunctionRegistry_Helpers.Wrappers.evNumber(point)
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let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
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aLambda,
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list{pointAsInternalExpression},
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environment,
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reducer,
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)
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let result = switch resultAsInternalExpression {
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| Ok(IEvNumber(x)) => Ok(x)
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| Error(_) =>
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Error(
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"Error 1 in Danger.integrate. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead",
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)
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| _ => Error("Error 2 in Danger.integrate")
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}
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result
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}
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// worked example in comments below, assuming min=0, max = 10
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let numTotalPoints = Belt.Float.toInt(numIntegrationPoints) // superflous declaration, but useful to keep track that we are interpreting "numIntegrationPoints" as the total number on which we evaluate the function, not e.g., as the inner integration points.
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let numInnerPoints = numTotalPoints - 2
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let numOuterPoints = 2
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let totalWeight = max -. min
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let weightForAnInnerPoint = totalWeight /. E.I.toFloat(numTotalPoints - 1)
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let weightForAnOuterPoint = totalWeight /. E.I.toFloat(numTotalPoints - 1) /. 2.0
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let innerPointIncrement = (max -. min) /. E.I.toFloat(numTotalPoints - 1)
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let innerXs = Belt.Array.makeBy(numInnerPoints, i =>
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min +. Belt_Float.fromInt(i + 1) *. innerPointIncrement
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)
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// Gotcha: makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
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let ysOptions = Belt.Array.map(innerXs, x => applyFunctionAtFloatToFloatOption(x))
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let okYs = E.A.R.filterOk(ysOptions)
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/* Logging, with a worked example. */
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// Useful for understanding what is happening.
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// assuming min = 0, max = 10, numTotalPoints=10, results below:
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let verbose = false
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if verbose {
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Js.Console.log2("numTotalPoints", numTotalPoints) // 5
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Js.Console.log2("numInnerPoints", numInnerPoints) // 3
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Js.Console.log2("numOuterPoints", numOuterPoints) // always 2
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Js.Console.log2("totalWeight", totalWeight) // 10 - 0 = 10
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Js.Console.log2("weightForAnInnerPoint", weightForAnInnerPoint) // 10/4 = 2.5
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Js.Console.log2("weightForAnOuterPoint", weightForAnOuterPoint) // 10/4/2 = 1.25
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Js.Console.log2(
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"weightForAnInnerPoint * numInnerPoints + weightForAnOuterPoint * numOuterPoints",
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weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +.
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weightForAnOuterPoint *. E.I.toFloat(numOuterPoints),
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) // should be 10
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Js.Console.log2(
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"sum of weights == totalWeight",
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weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +.
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weightForAnOuterPoint *. E.I.toFloat(numOuterPoints) == totalWeight,
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) // true
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Js.Console.log2("innerPointIncrement", innerPointIncrement) // (10-0)/4 = 2.5
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Js.Console.log2("innerXs", innerXs) // 2.5, 5, 7.5
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Js.Console.log2("ysOptions", ysOptions)
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Js.Console.log2("okYs", okYs)
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}
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//This is pretty hacky. It should use a result type instead of checking that length matches.
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let result = if E.A.length(ysOptions) == E.A.length(okYs) {
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let innerPointsSum = okYs->E.A.reduce(0.0, (a, b) => a +. b)
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let resultWithOuterPoints = switch (
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applyFunctionAtFloatToFloatOption(min),
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applyFunctionAtFloatToFloatOption(max),
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) {
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| (Ok(yMin), Ok(yMax)) => {
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let result =
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(yMin +. yMax) *. weightForAnOuterPoint +. innerPointsSum *. weightForAnInnerPoint
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let wrappedResult = result->ReducerInterface_InternalExpressionValue.IEvNumber->Ok
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wrappedResult
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}
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| (Error(b), _) => Error(b)
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| (_, Error(b)) => Error(b)
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}
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resultWithOuterPoints
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} else {
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Error(
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"Integration error 3 in Danger.integrate. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead",
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)
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}
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result
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}
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}
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module Lib = {
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// Integral in terms of function, min, max, num points
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// Note that execution time will be more predictable, because it
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// will only depend on num points and the complexity of the function
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let integrateFunctionBetweenWithNumIntegrationPoints = Function.make(
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~name="integrateFunctionBetweenWithNumIntegrationPoints",
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~nameSpace,
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~output=EvtNumber,
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~requiresNamespace=false,
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~examples=[`Danger.integrateFunctionBetweenWithNumIntegrationPoints({|x| x+1}, 1, 10, 10)`],
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// should be [x^2/2 + x]1_10 = (100/2 + 10) - (1/2 + 1) = 60 - 1.5 = 58.5
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// https://www.wolframalpha.com/input?i=integrate+x%2B1+from+1+to+10
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~definitions=[
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FnDefinition.make(
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~name="integrateFunctionBetweenWithNumIntegrationPoints",
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~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
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~run=(inputs, _, env, reducer) => {
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let result = switch inputs {
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| [_, _, _, IEvNumber(0.0)] =>
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Error("Integration error 4 in Danger.integrate: Increment can't be 0.")
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| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(numIntegrationPoints)] =>
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Helpers.integrateFunctionBetweenWithNumIntegrationPoints(
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aLambda,
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min,
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max,
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numIntegrationPoints,
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env,
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reducer,
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)
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| _ =>
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Error(
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"Integration error 5 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
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)
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}
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result
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},
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(),
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),
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],
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(),
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)
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// Integral in terms of function, min, max, epsilon (distance between points)
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// Execution time will be less predictable, because it
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// will depend on min, max and epsilon together,
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// as well and the complexity of the function
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let integrateFunctionBetweenWithEpsilon = Function.make(
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~name="integrateFunctionBetweenWithEpsilon",
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~nameSpace,
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~output=EvtNumber,
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~requiresNamespace=false,
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~examples=[`Danger.integrateFunctionBetweenWithEpsilon({|x| x+1}, 1, 10, 0.1)`],
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~definitions=[
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FnDefinition.make(
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~name="integrateFunctionBetweenWithEpsilon",
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~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
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~run=(inputs, _, env, reducer) => {
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let result = switch inputs {
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| [_, _, _, IEvNumber(0.0)] =>
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Error("Integration error in Danger.integrate: Increment can't be 0.")
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| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(epsilon)] =>
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Helpers.integrateFunctionBetweenWithNumIntegrationPoints(
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aLambda,
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min,
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max,
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(max -. min) /. epsilon,
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env,
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reducer,
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)->E.R2.errMap(_ =>
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"Integration error 7 in Danger.integrate. Something went wrong along the way"
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)
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| _ =>
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Error(
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"Integration error 8 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
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)
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}
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result
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},
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(),
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),
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],
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(),
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)
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}
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}
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module Internals = {
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// Probability functions
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@ -65,100 +246,7 @@ module Internals = {
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->Belt.Array.map(FunctionRegistry_Helpers.Wrappers.evNumber)
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->FunctionRegistry_Helpers.Wrappers.evArray
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let integrateFunctionBetweenWithNumIntegrationPoints = (
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aLambda,
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min: float,
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max: float,
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numIntegrationPoints: float, // cast as int?
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environment,
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reducer,
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) => {
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let applyFunctionAtFloatToFloatOption = (point: float) => {
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// Defined here so that it has access to environment, reducer
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let pointAsInternalExpression = FunctionRegistry_Helpers.Wrappers.evNumber(point)
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let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
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aLambda,
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list{pointAsInternalExpression},
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environment,
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reducer,
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)
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let result = switch resultAsInternalExpression {
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| Ok(IEvNumber(x)) => Ok(x)
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| Error(_) =>
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Error(
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"Error 1 in Danger.integrate. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead",
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)
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| _ => Error("Error 2 in Danger.integrate")
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}
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result
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}
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// worked example in comments below, assuming min=0, max = 10
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let numTotalPoints = Belt.Float.toInt(numIntegrationPoints) // superflous declaration, but useful to keep track that we are interpreting "numIntegrationPoints" as the total number on which we evaluate the function, not e.g., as the inner integration points.
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let numInnerPoints = numTotalPoints - 2
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let numOuterPoints = 2
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let totalWeight = max -. min
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let weightForAnInnerPoint = totalWeight /. E.I.toFloat(numTotalPoints - 1)
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let weightForAnOuterPoint = totalWeight /. E.I.toFloat(numTotalPoints - 1) /. 2.0
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let innerPointIncrement = (max -. min) /. E.I.toFloat(numTotalPoints - 1)
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let innerXs = Belt.Array.makeBy(numInnerPoints, i =>
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min +. Belt_Float.fromInt(i + 1) *. innerPointIncrement
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)
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// Gotcha: makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
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let ysOptions = Belt.Array.map(innerXs, x => applyFunctionAtFloatToFloatOption(x))
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let okYs = E.A.R.filterOk(ysOptions)
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/* Logging, with a worked example. */
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// Useful for understanding what is happening.
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// assuming min = 0, max = 10, numTotalPoints=10, results below:
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let verbose = false
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if verbose {
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Js.Console.log2("numTotalPoints", numTotalPoints) // 5
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Js.Console.log2("numInnerPoints", numInnerPoints) // 3
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Js.Console.log2("numOuterPoints", numOuterPoints) // always 2
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Js.Console.log2("totalWeight", totalWeight) // 10 - 0 = 10
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Js.Console.log2("weightForAnInnerPoint", weightForAnInnerPoint) // 10/4 = 2.5
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Js.Console.log2("weightForAnOuterPoint", weightForAnOuterPoint) // 10/4/2 = 1.25
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Js.Console.log2(
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"weightForAnInnerPoint * numInnerPoints + weightForAnOuterPoint * numOuterPoints",
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weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +.
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weightForAnOuterPoint *. E.I.toFloat(numOuterPoints),
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) // should be 10
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Js.Console.log2(
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"sum of weights == totalWeight",
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weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +.
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weightForAnOuterPoint *. E.I.toFloat(numOuterPoints) == totalWeight,
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) // true
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Js.Console.log2("innerPointIncrement", innerPointIncrement) // (10-0)/4 = 2.5
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Js.Console.log2("innerXs", innerXs) // 2.5, 5, 7.5
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Js.Console.log2("ysOptions", ysOptions)
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Js.Console.log2("okYs", okYs)
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}
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//This is pretty hacky. It should use a result type instead of checking that length matches.
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let result = if E.A.length(ysOptions) == E.A.length(okYs) {
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let innerPointsSum = okYs->E.A.reduce(0.0, (a, b) => a +. b)
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let resultWithOuterPoints = switch (
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applyFunctionAtFloatToFloatOption(min),
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applyFunctionAtFloatToFloatOption(max),
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) {
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| (Ok(yMin), Ok(yMax)) => {
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let result =
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(yMin +. yMax) *. weightForAnOuterPoint +. innerPointsSum *. weightForAnInnerPoint
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let wrappedResult = result->ReducerInterface_InternalExpressionValue.IEvNumber->Ok
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wrappedResult
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}
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| (Error(b), _) => Error(b)
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| (_, Error(b)) => Error(b)
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}
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resultWithOuterPoints
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} else {
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Error(
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"Integration error 3 in Danger.integrate. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead",
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)
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}
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result
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}
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// Diminishing returns
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// Helpers
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type diminishingReturnsAccumulatorInner = {
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@ -272,92 +360,13 @@ module Internals = {
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}
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let library = [
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Combinatorics.Lib.laplace,
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Combinatorics.Lib.factorial,
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Combinatorics.Lib.choose,
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Combinatorics.Lib.binomial,
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// Integral in terms of function, min, max, num points
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// Note that execution time will be more predictable, because it
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// will only depend on num points and the complexity of the function
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Function.make(
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~name="integrateFunctionBetweenWithNumIntegrationPoints",
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~nameSpace,
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~output=EvtNumber,
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~requiresNamespace=false,
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~examples=[`Danger.integrateFunctionBetweenWithNumIntegrationPoints({|x| x+1}, 1, 10, 10)`],
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// should be [x^2/2 + x]1_10 = (100/2 + 10) - (1/2 + 1) = 60 - 1.5 = 58.5
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// https://www.wolframalpha.com/input?i=integrate+x%2B1+from+1+to+10
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~definitions=[
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FnDefinition.make(
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~name="integrateFunctionBetweenWithNumIntegrationPoints",
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~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
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~run=(inputs, _, env, reducer) => {
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let result = switch inputs {
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| [_, _, _, IEvNumber(0.0)] =>
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Error("Integration error 4 in Danger.integrate: Increment can't be 0.")
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| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(numIntegrationPoints)] =>
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Internals.integrateFunctionBetweenWithNumIntegrationPoints(
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aLambda,
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min,
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max,
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numIntegrationPoints,
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env,
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reducer,
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)
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| _ =>
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Error(
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"Integration error 5 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
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)
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}
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result
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},
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(),
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),
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],
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(),
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),
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// Integral in terms of function, min, max, epsilon (distance between points)
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// Execution time will be less predictable, because it
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// will depend on min, max and epsilon together,
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// as well and the complexity of the function
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Function.make(
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~name="integrateFunctionBetweenWithEpsilon",
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~nameSpace,
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~output=EvtNumber,
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~requiresNamespace=false,
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~examples=[`Danger.integrateFunctionBetweenWithEpsilon({|x| x+1}, 1, 10, 0.1)`],
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~definitions=[
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FnDefinition.make(
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~name="integrateFunctionBetweenWithEpsilon",
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~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
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~run=(inputs, _, env, reducer) => {
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let result = switch inputs {
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| [_, _, _, IEvNumber(0.0)] =>
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Error("Integration error in Danger.integrate: Increment can't be 0.")
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| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(epsilon)] =>
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Internals.integrateFunctionBetweenWithNumIntegrationPoints(
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aLambda,
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min,
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max,
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(max -. min) /. epsilon,
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env,
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reducer,
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)->E.R2.errMap(_ =>
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"Integration error 7 in Danger.integrate. Something went wrong along the way"
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)
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| _ =>
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Error(
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"Integration error 8 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
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)
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}
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result
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},
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(),
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),
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],
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(),
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),
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// Diminishing marginal return functions
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// There are functions diminishingMarginalReturnsForFunctions2 through diminishingMarginalReturnsForFunctions7
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// Because of this bug: <https://github.com/quantified-uncertainty/squiggle/issues/1090>
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