cleanup: Move integrals to its own module
This commit is contained in:
parent
8ddd1a166a
commit
edce22050a
|
|
@ -57,6 +57,187 @@ module Combinatorics = {
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
module Integration = {
|
||||||
|
let Helpers = {
|
||||||
|
let integrateFunctionBetweenWithNumIntegrationPoints = (
|
||||||
|
aLambda,
|
||||||
|
min: float,
|
||||||
|
max: float,
|
||||||
|
numIntegrationPoints: float, // cast as int?
|
||||||
|
environment,
|
||||||
|
reducer,
|
||||||
|
) => {
|
||||||
|
let applyFunctionAtFloatToFloatOption = (point: float) => {
|
||||||
|
// Defined here so that it has access to environment, reducer
|
||||||
|
let pointAsInternalExpression = FunctionRegistry_Helpers.Wrappers.evNumber(point)
|
||||||
|
let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
|
||||||
|
aLambda,
|
||||||
|
list{pointAsInternalExpression},
|
||||||
|
environment,
|
||||||
|
reducer,
|
||||||
|
)
|
||||||
|
let result = switch resultAsInternalExpression {
|
||||||
|
| Ok(IEvNumber(x)) => Ok(x)
|
||||||
|
| Error(_) =>
|
||||||
|
Error(
|
||||||
|
"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",
|
||||||
|
)
|
||||||
|
| _ => Error("Error 2 in Danger.integrate")
|
||||||
|
}
|
||||||
|
result
|
||||||
|
}
|
||||||
|
// worked example in comments below, assuming min=0, max = 10
|
||||||
|
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.
|
||||||
|
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
|
||||||
|
)
|
||||||
|
// Gotcha: 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, with a worked example. */
|
||||||
|
// Useful for understanding what is happening.
|
||||||
|
// assuming min = 0, max = 10, numTotalPoints=10, results below:
|
||||||
|
let verbose = false
|
||||||
|
if verbose {
|
||||||
|
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)
|
||||||
|
}
|
||||||
|
|
||||||
|
//This is pretty hacky. It should use a result type instead of checking that length matches.
|
||||||
|
let result = if E.A.length(ysOptions) == E.A.length(okYs) {
|
||||||
|
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
|
||||||
|
} else {
|
||||||
|
Error(
|
||||||
|
"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",
|
||||||
|
)
|
||||||
|
}
|
||||||
|
result
|
||||||
|
}
|
||||||
|
}
|
||||||
|
module Lib = {
|
||||||
|
// Integral in terms of function, min, max, num points
|
||||||
|
// Note that execution time will be more predictable, because it
|
||||||
|
// will only depend on num points and the complexity of the function
|
||||||
|
let integrateFunctionBetweenWithNumIntegrationPoints = Function.make(
|
||||||
|
~name="integrateFunctionBetweenWithNumIntegrationPoints",
|
||||||
|
~nameSpace,
|
||||||
|
~output=EvtNumber,
|
||||||
|
~requiresNamespace=false,
|
||||||
|
~examples=[`Danger.integrateFunctionBetweenWithNumIntegrationPoints({|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="integrateFunctionBetweenWithNumIntegrationPoints",
|
||||||
|
~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
|
||||||
|
~run=(inputs, _, env, reducer) => {
|
||||||
|
let result = switch inputs {
|
||||||
|
| [_, _, _, IEvNumber(0.0)] =>
|
||||||
|
Error("Integration error 4 in Danger.integrate: Increment can't be 0.")
|
||||||
|
| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(numIntegrationPoints)] =>
|
||||||
|
Helpers.integrateFunctionBetweenWithNumIntegrationPoints(
|
||||||
|
aLambda,
|
||||||
|
min,
|
||||||
|
max,
|
||||||
|
numIntegrationPoints,
|
||||||
|
env,
|
||||||
|
reducer,
|
||||||
|
)
|
||||||
|
| _ =>
|
||||||
|
Error(
|
||||||
|
"Integration error 5 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
|
||||||
|
)
|
||||||
|
}
|
||||||
|
result
|
||||||
|
},
|
||||||
|
(),
|
||||||
|
),
|
||||||
|
],
|
||||||
|
(),
|
||||||
|
)
|
||||||
|
// Integral in terms of function, min, max, epsilon (distance between points)
|
||||||
|
// Execution time will be less predictable, because it
|
||||||
|
// will depend on min, max and epsilon together,
|
||||||
|
// as well and the complexity of the function
|
||||||
|
let integrateFunctionBetweenWithEpsilon = Function.make(
|
||||||
|
~name="integrateFunctionBetweenWithEpsilon",
|
||||||
|
~nameSpace,
|
||||||
|
~output=EvtNumber,
|
||||||
|
~requiresNamespace=false,
|
||||||
|
~examples=[`Danger.integrateFunctionBetweenWithEpsilon({|x| x+1}, 1, 10, 0.1)`],
|
||||||
|
~definitions=[
|
||||||
|
FnDefinition.make(
|
||||||
|
~name="integrateFunctionBetweenWithEpsilon",
|
||||||
|
~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(epsilon)] =>
|
||||||
|
Helpers.integrateFunctionBetweenWithNumIntegrationPoints(
|
||||||
|
aLambda,
|
||||||
|
min,
|
||||||
|
max,
|
||||||
|
(max -. min) /. epsilon,
|
||||||
|
env,
|
||||||
|
reducer,
|
||||||
|
)->E.R2.errMap(_ =>
|
||||||
|
"Integration error 7 in Danger.integrate. Something went wrong along the way"
|
||||||
|
)
|
||||||
|
| _ =>
|
||||||
|
Error(
|
||||||
|
"Integration error 8 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
|
||||||
|
)
|
||||||
|
}
|
||||||
|
result
|
||||||
|
},
|
||||||
|
(),
|
||||||
|
),
|
||||||
|
],
|
||||||
|
(),
|
||||||
|
)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
module Internals = {
|
module Internals = {
|
||||||
// Probability functions
|
// Probability functions
|
||||||
|
|
||||||
|
|
@ -65,99 +246,6 @@ module Internals = {
|
||||||
->Belt.Array.map(FunctionRegistry_Helpers.Wrappers.evNumber)
|
->Belt.Array.map(FunctionRegistry_Helpers.Wrappers.evNumber)
|
||||||
->FunctionRegistry_Helpers.Wrappers.evArray
|
->FunctionRegistry_Helpers.Wrappers.evArray
|
||||||
|
|
||||||
let integrateFunctionBetweenWithNumIntegrationPoints = (
|
|
||||||
aLambda,
|
|
||||||
min: float,
|
|
||||||
max: float,
|
|
||||||
numIntegrationPoints: float, // cast as int?
|
|
||||||
environment,
|
|
||||||
reducer,
|
|
||||||
) => {
|
|
||||||
let applyFunctionAtFloatToFloatOption = (point: float) => {
|
|
||||||
// Defined here so that it has access to environment, reducer
|
|
||||||
let pointAsInternalExpression = FunctionRegistry_Helpers.Wrappers.evNumber(point)
|
|
||||||
let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
|
|
||||||
aLambda,
|
|
||||||
list{pointAsInternalExpression},
|
|
||||||
environment,
|
|
||||||
reducer,
|
|
||||||
)
|
|
||||||
let result = switch resultAsInternalExpression {
|
|
||||||
| Ok(IEvNumber(x)) => Ok(x)
|
|
||||||
| Error(_) =>
|
|
||||||
Error(
|
|
||||||
"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",
|
|
||||||
)
|
|
||||||
| _ => Error("Error 2 in Danger.integrate")
|
|
||||||
}
|
|
||||||
result
|
|
||||||
}
|
|
||||||
// worked example in comments below, assuming min=0, max = 10
|
|
||||||
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.
|
|
||||||
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
|
|
||||||
)
|
|
||||||
// Gotcha: 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, with a worked example. */
|
|
||||||
// Useful for understanding what is happening.
|
|
||||||
// assuming min = 0, max = 10, numTotalPoints=10, results below:
|
|
||||||
let verbose = false
|
|
||||||
if verbose {
|
|
||||||
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)
|
|
||||||
}
|
|
||||||
|
|
||||||
//This is pretty hacky. It should use a result type instead of checking that length matches.
|
|
||||||
let result = if E.A.length(ysOptions) == E.A.length(okYs) {
|
|
||||||
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
|
|
||||||
} else {
|
|
||||||
Error(
|
|
||||||
"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",
|
|
||||||
)
|
|
||||||
}
|
|
||||||
result
|
|
||||||
}
|
|
||||||
|
|
||||||
// Diminishing returns
|
// Diminishing returns
|
||||||
// Helpers
|
// Helpers
|
||||||
|
|
@ -272,92 +360,13 @@ module Internals = {
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
let library = [
|
let library = [
|
||||||
Combinatorics.Lib.laplace,
|
Combinatorics.Lib.laplace,
|
||||||
Combinatorics.Lib.factorial,
|
Combinatorics.Lib.factorial,
|
||||||
Combinatorics.Lib.choose,
|
Combinatorics.Lib.choose,
|
||||||
Combinatorics.Lib.binomial,
|
Combinatorics.Lib.binomial,
|
||||||
// Integral in terms of function, min, max, num points
|
|
||||||
// Note that execution time will be more predictable, because it
|
|
||||||
// will only depend on num points and the complexity of the function
|
|
||||||
Function.make(
|
|
||||||
~name="integrateFunctionBetweenWithNumIntegrationPoints",
|
|
||||||
~nameSpace,
|
|
||||||
~output=EvtNumber,
|
|
||||||
~requiresNamespace=false,
|
|
||||||
~examples=[`Danger.integrateFunctionBetweenWithNumIntegrationPoints({|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="integrateFunctionBetweenWithNumIntegrationPoints",
|
|
||||||
~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber],
|
|
||||||
~run=(inputs, _, env, reducer) => {
|
|
||||||
let result = switch inputs {
|
|
||||||
| [_, _, _, IEvNumber(0.0)] =>
|
|
||||||
Error("Integration error 4 in Danger.integrate: Increment can't be 0.")
|
|
||||||
| [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(numIntegrationPoints)] =>
|
|
||||||
Internals.integrateFunctionBetweenWithNumIntegrationPoints(
|
|
||||||
aLambda,
|
|
||||||
min,
|
|
||||||
max,
|
|
||||||
numIntegrationPoints,
|
|
||||||
env,
|
|
||||||
reducer,
|
|
||||||
)
|
|
||||||
| _ =>
|
|
||||||
Error(
|
|
||||||
"Integration error 5 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
|
|
||||||
)
|
|
||||||
}
|
|
||||||
result
|
|
||||||
},
|
|
||||||
(),
|
|
||||||
),
|
|
||||||
],
|
|
||||||
(),
|
|
||||||
),
|
|
||||||
// Integral in terms of function, min, max, epsilon (distance between points)
|
|
||||||
// Execution time will be less predictable, because it
|
|
||||||
// will depend on min, max and epsilon together,
|
|
||||||
// as well and the complexity of the function
|
|
||||||
Function.make(
|
|
||||||
~name="integrateFunctionBetweenWithEpsilon",
|
|
||||||
~nameSpace,
|
|
||||||
~output=EvtNumber,
|
|
||||||
~requiresNamespace=false,
|
|
||||||
~examples=[`Danger.integrateFunctionBetweenWithEpsilon({|x| x+1}, 1, 10, 0.1)`],
|
|
||||||
~definitions=[
|
|
||||||
FnDefinition.make(
|
|
||||||
~name="integrateFunctionBetweenWithEpsilon",
|
|
||||||
~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(epsilon)] =>
|
|
||||||
Internals.integrateFunctionBetweenWithNumIntegrationPoints(
|
|
||||||
aLambda,
|
|
||||||
min,
|
|
||||||
max,
|
|
||||||
(max -. min) /. epsilon,
|
|
||||||
env,
|
|
||||||
reducer,
|
|
||||||
)->E.R2.errMap(_ =>
|
|
||||||
"Integration error 7 in Danger.integrate. Something went wrong along the way"
|
|
||||||
)
|
|
||||||
| _ =>
|
|
||||||
Error(
|
|
||||||
"Integration error 8 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))",
|
|
||||||
)
|
|
||||||
}
|
|
||||||
result
|
|
||||||
},
|
|
||||||
(),
|
|
||||||
),
|
|
||||||
],
|
|
||||||
(),
|
|
||||||
),
|
|
||||||
// Diminishing marginal return functions
|
// Diminishing marginal return functions
|
||||||
// There are functions diminishingMarginalReturnsForFunctions2 through diminishingMarginalReturnsForFunctions7
|
// There are functions diminishingMarginalReturnsForFunctions2 through diminishingMarginalReturnsForFunctions7
|
||||||
// Because of this bug: <https://github.com/quantified-uncertainty/squiggle/issues/1090>
|
// Because of this bug: <https://github.com/quantified-uncertainty/squiggle/issues/1090>
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue
Block a user