feat: In Danger, add dmr for many functions

Still to be tested
This commit is contained in:
NunoSempere 2022-09-05 17:05:25 +02:00
parent 2f33559e77
commit 8bdfa03799

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@ -175,6 +175,13 @@ module Internals = {
optimalAllocations: array<float>, optimalAllocations: array<float>,
currentMarginalReturns: result<array<float>, string>, currentMarginalReturns: result<array<float>, string>,
} }
let findBiggestElementIndex = xs =>
E.A.reducei(xs, 0, (acc, newElement, index) => {
switch newElement > xs[acc] {
| true => index
| false => acc
}
})
type diminishingReturnsAccumulator = result<diminishingReturnsAccumulatorInner, string> type diminishingReturnsAccumulator = result<diminishingReturnsAccumulatorInner, string>
let diminishingMarginalReturnsForTwoFunctions = ( let diminishingMarginalReturnsForTwoFunctions = (
lambda1, lambda1,
@ -214,13 +221,6 @@ module Internals = {
let increment = funds /. numDivisions let increment = funds /. numDivisions
let arrayOfIncrements = Belt.Array.makeBy(numDivisionsInt, _ => increment) let arrayOfIncrements = Belt.Array.makeBy(numDivisionsInt, _ => increment)
let findBiggestElementIndex = xs =>
E.A.reducei(xs, 0, (acc, newElement, index) => {
switch newElement > xs[acc] {
| true => index
| false => acc
}
})
let initAccumulator: diminishingReturnsAccumulator = Ok({ let initAccumulator: diminishingReturnsAccumulator = Ok({
optimalAllocations: [0.0, 0.0], optimalAllocations: [0.0, 0.0],
currentMarginalReturns: E.A.R.firstErrorOrOpen([ currentMarginalReturns: E.A.R.firstErrorOrOpen([
@ -278,6 +278,115 @@ module Internals = {
} }
optimalAllocationResult optimalAllocationResult
} }
let diminishingMarginalReturnsForManyFunctions = (
innerLambdas,
funds,
approximateIncrement,
environment,
reducer,
) => {
/*
Two possible algorithms (n=funds/increment, m=num lambdas)
1. O(n): Iterate through value on next n dollars. At each step, only compute the new marginal return of the function which is spent
2. O(n*m): Iterate through all possible spending combinations. Fun is, it doesn't assume that the returns of marginal spending are diminishing.
*/
let individuallyWrappedLambdas = E.A.fmap(possibleLambda =>
switch possibleLambda {
| ReducerInterface_InternalExpressionValue.IEvLambda(lambda) => Ok(lambda)
| _ =>
Error(
"Error in diminishingMarginalReturnsForManyFunctions: One of the elements in the function array is not a function",
)
}
, innerLambdas)
let collectivelyWrappedLambdas = E.A.R.firstErrorOrOpen(individuallyWrappedLambdas)
let result = switch collectivelyWrappedLambdas {
| Ok(lambdas) => {
let applyFunctionAtFloatToFloatOption = (lambda, point: float) => {
// Defined here so that it has access to environment, reducer
let pointAsInternalExpression = castFloatToInternalNumber(point)
let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall(
lambda,
list{pointAsInternalExpression},
environment,
reducer,
)
let result = switch resultAsInternalExpression {
| Ok(IEvNumber(x)) => Ok(x)
| Error(_) =>
Error(
"Integration 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("Integration error 2 in Danger.integrate")
}
result
}
let numDivisions = Js.Math.round(funds /. approximateIncrement)
let numDivisionsInt = Belt.Float.toInt(numDivisions)
let increment = funds /. numDivisions
let arrayOfIncrements = Belt.Array.makeBy(numDivisionsInt, _ => increment)
let numLambdas = E.A.length(lambdas)
let initAccumulator: diminishingReturnsAccumulator = Ok({
optimalAllocations: Belt.Array.makeBy(numLambdas, _ => 0.0),
currentMarginalReturns: E.A.fmap(
lambda => applyFunctionAtFloatToFloatOption(lambda, 0.0),
lambdas,
)->E.A.R.firstErrorOrOpen,
})
let optimalAllocationEndAccumulator = E.A.reduce(arrayOfIncrements, initAccumulator, (
acc,
newIncrement,
) => {
switch acc {
| Ok(accInner) => {
let oldMarginalReturnsWrapped = accInner.currentMarginalReturns
let newAccWrapped = switch oldMarginalReturnsWrapped {
| Ok(oldMarginalReturns) => {
let indexOfBiggestDMR = findBiggestElementIndex(oldMarginalReturns)
let newOptimalAllocations = Belt.Array.copy(accInner.optimalAllocations)
let newOptimalAllocationsi =
newOptimalAllocations[indexOfBiggestDMR] +. newIncrement
newOptimalAllocations[indexOfBiggestDMR] = newOptimalAllocationsi
let lambdai = lambdas[indexOfBiggestDMR]
let newMarginalResultsLambdai = applyFunctionAtFloatToFloatOption(
lambdai,
newOptimalAllocationsi,
)
let newCurrentMarginalReturns = switch newMarginalResultsLambdai {
| Ok(value) => {
let result = Belt.Array.copy(oldMarginalReturns)
result[indexOfBiggestDMR] = value
Ok(result)
}
| Error(b) => Error(b)
}
let newAcc: diminishingReturnsAccumulatorInner = {
optimalAllocations: newOptimalAllocations,
currentMarginalReturns: newCurrentMarginalReturns,
}
Ok(newAcc)
}
| Error(b) => Error(b)
}
newAccWrapped
}
| Error(b) => Error(b)
}
})
let optimalAllocationResult = switch optimalAllocationEndAccumulator {
| Ok(inner) => Ok(castArrayOfFloatsToInternalArrayOfInternals(inner.optimalAllocations))
| Error(b) => Error(b)
}
optimalAllocationResult
/*let result = [0.0, 0.0]->castArrayOfFloatsToInternalArrayOfInternals->Ok
result*/
}
| Error(b) => Error(b)
}
result
}
} }
let library = [ let library = [
@ -457,7 +566,7 @@ let library = [
~nameSpace, ~nameSpace,
~output=EvtArray, ~output=EvtArray,
~requiresNamespace=false, ~requiresNamespace=false,
~examples=[`Danger.diminishingMarginalReturnsForTwoFunctions({|x| x+1}, {|y| 10}, 100, 1)`], ~examples=[`Danger.diminishingMarginalReturnsForTwoFunctions({|x| x+1}, {|y| 10}, 100, 0.01)`],
~definitions=[ ~definitions=[
FnDefinition.make( FnDefinition.make(
~name="diminishingMarginalReturnsForTwoFunctions", ~name="diminishingMarginalReturnsForTwoFunctions",
@ -485,4 +594,33 @@ let library = [
], ],
(), (),
), ),
Function.make(
~name="diminishingMarginalReturnsForManyFunctions",
~nameSpace,
~output=EvtArray,
~requiresNamespace=false,
~examples=[
`Danger.diminishingMarginalReturnsForManyFunctions([{|x| x+1}, {|y| 10} , {|z| 20 - 2*z}], 100, 0.01)`,
],
~definitions=[
FnDefinition.make(
~name="diminishingMarginalReturnsForManyFunctions",
~inputs=[FRTypeArray(FRTypeLambda), FRTypeNumber, FRTypeNumber],
~run=(inputs, _, env, reducer) =>
switch inputs {
| [IEvArray(innerlambdas), IEvNumber(funds), IEvNumber(approximateIncrement)] =>
Internals.diminishingMarginalReturnsForManyFunctions(
innerlambdas,
funds,
approximateIncrement,
env,
reducer,
)
| _ => Error("Error in Danger.diminishingMarginalReturnsForTwoFunctions")
},
(),
),
],
(),
),
] ]