Merge pull request #402 from quantified-uncertainty/algebraic-combination-refactor
Algebraic combination refactor
This commit is contained in:
commit
20685ea8cb
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@ -92,11 +92,11 @@ describe("eval on distribution functions", () => {
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testEval("log(2, uniform(5,8))", "Ok(Sample Set Distribution)")
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testEval(
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"log(normal(5,2), 3)",
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"Error(Distribution Math Error: Logarithm of input error: First input must completely greater than 0)",
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"Error(Distribution Math Error: Logarithm of input error: First input must be completely greater than 0)",
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)
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testEval(
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"log(normal(5,2), normal(10,1))",
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"Error(Distribution Math Error: Logarithm of input error: First input must completely greater than 0)",
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"Error(Distribution Math Error: Logarithm of input error: First input must be completely greater than 0)",
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)
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testEval("log(uniform(5,8))", "Ok(Sample Set Distribution)")
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testEval("log10(uniform(5,8))", "Ok(Sample Set Distribution)")
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@ -150,144 +150,143 @@ let truncate = Truncate.run
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of a new variable that is the result of the operation on A and B.
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For instance, normal(0, 1) + normal(1, 1) -> normal(1, 2).
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In general, this is implemented via convolution.
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TODO: It would be useful to be able to pass in a paramater to get this to run either with convolution or monte carlo.
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*/
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module AlgebraicCombination = {
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let runConvolution = (
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toPointSet: toPointSetFn,
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arithmeticOperation: Operation.convolutionOperation,
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t1: t,
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t2: t,
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) =>
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E.R.merge(toPointSet(t1), toPointSet(t2))->E.R2.fmap(((a, b)) =>
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PointSetDist.combineAlgebraically(arithmeticOperation, a, b)
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)
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let runMonteCarlo = (
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toSampleSet: toSampleSetFn,
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arithmeticOperation: Operation.algebraicOperation,
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t1: t,
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t2: t,
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): result<t, error> => {
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let fn = Operation.Algebraic.toFn(arithmeticOperation)
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E.R.merge(toSampleSet(t1), toSampleSet(t2))
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->E.R.bind(((t1, t2)) => {
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SampleSetDist.map2(~fn, ~t1, ~t2)->E.R2.errMap(x => DistributionTypes.OperationError(x))
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})
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->E.R2.fmap(r => DistributionTypes.SampleSet(r))
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}
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/*
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module InputValidator = {
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/*
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It would be good to also do a check to make sure that probability mass for the second
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operand, at value 1.0, is 0 (or approximately 0). However, we'd ideally want to check
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that both the probability mass and the probability density are greater than zero.
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Right now we don't yet have a way of getting probability mass, so I'll leave this for later.
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*/
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let getLogarithmInputError = (t1: t, t2: t, ~toPointSetFn: toPointSetFn): option<error> => {
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let firstOperandIsGreaterThanZero =
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toFloatOperation(
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t1,
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~toPointSetFn,
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~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
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) |> E.R.fmap(r => r > 0.)
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let secondOperandIsGreaterThanZero =
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toFloatOperation(
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t2,
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~toPointSetFn,
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~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
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) |> E.R.fmap(r => r > 0.)
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let items = E.A.R.firstErrorOrOpen([
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firstOperandIsGreaterThanZero,
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secondOperandIsGreaterThanZero,
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])
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switch items {
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| Error(r) => Some(r)
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| Ok([true, _]) =>
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Some(LogarithmOfDistributionError("First input must completely greater than 0"))
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| Ok([false, true]) =>
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Some(LogarithmOfDistributionError("Second input must completely greater than 0"))
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| Ok([false, false]) => None
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| Ok(_) => Some(Unreachable)
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let getLogarithmInputError = (t1: t, t2: t, ~toPointSetFn: toPointSetFn): option<error> => {
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let firstOperandIsGreaterThanZero =
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toFloatOperation(
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t1,
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~toPointSetFn,
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~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
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) |> E.R.fmap(r => r > 0.)
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let secondOperandIsGreaterThanZero =
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toFloatOperation(
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t2,
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~toPointSetFn,
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~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
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) |> E.R.fmap(r => r > 0.)
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let items = E.A.R.firstErrorOrOpen([
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firstOperandIsGreaterThanZero,
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secondOperandIsGreaterThanZero,
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])
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switch items {
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| Error(r) => Some(r)
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| Ok([true, _]) =>
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Some(LogarithmOfDistributionError("First input must be completely greater than 0"))
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| Ok([false, true]) =>
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Some(LogarithmOfDistributionError("Second input must be completely greater than 0"))
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| Ok([false, false]) => None
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| Ok(_) => Some(Unreachable)
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}
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}
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let run = (t1: t, t2: t, ~toPointSetFn: toPointSetFn, ~arithmeticOperation): option<error> => {
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if arithmeticOperation == #Logarithm {
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getLogarithmInputError(t1, t2, ~toPointSetFn)
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} else {
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None
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}
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}
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}
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let getInvalidOperationError = (
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t1: t,
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t2: t,
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~toPointSetFn: toPointSetFn,
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module StrategyCallOnValidatedInputs = {
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let convolution = (
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toPointSet: toPointSetFn,
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arithmeticOperation: Operation.convolutionOperation,
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t1: t,
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t2: t,
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): result<t, error> =>
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E.R.merge(toPointSet(t1), toPointSet(t2))
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->E.R2.fmap(((a, b)) => PointSetDist.combineAlgebraically(arithmeticOperation, a, b))
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->E.R2.fmap(r => DistributionTypes.PointSet(r))
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let monteCarlo = (
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toSampleSet: toSampleSetFn,
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arithmeticOperation: Operation.algebraicOperation,
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t1: t,
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t2: t,
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): result<t, error> => {
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let fn = Operation.Algebraic.toFn(arithmeticOperation)
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E.R.merge(toSampleSet(t1), toSampleSet(t2))
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->E.R.bind(((t1, t2)) => {
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SampleSetDist.map2(~fn, ~t1, ~t2)->E.R2.errMap(x => DistributionTypes.OperationError(x))
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})
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->E.R2.fmap(r => DistributionTypes.SampleSet(r))
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}
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let symbolic = (
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arithmeticOperation: Operation.algebraicOperation,
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t1: t,
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t2: t,
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): SymbolicDistTypes.analyticalSimplificationResult => {
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switch (t1, t2) {
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| (DistributionTypes.Symbolic(d1), DistributionTypes.Symbolic(d2)) =>
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SymbolicDist.T.tryAnalyticalSimplification(d1, d2, arithmeticOperation)
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| _ => #NoSolution
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}
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}
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}
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module StrategyChooser = {
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type specificStrategy = [#AsSymbolic | #AsMonteCarlo | #AsConvolution]
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//I'm (Ozzie) really just guessing here, very little idea what's best
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let expectedConvolutionCost: t => int = x =>
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switch x {
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| Symbolic(#Float(_)) => MagicNumbers.OpCost.floatCost
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| Symbolic(_) => MagicNumbers.OpCost.symbolicCost
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| PointSet(Discrete(m)) => m.xyShape->XYShape.T.length
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| PointSet(Mixed(_)) => MagicNumbers.OpCost.mixedCost
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| PointSet(Continuous(_)) => MagicNumbers.OpCost.continuousCost
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| _ => MagicNumbers.OpCost.wildcardCost
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}
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let run = (~t1: t, ~t2: t, ~arithmeticOperation): specificStrategy => {
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switch StrategyCallOnValidatedInputs.symbolic(arithmeticOperation, t1, t2) {
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| #AnalyticalSolution(_)
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| #Error(_) =>
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#AsSymbolic
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| #NoSolution =>
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if Operation.Convolution.canDoAlgebraicOperation(arithmeticOperation) {
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expectedConvolutionCost(t1) * expectedConvolutionCost(t2) >
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MagicNumbers.OpCost.monteCarloCost
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? #AsMonteCarlo
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: #AsConvolution
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} else {
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#AsMonteCarlo
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}
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}
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}
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}
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let runStrategyOnValidatedInputs = (
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~t1: t,
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~t2: t,
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~arithmeticOperation,
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): option<error> => {
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if arithmeticOperation == #Logarithm {
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getLogarithmInputError(t1, t2, ~toPointSetFn)
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} else {
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None
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}
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}
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//I'm (Ozzie) really just guessing here, very little idea what's best
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let expectedConvolutionCost: t => int = x =>
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switch x {
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| Symbolic(#Float(_)) => MagicNumbers.OpCost.floatCost
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| Symbolic(_) => MagicNumbers.OpCost.symbolicCost
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| PointSet(Discrete(m)) => m.xyShape->XYShape.T.length
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| PointSet(Mixed(_)) => MagicNumbers.OpCost.mixedCost
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| PointSet(Continuous(_)) => MagicNumbers.OpCost.continuousCost
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| _ => MagicNumbers.OpCost.wildcardCost
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}
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type calculationStrategy = MonteCarloStrat | ConvolutionStrat(Operation.convolutionOperation)
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let chooseConvolutionOrMonteCarloDefault = (
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op: Operation.algebraicOperation,
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t2: t,
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t1: t,
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): calculationStrategy =>
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switch op {
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| #Divide
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| #Power
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| #Logarithm =>
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MonteCarloStrat
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| (#Add | #Subtract | #Multiply) as convOp =>
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expectedConvolutionCost(t1) * expectedConvolutionCost(t2) > MagicNumbers.OpCost.monteCarloCost
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? MonteCarloStrat
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: ConvolutionStrat(convOp)
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}
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let tryAnalyticalSimplification = (
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arithmeticOperation: Operation.algebraicOperation,
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t1: t,
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t2: t,
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): option<SymbolicDistTypes.analyticalSimplificationResult> => {
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switch (t1, t2) {
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| (DistributionTypes.Symbolic(d1), DistributionTypes.Symbolic(d2)) =>
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Some(SymbolicDist.T.tryAnalyticalSimplification(d1, d2, arithmeticOperation))
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| _ => None
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}
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}
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let runDefault = (
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t1: t,
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~strategy: StrategyChooser.specificStrategy,
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~toPointSetFn: toPointSetFn,
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~toSampleSetFn: toSampleSetFn,
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~arithmeticOperation,
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~t2: t,
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): result<t, error> => {
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switch tryAnalyticalSimplification(arithmeticOperation, t1, t2) {
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| Some(#AnalyticalSolution(symbolicDist)) => Ok(Symbolic(symbolicDist))
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| Some(#Error(e)) => Error(OperationError(e))
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| Some(#NoSolution)
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| None =>
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switch getInvalidOperationError(t1, t2, ~toPointSetFn, ~arithmeticOperation) {
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| Some(e) => Error(e)
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| None =>
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switch chooseConvolutionOrMonteCarloDefault(arithmeticOperation, t1, t2) {
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| MonteCarloStrat => runMonteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
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| ConvolutionStrat(convOp) =>
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runConvolution(toPointSetFn, convOp, t1, t2)->E.R2.fmap(r => DistributionTypes.PointSet(
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r,
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))
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}
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switch strategy {
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| #AsMonteCarlo =>
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StrategyCallOnValidatedInputs.monteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
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| #AsSymbolic =>
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switch StrategyCallOnValidatedInputs.symbolic(arithmeticOperation, t1, t2) {
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| #AnalyticalSolution(symbolicDist) => Ok(Symbolic(symbolicDist))
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| #Error(e) => Error(OperationError(e))
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| #NoSolution => Error(Unreachable)
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}
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| #AsConvolution =>
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switch Operation.Convolution.fromAlgebraicOperation(arithmeticOperation) {
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| Some(convOp) => StrategyCallOnValidatedInputs.convolution(toPointSetFn, convOp, t1, t2)
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| None => Error(Unreachable)
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}
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}
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}
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@ -300,27 +299,38 @@ module AlgebraicCombination = {
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~arithmeticOperation: Operation.algebraicOperation,
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~t2: t,
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): result<t, error> => {
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switch strategy {
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| AsDefault => runDefault(t1, ~toPointSetFn, ~toSampleSetFn, ~arithmeticOperation, ~t2)
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| AsSymbolic =>
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switch tryAnalyticalSimplification(arithmeticOperation, t1, t2) {
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| Some(#AnalyticalSolution(symbolicDist)) => Ok(Symbolic(symbolicDist))
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| Some(#NoSolution) => Error(RequestedStrategyInvalidError(`No analytical solution`))
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| None => Error(RequestedStrategyInvalidError("Inputs were not even symbolic"))
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| Some(#Error(err)) => Error(OperationError(err))
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let invalidOperationError = InputValidator.run(t1, t2, ~arithmeticOperation, ~toPointSetFn)
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switch (invalidOperationError, strategy) {
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| (Some(e), _) => Error(e)
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| (None, AsDefault) => {
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let chooseStrategy = StrategyChooser.run(~arithmeticOperation, ~t1, ~t2)
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runStrategyOnValidatedInputs(
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~t1,
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~t2,
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~strategy=chooseStrategy,
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~arithmeticOperation,
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~toPointSetFn,
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~toSampleSetFn,
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)
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}
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| AsConvolution => {
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let errString = opString => `Can't convolve on ${opString}`
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switch arithmeticOperation {
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| (#Add | #Subtract | #Multiply) as convOp =>
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runConvolution(toPointSetFn, convOp, t1, t2)->E.R2.fmap(r => DistributionTypes.PointSet(
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r,
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))
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| (#Divide | #Power | #Logarithm) as op =>
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op->Operation.Algebraic.toString->errString->RequestedStrategyInvalidError->Error
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| (None, AsMonteCarlo) =>
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StrategyCallOnValidatedInputs.monteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
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| (None, AsSymbolic) =>
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switch StrategyCallOnValidatedInputs.symbolic(arithmeticOperation, t1, t2) {
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| #AnalyticalSolution(symbolicDist) => Ok(Symbolic(symbolicDist))
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| #NoSolution => Error(RequestedStrategyInvalidError(`No analytic solution for inputs`))
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| #Error(err) => Error(OperationError(err))
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}
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| (None, AsConvolution) =>
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switch Operation.Convolution.fromAlgebraicOperation(arithmeticOperation) {
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| None => {
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let errString = `Convolution not supported for ${Operation.Algebraic.toString(
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arithmeticOperation,
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)}`
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Error(RequestedStrategyInvalidError(errString))
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}
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| Some(convOp) => StrategyCallOnValidatedInputs.convolution(toPointSetFn, convOp, t1, t2)
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}
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| AsMonteCarlo => runMonteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
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}
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}
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}
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@ -29,6 +29,18 @@ type distToFloatOperation = [
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module Convolution = {
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type t = convolutionOperation
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//Only a selection of operations are supported by convolution.
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let fromAlgebraicOperation = (op: algebraicOperation): option<convolutionOperation> =>
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switch op {
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| #Add => Some(#Add)
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| #Subtract => Some(#Subtract)
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| #Multiply => Some(#Multiply)
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| #Divide | #Power | #Logarithm => None
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}
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let canDoAlgebraicOperation = (op: algebraicOperation): bool =>
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fromAlgebraicOperation(op)->E.O.isSome
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let toFn: (t, float, float) => float = x =>
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switch x {
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| #Add => \"+."
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|
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