Big refactor towards proper distTree, still slow and untested
This commit is contained in:
Sebastian Kosch
parent
bc271a090b
commit
f6c1918b12
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@ -74,6 +74,21 @@ module Continuous = {
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(fn, {xyShape, interpolation}: t): option(DistTypes.continuousShape) =>
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fn(xyShape) |> E.O.fmap(make(interpolation));
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let empty: DistTypes.continuousShape = {xyShape: XYShape.T.empty, interpolation: `Linear};
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let combine =
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(fn, t1: DistTypes.continuousShape, t2: DistTypes.continuousShape)
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: DistTypes.continuousShape => {
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make(`Linear, XYShape.Combine.combine(
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~xsSelection=ALL_XS,
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~xToYSelection=XYShape.XtoY.linear,
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~fn,
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t1.xyShape,
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t2.xyShape,
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));
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};
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let reduce = (fn, items) =>
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items |> E.A.fold_left(combine(fn), empty);
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let toLinear = (t: t): option(t) => {
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switch (t) {
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| {interpolation: `Stepwise, xyShape} =>
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@ -166,6 +181,7 @@ module Discrete = {
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let sortedByX = (t: DistTypes.discreteShape) =>
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t |> XYShape.T.zip |> XYShape.Zipped.sortByX;
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let empty = XYShape.T.empty;
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let make = (s: DistTypes.discreteShape) => s;
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let combine =
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(fn, t1: DistTypes.discreteShape, t2: DistTypes.discreteShape)
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: DistTypes.discreteShape => {
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@ -179,6 +179,12 @@ module Combine = {
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t1: T.t,
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t2: T.t,
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) => {
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switch ((E.A.length(t1.xs), E.A.length(t2.xs))) {
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| (0, 0) => T.empty
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| (0, _) => t2
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| (_, 0) => t1
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| (_, _) => {
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let allXs =
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switch (xsSelection) {
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| ALL_XS => Ts.allXs([|t1, t2|])
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@ -188,7 +194,10 @@ module Combine = {
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let allYs =
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allXs |> E.A.fmap(x => fn(xToYSelection(x, t1), xToYSelection(x, t2)));
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T.fromArrays(allXs, allYs);
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}
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}
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};
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let combineLinear = combine(~xToYSelection=XtoY.linear);
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@ -43,7 +43,7 @@ module ShapeRenderer = {
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module Symbolic = {
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type inputs = {length: int};
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type outputs = {
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graph: SymbolicDist.bigDist,
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graph: SymbolicDist.distTree,
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shape: DistTypes.shape,
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};
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let make = (graph, shape) => {graph, shape};
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@ -88,73 +88,69 @@ module MathAdtToDistDst = {
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);
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};
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let normal: array(arg) => result(SymbolicDist.bigDist, string) =
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let normal: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(mean), Value(stdev)|] =>
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Ok(`Simple(`Normal({mean, stdev})))
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Ok(`Distribution(`Normal({mean, stdev})))
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| _ => Error("Wrong number of variables in normal distribution");
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let lognormal: array(arg) => result(SymbolicDist.bigDist, string) =
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let lognormal: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(mu), Value(sigma)|] => Ok(`Simple(`Lognormal({mu, sigma})))
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| [|Value(mu), Value(sigma)|] => Ok(`Distribution(`Lognormal({mu, sigma})))
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| [|Object(o)|] => {
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let g = Js.Dict.get(o);
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switch (g("mean"), g("stdev"), g("mu"), g("sigma")) {
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| (Some(Value(mean)), Some(Value(stdev)), _, _) =>
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Ok(`Simple(SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev)))
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Ok(`Distribution(SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev)))
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| (_, _, Some(Value(mu)), Some(Value(sigma))) =>
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Ok(`Simple(`Lognormal({mu, sigma})))
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Ok(`Distribution(`Lognormal({mu, sigma})))
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| _ => Error("Lognormal distribution would need mean and stdev")
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};
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}
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| _ => Error("Wrong number of variables in lognormal distribution");
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let to_: array(arg) => result(SymbolicDist.bigDist, string) =
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let to_: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(low), Value(high)|] when low <= 0.0 && low < high=> {
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Ok(`Simple(SymbolicDist.Normal.from90PercentCI(low, high)));
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Ok(`Distribution(SymbolicDist.Normal.from90PercentCI(low, high)));
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}
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| [|Value(low), Value(high)|] when low < high => {
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Ok(`Simple(SymbolicDist.Lognormal.from90PercentCI(low, high)));
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Ok(`Distribution(SymbolicDist.Lognormal.from90PercentCI(low, high)));
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}
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| [|Value(_), Value(_)|] =>
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Error("Low value must be less than high value.")
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| _ => Error("Wrong number of variables in lognormal distribution");
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let uniform: array(arg) => result(SymbolicDist.bigDist, string) =
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let uniform: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(low), Value(high)|] => Ok(`Simple(`Uniform({low, high})))
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| [|Value(low), Value(high)|] => Ok(`Distribution(`Uniform({low, high})))
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| _ => Error("Wrong number of variables in lognormal distribution");
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let beta: array(arg) => result(SymbolicDist.bigDist, string) =
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let beta: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(alpha), Value(beta)|] => Ok(`Simple(`Beta({alpha, beta})))
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| [|Value(alpha), Value(beta)|] => Ok(`Distribution(`Beta({alpha, beta})))
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| _ => Error("Wrong number of variables in lognormal distribution");
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let exponential: array(arg) => result(SymbolicDist.bigDist, string) =
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let exponential: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(rate)|] => Ok(`Simple(`Exponential({rate: rate})))
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| [|Value(rate)|] => Ok(`Distribution(`Exponential({rate: rate})))
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| _ => Error("Wrong number of variables in Exponential distribution");
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let cauchy: array(arg) => result(SymbolicDist.bigDist, string) =
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let cauchy: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(local), Value(scale)|] =>
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Ok(`Simple(`Cauchy({local, scale})))
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Ok(`Distribution(`Cauchy({local, scale})))
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| _ => Error("Wrong number of variables in cauchy distribution");
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let triangular: array(arg) => result(SymbolicDist.bigDist, string) =
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let triangular: array(arg) => result(SymbolicDist.distTree, string) =
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fun
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| [|Value(low), Value(medium), Value(high)|] =>
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Ok(`Simple(`Triangular({low, medium, high})))
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Ok(`Distribution(`Triangular({low, medium, high})))
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| _ => Error("Wrong number of variables in triangle distribution");
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/*let add: array(arg) => result(SymbolicDist.bigDist, string) =
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fun
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| */
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let multiModal =
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(
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args: array(result(SymbolicDist.bigDist, string)),
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args: array(result(SymbolicDist.distTree, string)),
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weights: option(array(float)),
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) => {
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let weights = weights |> E.O.default([||]);
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@ -162,8 +158,14 @@ module MathAdtToDistDst = {
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args
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|> E.A.fmap(
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fun
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| Ok(`Simple(d)) => Ok(`Simple(d))
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| Ok(`PointwiseCombination(dists)) => Ok(`PointwiseCombination(dists))
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| Ok(`Distribution(d)) => Ok(`Distribution(d))
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| Ok(`Combination(t1, t2, op)) => Ok(`Combination(t1, t2, op))
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| Ok(`PointwiseSum(t1, t2)) => Ok(`PointwiseSum(t1, t2))
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| Ok(`PointwiseProduct(t1, t2)) => Ok(`PointwiseProduct(t1, t2))
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| Ok(`Normalize(t)) => Ok(`Normalize(t))
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| Ok(`LeftTruncate(t, x)) => Ok(`LeftTruncate(t, x))
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| Ok(`RightTruncate(t, x)) => Ok(`RightTruncate(t, x))
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| Ok(`Render(t)) => Ok(`Render(t))
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| Error(e) => Error(e)
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| _ => Error("Unexpected dist")
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);
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@ -175,16 +177,26 @@ module MathAdtToDistDst = {
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| Some(Error(e)) => Error(e)
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| None when withoutErrors |> E.A.length == 0 =>
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Error("Multimodals need at least one input")
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| _ =>
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withoutErrors
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|> E.A.fmapi((index, item) =>
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(item, weights |> E.A.get(_, index) |> E.O.default(1.0))
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)
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|> (r => Ok(`PointwiseCombination(r)))
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| _ => {
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let components = withoutErrors
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|> E.A.fmapi((index, t) => {
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let w = weights |> E.A.get(_, index) |> E.O.default(1.0);
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`VerticalScaling(t, `Distribution(`Float(w)))
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});
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let pointwiseSum = components
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|> Js.Array.sliceFrom(1)
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|> E.A.fold_left((acc, x) => {
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`PointwiseSum(acc, x)
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}, E.A.unsafe_get(components, 0))
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Ok(`Normalize(pointwiseSum))
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}
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};
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};
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let arrayParser = (args:array(arg)):result(SymbolicDist.bigDist, string) => {
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let arrayParser = (args:array(arg)):result(SymbolicDist.distTree, string) => {
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let samples = args
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|> E.A.fmap(
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fun
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@ -200,13 +212,13 @@ module MathAdtToDistDst = {
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SymbolicDist.ContinuousShape.make(_pdf, cdf)
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});
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switch(shape){
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| Some(s) => Ok(`Simple(`ContinuousShape(s)))
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| Some(s) => Ok(`Distribution(`ContinuousShape(s)))
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| None => Error("Rendering did not work")
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}
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}
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let rec functionParser = (r): result(SymbolicDist.bigDist, string) =>
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let rec functionParser = (r): result(SymbolicDist.distTree, string) =>
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r
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|> (
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fun
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@ -218,7 +230,7 @@ module MathAdtToDistDst = {
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| Fn({name: "exponential", args}) => exponential(args)
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| Fn({name: "cauchy", args}) => cauchy(args)
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| Fn({name: "triangular", args}) => triangular(args)
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| Value(f) => Ok(`Simple(`Float(f)))
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| Value(f) => Ok(`Distribution(`Float(f)))
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| Fn({name: "mm", args}) => {
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let weights =
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args
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@ -245,25 +257,54 @@ module MathAdtToDistDst = {
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let dists = possibleDists |> E.A.fmap(functionParser);
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multiModal(dists, weights);
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}
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//| Fn({name: "add", args}) => add(args)
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| Fn({name: "add", args}) => {
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args
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|> E.A.fmap(functionParser)
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|> (fun
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| [|Ok(l), Ok(r)|] => Ok(`Combination(l, r, `AddOperation))
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| _ => Error("Addition needs two operands"))
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}
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| Fn({name: "subtract", args}) => {
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args
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|> E.A.fmap(functionParser)
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|> (fun
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| [|Ok(l), Ok(r)|] => Ok(`Combination(l, r, `SubtractOperation))
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| _ => Error("Subtraction needs two operands"))
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}
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| Fn({name: "multiply", args}) => {
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args
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|> E.A.fmap(functionParser)
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|> (fun
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| [|Ok(l), Ok(r)|] => Ok(`Combination(l, r, `MultiplyOperation))
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| _ => Error("Multiplication needs two operands"))
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}
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| Fn({name: "divide", args}) => {
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args
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|> E.A.fmap(functionParser)
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|> (fun
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| [|Ok(l), Ok(`Distribution(`Float(0.0)))|] => Error("Division by zero")
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| [|Ok(l), Ok(r)|] => Ok(`Combination(l, r, `DivideOperation))
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| _ => Error("Division needs two operands"))
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}
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| Fn({name}) => Error(name ++ ": function not supported")
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| _ => {
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Error("This type not currently supported");
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}
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);
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let topLevel = (r): result(SymbolicDist.bigDist, string) =>
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let topLevel = (r): result(SymbolicDist.distTree, string) =>
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r
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|> (
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fun
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| Fn(_) => functionParser(r)
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| Value(r) => Ok(`Simple(`Float(r)))
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| Value(r) => Ok(`Distribution(`Float(r)))
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| Array(r) => arrayParser(r)
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| Symbol(_) => Error("Symbol not valid as top level")
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| Object(_) => Error("Object not valid as top level")
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);
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let run = (r): result(SymbolicDist.bigDist, string) =>
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let run = (r): result(SymbolicDist.distTree, string) =>
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r |> MathAdtCleaner.run |> topLevel;
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};
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@ -50,41 +50,28 @@ type dist = [
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| `Float(float) // Dirac delta at x. Practically useful only in the context of multimodals.
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];
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/* Build a tree.
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type integral = float;
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type cutoffX = float;
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type operation = [
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| `AddOperation
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| `SubtractOperation
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| `MultiplyOperation
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| `DivideOperation
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| `ExponentiateOperation
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];
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Multiple operations possible:
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- PointwiseSum(Scalar, Scalar)
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- PointwiseSum(WeightedDist, WeightedDist)
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- PointwiseProduct(Scalar, Scalar)
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- PointwiseProduct(Scalar, WeightedDist)
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- PointwiseProduct(WeightedDist, WeightedDist)
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- IndependentVariableSum(WeightedDist, WeightedDist) [i.e., convolution]
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- IndependentVariableProduct(WeightedDist, WeightedDist) [i.e. distribution product]
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*/
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/*type weightedDist = (float, dist);
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type bigDistTree =
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/* | DistLeaf(dist) */
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/* | ScalarLeaf(float) */
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/* | PointwiseScalarDistProduct(DistLeaf(d), ScalarLeaf(s)) */
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| WeightedDistLeaf(weightedDist)
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| PointwiseNormalizedDistSum(array(bigDistTree));
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let rec treeIntegral = item => {
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switch (item) {
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| WeightedDistLeaf((w, d)) => w
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| PointwiseNormalizedDistSum(childTrees) =>
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childTrees |> E.A.fmap(treeIntegral) |> E.A.Floats.sum
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};
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};*/
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/* bigDist can either be a single distribution, or a
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PointwiseCombination, i.e. an array of (dist, weight) tuples */
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type bigDist = [ | `Simple(dist) | `PointwiseCombination(pointwiseAdd)]
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and pointwiseAdd = array((bigDist, float));
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type distTree = [
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| `Distribution(dist)
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| `Combination(distTree, distTree, operation)
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| `PointwiseSum(distTree, distTree)
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| `PointwiseProduct(distTree, distTree)
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| `VerticalScaling(distTree, distTree)
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| `Normalize(distTree)
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| `LeftTruncate(distTree, cutoffX)
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| `RightTruncate(distTree, cutoffX)
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| `Render(distTree)
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]
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and weightedDists = array((distTree, float));
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module ContinuousShape = {
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type t = continuousShape;
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@ -326,138 +313,331 @@ module GenericSimple = {
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};
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};
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module PointwiseAddDistributionsWeighted = {
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type t = pointwiseAdd;
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module DistTree = {
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type nodeResult = [
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| `Distribution(dist)
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// RenderedShape: continuous xyShape, discrete xyShape, total value.
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| `RenderedShape(DistTypes.continuousShape, DistTypes.discreteShape, integral)
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];
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let normalizeWeights = (weightedDists: t) => {
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let total = weightedDists |> E.A.fmap(snd) |> E.A.Floats.sum;
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weightedDists |> E.A.fmap(((d, w)) => (d, w /. total));
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let evaluateDistribution = (d: dist): nodeResult => {
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// certain distributions we may want to evaluate to RenderedShapes right away, e.g. discrete
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`Distribution(d)
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};
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let rec pdf = (x: float, weightedNormalizedDists: t) =>
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weightedNormalizedDists
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|> E.A.fmap(((d, w)) => {
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// This is a performance bottleneck!
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// Using raw JS here so we can use native for loops and access array elements
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// directly, without option checks.
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let jsCombinationConvolve: (array(float), array(float), array(float), array(float), float => float => float) => (array(float), array(float)) = [%bs.raw
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{|
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function (s1xs, s1ys, s2xs, s2ys, func) {
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const r = new Map();
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// To convolve, add the xs and multiply the ys:
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for (let i = 0; i < s1xs.length; i++) {
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for (let j = 0; j < s2xs.length; j++) {
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const x = func(s1xs[i], s2xs[j]);
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const cv = r.get(x) | 0;
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r.set(x, cv + s1ys[i] * s2ys[j]); // add up the ys, if same x
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}
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}
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const rxys = [...r.entries()];
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rxys.sort(([x1, y1], [x2, y2]) => x1 - x2);
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const rxs = new Array(rxys.length);
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const rys = new Array(rxys.length);
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for (let i = 0; i < rxys.length; i++) {
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rxs[i] = rxys[i][0];
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rys[i] = rxys[i][1];
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}
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return [rxs, rys];
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}
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|}];
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let funcFromOp = (op: operation) => {
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switch (op) {
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| `AddOperation => (+.)
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| `SubtractOperation => (-.)
|
||||
| `MultiplyOperation => (*.)
|
||||
| `DivideOperation => (/.)
|
||||
| `ExponentiateOperation => (**)
|
||||
}
|
||||
}
|
||||
|
||||
let renderDistributionToXYShape = (d: dist, sampleCount: int): (DistTypes.continuousShape, DistTypes.discreteShape) => {
|
||||
// render the distribution into an XY shape
|
||||
switch (d) {
|
||||
| `PointwiseCombination(ts) => pdf(x, ts) *. w
|
||||
| `Simple(d) => GenericSimple.pdf(x, d) *. w
|
||||
}
|
||||
})
|
||||
|> E.A.Floats.sum;
|
||||
|
||||
// TODO: perhaps rename into minCdfX?
|
||||
// TODO: how should nonexistent min values be handled? They should never happen
|
||||
let rec min = (dists: t) =>
|
||||
dists
|
||||
|> E.A.fmap(((d, w)) => {
|
||||
switch (d) {
|
||||
| `PointwiseCombination(ts) => E.O.toExn("Dist has no min", min(ts))
|
||||
| `Simple(d) => GenericSimple.min(d)
|
||||
}
|
||||
})
|
||||
|> E.A.min;
|
||||
|
||||
// TODO: perhaps rename into minCdfX?
|
||||
let rec max = (dists: t) =>
|
||||
dists
|
||||
|> E.A.fmap(((d, w)) => {
|
||||
switch (d) {
|
||||
| `PointwiseCombination(ts) => E.O.toExn("Dist has no max", max(ts))
|
||||
| `Simple(d) => GenericSimple.max(d)
|
||||
}
|
||||
})
|
||||
|> E.A.max;
|
||||
|
||||
|
||||
/*let rec discreteShape = (dists: t, sampleCount: int) => {
|
||||
let discrete =
|
||||
dists
|
||||
|> E.A.fmap(((x, w)) => {
|
||||
switch (d) {
|
||||
| `Float(d) => Some((d, w)) // if the distribution is just a number, then the weight is considered the y
|
||||
| _ => None
|
||||
}
|
||||
})
|
||||
|> E.A.O.concatSomes
|
||||
|> E.A.fmap(((x, y)) =>
|
||||
({xs: [|x|], ys: [|y|]}: DistTypes.xyShape)
|
||||
)
|
||||
// take an array of xyShapes and combine them together
|
||||
//* r
|
||||
|> (
|
||||
fun
|
||||
| `Float(r) => Some((r, e))
|
||||
| _ => None
|
||||
)
|
||||
)*/
|
||||
|> Distributions.Discrete.reduce((+.));
|
||||
discrete;
|
||||
};*/
|
||||
|
||||
|
||||
let rec findContinuousXs = (dists: t, sampleCount: int) => {
|
||||
// we need to go through the tree of distributions and, for the continuous ones, find the xs at which
|
||||
// later, all distributions will get evaluated.
|
||||
|
||||
// we want to accumulate a set of xs.
|
||||
let xs: array(float) =
|
||||
dists
|
||||
|> E.A.fold_left((accXs, (d, w)) => {
|
||||
switch (d) {
|
||||
| `Simple(t) when (GenericSimple.contType(t) == `Discrete) => accXs
|
||||
| `Simple(d) => {
|
||||
let xs = GenericSimple.interpolateXs(~xSelection=`ByWeight, d, sampleCount)
|
||||
|
||||
E.A.append(accXs, xs)
|
||||
}
|
||||
| `PointwiseCombination(ts) => {
|
||||
let xs = findContinuousXs(ts, sampleCount);
|
||||
E.A.append(accXs, xs)
|
||||
| `Float(v) => (Distributions.Continuous.empty, {xs: [|v|], ys: [|1.0|]})
|
||||
| _ => {
|
||||
let xs = GenericSimple.interpolateXs(~xSelection=`ByWeight, d, sampleCount);
|
||||
let ys = xs |> E.A.fmap(x => GenericSimple.pdf(x, d));
|
||||
(Distributions.Continuous.make(`Linear, {xs: xs, ys: ys}), XYShape.T.empty)
|
||||
}
|
||||
}
|
||||
}, [||]);
|
||||
xs
|
||||
};
|
||||
|
||||
/* Accumulate (accContShapes, accDistShapes), each of which is an array of {xs, ys} shapes. */
|
||||
let rec accumulateContAndDiscShapes = (dists: t, continuousXs: array(float), currentWeight) => {
|
||||
let normalized = normalizeWeights(dists);
|
||||
let combinationDistributionOfXYShapes = (sc1: DistTypes.continuousShape, // continuous shape
|
||||
sd1: DistTypes.discreteShape, // discrete shape
|
||||
sc2: DistTypes.continuousShape,
|
||||
sd2: DistTypes.discreteShape, func): (DistTypes.continuousShape, DistTypes.discreteShape) => {
|
||||
|
||||
normalized
|
||||
|> E.A.fold_left(((accContShapes: array(DistTypes.xyShape), accDiscShapes: array(DistTypes.xyShape)), (d, w)) => {
|
||||
switch (d) {
|
||||
let (ccxs, ccys) = jsCombinationConvolve(sc1.xyShape.xs, sc1.xyShape.ys, sc2.xyShape.xs, sc2.xyShape.ys, func);
|
||||
let (dcxs, dcys) = jsCombinationConvolve(sd1.xs, sd1.ys, sc2.xyShape.xs, sc2.xyShape.ys, func);
|
||||
let (cdxs, cdys) = jsCombinationConvolve(sc1.xyShape.xs, sc1.xyShape.ys, sd2.xs, sd2.ys, func);
|
||||
let (ddxs, ddys) = jsCombinationConvolve(sd1.xs, sd1.ys, sd2.xs, sd2.ys, func);
|
||||
|
||||
| `Simple(`Float(x)) => {
|
||||
let ds: DistTypes.xyShape = {xs: [|x|], ys: [|w *. currentWeight|]};
|
||||
(accContShapes, E.A.append(accDiscShapes, [|ds|]))
|
||||
}
|
||||
let ccxy = Distributions.Continuous.make(`Linear, {xs: ccxs, ys: ccys});
|
||||
let dcxy = Distributions.Continuous.make(`Linear, {xs: dcxs, ys: dcys});
|
||||
let cdxy = Distributions.Continuous.make(`Linear, {xs: cdxs, ys: cdys});
|
||||
// the continuous parts are added up; only the discrete-discrete sum is discrete
|
||||
let continuousShapeSum = Distributions.Continuous.reduce((+.), [|ccxy, dcxy, cdxy|]);
|
||||
|
||||
| `Simple(d) when (GenericSimple.contType(d) == `Continuous) => {
|
||||
let ys = continuousXs |> E.A.fmap(x => GenericSimple.pdf(x, d) *. w *. currentWeight);
|
||||
let cs = XYShape.T.fromArrays(continuousXs, ys);
|
||||
let ddxy: DistTypes.discreteShape = {xs: cdxs, ys: cdys};
|
||||
|
||||
(E.A.append(accContShapes, [|cs|]), accDiscShapes)
|
||||
}
|
||||
|
||||
| `Simple(d) => (accContShapes, accDiscShapes) // default -- should never happen
|
||||
|
||||
| `PointwiseCombination(ts) => {
|
||||
let (cs, ds) = accumulateContAndDiscShapes(ts, continuousXs, w *. currentWeight);
|
||||
(E.A.append(accContShapes, cs), E.A.append(accDiscShapes, ds))
|
||||
}
|
||||
}
|
||||
|
||||
}, ([||]: array(DistTypes.xyShape), [||]: array(DistTypes.xyShape)))
|
||||
(continuousShapeSum, ddxy)
|
||||
};
|
||||
|
||||
/*
|
||||
We will assume that each dist (of t) in the multimodal has a total of one.
|
||||
We can therefore normalize the weights of the parts.
|
||||
let evaluateCombinationDistribution = (et1: nodeResult, et2: nodeResult, op: operation, sampleCount: int) => {
|
||||
/* return either a Distribution or a RenderedShape. Must integrate to 1. */
|
||||
|
||||
However, a multimodal can consist of both discrete and continuous shapes.
|
||||
These need to be added and collected individually.
|
||||
*/
|
||||
let toShape = (dists: t, sampleCount: int) => {
|
||||
let continuousXs = findContinuousXs(dists, sampleCount);
|
||||
let func = funcFromOp(op);
|
||||
switch ((et1, et2, op)) {
|
||||
/* Known cases: replace symbolic with symbolic distribution */
|
||||
| (`Distribution(`Float(v1)), `Distribution(`Float(v2)), _) => {
|
||||
`Distribution(`Float(func(v1, v2)))
|
||||
}
|
||||
|
||||
| (`Distribution(`Float(v1)), `Distribution(`Normal(n2)), `AddOperation) => {
|
||||
let n: normal = {mean: v1 +. n2.mean, stdev: n2.stdev};
|
||||
`Distribution(`Normal(n))
|
||||
}
|
||||
|
||||
| (`Distribution(`Normal(n1)), `Distribution(`Normal(n2)), `AddOperation) => {
|
||||
let n: normal = {mean: n1.mean +. n2.mean, stdev: sqrt(n1.stdev ** 2. +. n2.stdev ** 2.)};
|
||||
`Distribution(`Normal(n));
|
||||
}
|
||||
|
||||
/* General cases: convolve the XYShapes */
|
||||
| (`Distribution(d1), `Distribution(d2), _) => {
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
let (sc2, sd2) = renderDistributionToXYShape(d2, sampleCount);
|
||||
let (sc, sd) = combinationDistributionOfXYShapes(sc1, sd1, sc2, sd2, func);
|
||||
`RenderedShape(sc, sd, 1.0)
|
||||
}
|
||||
| (`Distribution(d1), `RenderedShape(sc2, sd2, i2), _) => {
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
let (sc, sd) = combinationDistributionOfXYShapes(sc1, sd1, sc2, sd2, func);
|
||||
`RenderedShape(sc, sd, i2)
|
||||
}
|
||||
| (`RenderedShape(sc1, sd1, i1), `Distribution(d2), _) => {
|
||||
let (sc2, sd2) = renderDistributionToXYShape(d2, sampleCount);
|
||||
let (sc, sd) = combinationDistributionOfXYShapes(sc1, sd1, sc2, sd2, func);
|
||||
`RenderedShape(sc, sd, i1);
|
||||
}
|
||||
| (`RenderedShape(sc1, sd1, i1), `RenderedShape(sc2, sd2, i2), _) => {
|
||||
// sum of two multimodals that have a continuous and discrete each.
|
||||
let (sc, sd) = combinationDistributionOfXYShapes(sc1, sd1, sc2, sd2, func);
|
||||
|
||||
`RenderedShape(sc, sd, i1);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
let evaluatePointwiseSum = (et1: nodeResult, et2: nodeResult, sampleCount: int) => {
|
||||
switch ((et1, et2)) {
|
||||
/* Known cases: */
|
||||
| (`Distribution(`Float(v1)), `Distribution(`Float(v2))) => {
|
||||
v1 == v2
|
||||
? `RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.make({xs: [|v1|], ys: [|2.|]}), 2.)
|
||||
: `RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.) // TODO: add warning: shouldn't pointwise add scalars.
|
||||
}
|
||||
| (`Distribution(`Float(v1)), `Distribution(d2)) => {
|
||||
let sd1: DistTypes.xyShape = {xs: [|v1|], ys: [|1.|]};
|
||||
let (sc2, sd2) = renderDistributionToXYShape(d2, sampleCount);
|
||||
`RenderedShape(sc2, Distributions.Discrete.reduce((+.), [|sd1, sd2|]), 2.)
|
||||
}
|
||||
| (`Distribution(d1), `Distribution(`Float(v2))) => {
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
let sd2: DistTypes.xyShape = {xs: [|v2|], ys: [|1.|]};
|
||||
`RenderedShape(sc1, Distributions.Discrete.reduce((+.), [|sd1, sd2|]), 2.)
|
||||
}
|
||||
| (`Distribution(d1), `Distribution(d2)) => {
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
let (sc2, sd2) = renderDistributionToXYShape(d2, sampleCount);
|
||||
`RenderedShape(Distributions.Continuous.reduce((+.), [|sc1, sc2|]), Distributions.Discrete.reduce((+.), [|sd1, sd2|]), 2.)
|
||||
}
|
||||
| (`Distribution(d1), `RenderedShape(sc2, sd2, i2))
|
||||
| (`RenderedShape(sc2, sd2, i2), `Distribution(d1)) => {
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
`RenderedShape(Distributions.Continuous.reduce((+.), [|sc1, sc2|]), Distributions.Discrete.reduce((+.), [|sd1, sd2|]), 1. +. i2)
|
||||
}
|
||||
| (`RenderedShape(sc1, sd1, i1), `RenderedShape(sc2, sd2, i2)) => {
|
||||
Js.log3("Reducing continuous rr", sc1, sc2);
|
||||
Js.log2("Continuous reduction:", Distributions.Continuous.reduce((+.), [|sc1, sc2|]));
|
||||
Js.log2("Discrete reduction:", Distributions.Discrete.reduce((+.), [|sd1, sd2|]));
|
||||
`RenderedShape(Distributions.Continuous.reduce((+.), [|sc1, sc2|]), Distributions.Discrete.reduce((+.), [|sd1, sd2|]), i1 +. i2)
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
let evaluatePointwiseProduct = (et1: nodeResult, et2: nodeResult, sampleCount: int) => {
|
||||
switch ((et1, et2)) {
|
||||
/* Known cases: */
|
||||
| (`Distribution(`Float(v1)), `Distribution(`Float(v2))) => {
|
||||
v1 == v2
|
||||
? `RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.make({xs: [|v1|], ys: [|1.|]}), 1.)
|
||||
: `RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.) // TODO: add warning: shouldn't pointwise multiply scalars.
|
||||
}
|
||||
| (`Distribution(`Float(v1)), `Distribution(d2)) => {
|
||||
// evaluate d2 at v1
|
||||
let y = GenericSimple.pdf(v1, d2);
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.make({xs: [|v1|], ys: [|y|]}), y)
|
||||
}
|
||||
| (`Distribution(d1), `Distribution(`Float(v2))) => {
|
||||
// evaluate d1 at v2
|
||||
let y = GenericSimple.pdf(v2, d1);
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.make({xs: [|v2|], ys: [|y|]}), y)
|
||||
}
|
||||
| (`Distribution(`Normal(n1)), `Distribution(`Normal(n2))) => {
|
||||
let mean = (n1.mean *. n2.stdev**2. +. n2.mean *. n1.stdev**2.) /. (n1.stdev**2. +. n2.stdev**2.);
|
||||
let stdev = 1. /. ((1. /. n1.stdev**2.) +. (1. /. n2.stdev**2.));
|
||||
let integral = 0; // TODO
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.)
|
||||
}
|
||||
/* General cases */
|
||||
| (`Distribution(d1), `Distribution(d2)) => {
|
||||
// NOT IMPLEMENTED YET
|
||||
// TODO: evaluate integral properly
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
let (sc2, sd2) = renderDistributionToXYShape(d2, sampleCount);
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.)
|
||||
}
|
||||
| (`Distribution(d1), `RenderedShape(sc2, sd2, i2)) => {
|
||||
// NOT IMPLEMENTED YET
|
||||
// TODO: evaluate integral properly
|
||||
let (sc1, sd1) = renderDistributionToXYShape(d1, sampleCount);
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.)
|
||||
}
|
||||
| (`RenderedShape(sc1, sd1, i1), `Distribution(d1)) => {
|
||||
// NOT IMPLEMENTED YET
|
||||
// TODO: evaluate integral properly
|
||||
let (sc2, sd2) = renderDistributionToXYShape(d1, sampleCount);
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.)
|
||||
}
|
||||
| (`RenderedShape(sc1, sd1, i1), `RenderedShape(sc2, sd2, i2)) => {
|
||||
`RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.)
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
let evaluateNormalize = (et: nodeResult, sampleCount: int) => {
|
||||
// just divide everything by the integral.
|
||||
switch (et) {
|
||||
| `RenderedShape(sc, sd, i) => {
|
||||
// loop through all ys and divide them by i
|
||||
let normalize = (s: DistTypes.xyShape): DistTypes.xyShape => {xs: s.xs, ys: s.ys |> E.A.fmap(y => y /. i)};
|
||||
|
||||
let scn = sc |> Distributions.Continuous.shapeMap(normalize);
|
||||
let sdn = sd |> normalize;
|
||||
|
||||
`RenderedShape(scn, sdn, 1.)
|
||||
}
|
||||
| `Distribution(d) => `Distribution(d) // any kind of atomic dist should already be normalized -- TODO: THIS IS ACTUALLY FALSE! E.g. pointwise product of normal * normal
|
||||
}
|
||||
};
|
||||
|
||||
let evaluateTruncate = (et: nodeResult, xc: cutoffX, compareFunc: (float, float) => bool, sampleCount: int) => {
|
||||
let cut = (s: DistTypes.xyShape): DistTypes.xyShape => {
|
||||
let (xs, ys) = s.ys
|
||||
|> Belt.Array.zip(s.xs)
|
||||
|> E.A.filter(((x, y)) => compareFunc(x, xc))
|
||||
|> Belt.Array.unzip
|
||||
|
||||
let cutShape: DistTypes.xyShape = {xs, ys};
|
||||
cutShape;
|
||||
};
|
||||
|
||||
switch (et) {
|
||||
| `Distribution(d) => {
|
||||
let (sc, sd) = renderDistributionToXYShape(d, sampleCount);
|
||||
|
||||
let scc = sc |> Distributions.Continuous.shapeMap(cut);
|
||||
let sdc = sd |> cut;
|
||||
|
||||
let newIntegral = 1.; // TODO
|
||||
|
||||
`RenderedShape(scc, sdc, newIntegral);
|
||||
}
|
||||
| `RenderedShape(sc, sd, i) => {
|
||||
let scc = sc |> Distributions.Continuous.shapeMap(cut);
|
||||
let sdc = sd |> cut;
|
||||
|
||||
let newIntegral = 1.; // TODO
|
||||
|
||||
`RenderedShape(scc, sdc, newIntegral);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
let evaluateVerticalScaling = (et1: nodeResult, et2: nodeResult, sampleCount: int) => {
|
||||
let scale = (i: float, s: DistTypes.xyShape): DistTypes.xyShape => {xs: s.xs, ys: s.ys |> E.A.fmap(y => y *. i)};
|
||||
|
||||
switch ((et1, et2)) {
|
||||
| (`Distribution(`Float(v)), `Distribution(d))
|
||||
| (`Distribution(d), `Distribution(`Float(v))) => {
|
||||
let (sc, sd) = renderDistributionToXYShape(d, sampleCount);
|
||||
|
||||
let scc = sc |> Distributions.Continuous.shapeMap(scale(v));
|
||||
let sdc = sd |> scale(v);
|
||||
|
||||
let newIntegral = v; // TODO
|
||||
|
||||
`RenderedShape(scc, sdc, newIntegral);
|
||||
}
|
||||
| (`Distribution(`Float(v)), `RenderedShape(sc, sd, i))
|
||||
| (`RenderedShape(sc, sd, i), `Distribution(`Float(v))) => {
|
||||
let scc = sc |> Distributions.Continuous.shapeMap(scale(v));
|
||||
let sdc = sd |> scale(v);
|
||||
|
||||
let newIntegral = v; // TODO
|
||||
|
||||
`RenderedShape(scc, sdc, newIntegral);
|
||||
}
|
||||
| _ => `RenderedShape(Distributions.Continuous.empty, Distributions.Discrete.empty, 0.) // TODO: give warning
|
||||
}
|
||||
}
|
||||
|
||||
let renderNode = (et: nodeResult, sampleCount: int) => {
|
||||
switch (et) {
|
||||
| `Distribution(d) => {
|
||||
let (sc, sd) = renderDistributionToXYShape(d, sampleCount);
|
||||
`RenderedShape(sc, sd, 1.0);
|
||||
}
|
||||
| s => s
|
||||
}
|
||||
}
|
||||
|
||||
let rec evaluateNode = (treeNode: distTree, sampleCount: int): nodeResult => {
|
||||
// returns either a new symbolic distribution
|
||||
switch (treeNode) {
|
||||
| `Distribution(d) => evaluateDistribution(d)
|
||||
| `Combination(t1, t2, op) => evaluateCombinationDistribution(evaluateNode(t1, sampleCount), evaluateNode(t2, sampleCount), op, sampleCount)
|
||||
| `PointwiseSum(t1, t2) => evaluatePointwiseSum(evaluateNode(t1, sampleCount), evaluateNode(t2, sampleCount), sampleCount)
|
||||
| `PointwiseProduct(t1, t2) => evaluatePointwiseProduct(evaluateNode(t1, sampleCount), evaluateNode(t2, sampleCount), sampleCount)
|
||||
| `VerticalScaling(t1, t2) => evaluateVerticalScaling(evaluateNode(t1, sampleCount), evaluateNode(t2, sampleCount), sampleCount)
|
||||
| `Normalize(t) => evaluateNormalize(evaluateNode(t, sampleCount), sampleCount)
|
||||
| `LeftTruncate(t, x) => evaluateTruncate(evaluateNode(t, sampleCount), x, (<=), sampleCount)
|
||||
| `RightTruncate(t, x) => evaluateTruncate(evaluateNode(t, sampleCount), x, (>=), sampleCount)
|
||||
| `Render(t) => renderNode(evaluateNode(t, sampleCount), sampleCount)
|
||||
}
|
||||
};
|
||||
|
||||
let toShape = (treeNode: distTree, sampleCount: int) => {
|
||||
/*let continuousXs = findContinuousXs(dists, sampleCount);
|
||||
continuousXs |> Array.fast_sort(compare);
|
||||
|
||||
let (contShapes, distShapes) = accumulateContAndDiscShapes(dists, continuousXs, 1.0);
|
||||
|
|
@ -469,60 +649,42 @@ module PointwiseAddDistributionsWeighted = {
|
|||
}, {xs: continuousXs, ys: Array.make(Array.length(continuousXs), 0.0)})
|
||||
|> Distributions.Continuous.make(`Linear);
|
||||
|
||||
let combinedDiscrete = Distributions.Discrete.reduce((+.), distShapes)
|
||||
let combinedDiscrete = Distributions.Discrete.reduce((+.), distShapes)*/
|
||||
|
||||
let shape = MixedShapeBuilder.buildSimple(~continuous=Some(combinedContinuous), ~discrete=combinedDiscrete);
|
||||
let treeShape = evaluateNode(`Render(`Normalize(treeNode)), sampleCount);
|
||||
switch (treeShape) {
|
||||
| `Distribution(_) => E.O.toExn("No shape found!", None)
|
||||
| `RenderedShape(sc, sd, _) => {
|
||||
let shape = MixedShapeBuilder.buildSimple(~continuous=Some(sc), ~discrete=sd);
|
||||
|
||||
shape |> E.O.toExt("");
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
let rec toString = (dists: t): string => {
|
||||
let distString =
|
||||
dists
|
||||
|> E.A.fmap(((d, _)) =>
|
||||
switch (d) {
|
||||
| `Simple(d) => GenericSimple.toString(d)
|
||||
| `PointwiseCombination(ts: t) => ts |> toString
|
||||
let rec toString = (treeNode: distTree): string => {
|
||||
let stringFromOp = op => switch (op) {
|
||||
| `AddOperation => " + "
|
||||
| `SubtractOperation => " - "
|
||||
| `MultiplyOperation => " * "
|
||||
| `DivideOperation => " / "
|
||||
| `ExponentiateOperation => "^"
|
||||
};
|
||||
|
||||
switch (treeNode) {
|
||||
| `Distribution(d) => GenericSimple.toString(d)
|
||||
| `Combination(t1, t2, op) => toString(t1) ++ stringFromOp(op) ++ toString(t2)
|
||||
| `PointwiseSum(t1, t2) => toString(t1) ++ " .+ " ++ toString(t2)
|
||||
| `PointwiseProduct(t1, t2) => toString(t1) ++ " .* " ++ toString(t2)
|
||||
| `VerticalScaling(t1, t2) => toString(t1) ++ " @ " ++ toString(t2)
|
||||
| `Normalize(t) => "normalize(" ++ toString(t) ++ ")"
|
||||
| `LeftTruncate(t, x) => "leftTruncate(" ++ toString(t) ++ ", " ++ string_of_float(x) ++ ")"
|
||||
| `RightTruncate(t, x) => "rightTruncate(" ++ toString(t) ++ ", " ++ string_of_float(x) ++ ")"
|
||||
}
|
||||
)
|
||||
|> Js.Array.joinWith(",");
|
||||
|
||||
// mm(normal(0,1), normal(1,2)) => "multimodal(normal(0,1), normal(1,2), )
|
||||
|
||||
let weights =
|
||||
dists
|
||||
|> E.A.fmap(((_, w)) =>
|
||||
Js.Float.toPrecisionWithPrecision(w, ~digits=2)
|
||||
)
|
||||
|> Js.Array.joinWith(",");
|
||||
|
||||
{j|multimodal($distString, [$weights])|j};
|
||||
};
|
||||
};
|
||||
|
||||
// assume that recursive pointwiseNormalizedDistSums are the only type of operation there is.
|
||||
// in the original, it was a list of (dist, weight) tuples. Now, it's a tree of (dist, weight) tuples, just that every
|
||||
// dist can be either a GenericSimple or another PointwiseAdd.
|
||||
let toString = (treeNode: distTree) => DistTree.toString(treeNode)
|
||||
|
||||
/*let toString = (r: bigDistTree) => {
|
||||
switch (r) {
|
||||
| WeightedDistLeaf((w, d)) => GenericWeighted.toString(w) // "normal "
|
||||
| PointwiseNormalizedDistSum(childTrees) => childTrees |> E.A.fmap(toString) |> Js.Array.joinWith("")
|
||||
}
|
||||
}*/
|
||||
|
||||
let toString = (r: bigDist) =>
|
||||
// we need to recursively create the string representation of the tree.
|
||||
r
|
||||
|> (
|
||||
fun
|
||||
| `Simple(d) => GenericSimple.toString(d)
|
||||
| `PointwiseCombination(d) =>
|
||||
PointwiseAddDistributionsWeighted.toString(d)
|
||||
);
|
||||
|
||||
let toShape = n =>
|
||||
fun
|
||||
| `Simple(d) => GenericSimple.toShape(~xSelection=`ByWeight, d, n)
|
||||
| `PointwiseCombination(d) =>
|
||||
PointwiseAddDistributionsWeighted.toShape(d, n);
|
||||
let toShape = (sampleCount: int, treeNode: distTree) =>
|
||||
DistTree.toShape(treeNode, sampleCount) //~xSelection=`ByWeight,
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user