Minor renames, and moved attemptAlgebraicOperation to SymbolicDist
This commit is contained in:
Ozzie Gooen
parent
491ac15f7b
commit
101824e500
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@ -382,10 +382,10 @@ describe("Shape", () => {
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let variance = stdev ** 2.0;
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let numSamples = 10000;
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open Distributions.Shape;
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let normal: SymbolicDist.dist = `Normal({mean, stdev});
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let normalShape = TreeNode.toShape(numSamples, `DistData(`Symbolic(normal)));
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let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
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let normalShape = TreeNode.toShape(numSamples, `Leaf(`SymbolicDist(normal)));
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let lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
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let lognormalShape = TreeNode.toShape(numSamples, `DistData(`Symbolic(lognormal)));
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let lognormalShape = TreeNode.toShape(numSamples, `Leaf(`SymbolicDist(lognormal)));
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makeTestCloseEquality(
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"Mean of a normal",
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@ -388,8 +388,8 @@ module Draw = {
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let stdev = 15.0;
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let numSamples = 3000;
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let normal: SymbolicDist.dist = `Normal({mean, stdev});
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let normalShape = TreeNode.toShape(numSamples, `DistData(`Symbolic(normal)));
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let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
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let normalShape = TreeNode.toShape(numSamples, `Leaf(`SymbolicDist(normal)));
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let xyShape: Types.xyShape =
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switch (normalShape) {
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| Mixed(_) => {xs: [||], ys: [||]}
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@ -398,9 +398,9 @@ module Draw = {
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};
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/* // To use a lognormal instead:
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let lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
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let lognormal = SymbolicTypes.Lognormal.fromMeanAndStdev(mean, stdev);
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let lognormalShape =
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SymbolicDist.GenericSimple.toShape(lognormal, numSamples);
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SymbolicTypes.GenericSimple.toShape(lognormal, numSamples);
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let lognormalXYShape: Types.xyShape =
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switch (lognormalShape) {
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| Mixed(_) => {xs: [||], ys: [||]}
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@ -89,26 +89,26 @@ module MathAdtToDistDst = {
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let normal: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(mean), Value(stdev)|] =>
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Ok(`DistData(`Symbolic(`Normal({mean, stdev}))))
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Ok(`Leaf(`SymbolicDist(`Normal({mean, stdev}))))
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| _ => Error("Wrong number of variables in normal distribution");
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let lognormal: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(mu), Value(sigma)|] =>
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Ok(`DistData(`Symbolic(`Lognormal({mu, sigma}))))
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Ok(`Leaf(`SymbolicDist(`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(
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`DistData(
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`Symbolic(
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`Leaf(
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`SymbolicDist(
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SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev),
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),
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),
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)
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| (_, _, Some(Value(mu)), Some(Value(sigma))) =>
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Ok(`DistData(`Symbolic(`Lognormal({mu, sigma}))))
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Ok(`Leaf(`SymbolicDist(`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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@ -118,15 +118,15 @@ module MathAdtToDistDst = {
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fun
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| [|Value(low), Value(high)|] when low <= 0.0 && low < high => {
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Ok(
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`DistData(
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`Symbolic(SymbolicDist.Normal.from90PercentCI(low, high)),
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`Leaf(
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`SymbolicDist(SymbolicDist.Normal.from90PercentCI(low, high)),
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),
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);
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}
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| [|Value(low), Value(high)|] when low < high => {
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Ok(
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`DistData(
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`Symbolic(SymbolicDist.Lognormal.from90PercentCI(low, high)),
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`Leaf(
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`SymbolicDist(SymbolicDist.Lognormal.from90PercentCI(low, high)),
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),
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);
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}
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@ -137,31 +137,31 @@ module MathAdtToDistDst = {
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let uniform: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(low), Value(high)|] =>
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Ok(`DistData(`Symbolic(`Uniform({low, high}))))
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Ok(`Leaf(`SymbolicDist(`Uniform({low, high}))))
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| _ => Error("Wrong number of variables in lognormal distribution");
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let beta: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(alpha), Value(beta)|] =>
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Ok(`DistData(`Symbolic(`Beta({alpha, beta}))))
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Ok(`Leaf(`SymbolicDist(`Beta({alpha, beta}))))
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| _ => Error("Wrong number of variables in lognormal distribution");
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let exponential: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(rate)|] =>
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Ok(`DistData(`Symbolic(`Exponential({rate: rate}))))
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Ok(`Leaf(`SymbolicDist(`Exponential({rate: rate}))))
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| _ => Error("Wrong number of variables in Exponential distribution");
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let cauchy: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(local), Value(scale)|] =>
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Ok(`DistData(`Symbolic(`Cauchy({local, scale}))))
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Ok(`Leaf(`SymbolicDist(`Cauchy({local, scale}))))
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| _ => Error("Wrong number of variables in cauchy distribution");
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let triangular: array(arg) => result(TreeNode.treeNode, string) =
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fun
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| [|Value(low), Value(medium), Value(high)|] =>
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Ok(`DistData(`Symbolic(`Triangular({low, medium, high}))))
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Ok(`Leaf(`SymbolicDist(`Triangular({low, medium, high}))))
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| _ => Error("Wrong number of variables in triangle distribution");
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let multiModal =
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@ -196,7 +196,7 @@ module MathAdtToDistDst = {
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`VerticalScaling((
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`Multiply,
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t,
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`DistData(`Symbolic(`Float(w))),
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`Leaf(`SymbolicDist(`Float(w))),
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)),
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);
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});
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@ -235,7 +235,7 @@ 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(`DistData(`Symbolic(`ContinuousShape(s))))
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| Some(s) => Ok(`Leaf(`SymbolicDist(`ContinuousShape(s))))
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| None => Error("Rendering did not work")
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};
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};
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@ -254,11 +254,11 @@ module MathAdtToDistDst = {
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| ("divide", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Divide, l, r))
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| ("divide", _) => Error("Division needs two operands")
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| ("pow", _) => Error("Exponentiation is not yet supported.")
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| ("leftTruncate", [|Ok(d), Ok(`DistData(`Symbolic(`Float(lc))))|]) =>
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| ("leftTruncate", [|Ok(d), Ok(`Leaf(`SymbolicDist(`Float(lc))))|]) =>
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toOkTrunctate((Some(lc), None, d))
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| ("leftTruncate", _) =>
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Error("leftTruncate needs two arguments: the expression and the cutoff")
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| ("rightTruncate", [|Ok(d), Ok(`DistData(`Symbolic(`Float(rc))))|]) =>
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| ("rightTruncate", [|Ok(d), Ok(`Leaf(`SymbolicDist(`Float(rc))))|]) =>
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toOkTrunctate((None, Some(rc), d))
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| ("rightTruncate", _) =>
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Error(
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@ -268,8 +268,8 @@ module MathAdtToDistDst = {
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"truncate",
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[|
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Ok(d),
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Ok(`DistData(`Symbolic(`Float(lc)))),
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Ok(`DistData(`Symbolic(`Float(rc)))),
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Ok(`Leaf(`SymbolicDist(`Float(lc)))),
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Ok(`Leaf(`SymbolicDist(`Float(rc)))),
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|],
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) =>
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toOkTrunctate((Some(lc), Some(rc), d))
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@ -333,7 +333,7 @@ module MathAdtToDistDst = {
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let rec nodeParser =
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fun
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| Value(f) => Ok(`DistData(`Symbolic(`Float(f))))
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| Value(f) => Ok(`Leaf(`SymbolicDist(`Float(f))))
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| Fn({name, args}) => functionParser(nodeParser, name, args)
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| _ => {
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Error("This type not currently supported");
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@ -1,52 +1,4 @@
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type normal = {
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mean: float,
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stdev: float,
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};
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type lognormal = {
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mu: float,
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sigma: float,
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};
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type uniform = {
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low: float,
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high: float,
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};
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type beta = {
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alpha: float,
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beta: float,
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};
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type exponential = {rate: float};
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type cauchy = {
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local: float,
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scale: float,
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};
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type triangular = {
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low: float,
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medium: float,
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high: float,
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};
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type continuousShape = {
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pdf: DistTypes.continuousShape,
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cdf: DistTypes.continuousShape,
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};
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type dist = [
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| `Normal(normal)
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| `Beta(beta)
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| `Lognormal(lognormal)
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| `Uniform(uniform)
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| `Exponential(exponential)
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| `Cauchy(cauchy)
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| `Triangular(triangular)
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| `ContinuousShape(continuousShape)
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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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open SymbolicTypes;
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module ContinuousShape = {
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type t = continuousShape;
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@ -124,11 +76,12 @@ module Normal = {
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`Normal({mean, stdev});
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};
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let operate = (operation: SymbolicTypes.Algebraic.t, n1: t, n2: t) => switch(operation){
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let operate = (operation: SymbolicTypes.Algebraic.t, n1: t, n2: t) =>
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switch (operation) {
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| `Add => Some(add(n1, n2))
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| `Subtract => Some(subtract(n1, n2))
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| _ => None
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}
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};
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};
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module Beta = {
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@ -177,11 +130,12 @@ module Lognormal = {
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let sigma = l1.sigma +. l2.sigma;
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`Lognormal({mu, sigma});
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};
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let operate = (operation: SymbolicTypes.Algebraic.t, n1: t, n2: t) => switch(operation){
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let operate = (operation: SymbolicTypes.Algebraic.t, n1: t, n2: t) =>
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switch (operation) {
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| `Multiply => Some(multiply(n1, n2))
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| `Divide => Some(divide(n1, n2))
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| _ => None
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}
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};
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};
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module Uniform = {
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@ -202,7 +156,7 @@ module Float = {
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let toString = Js.Float.toString;
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};
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module GenericDistFunctions = {
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module T = {
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let minCdfValue = 0.0001;
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let maxCdfValue = 0.9999;
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@ -232,7 +186,7 @@ module GenericDistFunctions = {
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| `ContinuousShape(n) => ContinuousShape.inv(x, n)
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};
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let sample: dist => float =
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let sample: symbolicDist => float =
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fun
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| `Normal(n) => Normal.sample(n)
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| `Triangular(n) => Triangular.sample(n)
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@ -244,7 +198,7 @@ module GenericDistFunctions = {
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| `Float(n) => Float.sample(n)
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| `ContinuousShape(n) => ContinuousShape.sample(n);
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let toString: dist => string =
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let toString: symbolicDist => string =
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fun
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| `Triangular(n) => Triangular.toString(n)
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| `Exponential(n) => Exponential.toString(n)
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@ -256,7 +210,7 @@ module GenericDistFunctions = {
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| `Float(n) => Float.toString(n)
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| `ContinuousShape(n) => ContinuousShape.toString(n);
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let min: dist => float =
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let min: symbolicDist => float =
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fun
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| `Triangular({low}) => low
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| `Exponential(n) => Exponential.inv(minCdfValue, n)
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@ -268,7 +222,7 @@ module GenericDistFunctions = {
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| `ContinuousShape(n) => ContinuousShape.inv(minCdfValue, n)
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| `Float(n) => n;
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let max: dist => float =
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let max: symbolicDist => float =
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fun
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| `Triangular(n) => n.high
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| `Exponential(n) => Exponential.inv(maxCdfValue, n)
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@ -280,7 +234,7 @@ module GenericDistFunctions = {
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| `Uniform({high}) => high
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| `Float(n) => n;
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let mean: dist => result(float, string) =
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let mean: symbolicDist => result(float, string) =
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fun
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| `Triangular(n) => Triangular.mean(n)
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| `Exponential(n) => Exponential.mean(n)
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@ -293,7 +247,7 @@ module GenericDistFunctions = {
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| `Float(n) => Float.mean(n);
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let interpolateXs =
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(~xSelection: [ | `Linear | `ByWeight]=`Linear, dist: dist, n) => {
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(~xSelection: [ | `Linear | `ByWeight]=`Linear, dist: symbolicDist, n) => {
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switch (xSelection, dist) {
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| (`Linear, _) => E.A.Floats.range(min(dist), max(dist), n)
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/* | (`ByWeight, `Uniform(n)) =>
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@ -306,4 +260,36 @@ module GenericDistFunctions = {
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ys |> E.A.fmap(y => inv(y, dist));
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};
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};
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/* This returns an optional that wraps a result. If the optional is None,
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there is no valid analytic solution. If it Some, it
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can still return an error if there is a serious problem,
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like in the casea of a divide by 0.
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*/
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type analyticalSolutionAttempt = [
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| `AnalyticalSolution(SymbolicTypes.symbolicDist)
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| `Error(string)
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| `NoSolution
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];
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let attemptAlgebraicOperation =
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(
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d1: symbolicDist,
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d2: symbolicDist,
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op: SymbolicTypes.algebraicOperation,
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)
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: analyticalSolutionAttempt =>
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switch (d1, d2) {
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| (`Float(v1), `Float(v2)) =>
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switch (SymbolicTypes.Algebraic.applyFn(op, v1, v2)) {
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| Ok(r) => `AnalyticalSolution(`Float(r))
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| Error(n) => `Error(n)
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}
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| (`Normal(v1), `Normal(v2)) =>
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Normal.operate(op, v1, v2)
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|> E.O.dimap(r => `AnalyticalSolution(r), () => `NoSolution)
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| (`Lognormal(v1), `Lognormal(v2)) =>
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Lognormal.operate(op, v1, v2)
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|> E.O.dimap(r => `AnalyticalSolution(r), () => `NoSolution)
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| _ => `NoSolution
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};
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};
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@ -1,7 +1,57 @@
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type normal = {
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mean: float,
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stdev: float,
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};
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type lognormal = {
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mu: float,
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sigma: float,
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};
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type uniform = {
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low: float,
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high: float,
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};
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type beta = {
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alpha: float,
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beta: float,
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};
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type exponential = {rate: float};
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type cauchy = {
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local: float,
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scale: float,
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};
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type triangular = {
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low: float,
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medium: float,
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high: float,
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};
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type continuousShape = {
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pdf: DistTypes.continuousShape,
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cdf: DistTypes.continuousShape,
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};
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type symbolicDist = [
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| `Normal(normal)
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| `Beta(beta)
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| `Lognormal(lognormal)
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| `Uniform(uniform)
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| `Exponential(exponential)
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| `Cauchy(cauchy)
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| `Triangular(triangular)
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| `ContinuousShape(continuousShape)
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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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type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
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type pointwiseOperation = [ | `Add | `Multiply];
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type scaleOperation = [ | `Multiply | `Exponentiate | `Log];
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type distToFloatOperation = [ | `Pdf(float) | `Inv(float) | `Mean | `Sample];
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type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
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module Algebraic = {
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type t = algebraicOperation;
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|
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@ -1,13 +1,12 @@
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/* This module represents a tree node. */
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open SymbolicTypes;
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// todo: Symbolic already has an arbitrary continuousShape option. It seems messy to have both.
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type distData = [
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| `Symbolic(SymbolicDist.dist)
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| `RenderedShape(DistTypes.shape)
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type leaf = [
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| `SymbolicDist(SymbolicTypes.symbolicDist)
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| `RenderedDist(DistTypes.shape)
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];
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/* TreeNodes are either Data (i.e. symbolic or rendered distributions) or Operations. Operations always refer to two child nodes.*/
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type treeNode = [ | `DistData(distData) | `Operation(operation)]
|
||||
type treeNode = [ | `Leaf(leaf) | `Operation(operation)]
|
||||
and operation = [
|
||||
| `AlgebraicCombination(algebraicOperation, treeNode, treeNode)
|
||||
| `PointwiseCombination(pointwiseOperation, treeNode, treeNode)
|
||||
|
|
@ -48,9 +47,8 @@ module TreeNode = {
|
|||
|
||||
let rec toString =
|
||||
fun
|
||||
| `DistData(`Symbolic(d)) =>
|
||||
SymbolicDist.GenericDistFunctions.toString(d)
|
||||
| `DistData(`RenderedShape(_)) => "[shape]"
|
||||
| `Leaf(`SymbolicDist(d)) => SymbolicDist.T.toString(d)
|
||||
| `Leaf(`RenderedDist(_)) => "[shape]"
|
||||
| `Operation(op) => Operation.toString(toString, op);
|
||||
|
||||
/* The following modules encapsulate everything we can do with
|
||||
|
|
@ -61,73 +59,34 @@ module TreeNode = {
|
|||
For instance, normal(0, 1) + normal(1, 1) -> normal(1, 2).
|
||||
In general, this is implemented via convolution. */
|
||||
module AlgebraicCombination = {
|
||||
let simplify = (algebraicOp, t1: t, t2: t): result(treeNode, string) => {
|
||||
let tryCombiningFloats: tResult =
|
||||
fun
|
||||
| `Operation(
|
||||
`AlgebraicCombination(
|
||||
algebraicOp,
|
||||
`DistData(`Symbolic(`Float(v1))),
|
||||
`DistData(`Symbolic(`Float(v2))),
|
||||
),
|
||||
) =>
|
||||
SymbolicTypes.Algebraic.applyFn(algebraicOp, v1, v2)
|
||||
|> E.R.fmap(r => `DistData(`Symbolic(`Float(r))))
|
||||
| t => Ok(t);
|
||||
|
||||
let optionToSymbolicResult = (t, o) =>
|
||||
o
|
||||
|> E.O.dimap(r => `DistData(`Symbolic(r)), () => t)
|
||||
|> (r => Ok(r));
|
||||
|
||||
let tryCombiningNormals: tResult =
|
||||
fun
|
||||
| `Operation(
|
||||
`AlgebraicCombination(
|
||||
operation,
|
||||
`DistData(`Symbolic(`Normal(n1))),
|
||||
`DistData(`Symbolic(`Normal(n2))),
|
||||
),
|
||||
) as t =>
|
||||
SymbolicDist.Normal.operate(operation, n1, n2)
|
||||
|> optionToSymbolicResult(t)
|
||||
| t => Ok(t);
|
||||
|
||||
let tryCombiningLognormals: tResult =
|
||||
fun
|
||||
| `Operation(
|
||||
`AlgebraicCombination(
|
||||
operation,
|
||||
`DistData(`Symbolic(`Lognormal(n1))),
|
||||
`DistData(`Symbolic(`Lognormal(n2))),
|
||||
),
|
||||
) as t =>
|
||||
SymbolicDist.Lognormal.operate(operation, n1, n2)
|
||||
|> optionToSymbolicResult(t)
|
||||
| t => Ok(t);
|
||||
|
||||
let originalTreeNode =
|
||||
`Operation(`AlgebraicCombination((algebraicOp, t1, t2)));
|
||||
|
||||
// Feedback: I like this pattern, kudos
|
||||
originalTreeNode
|
||||
|> tryCombiningFloats
|
||||
|> E.R.bind(_, tryCombiningNormals)
|
||||
|> E.R.bind(_, tryCombiningLognormals);
|
||||
};
|
||||
let toTreeNode = (op, t1, t2) =>
|
||||
`Operation(`AlgebraicCombination((op, t1, t2)));
|
||||
let tryAnalyticalSolution =
|
||||
fun
|
||||
| `Operation(
|
||||
`AlgebraicCombination(
|
||||
operation,
|
||||
`Leaf(`SymbolicDist(d1)),
|
||||
`Leaf(`SymbolicDist(d2)),
|
||||
),
|
||||
) as t =>
|
||||
switch (SymbolicDist.T.attemptAlgebraicOperation(d1, d2, operation)) {
|
||||
| `AnalyticalSolution(symbolicDist) =>
|
||||
Ok(`Leaf(`SymbolicDist(symbolicDist)))
|
||||
| `Error(er) => Error(er)
|
||||
| `NoSolution => Ok(t)
|
||||
}
|
||||
| t => Ok(t);
|
||||
|
||||
// todo: I don't like the name evaluateNumerically that much, if this renders and does it algebraically. It's tricky.
|
||||
let evaluateNumerically = (algebraicOp, operationToDistData, t1, t2) => {
|
||||
let evaluateNumerically = (algebraicOp, operationToLeaf, t1, t2) => {
|
||||
// force rendering into shapes
|
||||
let renderShape = r => operationToDistData(`Render(r));
|
||||
let renderShape = r => operationToLeaf(`Render(r));
|
||||
switch (renderShape(t1), renderShape(t2)) {
|
||||
| (
|
||||
Ok(`DistData(`RenderedShape(s1))),
|
||||
Ok(`DistData(`RenderedShape(s2))),
|
||||
) =>
|
||||
| (Ok(`Leaf(`RenderedDist(s1))), Ok(`Leaf(`RenderedDist(s2)))) =>
|
||||
Ok(
|
||||
`DistData(
|
||||
`RenderedShape(
|
||||
`Leaf(
|
||||
`RenderedDist(
|
||||
Distributions.Shape.combineAlgebraically(algebraicOp, s1, s2),
|
||||
),
|
||||
),
|
||||
|
|
@ -138,42 +97,40 @@ module TreeNode = {
|
|||
};
|
||||
};
|
||||
|
||||
let evaluateToDistData =
|
||||
let evaluateToLeaf =
|
||||
(
|
||||
algebraicOp: SymbolicTypes.algebraicOperation,
|
||||
operationToDistData,
|
||||
operationToLeaf,
|
||||
t1: t,
|
||||
t2: t,
|
||||
)
|
||||
: result(treeNode, string) =>
|
||||
algebraicOp
|
||||
|> simplify(_, t1, t2)
|
||||
|> toTreeNode(_, t1, t2)
|
||||
|> tryAnalyticalSolution
|
||||
|> E.R.bind(
|
||||
_,
|
||||
fun
|
||||
| `DistData(d) => Ok(`DistData(d)) // the analytical simplifaction worked, nice!
|
||||
| `Leaf(d) => Ok(`Leaf(d)) // the analytical simplifaction worked, nice!
|
||||
| `Operation(_) =>
|
||||
// if not, run the convolution
|
||||
evaluateNumerically(algebraicOp, operationToDistData, t1, t2),
|
||||
evaluateNumerically(algebraicOp, operationToLeaf, t1, t2),
|
||||
);
|
||||
};
|
||||
|
||||
module VerticalScaling = {
|
||||
let evaluateToDistData = (scaleOp, operationToDistData, t, scaleBy) => {
|
||||
let evaluateToLeaf = (scaleOp, operationToLeaf, t, scaleBy) => {
|
||||
// scaleBy has to be a single float, otherwise we'll return an error.
|
||||
let fn = SymbolicTypes.Scale.toFn(scaleOp);
|
||||
let knownIntegralSumFn =
|
||||
SymbolicTypes.Scale.toKnownIntegralSumFn(scaleOp);
|
||||
let renderedShape = operationToDistData(`Render(t));
|
||||
let renderedShape = operationToLeaf(`Render(t));
|
||||
|
||||
switch (renderedShape, scaleBy) {
|
||||
| (
|
||||
Ok(`DistData(`RenderedShape(rs))),
|
||||
`DistData(`Symbolic(`Float(sm))),
|
||||
) =>
|
||||
| (Ok(`Leaf(`RenderedDist(rs))), `Leaf(`SymbolicDist(`Float(sm)))) =>
|
||||
Ok(
|
||||
`DistData(
|
||||
`RenderedShape(
|
||||
`Leaf(
|
||||
`RenderedDist(
|
||||
Distributions.Shape.T.mapY(
|
||||
~knownIntegralSumFn=knownIntegralSumFn(sm),
|
||||
fn(sm),
|
||||
|
|
@ -189,18 +146,15 @@ module TreeNode = {
|
|||
};
|
||||
|
||||
module PointwiseCombination = {
|
||||
let pointwiseAdd = (operationToDistData, t1, t2) => {
|
||||
let renderedShape1 = operationToDistData(`Render(t1));
|
||||
let renderedShape2 = operationToDistData(`Render(t2));
|
||||
let pointwiseAdd = (operationToLeaf, t1, t2) => {
|
||||
let renderedShape1 = operationToLeaf(`Render(t1));
|
||||
let renderedShape2 = operationToLeaf(`Render(t2));
|
||||
|
||||
switch (renderedShape1, renderedShape2) {
|
||||
| (
|
||||
Ok(`DistData(`RenderedShape(rs1))),
|
||||
Ok(`DistData(`RenderedShape(rs2))),
|
||||
) =>
|
||||
| (Ok(`Leaf(`RenderedDist(rs1))), Ok(`Leaf(`RenderedDist(rs2)))) =>
|
||||
Ok(
|
||||
`DistData(
|
||||
`RenderedShape(
|
||||
`Leaf(
|
||||
`RenderedDist(
|
||||
Distributions.Shape.combinePointwise(
|
||||
~knownIntegralSumsFn=(a, b) => Some(a +. b),
|
||||
(+.),
|
||||
|
|
@ -216,18 +170,18 @@ module TreeNode = {
|
|||
};
|
||||
};
|
||||
|
||||
let pointwiseMultiply = (operationToDistData, t1, t2) => {
|
||||
let pointwiseMultiply = (operationToLeaf, t1, t2) => {
|
||||
// TODO: construct a function that we can easily sample from, to construct
|
||||
// a RenderedShape. Use the xMin and xMax of the rendered shapes to tell the sampling function where to look.
|
||||
// a RenderedDist. Use the xMin and xMax of the rendered shapes to tell the sampling function where to look.
|
||||
Error(
|
||||
"Pointwise multiplication not yet supported.",
|
||||
);
|
||||
};
|
||||
|
||||
let evaluateToDistData = (pointwiseOp, operationToDistData, t1, t2) => {
|
||||
let evaluateToLeaf = (pointwiseOp, operationToLeaf, t1, t2) => {
|
||||
switch (pointwiseOp) {
|
||||
| `Add => pointwiseAdd(operationToDistData, t1, t2)
|
||||
| `Multiply => pointwiseMultiply(operationToDistData, t1, t2)
|
||||
| `Add => pointwiseAdd(operationToLeaf, t1, t2)
|
||||
| `Multiply => pointwiseMultiply(operationToLeaf, t1, t2)
|
||||
};
|
||||
};
|
||||
};
|
||||
|
|
@ -236,18 +190,17 @@ module TreeNode = {
|
|||
module Simplify = {
|
||||
let tryTruncatingNothing: tResult =
|
||||
fun
|
||||
| `Operation(`Truncate(None, None, `DistData(d))) =>
|
||||
Ok(`DistData(d))
|
||||
| `Operation(`Truncate(None, None, `Leaf(d))) => Ok(`Leaf(d))
|
||||
| t => Ok(t);
|
||||
|
||||
let tryTruncatingUniform: tResult =
|
||||
fun
|
||||
| `Operation(`Truncate(lc, rc, `DistData(`Symbolic(`Uniform(u))))) => {
|
||||
| `Operation(`Truncate(lc, rc, `Leaf(`SymbolicDist(`Uniform(u))))) => {
|
||||
// just create a new Uniform distribution
|
||||
let newLow = max(E.O.default(neg_infinity, lc), u.low);
|
||||
let newHigh = min(E.O.default(infinity, rc), u.high);
|
||||
Ok(
|
||||
`DistData(`Symbolic(`Uniform({low: newLow, high: newHigh}))),
|
||||
`Leaf(`SymbolicDist(`Uniform({low: newLow, high: newHigh}))),
|
||||
);
|
||||
}
|
||||
| t => Ok(t);
|
||||
|
|
@ -262,27 +215,26 @@ module TreeNode = {
|
|||
};
|
||||
};
|
||||
|
||||
let evaluateNumerically =
|
||||
(leftCutoff, rightCutoff, operationToDistData, t) => {
|
||||
let evaluateNumerically = (leftCutoff, rightCutoff, operationToLeaf, t) => {
|
||||
// TODO: use named args in renderToShape; if we're lucky we can at least get the tail
|
||||
// of a distribution we otherwise wouldn't get at all
|
||||
let renderedShape = operationToDistData(`Render(t));
|
||||
let renderedShape = operationToLeaf(`Render(t));
|
||||
|
||||
switch (renderedShape) {
|
||||
| Ok(`DistData(`RenderedShape(rs))) =>
|
||||
| Ok(`Leaf(`RenderedDist(rs))) =>
|
||||
let truncatedShape =
|
||||
rs |> Distributions.Shape.T.truncate(leftCutoff, rightCutoff);
|
||||
Ok(`DistData(`RenderedShape(rs)));
|
||||
Ok(`Leaf(`RenderedDist(rs)));
|
||||
| Error(e1) => Error(e1)
|
||||
| _ => Error("Could not truncate distribution.")
|
||||
};
|
||||
};
|
||||
|
||||
let evaluateToDistData =
|
||||
let evaluateToLeaf =
|
||||
(
|
||||
leftCutoff: option(float),
|
||||
rightCutoff: option(float),
|
||||
operationToDistData,
|
||||
operationToLeaf,
|
||||
t: treeNode,
|
||||
)
|
||||
: result(treeNode, string) => {
|
||||
|
|
@ -291,31 +243,23 @@ module TreeNode = {
|
|||
|> E.R.bind(
|
||||
_,
|
||||
fun
|
||||
| `DistData(d) => Ok(`DistData(d)) // the analytical simplifaction worked, nice!
|
||||
| `Leaf(d) => Ok(`Leaf(d)) // the analytical simplifaction worked, nice!
|
||||
| `Operation(_) =>
|
||||
evaluateNumerically(
|
||||
leftCutoff,
|
||||
rightCutoff,
|
||||
operationToDistData,
|
||||
t,
|
||||
),
|
||||
evaluateNumerically(leftCutoff, rightCutoff, operationToLeaf, t),
|
||||
); // if not, run the convolution
|
||||
};
|
||||
};
|
||||
|
||||
module Normalize = {
|
||||
let rec evaluateToDistData =
|
||||
(operationToDistData, t: treeNode): result(treeNode, string) => {
|
||||
let rec evaluateToLeaf =
|
||||
(operationToLeaf, t: treeNode): result(treeNode, string) => {
|
||||
switch (t) {
|
||||
| `DistData(`Symbolic(_)) => Ok(t)
|
||||
| `DistData(`RenderedShape(s)) =>
|
||||
| `Leaf(`SymbolicDist(_)) => Ok(t)
|
||||
| `Leaf(`RenderedDist(s)) =>
|
||||
let normalized = Distributions.Shape.T.normalize(s);
|
||||
Ok(`DistData(`RenderedShape(normalized)));
|
||||
Ok(`Leaf(`RenderedDist(normalized)));
|
||||
| `Operation(op) =>
|
||||
E.R.bind(
|
||||
operationToDistData(op),
|
||||
evaluateToDistData(operationToDistData),
|
||||
)
|
||||
E.R.bind(operationToLeaf(op), evaluateToLeaf(operationToLeaf))
|
||||
};
|
||||
};
|
||||
};
|
||||
|
|
@ -324,14 +268,14 @@ module TreeNode = {
|
|||
let evaluateFromSymbolic = (distToFloatOp: distToFloatOperation, s) => {
|
||||
let value =
|
||||
switch (distToFloatOp) {
|
||||
| `Pdf(f) => Ok(SymbolicDist.GenericDistFunctions.pdf(f, s))
|
||||
| `Inv(f) => Ok(SymbolicDist.GenericDistFunctions.inv(f, s))
|
||||
| `Sample => Ok(SymbolicDist.GenericDistFunctions.sample(s))
|
||||
| `Mean => SymbolicDist.GenericDistFunctions.mean(s)
|
||||
| `Pdf(f) => Ok(SymbolicDist.T.pdf(f, s))
|
||||
| `Inv(f) => Ok(SymbolicDist.T.inv(f, s))
|
||||
| `Sample => Ok(SymbolicDist.T.sample(s))
|
||||
| `Mean => SymbolicDist.T.mean(s)
|
||||
};
|
||||
E.R.bind(value, v => Ok(`DistData(`Symbolic(`Float(v)))));
|
||||
E.R.bind(value, v => Ok(`Leaf(`SymbolicDist(`Float(v)))));
|
||||
};
|
||||
let evaluateFromRenderedShape =
|
||||
let evaluateFromRenderedDist =
|
||||
(distToFloatOp: distToFloatOperation, rs: DistTypes.shape)
|
||||
: result(treeNode, string) => {
|
||||
let value =
|
||||
|
|
@ -341,45 +285,45 @@ module TreeNode = {
|
|||
| `Sample => Ok(Distributions.Shape.sample(rs))
|
||||
| `Mean => Ok(Distributions.Shape.T.mean(rs))
|
||||
};
|
||||
E.R.bind(value, v => Ok(`DistData(`Symbolic(`Float(v)))));
|
||||
E.R.bind(value, v => Ok(`Leaf(`SymbolicDist(`Float(v)))));
|
||||
};
|
||||
let rec evaluateToDistData =
|
||||
let rec evaluateToLeaf =
|
||||
(
|
||||
distToFloatOp: distToFloatOperation,
|
||||
operationToDistData,
|
||||
operationToLeaf,
|
||||
t: treeNode,
|
||||
)
|
||||
: result(treeNode, string) => {
|
||||
switch (t) {
|
||||
| `DistData(`Symbolic(s)) => evaluateFromSymbolic(distToFloatOp, s) // we want to evaluate the distToFloatOp on the symbolic dist
|
||||
| `DistData(`RenderedShape(rs)) =>
|
||||
evaluateFromRenderedShape(distToFloatOp, rs)
|
||||
| `Leaf(`SymbolicDist(s)) => evaluateFromSymbolic(distToFloatOp, s) // we want to evaluate the distToFloatOp on the symbolic dist
|
||||
| `Leaf(`RenderedDist(rs)) =>
|
||||
evaluateFromRenderedDist(distToFloatOp, rs)
|
||||
| `Operation(op) =>
|
||||
E.R.bind(
|
||||
operationToDistData(op),
|
||||
evaluateToDistData(distToFloatOp, operationToDistData),
|
||||
operationToLeaf(op),
|
||||
evaluateToLeaf(distToFloatOp, operationToLeaf),
|
||||
)
|
||||
};
|
||||
};
|
||||
};
|
||||
|
||||
module Render = {
|
||||
let rec evaluateToRenderedShape =
|
||||
let rec evaluateToRenderedDist =
|
||||
(
|
||||
operationToDistData: operation => result(t, string),
|
||||
operationToLeaf: operation => result(t, string),
|
||||
sampleCount: int,
|
||||
t: treeNode,
|
||||
)
|
||||
: result(t, string) => {
|
||||
switch (t) {
|
||||
| `DistData(`RenderedShape(s)) => Ok(`DistData(`RenderedShape(s))) // already a rendered shape, we're done here
|
||||
| `DistData(`Symbolic(d)) =>
|
||||
| `Leaf(`RenderedDist(s)) => Ok(`Leaf(`RenderedDist(s))) // already a rendered shape, we're done here
|
||||
| `Leaf(`SymbolicDist(d)) =>
|
||||
// todo: move to dist
|
||||
switch (d) {
|
||||
| `Float(v) =>
|
||||
Ok(
|
||||
`DistData(
|
||||
`RenderedShape(
|
||||
`Leaf(
|
||||
`RenderedDist(
|
||||
Discrete(
|
||||
Distributions.Discrete.make(
|
||||
{xs: [|v|], ys: [|1.0|]},
|
||||
|
|
@ -391,16 +335,15 @@ module TreeNode = {
|
|||
)
|
||||
| _ =>
|
||||
let xs =
|
||||
SymbolicDist.GenericDistFunctions.interpolateXs(
|
||||
SymbolicDist.T.interpolateXs(
|
||||
~xSelection=`ByWeight,
|
||||
d,
|
||||
sampleCount,
|
||||
);
|
||||
let ys =
|
||||
xs |> E.A.fmap(x => SymbolicDist.GenericDistFunctions.pdf(x, d));
|
||||
let ys = xs |> E.A.fmap(x => SymbolicDist.T.pdf(x, d));
|
||||
Ok(
|
||||
`DistData(
|
||||
`RenderedShape(
|
||||
`Leaf(
|
||||
`RenderedDist(
|
||||
Continuous(
|
||||
Distributions.Continuous.make(
|
||||
`Linear,
|
||||
|
|
@ -414,57 +357,57 @@ module TreeNode = {
|
|||
}
|
||||
| `Operation(op) =>
|
||||
E.R.bind(
|
||||
operationToDistData(op),
|
||||
evaluateToRenderedShape(operationToDistData, sampleCount),
|
||||
operationToLeaf(op),
|
||||
evaluateToRenderedDist(operationToLeaf, sampleCount),
|
||||
)
|
||||
};
|
||||
};
|
||||
};
|
||||
|
||||
let rec operationToDistData =
|
||||
let rec operationToLeaf =
|
||||
(sampleCount: int, op: operation): result(t, string) => {
|
||||
// the functions that convert the Operation nodes to DistData nodes need to
|
||||
// the functions that convert the Operation nodes to Leaf nodes need to
|
||||
// have a way to call this function on their children, if their children are themselves Operation nodes.
|
||||
switch (op) {
|
||||
| `AlgebraicCombination(algebraicOp, t1, t2) =>
|
||||
AlgebraicCombination.evaluateToDistData(
|
||||
AlgebraicCombination.evaluateToLeaf(
|
||||
algebraicOp,
|
||||
operationToDistData(sampleCount),
|
||||
operationToLeaf(sampleCount),
|
||||
t1,
|
||||
t2 // we want to give it the option to render or simply leave it as is
|
||||
)
|
||||
| `PointwiseCombination(pointwiseOp, t1, t2) =>
|
||||
PointwiseCombination.evaluateToDistData(
|
||||
PointwiseCombination.evaluateToLeaf(
|
||||
pointwiseOp,
|
||||
operationToDistData(sampleCount),
|
||||
operationToLeaf(sampleCount),
|
||||
t1,
|
||||
t2,
|
||||
)
|
||||
| `VerticalScaling(scaleOp, t, scaleBy) =>
|
||||
VerticalScaling.evaluateToDistData(
|
||||
VerticalScaling.evaluateToLeaf(
|
||||
scaleOp,
|
||||
operationToDistData(sampleCount),
|
||||
operationToLeaf(sampleCount),
|
||||
t,
|
||||
scaleBy,
|
||||
)
|
||||
| `Truncate(leftCutoff, rightCutoff, t) =>
|
||||
Truncate.evaluateToDistData(
|
||||
Truncate.evaluateToLeaf(
|
||||
leftCutoff,
|
||||
rightCutoff,
|
||||
operationToDistData(sampleCount),
|
||||
operationToLeaf(sampleCount),
|
||||
t,
|
||||
)
|
||||
| `FloatFromDist(distToFloatOp, t) =>
|
||||
FloatFromDist.evaluateToDistData(
|
||||
FloatFromDist.evaluateToLeaf(
|
||||
distToFloatOp,
|
||||
operationToDistData(sampleCount),
|
||||
operationToLeaf(sampleCount),
|
||||
t,
|
||||
)
|
||||
| `Normalize(t) =>
|
||||
Normalize.evaluateToDistData(operationToDistData(sampleCount), t)
|
||||
Normalize.evaluateToLeaf(operationToLeaf(sampleCount), t)
|
||||
| `Render(t) =>
|
||||
Render.evaluateToRenderedShape(
|
||||
operationToDistData(sampleCount),
|
||||
Render.evaluateToRenderedDist(
|
||||
operationToLeaf(sampleCount),
|
||||
sampleCount,
|
||||
t,
|
||||
)
|
||||
|
|
@ -474,23 +417,23 @@ module TreeNode = {
|
|||
/* This function recursively goes through the nodes of the parse tree,
|
||||
replacing each Operation node and its subtree with a Data node.
|
||||
Whenever possible, the replacement produces a new Symbolic Data node,
|
||||
but most often it will produce a RenderedShape.
|
||||
This function is used mainly to turn a parse tree into a single RenderedShape
|
||||
but most often it will produce a RenderedDist.
|
||||
This function is used mainly to turn a parse tree into a single RenderedDist
|
||||
that can then be displayed to the user. */
|
||||
let toDistData = (treeNode: t, sampleCount: int): result(t, string) => {
|
||||
let toLeaf = (treeNode: t, sampleCount: int): result(t, string) => {
|
||||
switch (treeNode) {
|
||||
| `DistData(d) => Ok(`DistData(d))
|
||||
| `Operation(op) => operationToDistData(sampleCount, op)
|
||||
| `Leaf(d) => Ok(`Leaf(d))
|
||||
| `Operation(op) => operationToLeaf(sampleCount, op)
|
||||
};
|
||||
};
|
||||
};
|
||||
|
||||
let toShape = (sampleCount: int, treeNode: treeNode) => {
|
||||
let renderResult =
|
||||
TreeNode.toDistData(`Operation(`Render(treeNode)), sampleCount);
|
||||
TreeNode.toLeaf(`Operation(`Render(treeNode)), sampleCount);
|
||||
|
||||
switch (renderResult) {
|
||||
| Ok(`DistData(`RenderedShape(rs))) =>
|
||||
| Ok(`Leaf(`RenderedDist(rs))) =>
|
||||
let continuous = Distributions.Shape.T.toContinuous(rs);
|
||||
let discrete = Distributions.Shape.T.toDiscrete(rs);
|
||||
let shape = MixedShapeBuilder.buildSimple(~continuous, ~discrete);
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user