Pulled out Continuous to its own file
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@ -23,7 +23,7 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// describe("Shape", () => {
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// describe("Continuous", () => {
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// open Distributions.Continuous;
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// open Continuous;
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// let continuous = make(`Linear, shape, None);
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// makeTest("minX", T.minX(continuous), 1.0);
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// makeTest("maxX", T.maxX(continuous), 8.0);
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@ -130,7 +130,7 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// });
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// describe("Discrete", () => {
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// open Distributions.Discrete;
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// open Discrete;
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// let shape: DistTypes.xyShape = {
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// xs: [|1., 4., 8.|],
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// ys: [|0.3, 0.5, 0.2|],
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@ -181,7 +181,7 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// makeTest(
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// "integral",
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// T.Integral.get(~cache=None, discrete),
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Stepwise,
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// {xs: [|1., 4., 8.|], ys: [|0.3, 0.8, 1.0|]},
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// None
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@ -189,8 +189,8 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// );
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// makeTest(
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// "integral with 1 element",
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// T.Integral.get(~cache=None, Distributions.Discrete.make({xs: [|0.0|], ys: [|1.0|]}, None)),
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// Distributions.Continuous.make(`Stepwise, {xs: [|0.0|], ys: [|1.0|]}, None),
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// T.Integral.get(~cache=None, Discrete.make({xs: [|0.0|], ys: [|1.0|]}, None)),
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// Continuous.make(`Stepwise, {xs: [|0.0|], ys: [|1.0|]}, None),
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// );
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// makeTest(
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// "integralXToY",
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@ -213,15 +213,15 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// xs: [|1., 4., 8.|],
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// ys: [|0.3, 0.5, 0.2|],
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// };
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// let discrete = Distributions.Discrete.make(discreteShape, None);
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// let discrete = Discrete.make(discreteShape, None);
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// let continuous =
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Linear,
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// {xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
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// None
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// )
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// |> Distributions.Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
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// let mixed = Distributions.Mixed.make(
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// |> Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
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// let mixed = Mixed.make(
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// ~continuous,
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// ~discrete,
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// );
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@ -230,9 +230,9 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// makeTest(
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// "mapY",
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// T.mapY(r => r *. 2.0, mixed),
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// Distributions.Mixed.make(
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// Mixed.make(
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// ~continuous=
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Linear,
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// {
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// xs: [|3., 7., 14.|],
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@ -244,7 +244,7 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// },
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// None
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// ),
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// ~discrete=Distributions.Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None)
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// ~discrete=Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None)
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// ),
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// );
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// makeTest(
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@ -265,10 +265,10 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// makeTest("integralEndY", T.Integral.sum(~cache=None, mixed), 1.0);
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// makeTest(
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// "scaleBy",
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// Distributions.Mixed.scaleBy(~scale=2.0, mixed),
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// Distributions.Mixed.make(
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// Mixed.scaleBy(~scale=2.0, mixed),
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// Mixed.make(
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// ~continuous=
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Linear,
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// {
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// xs: [|3., 7., 14.|],
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@ -280,13 +280,13 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// },
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// None
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// ),
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// ~discrete=Distributions.Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None),
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// ~discrete=Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None),
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// ),
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// );
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// makeTest(
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// "integral",
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// T.Integral.get(~cache=None, mixed),
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Linear,
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// {
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// xs: [|1.00007, 1.00007, 3., 4., 4.00007, 7., 8., 8.00007, 14.|],
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@ -313,16 +313,16 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// xs: [|1., 4., 8.|],
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// ys: [|0.3, 0.5, 0.2|],
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// };
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// let discrete = Distributions.Discrete.make(discreteShape, None);
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// let discrete = Discrete.make(discreteShape, None);
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// let continuous =
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Linear,
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// {xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
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// None
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// )
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// |> Distributions.Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
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// |> Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
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// let mixed =
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// Distributions.Mixed.make(
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// Mixed.make(
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// ~continuous,
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// ~discrete,
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// );
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@ -354,7 +354,7 @@ let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
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// "integral",
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// T.Integral.get(~cache=None, distPlus) |> T.toContinuous,
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// Some(
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// Distributions.Continuous.make(
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// Continuous.make(
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// `Linear,
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// {
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// xs: [|1.00007, 1.00007, 3., 4., 4.00007, 7., 8., 8.00007, 14.|],
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@ -1 +1 @@
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let entries = EntryTypes.[Continuous.entry,ExpressionTreeExamples.entry];
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let entries = EntryTypes.[Continuous2.entry,ExpressionTreeExamples.entry];
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@ -44,7 +44,7 @@ module DemoDist = {
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DistPlus.make(
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~shape=
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Continuous(
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Distributions.Continuous.make(`Linear, {xs, ys}, None),
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Continuous.make(`Linear, {xs, ys}, None),
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),
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~domain=Complete,
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~unit=UnspecifiedDistribution,
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@ -291,8 +291,8 @@ module Draw = {
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/*
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let continuousShape =
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Convert.canvasShapeToContinuousShape(~canvasShape, ~canvasElement);
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let mean = Distributions.Continuous.T.mean(continuousShape);
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let variance = Distributions.Continuous.T.variance(continuousShape);
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let mean = Continuous.T.mean(continuousShape);
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let variance = Continuous.T.variance(continuousShape);
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let meanLocation =
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Convert.findClosestInOrderedArrayDangerously(mean, canvasShape.xValues);
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let meanLocationCanvasX = canvasShape.ws[meanLocation];
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@ -394,7 +394,7 @@ module Draw = {
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switch (normalShape) {
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| Mixed(_) => {xs: [||], ys: [||]}
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| Discrete(_) => {xs: [||], ys: [||]}
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| Continuous(m) => Distributions.Continuous.getShape(m)
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| Continuous(m) => Continuous.getShape(m)
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};
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/* // To use a lognormal instead:
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@ -405,7 +405,7 @@ module Draw = {
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switch (lognormalShape) {
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| Mixed(_) => {xs: [||], ys: [||]}
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| Discrete(_) => {xs: [||], ys: [||]}
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| Continuous(m) => Distributions.Continuous.getShape(m)
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| Continuous(m) => Continuous.getShape(m)
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};
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*/
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@ -669,11 +669,11 @@ module State = {
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/* create a cdf from a pdf */
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let _pdf =
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Distributions.Continuous.T.normalize(
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Continuous.T.normalize(
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pdf,
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);
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let cdf = Distributions.Continuous.T.integral(~cache=None, _pdf);
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let cdf = Continuous.T.integral(~cache=None, _pdf);
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let xs = [||];
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let ys = [||];
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for (i in 1 to 999) {
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@ -87,7 +87,7 @@ let table = (distPlus, x) => {
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{distPlus
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|> DistPlus.T.toContinuous
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|> E.O.fmap(
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Distributions.Continuous.T.Integral.sum(~cache=None),
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Continuous.T.Integral.sum(~cache=None),
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)
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|> E.O.fmap(E.Float.with2DigitsPrecision)
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|> E.O.default("")
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@ -97,7 +97,7 @@ let table = (distPlus, x) => {
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{distPlus
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|> DistPlus.T.normalizedToContinuous
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|> E.O.fmap(
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Distributions.Continuous.T.Integral.sum(~cache=None),
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Continuous.T.Integral.sum(~cache=None),
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)
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|> E.O.fmap(E.Float.with2DigitsPrecision)
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|> E.O.default("")
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@ -106,7 +106,7 @@ let table = (distPlus, x) => {
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<td className="px-4 py-2 border ">
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{distPlus
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|> DistPlus.T.toDiscrete
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|> E.O.fmap(Distributions.Discrete.T.Integral.sum(~cache=None))
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|> E.O.fmap(Discrete.T.Integral.sum(~cache=None))
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|> E.O.fmap(E.Float.with2DigitsPrecision)
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|> E.O.default("")
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|> ReasonReact.string}
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@ -114,7 +114,7 @@ let table = (distPlus, x) => {
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<td className="px-4 py-2 border ">
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{distPlus
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|> DistPlus.T.normalizedToDiscrete
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|> E.O.fmap(Distributions.Discrete.T.Integral.sum(~cache=None))
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|> E.O.fmap(Discrete.T.Integral.sum(~cache=None))
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|> E.O.fmap(E.Float.with2DigitsPrecision)
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|> E.O.default("")
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|> ReasonReact.string}
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@ -225,11 +225,11 @@ module DistPlusChart = {
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[@react.component]
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let make = (~distPlus: DistTypes.distPlus, ~config: chartConfig, ~onHover) => {
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open DistPlus;
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let discrete = distPlus |> T.normalizedToDiscrete |> E.O.fmap(Distributions.Discrete.getShape);
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let discrete = distPlus |> T.normalizedToDiscrete |> E.O.fmap(Discrete.getShape);
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let continuous =
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distPlus
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|> T.normalizedToContinuous
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|> E.O.fmap(Distributions.Continuous.getShape);
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|> E.O.fmap(Continuous.getShape);
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let range = T.xTotalRange(distPlus);
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// // We subtract a bit from the range to make sure that it fits. Maybe this should be done in d3 instead.
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@ -280,8 +280,8 @@ module IntegralChart = {
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let integral = distPlus.integralCache;
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let continuous =
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integral
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|> Distributions.Continuous.toLinear
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|> E.O.fmap(Distributions.Continuous.getShape);
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|> Continuous.toLinear
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|> E.O.fmap(Continuous.getShape);
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let minX = {
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distPlus |> DistPlus.T.Integral.yToX(~cache=None, 0.00001);
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};
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275
src/distPlus/distribution/Continuous.re
Normal file
275
src/distPlus/distribution/Continuous.re
Normal file
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@ -0,0 +1,275 @@
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open Distributions;
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type t = DistTypes.continuousShape;
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let getShape = (t: t) => t.xyShape;
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let interpolation = (t: t) => t.interpolation;
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let make = (interpolation, xyShape, knownIntegralSum): t => {
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xyShape,
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interpolation,
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knownIntegralSum,
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};
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let shapeMap = (fn, {xyShape, interpolation, knownIntegralSum}: t): t => {
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xyShape: fn(xyShape),
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interpolation,
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knownIntegralSum,
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};
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let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
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let oShapeMap =
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(fn, {xyShape, interpolation, knownIntegralSum}: t)
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: option(DistTypes.continuousShape) =>
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fn(xyShape) |> E.O.fmap(make(interpolation, _, knownIntegralSum));
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let empty: DistTypes.continuousShape = {
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xyShape: XYShape.T.empty,
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interpolation: `Linear,
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knownIntegralSum: Some(0.0),
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};
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let combinePointwise =
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(
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~knownIntegralSumsFn,
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fn: (float, float) => float,
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t1: DistTypes.continuousShape,
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t2: DistTypes.continuousShape,
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)
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: DistTypes.continuousShape => {
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// If we're adding the distributions, and we know the total of each, then we
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// can just sum them up. Otherwise, all bets are off.
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let combinedIntegralSum =
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Common.combineIntegralSums(
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knownIntegralSumsFn,
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t1.knownIntegralSum,
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t2.knownIntegralSum,
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);
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make(
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`Linear,
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XYShape.PointwiseCombination.combineLinear(
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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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combinedIntegralSum,
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);
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};
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let toLinear = (t: t): option(t) => {
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switch (t) {
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| {interpolation: `Stepwise, xyShape, knownIntegralSum} =>
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xyShape
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|> XYShape.Range.stepsToContinuous
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|> E.O.fmap(make(`Linear, _, knownIntegralSum))
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| {interpolation: `Linear} => Some(t)
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};
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};
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let shapeFn = (fn, t: t) => t |> getShape |> fn;
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let updateKnownIntegralSum = (knownIntegralSum, t: t): t => {
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...t,
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knownIntegralSum,
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};
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let reduce =
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(
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~knownIntegralSumsFn: (float, float) => option(float)=(_, _) => None,
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fn,
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continuousShapes,
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) =>
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continuousShapes
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|> E.A.fold_left(combinePointwise(~knownIntegralSumsFn, fn), empty);
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let mapY = (~knownIntegralSumFn=_ => None, fn, t: t) => {
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let u = E.O.bind(_, knownIntegralSumFn);
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let yMapFn = shapeMap(XYShape.T.mapY(fn));
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t |> yMapFn |> updateKnownIntegralSum(u(t.knownIntegralSum));
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};
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let scaleBy = (~scale=1.0, t: t): t => {
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t
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|> mapY((r: float) => r *. scale)
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|> updateKnownIntegralSum(
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E.O.bind(t.knownIntegralSum, v => Some(scale *. v)),
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);
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};
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module T =
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Dist({
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type t = DistTypes.continuousShape;
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type integral = DistTypes.continuousShape;
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let minX = shapeFn(XYShape.T.minX);
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let maxX = shapeFn(XYShape.T.maxX);
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let mapY = mapY;
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let toDiscreteProbabilityMassFraction = _ => 0.0;
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let toShape = (t: t): DistTypes.shape => Continuous(t);
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let xToY = (f, {interpolation, xyShape}: t) => {
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(
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switch (interpolation) {
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| `Stepwise =>
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xyShape |> XYShape.XtoY.stepwiseIncremental(f) |> E.O.default(0.0)
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| `Linear => xyShape |> XYShape.XtoY.linear(f)
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}
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)
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|> DistTypes.MixedPoint.makeContinuous;
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};
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let truncate =
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(leftCutoff: option(float), rightCutoff: option(float), t: t) => {
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let lc = E.O.default(neg_infinity, leftCutoff);
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let rc = E.O.default(infinity, rightCutoff);
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let truncatedZippedPairs =
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t
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|> getShape
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|> XYShape.T.zip
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|> XYShape.Zipped.filterByX(x => x >= lc && x <= rc);
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let eps = (t |> getShape |> XYShape.T.xTotalRange) *. 0.0001;
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let leftNewPoint =
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leftCutoff |> E.O.dimap(lc => [|(lc -. eps, 0.)|], _ => [||]);
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let rightNewPoint =
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rightCutoff |> E.O.dimap(rc => [|(rc +. eps, 0.)|], _ => [||]);
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let truncatedZippedPairsWithNewPoints =
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E.A.concatMany([|leftNewPoint, truncatedZippedPairs, rightNewPoint|]);
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let truncatedShape =
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XYShape.T.fromZippedArray(truncatedZippedPairsWithNewPoints);
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make(`Linear, truncatedShape, None);
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};
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// TODO: This should work with stepwise plots.
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let integral = (~cache, t) =>
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if (t |> getShape |> XYShape.T.length > 0) {
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switch (cache) {
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| Some(cache) => cache
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| None =>
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t
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|> getShape
|
||||
|> XYShape.Range.integrateWithTriangles
|
||||
|> E.O.toExt("This should not have happened")
|
||||
|> make(`Linear, _, None)
|
||||
};
|
||||
} else {
|
||||
make(`Linear, {xs: [|neg_infinity|], ys: [|0.0|]}, None);
|
||||
};
|
||||
|
||||
let downsample = (~cache=None, length, t): t =>
|
||||
t
|
||||
|> shapeMap(
|
||||
XYShape.XsConversion.proportionByProbabilityMass(
|
||||
length,
|
||||
integral(~cache, t).xyShape,
|
||||
),
|
||||
);
|
||||
let integralEndY = (~cache, t: t) =>
|
||||
t.knownIntegralSum |> E.O.default(t |> integral(~cache) |> lastY);
|
||||
let integralXtoY = (~cache, f, t: t) =>
|
||||
t |> integral(~cache) |> shapeFn(XYShape.XtoY.linear(f));
|
||||
let integralYtoX = (~cache, f, t: t) =>
|
||||
t |> integral(~cache) |> shapeFn(XYShape.YtoX.linear(f));
|
||||
let toContinuous = t => Some(t);
|
||||
let toDiscrete = _ => None;
|
||||
|
||||
let normalize = (t: t): t => {
|
||||
t
|
||||
|> scaleBy(~scale=1. /. integralEndY(~cache=None, t))
|
||||
|> updateKnownIntegralSum(Some(1.0));
|
||||
};
|
||||
|
||||
let normalizedToContinuous = t => Some(t |> normalize);
|
||||
let normalizedToDiscrete = _ => None;
|
||||
|
||||
let mean = (t: t) => {
|
||||
let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 2.0 /. 2.0;
|
||||
let indefiniteIntegralLinear = (p, a, b) =>
|
||||
a *. p ** 2.0 /. 2.0 +. b *. p ** 3.0 /. 3.0;
|
||||
|
||||
XYShape.Analysis.integrateContinuousShape(
|
||||
~indefiniteIntegralStepwise,
|
||||
~indefiniteIntegralLinear,
|
||||
t,
|
||||
);
|
||||
};
|
||||
let variance = (t: t): float =>
|
||||
XYShape.Analysis.getVarianceDangerously(
|
||||
t,
|
||||
mean,
|
||||
XYShape.Analysis.getMeanOfSquaresContinuousShape,
|
||||
);
|
||||
});
|
||||
|
||||
/* This simply creates multiple copies of the continuous distribution, scaled and shifted according to
|
||||
each discrete data point, and then adds them all together. */
|
||||
let combineAlgebraicallyWithDiscrete =
|
||||
(
|
||||
~downsample=false,
|
||||
op: ExpressionTypes.algebraicOperation,
|
||||
t1: t,
|
||||
t2: DistTypes.discreteShape,
|
||||
) => {
|
||||
let t1s = t1 |> getShape;
|
||||
let t2s = t2.xyShape; // would like to use Discrete.getShape here, but current file structure doesn't allow for that
|
||||
let t1n = t1s |> XYShape.T.length;
|
||||
let t2n = t2s |> XYShape.T.length;
|
||||
|
||||
let fn = Operation.Algebraic.toFn(op);
|
||||
|
||||
let outXYShapes: array(array((float, float))) =
|
||||
Belt.Array.makeUninitializedUnsafe(t2n);
|
||||
|
||||
for (j in 0 to t2n - 1) {
|
||||
// for each one of the discrete points
|
||||
// create a new distribution, as long as the original continuous one
|
||||
|
||||
let dxyShape: array((float, float)) =
|
||||
Belt.Array.makeUninitializedUnsafe(t1n);
|
||||
for (i in 0 to t1n - 1) {
|
||||
let _ =
|
||||
Belt.Array.set(
|
||||
dxyShape,
|
||||
i,
|
||||
(fn(t1s.xs[i], t2s.xs[j]), t1s.ys[i] *. t2s.ys[j]),
|
||||
);
|
||||
();
|
||||
};
|
||||
|
||||
let _ = Belt.Array.set(outXYShapes, j, dxyShape);
|
||||
();
|
||||
};
|
||||
|
||||
let combinedIntegralSum =
|
||||
Common.combineIntegralSums(
|
||||
(a, b) => Some(a *. b),
|
||||
t1.knownIntegralSum,
|
||||
t2.knownIntegralSum,
|
||||
);
|
||||
|
||||
outXYShapes
|
||||
|> E.A.fmap(s => {
|
||||
let xyShape = XYShape.T.fromZippedArray(s);
|
||||
make(`Linear, xyShape, None);
|
||||
})
|
||||
|> reduce((+.))
|
||||
|> updateKnownIntegralSum(combinedIntegralSum);
|
||||
};
|
||||
|
||||
let combineAlgebraically =
|
||||
(~downsample=false, op: ExpressionTypes.algebraicOperation, t1: t, t2: t) => {
|
||||
let s1 = t1 |> getShape;
|
||||
let s2 = t2 |> getShape;
|
||||
let t1n = s1 |> XYShape.T.length;
|
||||
let t2n = s2 |> XYShape.T.length;
|
||||
if (t1n == 0 || t2n == 0) {
|
||||
empty;
|
||||
} else {
|
||||
let combinedShape =
|
||||
AlgebraicShapeCombination.combineShapesContinuousContinuous(op, s1, s2);
|
||||
let combinedIntegralSum =
|
||||
Common.combineIntegralSums(
|
||||
(a, b) => Some(a *. b),
|
||||
t1.knownIntegralSum,
|
||||
t2.knownIntegralSum,
|
||||
);
|
||||
// return a new Continuous distribution
|
||||
make(`Linear, combinedShape, combinedIntegralSum);
|
||||
};
|
||||
};
|
210
src/distPlus/distribution/Discrete.re
Normal file
210
src/distPlus/distribution/Discrete.re
Normal file
|
@ -0,0 +1,210 @@
|
|||
open Distributions;
|
||||
|
||||
type t = DistTypes.discreteShape;
|
||||
|
||||
let make = (xyShape, knownIntegralSum): t => {xyShape, knownIntegralSum};
|
||||
let shapeMap = (fn, {xyShape, knownIntegralSum}: t): t => {
|
||||
xyShape: fn(xyShape),
|
||||
knownIntegralSum,
|
||||
};
|
||||
let getShape = (t: t) => t.xyShape;
|
||||
let oShapeMap = (fn, {xyShape, knownIntegralSum}: t): option(t) =>
|
||||
fn(xyShape) |> E.O.fmap(make(_, knownIntegralSum));
|
||||
|
||||
let empty: t = {xyShape: XYShape.T.empty, knownIntegralSum: Some(0.0)};
|
||||
let shapeFn = (fn, t: t) => t |> getShape |> fn;
|
||||
|
||||
let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
|
||||
|
||||
let combinePointwise =
|
||||
(
|
||||
~knownIntegralSumsFn,
|
||||
fn,
|
||||
t1: DistTypes.discreteShape,
|
||||
t2: DistTypes.discreteShape,
|
||||
)
|
||||
: DistTypes.discreteShape => {
|
||||
let combinedIntegralSum =
|
||||
Common.combineIntegralSums(
|
||||
knownIntegralSumsFn,
|
||||
t1.knownIntegralSum,
|
||||
t2.knownIntegralSum,
|
||||
);
|
||||
|
||||
make(
|
||||
XYShape.PointwiseCombination.combine(
|
||||
~xsSelection=ALL_XS,
|
||||
~xToYSelection=XYShape.XtoY.stepwiseIfAtX,
|
||||
~fn=(a, b) => fn(E.O.default(0.0, a), E.O.default(0.0, b)), // stepwiseIfAtX returns option(float), so this fn needs to handle None
|
||||
t1.xyShape,
|
||||
t2.xyShape,
|
||||
),
|
||||
combinedIntegralSum,
|
||||
);
|
||||
};
|
||||
|
||||
let reduce =
|
||||
(~knownIntegralSumsFn=(_, _) => None, fn, discreteShapes)
|
||||
: DistTypes.discreteShape =>
|
||||
discreteShapes
|
||||
|> E.A.fold_left(combinePointwise(~knownIntegralSumsFn, fn), empty);
|
||||
|
||||
let updateKnownIntegralSum = (knownIntegralSum, t: t): t => {
|
||||
...t,
|
||||
knownIntegralSum,
|
||||
};
|
||||
|
||||
/* This multiples all of the data points together and creates a new discrete distribution from the results.
|
||||
Data points at the same xs get added together. It may be a good idea to downsample t1 and t2 before and/or the result after. */
|
||||
let combineAlgebraically =
|
||||
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t) => {
|
||||
let t1s = t1 |> getShape;
|
||||
let t2s = t2 |> getShape;
|
||||
let t1n = t1s |> XYShape.T.length;
|
||||
let t2n = t2s |> XYShape.T.length;
|
||||
|
||||
let combinedIntegralSum =
|
||||
Common.combineIntegralSums(
|
||||
(s1, s2) => Some(s1 *. s2),
|
||||
t1.knownIntegralSum,
|
||||
t2.knownIntegralSum,
|
||||
);
|
||||
|
||||
let fn = Operation.Algebraic.toFn(op);
|
||||
let xToYMap = E.FloatFloatMap.empty();
|
||||
|
||||
for (i in 0 to t1n - 1) {
|
||||
for (j in 0 to t2n - 1) {
|
||||
let x = fn(t1s.xs[i], t2s.xs[j]);
|
||||
let cv = xToYMap |> E.FloatFloatMap.get(x) |> E.O.default(0.);
|
||||
let my = t1s.ys[i] *. t2s.ys[j];
|
||||
let _ = Belt.MutableMap.set(xToYMap, x, cv +. my);
|
||||
();
|
||||
};
|
||||
};
|
||||
|
||||
let rxys = xToYMap |> E.FloatFloatMap.toArray |> XYShape.Zipped.sortByX;
|
||||
|
||||
let combinedShape = XYShape.T.fromZippedArray(rxys);
|
||||
|
||||
make(combinedShape, combinedIntegralSum);
|
||||
};
|
||||
|
||||
let mapY = (~knownIntegralSumFn=previousKnownIntegralSum => None, fn, t: t) => {
|
||||
let u = E.O.bind(_, knownIntegralSumFn);
|
||||
let yMapFn = shapeMap(XYShape.T.mapY(fn));
|
||||
|
||||
t |> yMapFn |> updateKnownIntegralSum(u(t.knownIntegralSum));
|
||||
};
|
||||
|
||||
let scaleBy = (~scale=1.0, t: t): t => {
|
||||
t
|
||||
|> mapY((r: float) => r *. scale)
|
||||
|> updateKnownIntegralSum(
|
||||
E.O.bind(t.knownIntegralSum, v => Some(scale *. v)),
|
||||
);
|
||||
};
|
||||
|
||||
module T =
|
||||
Dist({
|
||||
type t = DistTypes.discreteShape;
|
||||
type integral = DistTypes.continuousShape;
|
||||
let integral = (~cache, t) =>
|
||||
if (t |> getShape |> XYShape.T.length > 0) {
|
||||
switch (cache) {
|
||||
| Some(c) => c
|
||||
| None =>
|
||||
Continuous.make(
|
||||
`Stepwise,
|
||||
XYShape.T.accumulateYs((+.), getShape(t)),
|
||||
None,
|
||||
)
|
||||
};
|
||||
} else {
|
||||
Continuous.make(
|
||||
`Stepwise,
|
||||
{xs: [|neg_infinity|], ys: [|0.0|]},
|
||||
None,
|
||||
);
|
||||
};
|
||||
|
||||
let integralEndY = (~cache, t: t) =>
|
||||
t.knownIntegralSum
|
||||
|> E.O.default(t |> integral(~cache) |> Continuous.lastY);
|
||||
let minX = shapeFn(XYShape.T.minX);
|
||||
let maxX = shapeFn(XYShape.T.maxX);
|
||||
let toDiscreteProbabilityMassFraction = _ => 1.0;
|
||||
let mapY = mapY;
|
||||
let toShape = (t: t): DistTypes.shape => Discrete(t);
|
||||
let toContinuous = _ => None;
|
||||
let toDiscrete = t => Some(t);
|
||||
|
||||
let normalize = (t: t): t => {
|
||||
t
|
||||
|> scaleBy(~scale=1. /. integralEndY(~cache=None, t))
|
||||
|> updateKnownIntegralSum(Some(1.0));
|
||||
};
|
||||
|
||||
let normalizedToContinuous = _ => None;
|
||||
let normalizedToDiscrete = t => Some(t); // TODO: this should be normalized!
|
||||
|
||||
let downsample = (~cache=None, i, t: t): t => {
|
||||
// It's not clear how to downsample a set of discrete points in a meaningful way.
|
||||
// The best we can do is to clip off the smallest values.
|
||||
let currentLength = t |> getShape |> XYShape.T.length;
|
||||
|
||||
if (i < currentLength && i >= 1 && currentLength > 1) {
|
||||
let clippedShape =
|
||||
t
|
||||
|> getShape
|
||||
|> XYShape.T.zip
|
||||
|> XYShape.Zipped.sortByY
|
||||
|> Belt.Array.reverse
|
||||
|> Belt.Array.slice(_, ~offset=0, ~len=i)
|
||||
|> XYShape.Zipped.sortByX
|
||||
|> XYShape.T.fromZippedArray;
|
||||
|
||||
make(clippedShape, None); // if someone needs the sum, they'll have to recompute it
|
||||
} else {
|
||||
t;
|
||||
};
|
||||
};
|
||||
|
||||
let truncate =
|
||||
(leftCutoff: option(float), rightCutoff: option(float), t: t): t => {
|
||||
let truncatedShape =
|
||||
t
|
||||
|> getShape
|
||||
|> XYShape.T.zip
|
||||
|> XYShape.Zipped.filterByX(x =>
|
||||
x >= E.O.default(neg_infinity, leftCutoff)
|
||||
|| x <= E.O.default(infinity, rightCutoff)
|
||||
)
|
||||
|> XYShape.T.fromZippedArray;
|
||||
|
||||
make(truncatedShape, None);
|
||||
};
|
||||
|
||||
let xToY = (f, t) =>
|
||||
t
|
||||
|> getShape
|
||||
|> XYShape.XtoY.stepwiseIfAtX(f)
|
||||
|> E.O.default(0.0)
|
||||
|> DistTypes.MixedPoint.makeDiscrete;
|
||||
|
||||
let integralXtoY = (~cache, f, t) =>
|
||||
t |> integral(~cache) |> Continuous.getShape |> XYShape.XtoY.linear(f);
|
||||
|
||||
let integralYtoX = (~cache, f, t) =>
|
||||
t |> integral(~cache) |> Continuous.getShape |> XYShape.YtoX.linear(f);
|
||||
|
||||
let mean = (t: t): float => {
|
||||
let s = getShape(t);
|
||||
E.A.reducei(s.xs, 0.0, (acc, x, i) => acc +. x *. s.ys[i]);
|
||||
};
|
||||
let variance = (t: t): float => {
|
||||
let getMeanOfSquares = t =>
|
||||
t |> shapeMap(XYShape.Analysis.squareXYShape) |> mean;
|
||||
XYShape.Analysis.getVarianceDangerously(t, mean, getMeanOfSquares);
|
||||
};
|
||||
});
|
|
@ -3,7 +3,7 @@ open DistTypes;
|
|||
type t = DistTypes.distPlus;
|
||||
|
||||
let shapeIntegral = shape =>
|
||||
Distributions.Shape.T.Integral.get(~cache=None, shape);
|
||||
Shape.T.Integral.get(~cache=None, shape);
|
||||
let make =
|
||||
(
|
||||
~shape,
|
||||
|
@ -53,11 +53,11 @@ module T =
|
|||
type t = DistTypes.distPlus;
|
||||
type integral = DistTypes.distPlus;
|
||||
let toShape = toShape;
|
||||
let toContinuous = shapeFn(Distributions.Shape.T.toContinuous);
|
||||
let toDiscrete = shapeFn(Distributions.Shape.T.toDiscrete);
|
||||
let toContinuous = shapeFn(Shape.T.toContinuous);
|
||||
let toDiscrete = shapeFn(Shape.T.toDiscrete);
|
||||
|
||||
let normalize = (t: t): t => {
|
||||
let normalizedShape = t |> toShape |> Distributions.Shape.T.normalize;
|
||||
let normalizedShape = t |> toShape |> Shape.T.normalize;
|
||||
t |> updateShape(normalizedShape);
|
||||
// TODO: also adjust for domainIncludedProbabilityMass here.
|
||||
};
|
||||
|
@ -66,7 +66,7 @@ module T =
|
|||
let truncatedShape =
|
||||
t
|
||||
|> toShape
|
||||
|> Distributions.Shape.T.truncate(leftCutoff, rightCutoff);
|
||||
|> Shape.T.truncate(leftCutoff, rightCutoff);
|
||||
|
||||
t |> updateShape(truncatedShape);
|
||||
};
|
||||
|
@ -74,9 +74,9 @@ module T =
|
|||
let normalizedToContinuous = (t: t) => {
|
||||
t
|
||||
|> toShape
|
||||
|> Distributions.Shape.T.normalizedToContinuous
|
||||
|> Shape.T.normalizedToContinuous
|
||||
|> E.O.fmap(
|
||||
Distributions.Continuous.T.mapY(
|
||||
Continuous.T.mapY(
|
||||
domainIncludedProbabilityMassAdjustment(t),
|
||||
),
|
||||
);
|
||||
|
@ -85,9 +85,9 @@ module T =
|
|||
let normalizedToDiscrete = (t: t) => {
|
||||
t
|
||||
|> toShape
|
||||
|> Distributions.Shape.T.normalizedToDiscrete
|
||||
|> Shape.T.normalizedToDiscrete
|
||||
|> E.O.fmap(
|
||||
Distributions.Discrete.T.mapY(
|
||||
Discrete.T.mapY(
|
||||
domainIncludedProbabilityMassAdjustment(t),
|
||||
),
|
||||
);
|
||||
|
@ -96,20 +96,20 @@ module T =
|
|||
let xToY = (f, t: t) =>
|
||||
t
|
||||
|> toShape
|
||||
|> Distributions.Shape.T.xToY(f)
|
||||
|> Shape.T.xToY(f)
|
||||
|> MixedPoint.fmap(domainIncludedProbabilityMassAdjustment(t));
|
||||
|
||||
let minX = shapeFn(Distributions.Shape.T.minX);
|
||||
let maxX = shapeFn(Distributions.Shape.T.maxX);
|
||||
let minX = shapeFn(Shape.T.minX);
|
||||
let maxX = shapeFn(Shape.T.maxX);
|
||||
let toDiscreteProbabilityMassFraction =
|
||||
shapeFn(Distributions.Shape.T.toDiscreteProbabilityMassFraction);
|
||||
shapeFn(Shape.T.toDiscreteProbabilityMassFraction);
|
||||
|
||||
// This bit is kind of awkward, could probably use rethinking.
|
||||
let integral = (~cache, t: t) =>
|
||||
updateShape(Continuous(t.integralCache), t);
|
||||
|
||||
let downsample = (~cache=None, i, t): t =>
|
||||
updateShape(t |> toShape |> Distributions.Shape.T.downsample(i), t);
|
||||
updateShape(t |> toShape |> Shape.T.downsample(i), t);
|
||||
// todo: adjust for limit, maybe?
|
||||
let mapY =
|
||||
(
|
||||
|
@ -118,12 +118,12 @@ module T =
|
|||
{shape, _} as t: t,
|
||||
)
|
||||
: t =>
|
||||
Distributions.Shape.T.mapY(~knownIntegralSumFn, fn, shape)
|
||||
Shape.T.mapY(~knownIntegralSumFn, fn, shape)
|
||||
|> updateShape(_, t);
|
||||
|
||||
// get the total of everything
|
||||
let integralEndY = (~cache as _, t: t) => {
|
||||
Distributions.Shape.T.Integral.sum(
|
||||
Shape.T.Integral.sum(
|
||||
~cache=Some(t.integralCache),
|
||||
toShape(t),
|
||||
);
|
||||
|
@ -131,7 +131,7 @@ module T =
|
|||
|
||||
// TODO: Fix this below, obviously. Adjust for limits
|
||||
let integralXtoY = (~cache as _, f, t: t) => {
|
||||
Distributions.Shape.T.Integral.xToY(
|
||||
Shape.T.Integral.xToY(
|
||||
~cache=Some(t.integralCache),
|
||||
f,
|
||||
toShape(t),
|
||||
|
@ -141,11 +141,11 @@ module T =
|
|||
|
||||
// TODO: This part is broken when there is a limit, if this is supposed to be taken into account.
|
||||
let integralYtoX = (~cache as _, f, t: t) => {
|
||||
Distributions.Shape.T.Integral.yToX(~cache=None, f, toShape(t));
|
||||
Shape.T.Integral.yToX(~cache=None, f, toShape(t));
|
||||
};
|
||||
|
||||
let mean = (t: t) => {
|
||||
Distributions.Shape.T.mean(t.shape);
|
||||
Shape.T.mean(t.shape);
|
||||
};
|
||||
let variance = (t: t) => Distributions.Shape.T.variance(t.shape);
|
||||
let variance = (t: t) => Shape.T.variance(t.shape);
|
||||
});
|
||||
|
|
File diff suppressed because it is too large
Load Diff
307
src/distPlus/distribution/Mixed.re
Normal file
307
src/distPlus/distribution/Mixed.re
Normal file
|
@ -0,0 +1,307 @@
|
|||
open Distributions;
|
||||
|
||||
type t = DistTypes.mixedShape;
|
||||
let make = (~continuous, ~discrete): t => {continuous, discrete};
|
||||
|
||||
let totalLength = (t: t): int => {
|
||||
let continuousLength =
|
||||
t.continuous |> Continuous.getShape |> XYShape.T.length;
|
||||
let discreteLength = t.discrete |> Discrete.getShape |> XYShape.T.length;
|
||||
|
||||
continuousLength + discreteLength;
|
||||
};
|
||||
|
||||
let scaleBy = (~scale=1.0, {discrete, continuous}: t): t => {
|
||||
let scaledDiscrete = Discrete.scaleBy(~scale, discrete);
|
||||
let scaledContinuous = Continuous.scaleBy(~scale, continuous);
|
||||
make(~discrete=scaledDiscrete, ~continuous=scaledContinuous);
|
||||
};
|
||||
|
||||
let toContinuous = ({continuous}: t) => Some(continuous);
|
||||
let toDiscrete = ({discrete}: t) => Some(discrete);
|
||||
|
||||
let combinePointwise = (~knownIntegralSumsFn, fn, t1: t, t2: t) => {
|
||||
let reducedDiscrete =
|
||||
[|t1, t2|]
|
||||
|> E.A.fmap(toDiscrete)
|
||||
|> E.A.O.concatSomes
|
||||
|> Discrete.reduce(~knownIntegralSumsFn, fn);
|
||||
|
||||
let reducedContinuous =
|
||||
[|t1, t2|]
|
||||
|> E.A.fmap(toContinuous)
|
||||
|> E.A.O.concatSomes
|
||||
|> Continuous.reduce(~knownIntegralSumsFn, fn);
|
||||
|
||||
make(~discrete=reducedDiscrete, ~continuous=reducedContinuous);
|
||||
};
|
||||
|
||||
module T =
|
||||
Dist({
|
||||
type t = DistTypes.mixedShape;
|
||||
type integral = DistTypes.continuousShape;
|
||||
let minX = ({continuous, discrete}: t) => {
|
||||
min(Continuous.T.minX(continuous), Discrete.T.minX(discrete));
|
||||
};
|
||||
let maxX = ({continuous, discrete}: t) =>
|
||||
max(Continuous.T.maxX(continuous), Discrete.T.maxX(discrete));
|
||||
let toShape = (t: t): DistTypes.shape => Mixed(t);
|
||||
|
||||
let toContinuous = toContinuous;
|
||||
let toDiscrete = toDiscrete;
|
||||
|
||||
let truncate =
|
||||
(
|
||||
leftCutoff: option(float),
|
||||
rightCutoff: option(float),
|
||||
{discrete, continuous}: t,
|
||||
) => {
|
||||
let truncatedContinuous =
|
||||
Continuous.T.truncate(leftCutoff, rightCutoff, continuous);
|
||||
let truncatedDiscrete =
|
||||
Discrete.T.truncate(leftCutoff, rightCutoff, discrete);
|
||||
|
||||
make(~discrete=truncatedDiscrete, ~continuous=truncatedContinuous);
|
||||
};
|
||||
|
||||
let normalize = (t: t): t => {
|
||||
let continuousIntegralSum =
|
||||
Continuous.T.Integral.sum(~cache=None, t.continuous);
|
||||
let discreteIntegralSum =
|
||||
Discrete.T.Integral.sum(~cache=None, t.discrete);
|
||||
let totalIntegralSum = continuousIntegralSum +. discreteIntegralSum;
|
||||
|
||||
let newContinuousSum = continuousIntegralSum /. totalIntegralSum;
|
||||
let newDiscreteSum = discreteIntegralSum /. totalIntegralSum;
|
||||
|
||||
let normalizedContinuous =
|
||||
t.continuous
|
||||
|> Continuous.scaleBy(~scale=1. /. newContinuousSum)
|
||||
|> Continuous.updateKnownIntegralSum(Some(newContinuousSum));
|
||||
let normalizedDiscrete =
|
||||
t.discrete
|
||||
|> Discrete.scaleBy(~scale=1. /. newDiscreteSum)
|
||||
|> Discrete.updateKnownIntegralSum(Some(newDiscreteSum));
|
||||
|
||||
make(~continuous=normalizedContinuous, ~discrete=normalizedDiscrete);
|
||||
};
|
||||
|
||||
let xToY = (x, t: t) => {
|
||||
// This evaluates the mixedShape at x, interpolating if necessary.
|
||||
// Note that we normalize entire mixedShape first.
|
||||
let {continuous, discrete}: t = normalize(t);
|
||||
let c = Continuous.T.xToY(x, continuous);
|
||||
let d = Discrete.T.xToY(x, discrete);
|
||||
DistTypes.MixedPoint.add(c, d); // "add" here just combines the two values into a single MixedPoint.
|
||||
};
|
||||
|
||||
let toDiscreteProbabilityMassFraction = ({discrete, continuous}: t) => {
|
||||
let discreteIntegralSum =
|
||||
Discrete.T.Integral.sum(~cache=None, discrete);
|
||||
let continuousIntegralSum =
|
||||
Continuous.T.Integral.sum(~cache=None, continuous);
|
||||
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
|
||||
|
||||
discreteIntegralSum /. totalIntegralSum;
|
||||
};
|
||||
|
||||
let downsample = (~cache=None, count, {discrete, continuous}: t): t => {
|
||||
// We will need to distribute the new xs fairly between the discrete and continuous shapes.
|
||||
// The easiest way to do this is to simply go by the previous probability masses.
|
||||
|
||||
// The cache really isn't helpful here, because we would need two separate caches
|
||||
let discreteIntegralSum =
|
||||
Discrete.T.Integral.sum(~cache=None, discrete);
|
||||
let continuousIntegralSum =
|
||||
Continuous.T.Integral.sum(~cache=None, continuous);
|
||||
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
|
||||
|
||||
// TODO: figure out what to do when the totalIntegralSum is zero.
|
||||
|
||||
let downsampledDiscrete =
|
||||
Discrete.T.downsample(
|
||||
int_of_float(
|
||||
float_of_int(count) *. (discreteIntegralSum /. totalIntegralSum),
|
||||
),
|
||||
discrete,
|
||||
);
|
||||
|
||||
let downsampledContinuous =
|
||||
Continuous.T.downsample(
|
||||
int_of_float(
|
||||
float_of_int(count) *. (continuousIntegralSum /. totalIntegralSum),
|
||||
),
|
||||
continuous,
|
||||
);
|
||||
|
||||
{discrete: downsampledDiscrete, continuous: downsampledContinuous};
|
||||
};
|
||||
|
||||
let normalizedToContinuous = (t: t) => Some(normalize(t).continuous);
|
||||
|
||||
let normalizedToDiscrete = ({discrete} as t: t) =>
|
||||
Some(normalize(t).discrete);
|
||||
|
||||
let integral = (~cache, {continuous, discrete}: t) => {
|
||||
switch (cache) {
|
||||
| Some(cache) => cache
|
||||
| None =>
|
||||
// note: if the underlying shapes aren't normalized, then these integrals won't be either!
|
||||
let continuousIntegral =
|
||||
Continuous.T.Integral.get(~cache=None, continuous);
|
||||
let discreteIntegral = Discrete.T.Integral.get(~cache=None, discrete);
|
||||
|
||||
Continuous.make(
|
||||
`Linear,
|
||||
XYShape.PointwiseCombination.combineLinear(
|
||||
~fn=(+.),
|
||||
Continuous.getShape(continuousIntegral),
|
||||
Continuous.getShape(discreteIntegral),
|
||||
),
|
||||
None,
|
||||
);
|
||||
};
|
||||
};
|
||||
|
||||
let integralEndY = (~cache, t: t) => {
|
||||
integral(~cache, t) |> Continuous.lastY;
|
||||
};
|
||||
|
||||
let integralXtoY = (~cache, f, t) => {
|
||||
t |> integral(~cache) |> Continuous.getShape |> XYShape.XtoY.linear(f);
|
||||
};
|
||||
|
||||
let integralYtoX = (~cache, f, t) => {
|
||||
t |> integral(~cache) |> Continuous.getShape |> XYShape.YtoX.linear(f);
|
||||
};
|
||||
|
||||
// This pipes all ys (continuous and discrete) through fn.
|
||||
// If mapY is a linear operation, we might be able to update the knownIntegralSums as well;
|
||||
// if not, they'll be set to None.
|
||||
let mapY =
|
||||
(
|
||||
~knownIntegralSumFn=previousIntegralSum => None,
|
||||
fn,
|
||||
{discrete, continuous}: t,
|
||||
)
|
||||
: t => {
|
||||
let u = E.O.bind(_, knownIntegralSumFn);
|
||||
|
||||
let yMappedDiscrete =
|
||||
discrete
|
||||
|> Discrete.T.mapY(fn)
|
||||
|> Discrete.updateKnownIntegralSum(u(discrete.knownIntegralSum));
|
||||
|
||||
let yMappedContinuous =
|
||||
continuous
|
||||
|> Continuous.T.mapY(fn)
|
||||
|> Continuous.updateKnownIntegralSum(u(continuous.knownIntegralSum));
|
||||
|
||||
{
|
||||
discrete: yMappedDiscrete,
|
||||
continuous: Continuous.T.mapY(fn, continuous),
|
||||
};
|
||||
};
|
||||
|
||||
let mean = ({discrete, continuous}: t): float => {
|
||||
let discreteMean = Discrete.T.mean(discrete);
|
||||
let continuousMean = Continuous.T.mean(continuous);
|
||||
|
||||
// the combined mean is the weighted sum of the two:
|
||||
let discreteIntegralSum =
|
||||
Discrete.T.Integral.sum(~cache=None, discrete);
|
||||
let continuousIntegralSum =
|
||||
Continuous.T.Integral.sum(~cache=None, continuous);
|
||||
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
|
||||
|
||||
(
|
||||
discreteMean
|
||||
*. discreteIntegralSum
|
||||
+. continuousMean
|
||||
*. continuousIntegralSum
|
||||
)
|
||||
/. totalIntegralSum;
|
||||
};
|
||||
|
||||
let variance = ({discrete, continuous} as t: t): float => {
|
||||
// the combined mean is the weighted sum of the two:
|
||||
let discreteIntegralSum =
|
||||
Discrete.T.Integral.sum(~cache=None, discrete);
|
||||
let continuousIntegralSum =
|
||||
Continuous.T.Integral.sum(~cache=None, continuous);
|
||||
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
|
||||
|
||||
let getMeanOfSquares = ({discrete, continuous} as t: t) => {
|
||||
let discreteMean =
|
||||
discrete
|
||||
|> Discrete.shapeMap(XYShape.Analysis.squareXYShape)
|
||||
|> Discrete.T.mean;
|
||||
let continuousMean =
|
||||
continuous |> XYShape.Analysis.getMeanOfSquaresContinuousShape;
|
||||
(
|
||||
discreteMean
|
||||
*. discreteIntegralSum
|
||||
+. continuousMean
|
||||
*. continuousIntegralSum
|
||||
)
|
||||
/. totalIntegralSum;
|
||||
};
|
||||
|
||||
switch (discreteIntegralSum /. totalIntegralSum) {
|
||||
| 1.0 => Discrete.T.variance(discrete)
|
||||
| 0.0 => Continuous.T.variance(continuous)
|
||||
| _ =>
|
||||
XYShape.Analysis.getVarianceDangerously(t, mean, getMeanOfSquares)
|
||||
};
|
||||
};
|
||||
});
|
||||
|
||||
let combineAlgebraically =
|
||||
(~downsample=false, op: ExpressionTypes.algebraicOperation, t1: t, t2: t)
|
||||
: t => {
|
||||
// Discrete convolution can cause a huge increase in the number of samples,
|
||||
// so we'll first downsample.
|
||||
|
||||
// An alternative (to be explored in the future) may be to first perform the full convolution and then to downsample the result;
|
||||
// to use non-uniform fast Fourier transforms (for addition only), add web workers or gpu.js, etc. ...
|
||||
|
||||
let downsampleIfTooLarge = (t: t) => {
|
||||
let sqtl = sqrt(float_of_int(totalLength(t)));
|
||||
sqtl > 10. && downsample ? T.downsample(int_of_float(sqtl), t) : t;
|
||||
};
|
||||
|
||||
let t1d = downsampleIfTooLarge(t1);
|
||||
let t2d = downsampleIfTooLarge(t2);
|
||||
|
||||
// continuous (*) continuous => continuous, but also
|
||||
// discrete (*) continuous => continuous (and vice versa). We have to take care of all combos and then combine them:
|
||||
let ccConvResult =
|
||||
Continuous.combineAlgebraically(
|
||||
~downsample=false,
|
||||
op,
|
||||
t1d.continuous,
|
||||
t2d.continuous,
|
||||
);
|
||||
let dcConvResult =
|
||||
Continuous.combineAlgebraicallyWithDiscrete(
|
||||
~downsample=false,
|
||||
op,
|
||||
t2d.continuous,
|
||||
t1d.discrete,
|
||||
);
|
||||
let cdConvResult =
|
||||
Continuous.combineAlgebraicallyWithDiscrete(
|
||||
~downsample=false,
|
||||
op,
|
||||
t1d.continuous,
|
||||
t2d.discrete,
|
||||
);
|
||||
let continuousConvResult =
|
||||
Continuous.reduce((+.), [|ccConvResult, dcConvResult, cdConvResult|]);
|
||||
|
||||
// ... finally, discrete (*) discrete => discrete, obviously:
|
||||
let discreteConvResult =
|
||||
Discrete.combineAlgebraically(op, t1d.discrete, t2d.discrete);
|
||||
|
||||
{discrete: discreteConvResult, continuous: continuousConvResult};
|
||||
};
|
|
@ -9,25 +9,25 @@ type assumptions = {
|
|||
};
|
||||
|
||||
let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete: option(DistTypes.discreteShape)): option(DistTypes.shape) => {
|
||||
let continuous = continuous |> E.O.default(Distributions.Continuous.make(`Linear, {xs: [||], ys: [||]}, Some(0.0)));
|
||||
let discrete = discrete |> E.O.default(Distributions.Discrete.make({xs: [||], ys: [||]}, Some(0.0)));
|
||||
let continuous = continuous |> E.O.default(Continuous.make(`Linear, {xs: [||], ys: [||]}, Some(0.0)));
|
||||
let discrete = discrete |> E.O.default(Discrete.make({xs: [||], ys: [||]}, Some(0.0)));
|
||||
let cLength =
|
||||
continuous
|
||||
|> Distributions.Continuous.getShape
|
||||
|> Continuous.getShape
|
||||
|> XYShape.T.xs
|
||||
|> E.A.length;
|
||||
let dLength = discrete |> Distributions.Discrete.getShape |> XYShape.T.xs |> E.A.length;
|
||||
let dLength = discrete |> Discrete.getShape |> XYShape.T.xs |> E.A.length;
|
||||
switch (cLength, dLength) {
|
||||
| (0 | 1, 0) => None
|
||||
| (0 | 1, _) => Some(Discrete(discrete))
|
||||
| (_, 0) => Some(Continuous(continuous))
|
||||
| (_, _) =>
|
||||
let discreteProbabilityMassFraction =
|
||||
Distributions.Discrete.T.Integral.sum(~cache=None, discrete);
|
||||
let discrete = Distributions.Discrete.T.normalize(discrete);
|
||||
let continuous = Distributions.Continuous.T.normalize(continuous);
|
||||
Discrete.T.Integral.sum(~cache=None, discrete);
|
||||
let discrete = Discrete.T.normalize(discrete);
|
||||
let continuous = Continuous.T.normalize(continuous);
|
||||
let mixedDist =
|
||||
Distributions.Mixed.make(
|
||||
Mixed.make(
|
||||
~continuous,
|
||||
~discrete
|
||||
);
|
||||
|
|
209
src/distPlus/distribution/Shape.re
Normal file
209
src/distPlus/distribution/Shape.re
Normal file
|
@ -0,0 +1,209 @@
|
|||
open Distributions;
|
||||
|
||||
type t = DistTypes.shape;
|
||||
let mapToAll = ((fn1, fn2, fn3), t: t) =>
|
||||
switch (t) {
|
||||
| Mixed(m) => fn1(m)
|
||||
| Discrete(m) => fn2(m)
|
||||
| Continuous(m) => fn3(m)
|
||||
};
|
||||
|
||||
let fmap = ((fn1, fn2, fn3), t: t): t =>
|
||||
switch (t) {
|
||||
| Mixed(m) => Mixed(fn1(m))
|
||||
| Discrete(m) => Discrete(fn2(m))
|
||||
| Continuous(m) => Continuous(fn3(m))
|
||||
};
|
||||
|
||||
let toMixed =
|
||||
mapToAll((
|
||||
m => m,
|
||||
d => Mixed.make(~discrete=d, ~continuous=Continuous.empty),
|
||||
c => Mixed.make(~discrete=Discrete.empty, ~continuous=c),
|
||||
));
|
||||
|
||||
let combineAlgebraically =
|
||||
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
|
||||
switch (t1, t2) {
|
||||
| (Continuous(m1), Continuous(m2)) =>
|
||||
DistTypes.Continuous(
|
||||
Continuous.combineAlgebraically(~downsample=true, op, m1, m2),
|
||||
)
|
||||
| (Discrete(m1), Discrete(m2)) =>
|
||||
DistTypes.Discrete(Discrete.combineAlgebraically(op, m1, m2))
|
||||
| (m1, m2) =>
|
||||
DistTypes.Mixed(
|
||||
Mixed.combineAlgebraically(
|
||||
~downsample=true,
|
||||
op,
|
||||
toMixed(m1),
|
||||
toMixed(m2),
|
||||
),
|
||||
)
|
||||
};
|
||||
};
|
||||
|
||||
let combinePointwise =
|
||||
(~knownIntegralSumsFn=(_, _) => None, fn, t1: t, t2: t) =>
|
||||
switch (t1, t2) {
|
||||
| (Continuous(m1), Continuous(m2)) =>
|
||||
DistTypes.Continuous(
|
||||
Continuous.combinePointwise(~knownIntegralSumsFn, fn, m1, m2),
|
||||
)
|
||||
| (Discrete(m1), Discrete(m2)) =>
|
||||
DistTypes.Discrete(
|
||||
Discrete.combinePointwise(~knownIntegralSumsFn, fn, m1, m2),
|
||||
)
|
||||
| (m1, m2) =>
|
||||
DistTypes.Mixed(
|
||||
Mixed.combinePointwise(
|
||||
~knownIntegralSumsFn,
|
||||
fn,
|
||||
toMixed(m1),
|
||||
toMixed(m2),
|
||||
),
|
||||
)
|
||||
};
|
||||
|
||||
// TODO: implement these functions
|
||||
let pdf = (f: float, t: t): float => {
|
||||
0.0;
|
||||
};
|
||||
|
||||
let inv = (f: float, t: t): float => {
|
||||
0.0;
|
||||
};
|
||||
|
||||
let sample = (t: t): float => {
|
||||
0.0;
|
||||
};
|
||||
|
||||
module T =
|
||||
Dist({
|
||||
type t = DistTypes.shape;
|
||||
type integral = DistTypes.continuousShape;
|
||||
|
||||
let xToY = (f: float) =>
|
||||
mapToAll((
|
||||
Mixed.T.xToY(f),
|
||||
Discrete.T.xToY(f),
|
||||
Continuous.T.xToY(f),
|
||||
));
|
||||
|
||||
let toShape = (t: t) => t;
|
||||
|
||||
let toContinuous = t => None;
|
||||
let toDiscrete = t => None;
|
||||
|
||||
let downsample = (~cache=None, i, t) =>
|
||||
fmap(
|
||||
(
|
||||
Mixed.T.downsample(i),
|
||||
Discrete.T.downsample(i),
|
||||
Continuous.T.downsample(i),
|
||||
),
|
||||
t,
|
||||
);
|
||||
|
||||
let truncate = (leftCutoff, rightCutoff, t): t =>
|
||||
fmap(
|
||||
(
|
||||
Mixed.T.truncate(leftCutoff, rightCutoff),
|
||||
Discrete.T.truncate(leftCutoff, rightCutoff),
|
||||
Continuous.T.truncate(leftCutoff, rightCutoff),
|
||||
),
|
||||
t,
|
||||
);
|
||||
|
||||
let toDiscreteProbabilityMassFraction = t => 0.0;
|
||||
let normalize =
|
||||
fmap((Mixed.T.normalize, Discrete.T.normalize, Continuous.T.normalize));
|
||||
let toContinuous =
|
||||
mapToAll((
|
||||
Mixed.T.toContinuous,
|
||||
Discrete.T.toContinuous,
|
||||
Continuous.T.toContinuous,
|
||||
));
|
||||
let toDiscrete =
|
||||
mapToAll((
|
||||
Mixed.T.toDiscrete,
|
||||
Discrete.T.toDiscrete,
|
||||
Continuous.T.toDiscrete,
|
||||
));
|
||||
|
||||
let toDiscreteProbabilityMassFraction =
|
||||
mapToAll((
|
||||
Mixed.T.toDiscreteProbabilityMassFraction,
|
||||
Discrete.T.toDiscreteProbabilityMassFraction,
|
||||
Continuous.T.toDiscreteProbabilityMassFraction,
|
||||
));
|
||||
|
||||
let normalizedToDiscrete =
|
||||
mapToAll((
|
||||
Mixed.T.normalizedToDiscrete,
|
||||
Discrete.T.normalizedToDiscrete,
|
||||
Continuous.T.normalizedToDiscrete,
|
||||
));
|
||||
let normalizedToContinuous =
|
||||
mapToAll((
|
||||
Mixed.T.normalizedToContinuous,
|
||||
Discrete.T.normalizedToContinuous,
|
||||
Continuous.T.normalizedToContinuous,
|
||||
));
|
||||
let minX = mapToAll((Mixed.T.minX, Discrete.T.minX, Continuous.T.minX));
|
||||
let integral = (~cache) =>
|
||||
mapToAll((
|
||||
Mixed.T.Integral.get(~cache=None),
|
||||
Discrete.T.Integral.get(~cache=None),
|
||||
Continuous.T.Integral.get(~cache=None),
|
||||
));
|
||||
let integralEndY = (~cache) =>
|
||||
mapToAll((
|
||||
Mixed.T.Integral.sum(~cache=None),
|
||||
Discrete.T.Integral.sum(~cache),
|
||||
Continuous.T.Integral.sum(~cache=None),
|
||||
));
|
||||
let integralXtoY = (~cache, f) => {
|
||||
mapToAll((
|
||||
Mixed.T.Integral.xToY(~cache, f),
|
||||
Discrete.T.Integral.xToY(~cache, f),
|
||||
Continuous.T.Integral.xToY(~cache, f),
|
||||
));
|
||||
};
|
||||
let integralYtoX = (~cache, f) => {
|
||||
mapToAll((
|
||||
Mixed.T.Integral.yToX(~cache, f),
|
||||
Discrete.T.Integral.yToX(~cache, f),
|
||||
Continuous.T.Integral.yToX(~cache, f),
|
||||
));
|
||||
};
|
||||
let maxX = mapToAll((Mixed.T.maxX, Discrete.T.maxX, Continuous.T.maxX));
|
||||
let mapY = (~knownIntegralSumFn=previousIntegralSum => None, fn) =>
|
||||
fmap((
|
||||
Mixed.T.mapY(~knownIntegralSumFn, fn),
|
||||
Discrete.T.mapY(~knownIntegralSumFn, fn),
|
||||
Continuous.T.mapY(~knownIntegralSumFn, fn),
|
||||
));
|
||||
|
||||
let mean = (t: t): float =>
|
||||
switch (t) {
|
||||
| Mixed(m) => Mixed.T.mean(m)
|
||||
| Discrete(m) => Discrete.T.mean(m)
|
||||
| Continuous(m) => Continuous.T.mean(m)
|
||||
};
|
||||
|
||||
let variance = (t: t): float =>
|
||||
switch (t) {
|
||||
| Mixed(m) => Mixed.T.variance(m)
|
||||
| Discrete(m) => Discrete.T.variance(m)
|
||||
| Continuous(m) => Continuous.T.variance(m)
|
||||
};
|
||||
});
|
||||
|
||||
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
|
||||
switch (distToFloatOp) {
|
||||
| `Pdf(f) => pdf(f, s)
|
||||
| `Inv(f) => inv(f, s)
|
||||
| `Sample => sample(s)
|
||||
| `Mean => T.mean(s)
|
||||
};
|
|
@ -8,8 +8,8 @@ let toShape = (sampleCount: int, node: node) => {
|
|||
switch (renderResult) {
|
||||
| Ok(`RenderedDist(rs)) =>
|
||||
// todo: Why is this here? It converts a mixed shape to a mixed shape.
|
||||
let continuous = Distributions.Shape.T.toContinuous(rs);
|
||||
let discrete = Distributions.Shape.T.toDiscrete(rs);
|
||||
let continuous = Shape.T.toContinuous(rs);
|
||||
let discrete = Shape.T.toDiscrete(rs);
|
||||
let shape = MixedShapeBuilder.buildSimple(~continuous, ~discrete);
|
||||
shape |> E.O.toExt("Could not build final shape.");
|
||||
| Ok(_) => E.O.toExn("Rendering failed.", None)
|
||||
|
|
|
@ -29,7 +29,7 @@ module AlgebraicCombination = {
|
|||
| (Ok(`RenderedDist(s1)), Ok(`RenderedDist(s2))) =>
|
||||
Ok(
|
||||
`RenderedDist(
|
||||
Distributions.Shape.combineAlgebraically(algebraicOp, s1, s2),
|
||||
Shape.combineAlgebraically(algebraicOp, s1, s2),
|
||||
),
|
||||
)
|
||||
| (Error(e1), _) => Error(e1)
|
||||
|
@ -68,7 +68,7 @@ module VerticalScaling = {
|
|||
| (Ok(`RenderedDist(rs)), `SymbolicDist(`Float(sm))) =>
|
||||
Ok(
|
||||
`RenderedDist(
|
||||
Distributions.Shape.T.mapY(
|
||||
Shape.T.mapY(
|
||||
~knownIntegralSumFn=knownIntegralSumFn(sm),
|
||||
fn(sm),
|
||||
rs,
|
||||
|
@ -87,7 +87,7 @@ module PointwiseCombination = {
|
|||
| (Ok(`RenderedDist(rs1)), Ok(`RenderedDist(rs2))) =>
|
||||
Ok(
|
||||
`RenderedDist(
|
||||
Distributions.Shape.combinePointwise(
|
||||
Shape.combinePointwise(
|
||||
~knownIntegralSumsFn=(a, b) => Some(a +. b),
|
||||
(+.),
|
||||
rs1,
|
||||
|
@ -141,7 +141,7 @@ module Truncate = {
|
|||
switch (render(evaluationParams, t)) {
|
||||
| Ok(`RenderedDist(rs)) =>
|
||||
let truncatedShape =
|
||||
rs |> Distributions.Shape.T.truncate(leftCutoff, rightCutoff);
|
||||
rs |> Shape.T.truncate(leftCutoff, rightCutoff);
|
||||
Ok(`RenderedDist(truncatedShape));
|
||||
| Error(e) => Error(e)
|
||||
| _ => Error("Could not truncate distribution.")
|
||||
|
@ -172,7 +172,7 @@ module Normalize = {
|
|||
let rec operationToLeaf = (evaluationParams, t: node): result(node, string) => {
|
||||
switch (t) {
|
||||
| `RenderedDist(s) =>
|
||||
Ok(`RenderedDist(Distributions.Shape.T.normalize(s)))
|
||||
Ok(`RenderedDist(Shape.T.normalize(s)))
|
||||
| `SymbolicDist(_) => Ok(t)
|
||||
| _ => evaluateAndRetry(evaluationParams, operationToLeaf, t)
|
||||
};
|
||||
|
@ -188,7 +188,7 @@ module FloatFromDist = {
|
|||
SymbolicDist.T.operate(distToFloatOp, s)
|
||||
|> E.R.bind(_, v => Ok(`SymbolicDist(`Float(v))))
|
||||
| `RenderedDist(rs) =>
|
||||
Distributions.Shape.operate(distToFloatOp, rs)
|
||||
Shape.operate(distToFloatOp, rs)
|
||||
|> (v => Ok(`SymbolicDist(`Float(v))))
|
||||
| _ =>
|
||||
t
|
||||
|
|
|
@ -217,12 +217,12 @@ module MathAdtToDistDst = {
|
|||
|> E.A.O.concatSomes;
|
||||
let outputs = Samples.T.fromSamples(samples);
|
||||
let pdf =
|
||||
outputs.shape |> E.O.bind(_, Distributions.Shape.T.toContinuous);
|
||||
outputs.shape |> E.O.bind(_, Shape.T.toContinuous);
|
||||
let shape =
|
||||
pdf
|
||||
|> E.O.fmap(pdf => {
|
||||
let _pdf = Distributions.Continuous.T.normalize(pdf);
|
||||
let cdf = Distributions.Continuous.T.integral(~cache=None, _pdf);
|
||||
let _pdf = Continuous.T.normalize(pdf);
|
||||
let cdf = Continuous.T.integral(~cache=None, _pdf);
|
||||
SymbolicDist.ContinuousShape.make(_pdf, cdf);
|
||||
});
|
||||
switch (shape) {
|
||||
|
|
|
@ -120,7 +120,7 @@ module T = {
|
|||
|> E.FloatFloatMap.fmap(r => r /. length)
|
||||
|> E.FloatFloatMap.toArray
|
||||
|> XYShape.T.fromZippedArray
|
||||
|> Distributions.Discrete.make(_, None);
|
||||
|> Discrete.make(_, None);
|
||||
|
||||
let pdf =
|
||||
continuousPart |> E.A.length > 5
|
||||
|
@ -150,7 +150,7 @@ module T = {
|
|||
~outputXYPoints=samplingInputs.outputXYPoints,
|
||||
formatUnitWidth(usedUnitWidth),
|
||||
)
|
||||
|> Distributions.Continuous.make(`Linear, _, None)
|
||||
|> Continuous.make(`Linear, _, None)
|
||||
|> (r => Some((r, foo)));
|
||||
}
|
||||
: None;
|
||||
|
|
|
@ -4,10 +4,10 @@ module ContinuousShape = {
|
|||
type t = continuousShape;
|
||||
let make = (pdf, cdf): t => {pdf, cdf};
|
||||
let pdf = (x, t: t) =>
|
||||
Distributions.Continuous.T.xToY(x, t.pdf).continuous;
|
||||
Continuous.T.xToY(x, t.pdf).continuous;
|
||||
// TODO: pdf and inv are currently the same, this seems broken.
|
||||
let inv = (p, t: t) =>
|
||||
Distributions.Continuous.T.xToY(p, t.pdf).continuous;
|
||||
Continuous.T.xToY(p, t.pdf).continuous;
|
||||
// TODO: Fix the sampling, to have it work correctly.
|
||||
let sample = (t: t) => 3.0;
|
||||
// TODO: Fix the mean, to have it work correctly.
|
||||
|
@ -300,13 +300,13 @@ module T = {
|
|||
switch (d) {
|
||||
| `Float(v) =>
|
||||
Discrete(
|
||||
Distributions.Discrete.make({xs: [|v|], ys: [|1.0|]}, Some(1.0)),
|
||||
Discrete.make({xs: [|v|], ys: [|1.0|]}, Some(1.0)),
|
||||
)
|
||||
| _ =>
|
||||
let xs = interpolateXs(~xSelection=`ByWeight, d, sampleCount);
|
||||
let ys = xs |> E.A.fmap(x => pdf(x, d));
|
||||
Continuous(
|
||||
Distributions.Continuous.make(`Linear, {xs, ys}, Some(1.0)),
|
||||
Continuous.make(`Linear, {xs, ys}, Some(1.0)),
|
||||
);
|
||||
};
|
||||
};
|
||||
|
|
Loading…
Reference in New Issue
Block a user