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Merge pull request #64 from foretold-app/seb/epic-fixes

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Fixes for a few more of the issues in the bugs doc
This commit is contained in:
Ozzie Gooen 2020-07-19 06:34:58 +01:00 committed by GitHub
commit 4072c47b70
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22 changed files with 950 additions and 750 deletions
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9
src/components/DistBuilder.re
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@ -142,12 +142,15 @@ module DemoDist = {
}, },
~distPlusIngredients, ~distPlusIngredients,
~shouldDownsample=options.downsampleTo |> E.O.isSome, ~shouldDownsample=options.downsampleTo |> E.O.isSome,
~recommendedLength=options.downsampleTo |> E.O.default(10000), ~recommendedLength=options.downsampleTo |> E.O.default(100),
(), (),
); );
let response = DistPlusRenderer.run(inputs); let response = DistPlusRenderer.run(inputs);
switch (RenderTypes.DistPlusRenderer.Outputs.distplus(response)) { switch (RenderTypes.DistPlusRenderer.Outputs.distplus(response)) {
| Some(distPlus) => <DistPlusPlot distPlus /> | Some(distPlus) => {
let normalizedDistPlus = DistPlus.T.normalize(distPlus);
<DistPlusPlot distPlus={normalizedDistPlus} />;
}
| _ => | _ =>
"Correct Guesstimator string input to show a distribution." "Correct Guesstimator string input to show a distribution."
|> R.ste |> R.ste
@ -171,7 +174,7 @@ let make = () => {
~onSubmit=({state}) => {None}, ~onSubmit=({state}) => {None},
~initialState={ ~initialState={
//guesstimatorString: "mm(normal(-10, 2), uniform(18, 25), lognormal({mean: 10, stdev: 8}), triangular(31,40,50))", //guesstimatorString: "mm(normal(-10, 2), uniform(18, 25), lognormal({mean: 10, stdev: 8}), triangular(31,40,50))",
guesstimatorString: "normal(0, 10) * 100", // , triangular(30, 40, 60) guesstimatorString: "mm(1, 2, 3, normal(2, 1))", // , triangular(30, 40, 60)
domainType: "Complete", domainType: "Complete",
xPoint: "50.0", xPoint: "50.0",
xPoint2: "60.0", xPoint2: "60.0",

8
src/components/Drawer.re
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@ -176,7 +176,8 @@ module Convert = {
let continuousShape: Types.continuousShape = { let continuousShape: Types.continuousShape = {
xyShape, xyShape,
interpolation: `Linear, interpolation: `Linear,
knownIntegralSum: None, integralSumCache: None,
integralCache: None,
}; };
let integral = XYShape.Analysis.integrateContinuousShape(continuousShape); let integral = XYShape.Analysis.integrateContinuousShape(continuousShape);
@ -188,7 +189,8 @@ module Convert = {
ys, ys,
}, },
interpolation: `Linear, interpolation: `Linear,
knownIntegralSum: Some(1.0), integralSumCache: Some(1.0),
integralCache: None,
}; };
continuousShape; continuousShape;
}; };
@ -674,7 +676,7 @@ module State = {
/* create a cdf from a pdf */ /* create a cdf from a pdf */
let _pdf = Continuous.T.normalize(pdf); let _pdf = Continuous.T.normalize(pdf);
let cdf = Continuous.T.integral(~cache=None, _pdf); let cdf = Continuous.T.integral(_pdf);
let xs = [||]; let xs = [||];
let ys = [||]; let ys = [||];
for (i in 1 to 999) { for (i in 1 to 999) {

70
src/components/charts/DistPlusPlot.re
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@ -51,13 +51,13 @@ let table = (distPlus, x) => {
</td> </td>
<td className="px-4 py-2 border "> <td className="px-4 py-2 border ">
{distPlus {distPlus
|> DistPlus.T.Integral.xToY(~cache=None, x) |> DistPlus.T.Integral.xToY(x)
|> E.Float.with2DigitsPrecision |> E.Float.with2DigitsPrecision
|> ReasonReact.string} |> ReasonReact.string}
</td> </td>
<td className="px-4 py-2 border "> <td className="px-4 py-2 border ">
{distPlus {distPlus
|> DistPlus.T.Integral.sum(~cache=None) |> DistPlus.T.Integral.sum
|> E.Float.with2DigitsPrecision |> E.Float.with2DigitsPrecision
|> ReasonReact.string} |> ReasonReact.string}
</td> </td>
@ -70,15 +70,9 @@ let table = (distPlus, x) => {
<td className="px-4 py-2"> <td className="px-4 py-2">
{"Continuous Total" |> ReasonReact.string} {"Continuous Total" |> ReasonReact.string}
</td> </td>
<td className="px-4 py-2">
{"Scaled Continuous Total" |> ReasonReact.string}
</td>
<td className="px-4 py-2"> <td className="px-4 py-2">
{"Discrete Total" |> ReasonReact.string} {"Discrete Total" |> ReasonReact.string}
</td> </td>
<td className="px-4 py-2">
{"Scaled Discrete Total" |> ReasonReact.string}
</td>
</tr> </tr>
</thead> </thead>
<tbody> <tbody>
@ -87,17 +81,7 @@ let table = (distPlus, x) => {
{distPlus {distPlus
|> DistPlus.T.toContinuous |> DistPlus.T.toContinuous
|> E.O.fmap( |> E.O.fmap(
Continuous.T.Integral.sum(~cache=None), Continuous.T.Integral.sum
)
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> DistPlus.T.normalizedToContinuous
|> E.O.fmap(
Continuous.T.Integral.sum(~cache=None),
) )
|> E.O.fmap(E.Float.with2DigitsPrecision) |> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("") |> E.O.default("")
@ -106,15 +90,7 @@ let table = (distPlus, x) => {
<td className="px-4 py-2 border "> <td className="px-4 py-2 border ">
{distPlus {distPlus
|> DistPlus.T.toDiscrete |> DistPlus.T.toDiscrete
|> E.O.fmap(Discrete.T.Integral.sum(~cache=None)) |> E.O.fmap(Discrete.T.Integral.sum)
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> DistPlus.T.normalizedToDiscrete
|> E.O.fmap(Discrete.T.Integral.sum(~cache=None))
|> E.O.fmap(E.Float.with2DigitsPrecision) |> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("") |> E.O.default("")
|> ReasonReact.string} |> ReasonReact.string}
@ -143,42 +119,42 @@ let percentiles = distPlus => {
<tr> <tr>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.01) |> DistPlus.T.Integral.yToX(0.01)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.05) |> DistPlus.T.Integral.yToX(0.05)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.25) |> DistPlus.T.Integral.yToX(0.25)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.5) |> DistPlus.T.Integral.yToX(0.5)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.75) |> DistPlus.T.Integral.yToX(0.75)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.95) |> DistPlus.T.Integral.yToX(0.95)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.99) |> DistPlus.T.Integral.yToX(0.99)
|> showFloat} |> showFloat}
</td> </td>
<td className="px-4 py-2 border"> <td className="px-4 py-2 border">
{distPlus {distPlus
|> DistPlus.T.Integral.yToX(~cache=None, 0.99999) |> DistPlus.T.Integral.yToX(0.99999)
|> showFloat} |> showFloat}
</td> </td>
</tr> </tr>
@ -214,6 +190,10 @@ let percentiles = distPlus => {
let adjustBoth = discreteProbabilityMassFraction => { let adjustBoth = discreteProbabilityMassFraction => {
let yMaxDiscreteDomainFactor = discreteProbabilityMassFraction; let yMaxDiscreteDomainFactor = discreteProbabilityMassFraction;
let yMaxContinuousDomainFactor = 1.0 -. discreteProbabilityMassFraction; let yMaxContinuousDomainFactor = 1.0 -. discreteProbabilityMassFraction;
// use the bigger proportion, such that whichever is the bigger proportion, the yMax is 1.
let yMax = (yMaxDiscreteDomainFactor > 0.5 ? yMaxDiscreteDomainFactor : yMaxContinuousDomainFactor); let yMax = (yMaxDiscreteDomainFactor > 0.5 ? yMaxDiscreteDomainFactor : yMaxContinuousDomainFactor);
( (
yMax /. yMaxDiscreteDomainFactor, yMax /. yMaxDiscreteDomainFactor,
@ -225,10 +205,11 @@ module DistPlusChart = {
[@react.component] [@react.component]
let make = (~distPlus: DistTypes.distPlus, ~config: chartConfig, ~onHover) => { let make = (~distPlus: DistTypes.distPlus, ~config: chartConfig, ~onHover) => {
open DistPlus; open DistPlus;
let discrete = distPlus |> T.normalizedToDiscrete |> E.O.fmap(Discrete.getShape);
let discrete = distPlus |> T.toDiscrete |> E.O.fmap(Discrete.getShape);
let continuous = let continuous =
distPlus distPlus
|> T.normalizedToContinuous |> T.toContinuous
|> E.O.fmap(Continuous.getShape); |> E.O.fmap(Continuous.getShape);
let range = T.xTotalRange(distPlus); let range = T.xTotalRange(distPlus);
@ -236,7 +217,7 @@ module DistPlusChart = {
// let minX = // let minX =
// switch ( // switch (
// distPlus // distPlus
// |> DistPlus.T.Integral.yToX(~cache=None, 0.0001), // |> DistPlus.T.Integral.yToX(0.0001),
// range, // range,
// ) { // ) {
// | (min, Some(range)) => Some(min -. range *. 0.001) // | (min, Some(range)) => Some(min -. range *. 0.001)
@ -244,18 +225,20 @@ module DistPlusChart = {
// }; // };
let minX = { let minX = {
distPlus |> DistPlus.T.Integral.yToX(~cache=None, 0.00001); distPlus |> DistPlus.T.Integral.yToX(0.00001);
}; };
let maxX = { let maxX = {
distPlus |> DistPlus.T.Integral.yToX(~cache=None, 0.99); distPlus |> DistPlus.T.Integral.yToX(0.99999);
}; };
let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson; let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson;
let discreteProbabilityMassFraction = let discreteProbabilityMassFraction =
distPlus |> DistPlus.T.toDiscreteProbabilityMassFraction; distPlus |> DistPlus.T.toDiscreteProbabilityMassFraction;
let (yMaxDiscreteDomainFactor, yMaxContinuousDomainFactor) = let (yMaxDiscreteDomainFactor, yMaxContinuousDomainFactor) =
adjustBoth(discreteProbabilityMassFraction); adjustBoth(discreteProbabilityMassFraction);
<DistributionPlot <DistributionPlot
xScale={config.xLog ? "log" : "linear"} xScale={config.xLog ? "log" : "linear"}
yScale={config.yLog ? "log" : "linear"} yScale={config.yLog ? "log" : "linear"}
@ -283,11 +266,11 @@ module IntegralChart = {
|> Continuous.toLinear |> Continuous.toLinear
|> E.O.fmap(Continuous.getShape); |> E.O.fmap(Continuous.getShape);
let minX = { let minX = {
distPlus |> DistPlus.T.Integral.yToX(~cache=None, 0.00001); distPlus |> DistPlus.T.Integral.yToX(0.00001);
}; };
let maxX = { let maxX = {
distPlus |> DistPlus.T.Integral.yToX(~cache=None, 0.99); distPlus |> DistPlus.T.Integral.yToX(0.99999);
}; };
let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson; let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson;
<DistributionPlot <DistributionPlot
@ -334,6 +317,7 @@ let make = (~distPlus: DistTypes.distPlus) => {
let (x, setX) = React.useState(() => 0.); let (x, setX) = React.useState(() => 0.);
let (state, dispatch) = let (state, dispatch) =
React.useReducer(DistPlusPlotReducer.reducer, DistPlusPlotReducer.init); React.useReducer(DistPlusPlotReducer.reducer, DistPlusPlotReducer.init);
<div> <div>
{state.distributions {state.distributions
|> E.L.fmapi((index, config) => |> E.L.fmapi((index, config) =>

2
src/components/charts/DistributionPlot/distPlotD3.js
View File

@ -427,7 +427,7 @@ export class DistPlotD3 {
addLollipopsChart(common) { addLollipopsChart(common) {
const data = this.getDataPoints('discrete'); const data = this.getDataPoints('discrete');
const yMin = 0.; //d3.min(this.attrs.data.discrete.ys); const yMin = 0.;
const yMax = d3.max(this.attrs.data.discrete.ys); const yMax = d3.max(this.attrs.data.discrete.ys);
// X axis. // X axis.

306
src/distPlus/distribution/AlgebraicShapeCombination.re
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@ -17,25 +17,25 @@ let toDiscretePointMassesFromTriangulars =
let n = s |> XYShape.T.length; let n = s |> XYShape.T.length;
// first, double up the leftmost and rightmost points: // first, double up the leftmost and rightmost points:
let {xs, ys}: XYShape.T.t = s; let {xs, ys}: XYShape.T.t = s;
let _ = Js.Array.unshift(xs[0], xs); Js.Array.unshift(xs[0], xs) |> ignore;
let _ = Js.Array.unshift(ys[0], ys); Js.Array.unshift(ys[0], ys) |> ignore;
let _ = Js.Array.push(xs[n - 1], xs); Js.Array.push(xs[n - 1], xs) |> ignore;
let _ = Js.Array.push(ys[n - 1], ys); Js.Array.push(ys[n - 1], ys) |> ignore;
let n = E.A.length(xs); let n = E.A.length(xs);
// squares and neighbourly products of the xs // squares and neighbourly products of the xs
let xsSq: array(float) = Belt.Array.makeUninitializedUnsafe(n); let xsSq: array(float) = Belt.Array.makeUninitializedUnsafe(n);
let xsProdN1: array(float) = Belt.Array.makeUninitializedUnsafe(n - 1); let xsProdN1: array(float) = Belt.Array.makeUninitializedUnsafe(n - 1);
let xsProdN2: array(float) = Belt.Array.makeUninitializedUnsafe(n - 2); let xsProdN2: array(float) = Belt.Array.makeUninitializedUnsafe(n - 2);
for (i in 0 to n - 1) { for (i in 0 to n - 1) {
let _ = Belt.Array.set(xsSq, i, xs[i] *. xs[i]); Belt.Array.set(xsSq, i, xs[i] *. xs[i]) |> ignore;
(); ();
}; };
for (i in 0 to n - 2) { for (i in 0 to n - 2) {
let _ = Belt.Array.set(xsProdN1, i, xs[i] *. xs[i + 1]); Belt.Array.set(xsProdN1, i, xs[i] *. xs[i + 1]) |> ignore;
(); ();
}; };
for (i in 0 to n - 3) { for (i in 0 to n - 3) {
let _ = Belt.Array.set(xsProdN2, i, xs[i] *. xs[i + 2]); Belt.Array.set(xsProdN2, i, xs[i] *. xs[i + 2]) |> ignore;
(); ();
}; };
// means and variances // means and variances
@ -45,12 +45,11 @@ let toDiscretePointMassesFromTriangulars =
if (inverse) { if (inverse) {
for (i in 1 to n - 2) { for (i in 1 to n - 2) {
let _ = Belt.Array.set(
Belt.Array.set( masses,
masses, i - 1,
i - 1, (xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2.,
(xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2., ) |> ignore;
);
// this only works when the whole triange is either on the left or on the right of zero // this only works when the whole triange is either on the left or on the right of zero
let a = xs[i - 1]; let a = xs[i - 1];
@ -71,43 +70,39 @@ let toDiscretePointMassesFromTriangulars =
-. inverseMean -. inverseMean
** 2.; ** 2.;
let _ = Belt.Array.set(means, i - 1, inverseMean); Belt.Array.set(means, i - 1, inverseMean) |> ignore;
let _ = Belt.Array.set(variances, i - 1, inverseVar); Belt.Array.set(variances, i - 1, inverseVar) |> ignore;
(); ();
}; };
{n: n - 2, masses, means, variances}; {n: n - 2, masses, means, variances};
} else { } else {
for (i in 1 to n - 2) { for (i in 1 to n - 2) {
// area of triangle = width * height / 2 // area of triangle = width * height / 2
let _ = Belt.Array.set(
Belt.Array.set( masses,
masses, i - 1,
i - 1, (xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2.,
(xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2., ) |> ignore;
);
// means of triangle = (a + b + c) / 3 // means of triangle = (a + b + c) / 3
let _ = Belt.Array.set(means, i - 1, (xs[i - 1] +. xs[i] +. xs[i + 1]) /. 3.) |> ignore;
Belt.Array.set(means, i - 1, (xs[i - 1] +. xs[i] +. xs[i + 1]) /. 3.);
// variance of triangle = (a^2 + b^2 + c^2 - ab - ac - bc) / 18 // variance of triangle = (a^2 + b^2 + c^2 - ab - ac - bc) / 18
let _ = Belt.Array.set(
Belt.Array.set( variances,
variances, i - 1,
i - 1, (
( xsSq[i - 1]
xsSq[i - 1] +. xsSq[i]
+. xsSq[i] +. xsSq[i + 1]
+. xsSq[i + 1] -. xsProdN1[i - 1]
-. xsProdN1[i - 1] -. xsProdN1[i]
-. xsProdN1[i] -. xsProdN2[i - 1]
-. xsProdN2[i - 1] )
) /. 18.,
/. 18., ) |> ignore;
);
(); ();
}; };
{n: n - 2, masses, means, variances}; {n: n - 2, masses, means, variances};
@ -115,7 +110,11 @@ let toDiscretePointMassesFromTriangulars =
}; };
let combineShapesContinuousContinuous = let combineShapesContinuousContinuous =
(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape) (
op: ExpressionTypes.algebraicOperation,
s1: DistTypes.xyShape,
s2: DistTypes.xyShape,
)
: DistTypes.xyShape => { : DistTypes.xyShape => {
let t1n = s1 |> XYShape.T.length; let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length; let t2n = s2 |> XYShape.T.length;
@ -123,10 +122,11 @@ let combineShapesContinuousContinuous =
// if we add the two distributions, we should probably use normal filters. // if we add the two distributions, we should probably use normal filters.
// if we multiply the two distributions, we should probably use lognormal filters. // if we multiply the two distributions, we should probably use lognormal filters.
let t1m = toDiscretePointMassesFromTriangulars(s1); let t1m = toDiscretePointMassesFromTriangulars(s1);
let t2m = switch (op) { let t2m =
switch (op) {
| `Divide => toDiscretePointMassesFromTriangulars(~inverse=true, s2) | `Divide => toDiscretePointMassesFromTriangulars(~inverse=true, s2)
| _ => toDiscretePointMassesFromTriangulars(~inverse=false, s2) | _ => toDiscretePointMassesFromTriangulars(~inverse=false, s2)
}; };
let combineMeansFn = let combineMeansFn =
switch (op) { switch (op) {
@ -163,7 +163,7 @@ let combineShapesContinuousContinuous =
for (i in 0 to t1m.n - 1) { for (i in 0 to t1m.n - 1) {
for (j in 0 to t2m.n - 1) { for (j in 0 to t2m.n - 1) {
let k = i * t2m.n + j; let k = i * t2m.n + j;
let _ = Belt.Array.set(masses, k, t1m.masses[i] *. t2m.masses[j]); Belt.Array.set(masses, k, t1m.masses[i] *. t2m.masses[j]) |> ignore;
let mean = combineMeansFn(t1m.means[i], t2m.means[j]); let mean = combineMeansFn(t1m.means[i], t2m.means[j]);
let variance = let variance =
@ -173,8 +173,8 @@ let combineShapesContinuousContinuous =
t1m.means[i], t1m.means[i],
t2m.means[j], t2m.means[j],
); );
let _ = Belt.Array.set(means, k, mean); Belt.Array.set(means, k, mean) |> ignore;
let _ = Belt.Array.set(variances, k, variance); Belt.Array.set(variances, k, variance) |> ignore;
// update bounds // update bounds
let minX = mean -. 2. *. sqrt(variance) *. 1.644854; let minX = mean -. 2. *. sqrt(variance) *. 1.644854;
let maxX = mean +. 2. *. sqrt(variance) *. 1.644854; let maxX = mean +. 2. *. sqrt(variance) *. 1.644854;
@ -190,66 +190,46 @@ let combineShapesContinuousContinuous =
// we now want to create a set of target points. For now, let's just evenly distribute 200 points between // we now want to create a set of target points. For now, let's just evenly distribute 200 points between
// between the outputMinX and outputMaxX // between the outputMinX and outputMaxX
let nOut = 300; let nOut = 300;
let outputXs: array(float) = E.A.Floats.range(outputMinX^, outputMaxX^, nOut); let outputXs: array(float) =
E.A.Floats.range(outputMinX^, outputMaxX^, nOut);
let outputYs: array(float) = Belt.Array.make(nOut, 0.0); let outputYs: array(float) = Belt.Array.make(nOut, 0.0);
// now, for each of the outputYs, accumulate from a Gaussian kernel over each input point. // now, for each of the outputYs, accumulate from a Gaussian kernel over each input point.
for (j in 0 to E.A.length(masses) - 1) { // go through all of the result points for (j in 0 to E.A.length(masses) - 1) {
let _ = if (variances[j] > 0. && masses[j] > 0.) { // go through all of the result points
for (i in 0 to E.A.length(outputXs) - 1) { // go through all of the target points if (variances[j] > 0. && masses[j] > 0.) {
for (i in 0 to E.A.length(outputXs) - 1) {
// go through all of the target points
let dx = outputXs[i] -. means[j]; let dx = outputXs[i] -. means[j];
let contribution = masses[j] *. exp(-. (dx ** 2.) /. (2. *. variances[j])) /. (sqrt(2. *. 3.14159276 *. variances[j])); let contribution =
let _ = Belt.Array.set(outputYs, i, outputYs[i] +. contribution); masses[j]
(); *. exp(-. (dx ** 2.) /. (2. *. variances[j]))
/. sqrt(2. *. 3.14159276 *. variances[j]);
Belt.Array.set(outputYs, i, outputYs[i] +. contribution) |> ignore;
}; };
();
}; };
();
}; };
{xs: outputXs, ys: outputYs}; {xs: outputXs, ys: outputYs};
}; };
let toDiscretePointMassesFromDiscrete = (s: DistTypes.xyShape): pointMassesWithMoments => { let toDiscretePointMassesFromDiscrete =
let n = s |> XYShape.T.length; (s: DistTypes.xyShape): pointMassesWithMoments => {
let {xs, ys}: XYShape.T.t = s; let {xs, ys}: XYShape.T.t = s;
let n = E.A.length(xs); let n = E.A.length(xs);
let masses: array(float) = Belt.Array.makeUninitializedUnsafe(n); // doesn't include the fake first and last points let masses: array(float) = Belt.Array.makeBy(n, i => ys[i]);
let means: array(float) = Belt.Array.makeUninitializedUnsafe(n); let means: array(float) = Belt.Array.makeBy(n, i => xs[i]);
let variances: array(float) = Belt.Array.makeUninitializedUnsafe(n); let variances: array(float) = Belt.Array.makeBy(n, i => 0.0);
for (i in 0 to n - 1) {
let _ =
Belt.Array.set(
masses,
i,
ys[i]
);
let _ =
Belt.Array.set(
means,
i,
xs[i]
);
let _ =
Belt.Array.set(
variances,
i,
0.0
);
();
};
{n, masses, means, variances}; {n, masses, means, variances};
}; };
let combineShapesContinuousDiscreteAdd = let combineShapesContinuousDiscrete =
(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape) (op: ExpressionTypes.algebraicOperation, continuousShape: DistTypes.xyShape, discreteShape: DistTypes.xyShape)
: DistTypes.xyShape => { : DistTypes.xyShape => {
let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length; let t1n = continuousShape |> XYShape.T.length;
let t2n = discreteShape |> XYShape.T.length;
// each x pair is added/subtracted // each x pair is added/subtracted
let fn = Operation.Algebraic.toFn(op); let fn = Operation.Algebraic.toFn(op);
@ -257,126 +237,48 @@ let combineShapesContinuousDiscreteAdd =
let outXYShapes: array(array((float, float))) = let outXYShapes: array(array((float, float))) =
Belt.Array.makeUninitializedUnsafe(t2n); Belt.Array.makeUninitializedUnsafe(t2n);
for (j in 0 to t2n - 1) { switch (op) {
// for each one of the discrete points | `Add
// create a new distribution, as long as the original continuous one | `Subtract =>
for (j in 0 to t2n - 1) {
let dxyShape: array((float, float)) = // creates a new continuous shape for each one of the discrete points, and collects them in outXYShapes.
Belt.Array.makeUninitializedUnsafe(t1n); let dxyShape: array((float, float)) =
for (i in 0 to t1n - 1) { Belt.Array.makeUninitializedUnsafe(t1n);
let _ = for (i in 0 to t1n - 1) {
Belt.Array.set( Belt.Array.set(
dxyShape, dxyShape,
i, i,
(fn(s1.xs[i], s2.xs[j]), s1.ys[i] *. s2.ys[j]), (fn(continuousShape.xs[i], discreteShape.xs[j]),
); continuousShape.ys[i] *. discreteShape.ys[j]),
) |> ignore;
();
};
Belt.Array.set(outXYShapes, j, dxyShape) |> ignore;
(); ();
}; }
| `Multiply
let _ = Belt.Array.set(outXYShapes, j, dxyShape); | `Divide =>
(); for (j in 0 to t2n - 1) {
// creates a new continuous shape for each one of the discrete points, and collects them in outXYShapes.
let dxyShape: array((float, float)) =
Belt.Array.makeUninitializedUnsafe(t1n);
for (i in 0 to t1n - 1) {
Belt.Array.set(
dxyShape,
i,
(fn(continuousShape.xs[i], discreteShape.xs[j]), continuousShape.ys[i] *. discreteShape.ys[j] /. discreteShape.xs[j]),
) |> ignore;
();
};
Belt.Array.set(outXYShapes, j, dxyShape) |> ignore;
();
}
}; };
outXYShapes outXYShapes
|> E.A.fold_left(XYShape.PointwiseCombination.combineLinear((+.)), XYShape.T.empty); |> E.A.fmap(XYShape.T.fromZippedArray)
}; |> E.A.fold_left(
XYShape.PointwiseCombination.combine((+.),
let combineShapesContinuousDiscreteMultiply = XYShape.XtoY.continuousInterpolator(`Linear, `UseZero)),
(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape) XYShape.T.empty);
: DistTypes.xyShape => {
let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length;
let t1m = toDiscretePointMassesFromTriangulars(s1);
let t2m = toDiscretePointMassesFromDiscrete(s2);
let combineMeansFn =
switch (op) {
| `Add => ((m1, m2) => m1 +. m2)
| `Subtract => ((m1, m2) => m1 -. m2)
| `Multiply => ((m1, m2) => m1 *. m2)
| `Divide => ((m1, m2) => m1 /. m2)
};
let combineVariancesFn =
switch (op) {
| `Add
| `Subtract => ((v1, v2, _, _) => v1 +. v2)
| `Multiply
| `Divide => (
(v1, v2, m1, m2) => v1 *. m2 ** 2.
)
};
let outputMinX: ref(float) = ref(infinity);
let outputMaxX: ref(float) = ref(neg_infinity);
let masses: array(float) =
Belt.Array.makeUninitializedUnsafe(t1m.n * t2m.n);
let means: array(float) =
Belt.Array.makeUninitializedUnsafe(t1m.n * t2m.n);
let variances: array(float) =
Belt.Array.makeUninitializedUnsafe(t1m.n * t2m.n);
// then convolve the two sets of pointMassesWithMoments
for (i in 0 to t1m.n - 1) {
for (j in 0 to t2m.n - 1) {
let k = i * t2m.n + j;
let _ = Belt.Array.set(masses, k, t1m.masses[i] *. t2m.masses[j]);
let mean = combineMeansFn(t1m.means[i], t2m.means[j]);
let variance =
combineVariancesFn(
t1m.variances[i],
t2m.variances[j],
t1m.means[i],
t2m.means[j],
);
let _ = Belt.Array.set(means, k, mean);
let _ = Belt.Array.set(variances, k, variance);
// update bounds
let minX = mean -. 2. *. sqrt(variance) *. 1.644854;
let maxX = mean +. 2. *. sqrt(variance) *. 1.644854;
if (minX < outputMinX^) {
outputMinX := minX;
};
if (maxX > outputMaxX^) {
outputMaxX := maxX;
};
};
};
// we now want to create a set of target points. For now, let's just evenly distribute 200 points between
// between the outputMinX and outputMaxX
let nOut = 300;
let outputXs: array(float) = E.A.Floats.range(outputMinX^, outputMaxX^, nOut);
let outputYs: array(float) = Belt.Array.make(nOut, 0.0);
// now, for each of the outputYs, accumulate from a Gaussian kernel over each input point.
for (j in 0 to E.A.length(masses) - 1) { // go through all of the result points
let _ = if (variances[j] > 0. && masses[j] > 0.) {
for (i in 0 to E.A.length(outputXs) - 1) { // go through all of the target points
let dx = outputXs[i] -. means[j];
let contribution = masses[j] *. exp(-. (dx ** 2.) /. (2. *. variances[j])) /. (sqrt(2. *. 3.14159276 *. variances[j]));
let _ = Belt.Array.set(outputYs, i, outputYs[i] +. contribution);
();
};
();
};
();
};
{xs: outputXs, ys: outputYs};
};
let combineShapesContinuousDiscrete =
(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
: DistTypes.xyShape => {
switch (op) {
| `Add
| `Subtract => combineShapesContinuousDiscreteAdd(op, s1, s2);
| `Multiply
| `Divide => combineShapesContinuousDiscreteMultiply(op, s1, s2);
};
}; };

200
src/distPlus/distribution/Continuous.re
View File

@ -3,30 +3,45 @@ open Distributions;
type t = DistTypes.continuousShape; type t = DistTypes.continuousShape;
let getShape = (t: t) => t.xyShape; let getShape = (t: t) => t.xyShape;
let interpolation = (t: t) => t.interpolation; let interpolation = (t: t) => t.interpolation;
let make = (interpolation, xyShape, knownIntegralSum): t => { let make = (~interpolation=`Linear, ~integralSumCache=None, ~integralCache=None, xyShape): t => {
xyShape, xyShape,
interpolation, interpolation,
knownIntegralSum, integralSumCache,
integralCache,
}; };
let shapeMap = (fn, {xyShape, interpolation, knownIntegralSum}: t): t => { let shapeMap = (fn, {xyShape, interpolation, integralSumCache, integralCache}: t): t => {
xyShape: fn(xyShape), xyShape: fn(xyShape),
interpolation, interpolation,
knownIntegralSum, integralSumCache,
integralCache,
}; };
let lastY = (t: t) => t |> getShape |> XYShape.T.lastY; let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
let oShapeMap = let oShapeMap =
(fn, {xyShape, interpolation, knownIntegralSum}: t) (fn, {xyShape, interpolation, integralSumCache, integralCache}: t)
: option(DistTypes.continuousShape) => : option(DistTypes.continuousShape) =>
fn(xyShape) |> E.O.fmap(make(interpolation, _, knownIntegralSum)); fn(xyShape) |> E.O.fmap(make(~interpolation, ~integralSumCache, ~integralCache));
let emptyIntegral: DistTypes.continuousShape = {
xyShape: {xs: [|neg_infinity|], ys: [|0.0|]},
interpolation: `Linear,
integralSumCache: Some(0.0),
integralCache: None,
};
let empty: DistTypes.continuousShape = { let empty: DistTypes.continuousShape = {
xyShape: XYShape.T.empty, xyShape: XYShape.T.empty,
interpolation: `Linear, interpolation: `Linear,
knownIntegralSum: Some(0.0), integralSumCache: Some(0.0),
integralCache: Some(emptyIntegral),
}; };
let stepwiseToLinear = (t: t): t =>
make(~integralSumCache=t.integralSumCache, ~integralCache=t.integralCache, XYShape.Range.stepwiseToLinear(t.xyShape));
let combinePointwise = let combinePointwise =
( (
~knownIntegralSumsFn, ~integralSumCachesFn=(_, _) => None,
~integralCachesFn: (t, t) => option(t) =(_, _) => None,
~distributionType: DistTypes.distributionType = `PDF,
fn: (float, float) => float, fn: (float, float) => float,
t1: DistTypes.continuousShape, t1: DistTypes.continuousShape,
t2: DistTypes.continuousShape, t2: DistTypes.continuousShape,
@ -36,59 +51,91 @@ let combinePointwise =
// can just sum them up. Otherwise, all bets are off. // can just sum them up. Otherwise, all bets are off.
let combinedIntegralSum = let combinedIntegralSum =
Common.combineIntegralSums( Common.combineIntegralSums(
knownIntegralSumsFn, integralSumCachesFn,
t1.knownIntegralSum, t1.integralSumCache,
t2.knownIntegralSum, t2.integralSumCache,
); );
// TODO: does it ever make sense to pointwise combine the integrals here?
// It could be done for pointwise additions, but is that ever needed?
// If combining stepwise and linear, we must convert the stepwise to linear first,
// i.e. add a point at the bottom of each step
let (t1, t2) = switch (t1.interpolation, t2.interpolation) {
| (`Linear, `Linear) => (t1, t2);
| (`Stepwise, `Stepwise) => (t1, t2);
| (`Linear, `Stepwise) => (t1, stepwiseToLinear(t2));
| (`Stepwise, `Linear) => (stepwiseToLinear(t1), t2);
};
let extrapolation = switch (distributionType) {
| `PDF => `UseZero
| `CDF => `UseOutermostPoints
};
let interpolator = XYShape.XtoY.continuousInterpolator(t1.interpolation, extrapolation);
make( make(
`Linear, ~integralSumCache=combinedIntegralSum,
XYShape.PointwiseCombination.combineLinear( XYShape.PointwiseCombination.combine(
~fn=(+.), (+.),
interpolator,
t1.xyShape, t1.xyShape,
t2.xyShape, t2.xyShape,
), ),
combinedIntegralSum,
); );
}; };
let toLinear = (t: t): option(t) => { let toLinear = (t: t): option(t) => {
switch (t) { switch (t) {
| {interpolation: `Stepwise, xyShape, knownIntegralSum} => | {interpolation: `Stepwise, xyShape, integralSumCache, integralCache} =>
xyShape xyShape
|> XYShape.Range.stepsToContinuous |> XYShape.Range.stepsToContinuous
|> E.O.fmap(make(`Linear, _, knownIntegralSum)) |> E.O.fmap(make(~integralSumCache, ~integralCache))
| {interpolation: `Linear} => Some(t) | {interpolation: `Linear} => Some(t)
}; };
}; };
let shapeFn = (fn, t: t) => t |> getShape |> fn; let shapeFn = (fn, t: t) => t |> getShape |> fn;
let updateKnownIntegralSum = (knownIntegralSum, t: t): t => {
let updateIntegralSumCache = (integralSumCache, t: t): t => {
...t, ...t,
knownIntegralSum, integralSumCache,
};
let updateIntegralCache = (integralCache, t: t): t => {
...t,
integralCache,
}; };
let reduce = let reduce =
( (
~knownIntegralSumsFn: (float, float) => option(float)=(_, _) => None, ~integralSumCachesFn: (float, float) => option(float)=(_, _) => None,
~integralCachesFn: (t, t) => option(t)=(_, _) => None,
fn, fn,
continuousShapes, continuousShapes,
) => ) =>
continuousShapes continuousShapes
|> E.A.fold_left(combinePointwise(~knownIntegralSumsFn, fn), empty); |> E.A.fold_left(combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn), empty);
let mapY = (~knownIntegralSumFn=_ => None, fn, t: t) => { let mapY = (~integralSumCacheFn=_ => None,
let u = E.O.bind(_, knownIntegralSumFn); ~integralCacheFn=_ => None,
let yMapFn = shapeMap(XYShape.T.mapY(fn)); ~fn, t: t) => {
make(
t |> yMapFn |> updateKnownIntegralSum(u(t.knownIntegralSum)); ~interpolation=t.interpolation,
~integralSumCache=t.integralSumCache |> E.O.bind(_, integralSumCacheFn),
~integralCache=t.integralCache |> E.O.bind(_, integralCacheFn),
t |> getShape |> XYShape.T.mapY(fn),
);
}; };
let scaleBy = (~scale=1.0, t: t): t => { let rec scaleBy = (~scale=1.0, t: t): t => {
let scaledIntegralSumCache = E.O.bind(t.integralSumCache, v => Some(scale *. v));
let scaledIntegralCache = E.O.bind(t.integralCache, v => Some(scaleBy(~scale, v)));
t t
|> mapY((r: float) => r *. scale) |> mapY(~fn=(r: float) => r *. scale)
|> updateKnownIntegralSum( |> updateIntegralSumCache(scaledIntegralSumCache)
E.O.bind(t.knownIntegralSum, v => Some(scale *. v)), |> updateIntegralCache(scaledIntegralCache)
);
}; };
module T = module T =
@ -98,6 +145,7 @@ module T =
let minX = shapeFn(XYShape.T.minX); let minX = shapeFn(XYShape.T.minX);
let maxX = shapeFn(XYShape.T.maxX); let maxX = shapeFn(XYShape.T.maxX);
let mapY = mapY; let mapY = mapY;
let updateIntegralCache = updateIntegralCache;
let toDiscreteProbabilityMassFraction = _ => 0.0; let toDiscreteProbabilityMassFraction = _ => 0.0;
let toShape = (t: t): DistTypes.shape => Continuous(t); let toShape = (t: t): DistTypes.shape => Continuous(t);
let xToY = (f, {interpolation, xyShape}: t) => { let xToY = (f, {interpolation, xyShape}: t) => {
@ -121,63 +169,56 @@ module T =
|> XYShape.T.zip |> XYShape.T.zip
|> XYShape.Zipped.filterByX(x => x >= lc && x <= rc); |> XYShape.Zipped.filterByX(x => x >= lc && x <= rc);
let eps = (t |> getShape |> XYShape.T.xTotalRange) *. 0.0001;
let leftNewPoint = let leftNewPoint =
leftCutoff |> E.O.dimap(lc => [|(lc -. eps, 0.)|], _ => [||]); leftCutoff |> E.O.dimap(lc => [|(lc -. epsilon_float, 0.)|], _ => [||]);
let rightNewPoint = let rightNewPoint =
rightCutoff |> E.O.dimap(rc => [|(rc +. eps, 0.)|], _ => [||]); rightCutoff |> E.O.dimap(rc => [|(rc +. epsilon_float, 0.)|], _ => [||]);
let truncatedZippedPairsWithNewPoints = let truncatedZippedPairsWithNewPoints =
E.A.concatMany([|leftNewPoint, truncatedZippedPairs, rightNewPoint|]); E.A.concatMany([|leftNewPoint, truncatedZippedPairs, rightNewPoint|]);
let truncatedShape = let truncatedShape =
XYShape.T.fromZippedArray(truncatedZippedPairsWithNewPoints); XYShape.T.fromZippedArray(truncatedZippedPairsWithNewPoints);
make(`Linear, truncatedShape, None); make(truncatedShape)
}; };
// TODO: This should work with stepwise plots. // TODO: This should work with stepwise plots.
let integral = (~cache, t) => let integral = (t) =>
if (t |> getShape |> XYShape.T.length > 0) { switch (getShape(t) |> XYShape.T.isEmpty, t.integralCache) {
switch (cache) { | (true, _) => emptyIntegral
| Some(cache) => cache | (false, Some(cache)) => cache
| None => | (false, None) =>
t t
|> getShape |> getShape
|> XYShape.Range.integrateWithTriangles |> XYShape.Range.integrateWithTriangles
|> E.O.toExt("This should not have happened") |> E.O.toExt("This should not have happened")
|> make(`Linear, _, None) |> make
};
} else {
make(`Linear, {xs: [|neg_infinity|], ys: [|0.0|]}, None);
}; };
let downsample = (~cache=None, length, t): t => let downsample = (length, t): t =>
t t
|> shapeMap( |> shapeMap(
XYShape.XsConversion.proportionByProbabilityMass( XYShape.XsConversion.proportionByProbabilityMass(
length, length,
integral(~cache, t).xyShape, integral(t).xyShape,
), ),
); );
let integralEndY = (~cache, t: t) => let integralEndY = (t: t) =>
t.knownIntegralSum |> E.O.default(t |> integral(~cache) |> lastY); t.integralSumCache |> E.O.default(t |> integral |> lastY);
let integralXtoY = (~cache, f, t: t) => let integralXtoY = (f, t: t) =>
t |> integral(~cache) |> shapeFn(XYShape.XtoY.linear(f)); t |> integral |> shapeFn(XYShape.XtoY.linear(f));
let integralYtoX = (~cache, f, t: t) => let integralYtoX = (f, t: t) =>
t |> integral(~cache) |> shapeFn(XYShape.YtoX.linear(f)); t |> integral |> shapeFn(XYShape.YtoX.linear(f));
let toContinuous = t => Some(t); let toContinuous = t => Some(t);
let toDiscrete = _ => None; let toDiscrete = _ => None;
let normalize = (t: t): t => { let normalize = (t: t): t => {
t t
|> scaleBy(~scale=1. /. integralEndY(~cache=None, t)) |> updateIntegralCache(Some(integral(t)))
|> updateKnownIntegralSum(Some(1.0)); |> scaleBy(~scale=1. /. integralEndY(t))
|> updateIntegralSumCache(Some(1.0));
}; };
let normalizedToContinuous = t => Some(t |> normalize);
let normalizedToDiscrete = _ => None;
let mean = (t: t) => { let mean = (t: t) => {
let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 2.0 /. 2.0; let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 2.0 /. 2.0;
let indefiniteIntegralLinear = (p, a, b) => let indefiniteIntegralLinear = (p, a, b) =>
@ -205,23 +246,28 @@ let combineAlgebraicallyWithDiscrete =
t1: t, t1: t,
t2: DistTypes.discreteShape, t2: DistTypes.discreteShape,
) => { ) => {
let s1 = t1 |> getShape; let t1s = t1 |> getShape;
let s2 = t2.xyShape; let t2s = t2.xyShape; // TODO would like to use Discrete.getShape here, but current file structure doesn't allow for that
let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length; if (XYShape.T.isEmpty(t1s) || XYShape.T.isEmpty(t2s)) {
if (t1n == 0 || t2n == 0) {
empty; empty;
} else { } else {
let combinedShape = let continuousAsLinear = switch (t1.interpolation) {
AlgebraicShapeCombination.combineShapesContinuousDiscrete(op, s1, s2); | `Linear => t1;
| `Stepwise => stepwiseToLinear(t1)
};
let combinedShape = AlgebraicShapeCombination.combineShapesContinuousDiscrete(op, continuousAsLinear |> getShape, t2s);
let combinedIntegralSum = let combinedIntegralSum =
Common.combineIntegralSums( Common.combineIntegralSums(
(a, b) => Some(a *. b), (a, b) => Some(a *. b),
t1.knownIntegralSum, t1.integralSumCache,
t2.knownIntegralSum, t2.integralSumCache,
); );
// return a new Continuous distribution
make(`Linear, combinedShape, combinedIntegralSum); // TODO: It could make sense to automatically transform the integrals here (shift or scale)
make(~interpolation=t1.interpolation, ~integralSumCache=combinedIntegralSum, combinedShape)
}; };
}; };
@ -239,10 +285,10 @@ let combineAlgebraically =
let combinedIntegralSum = let combinedIntegralSum =
Common.combineIntegralSums( Common.combineIntegralSums(
(a, b) => Some(a *. b), (a, b) => Some(a *. b),
t1.knownIntegralSum, t1.integralSumCache,
t2.knownIntegralSum, t2.integralSumCache,
); );
// return a new Continuous distribution // return a new Continuous distribution
make(`Linear, combinedShape, combinedIntegralSum); make(~integralSumCache=combinedIntegralSum, combinedShape);
}; };
}; };

190
src/distPlus/distribution/Discrete.re
View File

@ -2,23 +2,37 @@ open Distributions;
type t = DistTypes.discreteShape; type t = DistTypes.discreteShape;
let make = (xyShape, knownIntegralSum): t => {xyShape, knownIntegralSum}; let make = (~integralSumCache=None, ~integralCache=None, xyShape): t => {xyShape, integralSumCache, integralCache};
let shapeMap = (fn, {xyShape, knownIntegralSum}: t): t => { let shapeMap = (fn, {xyShape, integralSumCache, integralCache}: t): t => {
xyShape: fn(xyShape), xyShape: fn(xyShape),
knownIntegralSum, integralSumCache,
integralCache
}; };
let getShape = (t: t) => t.xyShape; let getShape = (t: t) => t.xyShape;
let oShapeMap = (fn, {xyShape, knownIntegralSum}: t): option(t) => let oShapeMap = (fn, {xyShape, integralSumCache, integralCache}: t): option(t) =>
fn(xyShape) |> E.O.fmap(make(_, knownIntegralSum)); fn(xyShape) |> E.O.fmap(make(~integralSumCache, ~integralCache));
let emptyIntegral: DistTypes.continuousShape = {
xyShape: {xs: [|neg_infinity|], ys: [|0.0|]},
interpolation: `Stepwise,
integralSumCache: Some(0.0),
integralCache: None,
};
let empty: DistTypes.discreteShape = {
xyShape: XYShape.T.empty,
integralSumCache: Some(0.0),
integralCache: Some(emptyIntegral),
};
let empty: t = {xyShape: XYShape.T.empty, knownIntegralSum: Some(0.0)};
let shapeFn = (fn, t: t) => t |> getShape |> fn; let shapeFn = (fn, t: t) => t |> getShape |> fn;
let lastY = (t: t) => t |> getShape |> XYShape.T.lastY; let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
let combinePointwise = let combinePointwise =
( (
~knownIntegralSumsFn, ~integralSumCachesFn = (_, _) => None,
~integralCachesFn: (DistTypes.continuousShape, DistTypes.continuousShape) => option(DistTypes.continuousShape) = (_, _) => None,
fn, fn,
t1: DistTypes.discreteShape, t1: DistTypes.discreteShape,
t2: DistTypes.discreteShape, t2: DistTypes.discreteShape,
@ -26,38 +40,47 @@ let combinePointwise =
: DistTypes.discreteShape => { : DistTypes.discreteShape => {
let combinedIntegralSum = let combinedIntegralSum =
Common.combineIntegralSums( Common.combineIntegralSums(
knownIntegralSumsFn, integralSumCachesFn,
t1.knownIntegralSum, t1.integralSumCache,
t2.knownIntegralSum, t2.integralSumCache,
); );
// TODO: does it ever make sense to pointwise combine the integrals here?
// It could be done for pointwise additions, but is that ever needed?
make( make(
~integralSumCache=combinedIntegralSum,
XYShape.PointwiseCombination.combine( XYShape.PointwiseCombination.combine(
~xsSelection=ALL_XS, (+.),
~xToYSelection=XYShape.XtoY.stepwiseIfAtX, XYShape.XtoY.discreteInterpolator,
~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, t1.xyShape,
t2.xyShape, t2.xyShape,
), ),
combinedIntegralSum,
); );
}; };
let reduce = let reduce =
(~knownIntegralSumsFn=(_, _) => None, fn, discreteShapes) (~integralSumCachesFn=(_, _) => None,
: DistTypes.discreteShape => ~integralCachesFn=(_, _) => None,
fn, discreteShapes)
: DistTypes.discreteShape =>
discreteShapes discreteShapes
|> E.A.fold_left(combinePointwise(~knownIntegralSumsFn, fn), empty); |> E.A.fold_left(combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn), empty);
let updateKnownIntegralSum = (knownIntegralSum, t: t): t => { let updateIntegralSumCache = (integralSumCache, t: t): t => {
...t, ...t,
knownIntegralSum, integralSumCache,
};
let updateIntegralCache = (integralCache, t: t): t => {
...t,
integralCache,
}; };
/* This multiples all of the data points together and creates a new discrete distribution from the results. /* 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. */ 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 = let combineAlgebraically =
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t) => { (op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
let t1s = t1 |> getShape; let t1s = t1 |> getShape;
let t2s = t2 |> getShape; let t2s = t2 |> getShape;
let t1n = t1s |> XYShape.T.length; let t1n = t1s |> XYShape.T.length;
@ -66,8 +89,8 @@ let combineAlgebraically =
let combinedIntegralSum = let combinedIntegralSum =
Common.combineIntegralSums( Common.combineIntegralSums(
(s1, s2) => Some(s1 *. s2), (s1, s2) => Some(s1 *. s2),
t1.knownIntegralSum, t1.integralSumCache,
t2.knownIntegralSum, t2.integralSumCache,
); );
let fn = Operation.Algebraic.toFn(op); let fn = Operation.Algebraic.toFn(op);
@ -87,84 +110,85 @@ let combineAlgebraically =
let combinedShape = XYShape.T.fromZippedArray(rxys); let combinedShape = XYShape.T.fromZippedArray(rxys);
make(combinedShape, combinedIntegralSum); make(~integralSumCache=combinedIntegralSum, combinedShape);
}; };
let mapY = (~knownIntegralSumFn=previousKnownIntegralSum => None, fn, t: t) => { let mapY = (~integralSumCacheFn=_ => None,
let u = E.O.bind(_, knownIntegralSumFn); ~integralCacheFn=_ => None,
let yMapFn = shapeMap(XYShape.T.mapY(fn)); ~fn, t: t) => {
make(
t |> yMapFn |> updateKnownIntegralSum(u(t.knownIntegralSum)); ~integralSumCache=t.integralSumCache |> E.O.bind(_, integralSumCacheFn),
~integralCache=t.integralCache |> E.O.bind(_, integralCacheFn),
t |> getShape |> XYShape.T.mapY(fn),
);
}; };
let scaleBy = (~scale=1.0, t: t): t => { let scaleBy = (~scale=1.0, t: t): t => {
let scaledIntegralSumCache = t.integralSumCache |> E.O.fmap((*.)(scale));
let scaledIntegralCache = t.integralCache |> E.O.fmap(Continuous.scaleBy(~scale));
t t
|> mapY((r: float) => r *. scale) |> mapY(~fn=(r: float) => r *. scale)
|> updateKnownIntegralSum( |> updateIntegralSumCache(scaledIntegralSumCache)
E.O.bind(t.knownIntegralSum, v => Some(scale *. v)), |> updateIntegralCache(scaledIntegralCache)
);
}; };
module T = module T =
Dist({ Dist({
type t = DistTypes.discreteShape; type t = DistTypes.discreteShape;
type integral = DistTypes.continuousShape; type integral = DistTypes.continuousShape;
let integral = (~cache, t) => let integral = (t) =>
if (t |> getShape |> XYShape.T.length > 0) { switch (getShape(t) |> XYShape.T.isEmpty, t.integralCache) {
switch (cache) { | (true, _) => emptyIntegral
| Some(c) => c | (false, Some(c)) => c
| None => | (false, None) => {
Continuous.make( let ts = getShape(t);
`Stepwise, // The first xy of this integral should always be the zero, to ensure nice plotting
XYShape.T.accumulateYs((+.), getShape(t)), let firstX = ts |> XYShape.T.minX;
None, let prependedZeroPoint: XYShape.T.t = {xs: [|firstX -. epsilon_float|], ys: [|0.|]};
) let integralShape =
}; ts
} else { |> XYShape.T.concat(prependedZeroPoint)
Continuous.make( |> XYShape.T.accumulateYs((+.));
`Stepwise,
{xs: [|neg_infinity|], ys: [|0.0|]}, Continuous.make(~interpolation=`Stepwise, integralShape);
None, }
);
}; };
let integralEndY = (~cache, t: t) => let integralEndY = (t: t) =>
t.knownIntegralSum t.integralSumCache
|> E.O.default(t |> integral(~cache) |> Continuous.lastY); |> E.O.default(t |> integral |> Continuous.lastY);
let minX = shapeFn(XYShape.T.minX); let minX = shapeFn(XYShape.T.minX);
let maxX = shapeFn(XYShape.T.maxX); let maxX = shapeFn(XYShape.T.maxX);
let toDiscreteProbabilityMassFraction = _ => 1.0; let toDiscreteProbabilityMassFraction = _ => 1.0;
let mapY = mapY; let mapY = mapY;
let updateIntegralCache = updateIntegralCache;
let toShape = (t: t): DistTypes.shape => Discrete(t); let toShape = (t: t): DistTypes.shape => Discrete(t);
let toContinuous = _ => None; let toContinuous = _ => None;
let toDiscrete = t => Some(t); let toDiscrete = t => Some(t);
let normalize = (t: t): t => { let normalize = (t: t): t => {
t t
|> scaleBy(~scale=1. /. integralEndY(~cache=None, t)) |> scaleBy(~scale=1. /. integralEndY(t))
|> updateKnownIntegralSum(Some(1.0)); |> updateIntegralSumCache(Some(1.0));
}; };
let normalizedToContinuous = _ => None; let downsample = (i, t: t): t => {
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. // 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. // The best we can do is to clip off the smallest values.
let currentLength = t |> getShape |> XYShape.T.length; let currentLength = t |> getShape |> XYShape.T.length;
if (i < currentLength && i >= 1 && currentLength > 1) { if (i < currentLength && i >= 1 && currentLength > 1) {
let clippedShape = t
t |> getShape
|> getShape |> XYShape.T.zip
|> XYShape.T.zip |> XYShape.Zipped.sortByY
|> XYShape.Zipped.sortByY |> Belt.Array.reverse
|> Belt.Array.reverse |> Belt.Array.slice(_, ~offset=0, ~len=i)
|> Belt.Array.slice(_, ~offset=0, ~len=i) |> XYShape.Zipped.sortByX
|> XYShape.Zipped.sortByX |> XYShape.T.fromZippedArray
|> XYShape.T.fromZippedArray; |> make;
make(clippedShape, None); // if someone needs the sum, they'll have to recompute it
} else { } else {
t; t;
}; };
@ -172,17 +196,15 @@ module T =
let truncate = let truncate =
(leftCutoff: option(float), rightCutoff: option(float), t: t): t => { (leftCutoff: option(float), rightCutoff: option(float), t: t): t => {
let truncatedShape = t
t |> getShape
|> getShape |> XYShape.T.zip
|> XYShape.T.zip |> XYShape.Zipped.filterByX(x =>
|> XYShape.Zipped.filterByX(x => x >= E.O.default(neg_infinity, leftCutoff)
x >= E.O.default(neg_infinity, leftCutoff) && x <= E.O.default(infinity, rightCutoff)
|| x <= E.O.default(infinity, rightCutoff) )
) |> XYShape.T.fromZippedArray
|> XYShape.T.fromZippedArray; |> make;
make(truncatedShape, None);
}; };
let xToY = (f, t) => let xToY = (f, t) =>
@ -192,11 +214,11 @@ module T =
|> E.O.default(0.0) |> E.O.default(0.0)
|> DistTypes.MixedPoint.makeDiscrete; |> DistTypes.MixedPoint.makeDiscrete;
let integralXtoY = (~cache, f, t) => let integralXtoY = (f, t) =>
t |> integral(~cache) |> Continuous.getShape |> XYShape.XtoY.linear(f); t |> integral |> Continuous.getShape |> XYShape.XtoY.linear(f);
let integralYtoX = (~cache, f, t) => let integralYtoX = (f, t) =>
t |> integral(~cache) |> Continuous.getShape |> XYShape.YtoX.linear(f); t |> integral |> Continuous.getShape |> XYShape.YtoX.linear(f);
let mean = (t: t): float => { let mean = (t: t): float => {
let s = getShape(t); let s = getShape(t);

50
src/distPlus/distribution/DistPlus.re
View File

@ -2,8 +2,7 @@ open DistTypes;
type t = DistTypes.distPlus; type t = DistTypes.distPlus;
let shapeIntegral = shape => let shapeIntegral = shape => Shape.T.Integral.get(shape);
Shape.T.Integral.get(~cache=None, shape);
let make = let make =
( (
~shape, ~shape,
@ -59,7 +58,6 @@ module T =
let normalize = (t: t): t => { let normalize = (t: t): t => {
let normalizedShape = t |> toShape |> Shape.T.normalize; let normalizedShape = t |> toShape |> Shape.T.normalize;
t |> updateShape(normalizedShape); t |> updateShape(normalizedShape);
// TODO: also adjust for domainIncludedProbabilityMass here.
}; };
let truncate = (leftCutoff, rightCutoff, t: t): t => { let truncate = (leftCutoff, rightCutoff, t: t): t => {
@ -71,28 +69,6 @@ module T =
t |> updateShape(truncatedShape); t |> updateShape(truncatedShape);
}; };
let normalizedToContinuous = (t: t) => {
t
|> toShape
|> Shape.T.normalizedToContinuous
|> E.O.fmap(
Continuous.T.mapY(
domainIncludedProbabilityMassAdjustment(t),
),
);
};
let normalizedToDiscrete = (t: t) => {
t
|> toShape
|> Shape.T.normalizedToDiscrete
|> E.O.fmap(
Discrete.T.mapY(
domainIncludedProbabilityMassAdjustment(t),
),
);
};
let xToY = (f, t: t) => let xToY = (f, t: t) =>
t t
|> toShape |> toShape
@ -105,34 +81,36 @@ module T =
shapeFn(Shape.T.toDiscreteProbabilityMassFraction); shapeFn(Shape.T.toDiscreteProbabilityMassFraction);
// This bit is kind of awkward, could probably use rethinking. // This bit is kind of awkward, could probably use rethinking.
let integral = (~cache, t: t) => let integral = (t: t) =>
updateShape(Continuous(t.integralCache), t); updateShape(Continuous(t.integralCache), t);
let downsample = (~cache=None, i, t): t => let updateIntegralCache = (integralCache: option(DistTypes.continuousShape), t) =>
update(~integralCache=E.O.default(t.integralCache, integralCache), t);
let downsample = (i, t): t =>
updateShape(t |> toShape |> Shape.T.downsample(i), t); updateShape(t |> toShape |> Shape.T.downsample(i), t);
// todo: adjust for limit, maybe? // todo: adjust for limit, maybe?
let mapY = let mapY =
( (
~knownIntegralSumFn=previousIntegralSum => None, ~integralSumCacheFn=previousIntegralSum => None,
fn, ~integralCacheFn=previousIntegralCache => None,
~fn,
{shape, _} as t: t, {shape, _} as t: t,
) )
: t => : t =>
Shape.T.mapY(~knownIntegralSumFn, fn, shape) Shape.T.mapY(~integralSumCacheFn, ~fn, shape)
|> updateShape(_, t); |> updateShape(_, t);
// get the total of everything // get the total of everything
let integralEndY = (~cache as _, t: t) => { let integralEndY = (t: t) => {
Shape.T.Integral.sum( Shape.T.Integral.sum(
~cache=Some(t.integralCache),
toShape(t), toShape(t),
); );
}; };
// TODO: Fix this below, obviously. Adjust for limits // TODO: Fix this below, obviously. Adjust for limits
let integralXtoY = (~cache as _, f, t: t) => { let integralXtoY = (f, t: t) => {
Shape.T.Integral.xToY( Shape.T.Integral.xToY(
~cache=Some(t.integralCache),
f, f,
toShape(t), toShape(t),
) )
@ -140,8 +118,8 @@ module T =
}; };
// TODO: This part is broken when there is a limit, if this is supposed to be taken into account. // 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) => { let integralYtoX = (f, t: t) => {
Shape.T.Integral.yToX(~cache=None, f, toShape(t)); Shape.T.Integral.yToX(f, toShape(t));
}; };
let mean = (t: t) => { let mean = (t: t) => {

4
src/distPlus/distribution/DistPlusTime.re
View File

@ -23,6 +23,6 @@
include DistPlus.T.Integral; include DistPlus.T.Integral;
let xToY = (f: TimeTypes.timeInVector, t: t) => { let xToY = (f: TimeTypes.timeInVector, t: t) => {
timeInVectorToX(f, t) timeInVectorToX(f, t)
|> E.O.fmap(x => DistPlus.T.Integral.xToY(~cache=None, x, t)); |> E.O.fmap(x => DistPlus.T.Integral.xToY(x, t));
}; };
}; };

26
src/distPlus/distribution/DistTypes.re
View File

@ -9,25 +9,45 @@ type domain =
| RightLimited(domainLimit) | RightLimited(domainLimit)
| LeftAndRightLimited(domainLimit, domainLimit); | LeftAndRightLimited(domainLimit, domainLimit);
type distributionType = [
| `PDF
| `CDF
];
type xyShape = { type xyShape = {
xs: array(float), xs: array(float),
ys: array(float), ys: array(float),
}; };
type interpolationStrategy = [
| `Stepwise
| `Linear
];
type extrapolationStrategy = [
| `UseZero
| `UseOutermostPoints
];
type interpolator = (xyShape, int, float) => float;
type continuousShape = { type continuousShape = {
xyShape, xyShape,
interpolation: [ | `Stepwise | `Linear], interpolation: interpolationStrategy,
knownIntegralSum: option(float), integralSumCache: option(float),
integralCache: option(continuousShape),
}; };
type discreteShape = { type discreteShape = {
xyShape, xyShape,
knownIntegralSum: option(float), integralSumCache: option(float),
integralCache: option(continuousShape),
}; };
type mixedShape = { type mixedShape = {
continuous: continuousShape, continuous: continuousShape,
discrete: discreteShape, discrete: discreteShape,
integralSumCache: option(float),
integralCache: option(continuousShape),
}; };
type shapeMonad('a, 'b, 'c) = type shapeMonad('a, 'b, 'c) =

39
src/distPlus/distribution/Distributions.re
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@ -4,22 +4,22 @@ module type dist = {
let minX: t => float; let minX: t => float;
let maxX: t => float; let maxX: t => float;
let mapY: let mapY:
(~knownIntegralSumFn: float => option(float)=?, float => float, t) => t; (~integralSumCacheFn: float => option(float)=?, ~integralCacheFn: DistTypes.continuousShape => option(DistTypes.continuousShape)=?, ~fn: float => float, t) => t;
let xToY: (float, t) => DistTypes.mixedPoint; let xToY: (float, t) => DistTypes.mixedPoint;
let toShape: t => DistTypes.shape; let toShape: t => DistTypes.shape;
let toContinuous: t => option(DistTypes.continuousShape); let toContinuous: t => option(DistTypes.continuousShape);
let toDiscrete: t => option(DistTypes.discreteShape); let toDiscrete: t => option(DistTypes.discreteShape);
let normalize: t => t; let normalize: t => t;
let normalizedToContinuous: t => option(DistTypes.continuousShape);
let normalizedToDiscrete: t => option(DistTypes.discreteShape);
let toDiscreteProbabilityMassFraction: t => float; let toDiscreteProbabilityMassFraction: t => float;
let downsample: (~cache: option(integral)=?, int, t) => t; let downsample: (int, t) => t;
let truncate: (option(float), option(float), t) => t; let truncate: (option(float), option(float), t) => t;
let integral: (~cache: option(integral), t) => integral; let updateIntegralCache: (option(DistTypes.continuousShape), t) => t;
let integralEndY: (~cache: option(integral), t) => float;
let integralXtoY: (~cache: option(integral), float, t) => float; let integral: (t) => integral;
let integralYtoX: (~cache: option(integral), float, t) => float; let integralEndY: (t) => float;
let integralXtoY: (float, t) => float;
let integralYtoX: (float, t) => float;
let mean: t => float; let mean: t => float;
let variance: t => float; let variance: t => float;
@ -41,11 +41,11 @@ module Dist = (T: dist) => {
let toDiscrete = T.toDiscrete; let toDiscrete = T.toDiscrete;
let normalize = T.normalize; let normalize = T.normalize;
let truncate = T.truncate; let truncate = T.truncate;
let normalizedToContinuous = T.normalizedToContinuous;
let normalizedToDiscrete = T.normalizedToDiscrete;
let mean = T.mean; let mean = T.mean;
let variance = T.variance; let variance = T.variance;
let updateIntegralCache = T.updateIntegralCache;
module Integral = { module Integral = {
type t = T.integral; type t = T.integral;
let get = T.integral; let get = T.integral;
@ -59,10 +59,23 @@ module Common = {
let combineIntegralSums = let combineIntegralSums =
( (
combineFn: (float, float) => option(float), combineFn: (float, float) => option(float),
t1KnownIntegralSum: option(float), t1IntegralSumCache: option(float),
t2KnownIntegralSum: option(float), t2IntegralSumCache: option(float),
) => { ) => {
switch (t1KnownIntegralSum, t2KnownIntegralSum) { switch (t1IntegralSumCache, t2IntegralSumCache) {
| (None, _)
| (_, None) => None
| (Some(s1), Some(s2)) => combineFn(s1, s2)
};
};
let combineIntegrals =
(
combineFn: (DistTypes.continuousShape, DistTypes.continuousShape) => option(DistTypes.continuousShape),
t1IntegralCache: option(DistTypes.continuousShape),
t2IntegralCache: option(DistTypes.continuousShape),
) => {
switch (t1IntegralCache, t2IntegralCache) {
| (None, _) | (None, _)
| (_, None) => None | (_, None) => None
| (Some(s1), Some(s2)) => combineFn(s1, s2) | (Some(s1), Some(s2)) => combineFn(s1, s2)

207
src/distPlus/distribution/Mixed.re
View File

@ -1,7 +1,7 @@
open Distributions; open Distributions;
type t = DistTypes.mixedShape; type t = DistTypes.mixedShape;
let make = (~continuous, ~discrete): t => {continuous, discrete}; let make = (~integralSumCache=None, ~integralCache=None, ~continuous, ~discrete): t => {continuous, discrete, integralSumCache, integralCache};
let totalLength = (t: t): int => { let totalLength = (t: t): int => {
let continuousLength = let continuousLength =
@ -11,29 +11,20 @@ let totalLength = (t: t): int => {
continuousLength + discreteLength; continuousLength + discreteLength;
}; };
let scaleBy = (~scale=1.0, {discrete, continuous}: t): t => { let scaleBy = (~scale=1.0, t: t): t => {
let scaledDiscrete = Discrete.scaleBy(~scale, discrete); let scaledDiscrete = Discrete.scaleBy(~scale, t.discrete);
let scaledContinuous = Continuous.scaleBy(~scale, continuous); let scaledContinuous = Continuous.scaleBy(~scale, t.continuous);
make(~discrete=scaledDiscrete, ~continuous=scaledContinuous); let scaledIntegralCache = E.O.bind(t.integralCache, v => Some(Continuous.scaleBy(~scale, v)));
let scaledIntegralSumCache = E.O.bind(t.integralSumCache, s => Some(s *. scale));
make(~discrete=scaledDiscrete, ~continuous=scaledContinuous, ~integralSumCache=scaledIntegralSumCache, ~integralCache=scaledIntegralCache);
}; };
let toContinuous = ({continuous}: t) => Some(continuous); let toContinuous = ({continuous}: t) => Some(continuous);
let toDiscrete = ({discrete}: t) => Some(discrete); let toDiscrete = ({discrete}: t) => Some(discrete);
let combinePointwise = (~knownIntegralSumsFn, fn, t1: t, t2: t) => { let updateIntegralCache = (integralCache, t: t): t => {
let reducedDiscrete = ...t,
[|t1, t2|] integralCache,
|> 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 = module T =
@ -47,6 +38,8 @@ module T =
max(Continuous.T.maxX(continuous), Discrete.T.maxX(discrete)); max(Continuous.T.maxX(continuous), Discrete.T.maxX(discrete));
let toShape = (t: t): DistTypes.shape => Mixed(t); let toShape = (t: t): DistTypes.shape => Mixed(t);
let updateIntegralCache = updateIntegralCache;
let toContinuous = toContinuous; let toContinuous = toContinuous;
let toDiscrete = toDiscrete; let toDiscrete = toDiscrete;
@ -61,29 +54,35 @@ module T =
let truncatedDiscrete = let truncatedDiscrete =
Discrete.T.truncate(leftCutoff, rightCutoff, discrete); Discrete.T.truncate(leftCutoff, rightCutoff, discrete);
make(~discrete=truncatedDiscrete, ~continuous=truncatedContinuous); make(~integralSumCache=None, ~integralCache=None, ~discrete=truncatedDiscrete, ~continuous=truncatedContinuous);
}; };
let normalize = (t: t): t => { let normalize = (t: t): t => {
let continuousIntegral = Continuous.T.Integral.get(t.continuous);
let discreteIntegral = Discrete.T.Integral.get(t.discrete);
let continuous = t.continuous |> Continuous.updateIntegralCache(Some(continuousIntegral));
let discrete = t.discrete |> Discrete.updateIntegralCache(Some(discreteIntegral));
let continuousIntegralSum = let continuousIntegralSum =
Continuous.T.Integral.sum(~cache=None, t.continuous); Continuous.T.Integral.sum(continuous);
let discreteIntegralSum = let discreteIntegralSum =
Discrete.T.Integral.sum(~cache=None, t.discrete); Discrete.T.Integral.sum(discrete);
let totalIntegralSum = continuousIntegralSum +. discreteIntegralSum; let totalIntegralSum = continuousIntegralSum +. discreteIntegralSum;
let newContinuousSum = continuousIntegralSum /. totalIntegralSum; let newContinuousSum = continuousIntegralSum /. totalIntegralSum;
let newDiscreteSum = discreteIntegralSum /. totalIntegralSum; let newDiscreteSum = discreteIntegralSum /. totalIntegralSum;
let normalizedContinuous = let normalizedContinuous =
t.continuous continuous
|> Continuous.scaleBy(~scale=1. /. newContinuousSum) |> Continuous.scaleBy(~scale=newContinuousSum /. continuousIntegralSum)
|> Continuous.updateKnownIntegralSum(Some(newContinuousSum)); |> Continuous.updateIntegralSumCache(Some(newContinuousSum));
let normalizedDiscrete = let normalizedDiscrete =
t.discrete discrete
|> Discrete.scaleBy(~scale=1. /. newDiscreteSum) |> Discrete.scaleBy(~scale=newDiscreteSum /. discreteIntegralSum)
|> Discrete.updateKnownIntegralSum(Some(newDiscreteSum)); |> Discrete.updateIntegralSumCache(Some(newDiscreteSum));
make(~continuous=normalizedContinuous, ~discrete=normalizedDiscrete); make(~integralSumCache=Some(1.0), ~integralCache=None, ~continuous=normalizedContinuous, ~discrete=normalizedDiscrete);
}; };
let xToY = (x, t: t) => { let xToY = (x, t: t) => {
@ -97,23 +96,22 @@ module T =
let toDiscreteProbabilityMassFraction = ({discrete, continuous}: t) => { let toDiscreteProbabilityMassFraction = ({discrete, continuous}: t) => {
let discreteIntegralSum = let discreteIntegralSum =
Discrete.T.Integral.sum(~cache=None, discrete); Discrete.T.Integral.sum(discrete);
let continuousIntegralSum = let continuousIntegralSum =
Continuous.T.Integral.sum(~cache=None, continuous); Continuous.T.Integral.sum(continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum; let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
discreteIntegralSum /. totalIntegralSum; discreteIntegralSum /. totalIntegralSum;
}; };
let downsample = (~cache=None, count, {discrete, continuous}: t): t => { let downsample = (count, t: t): t => {
// We will need to distribute the new xs fairly between the discrete and continuous shapes. // 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 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 = let discreteIntegralSum =
Discrete.T.Integral.sum(~cache=None, discrete); Discrete.T.Integral.sum(t.discrete);
let continuousIntegralSum = let continuousIntegralSum =
Continuous.T.Integral.sum(~cache=None, continuous); Continuous.T.Integral.sum(t.continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum; let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
// TODO: figure out what to do when the totalIntegralSum is zero. // TODO: figure out what to do when the totalIntegralSum is zero.
@ -123,7 +121,7 @@ module T =
int_of_float( int_of_float(
float_of_int(count) *. (discreteIntegralSum /. totalIntegralSum), float_of_int(count) *. (discreteIntegralSum /. totalIntegralSum),
), ),
discrete, t.discrete,
); );
let downsampledContinuous = let downsampledContinuous =
@ -131,75 +129,71 @@ module T =
int_of_float( int_of_float(
float_of_int(count) *. (continuousIntegralSum /. totalIntegralSum), float_of_int(count) *. (continuousIntegralSum /. totalIntegralSum),
), ),
continuous, t.continuous,
); );
{discrete: downsampledDiscrete, continuous: downsampledContinuous}; {...t, discrete: downsampledDiscrete, continuous: downsampledContinuous};
}; };
let normalizedToContinuous = (t: t) => Some(normalize(t).continuous); let integral = (t: t) => {
switch (t.integralCache) {
let normalizedToDiscrete = ({discrete} as t: t) =>
Some(normalize(t).discrete);
let integral = (~cache, {continuous, discrete}: t) => {
switch (cache) {
| Some(cache) => cache | Some(cache) => cache
| None => | None =>
// note: if the underlying shapes aren't normalized, then these integrals won't be either! // note: if the underlying shapes aren't normalized, then these integrals won't be either -- but that's the way it should be.
let continuousIntegral = let continuousIntegral = Continuous.T.Integral.get(t.continuous);
Continuous.T.Integral.get(~cache=None, continuous); let discreteIntegral = Continuous.stepwiseToLinear(Discrete.T.Integral.get(t.discrete));
let discreteIntegral = Discrete.T.Integral.get(~cache=None, discrete);
Continuous.make( Continuous.make(
`Linear, XYShape.PointwiseCombination.combine(
XYShape.PointwiseCombination.combineLinear( (+.),
~fn=(+.), XYShape.XtoY.continuousInterpolator(`Linear, `UseOutermostPoints),
Continuous.getShape(continuousIntegral), Continuous.getShape(continuousIntegral),
Continuous.getShape(discreteIntegral), Continuous.getShape(discreteIntegral),
), ),
None,
); );
}; };
}; };
let integralEndY = (~cache, t: t) => { let integralEndY = (t: t) => {
integral(~cache, t) |> Continuous.lastY; t |> integral |> Continuous.lastY;
}; };
let integralXtoY = (~cache, f, t) => { let integralXtoY = (f, t) => {
t |> integral(~cache) |> Continuous.getShape |> XYShape.XtoY.linear(f); t |> integral |> Continuous.getShape |> XYShape.XtoY.linear(f);
}; };
let integralYtoX = (~cache, f, t) => { let integralYtoX = (f, t) => {
t |> integral(~cache) |> Continuous.getShape |> XYShape.YtoX.linear(f); t |> integral |> Continuous.getShape |> XYShape.YtoX.linear(f);
}; };
// This pipes all ys (continuous and discrete) through fn. // 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 mapY is a linear operation, we might be able to update the integralSumCaches as well;
// if not, they'll be set to None. // if not, they'll be set to None.
let mapY = let mapY =
( (
~knownIntegralSumFn=previousIntegralSum => None, ~integralSumCacheFn=previousIntegralSum => None,
fn, ~integralCacheFn=previousIntegral => None,
{discrete, continuous}: t, ~fn,
t: t,
) )
: t => { : t => {
let u = E.O.bind(_, knownIntegralSumFn); let yMappedDiscrete: DistTypes.discreteShape =
t.discrete
|> Discrete.T.mapY(~fn)
|> Discrete.updateIntegralSumCache(E.O.bind(t.discrete.integralSumCache, integralSumCacheFn))
|> Discrete.updateIntegralCache(E.O.bind(t.discrete.integralCache, integralCacheFn));
let yMappedDiscrete = let yMappedContinuous: DistTypes.continuousShape =
discrete t.continuous
|> Discrete.T.mapY(fn) |> Continuous.T.mapY(~fn)
|> Discrete.updateKnownIntegralSum(u(discrete.knownIntegralSum)); |> Continuous.updateIntegralSumCache(E.O.bind(t.continuous.integralSumCache, integralSumCacheFn))
|> Continuous.updateIntegralCache(E.O.bind(t.continuous.integralCache, integralCacheFn));
let yMappedContinuous =
continuous
|> Continuous.T.mapY(fn)
|> Continuous.updateKnownIntegralSum(u(continuous.knownIntegralSum));
{ {
discrete: yMappedDiscrete, discrete: yMappedDiscrete,
continuous: Continuous.T.mapY(fn, continuous), continuous: yMappedContinuous,
integralSumCache: E.O.bind(t.integralSumCache, integralSumCacheFn),
integralCache: E.O.bind(t.integralCache, integralCacheFn),
}; };
}; };
@ -208,10 +202,8 @@ module T =
let continuousMean = Continuous.T.mean(continuous); let continuousMean = Continuous.T.mean(continuous);
// the combined mean is the weighted sum of the two: // the combined mean is the weighted sum of the two:
let discreteIntegralSum = let discreteIntegralSum = Discrete.T.Integral.sum(discrete);
Discrete.T.Integral.sum(~cache=None, discrete); let continuousIntegralSum = Continuous.T.Integral.sum(continuous);
let continuousIntegralSum =
Continuous.T.Integral.sum(~cache=None, continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum; let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
( (
@ -225,10 +217,8 @@ module T =
let variance = ({discrete, continuous} as t: t): float => { let variance = ({discrete, continuous} as t: t): float => {
// the combined mean is the weighted sum of the two: // the combined mean is the weighted sum of the two:
let discreteIntegralSum = let discreteIntegralSum = Discrete.T.Integral.sum(discrete);
Discrete.T.Integral.sum(~cache=None, discrete); let continuousIntegralSum = Continuous.T.Integral.sum(continuous);
let continuousIntegralSum =
Continuous.T.Integral.sum(~cache=None, continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum; let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
let getMeanOfSquares = ({discrete, continuous}: t) => { let getMeanOfSquares = ({discrete, continuous}: t) => {
@ -279,27 +269,64 @@ let combineAlgebraically =
let ccConvResult = let ccConvResult =
Continuous.combineAlgebraically( Continuous.combineAlgebraically(
op, op,
t1d.continuous, t1.continuous,
t2d.continuous, t2.continuous,
); );
let dcConvResult = let dcConvResult =
Continuous.combineAlgebraicallyWithDiscrete( Continuous.combineAlgebraicallyWithDiscrete(
op, op,
t2d.continuous, t2.continuous,
t1d.discrete, t1.discrete,
); );
let cdConvResult = let cdConvResult =
Continuous.combineAlgebraicallyWithDiscrete( Continuous.combineAlgebraicallyWithDiscrete(
op, op,
t1d.continuous, t1.continuous,
t2d.discrete, t2.discrete,
); );
let continuousConvResult = let continuousConvResult =
Continuous.reduce((+.), [|ccConvResult, dcConvResult, cdConvResult|]); Continuous.reduce((+.), [|ccConvResult, dcConvResult, cdConvResult|]);
// ... finally, discrete (*) discrete => discrete, obviously: // ... finally, discrete (*) discrete => discrete, obviously:
let discreteConvResult = let discreteConvResult =
Discrete.combineAlgebraically(op, t1d.discrete, t2d.discrete); Discrete.combineAlgebraically(op, t1.discrete, t2.discrete);
{discrete: discreteConvResult, continuous: continuousConvResult}; let combinedIntegralSum =
Common.combineIntegralSums(
(a, b) => Some(a *. b),
t1.integralSumCache,
t2.integralSumCache,
);
{discrete: discreteConvResult, continuous: continuousConvResult, integralSumCache: combinedIntegralSum, integralCache: None};
};
let combinePointwise = (~integralSumCachesFn = (_, _) => None, ~integralCachesFn = (_, _) => None, fn, t1: t, t2: t): t => {
let reducedDiscrete =
[|t1, t2|]
|> E.A.fmap(toDiscrete)
|> E.A.O.concatSomes
|> Discrete.reduce(~integralSumCachesFn, ~integralCachesFn, fn);
let reducedContinuous =
[|t1, t2|]
|> E.A.fmap(toContinuous)
|> E.A.O.concatSomes
|> Continuous.reduce(~integralSumCachesFn, ~integralCachesFn, fn);
let combinedIntegralSum =
Common.combineIntegralSums(
integralSumCachesFn,
t1.integralSumCache,
t2.integralSumCache,
);
let combinedIntegral =
Common.combineIntegrals(
integralCachesFn,
t1.integralCache,
t2.integralCache,
);
make(~integralSumCache=combinedIntegralSum, ~integralCache=combinedIntegral, ~discrete=reducedDiscrete, ~continuous=reducedContinuous);
}; };

14
src/distPlus/distribution/MixedShapeBuilder.re
View File

@ -9,8 +9,8 @@ type assumptions = {
}; };
let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete: option(DistTypes.discreteShape)): option(DistTypes.shape) => { let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete: option(DistTypes.discreteShape)): option(DistTypes.shape) => {
let continuous = continuous |> E.O.default(Continuous.make(`Linear, {xs: [||], ys: [||]}, Some(0.0))); let continuous = continuous |> E.O.default(Continuous.make(~integralSumCache=Some(0.0), {xs: [||], ys: [||]}));
let discrete = discrete |> E.O.default(Discrete.make({xs: [||], ys: [||]}, Some(0.0))); let discrete = discrete |> E.O.default(Discrete.make(~integralSumCache=Some(0.0), {xs: [||], ys: [||]}));
let cLength = let cLength =
continuous continuous
|> Continuous.getShape |> Continuous.getShape
@ -22,15 +22,13 @@ let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete: op
| (0 | 1, _) => Some(Discrete(discrete)) | (0 | 1, _) => Some(Discrete(discrete))
| (_, 0) => Some(Continuous(continuous)) | (_, 0) => Some(Continuous(continuous))
| (_, _) => | (_, _) =>
let discreteProbabilityMassFraction =
Discrete.T.Integral.sum(~cache=None, discrete);
let discrete = Discrete.T.normalize(discrete);
let continuous = Continuous.T.normalize(continuous);
let mixedDist = let mixedDist =
Mixed.make( Mixed.make(
~integralSumCache=None,
~integralCache=None,
~continuous, ~continuous,
~discrete ~discrete,
); );
Some(Mixed(mixedDist)); Some(Mixed(mixedDist));
}; };
}; };

133
src/distPlus/distribution/Shape.re
View File

@ -15,42 +15,54 @@ let fmap = ((fn1, fn2, fn3), t: t): t =>
| Continuous(m) => Continuous(fn3(m)) | Continuous(m) => Continuous(fn3(m))
}; };
let toMixed = let toMixed =
mapToAll(( mapToAll((
m => m, m => m,
d => Mixed.make(~discrete=d, ~continuous=Continuous.empty), d => Mixed.make(~integralSumCache=d.integralSumCache, ~integralCache=d.integralCache, ~discrete=d, ~continuous=Continuous.empty),
c => Mixed.make(~discrete=Discrete.empty, ~continuous=c), c => Mixed.make(~integralSumCache=c.integralSumCache, ~integralCache=c.integralCache, ~discrete=Discrete.empty, ~continuous=c),
)); ));
let combineAlgebraically = let combineAlgebraically =
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => { (op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
switch (t1, t2) { switch (t1, t2) {
| (Continuous(m1), Continuous(m2)) => | (Continuous(m1), Continuous(m2)) =>
DistTypes.Continuous(Continuous.combineAlgebraically(op, m1, m2)) Continuous.combineAlgebraically(op, m1, m2) |> Continuous.T.toShape;
| (Continuous(m1), Discrete(m2))
| (Discrete(m2), Continuous(m1)) =>
Continuous.combineAlgebraicallyWithDiscrete(op, m1, m2) |> Continuous.T.toShape
| (Discrete(m1), Discrete(m2)) => | (Discrete(m1), Discrete(m2)) =>
DistTypes.Discrete(Discrete.combineAlgebraically(op, m1, m2)) Discrete.combineAlgebraically(op, m1, m2) |> Discrete.T.toShape
| (m1, m2) => | (m1, m2) =>
DistTypes.Mixed( Mixed.combineAlgebraically(
Mixed.combineAlgebraically(op, toMixed(m1), toMixed(m2)), op,
toMixed(m1),
toMixed(m2),
) )
|> Mixed.T.toShape
}; };
}; };
let combinePointwise = let combinePointwise =
(~knownIntegralSumsFn=(_, _) => None, fn, t1: t, t2: t) => (~integralSumCachesFn: (float, float) => option(float) = (_, _) => None,
~integralCachesFn: (DistTypes.continuousShape, DistTypes.continuousShape) => option(DistTypes.continuousShape) = (_, _) => None,
fn,
t1: t,
t2: t) =>
switch (t1, t2) { switch (t1, t2) {
| (Continuous(m1), Continuous(m2)) => | (Continuous(m1), Continuous(m2)) =>
DistTypes.Continuous( DistTypes.Continuous(
Continuous.combinePointwise(~knownIntegralSumsFn, fn, m1, m2), Continuous.combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn, m1, m2),
) )
| (Discrete(m1), Discrete(m2)) => | (Discrete(m1), Discrete(m2)) =>
DistTypes.Discrete( DistTypes.Discrete(
Discrete.combinePointwise(~knownIntegralSumsFn, fn, m1, m2), Discrete.combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn, m1, m2),
) )
| (m1, m2) => | (m1, m2) =>
DistTypes.Mixed( DistTypes.Mixed(
Mixed.combinePointwise( Mixed.combinePointwise(
~knownIntegralSumsFn, ~integralSumCachesFn,
~integralCachesFn,
fn, fn,
toMixed(m1), toMixed(m1),
toMixed(m2), toMixed(m2),
@ -58,15 +70,6 @@ let combinePointwise =
) )
}; };
// TODO: implement these functions
let pdf = (f: float, t: t): float => {
0.0;
};
let inv = (f: float, t: t): float => {
0.0;
};
module T = module T =
Dist({ Dist({
type t = DistTypes.shape; type t = DistTypes.shape;
@ -84,7 +87,7 @@ module T =
let toContinuous = t => None; let toContinuous = t => None;
let toDiscrete = t => None; let toDiscrete = t => None;
let downsample = (~cache=None, i, t) => let downsample = (i, t) =>
fmap( fmap(
( (
Mixed.T.downsample(i), Mixed.T.downsample(i),
@ -105,8 +108,21 @@ module T =
); );
let toDiscreteProbabilityMassFraction = t => 0.0; let toDiscreteProbabilityMassFraction = t => 0.0;
let normalize = let normalize =
fmap((Mixed.T.normalize, Discrete.T.normalize, Continuous.T.normalize)); fmap((
Mixed.T.normalize,
Discrete.T.normalize,
Continuous.T.normalize
));
let updateIntegralCache = (integralCache, t: t): t =>
fmap((
Mixed.T.updateIntegralCache(integralCache),
Discrete.T.updateIntegralCache(integralCache),
Continuous.T.updateIntegralCache(integralCache),
), t);
let toContinuous = let toContinuous =
mapToAll(( mapToAll((
Mixed.T.toContinuous, Mixed.T.toContinuous,
@ -127,51 +143,39 @@ module T =
Continuous.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 minX = mapToAll((Mixed.T.minX, Discrete.T.minX, Continuous.T.minX));
let integral = (~cache) => let integral =
mapToAll(( mapToAll((
Mixed.T.Integral.get(~cache=None), Mixed.T.Integral.get,
Discrete.T.Integral.get(~cache=None), Discrete.T.Integral.get,
Continuous.T.Integral.get(~cache=None), Continuous.T.Integral.get,
)); ));
let integralEndY = (~cache) => let integralEndY =
mapToAll(( mapToAll((
Mixed.T.Integral.sum(~cache=None), Mixed.T.Integral.sum,
Discrete.T.Integral.sum(~cache), Discrete.T.Integral.sum,
Continuous.T.Integral.sum(~cache=None), Continuous.T.Integral.sum,
)); ));
let integralXtoY = (~cache, f) => { let integralXtoY = (f) => {
mapToAll(( mapToAll((
Mixed.T.Integral.xToY(~cache, f), Mixed.T.Integral.xToY(f),
Discrete.T.Integral.xToY(~cache, f), Discrete.T.Integral.xToY(f),
Continuous.T.Integral.xToY(~cache, f), Continuous.T.Integral.xToY(f),
)); ));
}; };
let integralYtoX = (~cache, f) => { let integralYtoX = (f) => {
mapToAll(( mapToAll((
Mixed.T.Integral.yToX(~cache, f), Mixed.T.Integral.yToX(f),
Discrete.T.Integral.yToX(~cache, f), Discrete.T.Integral.yToX(f),
Continuous.T.Integral.yToX(~cache, f), Continuous.T.Integral.yToX(f),
)); ));
}; };
let maxX = mapToAll((Mixed.T.maxX, Discrete.T.maxX, Continuous.T.maxX)); let maxX = mapToAll((Mixed.T.maxX, Discrete.T.maxX, Continuous.T.maxX));
let mapY = (~knownIntegralSumFn=previousIntegralSum => None, fn) => let mapY = (~integralSumCacheFn=previousIntegralSum => None, ~integralCacheFn=previousIntegral=>None, ~fn) =>
fmap(( fmap((
Mixed.T.mapY(~knownIntegralSumFn, fn), Mixed.T.mapY(~integralSumCacheFn, ~integralCacheFn, ~fn),
Discrete.T.mapY(~knownIntegralSumFn, fn), Discrete.T.mapY(~integralSumCacheFn, ~integralCacheFn, ~fn),
Continuous.T.mapY(~knownIntegralSumFn, fn), Continuous.T.mapY(~integralSumCacheFn, ~integralCacheFn, ~fn),
)); ));
let mean = (t: t): float => let mean = (t: t): float =>
@ -189,6 +193,14 @@ module T =
}; };
}); });
let pdf = (f: float, t: t) => {
let mixedPoint: DistTypes.mixedPoint = T.xToY(f, t);
mixedPoint.continuous +. mixedPoint.discrete;
};
let inv = T.Integral.yToX;
let cdf = T.Integral.xToY;
let doN = (n, fn) => { let doN = (n, fn) => {
let items = Belt.Array.make(n, 0.0); let items = Belt.Array.make(n, 0.0);
for (x in 0 to n - 1) { for (x in 0 to n - 1) {
@ -198,21 +210,24 @@ let doN = (n, fn) => {
items; items;
}; };
let sample = (cache, t: t): float => { let sample = (t: t): float => {
let randomItem = Random.float(1.); let randomItem = Random.float(1.);
let bar = T.Integral.yToX(~cache, randomItem, t); let bar = t |> T.Integral.yToX(randomItem);
bar; bar;
}; };
let sampleNRendered = (n, dist) => { let sampleNRendered = (n, dist) => {
let integralCache = T.Integral.get(~cache=None, dist); let integralCache = T.Integral.get(dist);
doN(n, () => sample(Some(integralCache), dist)); let distWithUpdatedIntegralCache = T.updateIntegralCache(Some(integralCache), dist);
doN(n, () => sample(distWithUpdatedIntegralCache));
}; };
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) => let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s): float =>
switch (distToFloatOp) { switch (distToFloatOp) {
| `Pdf(f) => pdf(f, s) | `Pdf(f) => pdf(f, s)
| `Cdf(f) => pdf(f, s)
| `Inv(f) => inv(f, s) | `Inv(f) => inv(f, s)
| `Sample => sample(None, s) | `Sample => sample(s)
| `Mean => T.mean(s) | `Mean => T.mean(s)
}; };

131
src/distPlus/distribution/XYShape.re
View File

@ -19,6 +19,7 @@ module T = {
let ys = (t: t) => t.ys; let ys = (t: t) => t.ys;
let length = (t: t) => E.A.length(t.xs); let length = (t: t) => E.A.length(t.xs);
let empty = {xs: [||], ys: [||]}; let empty = {xs: [||], ys: [||]};
let isEmpty = (t: t) => length(t) == 0;
let minX = (t: t) => t |> xs |> E.A.Sorted.min |> extImp; let minX = (t: t) => t |> xs |> E.A.Sorted.min |> extImp;
let maxX = (t: t) => t |> xs |> E.A.Sorted.max |> extImp; let maxX = (t: t) => t |> xs |> E.A.Sorted.max |> extImp;
let firstY = (t: t) => t |> ys |> E.A.first |> extImp; let firstY = (t: t) => t |> ys |> E.A.first |> extImp;
@ -32,6 +33,11 @@ module T = {
let accumulateYs = (fn, p: t) => { let accumulateYs = (fn, p: t) => {
fromArray((p.xs, E.A.accumulate(fn, p.ys))); fromArray((p.xs, E.A.accumulate(fn, p.ys)));
}; };
let concat = (t1: t, t2: t) => {
let cxs = Array.concat([t1.xs, t2.xs]);
let cys = Array.concat([t1.ys, t2.ys]);
{xs: cxs, ys: cys};
};
let fromZippedArray = (pairs: array((float, float))): t => let fromZippedArray = (pairs: array((float, float))): t =>
pairs |> Belt.Array.unzip |> fromArray; pairs |> Belt.Array.unzip |> fromArray;
let equallyDividedXs = (t: t, newLength) => { let equallyDividedXs = (t: t, newLength) => {
@ -137,6 +143,63 @@ module XtoY = {
}; };
n; n;
}; };
/* Returns a between-points-interpolating function that can be used with PointwiseCombination.combine.
Interpolation can either be stepwise (using the value on the left) or linear. Extrapolation can be `UseZero or `UseOutermostPoints. */
let continuousInterpolator = (interpolation: DistTypes.interpolationStrategy, extrapolation: DistTypes.extrapolationStrategy): interpolator => {
switch (interpolation, extrapolation) {
| (`Linear, `UseZero) => (t: T.t, leftIndex: int, x: float) => {
if (leftIndex < 0) {
0.0
} else if (leftIndex >= T.length(t) - 1) {
0.0
} else {
let x1 = t.xs[leftIndex];
let x2 = t.xs[leftIndex + 1];
let y1 = t.ys[leftIndex];
let y2 = t.ys[leftIndex + 1];
let fraction = (x -. x1) /. (x2 -. x1);
y1 *. (1. -. fraction) +. y2 *. fraction;
};
}
| (`Linear, `UseOutermostPoints) => (t: T.t, leftIndex: int, x: float) => {
if (leftIndex < 0) {
t.ys[0];
} else if (leftIndex >= T.length(t) - 1) {
t.ys[T.length(t) - 1]
} else {
let x1 = t.xs[leftIndex];
let x2 = t.xs[leftIndex + 1];
let y1 = t.ys[leftIndex];
let y2 = t.ys[leftIndex + 1];
let fraction = (x -. x1) /. (x2 -. x1);
y1 *. (1. -. fraction) +. y2 *. fraction;
};
}
| (`Stepwise, `UseZero) => (t: T.t, leftIndex: int, x: float) => {
if (leftIndex < 0) {
0.0
} else if (leftIndex >= T.length(t) - 1) {
0.0
} else {
t.ys[leftIndex];
}
}
| (`Stepwise, `UseOutermostPoints) => (t: T.t, leftIndex: int, x: float) => {
if (leftIndex < 0) {
t.ys[0];
} else if (leftIndex >= T.length(t) - 1) {
t.ys[T.length(t) - 1]
} else {
t.ys[leftIndex];
}
}
}
};
/* Returns a between-points-interpolating function that can be used with PointwiseCombination.combine.
For discrete distributions, the probability density between points is zero, so we just return zero here. */
let discreteInterpolator: interpolator = (t: T.t, leftIndex: int, x: float) => 0.0;
}; };
module XsConversion = { module XsConversion = {
@ -171,24 +234,22 @@ module Zipped = {
}; };
module PointwiseCombination = { module PointwiseCombination = {
type xsSelection =
| ALL_XS
| XS_EVENLY_DIVIDED(int);
let combineLinear = [%raw {| // : (float => float => float, T.t, T.t) => T.t // t1Interpolator and t2Interpolator are functions from XYShape.XtoY, e.g. linearBetweenPointsExtrapolateFlat.
let combine = [%raw {| // : (float => float => float, T.t, T.t, bool) => T.t
// This function combines two xyShapes by looping through both of them simultaneously. // This function combines two xyShapes by looping through both of them simultaneously.
// It always moves on to the next smallest x, whether that's in the first or second input's xs, // It always moves on to the next smallest x, whether that's in the first or second input's xs,
// and interpolates the value on the other side, thus accumulating xs and ys. // and interpolates the value on the other side, thus accumulating xs and ys.
// In this implementation (unlike in XtoY.linear above), values outside of a shape's xs are considered 0.0 (instead of firstY or lastY).
// This is written in raw JS because this can still be a bottleneck, and using refs for the i and j indices is quite painful. // This is written in raw JS because this can still be a bottleneck, and using refs for the i and j indices is quite painful.
function(fn, t1, t2) { function(fn, interpolator, t1, t2) {
let t1n = t1.xs.length; let t1n = t1.xs.length;
let t2n = t2.xs.length; let t2n = t2.xs.length;
let outX = []; let outX = [];
let outY = []; let outY = [];
let i = -1; let i = -1;
let j = -1; let j = -1;
while (i <= t1n - 1 && j <= t2n - 1) { while (i <= t1n - 1 && j <= t2n - 1) {
let x, ya, yb; let x, ya, yb;
if (j == t2n - 1 && i < t1n - 1 || if (j == t2n - 1 && i < t1n - 1 ||
@ -198,8 +259,7 @@ module PointwiseCombination = {
x = t1.xs[i]; x = t1.xs[i];
ya = t1.ys[i]; ya = t1.ys[i];
let bFraction = (x - (t2.xs[j] || x)) / ((t2.xs[j+1] || x) - (t2.xs[j] || 0)); yb = interpolator(t2, j, x);
yb = (t2.ys[j] || 0) * (1-bFraction) + (t2.ys[j+1] || 0) * bFraction;
} else if (i == t1n - 1 && j < t2n - 1 || } else if (i == t1n - 1 && j < t2n - 1 ||
t1.xs[i+1] > t2.xs[j+1]) { // if b has to catch up to a, or if a is already done t1.xs[i+1] > t2.xs[j+1]) { // if b has to catch up to a, or if a is already done
j++; j++;
@ -207,8 +267,7 @@ module PointwiseCombination = {
x = t2.xs[j]; x = t2.xs[j];
yb = t2.ys[j]; yb = t2.ys[j];
let aFraction = (x - (t1.xs[i] || x)) / ((t1.xs[i+1] || x) - (t1.xs[i] || 0)); ya = interpolator(t1, i, x);
ya = (t1.ys[i] || 0) * (1-aFraction) + (t1.ys[i+1] || 0) * aFraction;
} else if (i < t1n - 1 && j < t2n && t1.xs[i+1] === t2.xs[j+1]) { // if they happen to be equal, move both ahead } else if (i < t1n - 1 && j < t2n && t1.xs[i+1] === t2.xs[j+1]) { // if they happen to be equal, move both ahead
i++; i++;
j++; j++;
@ -227,15 +286,16 @@ module PointwiseCombination = {
outX.push(x); outX.push(x);
outY.push(fn(ya, yb)); outY.push(fn(ya, yb));
} }
return {xs: outX, ys: outY}; return {xs: outX, ys: outY};
} }
|}]; |}];
let combine = let combineEvenXs =
( (
~xToYSelection: (float, T.t) => 'a,
~xsSelection=ALL_XS,
~fn, ~fn,
~xToYSelection,
sampleCount,
t1: T.t, t1: T.t,
t2: T.t, t2: T.t,
) => { ) => {
@ -245,25 +305,15 @@ module PointwiseCombination = {
| (0, _) => t2 | (0, _) => t2
| (_, 0) => t1 | (_, 0) => t1
| (_, _) => { | (_, _) => {
let allXs = let allXs = Ts.equallyDividedXs([|t1, t2|], sampleCount);
switch (xsSelection) {
| ALL_XS => Ts.allXs([|t1, t2|])
| XS_EVENLY_DIVIDED(sampleCount) =>
Ts.equallyDividedXs([|t1, t2|], sampleCount)
};
let allYs = let allYs = allXs |> E.A.fmap(x => fn(xToYSelection(x, t1), xToYSelection(x, t2)));
allXs |> E.A.fmap(x => fn(xToYSelection(x, t1), xToYSelection(x, t2)));
T.fromArrays(allXs, allYs); T.fromArrays(allXs, allYs);
} }
} }
}; };
//let combineLinear = combine(~xToYSelection=XtoY.linear);
let combineStepwise = combine(~xToYSelection=XtoY.stepwiseIncremental);
let combineIfAtX = combine(~xToYSelection=XtoY.stepwiseIfAtX);
// TODO: I'd bet this is pretty slow. Maybe it would be faster to intersperse Xs and Ys separately. // TODO: I'd bet this is pretty slow. Maybe it would be faster to intersperse Xs and Ys separately.
let intersperse = (t1: T.t, t2: T.t) => { let intersperse = (t1: T.t, t2: T.t) => {
E.A.intersperse(T.zip(t1), T.zip(t2)) |> T.fromZippedArray; E.A.intersperse(T.zip(t1), T.zip(t2)) |> T.fromZippedArray;
@ -324,8 +374,31 @@ module Range = {
let derivative = mapYsBasedOnRanges(delta_y_over_delta_x); let derivative = mapYsBasedOnRanges(delta_y_over_delta_x);
// TODO: It would be nicer if this the diff didn't change the first element, and also maybe if there were a more elegant way of doing this. let stepwiseToLinear = ({xs, ys}: T.t): T.t => {
// adds points at the bottom of each step.
let length = E.A.length(xs);
let newXs: array(float) = Belt.Array.makeUninitializedUnsafe(2 * length);
let newYs: array(float) = Belt.Array.makeUninitializedUnsafe(2 * length);
Belt.Array.set(newXs, 0, xs[0] -. epsilon_float) |> ignore;
Belt.Array.set(newYs, 0, 0.) |> ignore;
Belt.Array.set(newXs, 1, xs[0]) |> ignore;
Belt.Array.set(newYs, 1, ys[0]) |> ignore;
for (i in 1 to E.A.length(xs) - 1) {
Belt.Array.set(newXs, i * 2, xs[i] -. epsilon_float) |> ignore;
Belt.Array.set(newYs, i * 2, ys[i-1]) |> ignore;
Belt.Array.set(newXs, i * 2 + 1, xs[i]) |> ignore;
Belt.Array.set(newYs, i * 2 + 1, ys[i]) |> ignore;
();
};
{xs: newXs, ys: newYs};
};
// TODO: I think this isn't needed by any functions anymore.
let stepsToContinuous = t => { let stepsToContinuous = t => {
// TODO: It would be nicer if this the diff didn't change the first element, and also maybe if there were a more elegant way of doing this.
let diff = T.xTotalRange(t) |> (r => r *. 0.00001); let diff = T.xTotalRange(t) |> (r => r *. 0.00001);
let items = let items =
switch (E.A.toRanges(Belt.Array.zip(t.xs, t.ys))) { switch (E.A.toRanges(Belt.Array.zip(t.xs, t.ys))) {
@ -356,10 +429,10 @@ let pointLogScore = (prediction, answer) =>
}; };
let logScorePoint = (sampleCount, t1, t2) => let logScorePoint = (sampleCount, t1, t2) =>
PointwiseCombination.combine( PointwiseCombination.combineEvenXs(
~xsSelection=XS_EVENLY_DIVIDED(sampleCount),
~xToYSelection=XtoY.linear,
~fn=pointLogScore, ~fn=pointLogScore,
~xToYSelection=XtoY.linear,
sampleCount,
t1, t1,
t2, t2,
) )

107
src/distPlus/expressionTree/ExpressionTreeEvaluator.re
View File

@ -20,61 +20,15 @@ module AlgebraicCombination = {
| _ => Ok(`AlgebraicCombination((operation, t1, t2))) | _ => Ok(`AlgebraicCombination((operation, t1, t2)))
}; };
let tryCombination = (n, algebraicOp, t1: node, t2: node) => { let combinationByRendering =
let sampleN = (evaluationParams, algebraicOp, t1: node, t2: node)
mapRenderable(Shape.sampleNRendered(n), SymbolicDist.T.sampleN(n)); : result(node, string) => {
switch (sampleN(t1), sampleN(t2)) { E.R.merge(
| (Some(a), Some(b)) => Render.ensureIsRenderedAndGetShape(evaluationParams, t1),
Some( Render.ensureIsRenderedAndGetShape(evaluationParams, t2),
Belt.Array.zip(a, b) )
|> E.A.fmap(((a, b)) => Operation.Algebraic.toFn(algebraicOp, a, b)), |> E.R.fmap(((a, b)) =>
) `RenderedDist(Shape.combineAlgebraically(algebraicOp, a, b))
| _ => None
};
};
let renderIfNotRendered = (params, t) =>
!renderable(t)
? switch (render(params, t)) {
| Ok(r) => Ok(r)
| Error(e) => Error(e)
}
: Ok(t);
let combineAsShapes =
(evaluationParams: evaluationParams, algebraicOp, t1: node, t2: node) => {
let i1 = renderIfNotRendered(evaluationParams, t1);
let i2 = renderIfNotRendered(evaluationParams, t2);
E.R.merge(i1, i2)
|> E.R.bind(
_,
((a, b)) => {
let samples =
tryCombination(
evaluationParams.samplingInputs.sampleCount,
algebraicOp,
a,
b,
);
let shape =
samples
|> E.O.fmap(
Samples.T.fromSamples(
~samplingInputs={
sampleCount:
Some(evaluationParams.samplingInputs.sampleCount),
outputXYPoints:
Some(evaluationParams.samplingInputs.outputXYPoints),
kernelWidth: evaluationParams.samplingInputs.kernelWidth,
},
),
)
|> E.O.bind(_, (r: RenderTypes.ShapeRenderer.Sampling.outputs) =>
r.shape
)
|> E.O.toResult("No response");
shape |> E.R.fmap(r => `Normalize(`RenderedDist(r)));
},
); );
}; };
@ -92,7 +46,7 @@ module AlgebraicCombination = {
_, _,
fun fun
| `SymbolicDist(d) as t => Ok(t) | `SymbolicDist(d) as t => Ok(t)
| _ => combineAsShapes(evaluationParams, algebraicOp, t1, t2), | _ => combinationByRendering(evaluationParams, algebraicOp, t1, t2),
); );
}; };
@ -101,16 +55,18 @@ module VerticalScaling = {
(evaluationParams: evaluationParams, scaleOp, t, scaleBy) => { (evaluationParams: evaluationParams, scaleOp, t, scaleBy) => {
// scaleBy has to be a single float, otherwise we'll return an error. // scaleBy has to be a single float, otherwise we'll return an error.
let fn = Operation.Scale.toFn(scaleOp); let fn = Operation.Scale.toFn(scaleOp);
let knownIntegralSumFn = Operation.Scale.toKnownIntegralSumFn(scaleOp); let integralSumCacheFn = Operation.Scale.toIntegralSumCacheFn(scaleOp);
let renderedShape = render(evaluationParams, t); let integralCacheFn = Operation.Scale.toIntegralCacheFn(scaleOp);
let renderedShape = Render.render(evaluationParams, t);
switch (renderedShape, scaleBy) { switch (renderedShape, scaleBy) {
| (Ok(`RenderedDist(rs)), `SymbolicDist(`Float(sm))) => | (Ok(`RenderedDist(rs)), `SymbolicDist(`Float(sm))) =>
Ok( Ok(
`RenderedDist( `RenderedDist(
Shape.T.mapY( Shape.T.mapY(
~knownIntegralSumFn=knownIntegralSumFn(sm), ~integralSumCacheFn=integralSumCacheFn(sm),
fn(sm), ~integralCacheFn=integralCacheFn(sm),
~fn=fn(sm),
rs, rs,
), ),
), ),
@ -122,13 +78,23 @@ module VerticalScaling = {
}; };
module PointwiseCombination = { module PointwiseCombination = {
let pointwiseAdd = (evaluationParams: evaluationParams, t1, t2) => { let pointwiseAdd = (evaluationParams: evaluationParams, t1: t, t2: t) => {
switch (render(evaluationParams, t1), render(evaluationParams, t2)) { switch (Render.render(evaluationParams, t1), Render.render(evaluationParams, t2)) {
| (Ok(`RenderedDist(rs1)), Ok(`RenderedDist(rs2))) => | (Ok(`RenderedDist(rs1)), Ok(`RenderedDist(rs2))) =>
Ok( Ok(
`RenderedDist( `RenderedDist(
Shape.combinePointwise( Shape.combinePointwise(
~knownIntegralSumsFn=(a, b) => Some(a +. b), ~integralSumCachesFn=(a, b) => Some(a +. b),
~integralCachesFn=
(a, b) =>
Some(
Continuous.combinePointwise(
~distributionType=`CDF,
(+.),
a,
b,
),
),
(+.), (+.),
rs1, rs1,
rs2, rs2,
@ -141,7 +107,7 @@ module PointwiseCombination = {
}; };
}; };
let pointwiseMultiply = (evaluationParams: evaluationParams, t1, t2) => { let pointwiseMultiply = (evaluationParams: evaluationParams, t1: t, t2: t) => {
// TODO: construct a function that we can easily sample from, to construct // TODO: construct a function that we can easily sample from, to construct
// a RenderedDist. 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( Error(
@ -150,7 +116,12 @@ module PointwiseCombination = {
}; };
let operationToLeaf = let operationToLeaf =
(evaluationParams: evaluationParams, pointwiseOp, t1, t2) => { (
evaluationParams: evaluationParams,
pointwiseOp: pointwiseOperation,
t1: t,
t2: t,
) => {
switch (pointwiseOp) { switch (pointwiseOp) {
| `Add => pointwiseAdd(evaluationParams, t1, t2) | `Add => pointwiseAdd(evaluationParams, t1, t2)
| `Multiply => pointwiseMultiply(evaluationParams, t1, t2) | `Multiply => pointwiseMultiply(evaluationParams, t1, t2)
@ -163,7 +134,7 @@ module Truncate = {
switch (leftCutoff, rightCutoff, t) { switch (leftCutoff, rightCutoff, t) {
| (None, None, t) => `Solution(t) | (None, None, t) => `Solution(t)
| (Some(lc), Some(rc), t) when lc > rc => | (Some(lc), Some(rc), t) when lc > rc =>
`Error("Left truncation bound must be smaller than right bound.") `Error("Left truncation bound must be smaller than right truncation bound.")
| (lc, rc, `SymbolicDist(`Uniform(u))) => | (lc, rc, `SymbolicDist(`Uniform(u))) =>
`Solution( `Solution(
`SymbolicDist(`Uniform(SymbolicDist.Uniform.truncate(lc, rc, u))), `SymbolicDist(`Uniform(SymbolicDist.Uniform.truncate(lc, rc, u))),
@ -174,9 +145,9 @@ module Truncate = {
let truncateAsShape = let truncateAsShape =
(evaluationParams: evaluationParams, leftCutoff, rightCutoff, t) => { (evaluationParams: evaluationParams, leftCutoff, rightCutoff, t) => {
// TODO: use named args in renderToShape; if we're lucky we can at least get the tail // TODO: use named args for xMin/xMax in renderToShape; if we're lucky we can at least get the tail
// of a distribution we otherwise wouldn't get at all // of a distribution we otherwise wouldn't get at all
switch (render(evaluationParams, t)) { switch (Render.ensureIsRendered(evaluationParams, t)) {
| Ok(`RenderedDist(rs)) => | Ok(`RenderedDist(rs)) =>
Ok(`RenderedDist(Shape.T.truncate(leftCutoff, rightCutoff, rs))) Ok(`RenderedDist(Shape.T.truncate(leftCutoff, rightCutoff, rs)))
| Error(e) => Error(e) | Error(e) => Error(e)

52
src/distPlus/expressionTree/ExpressionTypes.re
View File

@ -1,7 +1,13 @@
type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide]; type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
type pointwiseOperation = [ | `Add | `Multiply]; type pointwiseOperation = [ | `Add | `Multiply];
type scaleOperation = [ | `Multiply | `Exponentiate | `Log]; type scaleOperation = [ | `Multiply | `Exponentiate | `Log];
type distToFloatOperation = [ | `Pdf(float) | `Inv(float) | `Mean | `Sample]; type distToFloatOperation = [
| `Pdf(float)
| `Cdf(float)
| `Inv(float)
| `Mean
| `Sample
];
module ExpressionTree = { module ExpressionTree = {
type node = [ type node = [
@ -31,26 +37,42 @@ module ExpressionTree = {
let evaluateNode = (evaluationParams: evaluationParams) => let evaluateNode = (evaluationParams: evaluationParams) =>
evaluationParams.evaluateNode(evaluationParams); evaluationParams.evaluateNode(evaluationParams);
let render = (evaluationParams: evaluationParams, r) =>
evaluateNode(evaluationParams, `Render(r));
let evaluateAndRetry = (evaluationParams, fn, node) => let evaluateAndRetry = (evaluationParams, fn, node) =>
node node
|> evaluationParams.evaluateNode(evaluationParams) |> evaluationParams.evaluateNode(evaluationParams)
|> E.R.bind(_, fn(evaluationParams)); |> E.R.bind(_, fn(evaluationParams));
let renderable = module Render = {
fun type t = node;
| `SymbolicDist(_) => true
| `RenderedDist(_) => true let render = (evaluationParams: evaluationParams, r) =>
| _ => false; `Render(r) |> evaluateNode(evaluationParams);
let ensureIsRendered = (params, t) =>
switch (t) {
| `RenderedDist(_) => Ok(t)
| _ =>
switch (render(params, t)) {
| Ok(`RenderedDist(r)) => Ok(`RenderedDist(r))
| Ok(_) => Error("Did not render as requested")
| Error(e) => Error(e)
}
};
let ensureIsRenderedAndGetShape = (params, t) =>
switch (ensureIsRendered(params, t)) {
| Ok(`RenderedDist(r)) => Ok(r)
| Ok(_) => Error("Did not render as requested")
| Error(e) => Error(e)
};
let getShape = (item: node) =>
switch (item) {
| `RenderedDist(r) => Some(r)
| _ => None
};
};
let mapRenderable = (renderedFn, symFn, item: node) =>
switch (item) {
| `SymbolicDist(s) => Some(symFn(s))
| `RenderedDist(r) => Some(renderedFn(r))
| _ => None
};
}; };
type simplificationResult = [ type simplificationResult = [

30
src/distPlus/expressionTree/MathJsParser.re
View File

@ -237,7 +237,8 @@ module MathAdtToDistDst = {
args: array(result(ExpressionTypes.ExpressionTree.node, string)), args: array(result(ExpressionTypes.ExpressionTree.node, string)),
) => { ) => {
let toOkAlgebraic = r => Ok(`AlgebraicCombination(r)); let toOkAlgebraic = r => Ok(`AlgebraicCombination(r));
let toOkTrunctate = r => Ok(`Truncate(r)); let toOkTruncate = r => Ok(`Truncate(r));
let toOkFloatFromDist = r => Ok(`FloatFromDist(r))
switch (name, args) { switch (name, args) {
| ("add", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Add, l, r)) | ("add", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Add, l, r))
| ("add", _) => Error("Addition needs two operands") | ("add", _) => Error("Addition needs two operands")
@ -249,11 +250,11 @@ module MathAdtToDistDst = {
| ("divide", _) => Error("Division needs two operands") | ("divide", _) => Error("Division needs two operands")
| ("pow", _) => Error("Exponentiation is not yet supported.") | ("pow", _) => Error("Exponentiation is not yet supported.")
| ("leftTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(lc)))|]) => | ("leftTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(lc)))|]) =>
toOkTrunctate((Some(lc), None, d)) toOkTruncate((Some(lc), None, d))
| ("leftTruncate", _) => | ("leftTruncate", _) =>
Error("leftTruncate needs two arguments: the expression and the cutoff") Error("leftTruncate needs two arguments: the expression and the cutoff")
| ("rightTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(rc)))|]) => | ("rightTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(rc)))|]) =>
toOkTrunctate((None, Some(rc), d)) toOkTruncate((None, Some(rc), d))
| ("rightTruncate", _) => | ("rightTruncate", _) =>
Error( Error(
"rightTruncate needs two arguments: the expression and the cutoff", "rightTruncate needs two arguments: the expression and the cutoff",
@ -266,9 +267,19 @@ module MathAdtToDistDst = {
Ok(`SymbolicDist(`Float(rc))), Ok(`SymbolicDist(`Float(rc))),
|], |],
) => ) =>
toOkTrunctate((Some(lc), Some(rc), d)) toOkTruncate((Some(lc), Some(rc), d))
| ("truncate", _) => | ("truncate", _) =>
Error("truncate needs three arguments: the expression and both cutoffs") Error("truncate needs three arguments: the expression and both cutoffs")
| ("pdf", [|Ok(d), Ok(`SymbolicDist(`Float(v)))|]) =>
toOkFloatFromDist((`Pdf(v), d))
| ("cdf", [|Ok(d), Ok(`SymbolicDist(`Float(v)))|]) =>
toOkFloatFromDist((`Cdf(v), d))
| ("inv", [|Ok(d), Ok(`SymbolicDist(`Float(v)))|]) =>
toOkFloatFromDist((`Inv(v), d))
| ("mean", [|Ok(d)|]) =>
toOkFloatFromDist((`Mean, d))
| ("sample", [|Ok(d)|]) =>
toOkFloatFromDist((`Sample, d))
| _ => Error("This type not currently supported") | _ => Error("This type not currently supported")
}; };
}; };
@ -316,11 +327,12 @@ module MathAdtToDistDst = {
| "pow" | "pow"
| "leftTruncate" | "leftTruncate"
| "rightTruncate" | "rightTruncate"
| "truncate" => operationParser(name, parseArgs()) | "truncate"
| "mean" as n | "mean"
| "inv" as n | "inv"
| "sample" as n | "sample"
| "pdf" as n | "cdf"
| "pdf" => operationParser(name, parseArgs())
| n => Error(n ++ "(...) is not currently supported") | n => Error(n ++ "(...) is not currently supported")
}; };
}; };

9
src/distPlus/expressionTree/Operation.re
View File

@ -41,6 +41,7 @@ module DistToFloat = {
let format = (operation, value) => let format = (operation, value) =>
switch (operation) { switch (operation) {
| `Cdf(f) => {j|cdf(x=$f,$value)|j}
| `Pdf(f) => {j|pdf(x=$f,$value)|j} | `Pdf(f) => {j|pdf(x=$f,$value)|j}
| `Inv(f) => {j|inv(x=$f,$value)|j} | `Inv(f) => {j|inv(x=$f,$value)|j}
| `Sample => "sample($value)" | `Sample => "sample($value)"
@ -63,11 +64,17 @@ module Scale = {
| `Log => {j|verticalLog($value, $scaleBy) |j} | `Log => {j|verticalLog($value, $scaleBy) |j}
}; };
let toKnownIntegralSumFn = let toIntegralSumCacheFn =
fun fun
| `Multiply => ((a, b) => Some(a *. b)) | `Multiply => ((a, b) => Some(a *. b))
| `Exponentiate => ((_, _) => None) | `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None); | `Log => ((_, _) => None);
let toIntegralCacheFn =
fun
| `Multiply => ((a, b) => None) // TODO: this could probably just be multiplied out (using Continuous.scaleBy)
| `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None);
}; };
module T = { module T = {

80
src/distPlus/expressionTree/SamplingDistribution.re Normal file
View File

@ -0,0 +1,80 @@
open ExpressionTypes.ExpressionTree;
let isSamplingDistribution: node => bool =
fun
| `SymbolicDist(_) => true
| `RenderedDist(_) => true
| _ => false;
let renderIfIsNotSamplingDistribution = (params, t) =>
!isSamplingDistribution(t)
? switch (Render.render(params, t)) {
| Ok(r) => Ok(r)
| Error(e) => Error(e)
}
: Ok(t);
let map = (~renderedDistFn, ~symbolicDistFn, node: node) =>
node
|> (
fun
| `RenderedDist(r) => Some(renderedDistFn(r))
| `SymbolicDist(s) => Some(symbolicDistFn(s))
| _ => None
);
let sampleN = n =>
map(
~renderedDistFn=Shape.sampleNRendered(n),
~symbolicDistFn=SymbolicDist.T.sampleN(n),
);
let getCombinationSamples = (n, algebraicOp, t1: node, t2: node) => {
switch (sampleN(n, t1), sampleN(n, t2)) {
| (Some(a), Some(b)) =>
Some(
Belt.Array.zip(a, b)
|> E.A.fmap(((a, b)) => Operation.Algebraic.toFn(algebraicOp, a, b)),
)
| _ => None
};
};
let combineShapesUsingSampling =
(evaluationParams: evaluationParams, algebraicOp, t1: node, t2: node) => {
let i1 = renderIfIsNotSamplingDistribution(evaluationParams, t1);
let i2 = renderIfIsNotSamplingDistribution(evaluationParams, t2);
E.R.merge(i1, i2)
|> E.R.bind(
_,
((a, b)) => {
let samples =
getCombinationSamples(
evaluationParams.samplingInputs.sampleCount,
algebraicOp,
a,
b,
);
// todo: This bottom part should probably be somewhere else.
let shape =
samples
|> E.O.fmap(
Samples.T.fromSamples(
~samplingInputs={
sampleCount:
Some(evaluationParams.samplingInputs.sampleCount),
outputXYPoints:
Some(evaluationParams.samplingInputs.outputXYPoints),
kernelWidth: evaluationParams.samplingInputs.kernelWidth,
},
),
)
|> E.O.bind(_, (r: RenderTypes.ShapeRenderer.Sampling.outputs) =>
r.shape
)
|> E.O.toResult("No response");
shape |> E.R.fmap(r => `Normalize(`RenderedDist(r)));
},
);
};

4
src/distPlus/renderers/samplesRenderer/Samples.re
View File

@ -120,7 +120,7 @@ module T = {
|> E.FloatFloatMap.fmap(r => r /. length) |> E.FloatFloatMap.fmap(r => r /. length)
|> E.FloatFloatMap.toArray |> E.FloatFloatMap.toArray
|> XYShape.T.fromZippedArray |> XYShape.T.fromZippedArray
|> Discrete.make(_, None); |> Discrete.make;
let pdf = let pdf =
continuousPart |> E.A.length > 5 continuousPart |> E.A.length > 5
@ -150,7 +150,7 @@ module T = {
~outputXYPoints=samplingInputs.outputXYPoints, ~outputXYPoints=samplingInputs.outputXYPoints,
formatUnitWidth(usedUnitWidth), formatUnitWidth(usedUnitWidth),
) )
|> Continuous.make(`Linear, _, None) |> Continuous.make
|> (r => Some((r, foo))); |> (r => Some((r, foo)));
} }
: None; : None;

29
src/distPlus/symbolic/SymbolicDist.re
View File

@ -3,6 +3,7 @@ open SymbolicTypes;
module Exponential = { module Exponential = {
type t = exponential; type t = exponential;
let pdf = (x, t: t) => Jstat.exponential##pdf(x, t.rate); let pdf = (x, t: t) => Jstat.exponential##pdf(x, t.rate);
let cdf = (x, t: t) => Jstat.exponential##cdf(x, t.rate);
let inv = (p, t: t) => Jstat.exponential##inv(p, t.rate); let inv = (p, t: t) => Jstat.exponential##inv(p, t.rate);
let sample = (t: t) => Jstat.exponential##sample(t.rate); let sample = (t: t) => Jstat.exponential##sample(t.rate);
let mean = (t: t) => Ok(Jstat.exponential##mean(t.rate)); let mean = (t: t) => Ok(Jstat.exponential##mean(t.rate));
@ -12,6 +13,7 @@ module Exponential = {
module Cauchy = { module Cauchy = {
type t = cauchy; type t = cauchy;
let pdf = (x, t: t) => Jstat.cauchy##pdf(x, t.local, t.scale); let pdf = (x, t: t) => Jstat.cauchy##pdf(x, t.local, t.scale);
let cdf = (x, t: t) => Jstat.cauchy##cdf(x, t.local, t.scale);
let inv = (p, t: t) => Jstat.cauchy##inv(p, t.local, t.scale); let inv = (p, t: t) => Jstat.cauchy##inv(p, t.local, t.scale);
let sample = (t: t) => Jstat.cauchy##sample(t.local, t.scale); let sample = (t: t) => Jstat.cauchy##sample(t.local, t.scale);
let mean = (_: t) => Error("Cauchy distributions have no mean value."); let mean = (_: t) => Error("Cauchy distributions have no mean value.");
@ -21,6 +23,7 @@ module Cauchy = {
module Triangular = { module Triangular = {
type t = triangular; type t = triangular;
let pdf = (x, t: t) => Jstat.triangular##pdf(x, t.low, t.high, t.medium); let pdf = (x, t: t) => Jstat.triangular##pdf(x, t.low, t.high, t.medium);
let cdf = (x, t: t) => Jstat.triangular##cdf(x, t.low, t.high, t.medium);
let inv = (p, t: t) => Jstat.triangular##inv(p, t.low, t.high, t.medium); let inv = (p, t: t) => Jstat.triangular##inv(p, t.low, t.high, t.medium);
let sample = (t: t) => Jstat.triangular##sample(t.low, t.high, t.medium); let sample = (t: t) => Jstat.triangular##sample(t.low, t.high, t.medium);
let mean = (t: t) => Ok(Jstat.triangular##mean(t.low, t.high, t.medium)); let mean = (t: t) => Ok(Jstat.triangular##mean(t.low, t.high, t.medium));
@ -30,6 +33,7 @@ module Triangular = {
module Normal = { module Normal = {
type t = normal; type t = normal;
let pdf = (x, t: t) => Jstat.normal##pdf(x, t.mean, t.stdev); let pdf = (x, t: t) => Jstat.normal##pdf(x, t.mean, t.stdev);
let cdf = (x, t: t) => Jstat.normal##cdf(x, t.mean, t.stdev);
let from90PercentCI = (low, high) => { let from90PercentCI = (low, high) => {
let mean = E.A.Floats.mean([|low, high|]); let mean = E.A.Floats.mean([|low, high|]);
@ -72,6 +76,7 @@ module Normal = {
module Beta = { module Beta = {
type t = beta; type t = beta;
let pdf = (x, t: t) => Jstat.beta##pdf(x, t.alpha, t.beta); let pdf = (x, t: t) => Jstat.beta##pdf(x, t.alpha, t.beta);
let cdf = (x, t: t) => Jstat.beta##cdf(x, t.alpha, t.beta);
let inv = (p, t: t) => Jstat.beta##inv(p, t.alpha, t.beta); let inv = (p, t: t) => Jstat.beta##inv(p, t.alpha, t.beta);
let sample = (t: t) => Jstat.beta##sample(t.alpha, t.beta); let sample = (t: t) => Jstat.beta##sample(t.alpha, t.beta);
let mean = (t: t) => Ok(Jstat.beta##mean(t.alpha, t.beta)); let mean = (t: t) => Ok(Jstat.beta##mean(t.alpha, t.beta));
@ -81,6 +86,7 @@ module Beta = {
module Lognormal = { module Lognormal = {
type t = lognormal; type t = lognormal;
let pdf = (x, t: t) => Jstat.lognormal##pdf(x, t.mu, t.sigma); let pdf = (x, t: t) => Jstat.lognormal##pdf(x, t.mu, t.sigma);
let cdf = (x, t: t) => Jstat.lognormal##cdf(x, t.mu, t.sigma);
let inv = (p, t: t) => Jstat.lognormal##inv(p, t.mu, t.sigma); let inv = (p, t: t) => Jstat.lognormal##inv(p, t.mu, t.sigma);
let mean = (t: t) => Ok(Jstat.lognormal##mean(t.mu, t.sigma)); let mean = (t: t) => Ok(Jstat.lognormal##mean(t.mu, t.sigma));
let sample = (t: t) => Jstat.lognormal##sample(t.mu, t.sigma); let sample = (t: t) => Jstat.lognormal##sample(t.mu, t.sigma);
@ -126,6 +132,7 @@ module Lognormal = {
module Uniform = { module Uniform = {
type t = uniform; type t = uniform;
let pdf = (x, t: t) => Jstat.uniform##pdf(x, t.low, t.high); let pdf = (x, t: t) => Jstat.uniform##pdf(x, t.low, t.high);
let cdf = (x, t: t) => Jstat.uniform##cdf(x, t.low, t.high);
let inv = (p, t: t) => Jstat.uniform##inv(p, t.low, t.high); let inv = (p, t: t) => Jstat.uniform##inv(p, t.low, t.high);
let sample = (t: t) => Jstat.uniform##sample(t.low, t.high); let sample = (t: t) => Jstat.uniform##sample(t.low, t.high);
let mean = (t: t) => Ok(Jstat.uniform##mean(t.low, t.high)); let mean = (t: t) => Ok(Jstat.uniform##mean(t.low, t.high));
@ -140,6 +147,7 @@ module Uniform = {
module Float = { module Float = {
type t = float; type t = float;
let pdf = (x, t: t) => x == t ? 1.0 : 0.0; let pdf = (x, t: t) => x == t ? 1.0 : 0.0;
let cdf = (x, t: t) => x >= t ? 1.0 : 0.0;
let inv = (p, t: t) => p < t ? 0.0 : 1.0; let inv = (p, t: t) => p < t ? 0.0 : 1.0;
let mean = (t: t) => Ok(t); let mean = (t: t) => Ok(t);
let sample = (t: t) => t; let sample = (t: t) => t;
@ -162,6 +170,18 @@ module T = {
| `Float(n) => Float.pdf(x, n) | `Float(n) => Float.pdf(x, n)
}; };
let cdf = (x, dist) =>
switch (dist) {
| `Normal(n) => Normal.cdf(x, n)
| `Triangular(n) => Triangular.cdf(x, n)
| `Exponential(n) => Exponential.cdf(x, n)
| `Cauchy(n) => Cauchy.cdf(x, n)
| `Lognormal(n) => Lognormal.cdf(x, n)
| `Uniform(n) => Uniform.cdf(x, n)
| `Beta(n) => Beta.cdf(x, n)
| `Float(n) => Float.cdf(x, n)
};
let inv = (x, dist) => let inv = (x, dist) =>
switch (dist) { switch (dist) {
| `Normal(n) => Normal.inv(x, n) | `Normal(n) => Normal.inv(x, n)
@ -244,6 +264,7 @@ module T = {
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) => let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
switch (distToFloatOp) { switch (distToFloatOp) {
| `Cdf(f) => Ok(cdf(f, s))
| `Pdf(f) => Ok(pdf(f, s)) | `Pdf(f) => Ok(pdf(f, s))
| `Inv(f) => Ok(inv(f, s)) | `Inv(f) => Ok(inv(f, s))
| `Sample => Ok(sample(s)) | `Sample => Ok(sample(s))
@ -295,10 +316,14 @@ module T = {
let toShape = (sampleCount, d: symbolicDist): DistTypes.shape => let toShape = (sampleCount, d: symbolicDist): DistTypes.shape =>
switch (d) { switch (d) {
| `Float(v) => | `Float(v) =>
Discrete(Discrete.make({xs: [|v|], ys: [|1.0|]}, Some(1.0))) Discrete(
Discrete.make(~integralSumCache=Some(1.0), {xs: [|v|], ys: [|1.0|]}),
)
| _ => | _ =>
let xs = interpolateXs(~xSelection=`ByWeight, d, sampleCount); let xs = interpolateXs(~xSelection=`ByWeight, d, sampleCount);
let ys = xs |> E.A.fmap(x => pdf(x, d)); let ys = xs |> E.A.fmap(x => pdf(x, d));
Continuous(Continuous.make(`Linear, {xs, ys}, Some(1.0))); Continuous(
Continuous.make(~integralSumCache=Some(1.0), {xs, ys}),
);
}; };
}; };