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Merge pull request #55 from foretold-app/ozzie-refactor

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SymbolicDist: the big refactor [Version 2]
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Ozzie Gooen 2020-07-06 12:41:02 +01:00 committed by GitHub
commit 93f3e12adc
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GPG Key ID: 4AEE18F83AFDEB23
33 changed files with 2290 additions and 1021 deletions
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92
__tests__/Distributions__Test.re
View File

@ -24,7 +24,7 @@ let makeTestCloseEquality = (~only=false, str, item1, item2, ~digits) =>
describe("Shape", () => {
describe("Continuous", () => {
open Distributions.Continuous;
let continuous = make(`Linear, shape);
let continuous = make(`Linear, shape, None);
makeTest("minX", T.minX(continuous), 1.0);
makeTest("maxX", T.maxX(continuous), 8.0);
makeTest(
@ -57,7 +57,7 @@ describe("Shape", () => {
);
});
describe("when Stepwise", () => {
let continuous = make(`Stepwise, shape);
let continuous = make(`Stepwise, shape, None);
makeTest(
"at 4.0",
T.xToY(4., continuous),
@ -89,7 +89,7 @@ describe("Shape", () => {
"toLinear",
{
let continuous =
make(`Stepwise, {xs: [|1., 4., 8.|], ys: [|0.1, 5., 1.0|]});
make(`Stepwise, {xs: [|1., 4., 8.|], ys: [|0.1, 5., 1.0|]}, None);
continuous |> toLinear |> E.O.fmap(getShape);
},
Some({
@ -100,7 +100,7 @@ describe("Shape", () => {
makeTest(
"toLinear",
{
let continuous = make(`Stepwise, {xs: [|0.0|], ys: [|0.3|]});
let continuous = make(`Stepwise, {xs: [|0.0|], ys: [|0.3|]}, None);
continuous |> toLinear |> E.O.fmap(getShape);
},
Some({xs: [|0.0|], ys: [|0.3|]}),
@ -123,7 +123,7 @@ describe("Shape", () => {
makeTest(
"integralEndY",
continuous
|> T.scaleToIntegralSum(~intendedSum=1.0)
|> T.normalize //scaleToIntegralSum(~intendedSum=1.0)
|> T.Integral.sum(~cache=None),
1.0,
);
@ -135,12 +135,12 @@ describe("Shape", () => {
xs: [|1., 4., 8.|],
ys: [|0.3, 0.5, 0.2|],
};
let discrete = shape;
let discrete = make(shape, None);
makeTest("minX", T.minX(discrete), 1.0);
makeTest("maxX", T.maxX(discrete), 8.0);
makeTest(
"mapY",
T.mapY(r => r *. 2.0, discrete) |> (r => r.ys),
T.mapY(r => r *. 2.0, discrete) |> (r => getShape(r).ys),
[|0.6, 1.0, 0.4|],
);
makeTest(
@ -160,19 +160,22 @@ describe("Shape", () => {
);
makeTest(
"scaleBy",
T.scaleBy(~scale=4.0, discrete),
{xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]},
scaleBy(~scale=4.0, discrete),
make({xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]}, None),
);
makeTest(
"scaleToIntegralSum",
T.scaleToIntegralSum(~intendedSum=4.0, discrete),
{xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]},
"normalize, then scale by 4.0",
discrete
|> T.normalize
|> scaleBy(~scale=4.0),
make({xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]}, None),
);
makeTest(
"scaleToIntegralSum: back and forth",
discrete
|> T.scaleToIntegralSum(~intendedSum=4.0)
|> T.scaleToIntegralSum(~intendedSum=1.0),
|> T.normalize
|> scaleBy(~scale=4.0)
|> T.normalize,
discrete,
);
makeTest(
@ -181,12 +184,13 @@ describe("Shape", () => {
Distributions.Continuous.make(
`Stepwise,
{xs: [|1., 4., 8.|], ys: [|0.3, 0.8, 1.0|]},
None
),
);
makeTest(
"integral with 1 element",
T.Integral.get(~cache=None, {xs: [|0.0|], ys: [|1.0|]}),
Distributions.Continuous.make(`Stepwise, {xs: [|0.0|], ys: [|1.0|]}),
T.Integral.get(~cache=None, Distributions.Discrete.make({xs: [|0.0|], ys: [|1.0|]}, None)),
Distributions.Continuous.make(`Stepwise, {xs: [|0.0|], ys: [|1.0|]}, None),
);
makeTest(
"integralXToY",
@ -205,27 +209,22 @@ describe("Shape", () => {
describe("Mixed", () => {
open Distributions.Mixed;
let discrete: DistTypes.xyShape = {
let discreteShape: DistTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|0.3, 0.5, 0.2|],
};
let discrete = Distributions.Discrete.make(discreteShape, None);
let continuous =
Distributions.Continuous.make(
`Linear,
{xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
None
)
|> Distributions.Continuous.T.scaleToIntegralSum(~intendedSum=1.0);
let mixed =
MixedShapeBuilder.build(
|> Distributions.Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
let mixed = Distributions.Mixed.make(
~continuous,
~discrete,
~assumptions={
continuous: ADDS_TO_CORRECT_PROBABILITY,
discrete: ADDS_TO_CORRECT_PROBABILITY,
discreteProbabilityMass: Some(0.5),
},
)
|> E.O.toExn("");
);
makeTest("minX", T.minX(mixed), 1.0);
makeTest("maxX", T.maxX(mixed), 14.0);
makeTest(
@ -243,9 +242,9 @@ describe("Shape", () => {
0.24775224775224775,
|],
},
None
),
~discrete={xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]},
~discreteProbabilityMassFraction=0.5,
~discrete=Distributions.Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None)
),
);
makeTest(
@ -266,7 +265,7 @@ describe("Shape", () => {
makeTest("integralEndY", T.Integral.sum(~cache=None, mixed), 1.0);
makeTest(
"scaleBy",
T.scaleBy(~scale=2.0, mixed),
Distributions.Mixed.scaleBy(~scale=2.0, mixed),
Distributions.Mixed.make(
~continuous=
Distributions.Continuous.make(
@ -279,9 +278,9 @@ describe("Shape", () => {
0.24775224775224775,
|],
},
None
),
~discrete={xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]},
~discreteProbabilityMassFraction=0.5,
~discrete=Distributions.Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None),
),
);
makeTest(
@ -302,34 +301,31 @@ describe("Shape", () => {
0.6913122927072927,
1.0,
|],
},
},
None,
),
);
});
describe("Distplus", () => {
open Distributions.DistPlus;
let discrete: DistTypes.xyShape = {
let discreteShape: DistTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|0.3, 0.5, 0.2|],
};
let discrete = Distributions.Discrete.make(discreteShape, None);
let continuous =
Distributions.Continuous.make(
`Linear,
{xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
None
)
|> Distributions.Continuous.T.scaleToIntegralSum(~intendedSum=1.0);
|> Distributions.Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
let mixed =
MixedShapeBuilder.build(
Distributions.Mixed.make(
~continuous,
~discrete,
~assumptions={
continuous: ADDS_TO_CORRECT_PROBABILITY,
discrete: ADDS_TO_CORRECT_PROBABILITY,
discreteProbabilityMass: Some(0.5),
},
)
|> E.O.toExn("");
);
let distPlus =
Distributions.DistPlus.make(
~shape=Mixed(mixed),
@ -374,6 +370,7 @@ describe("Shape", () => {
1.0,
|],
},
None,
),
),
);
@ -385,11 +382,10 @@ describe("Shape", () => {
let variance = stdev ** 2.0;
let numSamples = 10000;
open Distributions.Shape;
let normal: SymbolicDist.dist = `Normal({mean, stdev});
let normalShape = SymbolicDist.GenericSimple.toShape(normal, numSamples);
let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
let normalShape = ExpressionTree.toShape(numSamples, `SymbolicDist(normal));
let lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
let lognormalShape =
SymbolicDist.GenericSimple.toShape(lognormal, numSamples);
let lognormalShape = ExpressionTree.toShape(numSamples, `SymbolicDist(lognormal));
makeTestCloseEquality(
"Mean of a normal",
@ -416,4 +412,4 @@ describe("Shape", () => {
~digits=0,
);
});
});
});

2
showcase/Entries.re
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@ -1 +1 @@
let entries = EntryTypes.[Continuous.entry];
let entries = EntryTypes.[Continuous.entry,ExpressionTreeExamples.entry];

2
showcase/entries/Continuous.re
View File

@ -84,4 +84,4 @@ let distributions = () =>
</div>
</div>;
let entry = EntryTypes.(entry(~title="Pdf", ~render=distributions));
let entry = EntryTypes.(entry(~title="Mixed Distributions", ~render=distributions));

71
showcase/entries/ExpressionTreeExamples.re Normal file
View File

@ -0,0 +1,71 @@
let setup = dist =>
RenderTypes.DistPlusRenderer.make(~distPlusIngredients=dist, ())
|> DistPlusRenderer.run
|> RenderTypes.DistPlusRenderer.Outputs.distplus
|> R.O.fmapOrNull(distPlus => <DistPlusPlot distPlus />);
let simpleExample = (guesstimatorString, ~problem="", ()) =>
<>
<p> {guesstimatorString |> ReasonReact.string} </p>
<p> {problem |> (e => "problem: " ++ e) |> ReasonReact.string} </p>
{setup(
RenderTypes.DistPlusRenderer.Ingredients.make(~guesstimatorString, ()),
)}
</>;
let distributions = () =>
<div>
<div>
<h2 className="text-gray-800 text-xl font-bold">
{"Initial Section" |> ReasonReact.string}
</h2>
{simpleExample(
"normal(-1, 1) + normal(5, 2)",
~problem="Tails look too flat",
(),
)}
{simpleExample(
"mm(normal(4,2), normal(10,1))",
~problem="Tails look too flat",
(),
)}
{simpleExample(
"normal(-1, 1) * normal(5, 2)",
~problem="This looks really weird",
(),
)}
{simpleExample(
"normal(1,2) * normal(2,2) * normal(3,1)",
~problem="Seems like important parts are cut off",
(),
)}
{simpleExample(
"mm(uniform(0, 1) , normal(3,2))",
~problem="Uniform distribution seems to break multimodal",
(),
)}
{simpleExample(
"truncate(mm(1 to 10, 10 to 30), 10, 20)",
~problem="Truncate seems to have no effect",
(),
)}
{simpleExample(
"normal(5,2)*(10^3)",
~problem="Multiplied items should be evaluated.",
(),
)}
{simpleExample(
"normal(5,10*3)",
~problem="At least simple operations in the distributions should be evaluated.",
(),
)}
{simpleExample(
"normal(5,10)^3",
~problem="Exponentiation not yet supported",
(),
)}
</div>
</div>;
let entry =
EntryTypes.(entry(~title="ExpressionTree", ~render=distributions));

37
src/components/DistBuilder.re
View File

@ -17,7 +17,7 @@ module FormConfig = [%lenses
//
sampleCount: string,
outputXYPoints: string,
truncateTo: string,
downsampleTo: string,
kernelWidth: string,
}
];
@ -25,7 +25,7 @@ module FormConfig = [%lenses
type options = {
sampleCount: int,
outputXYPoints: int,
truncateTo: option(int),
downsampleTo: option(int),
kernelWidth: option(float),
};
@ -115,7 +115,7 @@ type inputs = {
samplingInputs: RenderTypes.ShapeRenderer.Sampling.inputs,
guesstimatorString: string,
length: int,
shouldTruncateSampledDistribution: int,
shouldDownsampleSampledDistribution: int,
};
module DemoDist = {
@ -141,8 +141,8 @@ module DemoDist = {
kernelWidth: options.kernelWidth,
},
~distPlusIngredients,
~shouldTruncate=options.truncateTo |> E.O.isSome,
~recommendedLength=options.truncateTo |> E.O.default(10000),
~shouldDownsample=options.downsampleTo |> E.O.isSome,
~recommendedLength=options.downsampleTo |> E.O.default(10000),
(),
);
let response = DistPlusRenderer.run(inputs);
@ -171,7 +171,8 @@ let make = () => {
~schema,
~onSubmit=({state}) => {None},
~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: "uniform(0, 1) * normal(1, 2) - 1",
domainType: "Complete",
xPoint: "50.0",
xPoint2: "60.0",
@ -180,9 +181,9 @@ let make = () => {
unitType: "UnspecifiedDistribution",
zero: MomentRe.momentNow(),
unit: "days",
sampleCount: "30000",
outputXYPoints: "10000",
truncateTo: "1000",
sampleCount: "3000",
outputXYPoints: "100",
downsampleTo: "100",
kernelWidth: "5",
},
(),
@ -210,7 +211,7 @@ let make = () => {
let sampleCount = reform.state.values.sampleCount |> Js.Float.fromString;
let outputXYPoints =
reform.state.values.outputXYPoints |> Js.Float.fromString;
let truncateTo = reform.state.values.truncateTo |> Js.Float.fromString;
let downsampleTo = reform.state.values.downsampleTo |> Js.Float.fromString;
let kernelWidth = reform.state.values.kernelWidth |> Js.Float.fromString;
let domain =
@ -252,20 +253,20 @@ let make = () => {
};
let options =
switch (sampleCount, outputXYPoints, truncateTo) {
switch (sampleCount, outputXYPoints, downsampleTo) {
| (_, _, _)
when
!Js.Float.isNaN(sampleCount)
&& !Js.Float.isNaN(outputXYPoints)
&& !Js.Float.isNaN(truncateTo)
&& !Js.Float.isNaN(downsampleTo)
&& sampleCount > 10.
&& outputXYPoints > 10. =>
Some({
sampleCount: sampleCount |> int_of_float,
outputXYPoints: outputXYPoints |> int_of_float,
truncateTo:
int_of_float(truncateTo) > 0
? Some(int_of_float(truncateTo)) : None,
downsampleTo:
int_of_float(downsampleTo) > 0
? Some(int_of_float(downsampleTo)) : None,
kernelWidth: kernelWidth == 0.0 ? None : Some(kernelWidth),
})
| _ => None
@ -287,7 +288,7 @@ let make = () => {
reform.state.values.unit,
reform.state.values.sampleCount,
reform.state.values.outputXYPoints,
reform.state.values.truncateTo,
reform.state.values.downsampleTo,
reform.state.values.kernelWidth,
reloader |> string_of_int,
|],
@ -481,7 +482,7 @@ let make = () => {
/>
</Col>
<Col span=4>
<FieldFloat field=FormConfig.TruncateTo label="Truncate To" />
<FieldFloat field=FormConfig.DownsampleTo label="Downsample To" />
</Col>
<Col span=4>
<FieldFloat field=FormConfig.KernelWidth label="Kernel Width" />
@ -496,4 +497,4 @@ let make = () => {
</Antd.Card>
<div className=Styles.spacer />
</div>;
};
};

6
src/components/DistBuilder2.re
View File

@ -44,14 +44,14 @@ module DemoDist = {
Distributions.DistPlus.make(
~shape=
Continuous(
Distributions.Continuous.make(`Linear, {xs, ys}),
Distributions.Continuous.make(`Linear, {xs, ys}, None),
),
~domain=Complete,
~unit=UnspecifiedDistribution,
~guesstimatorString=None,
(),
)
|> Distributions.DistPlus.T.scaleToIntegralSum(~intendedSum=1.0);
|> Distributions.DistPlus.T.normalize;
<DistPlusPlot distPlus />;
};
<Antd.Card title={"Distribution" |> R.ste}>
@ -102,4 +102,4 @@ let make = () => {
</Antd.Card>
<div className=Styles.spacer />
</div>;
};
};

8
src/components/DistBuilder3.re
View File

@ -37,13 +37,13 @@ module DemoDist = {
let parsed1 = MathJsParser.fromString(guesstimatorString);
let shape =
switch (parsed1) {
| Ok(r) => Some(SymbolicDist.toShape(10000, r))
| Ok(r) => Some(ExpressionTree.toShape(10000, r))
| _ => None
};
let str =
switch (parsed1) {
| Ok(r) => SymbolicDist.toString(r)
| Ok(r) => ExpressionTree.toString(r)
| Error(e) => e
};
@ -58,7 +58,7 @@ module DemoDist = {
~guesstimatorString=None,
(),
)
|> Distributions.DistPlus.T.scaleToIntegralSum(~intendedSum=1.0);
|> Distributions.DistPlus.T.normalize;
<DistPlusPlot distPlus />;
})
|> E.O.default(ReasonReact.null);
@ -111,4 +111,4 @@ let make = () => {
</Antd.Card>
<div className=Styles.spacer />
</div>;
};
};

16
src/components/Drawer.re
View File

@ -177,6 +177,7 @@ module Convert = {
let continuousShape: Types.continuousShape = {
xyShape,
interpolation: `Linear,
knownIntegralSum: None,
};
let integral = XYShape.Analysis.integrateContinuousShape(continuousShape);
@ -188,6 +189,7 @@ module Convert = {
ys,
},
interpolation: `Linear,
knownIntegralSum: Some(1.0),
};
continuousShape;
};
@ -386,8 +388,8 @@ module Draw = {
let stdev = 15.0;
let numSamples = 3000;
let normal: SymbolicDist.dist = `Normal({mean, stdev});
let normalShape = SymbolicDist.GenericSimple.toShape(normal, numSamples);
let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
let normalShape = ExpressionTree.toShape(numSamples, `SymbolicDist(normal));
let xyShape: Types.xyShape =
switch (normalShape) {
| Mixed(_) => {xs: [||], ys: [||]}
@ -396,9 +398,9 @@ module Draw = {
};
/* // To use a lognormal instead:
let lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
let lognormal = SymbolicTypes.Lognormal.fromMeanAndStdev(mean, stdev);
let lognormalShape =
SymbolicDist.GenericSimple.toShape(lognormal, numSamples);
SymbolicTypes.GenericSimple.toShape(lognormal, numSamples);
let lognormalXYShape: Types.xyShape =
switch (lognormalShape) {
| Mixed(_) => {xs: [||], ys: [||]}
@ -667,9 +669,7 @@ module State = {
/* create a cdf from a pdf */
let _pdf =
Distributions.Continuous.T.scaleToIntegralSum(
~cache=None,
~intendedSum=1.0,
Distributions.Continuous.T.normalize(
pdf,
);
@ -986,4 +986,4 @@ let make = () => {
</form>
</Antd.Card>
</Antd.Card>;
};
};

32
src/components/charts/DistPlusPlot.re
View File

@ -95,7 +95,7 @@ let table = (distPlus, x) => {
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.toScaledContinuous
|> Distributions.DistPlus.T.normalizedToContinuous
|> E.O.fmap(
Distributions.Continuous.T.Integral.sum(~cache=None),
)
@ -113,7 +113,7 @@ let table = (distPlus, x) => {
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.toScaledDiscrete
|> Distributions.DistPlus.T.normalizedToDiscrete
|> E.O.fmap(Distributions.Discrete.T.Integral.sum(~cache=None))
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
@ -211,15 +211,13 @@ let percentiles = distPlus => {
</div>;
};
let adjustBoth = discreteProbabilityMass => {
let yMaxDiscreteDomainFactor = discreteProbabilityMass;
let yMaxContinuousDomainFactor = 1.0 -. discreteProbabilityMass;
let yMax =
yMaxDiscreteDomainFactor > yMaxContinuousDomainFactor
? yMaxDiscreteDomainFactor : yMaxContinuousDomainFactor;
let adjustBoth = discreteProbabilityMassFraction => {
let yMaxDiscreteDomainFactor = discreteProbabilityMassFraction;
let yMaxContinuousDomainFactor = 1.0 -. discreteProbabilityMassFraction;
let yMax = (yMaxDiscreteDomainFactor > 0.5 ? yMaxDiscreteDomainFactor : yMaxContinuousDomainFactor);
(
1.0 /. (yMaxDiscreteDomainFactor /. yMax),
1.0 /. (yMaxContinuousDomainFactor /. yMax),
yMax /. yMaxDiscreteDomainFactor,
yMax /. yMaxContinuousDomainFactor,
);
};
@ -227,10 +225,10 @@ module DistPlusChart = {
[@react.component]
let make = (~distPlus: DistTypes.distPlus, ~config: chartConfig, ~onHover) => {
open Distributions.DistPlus;
let discrete = distPlus |> T.toScaledDiscrete;
let discrete = distPlus |> T.normalizedToDiscrete |> E.O.fmap(Distributions.Discrete.getShape);
let continuous =
distPlus
|> T.toScaledContinuous
|> T.normalizedToContinuous
|> E.O.fmap(Distributions.Continuous.getShape);
let range = T.xTotalRange(distPlus);
@ -254,10 +252,10 @@ module DistPlusChart = {
};
let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson;
let toDiscreteProbabilityMass =
distPlus |> Distributions.DistPlus.T.toDiscreteProbabilityMass;
let discreteProbabilityMassFraction =
distPlus |> Distributions.DistPlus.T.toDiscreteProbabilityMassFraction;
let (yMaxDiscreteDomainFactor, yMaxContinuousDomainFactor) =
adjustBoth(toDiscreteProbabilityMass);
adjustBoth(discreteProbabilityMassFraction);
<DistributionPlot
xScale={config.xLog ? "log" : "linear"}
yScale={config.yLog ? "log" : "linear"}
@ -339,7 +337,7 @@ let make = (~distPlus: DistTypes.distPlus) => {
<div>
{state.distributions
|> E.L.fmapi((index, config) =>
<div className="flex">
<div className="flex" key={string_of_int(index)}>
<div className="w-4/5">
<Chart distPlus config onHover={r => {setX(_ => r)}} />
</div>
@ -406,4 +404,4 @@ let make = (~distPlus: DistTypes.distPlus) => {
{state.showStats ? table(distPlus, x) : ReasonReact.null}
{state.showPercentiles ? percentiles(distPlus) : ReasonReact.null}
</div>;
};
};

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

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

210
src/distPlus/distribution/AlgebraicShapeCombination.re Normal file
View File

@ -0,0 +1,210 @@
type pointMassesWithMoments = {
n: int,
masses: array(float),
means: array(float),
variances: array(float),
};
/* This function takes a continuous distribution and efficiently approximates it as
point masses that have variances associated with them.
We estimate the means and variances from overlapping triangular distributions which we imagine are making up the
XYShape.
We can then use the algebra of random variables to "convolve" the point masses and their variances,
and finally reconstruct a new distribution from them, e.g. using a Fast Gauss Transform or Raykar et al. (2007). */
let toDiscretePointMassesFromTriangulars =
(~inverse=false, s: XYShape.T.t): pointMassesWithMoments => {
// TODO: what if there is only one point in the distribution?
let n = s |> XYShape.T.length;
// first, double up the leftmost and rightmost points:
let {xs, ys}: XYShape.T.t = s;
let _ = Js.Array.unshift(xs[0], xs);
let _ = Js.Array.unshift(ys[0], ys);
let _ = Js.Array.push(xs[n - 1], xs);
let _ = Js.Array.push(ys[n - 1], ys);
let n = E.A.length(xs);
// squares and neighbourly products of the xs
let xsSq: array(float) = Belt.Array.makeUninitializedUnsafe(n);
let xsProdN1: array(float) = Belt.Array.makeUninitializedUnsafe(n - 1);
let xsProdN2: array(float) = Belt.Array.makeUninitializedUnsafe(n - 2);
for (i in 0 to n - 1) {
let _ = Belt.Array.set(xsSq, i, xs[i] *. xs[i]);
();
};
for (i in 0 to n - 2) {
let _ = Belt.Array.set(xsProdN1, i, xs[i] *. xs[i + 1]);
();
};
for (i in 0 to n - 3) {
let _ = Belt.Array.set(xsProdN2, i, xs[i] *. xs[i + 2]);
();
};
// means and variances
let masses: array(float) = Belt.Array.makeUninitializedUnsafe(n - 2); // doesn't include the fake first and last points
let means: array(float) = Belt.Array.makeUninitializedUnsafe(n - 2);
let variances: array(float) = Belt.Array.makeUninitializedUnsafe(n - 2);
if (inverse) {
for (i in 1 to n - 2) {
let _ =
Belt.Array.set(
masses,
i - 1,
(xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2.,
);
// this only works when the whole triange is either on the left or on the right of zero
let a = xs[i - 1];
let c = xs[i];
let b = xs[i + 1];
// These are the moments of the reciprocal of a triangular distribution, as symbolically integrated by Mathematica.
// They're probably pretty close to invMean ~ 1/mean = 3/(a+b+c) and invVar. But I haven't worked out
// the worst case error, so for now let's use these monster equations
let inverseMean =
2.
*. (a *. log(a /. c) /. (a -. c) +. b *. log(c /. b) /. (b -. c))
/. (a -. b);
let inverseVar =
2.
*. (log(c /. a) /. (a -. c) +. b *. log(b /. c) /. (b -. c))
/. (a -. b)
-. inverseMean
** 2.;
let _ = Belt.Array.set(means, i - 1, inverseMean);
let _ = Belt.Array.set(variances, i - 1, inverseVar);
();
};
{n: n - 2, masses, means, variances};
} else {
for (i in 1 to n - 2) {
// area of triangle = width * height / 2
let _ =
Belt.Array.set(
masses,
i - 1,
(xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2.,
);
// means of triangle = (a + b + c) / 3
let _ =
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
let _ =
Belt.Array.set(
variances,
i - 1,
(
xsSq[i - 1]
+. xsSq[i]
+. xsSq[i + 1]
-. xsProdN1[i - 1]
-. xsProdN1[i]
-. xsProdN2[i - 1]
)
/. 18.,
);
();
};
{n: n - 2, masses, means, variances};
};
};
let combineShapesContinuousContinuous =
(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
: DistTypes.xyShape => {
let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length;
// if we add the two distributions, we should probably use normal filters.
// if we multiply the two distributions, we should probably use lognormal filters.
let t1m = toDiscretePointMassesFromTriangulars(s1);
let t2m = switch (op) {
| `Divide => toDiscretePointMassesFromTriangulars(~inverse=true, s2)
| _ => toDiscretePointMassesFromTriangulars(~inverse=false, s2)
};
let combineMeansFn =
switch (op) {
| `Add => ((m1, m2) => m1 +. m2)
| `Subtract => ((m1, m2) => m1 -. m2)
| `Multiply => ((m1, m2) => m1 *. m2)
| `Divide => ((m1, mInv2) => m1 *. mInv2)
}; // note: here, mInv2 = mean(1 / t2) ~= 1 / mean(t2)
// converts the variances and means of the two inputs into the variance of the output
let combineVariancesFn =
switch (op) {
| `Add => ((v1, v2, m1, m2) => v1 +. v2)
| `Subtract => ((v1, v2, m1, m2) => v1 +. v2)
| `Multiply => (
(v1, v2, m1, m2) => v1 *. v2 +. v1 *. m2 ** 2. +. v2 *. m1 ** 2.
)
| `Divide => (
(v1, vInv2, m1, mInv2) =>
v1 *. vInv2 +. v1 *. mInv2 ** 2. +. vInv2 *. m1 ** 2.
)
};
// TODO: If operating on two positive-domain distributions, we should take that into account
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 -. variance *. 1.644854;
let maxX = mean +. 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) {
let _ = if (variances[j] > 0.) {
for (i in 0 to E.A.length(outputXs) - 1) {
let dx = outputXs[i] -. means[j];
let contribution = masses[j] *. exp(-. (dx ** 2.) /. (2. *. variances[j]));
let _ = Belt.Array.set(outputYs, i, outputYs[i] +. contribution);
();
};
();
};
();
};
{xs: outputXs, ys: outputYs};
};

10
src/distPlus/distribution/DistTypes.re
View File

@ -17,14 +17,18 @@ type xyShape = {
type continuousShape = {
xyShape,
interpolation: [ | `Stepwise | `Linear],
knownIntegralSum: option(float),
};
type discreteShape = xyShape;
type discreteShape = {
xyShape,
knownIntegralSum: option(float),
};
type mixedShape = {
continuous: continuousShape,
discrete: discreteShape,
discreteProbabilityMassFraction: float,
// discreteProbabilityMassFraction: float,
};
type shapeMonad('a, 'b, 'c) =
@ -153,4 +157,4 @@ module MixedPoint = {
};
let add = combine2((a, b) => a +. b);
};
};

1140
src/distPlus/distribution/Distributions.re
View File

File diff suppressed because it is too large Load Diff

85
src/distPlus/distribution/MixedShapeBuilder.re
View File

@ -8,14 +8,15 @@ type assumptions = {
discreteProbabilityMass: option(float),
};
let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete): option(DistTypes.shape) => {
let continuous = continuous |> E.O.default(Distributions.Continuous.make(`Linear, {xs: [||], ys: [||]}))
let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete: option(DistTypes.discreteShape)): option(DistTypes.shape) => {
let continuous = continuous |> E.O.default(Distributions.Continuous.make(`Linear, {xs: [||], ys: [||]}, Some(0.0)));
let discrete = discrete |> E.O.default(Distributions.Discrete.make({xs: [||], ys: [||]}, Some(0.0)));
let cLength =
continuous
|> Distributions.Continuous.getShape
|> XYShape.T.xs
|> E.A.length;
let dLength = discrete |> XYShape.T.xs |> E.A.length;
let dLength = discrete |> Distributions.Discrete.getShape |> XYShape.T.xs |> E.A.length;
switch (cLength, dLength) {
| (0 | 1, 0) => None
| (0 | 1, _) => Some(Discrete(discrete))
@ -23,83 +24,13 @@ let buildSimple = (~continuous: option(DistTypes.continuousShape), ~discrete): o
| (_, _) =>
let discreteProbabilityMassFraction =
Distributions.Discrete.T.Integral.sum(~cache=None, discrete);
let discrete =
Distributions.Discrete.T.scaleToIntegralSum(~intendedSum=1.0, discrete);
let continuous =
Distributions.Continuous.T.scaleToIntegralSum(
~intendedSum=1.0,
continuous,
);
let discrete = Distributions.Discrete.T.normalize(discrete);
let continuous = Distributions.Continuous.T.normalize(continuous);
let mixedDist =
Distributions.Mixed.make(
~continuous,
~discrete,
~discreteProbabilityMassFraction,
~discrete
);
Some(Mixed(mixedDist));
};
};
// TODO: Delete, only being used in tests
let build = (~continuous, ~discrete, ~assumptions) =>
switch (assumptions) {
| {
continuous: ADDS_TO_CORRECT_PROBABILITY,
discrete: ADDS_TO_CORRECT_PROBABILITY,
discreteProbabilityMass: Some(r),
} =>
// TODO: Fix this, it's wrong :(
Some(
Distributions.Mixed.make(
~continuous,
~discrete,
~discreteProbabilityMassFraction=r,
),
)
| {
continuous: ADDS_TO_1,
discrete: ADDS_TO_1,
discreteProbabilityMass: Some(r),
} =>
Some(
Distributions.Mixed.make(
~continuous,
~discrete,
~discreteProbabilityMassFraction=r,
),
)
| {
continuous: ADDS_TO_1,
discrete: ADDS_TO_1,
discreteProbabilityMass: None,
} =>
None
| {
continuous: ADDS_TO_CORRECT_PROBABILITY,
discrete: ADDS_TO_1,
discreteProbabilityMass: None,
} =>
None
| {
continuous: ADDS_TO_1,
discrete: ADDS_TO_CORRECT_PROBABILITY,
discreteProbabilityMass: None,
} =>
let discreteProbabilityMassFraction =
Distributions.Discrete.T.Integral.sum(~cache=None, discrete);
let discrete =
Distributions.Discrete.T.scaleToIntegralSum(~intendedSum=1.0, discrete);
Some(
Distributions.Mixed.make(
~continuous,
~discrete,
~discreteProbabilityMassFraction,
),
);
| _ => None
};
};

64
src/distPlus/distribution/XYShape.re
View File

@ -9,7 +9,7 @@ let interpolate =
};
// TODO: Make sure that shapes cannot be empty.
let extImp = E.O.toExt("Should not be possible");
let extImp = E.O.toExt("Tried to perform an operation on an empty XYShape.");
module T = {
type t = xyShape;
@ -17,6 +17,7 @@ module T = {
type ts = array(xyShape);
let xs = (t: t) => t.xs;
let ys = (t: t) => t.ys;
let length = (t: t) => E.A.length(t.xs);
let empty = {xs: [||], ys: [||]};
let minX = (t: t) => t |> xs |> E.A.Sorted.min |> extImp;
let maxX = (t: t) => t |> xs |> E.A.Sorted.max |> extImp;
@ -154,7 +155,9 @@ module XsConversion = {
let proportionByProbabilityMass =
(newLength: int, integral: T.t, t: T.t): T.t => {
equallyDivideXByMass(newLength, integral) |> _replaceWithXs(_, t);
integral
|> equallyDivideXByMass(newLength) // creates a new set of xs at evenly spaced percentiles
|> _replaceWithXs(_, t); // linearly interpolates new ys for the new xs
};
};
@ -164,9 +167,10 @@ module Zipped = {
let compareXs = ((x1, _), (x2, _)) => x1 > x2 ? 1 : 0;
let sortByY = (t: zipped) => t |> E.A.stableSortBy(_, compareYs);
let sortByX = (t: zipped) => t |> E.A.stableSortBy(_, compareXs);
let filterByX = (testFn: (float => bool), t: zipped) => t |> E.A.filter(((x, _)) => testFn(x));
};
module Combine = {
module PointwiseCombination = {
type xsSelection =
| ALL_XS
| XS_EVENLY_DIVIDED(int);
@ -179,16 +183,25 @@ module Combine = {
t1: T.t,
t2: T.t,
) => {
let allXs =
switch (xsSelection) {
| ALL_XS => Ts.allXs([|t1, t2|])
| XS_EVENLY_DIVIDED(sampleCount) =>
Ts.equallyDividedXs([|t1, t2|], sampleCount)
};
let allYs =
allXs |> E.A.fmap(x => fn(xToYSelection(x, t1), xToYSelection(x, t2)));
T.fromArrays(allXs, allYs);
switch ((E.A.length(t1.xs), E.A.length(t2.xs))) {
| (0, 0) => T.empty
| (0, _) => t2
| (_, 0) => t1
| (_, _) => {
let allXs =
switch (xsSelection) {
| ALL_XS => Ts.allXs([|t1, t2|])
| XS_EVENLY_DIVIDED(sampleCount) =>
Ts.equallyDividedXs([|t1, t2|], sampleCount)
};
let allYs =
allXs |> E.A.fmap(x => fn(xToYSelection(x, t1), xToYSelection(x, t2)));
T.fromArrays(allXs, allYs);
}
}
};
let combineLinear = combine(~xToYSelection=XtoY.linear);
@ -244,8 +257,8 @@ module Range = {
Belt.Array.set(
cumulativeY,
x + 1,
(xs[x + 1] -. xs[x])
*. ((ys[x] +. ys[x + 1]) /. 2.)
(xs[x + 1] -. xs[x]) // dx
*. ((ys[x] +. ys[x + 1]) /. 2.) // (1/2) * (avgY)
+. cumulativeY[x],
);
();
@ -265,7 +278,7 @@ module Range = {
items
|> Belt.Array.map(_, rangePointAssumingSteps)
|> T.fromZippedArray
|> Combine.intersperse(t |> T.mapX(e => e +. diff)),
|> PointwiseCombination.intersperse(t |> T.mapX(e => e +. diff)),
)
| _ => Some(t)
};
@ -287,7 +300,7 @@ let pointLogScore = (prediction, answer) =>
};
let logScorePoint = (sampleCount, t1, t2) =>
Combine.combine(
PointwiseCombination.combine(
~xsSelection=XS_EVENLY_DIVIDED(sampleCount),
~xToYSelection=XtoY.linear,
~fn=pointLogScore,
@ -315,6 +328,7 @@ module Analysis = {
0.0,
(acc, _x, i) => {
let areaUnderIntegral =
// TODO Take this switch statement out of the loop body
switch (t.interpolation, i) {
| (_, 0) => 0.0
| (`Stepwise, _) =>
@ -323,12 +337,16 @@ module Analysis = {
| (`Linear, _) =>
let x1 = xs[i - 1];
let x2 = xs[i];
let h1 = ys[i - 1];
let h2 = ys[i];
let b = (h1 -. h2) /. (x1 -. x2);
let a = h1 -. b *. x1;
indefiniteIntegralLinear(x2, a, b)
-. indefiniteIntegralLinear(x1, a, b);
if (x1 == x2) {
0.0
} else {
let h1 = ys[i - 1];
let h2 = ys[i];
let b = (h1 -. h2) /. (x1 -. x2);
let a = h1 -. b *. x1;
indefiniteIntegralLinear(x2, a, b)
-. indefiniteIntegralLinear(x1, a, b);
};
};
acc +. areaUnderIntegral;
},
@ -354,4 +372,4 @@ module Analysis = {
};
let squareXYShape = T.mapX(x => x ** 2.0)
};
};

23
src/distPlus/expressionTree/ExpressionTree.re Normal file
View File

@ -0,0 +1,23 @@
open ExpressionTypes.ExpressionTree;
let toShape = (sampleCount: int, node: node) => {
let renderResult =
`Render(`Normalize(node))
|> ExpressionTreeEvaluator.toLeaf({sampleCount: sampleCount});
switch (renderResult) {
| Ok(`RenderedDist(rs)) =>
let continuous = Distributions.Shape.T.toContinuous(rs);
let discrete = Distributions.Shape.T.toDiscrete(rs);
let shape = MixedShapeBuilder.buildSimple(~continuous, ~discrete);
shape |> E.O.toExt("Could not build final shape.");
| Ok(_) => E.O.toExn("Rendering failed.", None)
| Error(message) => E.O.toExn("No shape found, error: " ++ message, None)
};
};
let rec toString =
fun
| `SymbolicDist(d) => SymbolicDist.T.toString(d)
| `RenderedDist(_) => "[shape]"
| op => Operation.T.toString(toString, op);

266
src/distPlus/expressionTree/ExpressionTreeEvaluator.re Normal file
View File

@ -0,0 +1,266 @@
open ExpressionTypes;
open ExpressionTypes.ExpressionTree;
type t = node;
type tResult = node => result(node, string);
type renderParams = {
sampleCount: int,
};
/* Given two random variables A and B, this returns the distribution
of a new variable that is the result of the operation on A and B.
For instance, normal(0, 1) + normal(1, 1) -> normal(1, 2).
In general, this is implemented via convolution. */
module AlgebraicCombination = {
let tryAnalyticalSimplification = (operation, t1: t, t2: t) =>
switch (operation, t1, t2) {
| (operation,
`SymbolicDist(d1),
`SymbolicDist(d2),
) =>
switch (SymbolicDist.T.tryAnalyticalSimplification(d1, d2, operation)) {
| `AnalyticalSolution(symbolicDist) => Ok(`SymbolicDist(symbolicDist))
| `Error(er) => Error(er)
| `NoSolution => Ok(`AlgebraicCombination(operation, t1, t2))
}
| _ => Ok(`AlgebraicCombination(operation, t1, t2))
};
let combineAsShapes = (toLeaf, renderParams, algebraicOp, t1, t2) => {
let renderShape = r => toLeaf(renderParams, `Render(r));
switch (renderShape(t1), renderShape(t2)) {
| (Ok(`RenderedDist(s1)), Ok(`RenderedDist(s2))) =>
Ok(
`RenderedDist(
Distributions.Shape.combineAlgebraically(algebraicOp, s1, s2),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Algebraic combination: rendering failed.")
};
};
let operationToLeaf =
(
toLeaf,
renderParams: renderParams,
algebraicOp: ExpressionTypes.algebraicOperation,
t1: t,
t2: t,
)
: result(node, string) =>
algebraicOp
|> tryAnalyticalSimplification(_, t1, t2)
|> E.R.bind(
_,
fun
| `SymbolicDist(d) as t => Ok(t)
| _ => combineAsShapes(toLeaf, renderParams, algebraicOp, t1, t2)
);
};
module VerticalScaling = {
let operationToLeaf = (toLeaf, renderParams, scaleOp, t, scaleBy) => {
// scaleBy has to be a single float, otherwise we'll return an error.
let fn = Operation.Scale.toFn(scaleOp);
let knownIntegralSumFn = Operation.Scale.toKnownIntegralSumFn(scaleOp);
let renderedShape = toLeaf(renderParams, `Render(t));
switch (renderedShape, scaleBy) {
| (Ok(`RenderedDist(rs)), `SymbolicDist(`Float(sm))) =>
Ok(
`RenderedDist(
Distributions.Shape.T.mapY(
~knownIntegralSumFn=knownIntegralSumFn(sm),
fn(sm),
rs,
),
),
)
| (Error(e1), _) => Error(e1)
| (_, _) => Error("Can only scale by float values.")
};
};
};
module PointwiseCombination = {
let pointwiseAdd = (toLeaf, renderParams, t1, t2) => {
let renderShape = r => toLeaf(renderParams, `Render(r));
switch (renderShape(t1), renderShape(t2)) {
| (Ok(`RenderedDist(rs1)), Ok(`RenderedDist(rs2))) =>
Ok(
`RenderedDist(
Distributions.Shape.combinePointwise(
~knownIntegralSumsFn=(a, b) => Some(a +. b),
(+.),
rs1,
rs2,
),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Pointwise combination: rendering failed.")
};
};
let pointwiseMultiply = (toLeaf, renderParams, t1, t2) => {
// 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.
Error(
"Pointwise multiplication not yet supported.",
);
};
let operationToLeaf = (toLeaf, renderParams, pointwiseOp, t1, t2) => {
switch (pointwiseOp) {
| `Add => pointwiseAdd(toLeaf, renderParams, t1, t2)
| `Multiply => pointwiseMultiply(toLeaf, renderParams, t1, t2)
};
};
};
module Truncate = {
let trySimplification = (leftCutoff, rightCutoff, t) => {
switch (leftCutoff, rightCutoff, t) {
| (None, None, t) => Ok(t)
| (lc, rc, `SymbolicDist(`Uniform(u))) => {
// just create a new Uniform distribution
let nu: SymbolicTypes.uniform = u;
let newLow = max(E.O.default(neg_infinity, lc), nu.low);
let newHigh = min(E.O.default(infinity, rc), nu.high);
Ok(`SymbolicDist(`Uniform({low: newLow, high: newHigh})));
}
| (_, _, t) => Ok(t)
};
};
let truncateAsShape = (toLeaf, renderParams, leftCutoff, rightCutoff, t) => {
// TODO: use named args in renderToShape; if we're lucky we can at least get the tail
// of a distribution we otherwise wouldn't get at all
let renderedShape = toLeaf(renderParams, `Render(t));
switch (renderedShape) {
| Ok(`RenderedDist(rs)) => {
let truncatedShape =
rs |> Distributions.Shape.T.truncate(leftCutoff, rightCutoff);
Ok(`RenderedDist(rs));
}
| Error(e1) => Error(e1)
| _ => Error("Could not truncate distribution.")
};
};
let operationToLeaf =
(
toLeaf,
renderParams,
leftCutoff: option(float),
rightCutoff: option(float),
t: node,
)
: result(node, string) => {
t
|> trySimplification(leftCutoff, rightCutoff)
|> E.R.bind(
_,
fun
| `SymbolicDist(d) as t => Ok(t)
| _ => truncateAsShape(toLeaf, renderParams, leftCutoff, rightCutoff, t),
);
};
};
module Normalize = {
let rec operationToLeaf = (toLeaf, renderParams, t: node): result(node, string) => {
switch (t) {
| `RenderedDist(s) =>
Ok(`RenderedDist(Distributions.Shape.T.normalize(s)))
| `SymbolicDist(_) => Ok(t)
| _ => t |> toLeaf(renderParams) |> E.R.bind(_, operationToLeaf(toLeaf, renderParams))
};
};
};
module FloatFromDist = {
let symbolicToLeaf = (distToFloatOp: distToFloatOperation, s) => {
SymbolicDist.T.operate(distToFloatOp, s)
|> E.R.bind(_, v => Ok(`SymbolicDist(`Float(v))));
};
let renderedToLeaf =
(distToFloatOp: distToFloatOperation, rs: DistTypes.shape)
: result(node, string) => {
Distributions.Shape.operate(distToFloatOp, rs)
|> (v => Ok(`SymbolicDist(`Float(v))));
};
let rec operationToLeaf =
(toLeaf, renderParams, distToFloatOp: distToFloatOperation, t: node)
: result(node, string) => {
switch (t) {
| `SymbolicDist(s) => symbolicToLeaf(distToFloatOp, s)
| `RenderedDist(rs) => renderedToLeaf(distToFloatOp, rs)
| _ => t |> toLeaf(renderParams) |> E.R.bind(_, operationToLeaf(toLeaf, renderParams, distToFloatOp))
};
};
};
module Render = {
let rec operationToLeaf =
(
toLeaf,
renderParams,
t: node,
)
: result(t, string) => {
switch (t) {
| `SymbolicDist(d) =>
Ok(`RenderedDist(SymbolicDist.T.toShape(renderParams.sampleCount, d)))
| `RenderedDist(_) as t => Ok(t) // already a rendered shape, we're done here
| _ => t |> toLeaf(renderParams) |> E.R.bind(_, operationToLeaf(toLeaf, renderParams))
};
};
};
/* This function recursively goes through the nodes of the parse tree,
replacing each Operation node and its subtree with a Data node.
Whenever possible, the replacement produces a new Symbolic Data node,
but most often it will produce a RenderedDist.
This function is used mainly to turn a parse tree into a single RenderedDist
that can then be displayed to the user. */
let rec toLeaf = (renderParams, node: t): result(t, string) => {
switch (node) {
// Leaf nodes just stay leaf nodes
| `SymbolicDist(_)
| `RenderedDist(_) => Ok(node)
// Operations need to be turned into leaves
| `AlgebraicCombination(algebraicOp, t1, t2) =>
AlgebraicCombination.operationToLeaf(
toLeaf,
renderParams,
algebraicOp,
t1,
t2
)
| `PointwiseCombination(pointwiseOp, t1, t2) =>
PointwiseCombination.operationToLeaf(
toLeaf,
renderParams,
pointwiseOp,
t1,
t2,
)
| `VerticalScaling(scaleOp, t, scaleBy) =>
VerticalScaling.operationToLeaf(
toLeaf, renderParams, scaleOp, t, scaleBy
)
| `Truncate(leftCutoff, rightCutoff, t) =>
Truncate.operationToLeaf(toLeaf, renderParams, leftCutoff, rightCutoff, t)
| `FloatFromDist(distToFloatOp, t) =>
FloatFromDist.operationToLeaf(toLeaf, renderParams, distToFloatOp, t)
| `Normalize(t) => Normalize.operationToLeaf(toLeaf, renderParams, t)
| `Render(t) => Render.operationToLeaf(toLeaf, renderParams, t)
};
};

20
src/distPlus/expressionTree/ExpressionTypes.re Normal file
View File

@ -0,0 +1,20 @@
type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
type pointwiseOperation = [ | `Add | `Multiply];
type scaleOperation = [ | `Multiply | `Exponentiate | `Log];
type distToFloatOperation = [ | `Pdf(float) | `Inv(float) | `Mean | `Sample];
module ExpressionTree = {
type node = [
// leaf nodes:
| `SymbolicDist(SymbolicTypes.symbolicDist)
| `RenderedDist(DistTypes.shape)
// operations:
| `AlgebraicCombination(algebraicOperation, node, node)
| `PointwiseCombination(pointwiseOperation, node, node)
| `VerticalScaling(scaleOperation, node, node)
| `Render(node)
| `Truncate(option(float), option(float), node)
| `Normalize(node)
| `FloatFromDist(distToFloatOperation, node)
];
};

368
src/distPlus/expressionTree/MathJsParser.re Normal file
View File

@ -0,0 +1,368 @@
module MathJsonToMathJsAdt = {
type arg =
| Symbol(string)
| Value(float)
| Fn(fn)
| Array(array(arg))
| Object(Js.Dict.t(arg))
and fn = {
name: string,
args: array(arg),
};
let rec run = (j: Js.Json.t) =>
Json.Decode.(
switch (field("mathjs", string, j)) {
| "FunctionNode" =>
let args = j |> field("args", array(run));
Some(
Fn({
name: j |> field("fn", field("name", string)),
args: args |> E.A.O.concatSomes,
}),
);
| "OperatorNode" =>
let args = j |> field("args", array(run));
Some(
Fn({
name: j |> field("fn", string),
args: args |> E.A.O.concatSomes,
}),
);
| "ConstantNode" =>
optional(field("value", Json.Decode.float), j)
|> E.O.fmap(r => Value(r))
| "ParenthesisNode" => j |> field("content", run)
| "ObjectNode" =>
let properties = j |> field("properties", dict(run));
Js.Dict.entries(properties)
|> E.A.fmap(((key, value)) => value |> E.O.fmap(v => (key, v)))
|> E.A.O.concatSomes
|> Js.Dict.fromArray
|> (r => Some(Object(r)));
| "ArrayNode" =>
let items = field("items", array(run), j);
Some(Array(items |> E.A.O.concatSomes));
| "SymbolNode" => Some(Symbol(field("name", string, j)))
| n =>
Js.log3("Couldn't parse mathjs node", j, n);
None;
}
);
};
module MathAdtToDistDst = {
open MathJsonToMathJsAdt;
module MathAdtCleaner = {
let transformWithSymbol = (f: float, s: string) =>
switch (s) {
| "K"
| "k" => f *. 1000.
| "M"
| "m" => f *. 1000000.
| "B"
| "b" => f *. 1000000000.
| "T"
| "t" => f *. 1000000000000.
| _ => f
};
let rec run =
fun
| Fn({name: "multiply", args: [|Value(f), Symbol(s)|]}) =>
Value(transformWithSymbol(f, s))
| Fn({name: "unaryMinus", args: [|Value(f)|]}) => Value((-1.0) *. f)
| Fn({name, args}) => Fn({name, args: args |> E.A.fmap(run)})
| Array(args) => Array(args |> E.A.fmap(run))
| Symbol(s) => Symbol(s)
| Value(v) => Value(v)
| Object(v) =>
Object(
v
|> Js.Dict.entries
|> E.A.fmap(((key, value)) => (key, run(value)))
|> Js.Dict.fromArray,
);
};
let normal:
array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(mean), Value(stdev)|] =>
Ok(`SymbolicDist(`Normal({mean, stdev})))
| _ => Error("Wrong number of variables in normal distribution");
let lognormal:
array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(mu), Value(sigma)|] =>
Ok(`SymbolicDist(`Lognormal({mu, sigma})))
| [|Object(o)|] => {
let g = Js.Dict.get(o);
switch (g("mean"), g("stdev"), g("mu"), g("sigma")) {
| (Some(Value(mean)), Some(Value(stdev)), _, _) =>
Ok(
`SymbolicDist(
SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev),
),
)
| (_, _, Some(Value(mu)), Some(Value(sigma))) =>
Ok(`SymbolicDist(`Lognormal({mu, sigma})))
| _ => Error("Lognormal distribution would need mean and stdev")
};
}
| _ => Error("Wrong number of variables in lognormal distribution");
let to_: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(low), Value(high)|] when low <= 0.0 && low < high => {
Ok(`SymbolicDist(SymbolicDist.Normal.from90PercentCI(low, high)));
}
| [|Value(low), Value(high)|] when low < high => {
Ok(
`SymbolicDist(SymbolicDist.Lognormal.from90PercentCI(low, high)),
);
}
| [|Value(_), Value(_)|] =>
Error("Low value must be less than high value.")
| _ => Error("Wrong number of variables in lognormal distribution");
let uniform:
array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(low), Value(high)|] =>
Ok(`SymbolicDist(`Uniform({low, high})))
| _ => Error("Wrong number of variables in lognormal distribution");
let beta: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(alpha), Value(beta)|] =>
Ok(`SymbolicDist(`Beta({alpha, beta})))
| _ => Error("Wrong number of variables in lognormal distribution");
let exponential:
array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(rate)|] => Ok(`SymbolicDist(`Exponential({rate: rate})))
| _ => Error("Wrong number of variables in Exponential distribution");
let cauchy:
array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(local), Value(scale)|] =>
Ok(`SymbolicDist(`Cauchy({local, scale})))
| _ => Error("Wrong number of variables in cauchy distribution");
let triangular:
array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(low), Value(medium), Value(high)|] =>
Ok(`SymbolicDist(`Triangular({low, medium, high})))
| _ => Error("Wrong number of variables in triangle distribution");
let multiModal =
(
args: array(result(ExpressionTypes.ExpressionTree.node, string)),
weights: option(array(float)),
) => {
let weights = weights |> E.O.default([||]);
/*let dists: =
args
|> E.A.fmap(
fun
| Ok(a) => a
| Error(e) => Error(e)
);*/
let firstWithError = args |> Belt.Array.getBy(_, Belt.Result.isError);
let withoutErrors = args |> E.A.fmap(E.R.toOption) |> E.A.O.concatSomes;
switch (firstWithError) {
| Some(Error(e)) => Error(e)
| None when withoutErrors |> E.A.length == 0 =>
Error("Multimodals need at least one input")
| _ =>
let components =
withoutErrors
|> E.A.fmapi((index, t) => {
let w = weights |> E.A.get(_, index) |> E.O.default(1.0);
`VerticalScaling((`Multiply, t, `SymbolicDist(`Float(w))));
});
let pointwiseSum =
components
|> Js.Array.sliceFrom(1)
|> E.A.fold_left(
(acc, x) => {`PointwiseCombination((`Add, acc, x))},
E.A.unsafe_get(components, 0),
);
Ok(`Normalize(pointwiseSum));
};
};
let arrayParser =
(args: array(arg))
: result(ExpressionTypes.ExpressionTree.node, string) => {
let samples =
args
|> E.A.fmap(
fun
| Value(n) => Some(n)
| _ => None,
)
|> E.A.O.concatSomes;
let outputs = Samples.T.fromSamples(samples);
let pdf =
outputs.shape |> E.O.bind(_, Distributions.Shape.T.toContinuous);
let shape =
pdf
|> E.O.fmap(pdf => {
let _pdf = Distributions.Continuous.T.normalize(pdf);
let cdf = Distributions.Continuous.T.integral(~cache=None, _pdf);
SymbolicDist.ContinuousShape.make(_pdf, cdf);
});
switch (shape) {
| Some(s) => Ok(`SymbolicDist(`ContinuousShape(s)))
| None => Error("Rendering did not work")
};
};
let operationParser =
(
name: string,
args: array(result(ExpressionTypes.ExpressionTree.node, string)),
) => {
let toOkAlgebraic = r => Ok(`AlgebraicCombination(r));
let toOkTrunctate = r => Ok(`Truncate(r));
switch (name, args) {
| ("add", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Add, l, r))
| ("add", _) => Error("Addition needs two operands")
| ("subtract", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Subtract, l, r))
| ("subtract", _) => Error("Subtraction needs two operands")
| ("multiply", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Multiply, l, r))
| ("multiply", _) => Error("Multiplication needs two operands")
| ("divide", [|Ok(l), Ok(r)|]) => toOkAlgebraic((`Divide, l, r))
| ("divide", _) => Error("Division needs two operands")
| ("pow", _) => Error("Exponentiation is not yet supported.")
| ("leftTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(lc)))|]) =>
toOkTrunctate((Some(lc), None, d))
| ("leftTruncate", _) =>
Error("leftTruncate needs two arguments: the expression and the cutoff")
| ("rightTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(rc)))|]) =>
toOkTrunctate((None, Some(rc), d))
| ("rightTruncate", _) =>
Error(
"rightTruncate needs two arguments: the expression and the cutoff",
)
| (
"truncate",
[|
Ok(d),
Ok(`SymbolicDist(`Float(lc))),
Ok(`SymbolicDist(`Float(rc))),
|],
) =>
toOkTrunctate((Some(lc), Some(rc), d))
| ("truncate", _) =>
Error("truncate needs three arguments: the expression and both cutoffs")
| _ => Error("This type not currently supported")
};
};
let functionParser = (nodeParser, name, args) => {
let parseArgs = () => args |> E.A.fmap(nodeParser);
switch (name) {
| "normal" => normal(args)
| "lognormal" => lognormal(args)
| "uniform" => uniform(args)
| "beta" => beta(args)
| "to" => to_(args)
| "exponential" => exponential(args)
| "cauchy" => cauchy(args)
| "triangular" => triangular(args)
| "mm" =>
let weights =
args
|> E.A.last
|> E.O.bind(
_,
fun
| Array(values) => Some(values)
| _ => None,
)
|> E.O.fmap(o =>
o
|> E.A.fmap(
fun
| Value(r) => Some(r)
| _ => None,
)
|> E.A.O.concatSomes
);
let possibleDists =
E.O.isSome(weights)
? Belt.Array.slice(args, ~offset=0, ~len=E.A.length(args) - 1)
: args;
let dists = possibleDists |> E.A.fmap(nodeParser);
multiModal(dists, weights);
| "add"
| "subtract"
| "multiply"
| "divide"
| "pow"
| "leftTruncate"
| "rightTruncate"
| "truncate" => operationParser(name, parseArgs())
| "mean" as n
| "inv" as n
| "sample" as n
| "pdf" as n
| n => Error(n ++ "(...) is not currently supported")
};
};
let rec nodeParser =
fun
| Value(f) => Ok(`SymbolicDist(`Float(f)))
| Fn({name, args}) => functionParser(nodeParser, name, args)
| _ => {
Error("This type not currently supported");
};
let topLevel =
fun
| Array(r) => arrayParser(r)
| Value(_) as r => nodeParser(r)
| Fn(_) as r => nodeParser(r)
| Symbol(_) => Error("Symbol not valid as top level")
| Object(_) => Error("Object not valid as top level");
let run = (r): result(ExpressionTypes.ExpressionTree.node, string) =>
r |> MathAdtCleaner.run |> topLevel;
};
let fromString = str => {
/* We feed the user-typed string into Mathjs.parseMath,
which returns a JSON with (hopefully) a single-element array.
This array element is the top-level node of a nested-object tree
representing the functions/arguments/values/etc. in the string.
The function MathJsonToMathJsAdt then recursively unpacks this JSON into a typed data structure we can use.
Inside of this function, MathAdtToDistDst is called whenever a distribution function is encountered.
*/
let mathJsToJson = Mathjs.parseMath(str);
let mathJsParse =
E.R.bind(mathJsToJson, r => {
switch (MathJsonToMathJsAdt.run(r)) {
| Some(r) => Ok(r)
| None => Error("MathJsParse Error")
}
});
let value = E.R.bind(mathJsParse, MathAdtToDistDst.run);
value;
};

0
src/distPlus/symbolic/Mathjs.re → src/distPlus/expressionTree/Mathjs.re
View File

9
src/distPlus/expressionTree/MathjsWrapper.js Normal file
View File

@ -0,0 +1,9 @@
const math = require("mathjs");
function parseMath(f) {
return JSON.parse(JSON.stringify(math.parse(f)))
};
module.exports = {
parseMath,
};

94
src/distPlus/expressionTree/Operation.re Normal file
View File

@ -0,0 +1,94 @@
open ExpressionTypes;
module Algebraic = {
type t = algebraicOperation;
let toFn: (t, float, float) => float =
fun
| `Add => (+.)
| `Subtract => (-.)
| `Multiply => ( *. )
| `Divide => (/.);
let applyFn = (t, f1, f2) => {
switch (t, f1, f2) {
| (`Divide, _, 0.) => Error("Cannot divide $v1 by zero.")
| _ => Ok(toFn(t, f1, f2))
};
};
let toString =
fun
| `Add => "+"
| `Subtract => "-"
| `Multiply => "*"
| `Divide => "/";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module Pointwise = {
type t = pointwiseOperation;
let toString =
fun
| `Add => "+"
| `Multiply => "*";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module DistToFloat = {
type t = distToFloatOperation;
let format = (operation, value) =>
switch (operation) {
| `Pdf(f) => {j|pdf(x=$f,$value)|j}
| `Inv(f) => {j|inv(x=$f,$value)|j}
| `Sample => "sample($value)"
| `Mean => "mean($value)"
};
};
module Scale = {
type t = scaleOperation;
let toFn =
fun
| `Multiply => ( *. )
| `Exponentiate => ( ** )
| `Log => ((a, b) => log(a) /. log(b));
let format = (operation: t, value, scaleBy) =>
switch (operation) {
| `Multiply => {j|verticalMultiply($value, $scaleBy) |j}
| `Exponentiate => {j|verticalExponentiate($value, $scaleBy) |j}
| `Log => {j|verticalLog($value, $scaleBy) |j}
};
let toKnownIntegralSumFn =
fun
| `Multiply => ((a, b) => Some(a *. b))
| `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None);
};
module T = {
let truncateToString =
(left: option(float), right: option(float), nodeToString) => {
let left = left |> E.O.dimap(Js.Float.toString, () => "-inf");
let right = right |> E.O.dimap(Js.Float.toString, () => "inf");
{j|truncate($nodeToString, $left, $right)|j};
};
let toString = nodeToString =>
fun
| `AlgebraicCombination(op, t1, t2) =>
Algebraic.format(op, nodeToString(t1), nodeToString(t2))
| `PointwiseCombination(op, t1, t2) =>
Pointwise.format(op, nodeToString(t1), nodeToString(t2))
| `VerticalScaling(scaleOp, t, scaleBy) =>
Scale.format(scaleOp, nodeToString(t), nodeToString(scaleBy))
| `Normalize(t) => "normalize(k" ++ nodeToString(t) ++ ")"
| `FloatFromDist(floatFromDistOp, t) =>
DistToFloat.format(floatFromDistOp, nodeToString(t))
| `Truncate(lc, rc, t) => truncateToString(lc, rc, nodeToString(t))
| `Render(t) => nodeToString(t)
| _ => ""; // SymbolicDist and RenderedDist are handled in ExpressionTree.toString.
};

16
src/distPlus/renderers/DistPlusRenderer.re
View File

@ -1,13 +1,13 @@
let truncateIfShould =
let downsampleIfShould =
(
{recommendedLength, shouldTruncate}: RenderTypes.DistPlusRenderer.inputs,
{recommendedLength, shouldDownsample}: RenderTypes.DistPlusRenderer.inputs,
outputs: RenderTypes.ShapeRenderer.Combined.outputs,
dist,
) => {
let willTruncate =
shouldTruncate
let willDownsample =
shouldDownsample
&& RenderTypes.ShapeRenderer.Combined.methodUsed(outputs) == `Sampling;
willTruncate ? dist |> Distributions.DistPlus.T.truncate(recommendedLength) : dist;
willDownsample ? dist |> Distributions.DistPlus.T.downsample(recommendedLength) : dist;
};
let run =
@ -21,7 +21,7 @@ let run =
~guesstimatorString=Some(inputs.distPlusIngredients.guesstimatorString),
(),
)
|> Distributions.DistPlus.T.scaleToIntegralSum(~intendedSum=1.0);
|> Distributions.DistPlus.T.normalize;
let outputs =
ShapeRenderer.run({
samplingInputs: inputs.samplingInputs,
@ -32,6 +32,6 @@ let run =
});
let shape = outputs |> RenderTypes.ShapeRenderer.Combined.getShape;
let dist =
shape |> E.O.fmap(toDist) |> E.O.fmap(truncateIfShould(inputs, outputs));
shape |> E.O.fmap(toDist) |> E.O.fmap(downsampleIfShould(inputs, outputs));
RenderTypes.DistPlusRenderer.Outputs.make(outputs, dist);
};
};

12
src/distPlus/renderers/RenderTypes.re
View File

@ -43,7 +43,7 @@ module ShapeRenderer = {
module Symbolic = {
type inputs = {length: int};
type outputs = {
graph: SymbolicDist.bigDist,
graph: ExpressionTypes.ExpressionTree.node,
shape: DistTypes.shape,
};
let make = (graph, shape) => {graph, shape};
@ -75,7 +75,7 @@ module ShapeRenderer = {
module DistPlusRenderer = {
let defaultRecommendedLength = 10000;
let defaultShouldTruncate = true;
let defaultShouldDownsample = true;
type ingredients = {
guesstimatorString: string,
domain: DistTypes.domain,
@ -85,7 +85,7 @@ module DistPlusRenderer = {
distPlusIngredients: ingredients,
samplingInputs: ShapeRenderer.Sampling.inputs,
recommendedLength: int,
shouldTruncate: bool,
shouldDownsample: bool,
};
module Ingredients = {
let make =
@ -105,7 +105,7 @@ module DistPlusRenderer = {
(
~samplingInputs=ShapeRenderer.Sampling.Inputs.empty,
~recommendedLength=defaultRecommendedLength,
~shouldTruncate=defaultShouldTruncate,
~shouldDownsample=defaultShouldDownsample,
~distPlusIngredients,
(),
)
@ -113,7 +113,7 @@ module DistPlusRenderer = {
distPlusIngredients,
samplingInputs,
recommendedLength,
shouldTruncate,
shouldDownsample,
};
type outputs = {
shapeRenderOutputs: ShapeRenderer.Combined.outputs,
@ -124,4 +124,4 @@ module DistPlusRenderer = {
let shapeRenderOutputs = (t:outputs) => t.shapeRenderOutputs
let make = (shapeRenderOutputs, distPlus) => {shapeRenderOutputs, distPlus};
}
};
};

4
src/distPlus/renderers/ShapeRenderer.re
View File

@ -21,7 +21,7 @@ let runSymbolic = (guesstimatorString, length) => {
|> E.R.fmap(g =>
RenderTypes.ShapeRenderer.Symbolic.make(
g,
SymbolicDist.toShape(length, g),
ExpressionTree.toShape(length, g),
)
);
};
@ -43,4 +43,4 @@ let run =
};
Js.log3("IS SOME?", symbolic |> E.R.toOption |> E.O.isSome, symbolic);
{symbolic: Some(symbolic), sampling};
};
};

6
src/distPlus/renderers/samplesRenderer/Guesstimator.re
View File

@ -4,10 +4,10 @@ type discrete = {
ys: array(float),
};
let jsToDistDiscrete = (d: discrete): DistTypes.discreteShape => {
let jsToDistDiscrete = (d: discrete): DistTypes.discreteShape => {xyShape: {
xs: xsGet(d),
ys: ysGet(d),
};
}, knownIntegralSum: None};
[@bs.module "./GuesstimatorLibrary.js"]
external stringToSamples: (string, int) => array(float) = "stringToSamples";
external stringToSamples: (string, int) => array(float) = "stringToSamples";

11
src/distPlus/renderers/samplesRenderer/Samples.re
View File

@ -115,11 +115,12 @@ module T = {
Array.fast_sort(compare, samples);
let (continuousPart, discretePart) = E.A.Sorted.Floats.split(samples);
let length = samples |> E.A.length |> float_of_int;
let discrete: DistTypes.xyShape =
let discrete: DistTypes.discreteShape =
discretePart
|> E.FloatFloatMap.fmap(r => r /. length)
|> E.FloatFloatMap.toArray
|> XYShape.T.fromZippedArray;
|> XYShape.T.fromZippedArray
|> Distributions.Discrete.make(_, None);
let pdf =
continuousPart |> E.A.length > 5
@ -149,14 +150,14 @@ module T = {
~outputXYPoints=samplingInputs.outputXYPoints,
formatUnitWidth(usedUnitWidth),
)
|> Distributions.Continuous.make(`Linear)
|> Distributions.Continuous.make(`Linear, _, None)
|> (r => Some((r, foo)));
}
: None;
let shape =
MixedShapeBuilder.buildSimple(
~continuous=pdf |> E.O.fmap(fst),
~discrete,
~discrete=Some(discrete),
);
let samplesParse: RenderTypes.ShapeRenderer.Sampling.outputs = {
continuousParseParams: pdf |> E.O.fmap(snd),
@ -196,4 +197,4 @@ module T = {
Some(fromSamples(~samplingInputs, samples));
};
};
};
};

273
src/distPlus/symbolic/MathJsParser.re
View File

@ -1,273 +0,0 @@
// todo: rename to SymbolicParser
module MathJsonToMathJsAdt = {
type arg =
| Symbol(string)
| Value(float)
| Fn(fn)
| Array(array(arg))
| Object(Js.Dict.t(arg))
and fn = {
name: string,
args: array(arg),
};
let rec run = (j: Js.Json.t) =>
Json.Decode.(
switch (field("mathjs", string, j)) {
| "FunctionNode" =>
let args = j |> field("args", array(run));
Some(
Fn({
name: j |> field("fn", field("name", string)),
args: args |> E.A.O.concatSomes,
}),
);
| "OperatorNode" =>
let args = j |> field("args", array(run));
Some(
Fn({
name: j |> field("fn", string),
args: args |> E.A.O.concatSomes,
}),
);
| "ConstantNode" =>
optional(field("value", Json.Decode.float), j)
|> E.O.fmap(r => Value(r))
| "ParenthesisNode" => j |> field("content", run)
| "ObjectNode" =>
let properties = j |> field("properties", dict(run));
Js.Dict.entries(properties)
|> E.A.fmap(((key, value)) => value |> E.O.fmap(v => (key, v)))
|> E.A.O.concatSomes
|> Js.Dict.fromArray
|> (r => Some(Object(r)));
| "ArrayNode" =>
let items = field("items", array(run), j);
Some(Array(items |> E.A.O.concatSomes));
| "SymbolNode" => Some(Symbol(field("name", string, j)))
| n =>
Js.log3("Couldn't parse mathjs node", j, n);
None;
}
);
};
module MathAdtToDistDst = {
open MathJsonToMathJsAdt;
module MathAdtCleaner = {
let transformWithSymbol = (f: float, s: string) =>
switch (s) {
| "K"
| "k" => f *. 1000.
| "M"
| "m" => f *. 1000000.
| "B"
| "b" => f *. 1000000000.
| "T"
| "t" => f *. 1000000000000.
| _ => f
};
let rec run =
fun
| Fn({name: "multiply", args: [|Value(f), Symbol(s)|]}) =>
Value(transformWithSymbol(f, s))
| Fn({name: "unaryMinus", args: [|Value(f)|]}) => Value((-1.0) *. f)
| Fn({name, args}) => Fn({name, args: args |> E.A.fmap(run)})
| Array(args) => Array(args |> E.A.fmap(run))
| Symbol(s) => Symbol(s)
| Value(v) => Value(v)
| Object(v) =>
Object(
v
|> Js.Dict.entries
|> E.A.fmap(((key, value)) => (key, run(value)))
|> Js.Dict.fromArray,
);
};
let normal: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(mean), Value(stdev)|] =>
Ok(`Simple(`Normal({mean, stdev})))
| _ => Error("Wrong number of variables in normal distribution");
let lognormal: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(mu), Value(sigma)|] => Ok(`Simple(`Lognormal({mu, sigma})))
| [|Object(o)|] => {
let g = Js.Dict.get(o);
switch (g("mean"), g("stdev"), g("mu"), g("sigma")) {
| (Some(Value(mean)), Some(Value(stdev)), _, _) =>
Ok(`Simple(SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev)))
| (_, _, Some(Value(mu)), Some(Value(sigma))) =>
Ok(`Simple(`Lognormal({mu, sigma})))
| _ => Error("Lognormal distribution would need mean and stdev")
};
}
| _ => Error("Wrong number of variables in lognormal distribution");
let to_: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(low), Value(high)|] when low <= 0.0 && low < high=> {
Ok(`Simple(SymbolicDist.Normal.from90PercentCI(low, high)));
}
| [|Value(low), Value(high)|] when low < high => {
Ok(`Simple(SymbolicDist.Lognormal.from90PercentCI(low, high)));
}
| [|Value(_), Value(_)|] =>
Error("Low value must be less than high value.")
| _ => Error("Wrong number of variables in lognormal distribution");
let uniform: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(low), Value(high)|] => Ok(`Simple(`Uniform({low, high})))
| _ => Error("Wrong number of variables in lognormal distribution");
let beta: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(alpha), Value(beta)|] => Ok(`Simple(`Beta({alpha, beta})))
| _ => Error("Wrong number of variables in lognormal distribution");
let exponential: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(rate)|] => Ok(`Simple(`Exponential({rate: rate})))
| _ => Error("Wrong number of variables in Exponential distribution");
let cauchy: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(local), Value(scale)|] =>
Ok(`Simple(`Cauchy({local, scale})))
| _ => Error("Wrong number of variables in cauchy distribution");
let triangular: array(arg) => result(SymbolicDist.bigDist, string) =
fun
| [|Value(low), Value(medium), Value(high)|] =>
Ok(`Simple(`Triangular({low, medium, high})))
| _ => Error("Wrong number of variables in triangle distribution");
let multiModal =
(
args: array(result(SymbolicDist.bigDist, string)),
weights: option(array(float)),
) => {
let weights = weights |> E.O.default([||]);
let dists =
args
|> E.A.fmap(
fun
| Ok(`Simple(n)) => Ok(n)
| Error(e) => Error(e)
| Ok(k) => Error(SymbolicDist.toString(k)),
);
let firstWithError = dists |> Belt.Array.getBy(_, Belt.Result.isError);
let withoutErrors = dists |> E.A.fmap(E.R.toOption) |> E.A.O.concatSomes;
switch (firstWithError) {
| Some(Error(e)) => Error(e)
| None when withoutErrors |> E.A.length == 0 =>
Error("Multimodals need at least one input")
| _ =>
withoutErrors
|> E.A.fmapi((index, item) =>
(item, weights |> E.A.get(_, index) |> E.O.default(1.0))
)
|> (r => Ok(`PointwiseCombination(r)))
};
};
let arrayParser = (args:array(arg)):result(SymbolicDist.bigDist, string) => {
let samples = args
|> E.A.fmap(
fun
| Value(n) => Some(n)
| _ => None
)
|> E.A.O.concatSomes
let outputs = Samples.T.fromSamples(samples);
let pdf = outputs.shape |> E.O.bind(_,Distributions.Shape.T.toContinuous)
let shape = pdf |> E.O.fmap(pdf => {
let _pdf = Distributions.Continuous.T.scaleToIntegralSum(~cache=None, ~intendedSum=1.0, pdf);
let cdf = Distributions.Continuous.T.integral(~cache=None, _pdf);
SymbolicDist.ContinuousShape.make(_pdf, cdf)
})
switch(shape){
| Some(s) => Ok(`Simple(`ContinuousShape(s)))
| None => Error("Rendering did not work")
}
}
let rec functionParser = (r): result(SymbolicDist.bigDist, string) =>
r
|> (
fun
| Fn({name: "normal", args}) => normal(args)
| Fn({name: "lognormal", args}) => lognormal(args)
| Fn({name: "uniform", args}) => uniform(args)
| Fn({name: "beta", args}) => beta(args)
| Fn({name: "to", args}) => to_(args)
| Fn({name: "exponential", args}) => exponential(args)
| Fn({name: "cauchy", args}) => cauchy(args)
| Fn({name: "triangular", args}) => triangular(args)
| Value(f) => Ok(`Simple(`Float(f)))
| Fn({name: "mm", args}) => {
let weights =
args
|> E.A.last
|> E.O.bind(
_,
fun
| Array(values) => Some(values)
| _ => None,
)
|> E.O.fmap(o =>
o
|> E.A.fmap(
fun
| Value(r) => Some(r)
| _ => None,
)
|> E.A.O.concatSomes
);
let possibleDists =
E.O.isSome(weights)
? Belt.Array.slice(args, ~offset=0, ~len=E.A.length(args) - 1)
: args;
let dists = possibleDists |> E.A.fmap(functionParser);
multiModal(dists, weights);
}
| Fn({name}) => Error(name ++ ": function not supported")
| _ => {
Error("This type not currently supported");
}
);
let topLevel = (r): result(SymbolicDist.bigDist, string) =>
r
|> (
fun
| Fn(_) => functionParser(r)
| Value(r) => Ok(`Simple(`Float(r)))
| Array(r) => arrayParser(r)
| Symbol(_) => Error("Symbol not valid as top level")
| Object(_) => Error("Object not valid as top level")
);
let run = (r): result(SymbolicDist.bigDist, string) =>
r |> MathAdtCleaner.run |> topLevel;
};
let fromString = str => {
let mathJsToJson = Mathjs.parseMath(str);
let mathJsParse =
E.R.bind(mathJsToJson, r =>
switch (MathJsonToMathJsAdt.run(r)) {
| Some(r) => Ok(r)
| None => Error("MathJsParse Error")
}
);
let value = E.R.bind(mathJsParse, MathAdtToDistDst.run);
value;
};

8
src/distPlus/symbolic/MathjsWrapper.js
View File

@ -1,8 +0,0 @@
const math = require("mathjs");
function parseMath(f){ return JSON.parse(JSON.stringify(math.parse(f))) };
module.exports = {
parseMath,
};

361
src/distPlus/symbolic/SymbolicDist.re
View File

@ -1,70 +1,18 @@
type normal = {
mean: float,
stdev: float,
};
type lognormal = {
mu: float,
sigma: float,
};
type uniform = {
low: float,
high: float,
};
type beta = {
alpha: float,
beta: float,
};
type exponential = {rate: float};
type cauchy = {
local: float,
scale: float,
};
type triangular = {
low: float,
medium: float,
high: float,
};
type continuousShape = {
pdf: DistTypes.continuousShape,
cdf: DistTypes.continuousShape,
};
type contType = [ | `Continuous | `Discrete];
type dist = [
| `Normal(normal)
| `Beta(beta)
| `Lognormal(lognormal)
| `Uniform(uniform)
| `Exponential(exponential)
| `Cauchy(cauchy)
| `Triangular(triangular)
| `ContinuousShape(continuousShape)
| `Float(float)
];
type pointwiseAdd = array((dist, float));
type bigDist = [ | `Simple(dist) | `PointwiseCombination(pointwiseAdd)];
open SymbolicTypes;
module ContinuousShape = {
type t = continuousShape;
let make = (pdf, cdf): t => {pdf, cdf};
let pdf = (x, t: t) =>
Distributions.Continuous.T.xToY(x, t.pdf).continuous;
// TODO: pdf and inv are currently the same, this seems broken.
let inv = (p, t: t) =>
Distributions.Continuous.T.xToY(p, t.pdf).continuous;
// TODO: Fix the sampling, to have it work correctly.
let sample = (t: t) => 3.0;
// TODO: Fix the mean, to have it work correctly.
let mean = (t: t) => Ok(0.0);
let toString = t => {j|CustomContinuousShape|j};
let contType: contType = `Continuous;
};
module Exponential = {
@ -72,8 +20,8 @@ module Exponential = {
let pdf = (x, t: t) => Jstat.exponential##pdf(x, t.rate);
let inv = (p, t: t) => Jstat.exponential##inv(p, t.rate);
let sample = (t: t) => Jstat.exponential##sample(t.rate);
let mean = (t: t) => Ok(Jstat.exponential##mean(t.rate));
let toString = ({rate}: t) => {j|Exponential($rate)|j};
let contType: contType = `Continuous;
};
module Cauchy = {
@ -81,8 +29,8 @@ module Cauchy = {
let pdf = (x, t: t) => Jstat.cauchy##pdf(x, t.local, t.scale);
let inv = (p, t: t) => Jstat.cauchy##inv(p, t.local, t.scale);
let sample = (t: t) => Jstat.cauchy##sample(t.local, t.scale);
let mean = (_: t) => Error("Cauchy distributions have no mean value.");
let toString = ({local, scale}: t) => {j|Cauchy($local, $scale)|j};
let contType: contType = `Continuous;
};
module Triangular = {
@ -90,8 +38,8 @@ module Triangular = {
let pdf = (x, t: t) => Jstat.triangular##pdf(x, t.low, t.high, t.medium);
let inv = (p, t: t) => Jstat.triangular##inv(p, t.low, t.high, t.medium);
let sample = (t: t) => Jstat.triangular##sample(t.low, t.high, t.medium);
let mean = (t: t) => Ok(Jstat.triangular##mean(t.low, t.high, t.medium));
let toString = ({low, medium, high}: t) => {j|Triangular($low, $medium, $high)|j};
let contType: contType = `Continuous;
};
module Normal = {
@ -105,8 +53,35 @@ module Normal = {
};
let inv = (p, t: t) => Jstat.normal##inv(p, t.mean, t.stdev);
let sample = (t: t) => Jstat.normal##sample(t.mean, t.stdev);
let mean = (t: t) => Ok(Jstat.normal##mean(t.mean, t.stdev));
let toString = ({mean, stdev}: t) => {j|Normal($mean,$stdev)|j};
let contType: contType = `Continuous;
let add = (n1: t, n2: t) => {
let mean = n1.mean +. n2.mean;
let stdev = sqrt(n1.stdev ** 2. +. n2.stdev ** 2.);
`Normal({mean, stdev});
};
let subtract = (n1: t, n2: t) => {
let mean = n1.mean -. n2.mean;
let stdev = sqrt(n1.stdev ** 2. +. n2.stdev ** 2.);
`Normal({mean, stdev});
};
// TODO: is this useful here at all? would need the integral as well ...
let pointwiseProduct = (n1: t, n2: t) => {
let mean =
(n1.mean *. n2.stdev ** 2. +. n2.mean *. n1.stdev ** 2.)
/. (n1.stdev ** 2. +. n2.stdev ** 2.);
let stdev = 1. /. (1. /. n1.stdev ** 2. +. 1. /. n2.stdev ** 2.);
`Normal({mean, stdev});
};
let operate = (operation: Operation.Algebraic.t, n1: t, n2: t) =>
switch (operation) {
| `Add => Some(add(n1, n2))
| `Subtract => Some(subtract(n1, n2))
| _ => None
};
};
module Beta = {
@ -114,17 +89,17 @@ module Beta = {
let pdf = (x, t: t) => Jstat.beta##pdf(x, t.alpha, t.beta);
let inv = (p, t: t) => Jstat.beta##inv(p, t.alpha, t.beta);
let sample = (t: t) => Jstat.beta##sample(t.alpha, t.beta);
let mean = (t: t) => Ok(Jstat.beta##mean(t.alpha, t.beta));
let toString = ({alpha, beta}: t) => {j|Beta($alpha,$beta)|j};
let contType: contType = `Continuous;
};
module Lognormal = {
type t = lognormal;
let pdf = (x, t: t) => Jstat.lognormal##pdf(x, t.mu, t.sigma);
let inv = (p, t: t) => Jstat.lognormal##inv(p, t.mu, t.sigma);
let mean = (t: t) => Ok(Jstat.lognormal##mean(t.mu, t.sigma));
let sample = (t: t) => Jstat.lognormal##sample(t.mu, t.sigma);
let toString = ({mu, sigma}: t) => {j|Lognormal($mu,$sigma)|j};
let contType: contType = `Continuous;
let from90PercentCI = (low, high) => {
let logLow = Js.Math.log(low);
let logHigh = Js.Math.log(high);
@ -144,6 +119,23 @@ module Lognormal = {
);
`Lognormal({mu, sigma});
};
let multiply = (l1, l2) => {
let mu = l1.mu +. l2.mu;
let sigma = l1.sigma +. l2.sigma;
`Lognormal({mu, sigma});
};
let divide = (l1, l2) => {
let mu = l1.mu -. l2.mu;
let sigma = l1.sigma +. l2.sigma;
`Lognormal({mu, sigma});
};
let operate = (operation: Operation.Algebraic.t, n1: t, n2: t) =>
switch (operation) {
| `Multiply => Some(multiply(n1, n2))
| `Divide => Some(divide(n1, n2))
| _ => None
};
};
module Uniform = {
@ -151,20 +143,20 @@ module Uniform = {
let pdf = (x, t: t) => Jstat.uniform##pdf(x, t.low, t.high);
let inv = (p, t: t) => Jstat.uniform##inv(p, t.low, t.high);
let sample = (t: t) => Jstat.uniform##sample(t.low, t.high);
let mean = (t: t) => Ok(Jstat.uniform##mean(t.low, t.high));
let toString = ({low, high}: t) => {j|Uniform($low,$high)|j};
let contType: contType = `Continuous;
};
module Float = {
type t = float;
let pdf = (x, t: t) => x == t ? 1.0 : 0.0;
let inv = (p, t: t) => p < t ? 0.0 : 1.0;
let mean = (t: t) => Ok(t);
let sample = (t: t) => t;
let toString = Js.Float.toString;
let contType: contType = `Discrete;
};
module GenericSimple = {
module T = {
let minCdfValue = 0.0001;
let maxCdfValue = 0.9999;
@ -181,19 +173,6 @@ module GenericSimple = {
| `ContinuousShape(n) => ContinuousShape.pdf(x, n)
};
let contType = (dist: dist): contType =>
switch (dist) {
| `Normal(_) => Normal.contType
| `Triangular(_) => Triangular.contType
| `Exponential(_) => Exponential.contType
| `Cauchy(_) => Cauchy.contType
| `Lognormal(_) => Lognormal.contType
| `Uniform(_) => Uniform.contType
| `Beta(_) => Beta.contType
| `Float(_) => Float.contType
| `ContinuousShape(_) => ContinuousShape.contType
};
let inv = (x, dist) =>
switch (dist) {
| `Normal(n) => Normal.inv(x, n)
@ -207,7 +186,7 @@ module GenericSimple = {
| `ContinuousShape(n) => ContinuousShape.inv(x, n)
};
let sample: dist => float =
let sample: symbolicDist => float =
fun
| `Normal(n) => Normal.sample(n)
| `Triangular(n) => Triangular.sample(n)
@ -219,7 +198,7 @@ module GenericSimple = {
| `Float(n) => Float.sample(n)
| `ContinuousShape(n) => ContinuousShape.sample(n);
let toString: dist => string =
let toString: symbolicDist => string =
fun
| `Triangular(n) => Triangular.toString(n)
| `Exponential(n) => Exponential.toString(n)
@ -231,7 +210,7 @@ module GenericSimple = {
| `Float(n) => Float.toString(n)
| `ContinuousShape(n) => ContinuousShape.toString(n);
let min: dist => float =
let min: symbolicDist => float =
fun
| `Triangular({low}) => low
| `Exponential(n) => Exponential.inv(minCdfValue, n)
@ -243,7 +222,7 @@ module GenericSimple = {
| `ContinuousShape(n) => ContinuousShape.inv(minCdfValue, n)
| `Float(n) => n;
let max: dist => float =
let max: symbolicDist => float =
fun
| `Triangular(n) => n.high
| `Exponential(n) => Exponential.inv(maxCdfValue, n)
@ -255,144 +234,84 @@ module GenericSimple = {
| `Uniform({high}) => high
| `Float(n) => n;
/* This function returns a list of x's at which to evaluate the overall distribution (for rendering).
This function is called separately for each individual distribution.
When called with xSelection=`Linear, this function will return (sampleCount) x's, evenly
distributed between the min and max of the distribution (whatever those are defined to be above).
When called with xSelection=`ByWeight, this function will distribute the x's such as to
match the cumulative shape of the distribution. This is slower but may give better results.
*/
let interpolateXs =
(~xSelection: [ | `Linear | `ByWeight]=`Linear, dist: dist, sampleCount) => {
switch (xSelection, dist) {
| (`Linear, _) => E.A.Floats.range(min(dist), max(dist), sampleCount)
| (`ByWeight, `Uniform(n)) =>
// In `ByWeight mode, uniform distributions get special treatment because we need two x's
// on either side for proper rendering (just left and right of the discontinuities).
let dx = 0.00001 *. (n.high -. n.low);
[|n.low -. dx, n.low +. dx, n.high -. dx, n.high +. dx|]
| (`ByWeight, _) =>
let ys = E.A.Floats.range(minCdfValue, maxCdfValue, sampleCount)
ys |> E.A.fmap(y => inv(y, dist))
};
};
let toShape =
(~xSelection: [ | `Linear | `ByWeight]=`Linear, dist: dist, sampleCount)
: DistTypes.shape => {
switch (dist) {
| `ContinuousShape(n) => n.pdf |> Distributions.Continuous.T.toShape
| dist =>
let xs = interpolateXs(~xSelection, dist, sampleCount);
let ys = xs |> E.A.fmap(r => pdf(r, dist));
XYShape.T.fromArrays(xs, ys)
|> Distributions.Continuous.make(`Linear, _)
|> Distributions.Continuous.T.toShape;
};
};
};
module PointwiseAddDistributionsWeighted = {
type t = pointwiseAdd;
let normalizeWeights = (dists: t) => {
let total = dists |> E.A.fmap(snd) |> E.A.Floats.sum;
dists |> E.A.fmap(((a, b)) => (a, b /. total));
};
let pdf = (x: float, dists: t) =>
dists
|> E.A.fmap(((e, w)) => GenericSimple.pdf(x, e) *. w)
|> E.A.Floats.sum;
let min = (dists: t) =>
dists |> E.A.fmap(d => d |> fst |> GenericSimple.min) |> E.A.min;
let max = (dists: t) =>
dists |> E.A.fmap(d => d |> fst |> GenericSimple.max) |> E.A.max;
let discreteShape = (dists: t, sampleCount: int) => {
let discrete =
dists
|> E.A.fmap(((r, e)) =>
r
|> (
fun
| `Float(r) => Some((r, e))
| _ => None
)
)
|> E.A.O.concatSomes
|> E.A.fmap(((x, y)) =>
({xs: [|x|], ys: [|y|]}: DistTypes.xyShape)
)
|> Distributions.Discrete.reduce((+.));
discrete;
};
let continuousShape = (dists: t, sampleCount: int) => {
let xs =
dists
|> E.A.fmap(r =>
r
|> fst
|> GenericSimple.interpolateXs(
~xSelection=`ByWeight,
_,
sampleCount / (dists |> E.A.length),
)
)
|> E.A.concatMany;
xs |> Array.fast_sort(compare);
let ys = xs |> E.A.fmap(pdf(_, dists));
XYShape.T.fromArrays(xs, ys) |> Distributions.Continuous.make(`Linear, _);
};
let toShape = (dists: t, sampleCount: int) => {
let normalized = normalizeWeights(dists);
let continuous =
normalized
|> E.A.filter(((r, _)) => GenericSimple.contType(r) == `Continuous)
|> continuousShape(_, sampleCount);
let discrete =
normalized
|> E.A.filter(((r, _)) => GenericSimple.contType(r) == `Discrete)
|> discreteShape(_, sampleCount);
let shape =
MixedShapeBuilder.buildSimple(~continuous=Some(continuous), ~discrete);
shape |> E.O.toExt("");
};
let toString = (dists: t) => {
let distString =
dists
|> E.A.fmap(d => GenericSimple.toString(fst(d)))
|> Js.Array.joinWith(",");
let weights =
dists
|> E.A.fmap(d =>
snd(d) |> Js.Float.toPrecisionWithPrecision(~digits=2)
)
|> Js.Array.joinWith(",");
{j|multimodal($distString, [$weights])|j};
};
};
let toString = (r: bigDist) =>
r
|> (
let mean: symbolicDist => result(float, string) =
fun
| `Simple(d) => GenericSimple.toString(d)
| `PointwiseCombination(d) =>
PointwiseAddDistributionsWeighted.toString(d)
);
| `Triangular(n) => Triangular.mean(n)
| `Exponential(n) => Exponential.mean(n)
| `Cauchy(n) => Cauchy.mean(n)
| `Normal(n) => Normal.mean(n)
| `Lognormal(n) => Lognormal.mean(n)
| `Beta(n) => Beta.mean(n)
| `ContinuousShape(n) => ContinuousShape.mean(n)
| `Uniform(n) => Uniform.mean(n)
| `Float(n) => Float.mean(n);
let toShape = n =>
fun
| `Simple(d) => GenericSimple.toShape(~xSelection=`ByWeight, d, n)
| `PointwiseCombination(d) =>
PointwiseAddDistributionsWeighted.toShape(d, n);
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
switch (distToFloatOp) {
| `Pdf(f) => Ok(pdf(f, s))
| `Inv(f) => Ok(inv(f, s))
| `Sample => Ok(sample(s))
| `Mean => mean(s)
};
let interpolateXs =
(~xSelection: [ | `Linear | `ByWeight]=`Linear, dist: symbolicDist, n) => {
switch (xSelection, dist) {
| (`Linear, _) => E.A.Floats.range(min(dist), max(dist), n)
/* | (`ByWeight, `Uniform(n)) =>
// In `ByWeight mode, uniform distributions get special treatment because we need two x's
// on either side for proper rendering (just left and right of the discontinuities).
let dx = 0.00001 *. (n.high -. n.low);
[|n.low -. dx, n.low +. dx, n.high -. dx, n.high +. dx|]; */
| (`ByWeight, _) =>
let ys = E.A.Floats.range(minCdfValue, maxCdfValue, n);
ys |> E.A.fmap(y => inv(y, dist));
};
};
/* Calling e.g. "Normal.operate" returns an optional that wraps a result.
If the optional is None, there is no valid analytic solution. If it Some, it
can still return an error if there is a serious problem,
like in the case of a divide by 0.
*/
type analyticalSimplificationResult = [
| `AnalyticalSolution(SymbolicTypes.symbolicDist)
| `Error(string)
| `NoSolution
];
let tryAnalyticalSimplification =
(
d1: symbolicDist,
d2: symbolicDist,
op: ExpressionTypes.algebraicOperation,
)
: analyticalSimplificationResult =>
switch (d1, d2) {
| (`Float(v1), `Float(v2)) =>
switch (Operation.Algebraic.applyFn(op, v1, v2)) {
| Ok(r) => `AnalyticalSolution(`Float(r))
| Error(n) => `Error(n)
}
| (`Normal(v1), `Normal(v2)) =>
Normal.operate(op, v1, v2)
|> E.O.dimap(r => `AnalyticalSolution(r), () => `NoSolution)
| (`Lognormal(v1), `Lognormal(v2)) =>
Lognormal.operate(op, v1, v2)
|> E.O.dimap(r => `AnalyticalSolution(r), () => `NoSolution)
| _ => `NoSolution
};
let toShape = (sampleCount, d: symbolicDist): DistTypes.shape =>
switch (d) {
| `Float(v) =>
Discrete(
Distributions.Discrete.make({xs: [|v|], ys: [|1.0|]}, Some(1.0)),
)
| _ =>
let xs = interpolateXs(~xSelection=`ByWeight, d, sampleCount);
let ys = xs |> E.A.fmap(x => pdf(x, d));
Continuous(
Distributions.Continuous.make(`Linear, {xs, ys}, Some(1.0)),
);
};
};

49
src/distPlus/symbolic/SymbolicTypes.re Normal file
View File

@ -0,0 +1,49 @@
type normal = {
mean: float,
stdev: float,
};
type lognormal = {
mu: float,
sigma: float,
};
type uniform = {
low: float,
high: float,
};
type beta = {
alpha: float,
beta: float,
};
type exponential = {rate: float};
type cauchy = {
local: float,
scale: float,
};
type triangular = {
low: float,
medium: float,
high: float,
};
type continuousShape = {
pdf: DistTypes.continuousShape,
cdf: DistTypes.continuousShape,
};
type symbolicDist = [
| `Normal(normal)
| `Beta(beta)
| `Lognormal(lognormal)
| `Uniform(uniform)
| `Exponential(exponential)
| `Cauchy(cauchy)
| `Triangular(triangular)
| `ContinuousShape(continuousShape)
| `Float(float) // Dirac delta at x. Practically useful only in the context of multimodals.
];

10
src/distPlus/utility/Jstat.re
View File

@ -5,6 +5,7 @@ type normal = {
[@bs.meth] "cdf": (float, float, float) => float,
[@bs.meth] "inv": (float, float, float) => float,
[@bs.meth] "sample": (float, float) => float,
[@bs.meth] "mean": (float, float) => float,
};
type lognormal = {
.
@ -12,6 +13,7 @@ type lognormal = {
[@bs.meth] "cdf": (float, float, float) => float,
[@bs.meth] "inv": (float, float, float) => float,
[@bs.meth] "sample": (float, float) => float,
[@bs.meth] "mean": (float, float) => float,
};
type uniform = {
.
@ -19,6 +21,7 @@ type uniform = {
[@bs.meth] "cdf": (float, float, float) => float,
[@bs.meth] "inv": (float, float, float) => float,
[@bs.meth] "sample": (float, float) => float,
[@bs.meth] "mean": (float, float) => float,
};
type beta = {
.
@ -26,6 +29,7 @@ type beta = {
[@bs.meth] "cdf": (float, float, float) => float,
[@bs.meth] "inv": (float, float, float) => float,
[@bs.meth] "sample": (float, float) => float,
[@bs.meth] "mean": (float, float) => float,
};
type exponential = {
.
@ -33,6 +37,7 @@ type exponential = {
[@bs.meth] "cdf": (float, float) => float,
[@bs.meth] "inv": (float, float) => float,
[@bs.meth] "sample": float => float,
[@bs.meth] "mean": float => float,
};
type cauchy = {
.
@ -47,6 +52,7 @@ type triangular = {
[@bs.meth] "cdf": (float, float, float, float) => float,
[@bs.meth] "inv": (float, float, float, float) => float,
[@bs.meth] "sample": (float, float, float) => float,
[@bs.meth] "mean": (float, float, float) => float,
};
// Pareto doesn't have sample for some reason
@ -61,6 +67,7 @@ type poisson = {
[@bs.meth] "pdf": (float, float) => float,
[@bs.meth] "cdf": (float, float) => float,
[@bs.meth] "sample": float => float,
[@bs.meth] "mean": float => float,
};
type weibull = {
.
@ -68,6 +75,7 @@ type weibull = {
[@bs.meth] "cdf": (float, float, float) => float,
[@bs.meth] "inv": (float, float, float) => float,
[@bs.meth] "sample": (float, float) => float,
[@bs.meth] "mean": (float, float) => float,
};
type binomial = {
.
@ -101,4 +109,4 @@ external quartiles: (array(float)) => array(float) = "quartiles";
[@bs.module "jstat"]
external quantiles: (array(float), array(float)) => array(float) = "quantiles";
[@bs.module "jstat"]
external percentile: (array(float), float, bool) => float = "percentile";
external percentile: (array(float), float, bool) => float = "percentile";

4
src/interface/FormBuilder.re
View File

@ -22,7 +22,7 @@ let propValue = (t: Prop.Value.t) => {
RenderTypes.DistPlusRenderer.make(
~distPlusIngredients=r,
~recommendedLength=10000,
~shouldTruncate=true,
~shouldDownsample=true,
(),
)
|> DistPlusRenderer.run
@ -105,4 +105,4 @@ module ModelForm = {
</div>
</div>;
};
};
};