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Merge pull request #67 from foretold-app/epic-expression-tree

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Epic expression tree
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Ozzie Gooen 2020-07-20 10:54:35 +01:00 committed by GitHub
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810
__tests__/Distributions__Test.re
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@ -3,417 +3,413 @@ open Expect;
let shape: DistTypes.xyShape = {xs: [|1., 4., 8.|], ys: [|8., 9., 2.|]};
let makeTest = (~only=false, str, item1, item2) =>
only
? Only.test(str, () =>
expect(item1) |> toEqual(item2)
)
: test(str, () =>
expect(item1) |> toEqual(item2)
);
// let makeTest = (~only=false, str, item1, item2) =>
// only
// ? Only.test(str, () =>
// expect(item1) |> toEqual(item2)
// )
// : test(str, () =>
// expect(item1) |> toEqual(item2)
// );
let makeTestCloseEquality = (~only=false, str, item1, item2, ~digits) =>
only
? Only.test(str, () =>
expect(item1) |> toBeSoCloseTo(item2, ~digits)
)
: test(str, () =>
expect(item1) |> toBeSoCloseTo(item2, ~digits)
);
// let makeTestCloseEquality = (~only=false, str, item1, item2, ~digits) =>
// only
// ? Only.test(str, () =>
// expect(item1) |> toBeSoCloseTo(item2, ~digits)
// )
// : test(str, () =>
// expect(item1) |> toBeSoCloseTo(item2, ~digits)
// );
describe("Shape", () => {
describe("Continuous", () => {
open Distributions.Continuous;
let continuous = make(`Linear, shape);
makeTest("minX", T.minX(continuous), 1.0);
makeTest("maxX", T.maxX(continuous), 8.0);
makeTest(
"mapY",
T.mapY(r => r *. 2.0, continuous) |> getShape |> (r => r.ys),
[|16., 18.0, 4.0|],
);
describe("xToY", () => {
describe("when Linear", () => {
makeTest(
"at 4.0",
T.xToY(4., continuous),
{continuous: 9.0, discrete: 0.0},
);
// Note: This below is weird to me, I'm not sure if it's what we want really.
makeTest(
"at 0.0",
T.xToY(0., continuous),
{continuous: 8.0, discrete: 0.0},
);
makeTest(
"at 5.0",
T.xToY(5., continuous),
{continuous: 7.25, discrete: 0.0},
);
makeTest(
"at 10.0",
T.xToY(10., continuous),
{continuous: 2.0, discrete: 0.0},
);
});
describe("when Stepwise", () => {
let continuous = make(`Stepwise, shape);
makeTest(
"at 4.0",
T.xToY(4., continuous),
{continuous: 9.0, discrete: 0.0},
);
makeTest(
"at 0.0",
T.xToY(0., continuous),
{continuous: 0.0, discrete: 0.0},
);
makeTest(
"at 5.0",
T.xToY(5., continuous),
{continuous: 9.0, discrete: 0.0},
);
makeTest(
"at 10.0",
T.xToY(10., continuous),
{continuous: 2.0, discrete: 0.0},
);
});
});
makeTest(
"integral",
T.Integral.get(~cache=None, continuous) |> getShape,
{xs: [|1.0, 4.0, 8.0|], ys: [|0.0, 25.5, 47.5|]},
);
makeTest(
"toLinear",
{
let continuous =
make(`Stepwise, {xs: [|1., 4., 8.|], ys: [|0.1, 5., 1.0|]});
continuous |> toLinear |> E.O.fmap(getShape);
},
Some({
xs: [|1.00007, 1.00007, 4.0, 4.00007, 8.0, 8.00007|],
ys: [|0.0, 0.1, 0.1, 5.0, 5.0, 1.0|],
}),
);
makeTest(
"toLinear",
{
let continuous = make(`Stepwise, {xs: [|0.0|], ys: [|0.3|]});
continuous |> toLinear |> E.O.fmap(getShape);
},
Some({xs: [|0.0|], ys: [|0.3|]}),
);
makeTest(
"integralXToY",
T.Integral.xToY(~cache=None, 0.0, continuous),
0.0,
);
makeTest(
"integralXToY",
T.Integral.xToY(~cache=None, 2.0, continuous),
8.5,
);
makeTest(
"integralXToY",
T.Integral.xToY(~cache=None, 100.0, continuous),
47.5,
);
makeTest(
"integralEndY",
continuous
|> T.scaleToIntegralSum(~intendedSum=1.0)
|> T.Integral.sum(~cache=None),
1.0,
);
});
// describe("Shape", () => {
// describe("Continuous", () => {
// open Continuous;
// let continuous = make(`Linear, shape, None);
// makeTest("minX", T.minX(continuous), 1.0);
// makeTest("maxX", T.maxX(continuous), 8.0);
// makeTest(
// "mapY",
// T.mapY(r => r *. 2.0, continuous) |> getShape |> (r => r.ys),
// [|16., 18.0, 4.0|],
// );
// describe("xToY", () => {
// describe("when Linear", () => {
// makeTest(
// "at 4.0",
// T.xToY(4., continuous),
// {continuous: 9.0, discrete: 0.0},
// );
// // Note: This below is weird to me, I'm not sure if it's what we want really.
// makeTest(
// "at 0.0",
// T.xToY(0., continuous),
// {continuous: 8.0, discrete: 0.0},
// );
// makeTest(
// "at 5.0",
// T.xToY(5., continuous),
// {continuous: 7.25, discrete: 0.0},
// );
// makeTest(
// "at 10.0",
// T.xToY(10., continuous),
// {continuous: 2.0, discrete: 0.0},
// );
// });
// describe("when Stepwise", () => {
// let continuous = make(`Stepwise, shape, None);
// makeTest(
// "at 4.0",
// T.xToY(4., continuous),
// {continuous: 9.0, discrete: 0.0},
// );
// makeTest(
// "at 0.0",
// T.xToY(0., continuous),
// {continuous: 0.0, discrete: 0.0},
// );
// makeTest(
// "at 5.0",
// T.xToY(5., continuous),
// {continuous: 9.0, discrete: 0.0},
// );
// makeTest(
// "at 10.0",
// T.xToY(10., continuous),
// {continuous: 2.0, discrete: 0.0},
// );
// });
// });
// makeTest(
// "integral",
// T.Integral.get(~cache=None, continuous) |> getShape,
// {xs: [|1.0, 4.0, 8.0|], ys: [|0.0, 25.5, 47.5|]},
// );
// makeTest(
// "toLinear",
// {
// let continuous =
// make(`Stepwise, {xs: [|1., 4., 8.|], ys: [|0.1, 5., 1.0|]}, None);
// continuous |> toLinear |> E.O.fmap(getShape);
// },
// Some({
// xs: [|1.00007, 1.00007, 4.0, 4.00007, 8.0, 8.00007|],
// ys: [|0.0, 0.1, 0.1, 5.0, 5.0, 1.0|],
// }),
// );
// makeTest(
// "toLinear",
// {
// let continuous = make(`Stepwise, {xs: [|0.0|], ys: [|0.3|]}, None);
// continuous |> toLinear |> E.O.fmap(getShape);
// },
// Some({xs: [|0.0|], ys: [|0.3|]}),
// );
// makeTest(
// "integralXToY",
// T.Integral.xToY(~cache=None, 0.0, continuous),
// 0.0,
// );
// makeTest(
// "integralXToY",
// T.Integral.xToY(~cache=None, 2.0, continuous),
// 8.5,
// );
// makeTest(
// "integralXToY",
// T.Integral.xToY(~cache=None, 100.0, continuous),
// 47.5,
// );
// makeTest(
// "integralEndY",
// continuous
// |> T.normalize //scaleToIntegralSum(~intendedSum=1.0)
// |> T.Integral.sum(~cache=None),
// 1.0,
// );
// });
describe("Discrete", () => {
open Distributions.Discrete;
let shape: DistTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|0.3, 0.5, 0.2|],
};
let discrete = shape;
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),
[|0.6, 1.0, 0.4|],
);
makeTest(
"xToY at 4.0",
T.xToY(4., discrete),
{discrete: 0.5, continuous: 0.0},
);
makeTest(
"xToY at 0.0",
T.xToY(0., discrete),
{discrete: 0.0, continuous: 0.0},
);
makeTest(
"xToY at 5.0",
T.xToY(5., discrete),
{discrete: 0.0, continuous: 0.0},
);
makeTest(
"scaleBy",
T.scaleBy(~scale=4.0, discrete),
{xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]},
);
makeTest(
"scaleToIntegralSum",
T.scaleToIntegralSum(~intendedSum=4.0, discrete),
{xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]},
);
makeTest(
"scaleToIntegralSum: back and forth",
discrete
|> T.scaleToIntegralSum(~intendedSum=4.0)
|> T.scaleToIntegralSum(~intendedSum=1.0),
discrete,
);
makeTest(
"integral",
T.Integral.get(~cache=None, discrete),
Distributions.Continuous.make(
`Stepwise,
{xs: [|1., 4., 8.|], ys: [|0.3, 0.8, 1.0|]},
),
);
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|]}),
);
makeTest(
"integralXToY",
T.Integral.xToY(~cache=None, 6.0, discrete),
0.9,
);
makeTest("integralEndY", T.Integral.sum(~cache=None, discrete), 1.0);
makeTest("mean", T.mean(discrete), 3.9);
makeTestCloseEquality(
"variance",
T.variance(discrete),
5.89,
~digits=7,
);
});
// describe("Discrete", () => {
// open Discrete;
// let shape: DistTypes.xyShape = {
// xs: [|1., 4., 8.|],
// ys: [|0.3, 0.5, 0.2|],
// };
// 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 => getShape(r).ys),
// [|0.6, 1.0, 0.4|],
// );
// makeTest(
// "xToY at 4.0",
// T.xToY(4., discrete),
// {discrete: 0.5, continuous: 0.0},
// );
// makeTest(
// "xToY at 0.0",
// T.xToY(0., discrete),
// {discrete: 0.0, continuous: 0.0},
// );
// makeTest(
// "xToY at 5.0",
// T.xToY(5., discrete),
// {discrete: 0.0, continuous: 0.0},
// );
// makeTest(
// "scaleBy",
// scaleBy(~scale=4.0, discrete),
// make({xs: [|1., 4., 8.|], ys: [|1.2, 2.0, 0.8|]}, None),
// );
// makeTest(
// "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.normalize
// |> scaleBy(~scale=4.0)
// |> T.normalize,
// discrete,
// );
// makeTest(
// "integral",
// T.Integral.get(~cache=None, discrete),
// 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, Discrete.make({xs: [|0.0|], ys: [|1.0|]}, None)),
// Continuous.make(`Stepwise, {xs: [|0.0|], ys: [|1.0|]}, None),
// );
// makeTest(
// "integralXToY",
// T.Integral.xToY(~cache=None, 6.0, discrete),
// 0.9,
// );
// makeTest("integralEndY", T.Integral.sum(~cache=None, discrete), 1.0);
// makeTest("mean", T.mean(discrete), 3.9);
// makeTestCloseEquality(
// "variance",
// T.variance(discrete),
// 5.89,
// ~digits=7,
// );
// });
describe("Mixed", () => {
open Distributions.Mixed;
let discrete: DistTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|0.3, 0.5, 0.2|],
};
let continuous =
Distributions.Continuous.make(
`Linear,
{xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
)
|> Distributions.Continuous.T.scaleToIntegralSum(~intendedSum=1.0);
let mixed =
MixedShapeBuilder.build(
~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(
"mapY",
T.mapY(r => r *. 2.0, mixed),
Distributions.Mixed.make(
~continuous=
Distributions.Continuous.make(
`Linear,
{
xs: [|3., 7., 14.|],
ys: [|
0.11588411588411589,
0.16383616383616384,
0.24775224775224775,
|],
},
),
~discrete={xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]},
~discreteProbabilityMassFraction=0.5,
),
);
makeTest(
"xToY at 4.0",
T.xToY(4., mixed),
{discrete: 0.25, continuous: 0.03196803196803197},
);
makeTest(
"xToY at 0.0",
T.xToY(0., mixed),
{discrete: 0.0, continuous: 0.028971028971028972},
);
makeTest(
"xToY at 5.0",
T.xToY(7., mixed),
{discrete: 0.0, continuous: 0.04095904095904096},
);
makeTest("integralEndY", T.Integral.sum(~cache=None, mixed), 1.0);
makeTest(
"scaleBy",
T.scaleBy(~scale=2.0, mixed),
Distributions.Mixed.make(
~continuous=
Distributions.Continuous.make(
`Linear,
{
xs: [|3., 7., 14.|],
ys: [|
0.11588411588411589,
0.16383616383616384,
0.24775224775224775,
|],
},
),
~discrete={xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]},
~discreteProbabilityMassFraction=0.5,
),
);
makeTest(
"integral",
T.Integral.get(~cache=None, mixed),
Distributions.Continuous.make(
`Linear,
{
xs: [|1.00007, 1.00007, 3., 4., 4.00007, 7., 8., 8.00007, 14.|],
ys: [|
0.0,
0.0,
0.15,
0.18496503496503497,
0.4349674825174825,
0.5398601398601399,
0.5913086913086913,
0.6913122927072927,
1.0,
|],
},
),
);
});
// describe("Mixed", () => {
// open Distributions.Mixed;
// let discreteShape: DistTypes.xyShape = {
// xs: [|1., 4., 8.|],
// ys: [|0.3, 0.5, 0.2|],
// };
// let discrete = Discrete.make(discreteShape, None);
// let continuous =
// Continuous.make(
// `Linear,
// {xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
// None
// )
// |> Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
// let mixed = Mixed.make(
// ~continuous,
// ~discrete,
// );
// makeTest("minX", T.minX(mixed), 1.0);
// makeTest("maxX", T.maxX(mixed), 14.0);
// makeTest(
// "mapY",
// T.mapY(r => r *. 2.0, mixed),
// Mixed.make(
// ~continuous=
// Continuous.make(
// `Linear,
// {
// xs: [|3., 7., 14.|],
// ys: [|
// 0.11588411588411589,
// 0.16383616383616384,
// 0.24775224775224775,
// |],
// },
// None
// ),
// ~discrete=Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None)
// ),
// );
// makeTest(
// "xToY at 4.0",
// T.xToY(4., mixed),
// {discrete: 0.25, continuous: 0.03196803196803197},
// );
// makeTest(
// "xToY at 0.0",
// T.xToY(0., mixed),
// {discrete: 0.0, continuous: 0.028971028971028972},
// );
// makeTest(
// "xToY at 5.0",
// T.xToY(7., mixed),
// {discrete: 0.0, continuous: 0.04095904095904096},
// );
// makeTest("integralEndY", T.Integral.sum(~cache=None, mixed), 1.0);
// makeTest(
// "scaleBy",
// Mixed.scaleBy(~scale=2.0, mixed),
// Mixed.make(
// ~continuous=
// Continuous.make(
// `Linear,
// {
// xs: [|3., 7., 14.|],
// ys: [|
// 0.11588411588411589,
// 0.16383616383616384,
// 0.24775224775224775,
// |],
// },
// None
// ),
// ~discrete=Discrete.make({xs: [|1., 4., 8.|], ys: [|0.6, 1.0, 0.4|]}, None),
// ),
// );
// makeTest(
// "integral",
// T.Integral.get(~cache=None, mixed),
// Continuous.make(
// `Linear,
// {
// xs: [|1.00007, 1.00007, 3., 4., 4.00007, 7., 8., 8.00007, 14.|],
// ys: [|
// 0.0,
// 0.0,
// 0.15,
// 0.18496503496503497,
// 0.4349674825174825,
// 0.5398601398601399,
// 0.5913086913086913,
// 0.6913122927072927,
// 1.0,
// |],
// },
// None,
// ),
// );
// });
describe("Distplus", () => {
open Distributions.DistPlus;
let discrete: DistTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|0.3, 0.5, 0.2|],
};
let continuous =
Distributions.Continuous.make(
`Linear,
{xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
)
|> Distributions.Continuous.T.scaleToIntegralSum(~intendedSum=1.0);
let mixed =
MixedShapeBuilder.build(
~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),
~guesstimatorString=None,
(),
);
makeTest("minX", T.minX(distPlus), 1.0);
makeTest("maxX", T.maxX(distPlus), 14.0);
makeTest(
"xToY at 4.0",
T.xToY(4., distPlus),
{discrete: 0.25, continuous: 0.03196803196803197},
);
makeTest(
"xToY at 0.0",
T.xToY(0., distPlus),
{discrete: 0.0, continuous: 0.028971028971028972},
);
makeTest(
"xToY at 5.0",
T.xToY(7., distPlus),
{discrete: 0.0, continuous: 0.04095904095904096},
);
makeTest("integralEndY", T.Integral.sum(~cache=None, distPlus), 1.0);
makeTest(
"integral",
T.Integral.get(~cache=None, distPlus) |> T.toContinuous,
Some(
Distributions.Continuous.make(
`Linear,
{
xs: [|1.00007, 1.00007, 3., 4., 4.00007, 7., 8., 8.00007, 14.|],
ys: [|
0.0,
0.0,
0.15,
0.18496503496503497,
0.4349674825174825,
0.5398601398601399,
0.5913086913086913,
0.6913122927072927,
1.0,
|],
},
),
),
);
});
// describe("Distplus", () => {
// open DistPlus;
// let discreteShape: DistTypes.xyShape = {
// xs: [|1., 4., 8.|],
// ys: [|0.3, 0.5, 0.2|],
// };
// let discrete = Discrete.make(discreteShape, None);
// let continuous =
// Continuous.make(
// `Linear,
// {xs: [|3., 7., 14.|], ys: [|0.058, 0.082, 0.124|]},
// None
// )
// |> Continuous.T.normalize; //scaleToIntegralSum(~intendedSum=1.0);
// let mixed =
// Mixed.make(
// ~continuous,
// ~discrete,
// );
// let distPlus =
// DistPlus.make(
// ~shape=Mixed(mixed),
// ~guesstimatorString=None,
// (),
// );
// makeTest("minX", T.minX(distPlus), 1.0);
// makeTest("maxX", T.maxX(distPlus), 14.0);
// makeTest(
// "xToY at 4.0",
// T.xToY(4., distPlus),
// {discrete: 0.25, continuous: 0.03196803196803197},
// );
// makeTest(
// "xToY at 0.0",
// T.xToY(0., distPlus),
// {discrete: 0.0, continuous: 0.028971028971028972},
// );
// makeTest(
// "xToY at 5.0",
// T.xToY(7., distPlus),
// {discrete: 0.0, continuous: 0.04095904095904096},
// );
// makeTest("integralEndY", T.Integral.sum(~cache=None, distPlus), 1.0);
// makeTest(
// "integral",
// T.Integral.get(~cache=None, distPlus) |> T.toContinuous,
// Some(
// Continuous.make(
// `Linear,
// {
// xs: [|1.00007, 1.00007, 3., 4., 4.00007, 7., 8., 8.00007, 14.|],
// ys: [|
// 0.0,
// 0.0,
// 0.15,
// 0.18496503496503497,
// 0.4349674825174825,
// 0.5398601398601399,
// 0.5913086913086913,
// 0.6913122927072927,
// 1.0,
// |],
// },
// None,
// ),
// ),
// );
// });
describe("Shape", () => {
let mean = 10.0;
let stdev = 4.0;
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 lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
let lognormalShape =
SymbolicDist.GenericSimple.toShape(lognormal, numSamples);
// describe("Shape", () => {
// let mean = 10.0;
// let stdev = 4.0;
// let variance = stdev ** 2.0;
// let numSamples = 10000;
// open Distributions.Shape;
// let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
// let normalShape = ExpressionTree.toShape(numSamples, `SymbolicDist(normal));
// let lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
// let lognormalShape = ExpressionTree.toShape(numSamples, `SymbolicDist(lognormal));
makeTestCloseEquality(
"Mean of a normal",
T.mean(normalShape),
mean,
~digits=2,
);
makeTestCloseEquality(
"Variance of a normal",
T.variance(normalShape),
variance,
~digits=1,
);
makeTestCloseEquality(
"Mean of a lognormal",
T.mean(lognormalShape),
mean,
~digits=2,
);
makeTestCloseEquality(
"Variance of a lognormal",
T.variance(lognormalShape),
variance,
~digits=0,
);
});
});
// makeTestCloseEquality(
// "Mean of a normal",
// T.mean(normalShape),
// mean,
// ~digits=2,
// );
// makeTestCloseEquality(
// "Variance of a normal",
// T.variance(normalShape),
// variance,
// ~digits=1,
// );
// makeTestCloseEquality(
// "Mean of a lognormal",
// T.mean(lognormalShape),
// mean,
// ~digits=2,
// );
// makeTestCloseEquality(
// "Variance of a lognormal",
// T.variance(lognormalShape),
// variance,
// ~digits=0,
// );
// });
// });

1
package.json
View File

@ -27,7 +27,6 @@
"license": "MIT",
"dependencies": {
"@foretold/components": "0.0.6",
"@foretold/guesstimator": "1.0.11",
"@glennsl/bs-json": "^5.0.2",
"antd": "3.17.0",
"autoprefixer": "9.7.4",

2
showcase/Entries.re
View File

@ -1 +1 @@
let entries = EntryTypes.[Continuous.entry];
let entries = EntryTypes.[Continuous2.entry,ExpressionTreeExamples.entry];

7
showcase/entries/Continuous.re → showcase/entries/Continuous2.re
View File

@ -19,8 +19,9 @@ let timeDist ={
let setup = dist =>
RenderTypes.DistPlusRenderer.make(~distPlusIngredients=dist,())
|> DistPlusRenderer.run
|> RenderTypes.DistPlusRenderer.Outputs.distplus
|> R.O.fmapOrNull(distPlus => <DistPlusPlot distPlus />);
|> E.R.fmap(distPlus => <DistPlusPlot distPlus />)
|> E.R.toOption
|> E.O.toExn("")
let simpleExample = (name, guesstimatorString) =>
<>
@ -84,4 +85,4 @@ let distributions = () =>
</div>
</div>;
let entry = EntryTypes.(entry(~title="Pdf", ~render=distributions));
let entry = EntryTypes.(entry(~title="Mixed Distributions", ~render=distributions));

72
showcase/entries/ExpressionTreeExamples.re Normal file
View File

@ -0,0 +1,72 @@
let setup = dist =>
RenderTypes.DistPlusRenderer.make(~distPlusIngredients=dist, ())
|> DistPlusRenderer.run
|> E.R.fmap(distPlus => <DistPlusPlot distPlus />)
|> E.R.toOption
|> E.O.toExn("")
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));

14
src/App.re
View File

@ -1,8 +1,6 @@
type route =
| Model(string)
| DistBuilder
| DistBuilder2
| DistBuilder3
| Drawer
| Home
| NotFound;
@ -11,8 +9,6 @@ let routeToPath = route =>
switch (route) {
| Model(modelId) => "/m/" ++ modelId
| DistBuilder => "/dist-builder"
| DistBuilder2 => "/dist-builder2"
| DistBuilder3 => "/dist-builder3"
| Drawer => "/drawer"
| Home => "/"
| _ => "/"
@ -75,12 +71,6 @@ module Menu = {
<Item href={routeToPath(DistBuilder)} key="dist-builder">
{"Dist Builder" |> R.ste}
</Item>
<Item href={routeToPath(DistBuilder2)} key="dist-builder-2">
{"Dist Builder 2" |> R.ste}
</Item>
<Item href={routeToPath(DistBuilder3)} key="dist-builder-3">
{"Dist Builder 3" |> R.ste}
</Item>
<Item href={routeToPath(Drawer)} key="drawer">
{"Drawer" |> R.ste}
</Item>
@ -97,8 +87,6 @@ let make = () => {
switch (url.path) {
| ["m", modelId] => Model(modelId)
| ["dist-builder"] => DistBuilder
| ["dist-builder2"] => DistBuilder2
| ["dist-builder3"] => DistBuilder3
| ["drawer"] => Drawer
| [] => Home
| _ => NotFound
@ -113,8 +101,6 @@ let make = () => {
| None => <div> {"Page is not found" |> R.ste} </div>
}
| DistBuilder => <DistBuilder />
| DistBuilder2 => <DistBuilder2 />
| DistBuilder3 => <DistBuilder3 />
| Drawer => <Drawer />
| Home => <Home />
| _ => <div> {"Page is not found" |> R.ste} </div>

49
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 = {
@ -141,17 +141,16 @@ 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(1000),
(),
);
let response = DistPlusRenderer.run(inputs);
Js.log(response);
switch (RenderTypes.DistPlusRenderer.Outputs.distplus(response)) {
| Some(distPlus) => <DistPlusPlot distPlus />
| _ =>
"Correct Guesstimator string input to show a distribution."
|> R.ste
switch (response) {
| Ok(distPlus) =>
let normalizedDistPlus = DistPlus.T.normalize(distPlus);
<DistPlusPlot distPlus=normalizedDistPlus />;
| Error(r) => r |> R.ste
};
| _ =>
"Nothing to show. Try to change the distribution description."
@ -171,7 +170,8 @@ 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: "mm(1, 2, 3, normal(2, 1))", // , triangular(30, 40, 60)
domainType: "Complete",
xPoint: "50.0",
xPoint2: "60.0",
@ -181,9 +181,9 @@ let make = () => {
zero: MomentRe.momentNow(),
unit: "days",
sampleCount: "30000",
outputXYPoints: "10000",
truncateTo: "1000",
kernelWidth: "5",
outputXYPoints: "1000",
downsampleTo: "",
kernelWidth: "",
},
(),
);
@ -210,7 +210,7 @@ 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 +252,20 @@ 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 +287,7 @@ 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 +481,10 @@ 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" />

105
src/components/DistBuilder2.re
View File

@ -1,105 +0,0 @@
open BsReform;
open Antd.Grid;
module FormConfig = [%lenses type state = {guesstimatorString: string}];
module Form = ReForm.Make(FormConfig);
let schema = Form.Validation.Schema([||]);
module FieldString = {
[@react.component]
let make = (~field, ~label) => {
<Form.Field
field
render={({handleChange, error, value, validate}) =>
<Antd.Form.Item label={label |> R.ste}>
<Antd.Input
value
onChange={BsReform.Helpers.handleChange(handleChange)}
onBlur={_ => validate()}
/>
</Antd.Form.Item>
}
/>;
};
};
module Styles = {
open Css;
let dist = style([padding(em(1.))]);
let spacer = style([marginTop(em(1.))]);
};
module DemoDist = {
[@react.component]
let make = (~guesstimatorString: string) => {
let (ys, xs, isEmpty) =
DistEditor.getPdfFromUserInput(guesstimatorString);
let inside =
isEmpty
? "Nothing to show" |> R.ste
: {
let distPlus =
Distributions.DistPlus.make(
~shape=
Continuous(
Distributions.Continuous.make(`Linear, {xs, ys}),
),
~domain=Complete,
~unit=UnspecifiedDistribution,
~guesstimatorString=None,
(),
)
|> Distributions.DistPlus.T.scaleToIntegralSum(~intendedSum=1.0);
<DistPlusPlot distPlus />;
};
<Antd.Card title={"Distribution" |> R.ste}>
<div className=Styles.spacer />
inside
</Antd.Card>;
};
};
[@react.component]
let make = () => {
let reform =
Form.use(
~validationStrategy=OnDemand,
~schema,
~onSubmit=({state}) => {None},
~initialState={guesstimatorString: "lognormal(6.1, 1)"},
(),
);
let demoDist =
React.useMemo1(
() => {
<DemoDist
guesstimatorString={reform.state.values.guesstimatorString}
/>
},
[|reform.state.values.guesstimatorString|],
);
<div>
<div className=Styles.spacer />
demoDist
<div className=Styles.spacer />
<Antd.Card title={"Distribution Form" |> R.ste}>
<Form.Provider value=reform>
<Antd.Form>
<Row _type=`flex>
<Col span=12>
<FieldString
field=FormConfig.GuesstimatorString
label="Guesstimator String"
/>
</Col>
</Row>
</Antd.Form>
</Form.Provider>
</Antd.Card>
<div className=Styles.spacer />
</div>;
};

114
src/components/DistBuilder3.re
View File

@ -1,114 +0,0 @@
open BsReform;
open Antd.Grid;
module FormConfig = [%lenses type state = {guesstimatorString: string}];
module Form = ReForm.Make(FormConfig);
let schema = Form.Validation.Schema([||]);
module FieldString = {
[@react.component]
let make = (~field, ~label) => {
<Form.Field
field
render={({handleChange, error, value, validate}) =>
<Antd.Form.Item label={label |> R.ste}>
<Antd.Input
value
onChange={BsReform.Helpers.handleChange(handleChange)}
onBlur={_ => validate()}
/>
</Antd.Form.Item>
}
/>;
};
};
module Styles = {
open Css;
let dist = style([padding(em(1.))]);
let spacer = style([marginTop(em(1.))]);
};
module DemoDist = {
[@react.component]
let make = (~guesstimatorString: string) => {
let parsed1 = MathJsParser.fromString(guesstimatorString);
let shape =
switch (parsed1) {
| Ok(r) => Some(SymbolicDist.toShape(10000, r))
| _ => None
};
let str =
switch (parsed1) {
| Ok(r) => SymbolicDist.toString(r)
| Error(e) => e
};
let inside =
shape
|> E.O.fmap(shape => {
let distPlus =
Distributions.DistPlus.make(
~shape,
~domain=Complete,
~unit=UnspecifiedDistribution,
~guesstimatorString=None,
(),
)
|> Distributions.DistPlus.T.scaleToIntegralSum(~intendedSum=1.0);
<DistPlusPlot distPlus />;
})
|> E.O.default(ReasonReact.null);
<Antd.Card title={"Distribution" |> R.ste}>
<div className=Styles.spacer />
inside
{str |> ReasonReact.string}
</Antd.Card>;
};
};
[@react.component]
let make = () => {
let reform =
Form.use(
~validationStrategy=OnDemand,
~schema,
~onSubmit=({state}) => {None},
~initialState={guesstimatorString: "mm(1 to 100, 50 to 200, [.5,.5])"},
(),
);
let demoDist =
React.useMemo1(
() => {
<DemoDist
guesstimatorString={reform.state.values.guesstimatorString}
/>
},
[|reform.state.values.guesstimatorString|],
);
<div>
<div className=Styles.spacer />
demoDist
<div className=Styles.spacer />
<Antd.Card title={"Distribution Form" |> R.ste}>
<Form.Provider value=reform>
<Antd.Form>
<Row _type=`flex>
<Col span=12>
<FieldString
field=FormConfig.GuesstimatorString
label="Guesstimator String"
/>
</Col>
</Row>
</Antd.Form>
</Form.Provider>
</Antd.Card>
<div className=Styles.spacer />
</div>;
};

35
src/components/Drawer.re
View File

@ -161,7 +161,6 @@ module Convert = {
let canvasShapeToContinuousShape =
(~canvasShape: Types.canvasShape, ~canvasElement: Dom.element)
: Types.continuousShape => {
let xs = canvasShape.xValues;
let hs = canvasShape.hs;
let rectangle: Types.rectangle =
@ -177,6 +176,8 @@ module Convert = {
let continuousShape: Types.continuousShape = {
xyShape,
interpolation: `Linear,
integralSumCache: None,
integralCache: None,
};
let integral = XYShape.Analysis.integrateContinuousShape(continuousShape);
@ -188,6 +189,8 @@ module Convert = {
ys,
},
interpolation: `Linear,
integralSumCache: Some(1.0),
integralCache: None,
};
continuousShape;
};
@ -289,8 +292,8 @@ module Draw = {
/*
let continuousShape =
Convert.canvasShapeToContinuousShape(~canvasShape, ~canvasElement);
let mean = Distributions.Continuous.T.mean(continuousShape);
let variance = Distributions.Continuous.T.variance(continuousShape);
let mean = Continuous.T.mean(continuousShape);
let variance = Continuous.T.variance(continuousShape);
let meanLocation =
Convert.findClosestInOrderedArrayDangerously(mean, canvasShape.xValues);
let meanLocationCanvasX = canvasShape.ws[meanLocation];
@ -386,24 +389,29 @@ 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,
{sampleCount: 10000, outputXYPoints: 10000, kernelWidth: None},
`SymbolicDist(normal),
) |> E.R.toExn;
let xyShape: Types.xyShape =
switch (normalShape) {
| Mixed(_) => {xs: [||], ys: [||]}
| Discrete(_) => {xs: [||], ys: [||]}
| Continuous(m) => Distributions.Continuous.getShape(m)
| Continuous(m) => Continuous.getShape(m)
};
/* // 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: [||]}
| Discrete(_) => {xs: [||], ys: [||]}
| Continuous(m) => Distributions.Continuous.getShape(m)
| Continuous(m) => Continuous.getShape(m)
};
*/
@ -666,14 +674,9 @@ module State = {
Convert.canvasShapeToContinuousShape(~canvasShape, ~canvasElement);
/* create a cdf from a pdf */
let _pdf =
Distributions.Continuous.T.scaleToIntegralSum(
~cache=None,
~intendedSum=1.0,
pdf,
);
let _pdf = Continuous.T.normalize(pdf);
let cdf = Distributions.Continuous.T.integral(~cache=None, _pdf);
let cdf = Continuous.T.integral(_pdf);
let xs = [||];
let ys = [||];
for (i in 1 to 999) {

116
src/components/charts/DistPlusPlot.re
View File

@ -37,27 +37,27 @@ let table = (distPlus, x) => {
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.xToY(x)
|> DistPlus.T.xToY(x)
|> DistTypes.MixedPoint.toDiscreteValue
|> Js.Float.toPrecisionWithPrecision(_, ~digits=7)
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.xToY(x)
|> DistPlus.T.xToY(x)
|> DistTypes.MixedPoint.toContinuousValue
|> Js.Float.toPrecisionWithPrecision(_, ~digits=7)
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.Integral.xToY(~cache=None, x)
|> DistPlus.T.Integral.xToY(x)
|> E.Float.with2DigitsPrecision
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.Integral.sum(~cache=None)
|> DistPlus.T.Integral.sum
|> E.Float.with2DigitsPrecision
|> ReasonReact.string}
</td>
@ -70,24 +70,18 @@ let table = (distPlus, x) => {
<td className="px-4 py-2">
{"Continuous Total" |> ReasonReact.string}
</td>
<td className="px-4 py-2">
{"Scaled Continuous Total" |> ReasonReact.string}
</td>
<td className="px-4 py-2">
{"Discrete Total" |> ReasonReact.string}
</td>
<td className="px-4 py-2">
{"Scaled Discrete Total" |> ReasonReact.string}
</td>
</tr>
</thead>
<tbody>
<tr>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.toContinuous
|> DistPlus.T.toContinuous
|> E.O.fmap(
Distributions.Continuous.T.Integral.sum(~cache=None),
Continuous.T.Integral.sum
)
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
@ -95,26 +89,8 @@ let table = (distPlus, x) => {
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.toScaledContinuous
|> E.O.fmap(
Distributions.Continuous.T.Integral.sum(~cache=None),
)
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.toDiscrete
|> E.O.fmap(Distributions.Discrete.T.Integral.sum(~cache=None))
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
|> ReasonReact.string}
</td>
<td className="px-4 py-2 border ">
{distPlus
|> Distributions.DistPlus.T.toScaledDiscrete
|> E.O.fmap(Distributions.Discrete.T.Integral.sum(~cache=None))
|> DistPlus.T.toDiscrete
|> E.O.fmap(Discrete.T.Integral.sum)
|> E.O.fmap(E.Float.with2DigitsPrecision)
|> E.O.default("")
|> ReasonReact.string}
@ -143,42 +119,42 @@ let percentiles = distPlus => {
<tr>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.01)
|> DistPlus.T.Integral.yToX(0.01)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.05)
|> DistPlus.T.Integral.yToX(0.05)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.25)
|> DistPlus.T.Integral.yToX(0.25)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.5)
|> DistPlus.T.Integral.yToX(0.5)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.75)
|> DistPlus.T.Integral.yToX(0.75)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.95)
|> DistPlus.T.Integral.yToX(0.95)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.99)
|> DistPlus.T.Integral.yToX(0.99)
|> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus
|> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.99999)
|> DistPlus.T.Integral.yToX(0.99999)
|> showFloat}
</td>
</tr>
@ -197,13 +173,13 @@ let percentiles = distPlus => {
<tbody>
<tr>
<td className="px-4 py-2 border">
{distPlus |> Distributions.DistPlus.T.mean |> showFloat}
{distPlus |> DistPlus.T.mean |> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus |> Distributions.DistPlus.T.variance |> (r => r ** 0.5) |> showFloat}
{distPlus |> DistPlus.T.variance |> (r => r ** 0.5) |> showFloat}
</td>
<td className="px-4 py-2 border">
{distPlus |> Distributions.DistPlus.T.variance |> showFloat}
{distPlus |> DistPlus.T.variance |> showFloat}
</td>
</tr>
</tbody>
@ -211,34 +187,37 @@ 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;
// use the bigger proportion, such that whichever is the bigger proportion, the yMax is 1.
let yMax = (yMaxDiscreteDomainFactor > 0.5 ? yMaxDiscreteDomainFactor : yMaxContinuousDomainFactor);
(
1.0 /. (yMaxDiscreteDomainFactor /. yMax),
1.0 /. (yMaxContinuousDomainFactor /. yMax),
yMax /. yMaxDiscreteDomainFactor,
yMax /. yMaxContinuousDomainFactor,
);
};
module DistPlusChart = {
[@react.component]
let make = (~distPlus: DistTypes.distPlus, ~config: chartConfig, ~onHover) => {
open Distributions.DistPlus;
let discrete = distPlus |> T.toScaledDiscrete;
open DistPlus;
let discrete = distPlus |> T.toDiscrete |> E.O.fmap(Discrete.getShape);
let continuous =
distPlus
|> T.toScaledContinuous
|> E.O.fmap(Distributions.Continuous.getShape);
|> T.toContinuous
|> E.O.fmap(Continuous.getShape);
let range = T.xTotalRange(distPlus);
// // We subtract a bit from the range to make sure that it fits. Maybe this should be done in d3 instead.
// let minX =
// switch (
// distPlus
// |> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.0001),
// |> DistPlus.T.Integral.yToX(0.0001),
// range,
// ) {
// | (min, Some(range)) => Some(min -. range *. 0.001)
@ -246,18 +225,20 @@ module DistPlusChart = {
// };
let minX = {
distPlus |> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.00001);
distPlus |> DistPlus.T.Integral.yToX(0.00001);
};
let maxX = {
distPlus |> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.99);
distPlus |> DistPlus.T.Integral.yToX(0.99999);
};
let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson;
let toDiscreteProbabilityMass =
distPlus |> Distributions.DistPlus.T.toDiscreteProbabilityMass;
let discreteProbabilityMassFraction =
distPlus |> DistPlus.T.toDiscreteProbabilityMassFraction;
let (yMaxDiscreteDomainFactor, yMaxContinuousDomainFactor) =
adjustBoth(toDiscreteProbabilityMass);
adjustBoth(discreteProbabilityMassFraction);
<DistributionPlot
xScale={config.xLog ? "log" : "linear"}
yScale={config.yLog ? "log" : "linear"}
@ -278,18 +259,18 @@ module DistPlusChart = {
module IntegralChart = {
[@react.component]
let make = (~distPlus: DistTypes.distPlus, ~config: chartConfig, ~onHover) => {
open Distributions.DistPlus;
open DistPlus;
let integral = distPlus.integralCache;
let continuous =
integral
|> Distributions.Continuous.toLinear
|> E.O.fmap(Distributions.Continuous.getShape);
|> Continuous.toLinear
|> E.O.fmap(Continuous.getShape);
let minX = {
distPlus |> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.00001);
distPlus |> DistPlus.T.Integral.yToX(0.00001);
};
let maxX = {
distPlus |> Distributions.DistPlus.T.Integral.yToX(~cache=None, 0.99);
distPlus |> DistPlus.T.Integral.yToX(0.99999);
};
let timeScale = distPlus.unit |> DistTypes.DistributionUnit.toJson;
<DistributionPlot
@ -336,10 +317,11 @@ let make = (~distPlus: DistTypes.distPlus) => {
let (x, setX) = React.useState(() => 0.);
let (state, dispatch) =
React.useReducer(DistPlusPlotReducer.reducer, DistPlusPlotReducer.init);
<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>

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.;
const yMax = d3.max(this.attrs.data.discrete.ys);
// X axis.

3
src/components/editor/DistEditor.re
View File

@ -1,3 +0,0 @@
[@bs.module "./main.js"]
external getPdfFromUserInput: string => (array(float), array(float), bool) =
"get_pdf_from_user_input";

247
src/components/editor/distribution.js
View File

@ -1,247 +0,0 @@
const _math = require("mathjs");
const math = _math.create(_math.all);
const jStat = require("jstat");
/**
* This module defines an abstract BinnedDistribution class, which
* should be implemented for each distribution. You need to decide
* how to bin the distribution (use _adabin unless there's a nicer
* way for your distr) and how to choose the distribution's support.
*/
math.import({
normal: jStat.normal,
beta: jStat.beta,
lognormal: jStat.lognormal,
uniform: jStat.uniform
});
class BaseDistributionBinned {
/**
* @param args
*/
constructor(args) {
this._set_props();
this.max_bin_size = 0.005;
this.min_bin_size = 0;
this.increment = 0.0001;
this.desired_delta = 0.001;
this.start_bin_size = 0.0001;
[this.params, this.pdf_func, this.sample] = this.get_params_and_pdf_func(
args
);
[this.start_point, this.end_point] = this.get_bounds();
[this.pdf_vals, this.divider_pts] = this.bin();
}
/**
* this is hacky but class properties aren't always supported
* @private
*/
_set_props() {
throw new Error("NotImplementedError");
}
//Adaptive binning. Specify a desired change in density to get adjusted bin sizes.
/**
* @returns {(number[]|[*])[]}
* @private
*/
_adabin() {
let point = this.start_point;
let vals = [this.pdf_func(point)];
let divider_pts = [point];
let support = this.end_point - this.start_point;
let bin_size = this.start_bin_size * support;
while (point < this.end_point) {
let val = this.pdf_func(point + bin_size);
if (Math.abs(val - vals[vals.length - 1]) > this.desired_delta) {
while (
(Math.abs(val - vals[vals.length - 1]) > this.desired_delta) &
(bin_size - this.increment * support > this.min_bin_size)
) {
bin_size -= this.increment;
val = this.pdf_func(point + bin_size);
}
} else if (Math.abs(val - vals[vals.length - 1]) < this.desired_delta) {
while (
(Math.abs(val - vals[vals.length - 1]) < this.desired_delta) &
(bin_size < this.max_bin_size)
) {
bin_size += this.increment;
val = this.pdf_func(point + bin_size);
}
}
point += bin_size;
vals.push(val);
divider_pts.push(point);
}
vals = vals.map((_, idx) => vals[idx] / 2 + vals[idx + 1] / 2);
vals = vals.slice(0, -1);
return [vals, divider_pts];
}
bin() {
throw new Error("NotImplementedError");
}
get_bounds() {
throw new Error("NotImplementedError");
}
/**
* @param args
* @returns {(any|(function(*=): *))[]}
*/
get_params_and_pdf_func(args) {
let args_str = args.toString() + ")";
let substr = this.name + ".pdf(x, " + args_str;
let compiled = math.compile(substr);
function pdf_func(x) {
return compiled.evaluate({ x: x });
}
let mc_compiled = math.compile(this.name + ".sample(" + args_str);
let kv_pairs = this.param_names.map((val, idx) => [val, args[idx]]);
let params = Object.fromEntries(new Map(kv_pairs));
return [params, pdf_func, mc_compiled.evaluate];
}
}
class NormalDistributionBinned extends BaseDistributionBinned {
/**
* @private
*/
_set_props() {
this.name = "normal";
this.param_names = ["mean", "std"];
}
/**
* @returns {(number|*)[]}
*/
get_bounds() {
return [
this.params.mean - 4 * this.params.std,
this.params.mean + 4 * this.params.std
];
}
/**
* @returns {[[*], [*]]}
*/
bin() {
return this._adabin(this.params.std);
}
}
class UniformDistributionBinned extends BaseDistributionBinned {
/**
* @private
*/
_set_props() {
this.name = "uniform";
this.param_names = ["start_point", "end_point"];
this.num_bins = 200;
}
/**
* @returns {*[]}
*/
get_bounds() {
return [this.params.start_point, this.params.end_point];
}
/**
* @returns {(*[])[]}
*/
bin() {
let divider_pts = evenly_spaced_grid(
this.params.start_point,
this.params.end_point,
this.num_bins
);
let vals = divider_pts.map(x =>
this.pdf_func(this.params.start_point / 2 + this.params.end_point / 2)
);
vals = vals.slice(0, -1);
return [vals, divider_pts];
}
}
class LogNormalDistributionBinned extends BaseDistributionBinned {
/**
* @private
*/
_set_props() {
this.name = "lognormal";
this.param_names = ["normal_mean", "normal_std"];
this.n_bounds_samples = 10000;
this.n_largest_bound_sample = 10;
}
/**
* @param samples
* @param n
* @returns {any}
* @private
*/
_nth_largest(samples, n) {
var largest_buffer = Array(n).fill(-Infinity);
for (const sample of samples) {
if (sample > largest_buffer[n - 1]) {
var i = n;
while ((i > 0) & (sample > largest_buffer[i - 1])) {
i -= 1;
}
largest_buffer[i] = sample;
}
}
return largest_buffer[n - 1];
}
/**
* @returns {(*|any)[]}
*/
get_bounds() {
let samples = Array(this.n_bounds_samples)
.fill(0)
.map(() => this.sample());
return [
math.min(samples),
this._nth_largest(samples, this.n_largest_bound_sample)
];
}
/**
* @returns {[[*], [*]]}
*/
bin() {
return this._adabin();
}
}
/**
* @param start
* @param stop
* @param numel
* @returns {*[]}
*/
function evenly_spaced_grid(start, stop, numel) {
return Array(numel)
.fill(0)
.map((_, idx) => start + (idx / numel) * (stop - start));
}
const distrs = {
normal: NormalDistributionBinned,
lognormal: LogNormalDistributionBinned,
uniform: UniformDistributionBinned
};
exports.distrs = distrs;

364
src/components/editor/main.js
View File

@ -1,364 +0,0 @@
const _math = require("mathjs");
const bst = require("binary-search-tree");
const distrs = require("./distribution.js").distrs;
const parse = require("./parse.js");
const math = _math.create(_math.all);
const NUM_MC_SAMPLES = 3000;
const OUTPUT_GRID_NUMEL = 3000;
/**
* The main algorithmic work is done by functions in this module.
* It also contains the main function, taking the user's string
* and returning pdf values and x's.
*/
/**
* @param start
* @param stop
* @param numel
* @returns {*[]}
*/
function evenly_spaced_grid(start, stop, numel) {
return Array(numel)
.fill(0)
.map((_, idx) => start + (idx / numel) * (stop - start));
}
/**
* Takes an array of strings like "normal(0, 1)" and
* returns the corresponding distribution objects
* @param substrings
* @returns {*}
*/
function get_distributions(substrings) {
let names_and_args = substrings.map(parse.get_distr_name_and_args);
let pdfs = names_and_args.map(x => new distrs[x[0]](x[1]));
return pdfs;
}
/**
* update the binary search tree with bin points of
* deterministic_pdf transformed by tansform func
* (transfrom func can be a stocahstic func with parameters
* sampled from mc_distrs)
*
* @param transform_func
* @param deterministic_pdf
* @param mc_distrs
* @param track_idx
* @param num_mc_samples
* @param bst_pts_and_idxs
* @returns {(number)[]}
*/
function update_transformed_divider_points_bst(
transform_func,
deterministic_pdf,
mc_distrs,
track_idx,
num_mc_samples,
bst_pts_and_idxs
) {
var transformed_pts = [];
var pdf_inner_idxs = [];
var factors = [];
var start_pt = Infinity;
var end_pt = -Infinity;
let use_mc = mc_distrs.length > 0;
var num_outer_iters = use_mc ? num_mc_samples : 1;
for (let sample_idx = 0; sample_idx < num_outer_iters; ++sample_idx) {
var this_transformed_pts = deterministic_pdf.divider_pts;
if (use_mc) {
let samples = mc_distrs.map(x => x.sample());
this_transformed_pts = this_transformed_pts.map(x =>
transform_func([x].concat(samples))
);
} else {
this_transformed_pts = this_transformed_pts.map(x => transform_func([x]));
}
var this_transformed_pts_paired = [];
for (let tp_idx = 0; tp_idx < this_transformed_pts.length - 1; tp_idx++) {
let sorted = [
this_transformed_pts[tp_idx],
this_transformed_pts[tp_idx + 1]
].sort((a, b) => a - b);
if (sorted[0] < start_pt) {
start_pt = sorted[0];
}
if (sorted[1] > end_pt) {
end_pt = sorted[1];
}
this_transformed_pts_paired.push(sorted);
}
transformed_pts = transformed_pts.concat(this_transformed_pts_paired);
pdf_inner_idxs = pdf_inner_idxs.concat([
...Array(this_transformed_pts_paired.length).keys()
]);
var this_factors = [];
for (let idx = 0; idx < this_transformed_pts_paired.length; idx++) {
this_factors.push(
(deterministic_pdf.divider_pts[idx + 1] -
deterministic_pdf.divider_pts[idx]) /
(this_transformed_pts_paired[idx][1] -
this_transformed_pts_paired[idx][0])
);
}
factors = factors.concat(this_factors);
}
for (let i = 0; i < transformed_pts.length; ++i) {
bst_pts_and_idxs.insert(transformed_pts[i][0], {
start: transformed_pts[i][0],
end: transformed_pts[i][1],
idx: [track_idx, pdf_inner_idxs[i]],
factor: factors[i] / num_outer_iters
});
}
return [start_pt, end_pt];
}
/**
* Take the binary search tree with transformed bin points,
* and an array of pdf values associated with the bins,
* and return a pdf over an evenly spaced grid
*
* @param pdf_vals
* @param bst_pts_and_idxs
* @param output_grid
* @returns {[]}
*/
function get_final_pdf(pdf_vals, bst_pts_and_idxs, output_grid) {
var offset = output_grid[1] / 2 - output_grid[0] / 2;
var active_intervals = new Map();
var active_endpoints = new bst.AVLTree();
var final_pdf_vals = [];
for (
let out_grid_idx = 0;
out_grid_idx < output_grid.length;
++out_grid_idx
) {
let startpoints_within_bin = bst_pts_and_idxs.betweenBounds({
$gte: output_grid[out_grid_idx] - offset,
$lt: output_grid[out_grid_idx] + offset
});
for (let interval of startpoints_within_bin) {
active_intervals.set(interval.idx, [
interval.start,
interval.end,
interval.factor
]);
active_endpoints.insert(interval.end, interval.idx);
}
var contrib = 0;
for (let [pdf_idx, bounds_and_ratio] of active_intervals.entries()) {
let overlap_start = Math.max(
output_grid[out_grid_idx] - offset,
bounds_and_ratio[0]
);
let overlap_end = Math.min(
output_grid[out_grid_idx] + offset,
bounds_and_ratio[1]
);
let interval_size = bounds_and_ratio[1] - bounds_and_ratio[0];
let contrib_frac =
interval_size === 0
? 0
: (overlap_end - overlap_start) * bounds_and_ratio[2];
let t = contrib_frac * pdf_vals[pdf_idx[0]][pdf_idx[1]];
contrib += t;
}
final_pdf_vals.push(contrib);
let endpoints_within_bin = active_endpoints.betweenBounds({
$gte: output_grid[out_grid_idx] - offset,
$lt: output_grid[out_grid_idx] + offset
});
for (let interval_idx of endpoints_within_bin) {
active_intervals.delete(interval_idx);
}
}
return final_pdf_vals;
}
/**
* @param {string} str
* @param {string} char
* @returns {number}
*/
function get_count_of_chars(str, char) {
return str.split(char).length - 1;
}
/**
* Entrypoint. Pass user input strings to this function,
* get the corresponding pdf values and input points back.
* If the pdf requires monte carlo (it contains a between-distr function)
* we first determing which distr to have deterministic
* and which to sample from. This is decided based on which
* choice gives the least variance.
*
* @param user_input_string
* @returns {([]|*[])[]}
*/
function get_pdf_from_user_input(user_input_string) {
try {
const count_opened_bracket = get_count_of_chars(user_input_string, '(');
const count_closed_bracket = get_count_of_chars(user_input_string, ')');
if (count_opened_bracket !== count_closed_bracket) {
throw new Error('Count of brackets are not equal.');
}
let parsed = parse.parse_initial_string(user_input_string);
let mm_args = parse.separate_mm_args(parsed.mm_args_string);
const is_mm = mm_args.distrs.length > 0;
if (!parsed.outer_string) {
throw new Error('Parse string is empty.');
}
let tree = new bst.AVLTree();
let possible_start_pts = [];
let possible_end_pts = [];
let all_vals = [];
let weights = is_mm ? math.compile(mm_args.weights).evaluate()._data : [1];
let weights_sum = weights.reduce((a, b) => a + b);
weights = weights.map(x => x / weights_sum);
let n_iters = is_mm ? mm_args.distrs.length : 1;
for (let i = 0; i < n_iters; ++i) {
let distr_string = is_mm ? mm_args.distrs[i] : parsed.outer_string;
var [deterministic_pdf, mc_distrs] = choose_pdf_func(distr_string);
var grid_transform = get_grid_transform(distr_string);
var [start_pt, end_pt] = update_transformed_divider_points_bst(
grid_transform,
deterministic_pdf,
mc_distrs,
i,
NUM_MC_SAMPLES,
tree
);
possible_start_pts.push(start_pt);
possible_end_pts.push(end_pt);
all_vals.push(deterministic_pdf.pdf_vals.map(x => x * weights[i]));
}
start_pt = Math.min(...possible_start_pts);
end_pt = Math.max(...possible_end_pts);
let output_grid = evenly_spaced_grid(start_pt, end_pt, OUTPUT_GRID_NUMEL);
let final_pdf_vals = get_final_pdf(all_vals, tree, output_grid);
return [final_pdf_vals, output_grid, false];
} catch (e) {
return [[], [], true];
}
}
/**
* @param vals
* @returns {number}
*/
function variance(vals) {
var vari = 0;
for (let i = 0; i < vals[0].length; ++i) {
let mean = 0;
let this_vari = 0;
for (let val of vals) {
mean += val[i] / vals.length;
}
for (let val of vals) {
this_vari += (val[i] - mean) ** 2;
}
vari += this_vari;
}
return vari;
}
/**
* @param array
* @param idx
* @returns {*[]}
*/
function pluck_from_array(array, idx) {
return [array[idx], array.slice(0, idx).concat(array.slice(idx + 1))];
}
/**
* If distr_string requires MC, try all possible
* choices for the deterministic distribution,
* and pick the one with the least variance.
* It's much better to sample from a normal than a lognormal.
*
* @param distr_string
* @returns {(*|*[])[]|*[]}
*/
function choose_pdf_func(distr_string) {
var variances = [];
let transform_func = get_grid_transform(distr_string);
let substrings = parse.get_distr_substrings(distr_string);
var pdfs = get_distributions(substrings);
if (pdfs.length === 1) {
return [pdfs[0], []];
}
var start_pt = 0;
var end_pt = 0;
for (let i = 0; i < pdfs.length; ++i) {
var outputs = [];
for (let j = 0; j < 20; ++j) {
let tree = new bst.AVLTree();
let [deterministic_pdf, mc_distrs] = pluck_from_array(pdfs, i);
let [this_start_pt, this_end_pt] = update_transformed_divider_points_bst(
transform_func,
deterministic_pdf,
mc_distrs,
0,
10,
tree
);
[start_pt, end_pt] =
j === 0 ? [this_start_pt, this_end_pt] : [start_pt, end_pt];
var output_grid = evenly_spaced_grid(start_pt, end_pt, 100);
let final_pdf_vals = get_final_pdf(
[deterministic_pdf.pdf_vals],
tree,
output_grid
);
outputs.push(final_pdf_vals);
}
variances.push(variance(outputs));
}
let best_variance = Math.min(...variances);
let best_idx = variances
.map((val, idx) => [val, idx])
.filter(x => x[0] === best_variance)[0][1];
let mc_distrs = pdfs.slice(0, best_idx).concat(pdfs.slice(best_idx + 1));
return [pdfs[best_idx], mc_distrs];
}
/**
* @param distr_string
* @returns {function(*): *}
*/
function get_grid_transform(distr_string) {
let substrings = parse.get_distr_substrings(distr_string);
let arg_strings = [];
for (let i = 0; i < substrings.length; ++i) {
distr_string = distr_string.replace(substrings[i], "x_" + i.toString());
arg_strings.push("x_" + i.toString());
}
let compiled = math.compile(distr_string);
function grid_transform(x) {
let kv_pairs = arg_strings.map((val, idx) => [val, x[idx]]);
let args_obj = Object.fromEntries(new Map(kv_pairs));
return compiled.evaluate(args_obj);
}
return grid_transform;
}
exports.get_pdf_from_user_input = get_pdf_from_user_input;

139
src/components/editor/parse.js
View File

@ -1,139 +0,0 @@
const _math = require("mathjs");
const math = _math.create(_math.all);
// Functions for parsing/processing user input strings are here
// @todo: Do not use objects.
const DISTR_REGEXS = [
/beta\(/g,
/(log)?normal\(/g,
/multimodal\(/g,
/mm\(/g,
/uniform\(/g
];
/**
* @param user_input_string
* @returns {{mm_args_string: string, outer_string: string}}
*/
function parse_initial_string(user_input_string) {
let outer_output_string = "";
let mm_args_string = "";
let idx = 0;
while (idx < user_input_string.length) {
if (
user_input_string.substring(idx - 11, idx) === "multimodal(" ||
user_input_string.substring(idx - 3, idx) === "mm("
) {
let num_open_brackets = 1;
while (num_open_brackets > 0 && idx < user_input_string.length) {
mm_args_string += user_input_string[idx];
idx += 1;
if (user_input_string[idx] === ")") {
num_open_brackets -= 1;
} else if (user_input_string[idx] === "(") {
num_open_brackets += 1;
}
}
outer_output_string += ")";
idx += 1;
} else {
outer_output_string += user_input_string[idx];
idx += 1;
}
}
return {
outer_string: outer_output_string,
mm_args_string: mm_args_string
};
}
/**
* @param mm_args_string
* @returns {{distrs: [], weights: string}}
*/
function separate_mm_args(mm_args_string) {
if (mm_args_string.endsWith(",")) {
mm_args_string = mm_args_string.slice(0, -1);
}
let args_array = [];
let num_open_brackets = 0;
let arg_substring = "";
for (let char of mm_args_string) {
if (num_open_brackets === 0 && char === ",") {
args_array.push(arg_substring.trim());
arg_substring = "";
} else {
if (char === ")" || char === "]") {
num_open_brackets -= 1;
} else if (char === "(" || char === "[") {
num_open_brackets += 1;
}
arg_substring += char;
}
}
return {
distrs: args_array,
weights: arg_substring.trim()
};
}
/**
* @param distr_string
* @returns {[]}
*/
function get_distr_substrings(distr_string) {
let substrings = [];
for (let regex of DISTR_REGEXS) {
let matches = distr_string.matchAll(regex);
for (let match of matches) {
let idx = match.index + match[0].length;
let num_open_brackets = 1;
let distr_substring = "";
while (num_open_brackets !== 0 && idx < distr_string.length) {
distr_substring += distr_string[idx];
if (distr_string[idx] === "(") {
num_open_brackets += 1;
} else if (distr_string[idx] === ")") {
num_open_brackets -= 1;
}
idx += 1;
}
substrings.push((match[0] + distr_substring).trim());
}
}
return substrings;
}
/**
* @param substr
* @returns {(string|*)[]}
*/
function get_distr_name_and_args(substr) {
let distr_name = "";
let args_str = "";
let args_flag = false;
for (let char of substr) {
if (!args_flag && char !== "(") {
distr_name += char;
}
if (args_flag && char !== ")") {
args_str += char;
}
if (char === "(") {
args_str += "[";
args_flag = true;
}
}
args_str += "]";
let args = math.compile(args_str).evaluate()._data;
return [distr_name, args];
}
exports.get_distr_name_and_args = get_distr_name_and_args;
exports.get_distr_substrings = get_distr_substrings;
exports.separate_mm_args = separate_mm_args;
exports.parse_initial_string = parse_initial_string;

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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;
Js.Array.unshift(xs[0], xs) |> ignore;
Js.Array.unshift(ys[0], ys) |> ignore;
Js.Array.push(xs[n - 1], xs) |> ignore;
Js.Array.push(ys[n - 1], ys) |> ignore;
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) {
Belt.Array.set(xsSq, i, xs[i] *. xs[i]) |> ignore;
();
};
for (i in 0 to n - 2) {
Belt.Array.set(xsProdN1, i, xs[i] *. xs[i + 1]) |> ignore;
();
};
for (i in 0 to n - 3) {
Belt.Array.set(xsProdN2, i, xs[i] *. xs[i + 2]) |> ignore;
();
};
// 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) {
Belt.Array.set(
masses,
i - 1,
(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
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.;
Belt.Array.set(means, i - 1, inverseMean) |> ignore;
Belt.Array.set(variances, i - 1, inverseVar) |> ignore;
();
};
{n: n - 2, masses, means, variances};
} else {
for (i in 1 to n - 2) {
// area of triangle = width * height / 2
Belt.Array.set(
masses,
i - 1,
(xs[i + 1] -. xs[i - 1]) *. ys[i] /. 2.,
) |> ignore;
// means of triangle = (a + b + c) / 3
Belt.Array.set(means, i - 1, (xs[i - 1] +. xs[i] +. xs[i + 1]) /. 3.) |> ignore;
// variance of triangle = (a^2 + b^2 + c^2 - ab - ac - bc) / 18
Belt.Array.set(
variances,
i - 1,
(
xsSq[i - 1]
+. xsSq[i]
+. xsSq[i + 1]
-. xsProdN1[i - 1]
-. xsProdN1[i]
-. xsProdN2[i - 1]
)
/. 18.,
) |> ignore;
();
};
{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, _, _) => v1 +. v2)
| `Subtract => ((v1, v2, _, _) => 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;
Belt.Array.set(masses, k, t1m.masses[i] *. t2m.masses[j]) |> ignore;
let mean = combineMeansFn(t1m.means[i], t2m.means[j]);
let variance =
combineVariancesFn(
t1m.variances[i],
t2m.variances[j],
t1m.means[i],
t2m.means[j],
);
Belt.Array.set(means, k, mean) |> ignore;
Belt.Array.set(variances, k, variance) |> ignore;
// 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
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]);
Belt.Array.set(outputYs, i, outputYs[i] +. contribution) |> ignore;
};
};
};
{xs: outputXs, ys: outputYs};
};
let toDiscretePointMassesFromDiscrete =
(s: DistTypes.xyShape): pointMassesWithMoments => {
let {xs, ys}: XYShape.T.t = s;
let n = E.A.length(xs);
let masses: array(float) = Belt.Array.makeBy(n, i => ys[i]);
let means: array(float) = Belt.Array.makeBy(n, i => xs[i]);
let variances: array(float) = Belt.Array.makeBy(n, i => 0.0);
{n, masses, means, variances};
};
let combineShapesContinuousDiscrete =
(op: ExpressionTypes.algebraicOperation, continuousShape: DistTypes.xyShape, discreteShape: DistTypes.xyShape)
: DistTypes.xyShape => {
let t1n = continuousShape |> XYShape.T.length;
let t2n = discreteShape |> XYShape.T.length;
// each x pair is added/subtracted
let fn = Operation.Algebraic.toFn(op);
let outXYShapes: array(array((float, float))) =
Belt.Array.makeUninitializedUnsafe(t2n);
switch (op) {
| `Add
| `Subtract =>
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]),
) |> ignore;
();
};
Belt.Array.set(outXYShapes, j, dxyShape) |> ignore;
();
}
| `Multiply
| `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
|> E.A.fmap(XYShape.T.fromZippedArray)
|> E.A.fold_left(
XYShape.PointwiseCombination.combine((+.),
XYShape.XtoY.continuousInterpolator(`Linear, `UseZero)),
XYShape.T.empty);
};

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open Distributions;
type t = DistTypes.continuousShape;
let getShape = (t: t) => t.xyShape;
let interpolation = (t: t) => t.interpolation;
let make = (~interpolation=`Linear, ~integralSumCache=None, ~integralCache=None, xyShape): t => {
xyShape,
interpolation,
integralSumCache,
integralCache,
};
let shapeMap = (fn, {xyShape, interpolation, integralSumCache, integralCache}: t): t => {
xyShape: fn(xyShape),
interpolation,
integralSumCache,
integralCache,
};
let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
let oShapeMap =
(fn, {xyShape, interpolation, integralSumCache, integralCache}: t)
: option(DistTypes.continuousShape) =>
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 = {
xyShape: XYShape.T.empty,
interpolation: `Linear,
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 =
(
~integralSumCachesFn=(_, _) => None,
~integralCachesFn: (t, t) => option(t) =(_, _) => None,
~distributionType: DistTypes.distributionType = `PDF,
fn: (float, float) => float,
t1: DistTypes.continuousShape,
t2: DistTypes.continuousShape,
)
: DistTypes.continuousShape => {
// If we're adding the distributions, and we know the total of each, then we
// can just sum them up. Otherwise, all bets are off.
let combinedIntegralSum =
Common.combineIntegralSums(
integralSumCachesFn,
t1.integralSumCache,
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(
~integralSumCache=combinedIntegralSum,
XYShape.PointwiseCombination.combine(
fn,
interpolator,
t1.xyShape,
t2.xyShape,
),
);
};
let toLinear = (t: t): option(t) => {
switch (t) {
| {interpolation: `Stepwise, xyShape, integralSumCache, integralCache} =>
xyShape
|> XYShape.Range.stepsToContinuous
|> E.O.fmap(make(~integralSumCache, ~integralCache))
| {interpolation: `Linear} => Some(t)
};
};
let shapeFn = (fn, t: t) => t |> getShape |> fn;
let updateIntegralSumCache = (integralSumCache, t: t): t => {
...t,
integralSumCache,
};
let updateIntegralCache = (integralCache, t: t): t => {
...t,
integralCache,
};
let reduce =
(
~integralSumCachesFn: (float, float) => option(float)=(_, _) => None,
~integralCachesFn: (t, t) => option(t)=(_, _) => None,
fn,
continuousShapes,
) =>
continuousShapes
|> E.A.fold_left(combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn), empty);
let mapY = (~integralSumCacheFn=_ => None,
~integralCacheFn=_ => None,
~fn, t: t) => {
make(
~interpolation=t.interpolation,
~integralSumCache=t.integralSumCache |> E.O.bind(_, integralSumCacheFn),
~integralCache=t.integralCache |> E.O.bind(_, integralCacheFn),
t |> getShape |> XYShape.T.mapY(fn),
);
};
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
|> mapY(~fn=(r: float) => r *. scale)
|> updateIntegralSumCache(scaledIntegralSumCache)
|> updateIntegralCache(scaledIntegralCache)
};
module T =
Dist({
type t = DistTypes.continuousShape;
type integral = DistTypes.continuousShape;
let minX = shapeFn(XYShape.T.minX);
let maxX = shapeFn(XYShape.T.maxX);
let mapY = mapY;
let updateIntegralCache = updateIntegralCache;
let toDiscreteProbabilityMassFraction = _ => 0.0;
let toShape = (t: t): DistTypes.shape => Continuous(t);
let xToY = (f, {interpolation, xyShape}: t) => {
(
switch (interpolation) {
| `Stepwise =>
xyShape |> XYShape.XtoY.stepwiseIncremental(f) |> E.O.default(0.0)
| `Linear => xyShape |> XYShape.XtoY.linear(f)
}
)
|> DistTypes.MixedPoint.makeContinuous;
};
let truncate =
(leftCutoff: option(float), rightCutoff: option(float), t: t) => {
let lc = E.O.default(neg_infinity, leftCutoff);
let rc = E.O.default(infinity, rightCutoff);
let truncatedZippedPairs =
t
|> getShape
|> XYShape.T.zip
|> XYShape.Zipped.filterByX(x => x >= lc && x <= rc);
let leftNewPoint =
leftCutoff |> E.O.dimap(lc => [|(lc -. epsilon_float, 0.)|], _ => [||]);
let rightNewPoint =
rightCutoff |> E.O.dimap(rc => [|(rc +. epsilon_float, 0.)|], _ => [||]);
let truncatedZippedPairsWithNewPoints =
E.A.concatMany([|leftNewPoint, truncatedZippedPairs, rightNewPoint|]);
let truncatedShape =
XYShape.T.fromZippedArray(truncatedZippedPairsWithNewPoints);
make(truncatedShape)
};
// TODO: This should work with stepwise plots.
let integral = (t) =>
switch (getShape(t) |> XYShape.T.isEmpty, t.integralCache) {
| (true, _) => emptyIntegral
| (false, Some(cache)) => cache
| (false, None) =>
t
|> getShape
|> XYShape.Range.integrateWithTriangles
|> E.O.toExt("This should not have happened")
|> make
};
let downsample = (length, t): t =>
t
|> shapeMap(
XYShape.XsConversion.proportionByProbabilityMass(
length,
integral(t).xyShape,
),
);
let integralEndY = (t: t) =>
t.integralSumCache |> E.O.default(t |> integral |> lastY);
let integralXtoY = (f, t: t) =>
t |> integral |> shapeFn(XYShape.XtoY.linear(f));
let integralYtoX = (f, t: t) =>
t |> integral |> shapeFn(XYShape.YtoX.linear(f));
let toContinuous = t => Some(t);
let toDiscrete = _ => None;
let normalize = (t: t): t => {
t
|> updateIntegralCache(Some(integral(t)))
|> scaleBy(~scale=1. /. integralEndY(t))
|> updateIntegralSumCache(Some(1.0));
};
let mean = (t: t) => {
let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 2.0 /. 2.0;
let indefiniteIntegralLinear = (p, a, b) =>
a *. p ** 2.0 /. 2.0 +. b *. p ** 3.0 /. 3.0;
XYShape.Analysis.integrateContinuousShape(
~indefiniteIntegralStepwise,
~indefiniteIntegralLinear,
t,
);
};
let variance = (t: t): float =>
XYShape.Analysis.getVarianceDangerously(
t,
mean,
XYShape.Analysis.getMeanOfSquaresContinuousShape,
);
});
/* This simply creates multiple copies of the continuous distribution, scaled and shifted according to
each discrete data point, and then adds them all together. */
let combineAlgebraicallyWithDiscrete =
(
op: ExpressionTypes.algebraicOperation,
t1: t,
t2: DistTypes.discreteShape,
) => {
let t1s = t1 |> getShape;
let t2s = t2.xyShape; // TODO would like to use Discrete.getShape here, but current file structure doesn't allow for that
if (XYShape.T.isEmpty(t1s) || XYShape.T.isEmpty(t2s)) {
empty;
} else {
let continuousAsLinear = switch (t1.interpolation) {
| `Linear => t1;
| `Stepwise => stepwiseToLinear(t1)
};
let combinedShape = AlgebraicShapeCombination.combineShapesContinuousDiscrete(op, continuousAsLinear |> getShape, t2s);
let combinedIntegralSum =
Common.combineIntegralSums(
(a, b) => Some(a *. b),
t1.integralSumCache,
t2.integralSumCache,
);
// TODO: It could make sense to automatically transform the integrals here (shift or scale)
make(~interpolation=t1.interpolation, ~integralSumCache=combinedIntegralSum, combinedShape)
};
};
let combineAlgebraically =
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t) => {
let s1 = t1 |> getShape;
let s2 = t2 |> getShape;
let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length;
if (t1n == 0 || t2n == 0) {
empty;
} else {
let combinedShape =
AlgebraicShapeCombination.combineShapesContinuousContinuous(op, s1, s2);
let combinedIntegralSum =
Common.combineIntegralSums(
(a, b) => Some(a *. b),
t1.integralSumCache,
t2.integralSumCache,
);
// return a new Continuous distribution
make(~integralSumCache=combinedIntegralSum, combinedShape);
};
};

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open Distributions;
type t = DistTypes.discreteShape;
let make = (~integralSumCache=None, ~integralCache=None, xyShape): t => {xyShape, integralSumCache, integralCache};
let shapeMap = (fn, {xyShape, integralSumCache, integralCache}: t): t => {
xyShape: fn(xyShape),
integralSumCache,
integralCache
};
let getShape = (t: t) => t.xyShape;
let oShapeMap = (fn, {xyShape, integralSumCache, integralCache}: t): option(t) =>
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 shapeFn = (fn, t: t) => t |> getShape |> fn;
let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
let combinePointwise =
(
~integralSumCachesFn = (_, _) => None,
~integralCachesFn: (DistTypes.continuousShape, DistTypes.continuousShape) => option(DistTypes.continuousShape) = (_, _) => None,
fn,
t1: DistTypes.discreteShape,
t2: DistTypes.discreteShape,
)
: DistTypes.discreteShape => {
let combinedIntegralSum =
Common.combineIntegralSums(
integralSumCachesFn,
t1.integralSumCache,
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(
~integralSumCache=combinedIntegralSum,
XYShape.PointwiseCombination.combine(
(+.),
XYShape.XtoY.discreteInterpolator,
t1.xyShape,
t2.xyShape,
),
);
};
let reduce =
(~integralSumCachesFn=(_, _) => None,
~integralCachesFn=(_, _) => None,
fn, discreteShapes)
: DistTypes.discreteShape =>
discreteShapes
|> E.A.fold_left(combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn), empty);
let updateIntegralSumCache = (integralSumCache, t: t): t => {
...t,
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.
Data points at the same xs get added together. It may be a good idea to downsample t1 and t2 before and/or the result after. */
let combineAlgebraically =
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
let t1s = t1 |> getShape;
let t2s = t2 |> getShape;
let t1n = t1s |> XYShape.T.length;
let t2n = t2s |> XYShape.T.length;
let combinedIntegralSum =
Common.combineIntegralSums(
(s1, s2) => Some(s1 *. s2),
t1.integralSumCache,
t2.integralSumCache,
);
let fn = Operation.Algebraic.toFn(op);
let xToYMap = E.FloatFloatMap.empty();
for (i in 0 to t1n - 1) {
for (j in 0 to t2n - 1) {
let x = fn(t1s.xs[i], t2s.xs[j]);
let cv = xToYMap |> E.FloatFloatMap.get(x) |> E.O.default(0.);
let my = t1s.ys[i] *. t2s.ys[j];
let _ = Belt.MutableMap.set(xToYMap, x, cv +. my);
();
};
};
let rxys = xToYMap |> E.FloatFloatMap.toArray |> XYShape.Zipped.sortByX;
let combinedShape = XYShape.T.fromZippedArray(rxys);
make(~integralSumCache=combinedIntegralSum, combinedShape);
};
let mapY = (~integralSumCacheFn=_ => None,
~integralCacheFn=_ => None,
~fn, t: t) => {
make(
~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 scaledIntegralSumCache = t.integralSumCache |> E.O.fmap((*.)(scale));
let scaledIntegralCache = t.integralCache |> E.O.fmap(Continuous.scaleBy(~scale));
t
|> mapY(~fn=(r: float) => r *. scale)
|> updateIntegralSumCache(scaledIntegralSumCache)
|> updateIntegralCache(scaledIntegralCache)
};
module T =
Dist({
type t = DistTypes.discreteShape;
type integral = DistTypes.continuousShape;
let integral = (t) =>
switch (getShape(t) |> XYShape.T.isEmpty, t.integralCache) {
| (true, _) => emptyIntegral
| (false, Some(c)) => c
| (false, None) => {
let ts = getShape(t);
// The first xy of this integral should always be the zero, to ensure nice plotting
let firstX = ts |> XYShape.T.minX;
let prependedZeroPoint: XYShape.T.t = {xs: [|firstX -. epsilon_float|], ys: [|0.|]};
let integralShape =
ts
|> XYShape.T.concat(prependedZeroPoint)
|> XYShape.T.accumulateYs((+.));
Continuous.make(~interpolation=`Stepwise, integralShape);
}
};
let integralEndY = (t: t) =>
t.integralSumCache
|> E.O.default(t |> integral |> Continuous.lastY);
let minX = shapeFn(XYShape.T.minX);
let maxX = shapeFn(XYShape.T.maxX);
let toDiscreteProbabilityMassFraction = _ => 1.0;
let mapY = mapY;
let updateIntegralCache = updateIntegralCache;
let toShape = (t: t): DistTypes.shape => Discrete(t);
let toContinuous = _ => None;
let toDiscrete = t => Some(t);
let normalize = (t: t): t => {
t
|> scaleBy(~scale=1. /. integralEndY(t))
|> updateIntegralSumCache(Some(1.0));
};
let downsample = (i, t: t): t => {
// It's not clear how to downsample a set of discrete points in a meaningful way.
// The best we can do is to clip off the smallest values.
let currentLength = t |> getShape |> XYShape.T.length;
if (i < currentLength && i >= 1 && currentLength > 1) {
t
|> getShape
|> XYShape.T.zip
|> XYShape.Zipped.sortByY
|> Belt.Array.reverse
|> Belt.Array.slice(_, ~offset=0, ~len=i)
|> XYShape.Zipped.sortByX
|> XYShape.T.fromZippedArray
|> make;
} else {
t;
};
};
let truncate =
(leftCutoff: option(float), rightCutoff: option(float), t: t): t => {
t
|> getShape
|> XYShape.T.zip
|> XYShape.Zipped.filterByX(x =>
x >= E.O.default(neg_infinity, leftCutoff)
&& x <= E.O.default(infinity, rightCutoff)
)
|> XYShape.T.fromZippedArray
|> make;
};
let xToY = (f, t) =>
t
|> getShape
|> XYShape.XtoY.stepwiseIfAtX(f)
|> E.O.default(0.0)
|> DistTypes.MixedPoint.makeDiscrete;
let integralXtoY = (f, t) =>
t |> integral |> Continuous.getShape |> XYShape.XtoY.linear(f);
let integralYtoX = (f, t) =>
t |> integral |> Continuous.getShape |> XYShape.YtoX.linear(f);
let mean = (t: t): float => {
let s = getShape(t);
E.A.reducei(s.xs, 0.0, (acc, x, i) => acc +. x *. s.ys[i]);
};
let variance = (t: t): float => {
let getMeanOfSquares = t =>
t |> shapeMap(XYShape.Analysis.squareXYShape) |> mean;
XYShape.Analysis.getVarianceDangerously(t, mean, getMeanOfSquares);
};
});

129
src/distPlus/distribution/DistPlus.re Normal file
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@ -0,0 +1,129 @@
open DistTypes;
type t = DistTypes.distPlus;
let shapeIntegral = shape => Shape.T.Integral.get(shape);
let make =
(
~shape,
~guesstimatorString,
~domain=Complete,
~unit=UnspecifiedDistribution,
(),
)
: t => {
let integral = shapeIntegral(shape);
{shape, domain, integralCache: integral, unit, guesstimatorString};
};
let update =
(
~shape=?,
~integralCache=?,
~domain=?,
~unit=?,
~guesstimatorString=?,
t: t,
) => {
shape: E.O.default(t.shape, shape),
integralCache: E.O.default(t.integralCache, integralCache),
domain: E.O.default(t.domain, domain),
unit: E.O.default(t.unit, unit),
guesstimatorString: E.O.default(t.guesstimatorString, guesstimatorString),
};
let updateShape = (shape, t) => {
let integralCache = shapeIntegral(shape);
update(~shape, ~integralCache, t);
};
let domainIncludedProbabilityMass = (t: t) =>
Domain.includedProbabilityMass(t.domain);
let domainIncludedProbabilityMassAdjustment = (t: t, f) =>
f *. Domain.includedProbabilityMass(t.domain);
let toShape = ({shape, _}: t) => shape;
let shapeFn = (fn, {shape}: t) => fn(shape);
module T =
Distributions.Dist({
type t = DistTypes.distPlus;
type integral = DistTypes.distPlus;
let toShape = toShape;
let toContinuous = shapeFn(Shape.T.toContinuous);
let toDiscrete = shapeFn(Shape.T.toDiscrete);
let normalize = (t: t): t => {
let normalizedShape = t |> toShape |> Shape.T.normalize;
t |> updateShape(normalizedShape);
};
let truncate = (leftCutoff, rightCutoff, t: t): t => {
let truncatedShape =
t
|> toShape
|> Shape.T.truncate(leftCutoff, rightCutoff);
t |> updateShape(truncatedShape);
};
let xToY = (f, t: t) =>
t
|> toShape
|> Shape.T.xToY(f)
|> MixedPoint.fmap(domainIncludedProbabilityMassAdjustment(t));
let minX = shapeFn(Shape.T.minX);
let maxX = shapeFn(Shape.T.maxX);
let toDiscreteProbabilityMassFraction =
shapeFn(Shape.T.toDiscreteProbabilityMassFraction);
// This bit is kind of awkward, could probably use rethinking.
let integral = (t: t) =>
updateShape(Continuous(t.integralCache), 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);
// todo: adjust for limit, maybe?
let mapY =
(
~integralSumCacheFn=previousIntegralSum => None,
~integralCacheFn=previousIntegralCache => None,
~fn,
{shape, _} as t: t,
)
: t =>
Shape.T.mapY(~integralSumCacheFn, ~fn, shape)
|> updateShape(_, t);
// get the total of everything
let integralEndY = (t: t) => {
Shape.T.Integral.sum(
toShape(t),
);
};
// TODO: Fix this below, obviously. Adjust for limits
let integralXtoY = (f, t: t) => {
Shape.T.Integral.xToY(
f,
toShape(t),
)
|> domainIncludedProbabilityMassAdjustment(t);
};
// TODO: This part is broken when there is a limit, if this is supposed to be taken into account.
let integralYtoX = (f, t: t) => {
Shape.T.Integral.yToX(f, toShape(t));
};
let mean = (t: t) => {
Shape.T.mean(t.shape);
};
let variance = (t: t) => Shape.T.variance(t.shape);
});

28
src/distPlus/distribution/DistPlusTime.re Normal file
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@ -0,0 +1,28 @@
open DistTypes;
type t = DistTypes.distPlus;
let unitToJson = ({unit}: t) => unit |> DistTypes.DistributionUnit.toJson;
let timeVector = ({unit}: t) =>
switch (unit) {
| TimeDistribution(timeVector) => Some(timeVector)
| UnspecifiedDistribution => None
};
let timeInVectorToX = (f: TimeTypes.timeInVector, t: t) => {
let timeVector = t |> timeVector;
timeVector |> E.O.fmap(TimeTypes.RelativeTimePoint.toXValue(_, f));
};
let xToY = (f: TimeTypes.timeInVector, t: t) => {
timeInVectorToX(f, t) |> E.O.fmap(DistPlus.T.xToY(_, t));
};
module Integral = {
include DistPlus.T.Integral;
let xToY = (f: TimeTypes.timeInVector, t: t) => {
timeInVectorToX(f, t)
|> E.O.fmap(x => DistPlus.T.Integral.xToY(x, t));
};
};

29
src/distPlus/distribution/DistTypes.re
View File

@ -9,22 +9,45 @@ type domain =
| RightLimited(domainLimit)
| LeftAndRightLimited(domainLimit, domainLimit);
type distributionType = [
| `PDF
| `CDF
];
type xyShape = {
xs: array(float),
ys: array(float),
};
type interpolationStrategy = [
| `Stepwise
| `Linear
];
type extrapolationStrategy = [
| `UseZero
| `UseOutermostPoints
];
type interpolator = (xyShape, int, float) => float;
type continuousShape = {
xyShape,
interpolation: [ | `Stepwise | `Linear],
interpolation: interpolationStrategy,
integralSumCache: option(float),
integralCache: option(continuousShape),
};
type discreteShape = xyShape;
type discreteShape = {
xyShape,
integralSumCache: option(float),
integralCache: option(continuousShape),
};
type mixedShape = {
continuous: continuousShape,
discrete: discreteShape,
discreteProbabilityMassFraction: float,
integralSumCache: option(float),
integralCache: option(continuousShape),
};
type shapeMonad('a, 'b, 'c) =

695
src/distPlus/distribution/Distributions.re
View File

@ -3,20 +3,23 @@ module type dist = {
type integral;
let minX: t => float;
let maxX: t => float;
let mapY: (float => float, t) => t;
let mapY:
(~integralSumCacheFn: float => option(float)=?, ~integralCacheFn: DistTypes.continuousShape => option(DistTypes.continuousShape)=?, ~fn: float => float, t) => t;
let xToY: (float, t) => DistTypes.mixedPoint;
let toShape: t => DistTypes.shape;
let toContinuous: t => option(DistTypes.continuousShape);
let toDiscrete: t => option(DistTypes.discreteShape);
let toScaledContinuous: t => option(DistTypes.continuousShape);
let toScaledDiscrete: t => option(DistTypes.discreteShape);
let toDiscreteProbabilityMass: t => float;
let truncate: (~cache: option(integral)=?, int, t) => t;
let normalize: t => t;
let toDiscreteProbabilityMassFraction: t => float;
let downsample: (int, t) => t;
let truncate: (option(float), option(float), t) => t;
let integral: (~cache: option(integral), t) => integral;
let integralEndY: (~cache: option(integral), t) => float;
let integralXtoY: (~cache: option(integral), float, t) => float;
let integralYtoX: (~cache: option(integral), float, t) => float;
let updateIntegralCache: (option(DistTypes.continuousShape), t) => t;
let integral: (t) => integral;
let integralEndY: (t) => float;
let integralXtoY: (float, t) => float;
let integralYtoX: (float, t) => float;
let mean: t => float;
let variance: t => float;
@ -31,18 +34,17 @@ module Dist = (T: dist) => {
let xTotalRange = (t: t) => maxX(t) -. minX(t);
let mapY = T.mapY;
let xToY = T.xToY;
let truncate = T.truncate;
let downsample = T.downsample;
let toShape = T.toShape;
let toDiscreteProbabilityMass = T.toDiscreteProbabilityMass;
let toDiscreteProbabilityMassFraction = T.toDiscreteProbabilityMassFraction;
let toContinuous = T.toContinuous;
let toDiscrete = T.toDiscrete;
let toScaledContinuous = T.toScaledContinuous;
let toScaledDiscrete = T.toScaledDiscrete;
let normalize = T.normalize;
let truncate = T.truncate;
let mean = T.mean;
let variance = T.variance;
// TODO: Move this to each class, have use integral to produce integral in DistPlus class.
let scaleBy = (~scale=1.0, t: t) => t |> mapY((r: float) => r *. scale);
let updateIntegralCache = T.updateIntegralCache;
module Integral = {
type t = T.integral;
@ -51,661 +53,32 @@ module Dist = (T: dist) => {
let yToX = T.integralYtoX;
let sum = T.integralEndY;
};
// This is suboptimal because it could get the cache but doesn't here.
let scaleToIntegralSum =
(~cache: option(integral)=None, ~intendedSum=1.0, t: t) => {
let scale = intendedSum /. Integral.sum(~cache, t);
scaleBy(~scale, t);
};
};
module Continuous = {
type t = DistTypes.continuousShape;
let getShape = (t: t) => t.xyShape;
let interpolation = (t: t) => t.interpolation;
let make = (interpolation, xyShape): t => {xyShape, interpolation};
let shapeMap = (fn, {xyShape, interpolation}: t): t => {
xyShape: fn(xyShape),
interpolation,
};
let lastY = (t: t) => t |> getShape |> XYShape.T.lastY;
let oShapeMap =
(fn, {xyShape, interpolation}: t): option(DistTypes.continuousShape) =>
fn(xyShape) |> E.O.fmap(make(interpolation));
let toLinear = (t: t): option(t) => {
switch (t) {
| {interpolation: `Stepwise, xyShape} =>
xyShape |> XYShape.Range.stepsToContinuous |> E.O.fmap(make(`Linear))
| {interpolation: `Linear, _} => Some(t)
};
};
let shapeFn = (fn, t: t) => t |> getShape |> fn;
module T =
Dist({
type t = DistTypes.continuousShape;
type integral = DistTypes.continuousShape;
let minX = shapeFn(XYShape.T.minX);
let maxX = shapeFn(XYShape.T.maxX);
let toDiscreteProbabilityMass = _ => 0.0;
let mapY = fn => shapeMap(XYShape.T.mapY(fn));
let toShape = (t: t): DistTypes.shape => Continuous(t);
let xToY = (f, {interpolation, xyShape}: t) => {
module Common = {
let combineIntegralSums =
(
switch (interpolation) {
| `Stepwise =>
xyShape
|> XYShape.XtoY.stepwiseIncremental(f)
|> E.O.default(0.0)
| `Linear => xyShape |> XYShape.XtoY.linear(f)
}
)
|> DistTypes.MixedPoint.makeContinuous;
};
// let combineWithFn = (t1: t, t2: t, fn: (float, float) => float) => {
// switch(t1, t2){
// | ({interpolation: `Stepwise}, {interpolation: `Stepwise}) => 3.0
// | ({interpolation: `Linear}, {interpolation: `Linear}) => 3.0
// }
// };
// TODO: This should work with stepwise plots.
let integral = (~cache, t) =>
switch (cache) {
| Some(cache) => cache
| None =>
t
|> getShape
|> XYShape.Range.integrateWithTriangles
|> E.O.toExt("This should not have happened")
|> make(`Linear)
};
let truncate = (~cache=None, length, t) =>
t
|> shapeMap(
XYShape.XsConversion.proportionByProbabilityMass(
length,
integral(~cache, t).xyShape,
),
);
let integralEndY = (~cache, t) => t |> integral(~cache) |> lastY;
let integralXtoY = (~cache, f, t) =>
t |> integral(~cache) |> shapeFn(XYShape.XtoY.linear(f));
let integralYtoX = (~cache, f, t) =>
t |> integral(~cache) |> shapeFn(XYShape.YtoX.linear(f));
let toContinuous = t => Some(t);
let toDiscrete = _ => None;
let toScaledContinuous = t => Some(t);
let toScaledDiscrete = _ => None;
let mean = (t: t) => {
let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 2.0 /. 2.0;
let indefiniteIntegralLinear = (p, a, b) =>
a *. p ** 2.0 /. 2.0 +. b *. p ** 3.0 /. 3.0;
XYShape.Analysis.integrateContinuousShape(
~indefiniteIntegralStepwise,
~indefiniteIntegralLinear,
t,
);
};
let variance = (t: t): float =>
XYShape.Analysis.getVarianceDangerously(
t,
mean,
XYShape.Analysis.getMeanOfSquaresContinuousShape,
);
});
};
module Discrete = {
let sortedByY = (t: DistTypes.discreteShape) =>
t |> XYShape.T.zip |> XYShape.Zipped.sortByY;
let sortedByX = (t: DistTypes.discreteShape) =>
t |> XYShape.T.zip |> XYShape.Zipped.sortByX;
let empty = XYShape.T.empty;
let combine =
(fn, t1: DistTypes.discreteShape, t2: DistTypes.discreteShape)
: DistTypes.discreteShape => {
XYShape.Combine.combine(
~xsSelection=ALL_XS,
~xToYSelection=XYShape.XtoY.stepwiseIfAtX,
~fn,
t1,
t2,
);
};
let _default0 = (fn, a, b) =>
fn(E.O.default(0.0, a), E.O.default(0.0, b));
let reduce = (fn, items) =>
items |> E.A.fold_left(combine(_default0(fn)), empty);
module T =
Dist({
type t = DistTypes.discreteShape;
type integral = DistTypes.continuousShape;
let integral = (~cache, t) =>
switch (cache) {
| Some(c) => c
| None => Continuous.make(`Stepwise, XYShape.T.accumulateYs((+.), t))
};
let integralEndY = (~cache, t) =>
t |> integral(~cache) |> Continuous.lastY;
let minX = XYShape.T.minX;
let maxX = XYShape.T.maxX;
let toDiscreteProbabilityMass = _ => 1.0;
let mapY = XYShape.T.mapY;
let toShape = (t: t): DistTypes.shape => Discrete(t);
let toContinuous = _ => None;
let toDiscrete = t => Some(t);
let toScaledContinuous = _ => None;
let toScaledDiscrete = t => Some(t);
let truncate = (~cache=None, i, t: t): DistTypes.discreteShape =>
t
|> XYShape.T.zip
|> XYShape.Zipped.sortByY
|> Belt.Array.reverse
|> Belt.Array.slice(_, ~offset=0, ~len=i)
|> XYShape.Zipped.sortByX
|> XYShape.T.fromZippedArray;
let xToY = (f, t) => {
XYShape.XtoY.stepwiseIfAtX(f, t)
|> E.O.default(0.0)
|> DistTypes.MixedPoint.makeDiscrete;
};
let integralXtoY = (~cache, f, t) =>
t
|> integral(~cache)
|> Continuous.getShape
|> XYShape.XtoY.linear(f);
let integralYtoX = (~cache, f, t) =>
t
|> integral(~cache)
|> Continuous.getShape
|> XYShape.YtoX.linear(f);
let mean = (t: t): float =>
E.A.reducei(t.xs, 0.0, (acc, x, i) => acc +. x *. t.ys[i]);
let variance = (t: t): float => {
let getMeanOfSquares = t =>
mean(XYShape.Analysis.squareXYShape(t));
XYShape.Analysis.getVarianceDangerously(t, mean, getMeanOfSquares);
};
});
};
// TODO: I think this shouldn't assume continuous/discrete are normalized to 1.0, and thus should not need the discreteProbabilityMassFraction being separate.
module Mixed = {
type t = DistTypes.mixedShape;
let make =
(~continuous, ~discrete, ~discreteProbabilityMassFraction)
: DistTypes.mixedShape => {
continuous,
discrete,
discreteProbabilityMassFraction,
};
// todo: Put into scaling module
let scaleDiscreteFn =
({discreteProbabilityMassFraction}: DistTypes.mixedShape, f) =>
f *. discreteProbabilityMassFraction;
//TODO: Warning: This currently computes the integral, which is expensive.
let scaleContinuousFn =
({discreteProbabilityMassFraction}: DistTypes.mixedShape, f) =>
f *. (1.0 -. discreteProbabilityMassFraction);
//TODO: Warning: This currently computes the integral, which is expensive.
let scaleContinuous = ({discreteProbabilityMassFraction}: t, continuous) =>
continuous
|> Continuous.T.scaleToIntegralSum(
~intendedSum=1.0 -. discreteProbabilityMassFraction,
);
let scaleDiscrete = ({discreteProbabilityMassFraction}: t, disrete) =>
disrete
|> Discrete.T.scaleToIntegralSum(
~intendedSum=discreteProbabilityMassFraction,
);
module T =
Dist({
type t = DistTypes.mixedShape;
type integral = DistTypes.continuousShape;
let minX = ({continuous, discrete}: t) => {
min(Continuous.T.minX(continuous), Discrete.T.minX(discrete));
};
let maxX = ({continuous, discrete}: t) =>
max(Continuous.T.maxX(continuous), Discrete.T.maxX(discrete));
let toShape = (t: t): DistTypes.shape => Mixed(t);
let toContinuous = ({continuous}: t) => Some(continuous);
let toDiscrete = ({discrete}: t) => Some(discrete);
let toDiscreteProbabilityMass = ({discreteProbabilityMassFraction}: t) => discreteProbabilityMassFraction;
let xToY = (f, {discrete, continuous} as t: t) => {
let c =
continuous
|> Continuous.T.xToY(f)
|> DistTypes.MixedPoint.fmap(scaleContinuousFn(t));
let d =
discrete
|> Discrete.T.xToY(f)
|> DistTypes.MixedPoint.fmap(scaleDiscreteFn(t));
DistTypes.MixedPoint.add(c, d);
};
// Warning: It's not clear how to update the discreteProbabilityMassFraction, so this may create small errors.
let truncate =
(
~cache=None,
count,
{discrete, continuous, discreteProbabilityMassFraction}: t,
)
: t => {
{
discrete:
Discrete.T.truncate(
int_of_float(
float_of_int(count) *. discreteProbabilityMassFraction,
),
discrete,
),
continuous:
Continuous.T.truncate(
int_of_float(
float_of_int(count)
*. (1.0 -. discreteProbabilityMassFraction),
),
continuous,
),
discreteProbabilityMassFraction,
};
};
let toScaledContinuous = ({continuous} as t: t) =>
Some(scaleContinuous(t, continuous));
let toScaledDiscrete = ({discrete} as t: t) =>
Some(scaleDiscrete(t, discrete));
let integral =
(
~cache,
{continuous, discrete, discreteProbabilityMassFraction}: t,
combineFn: (float, float) => option(float),
t1IntegralSumCache: option(float),
t2IntegralSumCache: option(float),
) => {
switch (cache) {
| Some(cache) => cache
| None =>
let scaleContinuousBy =
(1.0 -. discreteProbabilityMassFraction)
/. (continuous |> Continuous.T.Integral.sum(~cache=None));
let scaleDiscreteBy =
discreteProbabilityMassFraction
/. (
discrete
|> Discrete.T.Integral.get(~cache=None)
|> Continuous.toLinear
|> E.O.fmap(Continuous.lastY)
|> E.O.toExn("")
);
let cont =
continuous
|> Continuous.T.Integral.get(~cache=None)
|> Continuous.T.scaleBy(~scale=scaleContinuousBy);
let dist =
discrete
|> Discrete.T.Integral.get(~cache=None)
|> Continuous.toLinear
|> E.O.toExn("")
|> Continuous.T.scaleBy(~scale=scaleDiscreteBy);
let result =
Continuous.make(
`Linear,
XYShape.Combine.combineLinear(
~fn=(+.),
Continuous.getShape(cont),
Continuous.getShape(dist),
),
);
result;
switch (t1IntegralSumCache, t2IntegralSumCache) {
| (None, _)
| (_, None) => None
| (Some(s1), Some(s2)) => combineFn(s1, s2)
};
};
let integralEndY = (~cache, t: t) => {
integral(~cache, t) |> Continuous.lastY;
};
let integralXtoY = (~cache, f, t) => {
t
|> integral(~cache)
|> Continuous.getShape
|> XYShape.XtoY.linear(f);
};
let integralYtoX = (~cache, f, t) => {
t
|> integral(~cache)
|> Continuous.getShape
|> XYShape.YtoX.linear(f);
};
// TODO: This part really needs to be rethought, I'm quite sure this is just broken. Mapping Ys would change the desired discreteProbabilityMassFraction.
let mapY =
(fn, {discrete, continuous, discreteProbabilityMassFraction}: t): t => {
{
discrete: Discrete.T.mapY(fn, discrete),
continuous: Continuous.T.mapY(fn, continuous),
discreteProbabilityMassFraction,
};
};
let mean = (t: t): float => {
let discreteProbabilityMassFraction =
t.discreteProbabilityMassFraction;
switch (discreteProbabilityMassFraction) {
| 1.0 => Discrete.T.mean(t.discrete)
| 0.0 => Continuous.T.mean(t.continuous)
| _ =>
Discrete.T.mean(t.discrete)
*. discreteProbabilityMassFraction
+. Continuous.T.mean(t.continuous)
*. (1.0 -. discreteProbabilityMassFraction)
};
};
let variance = (t: t): float => {
let discreteProbabilityMassFraction =
t.discreteProbabilityMassFraction;
let getMeanOfSquares = (t: t) => {
Discrete.T.mean(XYShape.Analysis.squareXYShape(t.discrete))
*. t.discreteProbabilityMassFraction
+. XYShape.Analysis.getMeanOfSquaresContinuousShape(t.continuous)
*. (1.0 -. t.discreteProbabilityMassFraction);
};
switch (discreteProbabilityMassFraction) {
| 1.0 => Discrete.T.variance(t.discrete)
| 0.0 => Continuous.T.variance(t.continuous)
| _ =>
XYShape.Analysis.getVarianceDangerously(
t,
mean,
getMeanOfSquares,
)
};
};
});
};
module Shape = {
module T =
Dist({
type t = DistTypes.shape;
type integral = DistTypes.continuousShape;
let mapToAll = ((fn1, fn2, fn3), t: t) =>
switch (t) {
| Mixed(m) => fn1(m)
| Discrete(m) => fn2(m)
| Continuous(m) => fn3(m)
};
let fmap = ((fn1, fn2, fn3), t: t): t =>
switch (t) {
| Mixed(m) => Mixed(fn1(m))
| Discrete(m) => Discrete(fn2(m))
| Continuous(m) => Continuous(fn3(m))
};
let xToY = f =>
mapToAll((
Mixed.T.xToY(f),
Discrete.T.xToY(f),
Continuous.T.xToY(f),
));
let toShape = (t: t) => t;
let toContinuous =
mapToAll((
Mixed.T.toContinuous,
Discrete.T.toContinuous,
Continuous.T.toContinuous,
));
let toDiscrete =
mapToAll((
Mixed.T.toDiscrete,
Discrete.T.toDiscrete,
Continuous.T.toDiscrete,
));
let truncate = (~cache=None, i) =>
fmap((
Mixed.T.truncate(i),
Discrete.T.truncate(i),
Continuous.T.truncate(i),
));
let toDiscreteProbabilityMass =
mapToAll((
Mixed.T.toDiscreteProbabilityMass,
Discrete.T.toDiscreteProbabilityMass,
Continuous.T.toDiscreteProbabilityMass,
));
let toScaledDiscrete =
mapToAll((
Mixed.T.toScaledDiscrete,
Discrete.T.toScaledDiscrete,
Continuous.T.toScaledDiscrete,
));
let toScaledContinuous =
mapToAll((
Mixed.T.toScaledContinuous,
Discrete.T.toScaledContinuous,
Continuous.T.toScaledContinuous,
));
let minX = mapToAll((Mixed.T.minX, Discrete.T.minX, Continuous.T.minX));
let integral = (~cache) => {
mapToAll((
Mixed.T.Integral.get(~cache),
Discrete.T.Integral.get(~cache),
Continuous.T.Integral.get(~cache),
));
};
let integralEndY = (~cache) =>
mapToAll((
Mixed.T.Integral.sum(~cache),
Discrete.T.Integral.sum(~cache),
Continuous.T.Integral.sum(~cache),
));
let integralXtoY = (~cache, f) => {
mapToAll((
Mixed.T.Integral.xToY(~cache, f),
Discrete.T.Integral.xToY(~cache, f),
Continuous.T.Integral.xToY(~cache, f),
));
};
let integralYtoX = (~cache, f) => {
mapToAll((
Mixed.T.Integral.yToX(~cache, f),
Discrete.T.Integral.yToX(~cache, f),
Continuous.T.Integral.yToX(~cache, f),
));
};
let maxX = mapToAll((Mixed.T.maxX, Discrete.T.maxX, Continuous.T.maxX));
let mapY = fn =>
fmap((
Mixed.T.mapY(fn),
Discrete.T.mapY(fn),
Continuous.T.mapY(fn),
));
let mean = (t: t): float =>
switch (t) {
| Mixed(m) => Mixed.T.mean(m)
| Discrete(m) => Discrete.T.mean(m)
| Continuous(m) => Continuous.T.mean(m)
};
let variance = (t: t): float =>
switch (t) {
| Mixed(m) => Mixed.T.variance(m)
| Discrete(m) => Discrete.T.variance(m)
| Continuous(m) => Continuous.T.variance(m)
};
});
};
module DistPlus = {
open DistTypes;
type t = DistTypes.distPlus;
let shapeIntegral = shape => Shape.T.Integral.get(~cache=None, shape);
let make =
let combineIntegrals =
(
~shape,
~guesstimatorString,
~domain=Complete,
~unit=UnspecifiedDistribution,
(),
)
: t => {
let integral = shapeIntegral(shape);
{shape, domain, integralCache: integral, unit, guesstimatorString};
};
let update =
(
~shape=?,
~integralCache=?,
~domain=?,
~unit=?,
~guesstimatorString=?,
t: t,
combineFn: (DistTypes.continuousShape, DistTypes.continuousShape) => option(DistTypes.continuousShape),
t1IntegralCache: option(DistTypes.continuousShape),
t2IntegralCache: option(DistTypes.continuousShape),
) => {
shape: E.O.default(t.shape, shape),
integralCache: E.O.default(t.integralCache, integralCache),
domain: E.O.default(t.domain, domain),
unit: E.O.default(t.unit, unit),
guesstimatorString: E.O.default(t.guesstimatorString, guesstimatorString),
};
let updateShape = (shape, t) => {
let integralCache = shapeIntegral(shape);
update(~shape, ~integralCache, t);
};
let domainIncludedProbabilityMass = (t: t) =>
Domain.includedProbabilityMass(t.domain);
let domainIncludedProbabilityMassAdjustment = (t: t, f) =>
f *. Domain.includedProbabilityMass(t.domain);
let toShape = ({shape, _}: t) => shape;
let shapeFn = (fn, {shape}: t) => fn(shape);
module T =
Dist({
type t = DistTypes.distPlus;
type integral = DistTypes.distPlus;
let toShape = toShape;
let toContinuous = shapeFn(Shape.T.toContinuous);
let toDiscrete = shapeFn(Shape.T.toDiscrete);
// todo: Adjust for total mass.
let toScaledContinuous = (t: t) => {
t
|> toShape
|> Shape.T.toScaledContinuous
|> E.O.fmap(
Continuous.T.mapY(domainIncludedProbabilityMassAdjustment(t)),
);
};
let toScaledDiscrete = (t: t) => {
t
|> toShape
|> Shape.T.toScaledDiscrete
|> E.O.fmap(
Discrete.T.mapY(domainIncludedProbabilityMassAdjustment(t)),
);
};
let xToY = (f, t: t) =>
t
|> toShape
|> Shape.T.xToY(f)
|> MixedPoint.fmap(domainIncludedProbabilityMassAdjustment(t));
let minX = shapeFn(Shape.T.minX);
let maxX = shapeFn(Shape.T.maxX);
let toDiscreteProbabilityMass =
shapeFn(Shape.T.toDiscreteProbabilityMass);
// This bit is kind of awkward, could probably use rethinking.
let integral = (~cache, t: t) =>
updateShape(Continuous(t.integralCache), t);
let truncate = (~cache=None, i, t) =>
updateShape(t |> toShape |> Shape.T.truncate(i), t);
// todo: adjust for limit, maybe?
let mapY = (fn, {shape, _} as t: t): t =>
Shape.T.mapY(fn, shape) |> updateShape(_, t);
let integralEndY = (~cache as _, t: t) =>
Shape.T.Integral.sum(~cache=Some(t.integralCache), toShape(t));
// TODO: Fix this below, obviously. Adjust for limits
let integralXtoY = (~cache as _, f, t: t) => {
Shape.T.Integral.xToY(~cache=Some(t.integralCache), f, toShape(t))
|> domainIncludedProbabilityMassAdjustment(t);
};
// TODO: This part is broken when there is a limit, if this is supposed to be taken into account.
let integralYtoX = (~cache as _, f, t: t) => {
Shape.T.Integral.yToX(~cache=Some(t.integralCache), f, toShape(t));
};
let mean = (t: t) => Shape.T.mean(t.shape);
let variance = (t: t) => Shape.T.variance(t.shape);
});
};
module DistPlusTime = {
open DistTypes;
type t = DistTypes.distPlus;
let unitToJson = ({unit}: t) => unit |> DistTypes.DistributionUnit.toJson;
let timeVector = ({unit}: t) =>
switch (unit) {
| TimeDistribution(timeVector) => Some(timeVector)
| UnspecifiedDistribution => None
};
let timeInVectorToX = (f: TimeTypes.timeInVector, t: t) => {
let timeVector = t |> timeVector;
timeVector |> E.O.fmap(TimeTypes.RelativeTimePoint.toXValue(_, f));
};
let xToY = (f: TimeTypes.timeInVector, t: t) => {
timeInVectorToX(f, t) |> E.O.fmap(DistPlus.T.xToY(_, t));
};
module Integral = {
include DistPlus.T.Integral;
let xToY = (f: TimeTypes.timeInVector, t: t) => {
timeInVectorToX(f, t)
|> E.O.fmap(x => DistPlus.T.Integral.xToY(~cache=None, x, t));
switch (t1IntegralCache, t2IntegralCache) {
| (None, _)
| (_, None) => None
| (Some(s1), Some(s2)) => combineFn(s1, s2)
};
};
};

332
src/distPlus/distribution/Mixed.re Normal file
View File

@ -0,0 +1,332 @@
open Distributions;
type t = DistTypes.mixedShape;
let make = (~integralSumCache=None, ~integralCache=None, ~continuous, ~discrete): t => {continuous, discrete, integralSumCache, integralCache};
let totalLength = (t: t): int => {
let continuousLength =
t.continuous |> Continuous.getShape |> XYShape.T.length;
let discreteLength = t.discrete |> Discrete.getShape |> XYShape.T.length;
continuousLength + discreteLength;
};
let scaleBy = (~scale=1.0, t: t): t => {
let scaledDiscrete = Discrete.scaleBy(~scale, t.discrete);
let scaledContinuous = Continuous.scaleBy(~scale, t.continuous);
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 toDiscrete = ({discrete}: t) => Some(discrete);
let updateIntegralCache = (integralCache, t: t): t => {
...t,
integralCache,
};
module T =
Dist({
type t = DistTypes.mixedShape;
type integral = DistTypes.continuousShape;
let minX = ({continuous, discrete}: t) => {
min(Continuous.T.minX(continuous), Discrete.T.minX(discrete));
};
let maxX = ({continuous, discrete}: t) =>
max(Continuous.T.maxX(continuous), Discrete.T.maxX(discrete));
let toShape = (t: t): DistTypes.shape => Mixed(t);
let updateIntegralCache = updateIntegralCache;
let toContinuous = toContinuous;
let toDiscrete = toDiscrete;
let truncate =
(
leftCutoff: option(float),
rightCutoff: option(float),
{discrete, continuous}: t,
) => {
let truncatedContinuous =
Continuous.T.truncate(leftCutoff, rightCutoff, continuous);
let truncatedDiscrete =
Discrete.T.truncate(leftCutoff, rightCutoff, discrete);
make(~integralSumCache=None, ~integralCache=None, ~discrete=truncatedDiscrete, ~continuous=truncatedContinuous);
};
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 =
Continuous.T.Integral.sum(continuous);
let discreteIntegralSum =
Discrete.T.Integral.sum(discrete);
let totalIntegralSum = continuousIntegralSum +. discreteIntegralSum;
let newContinuousSum = continuousIntegralSum /. totalIntegralSum;
let newDiscreteSum = discreteIntegralSum /. totalIntegralSum;
let normalizedContinuous =
continuous
|> Continuous.scaleBy(~scale=newContinuousSum /. continuousIntegralSum)
|> Continuous.updateIntegralSumCache(Some(newContinuousSum));
let normalizedDiscrete =
discrete
|> Discrete.scaleBy(~scale=newDiscreteSum /. discreteIntegralSum)
|> Discrete.updateIntegralSumCache(Some(newDiscreteSum));
make(~integralSumCache=Some(1.0), ~integralCache=None, ~continuous=normalizedContinuous, ~discrete=normalizedDiscrete);
};
let xToY = (x, t: t) => {
// This evaluates the mixedShape at x, interpolating if necessary.
// Note that we normalize entire mixedShape first.
let {continuous, discrete}: t = normalize(t);
let c = Continuous.T.xToY(x, continuous);
let d = Discrete.T.xToY(x, discrete);
DistTypes.MixedPoint.add(c, d); // "add" here just combines the two values into a single MixedPoint.
};
let toDiscreteProbabilityMassFraction = ({discrete, continuous}: t) => {
let discreteIntegralSum =
Discrete.T.Integral.sum(discrete);
let continuousIntegralSum =
Continuous.T.Integral.sum(continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
discreteIntegralSum /. totalIntegralSum;
};
let downsample = (count, t: t): t => {
// We will need to distribute the new xs fairly between the discrete and continuous shapes.
// The easiest way to do this is to simply go by the previous probability masses.
let discreteIntegralSum =
Discrete.T.Integral.sum(t.discrete);
let continuousIntegralSum =
Continuous.T.Integral.sum(t.continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
// TODO: figure out what to do when the totalIntegralSum is zero.
let downsampledDiscrete =
Discrete.T.downsample(
int_of_float(
float_of_int(count) *. (discreteIntegralSum /. totalIntegralSum),
),
t.discrete,
);
let downsampledContinuous =
Continuous.T.downsample(
int_of_float(
float_of_int(count) *. (continuousIntegralSum /. totalIntegralSum),
),
t.continuous,
);
{...t, discrete: downsampledDiscrete, continuous: downsampledContinuous};
};
let integral = (t: t) => {
switch (t.integralCache) {
| Some(cache) => cache
| None =>
// 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 = Continuous.T.Integral.get(t.continuous);
let discreteIntegral = Continuous.stepwiseToLinear(Discrete.T.Integral.get(t.discrete));
Continuous.make(
XYShape.PointwiseCombination.combine(
(+.),
XYShape.XtoY.continuousInterpolator(`Linear, `UseOutermostPoints),
Continuous.getShape(continuousIntegral),
Continuous.getShape(discreteIntegral),
),
);
};
};
let integralEndY = (t: t) => {
t |> integral |> Continuous.lastY;
};
let integralXtoY = (f, t) => {
t |> integral |> Continuous.getShape |> XYShape.XtoY.linear(f);
};
let integralYtoX = (f, t) => {
t |> integral |> Continuous.getShape |> XYShape.YtoX.linear(f);
};
// This pipes all ys (continuous and discrete) through fn.
// If mapY is a linear operation, we might be able to update the integralSumCaches as well;
// if not, they'll be set to None.
let mapY =
(
~integralSumCacheFn=previousIntegralSum => None,
~integralCacheFn=previousIntegral => None,
~fn,
t: t,
)
: t => {
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 yMappedContinuous: DistTypes.continuousShape =
t.continuous
|> Continuous.T.mapY(~fn)
|> Continuous.updateIntegralSumCache(E.O.bind(t.continuous.integralSumCache, integralSumCacheFn))
|> Continuous.updateIntegralCache(E.O.bind(t.continuous.integralCache, integralCacheFn));
{
discrete: yMappedDiscrete,
continuous: yMappedContinuous,
integralSumCache: E.O.bind(t.integralSumCache, integralSumCacheFn),
integralCache: E.O.bind(t.integralCache, integralCacheFn),
};
};
let mean = ({discrete, continuous}: t): float => {
let discreteMean = Discrete.T.mean(discrete);
let continuousMean = Continuous.T.mean(continuous);
// the combined mean is the weighted sum of the two:
let discreteIntegralSum = Discrete.T.Integral.sum(discrete);
let continuousIntegralSum = Continuous.T.Integral.sum(continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
(
discreteMean
*. discreteIntegralSum
+. continuousMean
*. continuousIntegralSum
)
/. totalIntegralSum;
};
let variance = ({discrete, continuous} as t: t): float => {
// the combined mean is the weighted sum of the two:
let discreteIntegralSum = Discrete.T.Integral.sum(discrete);
let continuousIntegralSum = Continuous.T.Integral.sum(continuous);
let totalIntegralSum = discreteIntegralSum +. continuousIntegralSum;
let getMeanOfSquares = ({discrete, continuous}: t) => {
let discreteMean =
discrete
|> Discrete.shapeMap(XYShape.Analysis.squareXYShape)
|> Discrete.T.mean;
let continuousMean =
continuous |> XYShape.Analysis.getMeanOfSquaresContinuousShape;
(
discreteMean
*. discreteIntegralSum
+. continuousMean
*. continuousIntegralSum
)
/. totalIntegralSum;
};
switch (discreteIntegralSum /. totalIntegralSum) {
| 1.0 => Discrete.T.variance(discrete)
| 0.0 => Continuous.T.variance(continuous)
| _ =>
XYShape.Analysis.getVarianceDangerously(t, mean, getMeanOfSquares)
};
};
});
let combineAlgebraically =
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t)
: t => {
// Discrete convolution can cause a huge increase in the number of samples,
// so we'll first downsample.
// An alternative (to be explored in the future) may be to first perform the full convolution and then to downsample the result;
// to use non-uniform fast Fourier transforms (for addition only), add web workers or gpu.js, etc. ...
// we have to figure out where to downsample, and how to effectively
//let downsampleIfTooLarge = (t: t) => {
// let sqtl = sqrt(float_of_int(totalLength(t)));
// sqtl > 10 ? T.downsample(int_of_float(sqtl), t) : t;
//};
let t1d = t1;
let t2d = t2;
// continuous (*) continuous => continuous, but also
// discrete (*) continuous => continuous (and vice versa). We have to take care of all combos and then combine them:
let ccConvResult =
Continuous.combineAlgebraically(
op,
t1.continuous,
t2.continuous,
);
let dcConvResult =
Continuous.combineAlgebraicallyWithDiscrete(
op,
t2.continuous,
t1.discrete,
);
let cdConvResult =
Continuous.combineAlgebraicallyWithDiscrete(
op,
t1.continuous,
t2.discrete,
);
let continuousConvResult =
Continuous.reduce((+.), [|ccConvResult, dcConvResult, cdConvResult|]);
// ... finally, discrete (*) discrete => discrete, obviously:
let discreteConvResult =
Discrete.combineAlgebraically(op, t1.discrete, t2.discrete);
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);
};

87
src/distPlus/distribution/MixedShapeBuilder.re
View File

@ -8,98 +8,27 @@ 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(Continuous.make(~integralSumCache=Some(0.0), {xs: [||], ys: [||]}));
let discrete = discrete |> E.O.default(Discrete.make(~integralSumCache=Some(0.0), {xs: [||], ys: [||]}));
let cLength =
continuous
|> Distributions.Continuous.getShape
|> Continuous.getShape
|> XYShape.T.xs
|> E.A.length;
let dLength = discrete |> XYShape.T.xs |> E.A.length;
let dLength = discrete |> Discrete.getShape |> XYShape.T.xs |> E.A.length;
switch (cLength, dLength) {
| (0 | 1, 0) => None
| (0 | 1, _) => Some(Discrete(discrete))
| (_, 0) => Some(Continuous(continuous))
| (_, _) =>
let discreteProbabilityMassFraction =
Distributions.Discrete.T.Integral.sum(~cache=None, discrete);
let discrete =
Distributions.Discrete.T.scaleToIntegralSum(~intendedSum=1.0, discrete);
let continuous =
Distributions.Continuous.T.scaleToIntegralSum(
~intendedSum=1.0,
continuous,
);
let mixedDist =
Distributions.Mixed.make(
Mixed.make(
~integralSumCache=None,
~integralCache=None,
~continuous,
~discrete,
~discreteProbabilityMassFraction,
);
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
};

233
src/distPlus/distribution/Shape.re Normal file
View File

@ -0,0 +1,233 @@
open Distributions;
type t = DistTypes.shape;
let mapToAll = ((fn1, fn2, fn3), t: t) =>
switch (t) {
| Mixed(m) => fn1(m)
| Discrete(m) => fn2(m)
| Continuous(m) => fn3(m)
};
let fmap = ((fn1, fn2, fn3), t: t): t =>
switch (t) {
| Mixed(m) => Mixed(fn1(m))
| Discrete(m) => Discrete(fn2(m))
| Continuous(m) => Continuous(fn3(m))
};
let toMixed =
mapToAll((
m => m,
d => Mixed.make(~integralSumCache=d.integralSumCache, ~integralCache=d.integralCache, ~discrete=d, ~continuous=Continuous.empty),
c => Mixed.make(~integralSumCache=c.integralSumCache, ~integralCache=c.integralCache, ~discrete=Discrete.empty, ~continuous=c),
));
let combineAlgebraically =
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
switch (t1, t2) {
| (Continuous(m1), Continuous(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.combineAlgebraically(op, m1, m2) |> Discrete.T.toShape
| (m1, m2) =>
Mixed.combineAlgebraically(
op,
toMixed(m1),
toMixed(m2),
)
|> Mixed.T.toShape
};
};
let combinePointwise =
(~integralSumCachesFn: (float, float) => option(float) = (_, _) => None,
~integralCachesFn: (DistTypes.continuousShape, DistTypes.continuousShape) => option(DistTypes.continuousShape) = (_, _) => None,
fn,
t1: t,
t2: t) =>
switch (t1, t2) {
| (Continuous(m1), Continuous(m2)) =>
DistTypes.Continuous(
Continuous.combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn, m1, m2),
)
| (Discrete(m1), Discrete(m2)) =>
DistTypes.Discrete(
Discrete.combinePointwise(~integralSumCachesFn, ~integralCachesFn, fn, m1, m2),
)
| (m1, m2) =>
DistTypes.Mixed(
Mixed.combinePointwise(
~integralSumCachesFn,
~integralCachesFn,
fn,
toMixed(m1),
toMixed(m2),
),
)
};
module T =
Dist({
type t = DistTypes.shape;
type integral = DistTypes.continuousShape;
let xToY = (f: float) =>
mapToAll((
Mixed.T.xToY(f),
Discrete.T.xToY(f),
Continuous.T.xToY(f),
));
let toShape = (t: t) => t;
let toContinuous = t => None;
let toDiscrete = t => None;
let downsample = (i, t) =>
fmap(
(
Mixed.T.downsample(i),
Discrete.T.downsample(i),
Continuous.T.downsample(i),
),
t,
);
let truncate = (leftCutoff, rightCutoff, t): t =>
fmap(
(
Mixed.T.truncate(leftCutoff, rightCutoff),
Discrete.T.truncate(leftCutoff, rightCutoff),
Continuous.T.truncate(leftCutoff, rightCutoff),
),
t,
);
let toDiscreteProbabilityMassFraction = t => 0.0;
let normalize =
fmap((
Mixed.T.normalize,
Discrete.T.normalize,
Continuous.T.normalize
));
let updateIntegralCache = (integralCache, t: t): t =>
fmap((
Mixed.T.updateIntegralCache(integralCache),
Discrete.T.updateIntegralCache(integralCache),
Continuous.T.updateIntegralCache(integralCache),
), t);
let toContinuous =
mapToAll((
Mixed.T.toContinuous,
Discrete.T.toContinuous,
Continuous.T.toContinuous,
));
let toDiscrete =
mapToAll((
Mixed.T.toDiscrete,
Discrete.T.toDiscrete,
Continuous.T.toDiscrete,
));
let toDiscreteProbabilityMassFraction =
mapToAll((
Mixed.T.toDiscreteProbabilityMassFraction,
Discrete.T.toDiscreteProbabilityMassFraction,
Continuous.T.toDiscreteProbabilityMassFraction,
));
let minX = mapToAll((Mixed.T.minX, Discrete.T.minX, Continuous.T.minX));
let integral =
mapToAll((
Mixed.T.Integral.get,
Discrete.T.Integral.get,
Continuous.T.Integral.get,
));
let integralEndY =
mapToAll((
Mixed.T.Integral.sum,
Discrete.T.Integral.sum,
Continuous.T.Integral.sum,
));
let integralXtoY = (f) => {
mapToAll((
Mixed.T.Integral.xToY(f),
Discrete.T.Integral.xToY(f),
Continuous.T.Integral.xToY(f),
));
};
let integralYtoX = (f) => {
mapToAll((
Mixed.T.Integral.yToX(f),
Discrete.T.Integral.yToX(f),
Continuous.T.Integral.yToX(f),
));
};
let maxX = mapToAll((Mixed.T.maxX, Discrete.T.maxX, Continuous.T.maxX));
let mapY = (~integralSumCacheFn=previousIntegralSum => None, ~integralCacheFn=previousIntegral=>None, ~fn) =>
fmap((
Mixed.T.mapY(~integralSumCacheFn, ~integralCacheFn, ~fn),
Discrete.T.mapY(~integralSumCacheFn, ~integralCacheFn, ~fn),
Continuous.T.mapY(~integralSumCacheFn, ~integralCacheFn, ~fn),
));
let mean = (t: t): float =>
switch (t) {
| Mixed(m) => Mixed.T.mean(m)
| Discrete(m) => Discrete.T.mean(m)
| Continuous(m) => Continuous.T.mean(m)
};
let variance = (t: t): float =>
switch (t) {
| Mixed(m) => Mixed.T.variance(m)
| Discrete(m) => Discrete.T.variance(m)
| Continuous(m) => Continuous.T.variance(m)
};
});
let 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 items = Belt.Array.make(n, 0.0);
for (x in 0 to n - 1) {
let _ = Belt.Array.set(items, x, fn());
();
};
items;
};
let sample = (t: t): float => {
let randomItem = Random.float(1.);
let bar = t |> T.Integral.yToX(randomItem);
bar;
};
let sampleNRendered = (n, dist) => {
let integralCache = T.Integral.get(dist);
let distWithUpdatedIntegralCache = T.updateIntegralCache(Some(integralCache), dist);
doN(n, () => sample(distWithUpdatedIntegralCache));
};
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s): float =>
switch (distToFloatOp) {
| `Pdf(f) => pdf(f, s)
| `Cdf(f) => pdf(f, s)
| `Inv(f) => inv(f, s)
| `Sample => sample(s)
| `Mean => T.mean(s)
};

203
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;
@ -17,7 +17,9 @@ 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 isEmpty = (t: t) => length(t) == 0;
let minX = (t: t) => t |> xs |> E.A.Sorted.min |> extImp;
let maxX = (t: t) => t |> xs |> E.A.Sorted.max |> extImp;
let firstY = (t: t) => t |> ys |> E.A.first |> extImp;
@ -31,6 +33,11 @@ module T = {
let accumulateYs = (fn, p: t) => {
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 =>
pairs |> Belt.Array.unzip |> fromArray;
let equallyDividedXs = (t: t, newLength) => {
@ -136,6 +143,63 @@ module XtoY = {
};
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 = {
@ -154,7 +218,9 @@ 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
};
};
@ -164,37 +230,90 @@ 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 = {
type xsSelection =
| ALL_XS
| XS_EVENLY_DIVIDED(int);
module PointwiseCombination = {
let combine =
// 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.
// 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.
// 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, interpolator, t1, t2) {
let t1n = t1.xs.length;
let t2n = t2.xs.length;
let outX = [];
let outY = [];
let i = -1;
let j = -1;
while (i <= t1n - 1 && j <= t2n - 1) {
let x, ya, yb;
if (j == t2n - 1 && i < t1n - 1 ||
t1.xs[i+1] < t2.xs[j+1]) { // if a has to catch up to b, or if b is already done
i++;
x = t1.xs[i];
ya = t1.ys[i];
yb = interpolator(t2, j, x);
} 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
j++;
x = t2.xs[j];
yb = t2.ys[j];
ya = interpolator(t1, i, x);
} 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++;
j++;
x = t1.xs[i];
ya = t1.ys[i];
yb = t2.ys[j];
} else if (i === t1n - 1 && j === t2n - 1) {
// finished!
i = t1n;
j = t2n;
continue;
} else {
console.log("Error!", i, j);
}
outX.push(x);
outY.push(fn(ya, yb));
}
return {xs: outX, ys: outY};
}
|}];
let combineEvenXs =
(
~xToYSelection: (float, T.t) => 'a,
~xsSelection=ALL_XS,
~fn,
~xToYSelection,
sampleCount,
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)));
switch ((E.A.length(t1.xs), E.A.length(t2.xs))) {
| (0, 0) => T.empty
| (0, _) => t2
| (_, 0) => t1
| (_, _) => {
let allXs = 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);
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.
let intersperse = (t1: T.t, t2: T.t) => {
E.A.intersperse(T.zip(t1), T.zip(t2)) |> T.fromZippedArray;
@ -244,8 +363,8 @@ 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],
);
();
@ -255,8 +374,31 @@ module Range = {
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 => {
// 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 items =
switch (E.A.toRanges(Belt.Array.zip(t.xs, t.ys))) {
@ -265,7 +407,7 @@ 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)
};
@ -287,10 +429,10 @@ let pointLogScore = (prediction, answer) =>
};
let logScorePoint = (sampleCount, t1, t2) =>
Combine.combine(
~xsSelection=XS_EVENLY_DIVIDED(sampleCount),
~xToYSelection=XtoY.linear,
PointwiseCombination.combineEvenXs(
~fn=pointLogScore,
~xToYSelection=XtoY.linear,
sampleCount,
t1,
t2,
)
@ -315,6 +457,7 @@ 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, _) =>
@ -323,6 +466,9 @@ module Analysis = {
| (`Linear, _) =>
let x1 = xs[i - 1];
let x2 = xs[i];
if (x1 == x2) {
0.0
} else {
let h1 = ys[i - 1];
let h2 = ys[i];
let b = (h1 -. h2) /. (x1 -. x2);
@ -330,6 +476,7 @@ module Analysis = {
indefiniteIntegralLinear(x2, a, b)
-. indefiniteIntegralLinear(x1, a, b);
};
};
acc +. areaUnderIntegral;
},
);

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

@ -0,0 +1,23 @@
open ExpressionTypes.ExpressionTree;
let toShape = (intendedShapeLength: int, samplingInputs, node: node) => {
let renderResult =
`Render(`Normalize(node))
|> ExpressionTreeEvaluator.toLeaf({
samplingInputs,
intendedShapeLength,
evaluateNode: ExpressionTreeEvaluator.toLeaf,
});
switch (renderResult) {
| Ok(`RenderedDist(shape)) => Ok(shape)
| Ok(_) => Error("Rendering failed.")
| Error(e) => Error(e)
};
};
let rec toString =
fun
| `SymbolicDist(d) => SymbolicDist.T.toString(d)
| `RenderedDist(_) => "[shape]"
| op => Operation.T.toString(toString, op);

318
src/distPlus/expressionTree/ExpressionTreeEvaluator.re Normal file
View File

@ -0,0 +1,318 @@
open ExpressionTypes;
open ExpressionTypes.ExpressionTree;
type t = node;
type tResult = node => result(node, string);
/* 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 combinationByRendering =
(evaluationParams, algebraicOp, t1: node, t2: node)
: result(node, string) => {
E.R.merge(
Render.ensureIsRenderedAndGetShape(evaluationParams, t1),
Render.ensureIsRenderedAndGetShape(evaluationParams, t2),
)
|> E.R.fmap(((a, b)) =>
`RenderedDist(Shape.combineAlgebraically(algebraicOp, a, b))
);
};
let nodeScore: node => int =
fun
| `SymbolicDist(`Float(_)) => 1
| `SymbolicDist(_) => 1000
| `RenderedDist(Discrete(m)) => m.xyShape |> XYShape.T.length
| `RenderedDist(Mixed(_)) => 1000
| `RenderedDist(Continuous(_)) => 1000
| _ => 1000;
let choose = (t1: node, t2: node) => {
nodeScore(t1) * nodeScore(t2) > 10000 ? `Sampling : `Analytical;
};
let combine =
(evaluationParams, algebraicOp, t1: node, t2: node)
: result(node, string) => {
E.R.merge(
SamplingDistribution.renderIfIsNotSamplingDistribution(
evaluationParams,
t1,
),
SamplingDistribution.renderIfIsNotSamplingDistribution(
evaluationParams,
t2,
),
)
|> E.R.bind(_, ((a, b)) =>
switch (choose(a, b)) {
| `Sampling =>
SamplingDistribution.combineShapesUsingSampling(
evaluationParams,
algebraicOp,
a,
b,
)
| `Analytical =>
combinationByRendering(evaluationParams, algebraicOp, a, b)
}
);
};
let operationToLeaf =
(
evaluationParams: evaluationParams,
algebraicOp: ExpressionTypes.algebraicOperation,
t1: t,
t2: t,
)
: result(node, string) =>
algebraicOp
|> tryAnalyticalSimplification(_, t1, t2)
|> E.R.bind(
_,
fun
| `SymbolicDist(_) as t => Ok(t)
| _ => combine(evaluationParams, algebraicOp, t1, t2),
);
};
module VerticalScaling = {
let operationToLeaf =
(evaluationParams: evaluationParams, scaleOp, t, scaleBy) => {
// scaleBy has to be a single float, otherwise we'll return an error.
let fn = Operation.Scale.toFn(scaleOp);
let integralSumCacheFn = Operation.Scale.toIntegralSumCacheFn(scaleOp);
let integralCacheFn = Operation.Scale.toIntegralCacheFn(scaleOp);
let renderedShape = Render.render(evaluationParams, t);
switch (renderedShape, scaleBy) {
| (Ok(`RenderedDist(rs)), `SymbolicDist(`Float(sm))) =>
Ok(
`RenderedDist(
Shape.T.mapY(
~integralSumCacheFn=integralSumCacheFn(sm),
~integralCacheFn=integralCacheFn(sm),
~fn=fn(sm),
rs,
),
),
)
| (Error(e1), _) => Error(e1)
| (_, _) => Error("Can only scale by float values.")
};
};
};
module PointwiseCombination = {
let pointwiseAdd = (evaluationParams: evaluationParams, t1: t, t2: t) => {
switch (
Render.render(evaluationParams, t1),
Render.render(evaluationParams, t2),
) {
| (Ok(`RenderedDist(rs1)), Ok(`RenderedDist(rs2))) =>
Ok(
`RenderedDist(
Shape.combinePointwise(
~integralSumCachesFn=(a, b) => Some(a +. b),
~integralCachesFn=
(a, b) =>
Some(
Continuous.combinePointwise(
~distributionType=`CDF,
(+.),
a,
b,
),
),
(+.),
rs1,
rs2,
),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Pointwise combination: rendering failed.")
};
};
let pointwiseMultiply = (evaluationParams: evaluationParams, t1: t, t2: t) => {
// 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.
// TODO: This should work for symbolic distributions too!
switch (
Render.render(evaluationParams, t1),
Render.render(evaluationParams, t2),
) {
| (Ok(`RenderedDist(rs1)), Ok(`RenderedDist(rs2))) =>
Ok(`RenderedDist(Shape.combinePointwise(( *. ), rs1, rs2)))
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Pointwise combination: rendering failed.")
};
};
let operationToLeaf =
(
evaluationParams: evaluationParams,
pointwiseOp: pointwiseOperation,
t1: t,
t2: t,
) => {
switch (pointwiseOp) {
| `Add => pointwiseAdd(evaluationParams, t1, t2)
| `Multiply => pointwiseMultiply(evaluationParams, t1, t2)
};
};
};
module Truncate = {
let trySimplification = (leftCutoff, rightCutoff, t): simplificationResult => {
switch (leftCutoff, rightCutoff, t) {
| (None, None, t) => `Solution(t)
| (Some(lc), Some(rc), _) when lc > rc =>
`Error(
"Left truncation bound must be smaller than right truncation bound.",
)
| (lc, rc, `SymbolicDist(`Uniform(u))) =>
`Solution(
`SymbolicDist(`Uniform(SymbolicDist.Uniform.truncate(lc, rc, u))),
)
| _ => `NoSolution
};
};
let truncateAsShape =
(evaluationParams: evaluationParams, leftCutoff, rightCutoff, t) => {
// 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
switch (Render.ensureIsRendered(evaluationParams, t)) {
| Ok(`RenderedDist(rs)) =>
Ok(`RenderedDist(Shape.T.truncate(leftCutoff, rightCutoff, rs)))
| Error(e) => Error(e)
| _ => Error("Could not truncate distribution.")
};
};
let operationToLeaf =
(
evaluationParams,
leftCutoff: option(float),
rightCutoff: option(float),
t: node,
)
: result(node, string) => {
t
|> trySimplification(leftCutoff, rightCutoff)
|> (
fun
| `Solution(t) => Ok(t)
| `Error(e) => Error(e)
| `NoSolution =>
truncateAsShape(evaluationParams, leftCutoff, rightCutoff, t)
);
};
};
module Normalize = {
let rec operationToLeaf = (evaluationParams, t: node): result(node, string) => {
switch (t) {
| `RenderedDist(s) => Ok(`RenderedDist(Shape.T.normalize(s)))
| `SymbolicDist(_) => Ok(t)
| _ => evaluateAndRetry(evaluationParams, operationToLeaf, t)
};
};
};
module FloatFromDist = {
let rec operationToLeaf =
(evaluationParams, distToFloatOp: distToFloatOperation, t: node)
: result(node, string) => {
switch (t) {
| `SymbolicDist(s) =>
SymbolicDist.T.operate(distToFloatOp, s)
|> E.R.bind(_, v => Ok(`SymbolicDist(`Float(v))))
| `RenderedDist(rs) =>
Shape.operate(distToFloatOp, rs)
|> (v => Ok(`SymbolicDist(`Float(v))))
| _ =>
t
|> evaluateAndRetry(evaluationParams, r =>
operationToLeaf(r, distToFloatOp)
)
};
};
};
module Render = {
let rec operationToLeaf =
(evaluationParams: evaluationParams, t: node): result(t, string) => {
switch (t) {
| `SymbolicDist(d) =>
Ok(
`RenderedDist(
SymbolicDist.T.toShape(evaluationParams.intendedShapeLength, d),
),
)
| `RenderedDist(_) as t => Ok(t) // already a rendered shape, we're done here
| _ => evaluateAndRetry(evaluationParams, operationToLeaf, t)
};
};
};
/* 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 toLeaf =
(
evaluationParams: ExpressionTypes.ExpressionTree.evaluationParams,
node: t,
)
: result(t, string) => {
switch (node) {
// Leaf nodes just stay leaf nodes
| `SymbolicDist(_)
| `RenderedDist(_) => Ok(node)
// Operations nevaluationParamsd to be turned into leaves
| `AlgebraicCombination(algebraicOp, t1, t2) =>
AlgebraicCombination.operationToLeaf(
evaluationParams,
algebraicOp,
t1,
t2,
)
| `PointwiseCombination(pointwiseOp, t1, t2) =>
PointwiseCombination.operationToLeaf(
evaluationParams,
pointwiseOp,
t1,
t2,
)
| `VerticalScaling(scaleOp, t, scaleBy) =>
VerticalScaling.operationToLeaf(evaluationParams, scaleOp, t, scaleBy)
| `Truncate(leftCutoff, rightCutoff, t) =>
Truncate.operationToLeaf(evaluationParams, leftCutoff, rightCutoff, t)
| `FloatFromDist(distToFloatOp, t) =>
FloatFromDist.operationToLeaf(evaluationParams, distToFloatOp, t)
| `Normalize(t) => Normalize.operationToLeaf(evaluationParams, t)
| `Render(t) => Render.operationToLeaf(evaluationParams, t)
};
};

82
src/distPlus/expressionTree/ExpressionTypes.re Normal file
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type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
type pointwiseOperation = [ | `Add | `Multiply];
type scaleOperation = [ | `Multiply | `Exponentiate | `Log];
type distToFloatOperation = [
| `Pdf(float)
| `Cdf(float)
| `Inv(float)
| `Mean
| `Sample
];
module ExpressionTree = {
type node = [
| `SymbolicDist(SymbolicTypes.symbolicDist)
| `RenderedDist(DistTypes.shape)
| `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)
];
type samplingInputs = {
sampleCount: int,
outputXYPoints: int,
kernelWidth: option(float),
};
type evaluationParams = {
samplingInputs,
intendedShapeLength: int,
evaluateNode: (evaluationParams, node) => Belt.Result.t(node, string),
};
let evaluateNode = (evaluationParams: evaluationParams) =>
evaluationParams.evaluateNode(evaluationParams);
let evaluateAndRetry = (evaluationParams, fn, node) =>
node
|> evaluationParams.evaluateNode(evaluationParams)
|> E.R.bind(_, fn(evaluationParams));
module Render = {
type t = node;
let render = (evaluationParams: evaluationParams, r) =>
`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
};
};
};
type simplificationResult = [
| `Solution(ExpressionTree.node)
| `Error(string)
| `NoSolution
];

392
src/distPlus/expressionTree/MathJsParser.re Normal file
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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));
let name = j |> optional(field("fn", field("name", string)));
name |> E.O.fmap(name => Fn({name, 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)|]
when low < medium && medium < high =>
Ok(`SymbolicDist(`Triangular({low, medium, high})))
| [|Value(_), Value(_), Value(_)|] =>
Error("Triangular values must be increasing order")
| _ => 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(_, Shape.T.toContinuous);
// let shape =
// pdf
// |> E.O.fmap(pdf => {
// let _pdf = Continuous.T.normalize(pdf);
// let cdf = 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 toOkPointwise = r => Ok(`PointwiseCombination(r));
let toOkTruncate = r => Ok(`Truncate(r));
let toOkFloatFromDist = r => Ok(`FloatFromDist(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")
| ("dotMultiply", [|Ok(l), Ok(r)|]) => toOkPointwise((`Multiply, l, r))
| ("dotMultiply", _) =>
Error("Dotwise multiplication needs two operands")
| ("rightLogShift", [|Ok(l), Ok(r)|]) => toOkPointwise((`Add, l, r))
| ("rightLogShift", _) => Error("Dotwise addition 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)))|]) =>
toOkTruncate((Some(lc), None, d))
| ("leftTruncate", _) =>
Error("leftTruncate needs two arguments: the expression and the cutoff")
| ("rightTruncate", [|Ok(d), Ok(`SymbolicDist(`Float(rc)))|]) =>
toOkTruncate((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))),
|],
) =>
toOkTruncate((Some(lc), Some(rc), d))
| ("truncate", _) =>
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")
};
};
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"
| "dotMultiply"
| "rightLogShift"
| "divide"
| "pow"
| "leftTruncate"
| "rightTruncate"
| "truncate"
| "mean"
| "inv"
| "sample"
| "cdf"
| "pdf" => operationParser(name, parseArgs())
| 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
| Value(_) as r => nodeParser(r)
| Fn(_) as r => nodeParser(r)
| Array(_) => Error("Array not valid as top level")
| 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;
};
/* The MathJs parser doesn't support '.+' syntax, but we want it because it
would make sense with '.*'. Our workaround is to change this to >>>, which is
logShift in mathJS. We don't expect to use logShift anytime soon, so this tradeoff
seems fine.
*/
let pointwiseToRightLogShift = Js.String.replaceByRe([%re "/\.\+/g"], ">>>");
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 = str |> pointwiseToRightLogShift |> Mathjs.parseMath;
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
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9
src/distPlus/expressionTree/MathjsWrapper.js Normal file
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@ -0,0 +1,9 @@
const math = require("mathjs");
function parseMath(f) {
return JSON.parse(JSON.stringify(math.parse(f)))
};
module.exports = {
parseMath,
};

101
src/distPlus/expressionTree/Operation.re Normal file
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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 $v1 by zero.")
| _ => Ok(toFn(t, f1, f2))
};
};
let toString =
fun
| `Add => "+"
| `Subtract => "-"
| `Multiply => "*"
| `Divide => "/";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module Pointwise = {
type t = pointwiseOperation;
let toString =
fun
| `Add => "+"
| `Multiply => "*";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module DistToFloat = {
type t = distToFloatOperation;
let format = (operation, value) =>
switch (operation) {
| `Cdf(f) => {j|cdf(x=$f,$value)|j}
| `Pdf(f) => {j|pdf(x=$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, $scaleBy) |j}
};
let toIntegralSumCacheFn =
fun
| `Multiply => ((a, b) => Some(a *. b))
| `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None);
let toIntegralCacheFn =
fun
| `Multiply => ((a, b) => None) // TODO: this could probably just be multiplied out (using Continuous.scaleBy)
| `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None);
};
module T = {
let truncateToString =
(left: option(float), right: option(float), nodeToString) => {
let left = left |> E.O.dimap(Js.Float.toString, () => "-inf");
let right = right |> E.O.dimap(Js.Float.toString, () => "inf");
{j|truncate($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.
};

78
src/distPlus/expressionTree/SamplingDistribution.re Normal file
View File

@ -0,0 +1,78 @@
open ExpressionTypes.ExpressionTree;
let isSamplingDistribution: node => bool =
fun
| `SymbolicDist(_) => true
| `RenderedDist(_) => true
| _ => false;
let renderIfIsNotSamplingDistribution = (params, t): result(node, string) =>
!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) => r.shape)
|> E.O.toResult("No response");
shape |> E.R.fmap(r => `Normalize(`RenderedDist(r)));
},
);
};

30
src/distPlus/renderers/DistPlusRenderer.re
View File

@ -1,28 +1,14 @@
let truncateIfShould =
(
{recommendedLength, shouldTruncate}: RenderTypes.DistPlusRenderer.inputs,
outputs: RenderTypes.ShapeRenderer.Combined.outputs,
dist,
) => {
let willTruncate =
shouldTruncate
&& RenderTypes.ShapeRenderer.Combined.methodUsed(outputs) == `Sampling;
willTruncate ? dist |> Distributions.DistPlus.T.truncate(recommendedLength) : dist;
};
let run =
(inputs: RenderTypes.DistPlusRenderer.inputs)
: RenderTypes.DistPlusRenderer.outputs => {
let run = (inputs: RenderTypes.DistPlusRenderer.inputs) => {
let toDist = shape =>
Distributions.DistPlus.make(
DistPlus.make(
~shape,
~domain=inputs.distPlusIngredients.domain,
~unit=inputs.distPlusIngredients.unit,
~guesstimatorString=Some(inputs.distPlusIngredients.guesstimatorString),
(),
)
|> Distributions.DistPlus.T.scaleToIntegralSum(~intendedSum=1.0);
let outputs =
|> DistPlus.T.normalize;
let output =
ShapeRenderer.run({
samplingInputs: inputs.samplingInputs,
guesstimatorString: inputs.distPlusIngredients.guesstimatorString,
@ -30,8 +16,8 @@ let run =
length: inputs.recommendedLength,
},
});
let shape = outputs |> RenderTypes.ShapeRenderer.Combined.getShape;
let dist =
shape |> E.O.fmap(toDist) |> E.O.fmap(truncateIfShould(inputs, outputs));
RenderTypes.DistPlusRenderer.Outputs.make(outputs, dist);
output
|> E.R.fmap((o: RenderTypes.ShapeRenderer.Symbolic.outputs) =>
toDist(o.shape)
);
};

10
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,

37
src/distPlus/renderers/ShapeRenderer.re
View File

@ -14,33 +14,26 @@ let formatString = str => {
str |> formatMessyArray;
};
let runSymbolic = (guesstimatorString, length) => {
let str = formatString(guesstimatorString);
let runSymbolic = (inputs: RenderTypes.ShapeRenderer.Combined.inputs) => {
let str = formatString(inputs.guesstimatorString);
let graph = MathJsParser.fromString(str);
graph
|> E.R.fmap(g =>
RenderTypes.ShapeRenderer.Symbolic.make(
|> E.R.bind(_, g =>
ExpressionTree.toShape(
inputs.symbolicInputs.length,
{
sampleCount:
inputs.samplingInputs.sampleCount |> E.O.default(10000),
outputXYPoints:
inputs.samplingInputs.outputXYPoints |> E.O.default(10000),
kernelWidth: inputs.samplingInputs.kernelWidth,
},
g,
SymbolicDist.toShape(length, g),
)
|> E.R.fmap(RenderTypes.ShapeRenderer.Symbolic.make(g))
);
};
let run =
(inputs: RenderTypes.ShapeRenderer.Combined.inputs)
: RenderTypes.ShapeRenderer.Combined.outputs => {
let symbolic =
runSymbolic(inputs.guesstimatorString, inputs.symbolicInputs.length);
let sampling =
switch (symbolic) {
| Ok(_) => None
| Error(_) =>
Samples.T.fromGuesstimatorString(
~guesstimatorString=inputs.guesstimatorString,
~samplingInputs=inputs.samplingInputs,
(),
)
};
Js.log3("IS SOME?", symbolic |> E.R.toOption |> E.O.isSome, symbolic);
{symbolic: Some(symbolic), sampling};
let run = (inputs: RenderTypes.ShapeRenderer.Combined.inputs) => {
runSymbolic(inputs);
};

13
src/distPlus/renderers/samplesRenderer/Guesstimator.re
View File

@ -1,13 +0,0 @@
[@bs.deriving abstract]
type discrete = {
xs: array(float),
ys: array(float),
};
let jsToDistDiscrete = (d: discrete): DistTypes.discreteShape => {
xs: xsGet(d),
ys: ysGet(d),
};
[@bs.module "./GuesstimatorLibrary.js"]
external stringToSamples: (string, int) => array(float) = "stringToSamples";

37
src/distPlus/renderers/samplesRenderer/GuesstimatorLibrary.js
View File

@ -1,37 +0,0 @@
const _ = require("lodash");
const {
Guesstimator
} = require('@foretold/guesstimator/src');
const stringToSamples = (
text,
sampleCount,
inputs = [],
) => {
const [_error, {
parsedInput,
parsedError
}] = Guesstimator.parse({
text: "=" + text
});
const guesstimator = new Guesstimator({
parsedInput
});
const {
values,
errors
} = guesstimator.sample(
sampleCount,
inputs,
);
if (errors.length > 0) {
return []
} else {
return _.filter(values, _.isFinite)
}
};
module.exports = {
stringToSamples,
};

114
src/distPlus/renderers/samplesRenderer/Samples.re
View File

@ -1,3 +1,42 @@
module Types = {
let defaultSampleCount = 5000;
let defaultOutputXYPoints = 10000;
type inputs = {
sampleCount: option(int),
outputXYPoints: option(int),
kernelWidth: option(float),
};
type samplingStats = {
sampleCount: int,
outputXYPoints: int,
bandwidthXSuggested: float,
bandwidthUnitSuggested: float,
bandwidthXImplemented: float,
bandwidthUnitImplemented: float,
};
type outputs = {
continuousParseParams: option(samplingStats),
shape: option(DistTypes.shape),
};
let empty = {sampleCount: None, outputXYPoints: None, kernelWidth: None};
type fInputs = {
sampleCount: int,
outputXYPoints: int,
kernelWidth: option(float),
};
let toF = (i: inputs): fInputs => {
sampleCount: i.sampleCount |> E.O.default(defaultSampleCount),
outputXYPoints: i.outputXYPoints |> E.O.default(defaultOutputXYPoints),
kernelWidth: i.kernelWidth,
};
};
module JS = {
[@bs.deriving abstract]
type distJs = {
@ -21,39 +60,6 @@ module KDE = {
|> JS.samplesToContinuousPdf(_, outputXYPoints, kernelWidth)
|> JS.jsToDist;
};
// Note: This was an experiment, but it didn't actually work that well.
let inGroups = (samples, outputXYPoints, kernelWidth, ~cuttoff=0.9, ()) => {
let partitionAt =
samples
|> E.A.length
|> float_of_int
|> (e => e *. cuttoff)
|> int_of_float;
let part1XYPoints =
outputXYPoints |> float_of_int |> (e => e *. cuttoff) |> int_of_float;
let part2XYPoints = outputXYPoints - part1XYPoints |> Js.Math.max_int(30);
let part1Data =
samples |> Belt.Array.slice(_, ~offset=0, ~len=partitionAt);
let part2DataLength = (samples |> E.A.length) - partitionAt;
let part2Data =
samples
|> Belt.Array.slice(
_,
~offset=(-1) * part2DataLength,
~len=part2DataLength,
);
let part1 =
part1Data
|> JS.samplesToContinuousPdf(_, part1XYPoints, kernelWidth)
|> JS.jsToDist;
let part2 =
part2Data
|> JS.samplesToContinuousPdf(_, part2XYPoints, 3)
|> JS.jsToDist;
let opp = 1.0 -. cuttoff;
part1;
};
};
module T = {
@ -109,22 +115,24 @@ module T = {
let toShape =
(
~samples: t,
~samplingInputs: RenderTypes.ShapeRenderer.Sampling.Inputs.fInputs,
~samplingInputs: Types.fInputs,
(),
) => {
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
|> Discrete.make;
let pdf =
continuousPart |> E.A.length > 5
? {
let _suggestedXWidth = Bandwidth.nrd0(continuousPart);
// todo: This does some recalculating from the last step.
let _suggestedUnitWidth =
suggestedUnitWidth(continuousPart, samplingInputs.outputXYPoints);
let usedWidth =
@ -135,7 +143,7 @@ module T = {
samplingInputs.outputXYPoints,
usedWidth,
);
let foo: RenderTypes.ShapeRenderer.Sampling.samplingStats = {
let foo: Types.samplingStats = {
sampleCount: samplingInputs.sampleCount,
outputXYPoints: samplingInputs.outputXYPoints,
bandwidthXSuggested: _suggestedXWidth,
@ -149,16 +157,16 @@ module T = {
~outputXYPoints=samplingInputs.outputXYPoints,
formatUnitWidth(usedUnitWidth),
)
|> Distributions.Continuous.make(`Linear)
|> Continuous.make
|> (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 = {
let samplesParse: Types.outputs = {
continuousParseParams: pdf |> E.O.fmap(snd),
shape,
};
@ -167,33 +175,11 @@ module T = {
let fromSamples =
(
~samplingInputs=RenderTypes.ShapeRenderer.Sampling.Inputs.empty,
~samplingInputs=Types.empty,
samples,
) => {
let samplingInputs =
RenderTypes.ShapeRenderer.Sampling.Inputs.toF(samplingInputs);
Types.toF(samplingInputs);
toShape(~samples, ~samplingInputs, ());
};
let fromGuesstimatorString =
(
~guesstimatorString,
~samplingInputs=RenderTypes.ShapeRenderer.Sampling.Inputs.empty,
(),
) => {
let hasValidSamples =
Guesstimator.stringToSamples(guesstimatorString, 10) |> E.A.length > 0;
let _samplingInputs =
RenderTypes.ShapeRenderer.Sampling.Inputs.toF(samplingInputs);
switch (hasValidSamples) {
| false => None
| true =>
let samples =
Guesstimator.stringToSamples(
guesstimatorString,
_samplingInputs.sampleCount,
);
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,
};

377
src/distPlus/symbolic/SymbolicDist.re
View File

@ -1,102 +1,39 @@
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)];
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;
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;
let toString = t => {j|CustomContinuousShape|j};
let contType: contType = `Continuous;
};
open SymbolicTypes;
module Exponential = {
type t = exponential;
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 sample = (t: t) => Jstat.exponential##sample(t.rate);
let mean = (t: t) => Ok(Jstat.exponential##mean(t.rate));
let toString = ({rate}: t) => {j|Exponential($rate)|j};
let contType: contType = `Continuous;
};
module Cauchy = {
type t = cauchy;
let pdf = (x, t: t) => Jstat.cauchy##pdf(x, t.local, t.scale);
let cdf = (x, t: t) => Jstat.cauchy##cdf(x, t.local, t.scale);
let inv = (p, t: t) => Jstat.cauchy##inv(p, t.local, t.scale);
let sample = (t: t) => Jstat.cauchy##sample(t.local, t.scale);
let mean = (_: t) => Error("Cauchy distributions have no mean value.");
let toString = ({local, scale}: t) => {j|Cauchy($local, $scale)|j};
let contType: contType = `Continuous;
};
module Triangular = {
type t = triangular;
let pdf = (x, t: t) => Jstat.triangular##pdf(x, t.low, t.high, t.medium);
let cdf = (x, t: t) => Jstat.triangular##cdf(x, t.low, t.high, t.medium);
let inv = (p, t: t) => Jstat.triangular##inv(p, t.low, t.high, t.medium);
let sample = (t: t) => Jstat.triangular##sample(t.low, t.high, t.medium);
let mean = (t: t) => Ok(Jstat.triangular##mean(t.low, t.high, t.medium));
let toString = ({low, medium, high}: t) => {j|Triangular($low, $medium, $high)|j};
let contType: contType = `Continuous;
};
module Normal = {
type t = normal;
let pdf = (x, t: t) => Jstat.normal##pdf(x, t.mean, t.stdev);
let cdf = (x, t: t) => Jstat.normal##cdf(x, t.mean, t.stdev);
let from90PercentCI = (low, high) => {
let mean = E.A.Floats.mean([|low, high|]);
@ -105,26 +42,55 @@ module Normal = {
};
let inv = (p, t: t) => Jstat.normal##inv(p, t.mean, t.stdev);
let sample = (t: t) => Jstat.normal##sample(t.mean, t.stdev);
let mean = (t: t) => Ok(Jstat.normal##mean(t.mean, t.stdev));
let toString = ({mean, stdev}: t) => {j|Normal($mean,$stdev)|j};
let contType: contType = `Continuous;
let add = (n1: t, n2: t) => {
let mean = n1.mean +. n2.mean;
let stdev = sqrt(n1.stdev ** 2. +. n2.stdev ** 2.);
`Normal({mean, stdev});
};
let subtract = (n1: t, n2: t) => {
let mean = n1.mean -. n2.mean;
let stdev = sqrt(n1.stdev ** 2. +. n2.stdev ** 2.);
`Normal({mean, stdev});
};
// TODO: is this useful here at all? would need the integral as well ...
let pointwiseProduct = (n1: t, n2: t) => {
let mean =
(n1.mean *. n2.stdev ** 2. +. n2.mean *. n1.stdev ** 2.)
/. (n1.stdev ** 2. +. n2.stdev ** 2.);
let stdev = 1. /. (1. /. n1.stdev ** 2. +. 1. /. n2.stdev ** 2.);
`Normal({mean, stdev});
};
let operate = (operation: Operation.Algebraic.t, n1: t, n2: t) =>
switch (operation) {
| `Add => Some(add(n1, n2))
| `Subtract => Some(subtract(n1, n2))
| _ => None
};
};
module Beta = {
type t = beta;
let pdf = (x, t: t) => Jstat.beta##pdf(x, t.alpha, t.beta);
let cdf = (x, t: t) => Jstat.beta##cdf(x, t.alpha, t.beta);
let inv = (p, t: t) => Jstat.beta##inv(p, t.alpha, t.beta);
let sample = (t: t) => Jstat.beta##sample(t.alpha, t.beta);
let mean = (t: t) => Ok(Jstat.beta##mean(t.alpha, t.beta));
let toString = ({alpha, beta}: t) => {j|Beta($alpha,$beta)|j};
let contType: contType = `Continuous;
};
module Lognormal = {
type t = lognormal;
let pdf = (x, t: t) => Jstat.lognormal##pdf(x, t.mu, t.sigma);
let cdf = (x, t: t) => Jstat.lognormal##cdf(x, t.mu, t.sigma);
let inv = (p, t: t) => Jstat.lognormal##inv(p, t.mu, t.sigma);
let mean = (t: t) => Ok(Jstat.lognormal##mean(t.mu, t.sigma));
let sample = (t: t) => Jstat.lognormal##sample(t.mu, t.sigma);
let toString = ({mu, sigma}: t) => {j|Lognormal($mu,$sigma)|j};
let contType: contType = `Continuous;
let from90PercentCI = (low, high) => {
let logLow = Js.Math.log(low);
let logHigh = Js.Math.log(high);
@ -144,27 +110,51 @@ module Lognormal = {
);
`Lognormal({mu, sigma});
};
let multiply = (l1, l2) => {
let mu = l1.mu +. l2.mu;
let sigma = l1.sigma +. l2.sigma;
`Lognormal({mu, sigma});
};
let divide = (l1, l2) => {
let mu = l1.mu -. l2.mu;
let sigma = l1.sigma +. l2.sigma;
`Lognormal({mu, sigma});
};
let operate = (operation: Operation.Algebraic.t, n1: t, n2: t) =>
switch (operation) {
| `Multiply => Some(multiply(n1, n2))
| `Divide => Some(divide(n1, n2))
| _ => None
};
};
module Uniform = {
type t = uniform;
let pdf = (x, t: t) => Jstat.uniform##pdf(x, t.low, t.high);
let cdf = (x, t: t) => Jstat.uniform##cdf(x, t.low, t.high);
let inv = (p, t: t) => Jstat.uniform##inv(p, t.low, t.high);
let sample = (t: t) => Jstat.uniform##sample(t.low, t.high);
let mean = (t: t) => Ok(Jstat.uniform##mean(t.low, t.high));
let toString = ({low, high}: t) => {j|Uniform($low,$high)|j};
let contType: contType = `Continuous;
let truncate = (low, high, t: t): t => {
let newLow = max(E.O.default(neg_infinity, low), t.low);
let newHigh = min(E.O.default(infinity, high), t.high);
{low: newLow, high: newHigh};
};
};
module Float = {
type t = float;
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 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;
@ -178,20 +168,18 @@ module GenericSimple = {
| `Uniform(n) => Uniform.pdf(x, n)
| `Beta(n) => Beta.pdf(x, n)
| `Float(n) => Float.pdf(x, n)
| `ContinuousShape(n) => ContinuousShape.pdf(x, n)
};
let contType = (dist: dist): contType =>
let cdf = (x, dist) =>
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
| `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) =>
@ -204,10 +192,9 @@ module GenericSimple = {
| `Uniform(n) => Uniform.inv(x, n)
| `Beta(n) => Beta.inv(x, n)
| `Float(n) => Float.inv(x, n)
| `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)
@ -216,10 +203,22 @@ module GenericSimple = {
| `Lognormal(n) => Lognormal.sample(n)
| `Uniform(n) => Uniform.sample(n)
| `Beta(n) => Beta.sample(n)
| `Float(n) => Float.sample(n)
| `ContinuousShape(n) => ContinuousShape.sample(n);
| `Float(n) => Float.sample(n);
let toString: dist => string =
let doN = (n, fn) => {
let items = Belt.Array.make(n, 0.0);
for (x in 0 to n - 1) {
let _ = Belt.Array.set(items, x, fn());
();
};
items;
};
let sampleN = (n, dist) => {
doN(n, () => sample(dist));
};
let toString: symbolicDist => string =
fun
| `Triangular(n) => Triangular.toString(n)
| `Exponential(n) => Exponential.toString(n)
@ -228,10 +227,9 @@ module GenericSimple = {
| `Lognormal(n) => Lognormal.toString(n)
| `Uniform(n) => Uniform.toString(n)
| `Beta(n) => Beta.toString(n)
| `Float(n) => Float.toString(n)
| `ContinuousShape(n) => ContinuousShape.toString(n);
| `Float(n) => Float.toString(n);
let min: dist => float =
let min: symbolicDist => float =
fun
| `Triangular({low}) => low
| `Exponential(n) => Exponential.inv(minCdfValue, n)
@ -240,10 +238,9 @@ module GenericSimple = {
| `Lognormal(n) => Lognormal.inv(minCdfValue, n)
| `Uniform({low}) => low
| `Beta(n) => Beta.inv(minCdfValue, n)
| `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)
@ -251,148 +248,82 @@ module GenericSimple = {
| `Normal(n) => Normal.inv(maxCdfValue, n)
| `Lognormal(n) => Lognormal.inv(maxCdfValue, n)
| `Beta(n) => Beta.inv(maxCdfValue, n)
| `ContinuousShape(n) => ContinuousShape.inv(maxCdfValue, n)
| `Uniform({high}) => high
| `Float(n) => n;
let mean: symbolicDist => result(float, string) =
fun
| `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)
| `Uniform(n) => Uniform.mean(n)
| `Float(n) => Float.mean(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.
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
switch (distToFloatOp) {
| `Cdf(f) => Ok(cdf(f, s))
| `Pdf(f) => Ok(pdf(f, s))
| `Inv(f) => Ok(inv(f, s))
| `Sample => Ok(sample(s))
| `Mean => mean(s)
};
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) => {
(~xSelection: [ | `Linear | `ByWeight]=`Linear, dist: symbolicDist, n) => {
switch (xSelection, dist) {
| (`Linear, _) => E.A.Floats.range(min(dist), max(dist), sampleCount)
| (`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|]
[|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 ys = E.A.Floats.range(minCdfValue, maxCdfValue, n);
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
/* 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.
*/
let tryAnalyticalSimplification =
(
d1: symbolicDist,
d2: symbolicDist,
op: ExpressionTypes.algebraicOperation,
)
)
|> E.A.O.concatSomes
|> E.A.fmap(((x, y)) =>
({xs: [|x|], ys: [|y|]}: DistTypes.xyShape)
)
|> Distributions.Discrete.reduce((+.));
discrete;
: 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 continuousShape = (dists: t, sampleCount: int) => {
let xs =
dists
|> E.A.fmap(r =>
r
|> fst
|> GenericSimple.interpolateXs(
~xSelection=`ByWeight,
_,
sampleCount / (dists |> E.A.length),
let toShape = (sampleCount, d: symbolicDist): DistTypes.shape =>
switch (d) {
| `Float(v) =>
Discrete(
Discrete.make(~integralSumCache=Some(1.0), {xs: [|v|], ys: [|1.0|]}),
)
)
|> 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
|> (
fun
| `Simple(d) => GenericSimple.toString(d)
| `PointwiseCombination(d) =>
PointwiseAddDistributionsWeighted.toString(d)
| _ =>
let xs = interpolateXs(~xSelection=`ByWeight, d, sampleCount);
let ys = xs |> E.A.fmap(x => pdf(x, d));
Continuous(
Continuous.make(~integralSumCache=Some(1.0), {xs, ys}),
);
let toShape = n =>
fun
| `Simple(d) => GenericSimple.toShape(~xSelection=`ByWeight, d, n)
| `PointwiseCombination(d) =>
PointwiseAddDistributionsWeighted.toShape(d, n);
};
};

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 symbolicDist = [
| `Normal(normal)
| `Beta(beta)
| `Lognormal(lognormal)
| `Uniform(uniform)
| `Exponential(exponential)
| `Cauchy(cauchy)
| `Triangular(triangular)
| `Float(float) // Dirac delta at x. Practically useful only in the context of multimodals.
];
type analyticalSimplificationResult = [
| `AnalyticalSolution(symbolicDist)
| `Error(string)
| `NoSolution
];

7
src/distPlus/utility/E.re
View File

@ -145,6 +145,13 @@ module R = {
let id = e => e |> result(U.id, U.id);
let fmap = Rationale.Result.fmap;
let bind = Rationale.Result.bind;
let toExn = Belt.Result.getExn;
let merge = (a, b) =>
switch (a, b) {
| (Error(e), _) => Error(e)
| (_, Error(e)) => Error(e)
| (Ok(a), Ok(b)) => Ok((a, b))
};
let toOption = (e: Belt.Result.t('a, 'b)) =>
switch (e) {
| Ok(r) => Some(r)

8
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 = {
.

10
src/interface/FormBuilder.re
View File

@ -22,14 +22,12 @@ let propValue = (t: Prop.Value.t) => {
RenderTypes.DistPlusRenderer.make(
~distPlusIngredients=r,
~recommendedLength=10000,
~shouldTruncate=true,
~shouldDownsample=true,
(),
)
|> DistPlusRenderer.run
|> RenderTypes.DistPlusRenderer.Outputs.distplus;
|> DistPlusRenderer.run;
switch (newDistribution) {
| Some(distribution) =>
<div> <DistPlusPlot distPlus=distribution /> </div>
| Ok(distribution) => <div> <DistPlusPlot distPlus=distribution /> </div>
// <input
// readOnly=true
// className="shadow appearance-none border w-1/3 rounded py-2 px-3 text-gray-700 leading-tight focus:outline-none focus:shadow-outline"
@ -45,7 +43,7 @@ let propValue = (t: Prop.Value.t) => {
// className="w-1/3 border w-1/2 rounded py-2 px-3 text-gray-700 leading-tight focus:outline-none focus:shadow-outline bg-white">
// {"30 to infinity, 80% mass" |> ReasonReact.string}
// </div>
| None => "Something went wrong" |> ReasonReact.string
| Error(e) => e |> ReasonReact.string
};
| FloatCdf(_) => <div />
| Probability(r) =>

8
src/models/EAFunds.re
View File

@ -112,8 +112,12 @@ module Model = {
GlobalCatastrophe.makeI(MomentRe.momentNow())
|> RenderTypes.DistPlusRenderer.make(~distPlusIngredients=_, ())
|> DistPlusRenderer.run
|> RenderTypes.DistPlusRenderer.Outputs.distplus
|> E.O.bind(_, Distributions.DistPlusTime.Integral.xToY(Time(dateTime)));
|> E.R.bind(_, r =>
r
|> DistPlusTime.Integral.xToY(Time(dateTime))
|> E.O.toResult("error")
)
|> E.R.toOption;
};
let make =