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First quick stab at mixed cdf integral

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This commit is contained in:
Ozzie Gooen 2020-02-18 19:01:11 +00:00
parent db023c0bef
commit 4d1cc7094f
4 changed files with 168 additions and 126 deletions
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48
__tests__/Foo/Foo__Test.re
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@ -9,38 +9,18 @@ let shape: DistributionTypes.xyShape = {
open Shape;
describe("Shape", () =>
describe("XYShape", () => {
test("#ySum", () =>
expect(XYShape.ySum(shape)) |> toEqual(19.0)
);
test("#volume", () => {
let shape: DistributionTypes.xyShape = {
xs: [|1., 5., 10.|],
ys: [|1., 2., 2.|],
};
expect(XYShape.volume(shape)) |> toEqual(Some(7.0));
});
test("#integral", () => {
let expected: DistributionTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|8., 17., 19.|],
};
expect(XYShape.volum2(shape)) |> toEqual(Some(expected));
});
test("#derivative", () => {
let expected: DistributionTypes.xyShape = {
xs: [|1., 4., 8.|],
ys: [|8., 1., 1.|],
};
expect(XYShape.derivative(shape)) |> toEqual(expected);
});
// test("#both", () => {
// let expected: DistributionTypes.xyShape = {
// xs: [|1., 4., 8.|],
// ys: [|8., 1., 1.|],
// };
// expect(shape |> XYShape.derivative |> XYShape.integral)
// |> toEqual(shape);
// });
})
describe("XYShape", () =>
test("#ySum", ()
=>
expect(XYShape.ySum(shape)) |> toEqual(19.0)
)
// test("#both", () => {
// let expected: DistributionTypes.xyShape = {
// xs: [|1., 4., 8.|],
// ys: [|8., 1., 1.|],
// };
// expect(shape |> XYShape.derivative |> XYShape.integral)
// |> toEqual(shape);
// });
)
);

20
showcase/entries/Continuous.re
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@ -8,7 +8,9 @@ let data: DistributionTypes.xyShape = {
let mixedDist =
GenericDistribution.make(
~generationSource=
GuesstimatorString("mm(uniform(10,12), normal(5,1), [.5,.5])"),
GuesstimatorString(
"mm(floor(uniform(40, 50)), normal(50,10), [.5,.5])",
),
~probabilityType=Pdf,
~domain=Complete,
~unit=Unspecified,
@ -42,14 +44,14 @@ let distributions = () =>
<h2> {"Basic Mixed Distribution" |> ReasonReact.string} </h2>
<GenericDistributionChart dist=mixedDist />
</div>
<div>
<h2> {"Time Distribution" |> ReasonReact.string} </h2>
<GenericDistributionChart dist=timeDist />
</div>
<div>
<h2> {"Domain Limited Distribution" |> ReasonReact.string} </h2>
<GenericDistributionChart dist=domainLimitedDist />
</div>
</div>;
// <div>
// <h2> {"Time Distribution" |> ReasonReact.string} </h2>
// <GenericDistributionChart dist=timeDist />
// </div>
// <div>
// <h2> {"Domain Limited Distribution" |> ReasonReact.string} </h2>
// <GenericDistributionChart dist=domainLimitedDist />
// </div>
let entry = EntryTypes.(entry(~title="Pdf", ~render=distributions));

35
src/components/charts/GenericDistributionChart.re
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@ -35,7 +35,11 @@ module Continuous = {
|> ReasonReact.string}
</th>
<th className="px-4 py-2 border ">
{Shape.Continuous.findY(x, Shape.XYShape.integral(data))
{Shape.Continuous.findY(
x,
Shape.XYShape.Range.integrateWithTriangles(data)
|> E.O.toExt(""),
)
|> E.Float.with2DigitsPrecision
|> ReasonReact.string}
</th>
@ -62,7 +66,34 @@ let make = (~dist) => {
}) =>
<div>
<Continuous data=n />
<Continuous data={n |> Shape.XYShape.integral} />
<Continuous
data={
n
|> Shape.XYShape.Range.integrateWithTriangles
|> E.O.toExt("")
|> Shape.XYShape.scaleCdfTo
}
/>
<Continuous
data={
n
|> Shape.XYShape.Range.integrateWithTriangles
|> E.O.toExt("")
|> Shape.XYShape.Range.derivative
|> E.O.toExt("")
}
/>
<Continuous
data={
n
|> Shape.XYShape.Range.integrateWithTriangles
|> E.O.toExt("")
|> Shape.XYShape.Range.derivative
|> E.O.toExt("")
|> Shape.XYShape.Range.integrateWithTriangles
|> E.O.toExt("")
}
/>
{d |> Shape.Discrete.scaleYToTotal(f) |> Shape.Discrete.render}
</div>
| _ => <div />

191
src/core/Shape.re
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@ -19,6 +19,14 @@ module XYShape = {
let fmap = (t: t, y): t => {xs: t.xs, ys: t.ys |> E.A.fmap(y)};
let scaleCdfTo = (~scaleTo=1., t: t) =>
switch (_lastElement(t.ys)) {
| Some(n) =>
let scaleBy = scaleTo /. n;
fmap(t, r => r *. scaleBy);
| None => t
};
let yFold = (fn, t: t) => {
E.A.fold_left(fn, 0., t.ys);
};
@ -28,92 +36,86 @@ module XYShape = {
let fromArray = ((xs, ys)): t => {xs, ys};
let fromArrays = (xs, ys): t => {xs, ys};
let transverse = (fn, p: t) => {
let (xs, ys) =
Belt.Array.zip(p.xs, p.ys)
->Belt.Array.reduce([||], (items, (x, y)) =>
switch (_lastElement(items)) {
| Some((_, yLast)) =>
Js.log3(y, yLast, fn(y, yLast));
Belt.Array.concat(items, [|(x, fn(y, yLast))|]);
| None => [|(x, y)|]
}
)
|> Belt.Array.unzip;
fromArrays(xs, ys);
let _transverse = fn =>
Belt.Array.reduce(_, [||], (items, (x, y)) =>
switch (_lastElement(items)) {
| Some((xLast, yLast)) =>
Belt.Array.concat(items, [|(x, fn(y, yLast))|])
| None => [|(x, y)|]
}
);
let _transverseShape = (fn, p: t) => {
Belt.Array.zip(p.xs, p.ys)
|> _transverse(fn)
|> Belt.Array.unzip
|> fromArray;
};
type zippedRange = ((float, float), (float, float));
let accumulateYs = _transverseShape((aCurrent, aLast) => aCurrent +. aLast);
let subtractYs = _transverseShape((aCurrent, aLast) => aCurrent -. aLast);
let inRanges = (fn, t: t) => {
let ranges: Belt.Result.t(array(zippedRange), string) =
Belt.Array.zip(t.xs, t.ys) |> E.A.toRanges;
ranges |> E.R.toOption |> E.O.fmap(fn);
};
module Range = {
// ((lastX, lastY), (nextX, nextY))
type zippedRange = ((float, float), (float, float));
let sum = Belt.Array.reduce(_, 0., (a, b) => a +. b);
let floatSum = Belt.Array.reduce(_, 0., (a, b) => a +. b);
let toT = r => r |> Belt.Array.unzip |> fromArray;
let nextX = ((_, (nextX, _)): zippedRange) => nextX;
let volume = {
let assumeLastY = (((lastX, lastY), (nextX, _)): zippedRange) =>
let rangeAreaAssumingSteps =
(((lastX, lastY), (nextX, _)): zippedRange) =>
(nextX -. lastX) *. lastY;
inRanges((inRanges: array(zippedRange)) =>
Belt.Array.map(inRanges, assumeLastY) |> sum
);
let rangeAreaAssumingTriangles =
(((lastX, lastY), (nextX, nextY)): zippedRange) =>
(nextX -. lastX) *. (lastY +. nextY) /. 2.;
let delta_y_over_delta_x =
(((lastX, lastY), (nextX, nextY)): zippedRange) =>
(nextY -. lastY) /. (nextX -. lastX);
let inRanges = (mapper, reducer, t: t) => {
Belt.Array.zip(t.xs, t.ys)
|> E.A.toRanges
|> E.R.toOption
|> E.O.fmap(r => r |> Belt.Array.map(_, mapper) |> reducer);
};
let mapYsBasedOnRanges = fn => inRanges(r => (nextX(r), fn(r)), toT);
let toStepFn = z => mapYsBasedOnRanges(rangeAreaAssumingSteps, z);
let integrateWithSteps = z =>
mapYsBasedOnRanges(rangeAreaAssumingSteps, z) |> E.O.fmap(accumulateYs);
let integrateWithTriangles = z =>
mapYsBasedOnRanges(rangeAreaAssumingTriangles, z)
|> E.O.fmap(accumulateYs);
let derivative = mapYsBasedOnRanges(delta_y_over_delta_x);
};
let volumeTriangle = {
let assumeLastY = (((lastX, lastY), (nextX, nextY)): zippedRange) =>
(nextX -. lastX) *. (lastY -. nextY) /. 2.;
inRanges((inRanges: array(zippedRange)) =>
Belt.Array.map(inRanges, assumeLastY) |> sum
);
};
let volum2 = {
let assumeLastY = (((lastX, lastY), (nextX, _)): zippedRange) => (
nextX,
(nextX -. lastX) *. lastY,
);
inRanges((inRanges: array(zippedRange)) =>
Belt.Array.map(inRanges, assumeLastY) |> Belt.Array.unzip |> fromArray
);
};
let diff = {
let assumeLastY = (((lastX, lastY), (nextX, _)): zippedRange) => (
nextX,
(lastY -. lastY) /. (nextX -. lastX),
);
inRanges((inRanges: array(zippedRange)) =>
Belt.Array.map(inRanges, assumeLastY) |> Belt.Array.unzip |> fromArray
);
};
let getY = (t: t, x: float) => x;
let findY = (t: t, x: float) => x;
let integral = transverse((aCurrent, aLast) => aCurrent +. aLast);
let derivative = transverse((aCurrent, aLast) => aCurrent -. aLast);
// let massWithin = (t: t, left: pointInRange, right: pointInRange) => {
// switch (left, right) {
// | (Unbounded, Unbounded) => t |> ySum
// | (Unbounded, X(f)) => t |> integral |> getY(t, 3.0)
// | (X(f), Unbounded) => ySum(t) -. getY(integral(t), f)
// | (X(l), X(r)) => getY(integral(t), r) -. getY(integral(t), l)
// };
// };
let findY = CdfLibrary.Distribution.findY;
let findX = CdfLibrary.Distribution.findX;
};
// let massWithin = (t: t, left: pointInRange, right: pointInRange) => {
// switch (left, right) {
// | (Unbounded, Unbounded) => t |> ySum
// | (Unbounded, X(f)) => t |> integral |> getY(t, 3.0)
// | (X(f), Unbounded) => ySum(t) -. getY(integral(t), f)
// | (X(l), X(r)) => getY(integral(t), r) -. getY(integral(t), l)
// };
// };
module Continuous = {
let fromArrays = XYShape.fromArrays;
let toJs = XYShape.toJs;
let toPdf = CdfLibrary.Distribution.toPdf;
let toCdf = CdfLibrary.Distribution.toCdf;
let toPdf = XYShape.Range.derivative;
let toCdf = XYShape.Range.integrateWithTriangles;
let findX = CdfLibrary.Distribution.findX;
let findY = CdfLibrary.Distribution.findY;
let findIntegralY = (f, r) => r |> toCdf |> E.O.fmap(findY(f));
};
module Discrete = {
@ -145,6 +147,18 @@ module Discrete = {
| Some((_, y)) => y
| None => 0.
};
let integrate = XYShape.accumulateYs;
let derivative = XYShape.subtractYs;
let findIntegralY = (f, t: t) =>
t
|> XYShape.Range.toStepFn
|> E.O.fmap(XYShape.accumulateYs)
|> E.O.fmap(CdfLibrary.Distribution.findY(f));
let findX = (f, t: t) =>
t |> XYShape.Range.toStepFn |> E.O.fmap(CdfLibrary.Distribution.findX(f));
};
module Mixed = {
@ -154,14 +168,36 @@ module Mixed = {
discreteProbabilityMassFraction,
};
let mixedMultiply =
(
t: DistributionTypes.mixedShape,
continuousComponent,
discreteComponent,
) => {
let diffFn = t.discreteProbabilityMassFraction;
continuousComponent *. (1.0 -. diffFn) +. discreteComponent *. diffFn;
};
type yPdfPoint = {
continuous: float,
discrete: float,
continuous: option(float),
discrete: option(float),
discreteProbabilityMassFraction: float,
};
let getY = (t: DistributionTypes.mixedShape, x: float): yPdfPoint => {
continuous: Continuous.findY(x, t.continuous),
discrete: Discrete.findY(x, t.discrete),
continuous: Continuous.findY(x, t.continuous) |> E.O.some,
discrete: Discrete.findY(x, t.discrete) |> E.O.some,
discreteProbabilityMassFraction: t.discreteProbabilityMassFraction,
};
let getYIntegral =
(t: DistributionTypes.mixedShape, x: float): option(float) => {
let c = t.continuous |> Continuous.findIntegralY(x);
let d = Discrete.findIntegralY(x, t.discrete);
switch (c, d) {
| (Some(c), Some(d)) => Some(mixedMultiply(t, c, d))
| _ => None
};
};
};
@ -175,13 +211,6 @@ module Any = {
| Continuous(continuousShape) =>
`continuous(Continuous.findY(x, continuousShape))
};
let massInRange = (t: t, left: pointInRange, right: pointInRange) =>
switch (t) {
| Mixed(m) => 3.0
| Discrete(discreteShape) => 2.0
| Continuous(continuousShape) => 3.0
};
};
module DomainMixed = {