First quick stab at mixed cdf integral

__tests__/Foo/Foo__Test.re

@@ -9,38 +9,18 @@ let shape: DistributionTypes.xyShape = {
 open Shape;
 
 describe("Shape", () =>
-  describe("XYShape", () => {
+  describe("XYShape", () =>
-    test("#ySum", () =>
+    test("#ySum", ()
-      expect(XYShape.ySum(shape)) |> toEqual(19.0)
+      =>
-    );
+        expect(XYShape.ySum(shape)) |> toEqual(19.0)
-    test("#volume", () => {
+      )
-      let shape: DistributionTypes.xyShape = {
+      // test("#both", () => {
-        xs: [|1., 5., 10.|],
+      //   let expected: DistributionTypes.xyShape = {
-        ys: [|1., 2., 2.|],
+      //     xs: [|1., 4., 8.|],
-      };
+      //     ys: [|8., 1., 1.|],
-      expect(XYShape.volume(shape)) |> toEqual(Some(7.0));
+      //   };
-    });
+      //   expect(shape |> XYShape.derivative |> XYShape.integral)
-    test("#integral", () => {
+      //   |> toEqual(shape);
-      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);
-    // });
-  })
 );

showcase/entries/Continuous.re

@@ -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));

src/components/charts/GenericDistributionChart.re

@@ -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 />

src/core/Shape.re

@@ -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 _transverse = fn =>
-    let (xs, ys) =
+    Belt.Array.reduce(_, [||], (items, (x, y)) =>
-      Belt.Array.zip(p.xs, p.ys)
+      switch (_lastElement(items)) {
-      ->Belt.Array.reduce([||], (items, (x, y)) =>
+      | Some((xLast, yLast)) =>
-          switch (_lastElement(items)) {
+        Belt.Array.concat(items, [|(x, fn(y, yLast))|])
-          | Some((_, yLast)) =>
+      | None => [|(x, y)|]
-            Js.log3(y, yLast, fn(y, yLast));
+      }
-            Belt.Array.concat(items, [|(x, fn(y, yLast))|]);
+    );
-          | None => [|(x, y)|]
+
-          }
+  let _transverseShape = (fn, p: t) => {
-        )
+    Belt.Array.zip(p.xs, p.ys)
-      |> Belt.Array.unzip;
+    |> _transverse(fn)
-    fromArrays(xs, ys);
+    |> 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) => {
+  module Range = {
-    let ranges: Belt.Result.t(array(zippedRange), string) =
+    // ((lastX, lastY), (nextX, nextY))
-      Belt.Array.zip(t.xs, t.ys) |> E.A.toRanges;
+    type zippedRange = ((float, float), (float, float));
-    ranges |> E.R.toOption |> E.O.fmap(fn);
-  };
 
-  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 rangeAreaAssumingSteps =
-    let assumeLastY = (((lastX, lastY), (nextX, _)): zippedRange) =>
+        (((lastX, lastY), (nextX, _)): zippedRange) =>
       (nextX -. lastX) *. lastY;
 
-    inRanges((inRanges: array(zippedRange)) =>
+    let rangeAreaAssumingTriangles =
-      Belt.Array.map(inRanges, assumeLastY) |> sum
+        (((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 findY = CdfLibrary.Distribution.findY;
-    let assumeLastY = (((lastX, lastY), (nextX, nextY)): zippedRange) =>
+  let findX = CdfLibrary.Distribution.findX;
-      (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 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 toPdf = XYShape.Range.derivative;
-  let toCdf = CdfLibrary.Distribution.toCdf;
+  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,
+    continuous: option(float),
-    discrete: float,
+    discrete: option(float),
+    discreteProbabilityMassFraction: float,
   };
 
   let getY = (t: DistributionTypes.mixedShape, x: float): yPdfPoint => {
-    continuous: Continuous.findY(x, t.continuous),
+    continuous: Continuous.findY(x, t.continuous) |> E.O.some,
-    discrete: Discrete.findY(x, t.discrete),
+    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 = {