First attempt at sampling

src/distPlus/distribution/Shape.re

@@ -26,18 +26,12 @@ let combineAlgebraically =
     (op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
   switch (t1, t2) {
   | (Continuous(m1), Continuous(m2)) =>
-    DistTypes.Continuous(
-      Continuous.combineAlgebraically(op, m1, m2),
-    )
+    DistTypes.Continuous(Continuous.combineAlgebraically(op, m1, m2))
   | (Discrete(m1), Discrete(m2)) =>
     DistTypes.Discrete(Discrete.combineAlgebraically(op, m1, m2))
   | (m1, m2) =>
     DistTypes.Mixed(
-      Mixed.combineAlgebraically(
-        op,
-        toMixed(m1),
-        toMixed(m2),
-      ),
+      Mixed.combineAlgebraically(op, toMixed(m1), toMixed(m2)),
     )
   };
 };
@@ -73,10 +67,6 @@ let inv = (f: float, t: t): float => {
   0.0;
 };
 
-let sample = (t: t): float => {
-  0.0;
-};
-
 module T =
   Dist({
     type t = DistTypes.shape;
@@ -199,10 +189,30 @@ module T =
       };
   });
 
+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 = (cache, t: t): float => {
+  let randomItem = Random.float(1.);
+  let bar = T.Integral.yToX(~cache, randomItem, t);
+  bar;
+};
+
+let sampleNRendered = (n, dist) => {
+  let integralCache = T.Integral.get(~cache=None, dist);
+  doN(n, () => sample(Some(integralCache), dist));
+};
+
 let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
   switch (distToFloatOp) {
   | `Pdf(f) => pdf(f, s)
   | `Inv(f) => inv(f, s)
-  | `Sample => sample(s)
+  | `Sample => sample(None, s)
   | `Mean => T.mean(s)
   };

src/distPlus/expressionTree/ExpressionTreeEvaluator.re

@@ -22,22 +22,56 @@ module AlgebraicCombination = {
     | _ => Ok(`AlgebraicCombination((operation, t1, t2)))
     };
 
-  let combineAsShapes =
-      (evaluationParams: evaluationParams, algebraicOp, t1, t2) => {
-    let renderShape = render(evaluationParams);
-    switch (renderShape(t1), renderShape(t2)) {
-    | (Ok(`RenderedDist(s1)), Ok(`RenderedDist(s2))) =>
-      Ok(
-        `RenderedDist(
-          Shape.combineAlgebraically(algebraicOp, s1, s2),
-        ),
+  let tryCombination = (n, algebraicOp, t1: node, t2: node) => {
+    let sampleN =
+      mapRenderable(Shape.sampleNRendered(n), SymbolicDist.T.sampleN(n));
+    switch (sampleN(t1), sampleN(t2)) {
+    | (Some(a), Some(b)) =>
+      Some(
+        Belt.Array.zip(a, b)
+        |> E.A.fmap(((a, b)) => Operation.Algebraic.toFn(algebraicOp, a, b)),
       )
-    | (Error(e1), _) => Error(e1)
-    | (_, Error(e2)) => Error(e2)
-    | _ => Error("Algebraic combination: rendering failed.")
+    | _ => None
     };
   };
 
+  let renderIfNotRendered = (params, t) =>
+    !renderable(t)
+      ? switch (render(params, t)) {
+        | Ok(r) => Ok(r)
+        | Error(e) => Error(e)
+        }
+      : Ok(t);
+
+  let combineAsShapes =
+      (evaluationParams: evaluationParams, algebraicOp, t1: node, t2: node) => {
+    let i1 = renderIfNotRendered(evaluationParams, t1);
+    let i2 = renderIfNotRendered(evaluationParams, t2);
+    E.R.merge(i1, i2)
+    |> E.R.bind(
+         _,
+         ((a, b)) => {
+           let samples = tryCombination(evaluationParams.sampleCount, algebraicOp, a, b);
+           let shape =
+             samples
+             |> E.O.fmap(
+                  Samples.T.fromSamples(
+                    ~samplingInputs={
+                      sampleCount: Some(evaluationParams.sampleCount),
+                      outputXYPoints: None,
+                      kernelWidth: None,
+                    },
+                  ),
+                )
+             |> E.O.bind(_, (r: RenderTypes.ShapeRenderer.Sampling.outputs) =>
+                  r.shape
+                )
+             |> E.O.toResult("No response");
+           shape |> E.R.fmap(r => `Normalize(`RenderedDist(r)));
+         },
+       );
+  };
+
   let operationToLeaf =
       (
         evaluationParams: evaluationParams,
@@ -125,11 +159,9 @@ module Truncate = {
     | (Some(lc), Some(rc), t) when lc > rc =>
       `Error("Left truncation bound must be smaller than right bound.")
     | (lc, rc, `SymbolicDist(`Uniform(u))) =>
-      // just create a new Uniform distribution
-      let nu: SymbolicTypes.uniform = u;
-      let newLow = max(E.O.default(neg_infinity, lc), nu.low);
-      let newHigh = min(E.O.default(infinity, rc), nu.high);
-      `Solution(`SymbolicDist(`Uniform({low: newLow, high: newHigh})));
+      `Solution(
+        `SymbolicDist(`Uniform(SymbolicDist.Uniform.truncate(lc, rc, u))),
+      )
     | _ => `NoSolution
     };
   };
@@ -140,9 +172,7 @@ module Truncate = {
     // of a distribution we otherwise wouldn't get at all
     switch (render(evaluationParams, t)) {
     | Ok(`RenderedDist(rs)) =>
-      let truncatedShape =
-        rs |> Shape.T.truncate(leftCutoff, rightCutoff);
-      Ok(`RenderedDist(truncatedShape));
+      Ok(`RenderedDist(Shape.T.truncate(leftCutoff, rightCutoff, rs)))
     | Error(e) => Error(e)
     | _ => Error("Could not truncate distribution.")
     };
@@ -171,8 +201,7 @@ module Truncate = {
 module Normalize = {
   let rec operationToLeaf = (evaluationParams, t: node): result(node, string) => {
     switch (t) {
-    | `RenderedDist(s) =>
-      Ok(`RenderedDist(Shape.T.normalize(s)))
+    | `RenderedDist(s) => Ok(`RenderedDist(Shape.T.normalize(s)))
     | `SymbolicDist(_) => Ok(t)
     | _ => evaluateAndRetry(evaluationParams, operationToLeaf, t)
     };

src/distPlus/expressionTree/ExpressionTypes.re

@@ -29,6 +29,17 @@ module ExpressionTree = {
 
   let evaluateAndRetry = (evaluationParams, fn, node) =>
     node |> evaluationParams.evaluateNode(evaluationParams) |> E.R.bind(_, fn(evaluationParams));
+
+  let renderable = fun
+  | `SymbolicDist(_) => true
+  | `RenderedDist(_) => true
+  | _ => false;
+
+  let mapRenderable = (renderedFn, symFn, item: node) => switch(item) {
+  | `SymbolicDist(s) => Some(symFn(s))
+  | `RenderedDist(r) => Some(renderedFn(r))
+  | _ => None
+  }
 };
 
 type simplificationResult = [

src/distPlus/symbolic/SymbolicDist.re

@@ -130,6 +130,11 @@ module Uniform = {
   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 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 = {
@@ -178,7 +183,20 @@ module T = {
     | `Lognormal(n) => Lognormal.sample(n)
     | `Uniform(n) => Uniform.sample(n)
     | `Beta(n) => Beta.sample(n)
-    | `Float(n) => Float.sample(n)
+    | `Float(n) => Float.sample(n);
+
+  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
@@ -189,7 +207,7 @@ module T = {
     | `Lognormal(n) => Lognormal.toString(n)
     | `Uniform(n) => Uniform.toString(n)
     | `Beta(n) => Beta.toString(n)
-    | `Float(n) => Float.toString(n)
+    | `Float(n) => Float.toString(n);
 
   let min: symbolicDist => float =
     fun
@@ -237,10 +255,10 @@ module T = {
     switch (xSelection, dist) {
     | (`Linear, _) => E.A.Floats.range(min(dist), max(dist), n)
     | (`ByWeight, `Uniform(n)) =>
-          // In `ByWeight mode, uniform distributions get special treatment because we need two x's
-          // on either side for proper rendering (just left and right of the discontinuities).
-            let dx = 0.00001 *. (n.high -. n.low);
-            [|n.low -. dx, n.low +. dx, n.high -. dx, n.high +. dx|];
+      // In `ByWeight mode, uniform distributions get special treatment because we need two x's
+      // on either side for proper rendering (just left and right of the discontinuities).
+      let dx = 0.00001 *. (n.high -. n.low);
+      [|n.low -. dx, n.low +. dx, n.high -. dx, n.high +. dx|];
     | (`ByWeight, _) =>
       let ys = E.A.Floats.range(minCdfValue, maxCdfValue, n);
       ys |> E.A.fmap(y => inv(y, dist));
@@ -277,14 +295,10 @@ module T = {
   let toShape = (sampleCount, d: symbolicDist): DistTypes.shape =>
     switch (d) {
     | `Float(v) =>
-      Discrete(
-        Discrete.make({xs: [|v|], ys: [|1.0|]}, Some(1.0)),
-      )
+      Discrete(Discrete.make({xs: [|v|], ys: [|1.0|]}, Some(1.0)))
     | _ =>
       let xs = interpolateXs(~xSelection=`ByWeight, d, sampleCount);
       let ys = xs |> E.A.fmap(x => pdf(x, d));
-      Continuous(
-        Continuous.make(`Linear, {xs, ys}, Some(1.0)),
-      );
+      Continuous(Continuous.make(`Linear, {xs, ys}, Some(1.0)));
     };
 };

src/distPlus/utility/E.re

@@ -145,6 +145,12 @@ module R = {
   let id = e => e |> result(U.id, U.id);
   let fmap = Rationale.Result.fmap;
   let bind = Rationale.Result.bind;
+  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)