Experimental: continuous/discrete multiplication
This commit is contained in:
Sebastian Kosch
parent
2ddf0c02cb
commit
35048fec0d
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@ -171,7 +171,7 @@ let make = () => {
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~onSubmit=({state}) => {None},
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~initialState={
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//guesstimatorString: "mm(normal(-10, 2), uniform(18, 25), lognormal({mean: 10, stdev: 8}), triangular(31,40,50))",
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guesstimatorString: "mm(normal(-5,1), normal(0, 1), normal(10, 1), normal(11, 1), normal(16, 1))", // , triangular(30, 40, 60)
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guesstimatorString: "normal(0, 10) * 100", // , triangular(30, 40, 60)
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domainType: "Complete",
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xPoint: "50.0",
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xPoint2: "60.0",
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@ -208,3 +208,175 @@ let combineShapesContinuousContinuous =
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{xs: outputXs, ys: outputYs};
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};
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let toDiscretePointMassesFromDiscrete = (s: DistTypes.xyShape): pointMassesWithMoments => {
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let n = s |> XYShape.T.length;
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let {xs, ys}: XYShape.T.t = s;
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let n = E.A.length(xs);
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let masses: array(float) = Belt.Array.makeUninitializedUnsafe(n); // doesn't include the fake first and last points
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let means: array(float) = Belt.Array.makeUninitializedUnsafe(n);
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let variances: array(float) = Belt.Array.makeUninitializedUnsafe(n);
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for (i in 0 to n - 1) {
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let _ =
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Belt.Array.set(
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masses,
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i,
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ys[i]
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);
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let _ =
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Belt.Array.set(
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means,
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i,
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xs[i]
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);
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let _ =
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Belt.Array.set(
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variances,
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i,
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0.0
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);
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();
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};
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{n, masses, means, variances};
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};
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let combineShapesContinuousDiscreteAdd =
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(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
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: DistTypes.xyShape => {
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let t1n = s1 |> XYShape.T.length;
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let t2n = s2 |> XYShape.T.length;
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// each x pair is added/subtracted
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let fn = Operation.Algebraic.toFn(op);
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let outXYShapes: array(array((float, float))) =
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Belt.Array.makeUninitializedUnsafe(t2n);
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for (j in 0 to t2n - 1) {
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// for each one of the discrete points
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// create a new distribution, as long as the original continuous one
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let dxyShape: array((float, float)) =
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Belt.Array.makeUninitializedUnsafe(t1n);
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for (i in 0 to t1n - 1) {
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let _ =
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Belt.Array.set(
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dxyShape,
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i,
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(fn(s1.xs[i], s2.xs[j]), s1.ys[i] *. s2.ys[j]),
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);
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();
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};
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let _ = Belt.Array.set(outXYShapes, j, dxyShape);
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();
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};
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outXYShapes
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|> E.A.fold_left(XYShape.PointwiseCombination.combineLinear((+.)), XYShape.T.empty);
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};
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let combineShapesContinuousDiscreteMultiply =
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(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
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: DistTypes.xyShape => {
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let t1n = s1 |> XYShape.T.length;
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let t2n = s2 |> XYShape.T.length;
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let t1m = toDiscretePointMassesFromTriangulars(s1);
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let t2m = toDiscretePointMassesFromDiscrete(s2);
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let combineMeansFn =
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switch (op) {
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| `Add => ((m1, m2) => m1 +. m2)
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| `Subtract => ((m1, m2) => m1 -. m2)
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| `Multiply => ((m1, m2) => m1 *. m2)
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| `Divide => ((m1, m2) => m1 /. m2)
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};
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let combineVariancesFn =
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switch (op) {
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| `Add
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| `Subtract => ((v1, v2, _, _) => v1 +. v2)
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| `Multiply
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| `Divide => (
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(v1, v2, m1, m2) => v1 *. m2 ** 2.
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)
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};
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let outputMinX: ref(float) = ref(infinity);
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let outputMaxX: ref(float) = ref(neg_infinity);
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let masses: array(float) =
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Belt.Array.makeUninitializedUnsafe(t1m.n * t2m.n);
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let means: array(float) =
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Belt.Array.makeUninitializedUnsafe(t1m.n * t2m.n);
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let variances: array(float) =
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Belt.Array.makeUninitializedUnsafe(t1m.n * t2m.n);
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// then convolve the two sets of pointMassesWithMoments
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for (i in 0 to t1m.n - 1) {
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for (j in 0 to t2m.n - 1) {
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let k = i * t2m.n + j;
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let _ = Belt.Array.set(masses, k, t1m.masses[i] *. t2m.masses[j]);
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let mean = combineMeansFn(t1m.means[i], t2m.means[j]);
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let variance =
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combineVariancesFn(
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t1m.variances[i],
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t2m.variances[j],
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t1m.means[i],
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t2m.means[j],
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);
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let _ = Belt.Array.set(means, k, mean);
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let _ = Belt.Array.set(variances, k, variance);
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// update bounds
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let minX = mean -. 2. *. sqrt(variance) *. 1.644854;
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let maxX = mean +. 2. *. sqrt(variance) *. 1.644854;
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if (minX < outputMinX^) {
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outputMinX := minX;
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};
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if (maxX > outputMaxX^) {
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outputMaxX := maxX;
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};
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};
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};
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// we now want to create a set of target points. For now, let's just evenly distribute 200 points between
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// between the outputMinX and outputMaxX
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let nOut = 300;
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let outputXs: array(float) = E.A.Floats.range(outputMinX^, outputMaxX^, nOut);
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let outputYs: array(float) = Belt.Array.make(nOut, 0.0);
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// now, for each of the outputYs, accumulate from a Gaussian kernel over each input point.
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for (j in 0 to E.A.length(masses) - 1) { // go through all of the result points
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let _ = if (variances[j] > 0. && masses[j] > 0.) {
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for (i in 0 to E.A.length(outputXs) - 1) { // go through all of the target points
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let dx = outputXs[i] -. means[j];
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let contribution = masses[j] *. exp(-. (dx ** 2.) /. (2. *. variances[j])) /. (sqrt(2. *. 3.14159276 *. variances[j]));
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let _ = Belt.Array.set(outputYs, i, outputYs[i] +. contribution);
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();
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};
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();
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};
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();
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};
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{xs: outputXs, ys: outputYs};
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};
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let combineShapesContinuousDiscrete =
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(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
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: DistTypes.xyShape => {
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switch (op) {
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| `Add
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| `Subtract => combineShapesContinuousDiscreteAdd(op, s1, s2);
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| `Multiply
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| `Divide => combineShapesContinuousDiscreteMultiply(op, s1, s2);
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};
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};
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@ -235,7 +235,7 @@ module Continuous = {
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t
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|> shapeMap(
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XYShape.XsConversion.proportionByProbabilityMass(
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length,
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length,
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integral(~cache, t).xyShape,
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),
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);
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@ -280,60 +280,37 @@ module Continuous = {
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each discrete data point, and then adds them all together. */
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let combineAlgebraicallyWithDiscrete =
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(
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~downsample=false,
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op: ExpressionTypes.algebraicOperation,
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t1: t,
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t2: DistTypes.discreteShape,
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) => {
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let t1s = t1 |> getShape;
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let t2s = t2.xyShape; // would like to use Discrete.getShape here, but current file structure doesn't allow for that
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let t1n = t1s |> XYShape.T.length;
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let t2n = t2s |> XYShape.T.length;
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let fn = Operation.Algebraic.toFn(op);
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let outXYShapes: array(array((float, float))) =
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Belt.Array.makeUninitializedUnsafe(t2n);
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for (j in 0 to t2n - 1) {
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// for each one of the discrete points
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// create a new distribution, as long as the original continuous one
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let dxyShape: array((float, float)) =
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Belt.Array.makeUninitializedUnsafe(t1n);
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for (i in 0 to t1n - 1) {
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let _ =
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Belt.Array.set(
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dxyShape,
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i,
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(fn(t1s.xs[i], t2s.xs[j]), t1s.ys[i] *. t2s.ys[j]),
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);
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();
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};
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let _ = Belt.Array.set(outXYShapes, j, dxyShape);
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();
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let s1 = t1 |> getShape;
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let s2 = t2.xyShape;
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let t1n = s1 |> XYShape.T.length;
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let t2n = s2 |> XYShape.T.length;
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if (t1n == 0 || t2n == 0) {
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empty;
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} else {
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let combinedShape =
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AlgebraicShapeCombination.combineShapesContinuousDiscrete(
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op,
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s1,
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s2,
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);
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let combinedIntegralSum =
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Common.combineIntegralSums(
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(a, b) => Some(a *. b),
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t1.knownIntegralSum,
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t2.knownIntegralSum,
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);
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// return a new Continuous distribution
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make(`Linear, combinedShape, combinedIntegralSum);
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};
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let combinedIntegralSum =
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Common.combineIntegralSums(
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(a, b) => Some(a *. b),
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t1.knownIntegralSum,
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t2.knownIntegralSum,
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);
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outXYShapes
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|> E.A.fmap(s => {
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let xyShape = XYShape.T.fromZippedArray(s);
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make(`Linear, xyShape, None);
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})
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|> reduce((+.))
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|> updateKnownIntegralSum(combinedIntegralSum);
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};
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let combineAlgebraically =
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(
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~downsample=false,
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op: ExpressionTypes.algebraicOperation,
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t1: t,
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t2: t,
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@ -475,6 +452,7 @@ module Discrete = {
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type integral = DistTypes.continuousShape;
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let integral = (~cache, t) =>
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if (t |> getShape |> XYShape.T.length > 0) {
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Js.log2("Integrating discrete shape", XYShape.T.accumulateYs((+.), getShape(t)));
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switch (cache) {
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| Some(c) => c
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| None =>
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@ -849,7 +827,6 @@ module Mixed = {
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let combineAlgebraically =
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(
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~downsample=false,
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op: ExpressionTypes.algebraicOperation,
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t1: t,
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t2: t,
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@ -861,33 +838,31 @@ module Mixed = {
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// An alternative (to be explored in the future) may be to first perform the full convolution and then to downsample the result;
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// to use non-uniform fast Fourier transforms (for addition only), add web workers or gpu.js, etc. ...
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let downsampleIfTooLarge = (t: t) => {
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let sqtl = sqrt(float_of_int(totalLength(t)));
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sqtl > 10. && downsample ? T.downsample(int_of_float(sqtl), t) : t;
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};
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// we have to figure out where to downsample, and how to effectively
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//let downsampleIfTooLarge = (t: t) => {
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// let sqtl = sqrt(float_of_int(totalLength(t)));
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// sqtl > 10 ? T.downsample(int_of_float(sqtl), t) : t;
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//};
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let t1d = downsampleIfTooLarge(t1);
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let t2d = downsampleIfTooLarge(t2);
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let t1d = t1; //downsampleIfTooLarge(t1);
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let t2d = t2; //downsampleIfTooLarge(t2);
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// continuous (*) continuous => continuous, but also
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// discrete (*) continuous => continuous (and vice versa). We have to take care of all combos and then combine them:
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let ccConvResult =
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Continuous.combineAlgebraically(
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~downsample=false,
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op,
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t1d.continuous,
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t2d.continuous,
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);
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let dcConvResult =
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Continuous.combineAlgebraicallyWithDiscrete(
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~downsample=false,
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op,
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t2d.continuous,
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t1d.discrete,
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);
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let cdConvResult =
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Continuous.combineAlgebraicallyWithDiscrete(
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~downsample=false,
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op,
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t1d.continuous,
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t2d.discrete,
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@ -931,14 +906,13 @@ module Shape = {
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switch (t1, t2) {
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| (Continuous(m1), Continuous(m2)) =>
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DistTypes.Continuous(
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Continuous.combineAlgebraically(~downsample=true, op, m1, m2),
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Continuous.combineAlgebraically(op, m1, m2),
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)
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| (Discrete(m1), Discrete(m2)) =>
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DistTypes.Discrete(Discrete.combineAlgebraically(op, m1, m2))
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| (m1, m2) =>
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DistTypes.Mixed(
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Mixed.combineAlgebraically(
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~downsample=true,
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op,
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toMixed(m1),
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toMixed(m2),
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