Pulled out XYShape to be more separate
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@ -1,7 +1,7 @@
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import {runAll} from '../rescript/ProgramEvaluator.gen';
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import type { Inputs_SamplingInputs_t as SamplingInputs, exportEnv, exportType, exportDistribution} from '../rescript/ProgramEvaluator.gen';
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export type { SamplingInputs, exportEnv, exportDistribution }
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export type {t as DistPlus} from '../rescript/pointSetDist/DistPlus.gen';
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export type {t as DistPlus} from '../rescript/OldInterpreter/DistPlus.gen';
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export let defaultSamplingInputs : SamplingInputs = {
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sampleCount : 10000,
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@ -0,0 +1,92 @@
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type genericDist =
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| PointSet(PointSetTypes.pointSetDist)
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| SampleSet(array<float>)
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| Symbolic(SymbolicDistTypes.symbolicDist)
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type error =
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| NotYetImplemented
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| Unreachable
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| DistributionVerticalShiftIsInvalid
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| Other(string)
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module Operation = {
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type direction =
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| Algebraic
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| Pointwise
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type arithmeticOperation = [
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| #Add
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| #Multiply
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| #Subtract
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| #Divide
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| #Exponentiate
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| #Logarithm
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]
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let arithmeticToFn = (arithmetic: arithmeticOperation) =>
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switch arithmetic {
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| #Add => \"+."
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| #Multiply => \"*."
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| #Subtract => \"-."
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| #Exponentiate => \"**"
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| #Divide => \"/."
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| #Logarithm => (a, b) => log(a) /. log(b)
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}
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type toFloat = [
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| #Cdf(float)
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| #Inv(float)
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| #Pdf(float)
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| #Mean
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| #Sample
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]
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}
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module DistributionOperation = {
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type toDist =
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| Normalize
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| ToPointSet
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| ToSampleSet(int)
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| Truncate(option<float>, option<float>)
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| Inspect
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type toFloatArray = Sample(int)
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type fromDist =
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| ToFloat(Operation.toFloat)
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| ToDist(toDist)
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| ToDistCombination(Operation.direction, Operation.arithmeticOperation, [#Dist(genericDist) | #Float(float)])
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| ToString
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type singleParamaterFunction =
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| FromDist(fromDist)
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| FromFloat(fromDist)
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type genericFunctionCallInfo =
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| FromDist(fromDist, genericDist)
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| FromFloat(fromDist, float)
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| Mixture(array<(genericDist, float)>)
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let distCallToString = (distFunction: fromDist): string =>
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switch distFunction {
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| ToFloat(#Cdf(r)) => `cdf(${E.Float.toFixed(r)})`
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| ToFloat(#Inv(r)) => `inv(${E.Float.toFixed(r)})`
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| ToFloat(#Mean) => `mean`
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| ToFloat(#Pdf(r)) => `pdf(${E.Float.toFixed(r)})`
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| ToFloat(#Sample) => `sample`
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| ToDist(Normalize) => `normalize`
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| ToDist(ToPointSet) => `toPointSet`
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| ToDist(ToSampleSet(r)) => `toSampleSet(${E.I.toString(r)})`
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| ToDist(Truncate(_, _)) => `truncate`
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| ToDist(Inspect) => `inspect`
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| ToString => `toString`
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| ToDistCombination(Algebraic, _, _) => `algebraic`
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| ToDistCombination(Pointwise, _, _) => `pointwise`
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}
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let toString = (d: genericFunctionCallInfo): string =>
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switch d {
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| FromDist(f, _) | FromFloat(f, _) => distCallToString(f)
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| Mixture(_) => `mixture`
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}
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}
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@ -118,13 +118,14 @@ let combineShapesContinuousContinuous = (
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| #Logarithm => (m1, m2) => log(m1) /. log(m2)
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} // note: here, mInv2 = mean(1 / t2) ~= 1 / mean(t2)
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// TODO: I don't know what the variances are for exponentatiation
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// TODO: I don't know what the variances are for exponentatiation or logarithms
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// converts the variances and means of the two inputs into the variance of the output
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let combineVariancesFn = switch op {
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| #Add => (v1, v2, _, _) => v1 +. v2
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| #Subtract => (v1, v2, _, _) => v1 +. v2
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| #Multiply => (v1, v2, m1, m2) => v1 *. v2 +. v1 *. m2 ** 2. +. v2 *. m1 ** 2.
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| #Exponentiate => (v1, v2, m1, m2) => v1 *. v2 +. v1 *. m2 ** 2. +. v2 *. m1 ** 2.
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| #Logarithm => (v1, v2, m1, m2) => v1 *. v2 +. v1 *. m2 ** 2. +. v2 *. m1 ** 2.
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| #Divide => (v1, vInv2, m1, mInv2) => v1 *. vInv2 +. v1 *. mInv2 ** 2. +. vInv2 *. m1 ** 2.
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}
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@ -1,6 +1,47 @@
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open Distributions
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type t = PointSetTypes.continuousShape
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module Analysis = {
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let integrate = (
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~indefiniteIntegralStepwise=(p, h1) => h1 *. p,
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~indefiniteIntegralLinear=(p, a, b) => a *. p +. b *. p ** 2.0 /. 2.0,
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t: t,
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): float => {
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let xs = t.xyShape.xs
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let ys = t.xyShape.ys
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E.A.reducei(xs, 0.0, (acc, _x, i) => {
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let areaUnderIntegral = // TODO Take this switch statement out of the loop body
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switch (t.interpolation, i) {
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| (_, 0) => 0.0
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| (#Stepwise, _) =>
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indefiniteIntegralStepwise(xs[i], ys[i - 1]) -.
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indefiniteIntegralStepwise(xs[i - 1], ys[i - 1])
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| (#Linear, _) =>
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let x1 = xs[i - 1]
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let x2 = xs[i]
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if x1 == x2 {
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0.0
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} else {
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let h1 = ys[i - 1]
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let h2 = ys[i]
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let b = (h1 -. h2) /. (x1 -. x2)
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let a = h1 -. b *. x1
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indefiniteIntegralLinear(x2, a, b) -. indefiniteIntegralLinear(x1, a, b)
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}
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}
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acc +. areaUnderIntegral
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})
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}
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let getMeanOfSquares = (t: t) => {
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let indefiniteIntegralLinear = (p, a, b) => a *. p ** 3.0 /. 3.0 +. b *. p ** 4.0 /. 4.0
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let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 3.0 /. 3.0
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integrate(~indefiniteIntegralStepwise, ~indefiniteIntegralLinear, t)
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}
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}
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let getShape = (t: t) => t.xyShape
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let interpolation = (t: t) => t.interpolation
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let make = (~interpolation=#Linear, ~integralSumCache=None, ~integralCache=None, xyShape): t => {
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@ -194,7 +235,7 @@ module T = Dist({
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let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 2.0 /. 2.0
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let indefiniteIntegralLinear = (p, a, b) => a *. p ** 2.0 /. 2.0 +. b *. p ** 3.0 /. 3.0
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XYShape.Analysis.integrateContinuousShape(
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Analysis.integrate(
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~indefiniteIntegralStepwise,
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~indefiniteIntegralLinear,
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t,
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@ -204,7 +245,7 @@ module T = Dist({
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XYShape.Analysis.getVarianceDangerously(
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t,
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mean,
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XYShape.Analysis.getMeanOfSquaresContinuousShape,
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Analysis.getMeanOfSquares,
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)
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})
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@ -209,8 +209,9 @@ module T = Dist({
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let s = getShape(t)
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E.A.reducei(s.xs, 0.0, (acc, x, i) => acc +. x *. s.ys[i])
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}
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let variance = (t: t): float => {
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let getMeanOfSquares = t => t |> shapeMap(XYShape.Analysis.squareXYShape) |> mean
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let getMeanOfSquares = t => t |> shapeMap(XYShape.T.square) |> mean
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XYShape.Analysis.getVarianceDangerously(t, mean, getMeanOfSquares)
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}
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})
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@ -213,8 +213,8 @@ module T = Dist({
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let getMeanOfSquares = ({discrete, continuous}: t) => {
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let discreteMean =
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discrete |> Discrete.shapeMap(XYShape.Analysis.squareXYShape) |> Discrete.T.mean
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let continuousMean = continuous |> XYShape.Analysis.getMeanOfSquaresContinuousShape
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discrete |> Discrete.shapeMap(XYShape.T.square) |> Discrete.T.mean
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let continuousMean = continuous |> Continuous.Analysis.getMeanOfSquares
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(discreteMean *. discreteIntegralSum +. continuousMean *. continuousIntegralSum) /.
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totalIntegralSum
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}
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@ -14,21 +14,10 @@ type distributionType = [
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| #CDF
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]
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type xyShape = {
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xs: array<float>,
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ys: array<float>,
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}
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type interpolationStrategy = [
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| #Stepwise
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| #Linear
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]
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type extrapolationStrategy = [
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| #UseZero
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| #UseOutermostPoints
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]
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type interpolator = (xyShape, int, float) => float
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type xyShape = XYShape.xyShape;
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type interpolationStrategy = XYShape.interpolationStrategy;
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type extrapolationStrategy = XYShape.extrapolationStrategy;
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type interpolator = XYShape.extrapolationStrategy;
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type rec continuousShape = {
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xyShape: xyShape,
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@ -1,4 +1,18 @@
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open PointSetTypes
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type xyShape = {
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xs: array<float>,
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ys: array<float>,
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}
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type interpolationStrategy = [
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| #Stepwise
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| #Linear
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]
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type extrapolationStrategy = [
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| #UseZero
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| #UseOutermostPoints
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]
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type interpolator = (xyShape, int, float) => float
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let interpolate = (xMin: float, xMax: float, yMin: float, yMax: float, xIntended: float): float => {
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let minProportion = (xMax -. xIntended) /. (xMax -. xMin)
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let xTotalRange = (t: t) => maxX(t) -. minX(t)
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let mapX = (fn, t: t): t => {xs: E.A.fmap(fn, t.xs), ys: t.ys}
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let mapY = (fn, t: t): t => {xs: t.xs, ys: E.A.fmap(fn, t.ys)}
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let square = mapX(x => x ** 2.0)
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let zip = ({xs, ys}: t) => Belt.Array.zip(xs, ys)
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let fromArray = ((xs, ys)): t => {xs: xs, ys: ys}
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let fromArrays = (xs, ys): t => {xs: xs, ys: ys}
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@ -126,8 +141,8 @@ module XtoY = {
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/* Returns a between-points-interpolating function that can be used with PointwiseCombination.combine.
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Interpolation can either be stepwise (using the value on the left) or linear. Extrapolation can be `UseZero or `UseOutermostPoints. */
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let continuousInterpolator = (
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interpolation: PointSetTypes.interpolationStrategy,
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extrapolation: PointSetTypes.extrapolationStrategy,
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interpolation: interpolationStrategy,
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extrapolation: extrapolationStrategy,
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): interpolator =>
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switch (interpolation, extrapolation) {
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| (#Linear, #UseZero) =>
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|> E.O.fmap(Pairs.y)
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module Analysis = {
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let integrateContinuousShape = (
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~indefiniteIntegralStepwise=(p, h1) => h1 *. p,
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~indefiniteIntegralLinear=(p, a, b) => a *. p +. b *. p ** 2.0 /. 2.0,
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t: PointSetTypes.continuousShape,
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): float => {
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let xs = t.xyShape.xs
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let ys = t.xyShape.ys
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E.A.reducei(xs, 0.0, (acc, _x, i) => {
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let areaUnderIntegral = // TODO Take this switch statement out of the loop body
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switch (t.interpolation, i) {
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| (_, 0) => 0.0
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| (#Stepwise, _) =>
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indefiniteIntegralStepwise(xs[i], ys[i - 1]) -.
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indefiniteIntegralStepwise(xs[i - 1], ys[i - 1])
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| (#Linear, _) =>
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let x1 = xs[i - 1]
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let x2 = xs[i]
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if x1 == x2 {
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0.0
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} else {
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let h1 = ys[i - 1]
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let h2 = ys[i]
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let b = (h1 -. h2) /. (x1 -. x2)
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let a = h1 -. b *. x1
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indefiniteIntegralLinear(x2, a, b) -. indefiniteIntegralLinear(x1, a, b)
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}
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}
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acc +. areaUnderIntegral
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})
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}
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let getMeanOfSquaresContinuousShape = (t: PointSetTypes.continuousShape) => {
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let indefiniteIntegralLinear = (p, a, b) => a *. p ** 3.0 /. 3.0 +. b *. p ** 4.0 /. 4.0
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let indefiniteIntegralStepwise = (p, h1) => h1 *. p ** 3.0 /. 3.0
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integrateContinuousShape(~indefiniteIntegralStepwise, ~indefiniteIntegralLinear, t)
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}
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let getVarianceDangerously = (t: 't, mean: 't => float, getMeanOfSquares: 't => float): float => {
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let meanSquared = mean(t) ** 2.0
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let meanOfSquares = getMeanOfSquares(t)
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meanOfSquares -. meanSquared
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}
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let squareXYShape = T.mapX(x => x ** 2.0)
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}
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