From 71e37c3a1e32272001db62e068a1e00623eed687 Mon Sep 17 00:00:00 2001 From: Michael BAUDIN Date: Sun, 12 May 2024 18:28:49 +0200 Subject: [PATCH] Improve unit tests of Faure sequence --- lib/test/CMakeLists.txt | 2 +- lib/test/t_FaureSequence_std.cxx | 59 +- lib/test/t_FaureSequence_std.expout | 1004 ------------------------ python/test/CMakeLists.txt | 2 +- python/test/t_FaureSequence_std.expout | 1004 ------------------------ python/test/t_FaureSequence_std.py | 106 ++- 6 files changed, 151 insertions(+), 2026 deletions(-) delete mode 100644 lib/test/t_FaureSequence_std.expout delete mode 100644 python/test/t_FaureSequence_std.expout diff --git a/lib/test/CMakeLists.txt b/lib/test/CMakeLists.txt index cf796c109e..314d17b35b 100644 --- a/lib/test/CMakeLists.txt +++ b/lib/test/CMakeLists.txt @@ -226,7 +226,7 @@ ot_check_test (Field_std) ot_check_test (ProcessSample_std) ot_check_test (RandomGenerator_std) ot_check_test (SobolSequence_std) -ot_check_test (FaureSequence_std) +ot_check_test (FaureSequence_std IGNOREOUT) ot_check_test (HaltonSequence_std IGNOREOUT) ot_check_test (HaselgroveSequence_std) ot_check_test (ReverseHaltonSequence_std) diff --git a/lib/test/t_FaureSequence_std.cxx b/lib/test/t_FaureSequence_std.cxx index 635733e2b1..565e148fb4 100644 --- a/lib/test/t_FaureSequence_std.cxx +++ b/lib/test/t_FaureSequence_std.cxx @@ -31,31 +31,74 @@ int main(int, char *[]) try { - // Create a Faure sequence + // Create 8 points from a Faure sequence in dimension 1 + Sample expected1D(8, 1); + expected1D[0] = Point({1.0 / 2.0}); + expected1D[1] = Point({1.0 / 4.0}); + expected1D[2] = Point({3.0 / 4.0}); + expected1D[3] = Point({1.0 / 8.0}); + expected1D[4] = Point({5.0 / 8.0}); + expected1D[5] = Point({3.0 / 8.0}); + expected1D[6] = Point({7.0 / 8.0}); + expected1D[7] = Point({1.0 / 16.0}); + FaureSequence sequence1D(1); + fullprint << sequence1D << std::endl; + Sample haltonSample1D(sequence1D.generate(8)); + assert_almost_equal(haltonSample1D, expected1D); + + // Create 8 points from a Faure sequence in dimension 2 + Sample expected2D(8, 2); + expected2D[0] = Point({0.5, 0.5}); + expected2D[1] = Point({0.25, 0.75}); + expected2D[2] = Point({0.75, 0.25}); + expected2D[3] = Point({0.125, 0.625}); + expected2D[4] = Point({0.625, 0.125}); + expected2D[5] = Point({0.375, 0.375}); + expected2D[6] = Point({0.875, 0.875}); + expected2D[7] = Point({0.0625, 0.9375}); + FaureSequence sequence2D(2); + fullprint << sequence2D << std::endl; + Sample haltonSample2D(sequence2D.generate(8)); + assert_almost_equal(haltonSample2D, expected2D); + + // Create 8 points from a Faure sequence in dimension 3 + Sample expected3D(8, 3); + expected3D[0] = Point({1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0}); + expected3D[1] = Point({2.0 / 3.0, 2.0 / 3.0, 2.0 / 3.0}); + expected3D[2] = Point({1.0 / 9.0, 4.0 / 9.0, 7.0 / 9.0}); + expected3D[3] = Point({4.0 / 9.0, 7.0 / 9.0, 1.0 / 9.0}); + expected3D[4] = Point({7.0 / 9.0, 1.0 / 9.0, 4.0 / 9.0}); + expected3D[5] = Point({2.0 / 9.0, 8.0 / 9.0, 5.0 / 9.0}); + expected3D[6] = Point({5.0 / 9.0, 2.0 / 9.0, 8.0 / 9.0}); + expected3D[7] = Point({8.0 / 9.0, 5.0 / 9.0, 2.0 / 9.0}); + FaureSequence sequence3D(3); + fullprint << sequence3D << std::endl; + Sample faureSample3D(sequence3D.generate(8)); + assert_almost_equal(faureSample3D, expected3D); + + // Create a Faure sequence in dimension 15 FaureSequence sequence(15); fullprint << sequence << std::endl; - - // Create a numerical sample of the sequence Sample faureSample(sequence.generate(10)); - fullprint << faureSample << std::endl; // Create another Faure' sequence of dimension 2 to estimate Pi in [0; 1)^2 UnsignedInteger dimension = 2; sequence = FaureSequence(dimension); UnsignedInteger pointInsideCircle = 0; - UnsignedInteger sampleSize = 1000; + UnsignedInteger sampleSize = std::pow(3, 7); // This is significant! for(UnsignedInteger i = 0; i < sampleSize; ++i) { Point faurePoint(sequence.generate()); - fullprint << faurePoint << std::endl; if(faurePoint.norm() < 1.0) ++ pointInsideCircle; } Scalar probabilityEstimate = 1.0 * pointInsideCircle / sampleSize; Scalar probability = M_PI / 4.0; - Scalar relativeError = std::abs(probability - probabilityEstimate) / probability; fullprint << "sample size=" << sampleSize << std::endl; - fullprint << "relative error to Pi=" << relativeError << std::endl; + fullprint << "computed probability =" << probabilityEstimate << std::endl; + fullprint << "expected probability =" << probability << std::endl; + Scalar rtol = 10.0 / sampleSize; + assert_almost_equal(probabilityEstimate, probability, rtol); } catch (TestFailed & ex) diff --git a/lib/test/t_FaureSequence_std.expout b/lib/test/t_FaureSequence_std.expout deleted file mode 100644 index d7dfc959d9..0000000000 --- a/lib/test/t_FaureSequence_std.expout +++ /dev/null @@ -1,1004 +0,0 @@ -class=FaureSequence modulus=17 seed=1 -class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=10 dimension=15 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values=[0.584961,0.0126953] -class=Point name=Unnamed dimension=2 values=[0.334961,0.262695] -class=Point name=Unnamed dimension=2 values=[0.834961,0.762695] -class=Point name=Unnamed dimension=2 values=[0.209961,0.137695] -class=Point name=Unnamed dimension=2 values=[0.709961,0.637695] -class=Point name=Unnamed dimension=2 values=[0.459961,0.887695] -class=Point name=Unnamed dimension=2 values=[0.959961,0.387695] -class=Point name=Unnamed dimension=2 values=[0.0537109,0.981445] -class=Point name=Unnamed dimension=2 values=[0.553711,0.481445] -class=Point name=Unnamed dimension=2 values=[0.303711,0.231445] -class=Point name=Unnamed dimension=2 values=[0.803711,0.731445] -class=Point name=Unnamed dimension=2 values=[0.178711,0.356445] -class=Point name=Unnamed dimension=2 values=[0.678711,0.856445] -class=Point name=Unnamed dimension=2 values=[0.428711,0.606445] -class=Point name=Unnamed dimension=2 values=[0.928711,0.106445] -class=Point name=Unnamed dimension=2 values=[0.116211,0.0439453] -class=Point name=Unnamed dimension=2 values=[0.616211,0.543945] -class=Point name=Unnamed dimension=2 values=[0.366211,0.793945] -class=Point name=Unnamed dimension=2 values=[0.866211,0.293945] -class=Point name=Unnamed dimension=2 values=[0.241211,0.668945] -class=Point name=Unnamed dimension=2 values=[0.741211,0.168945] -class=Point name=Unnamed dimension=2 values=[0.491211,0.418945] -class=Point name=Unnamed dimension=2 values=[0.991211,0.918945] -class=Point name=Unnamed dimension=2 values=[0.0146484,0.0830078] -class=Point name=Unnamed dimension=2 values=[0.514648,0.583008] -class=Point name=Unnamed dimension=2 values=[0.264648,0.833008] -class=Point name=Unnamed dimension=2 values=[0.764648,0.333008] -class=Point name=Unnamed dimension=2 values=[0.139648,0.708008] -class=Point name=Unnamed dimension=2 values=[0.639648,0.208008] -class=Point name=Unnamed dimension=2 values=[0.389648,0.458008] -class=Point name=Unnamed dimension=2 values=[0.889648,0.958008] -class=Point name=Unnamed dimension=2 values=[0.0771484,0.895508] -class=Point name=Unnamed dimension=2 values=[0.577148,0.395508] -class=Point name=Unnamed dimension=2 values=[0.327148,0.145508] -class=Point name=Unnamed dimension=2 values=[0.827148,0.645508] -class=Point name=Unnamed dimension=2 values=[0.202148,0.270508] -class=Point name=Unnamed dimension=2 values=[0.702148,0.770508] -class=Point name=Unnamed dimension=2 values=[0.452148,0.520508] -class=Point name=Unnamed dimension=2 values=[0.952148,0.0205078] -class=Point name=Unnamed dimension=2 values=[0.0458984,0.614258] -class=Point name=Unnamed dimension=2 values=[0.545898,0.114258] -class=Point name=Unnamed dimension=2 values=[0.295898,0.364258] -class=Point name=Unnamed dimension=2 values=[0.795898,0.864258] -class=Point name=Unnamed dimension=2 values=[0.170898,0.239258] -class=Point name=Unnamed dimension=2 values=[0.670898,0.739258] -class=Point name=Unnamed dimension=2 values=[0.420898,0.989258] -class=Point name=Unnamed dimension=2 values=[0.920898,0.489258] -class=Point name=Unnamed dimension=2 values=[0.108398,0.426758] -class=Point name=Unnamed dimension=2 values=[0.608398,0.926758] -class=Point name=Unnamed dimension=2 values=[0.358398,0.676758] -class=Point name=Unnamed dimension=2 values=[0.858398,0.176758] -class=Point name=Unnamed dimension=2 values=[0.233398,0.801758] -class=Point name=Unnamed dimension=2 values=[0.733398,0.301758] -class=Point name=Unnamed dimension=2 values=[0.483398,0.0517578] -class=Point name=Unnamed dimension=2 values=[0.983398,0.551758] -class=Point name=Unnamed dimension=2 values=[0.0302734,0.848633] -class=Point name=Unnamed dimension=2 values=[0.530273,0.348633] -class=Point name=Unnamed dimension=2 values=[0.280273,0.0986328] -class=Point name=Unnamed dimension=2 values=[0.780273,0.598633] -class=Point name=Unnamed dimension=2 values=[0.155273,0.473633] -class=Point name=Unnamed dimension=2 values=[0.655273,0.973633] -class=Point name=Unnamed dimension=2 values=[0.405273,0.723633] -class=Point name=Unnamed dimension=2 values=[0.905273,0.223633] -class=Point name=Unnamed dimension=2 values=[0.0927734,0.161133] -sample size=1000 -relative error to Pi=0.000766282 diff --git a/python/test/CMakeLists.txt b/python/test/CMakeLists.txt index 9900edbb62..f7e6dc0cc0 100644 --- a/python/test/CMakeLists.txt +++ b/python/test/CMakeLists.txt @@ -218,7 +218,7 @@ ot_pyinstallcheck_test (Field_draw) ot_pyinstallcheck_test (ProcessSample_std) ot_pyinstallcheck_test (RandomGenerator_std) ot_pyinstallcheck_test (SobolSequence_std IGNOREOUT) -ot_pyinstallcheck_test (FaureSequence_std) +ot_pyinstallcheck_test (FaureSequence_std IGNOREOUT) ot_pyinstallcheck_test (HaltonSequence_std IGNOREOUT) ot_pyinstallcheck_test (HaselgroveSequence_std) ot_pyinstallcheck_test (ReverseHaltonSequence_std) diff --git a/python/test/t_FaureSequence_std.expout b/python/test/t_FaureSequence_std.expout deleted file mode 100644 index 2fb5fb0bf8..0000000000 --- a/python/test/t_FaureSequence_std.expout +++ /dev/null @@ -1,1004 +0,0 @@ -class=FaureSequence modulus=17 seed=1 -class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=10 dimension=15 data=[[0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235,0.0588235],[0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647,0.117647],[0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471,0.176471],[0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294,0.235294],[0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118,0.294118],[0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941,0.352941],[0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765,0.411765],[0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588,0.470588],[0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412,0.529412],[0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235,0.588235]] 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values=[0.420898,0.989258] -class=Point name=Unnamed dimension=2 values=[0.920898,0.489258] -class=Point name=Unnamed dimension=2 values=[0.108398,0.426758] -class=Point name=Unnamed dimension=2 values=[0.608398,0.926758] -class=Point name=Unnamed dimension=2 values=[0.358398,0.676758] -class=Point name=Unnamed dimension=2 values=[0.858398,0.176758] -class=Point name=Unnamed dimension=2 values=[0.233398,0.801758] -class=Point name=Unnamed dimension=2 values=[0.733398,0.301758] -class=Point name=Unnamed dimension=2 values=[0.483398,0.0517578] -class=Point name=Unnamed dimension=2 values=[0.983398,0.551758] -class=Point name=Unnamed dimension=2 values=[0.0302734,0.848633] -class=Point name=Unnamed dimension=2 values=[0.530273,0.348633] -class=Point name=Unnamed dimension=2 values=[0.280273,0.0986328] -class=Point name=Unnamed dimension=2 values=[0.780273,0.598633] -class=Point name=Unnamed dimension=2 values=[0.155273,0.473633] -class=Point name=Unnamed dimension=2 values=[0.655273,0.973633] -class=Point name=Unnamed dimension=2 values=[0.405273,0.723633] -class=Point name=Unnamed dimension=2 values=[0.905273,0.223633] -class=Point name=Unnamed dimension=2 values=[0.0927734,0.161133] -sample size= 1000 -relative error to Pi=7.662822e-04 diff --git a/python/test/t_FaureSequence_std.py b/python/test/t_FaureSequence_std.py index 5f5b3bc64f..32d86a899a 100755 --- a/python/test/t_FaureSequence_std.py +++ b/python/test/t_FaureSequence_std.py @@ -1,31 +1,121 @@ #! /usr/bin/env python import openturns as ot +import openturns.testing as ott import math as m ot.TESTPREAMBLE() -# Create a Faure -sequence = ot.FaureSequence(15) +# First 8 points of Faure sequence in dimension 1 +expected = ot.Sample( + [ + [1.0 / 2.0], + [1.0 / 4.0], + [3.0 / 4.0], + [1.0 / 8.0], + [5.0 / 8.0], + [3.0 / 8.0], + [7.0 / 8.0], + [1.0 / 16.0], + ] +) +sequence = ot.FaureSequence(1) +print(sequence) +faureSample = sequence.generate(8) +ott.assert_almost_equal(faureSample, expected) + +# First 8 points of Faure sequence in dimension 2 +expected = ot.Sample( + [ + [0.5, 0.5], + [0.25, 0.75], + [0.75, 0.25], + [0.125, 0.625], + [0.625, 0.125], + [0.375, 0.375], + [0.875, 0.875], + [0.0625, 0.9375], + ] +) +sequence = ot.FaureSequence(2) +print(sequence) +faureSample = sequence.generate(8) +ott.assert_almost_equal(faureSample, expected) + +# First 8 points of Faure sequence in dimension 3 +expected = ot.Sample( + [ + [1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0], + [2.0 / 3.0, 2.0 / 3.0, 2.0 / 3.0], + [1.0 / 9.0, 4.0 / 9.0, 7.0 / 9.0], + [4.0 / 9.0, 7.0 / 9.0, 1.0 / 9.0], + [7.0 / 9.0, 1.0 / 9.0, 4.0 / 9.0], + [2.0 / 9.0, 8.0 / 9.0, 5.0 / 9.0], + [5.0 / 9.0, 2.0 / 9.0, 8.0 / 9.0], + [8.0 / 9.0, 5.0 / 9.0, 2.0 / 9.0], + ] +) +sequence = ot.FaureSequence(3) print(sequence) +faureSample = sequence.generate(8) +ott.assert_almost_equal(faureSample, expected) -# Create a numerical sample of the sequence +# Create a Faure sequence in dimension 15 +sequence = ot.FaureSequence(15) +print(sequence) faureSample = sequence.generate(10) -print(repr(faureSample)) # Create another Faure' sequence of dimension 2 to estimate Pi in [0 1)^2 dimension = 2 sequence = ot.FaureSequence(dimension) pointInsideCircle = 0 -sampleSize = 1000 +sampleSize = 3 ** 7 # This is significant! for i in range(sampleSize): faurePoint = sequence.generate() - print(faurePoint.__repr__()) if faurePoint.norm() < 1.0: pointInsideCircle = pointInsideCircle + 1 probabilityEstimate = (1.0 * pointInsideCircle) / sampleSize probability = m.pi / 4.0 -relativeError = abs(probability - probabilityEstimate) / probability print("sample size=", sampleSize) -print("relative error to Pi=%e" % relativeError) +print("computed probability =", probabilityEstimate) +print("expected probability =", probability) +rtol = 10.0 / sampleSize +ott.assert_almost_equal(probability, probabilityEstimate, rtol) + +# Test against GSobol' test function +# https://github.com/openturns/openturns/issues/2653 +a = [0.0, 9.0, 99.0] + + +def GSobolModel(X): + X = ot.Point(X) + d = X.getDimension() + Y = 1.0 + for i in range(d): + Y *= (abs(4.0 * X[i] - 2.0) + a[i]) / (1.0 + a[i]) + return ot.Point([Y]) + + +dimension = 3 +gSobolFunction = ot.PythonFunction(dimension, 1, GSobolModel) +gSobolFunction.setOutputDescription(["Y"]) + +# Define the distribution +distributionList = [ot.Uniform(0.0, 1.0) for i in range(dimension)] +distribution = ot.ComposedDistribution(distributionList) + +# Compute Mean +gSobolMean = 1.0 +basis = 3 # ie the smallest prime number greater or equal to the dimension +sampleSize = basis**7 # This is significant! +sequence = ot.FaureSequence() +experiment_QMC = ot.LowDiscrepancyExperiment(sequence, distribution, sampleSize, False) +inputSample = experiment_QMC.generate() +outputSample = gSobolFunction(inputSample) +computedMean = outputSample.computeMean()[0] +print("sample size=", sampleSize) +print("computed mean =", computedMean) +print("expected mean =", gSobolMean) +rtol = 10.0 / sampleSize +ott.assert_almost_equal(computedMean, gSobolMean, rtol)