From d61bd1fc16186ab8db4c1b063302e1731a1666ef Mon Sep 17 00:00:00 2001 From: Michael BAUDIN Date: Fri, 7 Jul 2023 23:14:10 +0200 Subject: [PATCH] Update t_FunctionalChaos_ishigami.py to use Ishigami use case --- python/test/t_FunctionalChaos_ishigami.expout | 128 +++++++++--------- python/test/t_FunctionalChaos_ishigami.py | 68 ++++------ 2 files changed, 87 insertions(+), 109 deletions(-) diff --git a/python/test/t_FunctionalChaos_ishigami.expout b/python/test/t_FunctionalChaos_ishigami.expout index 81121d5cdcb..0895c5b4705 100644 --- a/python/test/t_FunctionalChaos_ishigami.expout +++ b/python/test/t_FunctionalChaos_ishigami.expout @@ -1,6 +1,6 @@ ################################### class=AdaptiveStrategy implementation=class=CleaningStrategy maximum size=20 significance factor=1e-06 derived from class=AdaptiveStrategyImplementation maximumDimension=84 -class=ProjectionStrategy implementation=class=LeastSquaresStrategy experiment=class=FixedExperiment name=Unnamed sample=class=Sample name=ComposedDistribution implementation=class=SampleImplementation name=ComposedDistribution size=250 dimension=3 description=[X0,X1,X2] 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weights=class=Point name=Unnamed dimension=250 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residuals= [0.0313673] relativeErrors= [0.0178023] mean=3.46342005 absolute error=0.0365799482 @@ -15,14 +15,14 @@ Sobol index [0,1,2] =0.00013721 absolute error=0.0001372088 Sobol total index 0 =0.57202851 absolute error=0.0144396556 Sobol total index 1 =0.42812329 absolute error=0.0142878525 Sobol total index 2 =0.25651466 absolute error=0.0128309938 -Sobol total index [0,1] =0.00001628 absolute error=0.0000162807 -Sobol total index [0,2] =0.25602203 absolute error=0.0123383686 -Sobol total index [1,2] =0.00035373 absolute error=0.0003537299 +Sobol total index [0,1] =0.00015349 absolute error=0.0001534896 +Sobol total index [0,2] =0.25615924 absolute error=0.0124755774 +Sobol total index [1,2] =0.00049094 absolute error=0.0004909387 Sobol total index [0,1,2] =0.00013721 absolute error=0.0001372088 -Sobol grouped index [0,1] =0.74348534 absolute error=0.7434853421 -Sobol grouped index [0,2] =0.57187671 absolute error=0.3281930437 -Sobol grouped index [1,2] =0.42797149 absolute error=0.4279714892 -Sobol grouped index [0,1,2] =1.00000000 absolute error=1.0000000000 +Sobol grouped index [0,1] =0.74348534 absolute error=0.0128309938 +Sobol grouped index [0,2] =0.57187671 absolute error=0.0142878525 +Sobol grouped index [1,2] =0.42797149 absolute error=0.0144396556 +Sobol grouped index [0,1,2] =1.00000000 absolute error=0.0000000000 Sobol grouped total index [0,1,2] =1.00000000 absolute error=0.0000000000 Part of variance 1, 1, [1,0,0], 0.1925 @@ -54,14 +54,14 @@ FunctionalChaosSobolIndices | Input | Name | Sobol' index | Total index | |-------|---------------|---------------|---------------| -| 0 | X0 | 0.315853 | 0.572029 | -| 1 | X1 | 0.427616 | 0.428123 | -| 2 | X2 | 1.68656e-06 | 0.256515 | +| 0 | X1 | 0.315853 | 0.572029 | +| 1 | X2 | 0.427616 | 0.428123 | +| 2 | X3 | 1.68656e-06 | 0.256515 | ################################### class=AdaptiveStrategy implementation=class=CleaningStrategy maximum size=20 significance factor=1e-06 derived from class=AdaptiveStrategyImplementation maximumDimension=84 -class=ProjectionStrategy implementation=class=LeastSquaresStrategy experiment=class=FixedExperiment name=Unnamed sample=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=250 dimension=3 description=[X0,X1,X2] 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weights=class=Point name=Unnamed dimension=250 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weights=class=Point name=Unnamed dimension=250 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residuals= [0.032434] relativeErrors= [0.0196503] mean=3.54042934 absolute error=0.0404293402 @@ -76,14 +76,14 @@ Sobol index [0,1,2] =0.00014240 absolute error=0.0001424047 Sobol total index 0 =0.54578713 absolute error=0.0118017299 Sobol total index 1 =0.45446361 absolute error=0.0120524673 Sobol total index 2 =0.23409305 absolute error=0.0095906113 -Sobol total index [0,1] =0.00050315 absolute error=0.0005031478 -Sobol total index [0,2] =0.23225190 absolute error=0.0114317673 -Sobol total index [1,2] =0.00130394 absolute error=0.0013039361 +Sobol total index [0,1] =0.00064555 absolute error=0.0006455525 +Sobol total index [0,2] =0.23239430 absolute error=0.0112893626 +Sobol total index [1,2] =0.00144634 absolute error=0.0014463408 Sobol total index [0,1,2] =0.00014240 absolute error=0.0001424047 -Sobol grouped index [0,1] =0.76590695 absolute error=0.7659069473 -Sobol grouped index [0,2] =0.54553639 absolute error=0.3018527238 -Sobol grouped index [1,2] =0.45421287 absolute error=0.4542128747 -Sobol grouped index [0,1,2] =1.00000000 absolute error=1.0000000000 +Sobol grouped index [0,1] =0.76590695 absolute error=0.0095906113 +Sobol grouped index [0,2] =0.54553639 absolute error=0.0120524673 +Sobol grouped index [1,2] =0.45421287 absolute error=0.0118017299 +Sobol grouped index [0,1,2] =1.00000000 absolute error=0.0000000000 Sobol grouped total index [0,1,2] =1.00000000 absolute error=0.0000000000 Part of variance 1, 1, [1,0,0], 0.1932 @@ -116,9 +116,9 @@ FunctionalChaosSobolIndices | Input | Name | Sobol' index | Total index | |-------|---------------|---------------|---------------| -| 0 | X0 | 0.31289 | 0.545787 | -| 1 | X1 | 0.452514 | 0.454464 | -| 2 | X2 | 0.000394815 | 0.234093 | +| 0 | X1 | 0.31289 | 0.545787 | +| 1 | X2 | 0.452514 | 0.454464 | +| 2 | X3 | 0.000394815 | 0.234093 | ################################### @@ -138,14 +138,14 @@ Sobol index [0,1,2] =0.00171843 absolute error=0.0017184293 Sobol total index 0 =0.56386484 absolute error=0.0062759857 Sobol total index 1 =0.43789799 absolute error=0.0045131590 Sobol total index 2 =0.24631494 absolute error=0.0026312723 -Sobol total index [0,1] =0.00004580 absolute error=0.0000458036 -Sobol total index [0,2] =0.24415868 absolute error=0.0004750191 -Sobol total index [1,2] =0.00043642 absolute error=0.0004364176 +Sobol total index [0,1] =0.00176423 absolute error=0.0017642330 +Sobol total index [0,2] =0.24587711 absolute error=0.0021934484 +Sobol total index [1,2] =0.00215485 absolute error=0.0021548469 Sobol total index [0,1,2] =0.00171843 absolute error=0.0017184293 -Sobol grouped index [0,1] =0.75368506 absolute error=0.7536850637 -Sobol grouped index [0,2] =0.56210201 absolute error=0.3184183502 -Sobol grouped index [1,2] =0.43613516 absolute error=0.4361351591 -Sobol grouped index [0,1,2] =1.00000000 absolute error=1.0000000000 +Sobol grouped index [0,1] =0.75368506 absolute error=0.0026312723 +Sobol grouped index [0,2] =0.56210201 absolute error=0.0045131590 +Sobol grouped index [1,2] =0.43613516 absolute error=0.0062759857 +Sobol grouped index [0,1,2] =1.00000000 absolute error=0.0000000000 Sobol grouped total index [0,1,2] =1.00000000 absolute error=0.0000000000 Part of variance 1, 1, [1,0,0], 0.1968 @@ -178,14 +178,14 @@ FunctionalChaosSobolIndices | Input | Name | Sobol' index | Total index | |-------|---------------|---------------|---------------| -| 0 | X0 | 0.317942 | 0.563865 | -| 1 | X1 | 0.435697 | 0.437898 | -| 2 | X2 | 1.40628e-06 | 0.246315 | +| 0 | X1 | 0.317942 | 0.563865 | +| 1 | X2 | 0.435697 | 0.437898 | +| 2 | X3 | 1.40628e-06 | 0.246315 | ################################### class=AdaptiveStrategy implementation=class=FixedStrategy derived from class=AdaptiveStrategyImplementation maximumDimension=84 -class=ProjectionStrategy implementation=class=LeastSquaresStrategy experiment=class=FixedExperiment name=Unnamed sample=class=Sample name=ComposedDistribution implementation=class=SampleImplementation name=ComposedDistribution size=250 dimension=3 description=[X0,X1,X2] 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weights=class=Point name=Unnamed dimension=250 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residuals= [0.0241084] relativeErrors= [0.0105163] mean=3.45801565 absolute error=0.0419843459 @@ -200,14 +200,14 @@ Sobol index [0,1,2] =0.00707950 absolute error=0.0070795030 Sobol total index 0 =0.55730528 absolute error=0.0002835755 Sobol total index 1 =0.45102832 absolute error=0.0086171717 Sobol total index 2 =0.25379662 absolute error=0.0101129549 -Sobol total index [0,1] =0.00254496 absolute error=0.0025449599 -Sobol total index [0,2] =0.24156455 absolute error=0.0021191136 -Sobol total index [1,2] =0.00386170 absolute error=0.0038616988 +Sobol total index [0,1] =0.00962446 absolute error=0.0096244629 +Sobol total index [0,2] =0.24864405 absolute error=0.0049603894 +Sobol total index [1,2] =0.01094120 absolute error=0.0109412018 Sobol total index [0,1,2] =0.00707950 absolute error=0.0070795030 -Sobol grouped index [0,1] =0.74620338 absolute error=0.7462033810 -Sobol grouped index [0,2] =0.54897168 absolute error=0.3052880194 -Sobol grouped index [1,2] =0.44269472 absolute error=0.4426947203 -Sobol grouped index [0,1,2] =1.00000000 absolute error=1.0000000000 +Sobol grouped index [0,1] =0.74620338 absolute error=0.0101129549 +Sobol grouped index [0,2] =0.54897168 absolute error=0.0086171717 +Sobol grouped index [1,2] =0.44269472 absolute error=0.0002835755 +Sobol grouped index [0,1,2] =1.00000000 absolute error=0.0000000000 Sobol grouped total index [0,1,2] =1.00000000 absolute error=0.0000000000 Part of variance 1, 1, [1,0,0], 0.1734 @@ -247,14 +247,14 @@ FunctionalChaosSobolIndices | Input | Name | Sobol' index | Total index | |-------|---------------|---------------|---------------| -| 0 | X0 | 0.306116 | 0.557305 | -| 1 | X1 | 0.437542 | 0.451028 | -| 2 | X2 | 0.00129087 | 0.253797 | +| 0 | X1 | 0.306116 | 0.557305 | +| 1 | X2 | 0.437542 | 0.451028 | +| 2 | X3 | 0.00129087 | 0.253797 | ################################### class=AdaptiveStrategy implementation=class=FixedStrategy derived from class=AdaptiveStrategyImplementation maximumDimension=84 -class=ProjectionStrategy implementation=class=LeastSquaresStrategy experiment=class=FixedExperiment name=Unnamed sample=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=250 dimension=3 description=[X0,X1,X2] 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weights=class=Point name=Unnamed dimension=250 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residuals= [0.0248146] relativeErrors= [0.0115022] mean=3.48612447 absolute error=0.0138755275 @@ -269,14 +269,14 @@ Sobol index [0,1,2] =0.00757555 absolute error=0.0075755522 Sobol total index 0 =0.54824000 absolute error=0.0093488551 Sobol total index 1 =0.46251801 absolute error=0.0201068669 Sobol total index 2 =0.24894582 absolute error=0.0052621606 -Sobol total index [0,1] =0.00771703 absolute error=0.0077170275 -Sobol total index [0,2] =0.23077723 absolute error=0.0129064377 -Sobol total index [1,2] =0.00605848 absolute error=0.0060584783 +Sobol total index [0,1] =0.01529258 absolute error=0.0152925796 +Sobol total index [0,2] =0.23835278 absolute error=0.0053308856 +Sobol total index [1,2] =0.01363403 absolute error=0.0136340305 Sobol total index [0,1,2] =0.00757555 absolute error=0.0075755522 -Sobol grouped index [0,1] =0.75105418 absolute error=0.7510541753 -Sobol grouped index [0,2] =0.53748199 absolute error=0.2937983243 -Sobol grouped index [1,2] =0.45176000 absolute error=0.4517599999 -Sobol grouped index [0,1,2] =1.00000000 absolute error=1.0000000000 +Sobol grouped index [0,1] =0.75105418 absolute error=0.0052621606 +Sobol grouped index [0,2] =0.53748199 absolute error=0.0201068669 +Sobol grouped index [1,2] =0.45176000 absolute error=0.0093488551 +Sobol grouped index [0,1,2] =1.00000000 absolute error=0.0000000000 Sobol grouped total index [0,1,2] =1.00000000 absolute error=0.0000000000 Part of variance 1, 1, [1,0,0], 0.2018 @@ -316,9 +316,9 @@ FunctionalChaosSobolIndices | Input | Name | Sobol' index | Total index | |-------|---------------|---------------|---------------| -| 0 | X0 | 0.30217 | 0.54824 | -| 1 | X1 | 0.441167 | 0.462518 | -| 2 | X2 | 0.00453457 | 0.248946 | +| 0 | X1 | 0.30217 | 0.54824 | +| 1 | X2 | 0.441167 | 0.462518 | +| 2 | X3 | 0.00453457 | 0.248946 | ################################### @@ -338,14 +338,14 @@ Sobol index [0,1,2] =0.00548925 absolute error=0.0054892488 Sobol total index 0 =0.57119967 absolute error=0.0136108134 Sobol total index 1 =0.43702709 absolute error=0.0053840510 Sobol total index 2 =0.25963010 absolute error=0.0159464355 -Sobol total index [0,1] =0.00314638 absolute error=0.0031463799 -Sobol total index [0,2] =0.25121369 absolute error=0.0075300230 -Sobol total index [1,2] =0.00251830 absolute error=0.0025182974 +Sobol total index [0,1] =0.00863563 absolute error=0.0086356287 +Sobol total index [0,2] =0.25670294 absolute error=0.0130192718 +Sobol total index [1,2] =0.00800755 absolute error=0.0080075462 Sobol total index [0,1,2] =0.00548925 absolute error=0.0054892488 -Sobol grouped index [0,1] =0.74036990 absolute error=0.7403699004 -Sobol grouped index [0,2] =0.56297291 absolute error=0.3192892421 -Sobol grouped index [1,2] =0.42880033 absolute error=0.4288003314 -Sobol grouped index [0,1,2] =1.00000000 absolute error=1.0000000000 +Sobol grouped index [0,1] =0.74036990 absolute error=0.0159464355 +Sobol grouped index [0,2] =0.56297291 absolute error=0.0053840510 +Sobol grouped index [1,2] =0.42880033 absolute error=0.0136108134 +Sobol grouped index [0,1,2] =1.00000000 absolute error=0.0000000000 Sobol grouped total index [0,1,2] =1.00000000 absolute error=0.0000000000 Part of variance 1, 1, [1,0,0], 0.1916 @@ -379,8 +379,8 @@ FunctionalChaosSobolIndices | Input | Name | Sobol' index | Total index | |-------|---------------|---------------|---------------| -| 0 | X0 | 0.31135 | 0.5712 | -| 1 | X1 | 0.425873 | 0.437027 | -| 2 | X2 | 0.000408866 | 0.25963 | +| 0 | X1 | 0.31135 | 0.5712 | +| 1 | X2 | 0.425873 | 0.437027 | +| 2 | X3 | 0.000408866 | 0.25963 | diff --git a/python/test/t_FunctionalChaos_ishigami.py b/python/test/t_FunctionalChaos_ishigami.py index 529809d5d50..9b3b6a20500 100755 --- a/python/test/t_FunctionalChaos_ishigami.py +++ b/python/test/t_FunctionalChaos_ishigami.py @@ -2,44 +2,22 @@ import openturns as ot import math as m +from openturns.usecases import ishigami_function ot.TESTPREAMBLE() # Problem parameters -dimension = 3 -a = 7.0 -b = 0.1 -# Reference analytical values -meanTh = a / 2 -covTh = (b ** 2 * m.pi ** 8) / 18.0 + (b * m.pi ** 4) / 5.0 + (a ** 2) / 8.0 + 1.0 / 2.0 -sob_1 = [ - (b * m.pi ** 4 / 5.0 + b ** 2 * m.pi ** 8 / 50.0 + 1.0 / 2.0) / covTh, - (a ** 2 / 8.0) / covTh, - 0.0, -] -sob_2 = [0.0, (b ** 2 * m.pi ** 8 / 18.0 - b ** 2 * m.pi ** 8 / 50.0) / covTh, 0.0] -sob_3 = [0.0] -sob_T1 = [ - sob_1[0] + sob_2[0] + sob_2[1] + sob_3[0], - sob_1[1] + sob_2[0] + sob_2[2] + sob_3[0], - sob_1[2] + sob_2[1] + sob_2[2] + sob_3[0], -] -sob_T2 = [ - sob_2[0] + sob_2[1] + sob_3[0], - sob_2[0] + sob_2[2] + sob_3[0], - sob_2[1] + sob_2[2] + sob_3[0], -] -sob_T3 = [sob_3[0]] -# Create the Ishigami function -inputVariables = ["xi1", "xi2", "xi3"] -formula = ot.Description(1) -formula[0] = ( - "sin(xi1) + (" + str(a) + ") * (sin(xi2)) ^ 2 + (" + str(b) + ") * xi3^4 * sin(xi1)" -) -model = ot.SymbolicFunction(inputVariables, formula) - -# Create the input distribution -distribution = ot.ComposedDistribution([ot.Uniform(-m.pi, m.pi)] * dimension) +im = ishigami_function.IshigamiModel() +distribution = im.distributionX +model = im.model +dimension = im.distributionX.getDimension() +sobolFirstOrderReference = [im.S1, im.S2, im.S3] +sobolSecondOrderReference = [im.S12, im.S13, im.S23] +sobolTotalReference = [im.ST1, im.ST2, im.ST3] +sobolInteractionTotalReference2 = [im.S12 + im.S123, im.S13 + im.S123, im.S23 + im.S123] +sobolInteractionTotalReference3 = [im.S123] +sobolGroupedIndex2 = [im.S1 + im.S2 + im.S12, im.S1 + im.S3 + im.S13, im.S2 + im.S3 + im.S23] +sobolGroupedIndex3 = [im.S1 + im.S2 + im.S3 + im.S12 + im.S13 + im.S23 + im.S123] # Create the orthogonal basis enumerateFunction = ot.LinearEnumerateFunction(dimension) @@ -102,10 +80,10 @@ # Post-process the results vector = ot.FunctionalChaosRandomVector(result) mean = vector.getMean()[0] - print("mean=%.8f" % mean, "absolute error=%.10f" % abs(mean - meanTh)) + print("mean=%.8f" % mean, "absolute error=%.10f" % abs(mean - im.expectation)) variance = vector.getCovariance()[0, 0] print( - "variance=%.8f" % variance, "absolute error=%.10f" % abs(variance - covTh) + "variance=%.8f" % variance, "absolute error=%.10f" % abs(variance - im.variance) ) sensitivity = ot.FunctionalChaosSobolIndices(result) for i in range(dimension): @@ -114,7 +92,7 @@ "Sobol index", i, "= %.8f" % value, - "absolute error=%.10f" % abs(value - sob_1[i]), + "absolute error=%.10f" % abs(value - sobolFirstOrderReference[i]), ) indices = ot.Indices(2) k = 0 @@ -127,7 +105,7 @@ "Sobol index", indices, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_2[k]), + "absolute error=%.10f" % abs(value - sobolSecondOrderReference[k]), ) k = k + 1 indices = ot.Indices([0, 1, 2]) @@ -136,7 +114,7 @@ "Sobol index", indices, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_3[0]), + "absolute error=%.10f" % abs(value - im.S123), ) for i in range(dimension): value = sensitivity.getSobolTotalIndex(i) @@ -144,7 +122,7 @@ "Sobol total index", i, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_T1[i]), + "absolute error=%.10f" % abs(value - sobolTotalReference[i]), ) indices = ot.Indices(2) k = 0 @@ -152,12 +130,12 @@ indices[0] = i for j in range(i + 1, dimension): indices[1] = j - value = sensitivity.getSobolIndex(indices) + value = sensitivity.getSobolTotalIndex(indices) print( "Sobol total index", indices, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_2[k]), + "absolute error=%.10f" % abs(value - sobolInteractionTotalReference2[k]), ) k = k + 1 indices = ot.Indices([0, 1, 2]) @@ -166,7 +144,7 @@ "Sobol total index ", indices, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_3[0]), + "absolute error=%.10f" % abs(value - sobolInteractionTotalReference3[0]), ) indices = ot.Indices(2) k = 0 @@ -179,7 +157,7 @@ "Sobol grouped index", indices, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_2[k]), + "absolute error=%.10f" % abs(value - sobolGroupedIndex2[k]), ) k = k + 1 indices = ot.Indices([0, 1, 2]) @@ -188,7 +166,7 @@ "Sobol grouped index ", indices, "=%.8f" % value, - "absolute error=%.10f" % abs(value - sob_3[0]), + "absolute error=%.10f" % abs(value - sobolGroupedIndex3[0]), ) indices = ot.Indices([0, 1, 2]) value = sensitivity.getSobolGroupedTotalIndex(indices)