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SoizeGhanem= class=SoizeGhanemFactory productPolynomial=class=OrthogonalProductPolynomialFactory univariate polynomial collection=[class=OrthogonalUniVariatePolynomialFamily implementation=class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=HermiteFactory measure=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=OrthogonalUniVariatePolynomialFamily implementation=class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=LegendreFactory measure=class=Uniform name=Uniform dimension=1 a=-1 b=1] measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 phi=class=LinearEnumerateFunction dimension=2 measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 hasIndependentCopula=true
SoizeGhanem( 0 )= 1
SoizeGhanem( 0 )( [0.5, 0.5] = [1]
SoizeGhanem( 1 )= x0
SoizeGhanem( 1 )( [0.5, 0.5] = [0.5]
SoizeGhanem( 2 )= 1.73205 * x1
SoizeGhanem( 2 )( [0.5, 0.5] = [0.866025]
SoizeGhanem( 3 )= -0.707107 + 0.707107 * x0^2
SoizeGhanem( 3 )( [0.5, 0.5] = [-0.53033]
SoizeGhanem( 4 )= x0 * 1.73205 * x1
SoizeGhanem( 4 )( [0.5, 0.5] = [0.433013]
M=
5x5
[[ 1 0 0 0 0 ]
[ 0 1 0 0 0 ]
[ 0 0 1 0 0 ]
[ 0 0 0 1 0 ]
[ 0 0 0 0 1 ]]
SoizeGhanem= class=SoizeGhanemFactory productPolynomial=class=OrthogonalProductPolynomialFactory univariate polynomial collection=[class=OrthogonalUniVariatePolynomialFamily implementation=class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=HermiteFactory measure=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=OrthogonalUniVariatePolynomialFamily implementation=class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=LegendreFactory measure=class=Uniform name=Uniform dimension=1 a=-1 b=1] measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 phi=class=LinearEnumerateFunction dimension=2 measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 hasIndependentCopula=false adaptationFactor=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,k] evaluationImplementation=class=SoizeGhanemFactorEvaluation measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 marginals=[class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=Uniform name=Uniform dimension=1 a=-1 b=1] useCopula=false gradientImplementation=class=CenteredFiniteDifferenceGradient name=Unnamed epsilon=class=Point name=Unnamed dimension=2 values=[1e-05,1e-05] evaluation=class=SoizeGhanemFactorEvaluation measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 marginals=[class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=Uniform name=Uniform dimension=1 a=-1 b=1] useCopula=false hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=2 values=[0.0001,0.0001] evaluation=class=SoizeGhanemFactorEvaluation measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 marginals=[class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=Uniform name=Uniform dimension=1 a=-1 b=1] useCopula=false
SoizeGhanem( 0 )= (1) * (([X0,X1]->1/sqrt(JointDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]])).computePDF(X0, X1))
SoizeGhanem( 0 )( [0.5, 0.5] = [0.881976]
SoizeGhanem( 1 )= (x0) * (([X0,X1]->1/sqrt(JointDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]])).computePDF(X0, X1))
SoizeGhanem( 1 )( [0.5, 0.5] = [0.440988]
SoizeGhanem( 2 )= (1.73205 * x1) * (([X0,X1]->1/sqrt(JointDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]])).computePDF(X0, X1))
SoizeGhanem( 2 )( [0.5, 0.5] = [0.763813]
SoizeGhanem( 3 )= (-0.707107 + 0.707107 * x0^2) * (([X0,X1]->1/sqrt(JointDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]])).computePDF(X0, X1))
SoizeGhanem( 3 )( [0.5, 0.5] = [-0.467738]
SoizeGhanem( 4 )= (x0 * 1.73205 * x1) * (([X0,X1]->1/sqrt(JointDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]])).computePDF(X0, X1))
SoizeGhanem( 4 )( [0.5, 0.5] = [0.381907]
M=
5x5
[[ 1 0 0 0 0 ]
[ 0 1 0 0 0 ]
[ 0 0 1 0 0 ]
[ 0 0 0 1 0 ]
[ 0 0 0 0 1 ]]
SoizeGhanem= class=SoizeGhanemFactory productPolynomial=class=OrthogonalProductPolynomialFactory univariate polynomial collection=[class=OrthogonalUniVariatePolynomialFamily implementation=class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=HermiteFactory measure=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=OrthogonalUniVariatePolynomialFamily implementation=class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=LegendreFactory measure=class=Uniform name=Uniform dimension=1 a=-1 b=1] measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 phi=class=LinearEnumerateFunction dimension=2 measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 hasIndependentCopula=false adaptationFactor=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[X0,X1,k] evaluationImplementation=class=SoizeGhanemFactorEvaluation measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 marginals=[class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=Uniform name=Uniform dimension=1 a=-1 b=1] useCopula=true copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] gradientImplementation=class=CenteredFiniteDifferenceGradient name=Unnamed epsilon=class=Point name=Unnamed dimension=2 values=[1e-05,1e-05] evaluation=class=SoizeGhanemFactorEvaluation measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 marginals=[class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=Uniform name=Uniform dimension=1 a=-1 b=1] useCopula=true copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=2 values=[0.0001,0.0001] evaluation=class=SoizeGhanemFactorEvaluation measure=class=JointDistribution name=JointDistribution dimension=2 copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1] marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1 marginals=[class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1],class=Uniform name=Uniform dimension=1 a=-1 b=1] useCopula=true copula=class=NormalCopula name=NormalCopula dimension=2 correlation=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1]
SoizeGhanem( 0 )= (1) * (([X0,X1]->1/sqrt(NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]).computePDF(Normal(mu = 0, sigma = 1).computeCDF(X0), Uniform(a = -1, b = 1).computeCDF(X1)))
SoizeGhanem( 0 )( [0.5, 0.5] = [0.881976]
SoizeGhanem( 1 )= (x0) * (([X0,X1]->1/sqrt(NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]).computePDF(Normal(mu = 0, sigma = 1).computeCDF(X0), Uniform(a = -1, b = 1).computeCDF(X1)))
SoizeGhanem( 1 )( [0.5, 0.5] = [0.440988]
SoizeGhanem( 2 )= (1.73205 * x1) * (([X0,X1]->1/sqrt(NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]).computePDF(Normal(mu = 0, sigma = 1).computeCDF(X0), Uniform(a = -1, b = 1).computeCDF(X1)))
SoizeGhanem( 2 )( [0.5, 0.5] = [0.763813]
SoizeGhanem( 3 )= (-0.707107 + 0.707107 * x0^2) * (([X0,X1]->1/sqrt(NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]).computePDF(Normal(mu = 0, sigma = 1).computeCDF(X0), Uniform(a = -1, b = 1).computeCDF(X1)))
SoizeGhanem( 3 )( [0.5, 0.5] = [-0.467738]
SoizeGhanem( 4 )= (x0 * 1.73205 * x1) * (([X0,X1]->1/sqrt(NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]).computePDF(Normal(mu = 0, sigma = 1).computeCDF(X0), Uniform(a = -1, b = 1).computeCDF(X1)))
SoizeGhanem( 4 )( [0.5, 0.5] = [0.381907]
M=
5x5
[[ 1 0 0 0 0 ]
[ 0 1 0 0 0 ]
[ 0 0 1 0 0 ]
[ 0 0 0 1 0 ]
[ 0 0 0 0 1 ]]
|
