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=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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,y0] evaluationImplementation=class=SoizeGhanemFactorEvaluation measure=class=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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(ComposedDistribution(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(ComposedDistribution(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(ComposedDistribution(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(ComposedDistribution(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(ComposedDistribution(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=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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,y0] evaluationImplementation=class=SoizeGhanemFactorEvaluation measure=class=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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=ComposedDistribution name=ComposedDistribution 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 ]]
