f = cb.model
# %%
# The random variable of interest Y is then
Y = ot.CompositeRandomVector(f, X)
Y.setDescription('Y')
# %%
# Taylor expansion
# ----------------
# %%
# Perform Taylor approximation to get the expected value of Y and the importance factors.
# %%
taylor = ot.TaylorExpansionMoments(Y)
taylor_mean_fo = taylor.getMeanFirstOrder()
taylor_mean_so = taylor.getMeanSecondOrder()
taylor_cov = taylor.getCovariance()
taylor_if = taylor.getImportanceFactors()
print('model evaluation calls number=', f.getGradientCallsNumber())
print('model gradient calls number=', f.getGradientCallsNumber())
print('model hessian calls number=', f.getHessianCallsNumber())
print('taylor mean first order=', taylor_mean_fo)
print('taylor variance=', taylor_cov)
print('taylor importance factors=', taylor_if)
# %%
graph = taylor.drawImportanceFactors()
view = viewer.View(graph)
formulas = ot.Description(3)
formulas[0] = 'a+b+c'
formulas[1] = 'a-b*c'
formulas[2] = '(a+2*b^2+3*c^3)/6'
analytical = ot.SymbolicFunction(input, formulas)
analytical.setName('analytical')
analytical.setOutputDescription(['z1', 'z2', 'z3'])
myStudy.add('analytical', analytical)
# Create a TaylorExpansionMoments algorithm
antecedent = ot.RandomVector(
ot.IndependentCopula(analytical.getInputDimension()))
antecedent.setName('antecedent')
composite = ot.CompositeRandomVector(analytical, antecedent)
composite.setName('composite')
taylorExpansionsMoments = ot.TaylorExpansionMoments(composite)
taylorExpansionsMoments.setName('taylorExpansionsMoments')
taylorExpansionsMoments.getMeanFirstOrder()
taylorExpansionsMoments.getMeanSecondOrder()
taylorExpansionsMoments.getCovariance()
myStudy.add('taylorExpansionsMoments', taylorExpansionsMoments)
# Create a FORMResult
input2 = ot.Description(2)
input2[0] = 'x'
input2[1] = 'y'
formula2 = ot.Description(1)
formula2[0] = 'y^2-x'
model = ot.SymbolicFunction(input2, formula2)
model.setName('sum')
for i in range(dim):
sigma[i] = 0.1 * (i + 1)
R = ot.CorrelationMatrix(dim)
for i in range(1, dim):
R[i, i - 1] = 0.25
distribution = ot.Normal(meanPoint, sigma, R)
# We create a distribution-based RandomVector
X = ot.RandomVector(distribution)
# We create a composite RandomVector Y from X and myFunction
Y = ot.RandomVector(myFunc, X)
# We create a quadraticCumul algorithm
algo = ot.TaylorExpansionMoments(Y)
# We test the attributes here
print('algo=', algo)
# We compute the several elements provided by the quadratic cumul algorithm
print('First order mean=', repr(algo.getMeanFirstOrder()))
print('Second order mean=', repr(algo.getMeanSecondOrder()))
print('Covariance=', repr(algo.getCovariance()))
print('Value at mean=', repr(algo.getValueAtMean()))
print('Gradient at mean=', repr(algo.getGradientAtMean()))
print('Hessian at mean=', repr(algo.getHessianAtMean()))
algo_1 = ot.TaylorExpansionMoments(Y.getMarginal(0))
print('Importance factors=', repr(algo_1.getImportanceFactors()))
