#! /usr/bin/env python

import openturns as ot

# We create a Function
myFunc = ot.SymbolicFunction(
    ["x1", "x2", "x3", "x4"],
    ["(x1*x1+x2^3*x1)/(2*x3*x3+x4^4+1)", "cos(x2*x2+x4)/(x1*x1+1+x3^4)"],
)

# We create a distribution
dim = myFunc.getInputDimension()
meanPoint = [0.2] * dim
sigma = [0.0] * dim
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.CompositeRandomVector(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()))