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#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
# First, compute the volume of the unit ball in R^n
a = -1.0
b = 1.0
formula = "1.0"
lower = list()
upper = list()
algo = ot.IteratedQuadrature(
ot.GaussKronrod(20, 1.0e-6, ot.GaussKronrodRule(ot.GaussKronrodRule.G3K7)))
for n in range(3):
inVars = ot.Description.BuildDefault(n + 1, "x")
inVarsBounds = inVars[0:n]
if (n > 0):
formula += "-" + inVars[n - 1] + "^2"
lower.append(
ot.NumericalMathFunction(inVarsBounds, ["-sqrt(" + formula + ")"]))
upper.append(
ot.NumericalMathFunction(inVarsBounds, ["sqrt(" + formula + ")"]))
integrand = ot.NumericalMathFunction(inVars, ["1.0"])
value = algo.integrate(integrand, a, b, lower, upper)[0]
print("dim=", n + 1, ", volume= %.12g" %
value, ", calls=", integrand.getCallsNumber())
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