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#! /usr/bin/env python
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.SymbolicFunction(inVarsBounds, ["-sqrt(" + formula + ")"]))
upper.append(ot.SymbolicFunction(inVarsBounds, ["sqrt(" + formula + ")"]))
integrand = ot.SymbolicFunction(inVars, ["1.0"])
value = algo.integrate(integrand, a, b, lower, upper)[0]
print(
"dim=", n + 1, ", volume= %.12g" % value, ", calls=", integrand.getCallsNumber()
)
# Second, integrate a multi-valued function
bounds = ot.Interval([-1.0] * 3, [1.0] * 3)
vars = ["x0", "x1", "x2"]
formulas = ["x0^2 + 2*x1^2 + 3*x2^2", "x2^2 + 2*x1^2 + 3*x0^2"]
integrand = ot.SymbolicFunction(vars, formulas)
value = algo.integrate(integrand, bounds)
print("value=", value, ", calls=", integrand.getCallsNumber())
print("Algo is based on", algo.getAlgorithm())
algo.setAlgorithm(ot.GaussLegendre([10]))
print("Algo is now based on", algo.getAlgorithm())
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