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#! /usr/bin/env python
import openturns as ot
import math
ot.TESTPREAMBLE()
# First, a smooth function
f = ot.SymbolicFunction("x", "sin(x)")
a = -2.5
b = 4.5
# Default parameters
algo = ot.GaussKronrod()
rules = ot.GaussKronrod.GetRules()
for i in range(len(rules)):
algo.setRule(rules[i])
print("Algo=", algo)
# High-level interface
error = ot.Point()
value = algo.integrate(f, ot.Interval(a, b), error)[0]
ref = math.cos(a) - math.cos(b)
print(
"value=%.6f" % value,
", ref=%.6f" % ref,
", true error below bound? ",
abs(ref - value) < algo.getMaximumError(),
", estimated error below bound? ",
error[0] < algo.getMaximumError(),
)
# Low-level interface
# ai = Point()
# bi = Point()
# fi = Sample()
# ei = Point()
# value2 = algo.integrate(f, a, b, error, ai, bi, fi, ei)[0]
# ai.add(b)
# g = f.draw(a, b, 512)
# lower = Cloud(ai, Point(ai.getDimension()))
# lower.setColor("magenta")
# g.add(lower)
# Second, a piecewise smooth function
f = ot.SymbolicFunction("x", "abs(sin(x))")
a = -2.5
b = 4.5
algo = ot.GaussKronrod()
rules = ot.GaussKronrod.GetRules()
rules[0] = ot.GaussKronrod.GetRuleFromName("G3K7")
for i in range(len(rules)):
algo.setRule(rules[i])
print("Algo=", algo)
error = ot.Point()
value = algo.integrate(f, ot.Interval(a, b), error)[0]
ref = 4.0 + math.cos(b) - math.cos(a)
print(
"value=%.6f" % value,
", ref=%.6f" % ref,
", true error below bound? ",
abs(ref - value) < algo.getMaximumError(),
", estimated error below bound? ",
error[0] < algo.getMaximumError(),
)
# Low-level interface
# ai = Point()
# bi = Point()
# fi = Sample()
# ei = Point()
# value2 = algo.integrate(f, a, b, error, ai, bi, fi, ei)[0]
# print "ai=", ai
# print "bi=", bi
# print "fi=", fi
# print "ei=", ei
# ai.add(b)
# g = f.draw(a, b, 512)
# lower = Cloud(ai, Point(ai.getDimension()))
# lower.setColor("magenta")
# g.add(lower)
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