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#! /usr/bin/env python
import openturns as ot
import math as m
ot.TESTPREAMBLE()
def printPoint(point, digits):
oss = "["
eps = pow(0.1, digits)
format = "%." + str(digits) + "f"
for i in range(point.getDimension()):
if i == 0:
sep = ""
else:
sep = ","
if m.fabs(point[i]) < eps:
oss += sep + format % m.fabs(point[i])
else:
oss += sep + format % point[i]
sep = ","
oss += "]"
return oss
# linear
levelFunction = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["x1+2*x2-3*x3+4*x4"])
startingPoint = ot.Point(4, 0.0)
algo = ot.Cobyla(ot.NearestPointProblem(levelFunction, 3.0))
algo.setStartingPoint(startingPoint)
print("algo=", algo)
algo.run()
result = algo.getResult()
print("x^=", printPoint(result.getOptimalPoint(), 4))
print("f(x^)=", printPoint(result.getOptimalValue(), 4))
print("lambda^=", printPoint(result.computeLagrangeMultipliers(), 4))
# non-linear
levelFunction = ot.SymbolicFunction(
["x1", "x2", "x3", "x4"], ["x1*cos(x1)+2*x2*x3-3*x3+4*x3*x4"]
)
startingPoint = ot.Point(4, 0.0)
algo = ot.Cobyla(ot.NearestPointProblem(levelFunction, 3.0))
algo.setStartingPoint(startingPoint)
algo.setMaximumCallsNumber(400)
algo.setMaximumAbsoluteError(1.0e-10)
algo.setMaximumRelativeError(1.0e-10)
algo.setMaximumResidualError(1.0e-10)
algo.setMaximumConstraintError(1.0e-10)
algo.run()
result = algo.getResult()
print("x^=", printPoint(result.getOptimalPoint(), 4))
print("f(x^)=", printPoint(result.getOptimalValue(), 4))
print("lambda^=", printPoint(result.computeLagrangeMultipliers(), 4))
# bounds
linear = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["x1+2*x2-3*x3+4*x4"])
dim = 4
startingPoint = [0.0] * dim
bounds = ot.Interval([-3.0] * dim, [5.0] * dim)
for minimization in [True, False]:
problem = ot.OptimizationProblem(linear, ot.Function(), ot.Function(), bounds)
problem.setMinimization(minimization)
algo = ot.Cobyla(problem)
algo.setMaximumCallsNumber(150)
algo.setStartingPoint(startingPoint)
print("algo=", algo)
algo.run()
result = algo.getResult()
print("x^=", printPoint(result.getOptimalPoint(), 4))
print("f(x^)=", printPoint(result.getOptimalValue(), 4))
print("lambda^=", printPoint(result.computeLagrangeMultipliers(), 4))
# empty problem
algo = ot.Cobyla()
try:
algo.run()
except Exception:
print("OK")
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