import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
# Create the mesher
mesher = ot.LevelSetMesher([50] * 2)
# Create a level set
function = ot.SymbolicFunction(['x0', 'x1'], ['10*(x0^3+x1)^2+x0^2'])
level = 0.5
set = ot.LevelSet(function, level)
# Mesh the level set
mesh = mesher.build(set, ot.Interval([-1.0] * 2, [1.0] * 2))
# Draw the first mesh
graph = mesh.draw()
graph.setXTitle('$x_0$')
graph.setYTitle('$x_1$')
fig = plt.figure(figsize=(10, 4))
plt.suptitle('Mesh of a level set')
graph_axis = fig.add_subplot(111)
graph_axis.set_xlim(auto=True)
View(graph, figure=fig, axes=[graph_axis], add_legend=True)
ot.ResourceMap.SetAsUnsignedInteger(
"OptimizationAlgorithm-DefaultMaximumIterationNumber", 1000)
ot.ResourceMap.SetAsUnsignedInteger(
"OptimizationAlgorithm-DefaultMaximumEvaluationNumber", 100000)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumAbsoluteError", 1.0e-7)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumRelativeError", 1.0e-7)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumResidualError", 1.0e-7)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumConstraintError", 1.0e-7)
ot.PlatformInfo.SetNumericalPrecision(2)
# The 1D mesher
mesher1D = ot.LevelSetMesher([7])
print("mesher1D=", mesher1D)
level = 0.5
function1D = ot.SymbolicFunction("x", "cos(x)/(1+0.1*x^2)")
levelSet1D = ot.LevelSet(function1D, ot.LessOrEqual(), level)
# Manual bounding box
mesh1D = mesher1D.build(levelSet1D, ot.Interval(-10.0, 10.0))
print("mesh1D=", mesh1D)
# The 2D mesher
mesher2D = ot.LevelSetMesher([5] * 2)
print("mesher2D=", mesher2D)
function2D = ot.SymbolicFunction(
points = [[1.0, 0.0, -1.0 / sqrt(2.0)], [-1.0, 0.0, -1.0 / sqrt(2.0)],
[0.0, 1.0, 1.0 / sqrt(2.0)], [0.0, -1.0, 1.0 / sqrt(2.0)]]
formula = ""
for i in range(len(points)):
if (i > 0):
formula += " + "
formula += "1.0/(" + buildFormula(points[i], i) + ")"
print(formula)
f = ot.SymbolicFunction(["x0", "x1", "x2"], ["-(" + formula + ")"])
ls = ot.LevelSet(f, level)
print("build mesh")
t0 = time()
mesh1 = ot.LevelSetMesher([N] * 3).build(ls, ot.Interval([-2.5] * 3,
[2.5] * 3), False,
True)
print("t (mesh1)=", time() - t0, "s")
mesh2 = ot.LevelSetMesher([3 * N] * 3).build(
ls, ot.Interval([-2.5] * 3, [2.5] * 3), True, True)
print("t (mesh1+mesh2)=", time() - t0, "s")
print("mesh1=", mesh1.getVerticesNumber(), "vertices and",
mesh1.getSimplicesNumber(), "simplices")
print("mesh2=", mesh2.getVerticesNumber(), "vertices and",
mesh2.getSimplicesNumber(), "simplices")
print("draw mesh")
t0 = time()
graph = mesh1.draw3D(True, pi / 16, 0, pi / 4, False, 1.0)
mesh2.setVertices(mesh2.getVertices() + ot.Point([-4.0, 0.0, 0.0]))
ot.ResourceMap.SetAsScalar("Mesh-AmbientFactor", 0.1)
ot.ResourceMap.SetAsScalar("Mesh-DiffuseFactor", 0.6)
N = 100
threshold = 1.0e-3
# Create a domain
f = ot.SymbolicFunction(
["x0", "x1"], ["1.0 - (1.2 + cos(_pi * x0))^2 - (1.2 + cos(_pi * x1))^2"])
level = 0.0
domain = ot.LevelSet(f, level)
interval = ot.Interval([-A] * 2, [A] * 2)
domain.setLowerBound(interval.getLowerBound())
domain.setUpperBound(interval.getUpperBound())
# Create the mesh
# To have a more symmetric mesh
ot.ResourceMap.SetAsBool("IntervalMesher-UseDiamond", True)
discretization = [N] * 2
mesh = ot.LevelSetMesher(discretization).build(domain, interval)
print("vertices=", mesh.getVerticesNumber())
# Second, a model with functional output
class FUNC(ot.OpenTURNSPythonFunction):
def __init__(self, mesh, KLResult):
super(FUNC, self).__init__(KLResult.getEigenValues().getSize(),
mesh.getVerticesNumber())
self.mesh_ = mesh
self.KLResult_ = KLResult
self.nc_ = 0
def _exec(self, X):
self.nc_ += 1
print("nc=", self.nc_)
ot.ResourceMap.SetAsUnsignedInteger(
"OptimizationAlgorithm-DefaultMaximumIteration", 1000)
ot.ResourceMap.SetAsUnsignedInteger(
"OptimizationAlgorithm-DefaultMaximumEvaluationNumber", 100000)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumAbsoluteError", 1.0e-7)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumRelativeError", 1.0e-7)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumResidualError", 1.0e-7)
ot.ResourceMap.SetAsScalar(
"OptimizationAlgorithm-DefaultMaximumConstraintError", 1.0e-7)
ot.PlatformInfo.SetNumericalPrecision(2)
# The 1D mesher
mesher1D = ot.LevelSetMesher([7])
print("mesher1D=", mesher1D)
level = 0.5
function1D = ot.SymbolicFunction("x", "cos(x)/(1+0.1*x^2)")
levelSet1D = ot.LevelSet(function1D, level)
# Automatic bounding box
mesh1D = mesher1D.build(levelSet1D)
print("mesh1D=", mesh1D)
# Manual bounding box
mesh1D = mesher1D.build(levelSet1D, ot.Interval(-10.0, 10.0))
print("mesh1D=", mesh1D)
# The 2D mesher