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#! /usr/bin/env python
import openturns as ot
import os
ot.TESTPREAMBLE()
# The function defining the level-set
inVars = ["x", "y"]
formula1 = ["x^4 + y^4"]
function1 = ot.SymbolicFunction(inVars, formula1)
levelSet1 = ot.LevelSet(function1, ot.LessOrEqual(), 1.0)
print("levelSet1=", levelSet1)
p0 = [-0.5, -0.5]
p1 = [0.5, 0.0]
p2 = [1.5, 0.0]
print("levelSet1 contains ", p0, "? ", p0 in levelSet1)
print("levelSet1 contains ", p1, "? ", p1 in levelSet1)
print("levelSet1 contains ", p2, "? ", p2 in levelSet1)
# Intersection
formula2 = ["(x-1)^2 + y^2"]
function2 = ot.SymbolicFunction(inVars, formula2)
levelSet2 = ot.LevelSet(function2, ot.LessOrEqual(), 1.0)
print("levelSet2=", levelSet2)
print("levelSet2 contains ", p0, "? ", levelSet2.contains(p0))
print("levelSet2 contains ", p1, "? ", levelSet2.contains(p1))
print("levelSet2 contains ", p2, "? ", levelSet2.contains(p2))
intersection = levelSet1.intersect(levelSet2)
print("intersection of ", levelSet1, " and ", levelSet2, " equals ", intersection)
print("intersection contains ", p0, "? ", intersection.contains(p0))
print("intersection contains ", p1, "? ", intersection.contains(p1))
print("intersection contains ", p2, "? ", intersection.contains(p2))
# Union
join = levelSet1.join(levelSet2)
print("join of ", levelSet1, " and ", levelSet2, " equals ", join)
print("join contains ", p0, "? ", join.contains(p0))
print("join contains ", p1, "? ", join.contains(p1))
print("join contains ", p2, "? ", join.contains(p2))
# check that f2 is not called when not needed
f1 = ot.SymbolicFunction(["x"], ["x"])
f2 = ot.MemoizeFunction(ot.SymbolicFunction(["x"], ["x/0"]))
f2.enableCache()
ls1 = ot.LevelSet(f1, ot.Less(), 0.0)
ls2 = ot.LevelSet(f2, ot.Less(), 0.0)
union = ls1.join(ls2)
intersection = ls1.intersect(ls2)
assert [-1.0] in union, "prune union"
assert f2.getCallsNumber() == 0, "union not pruned"
assert [1.0] not in intersection, "prune intersection"
assert f2.getCallsNumber() == 0, "intersection not pruned"
# save/load
if ot.PlatformInfo.HasFeature("libxml2"):
fname = "levelset.xml"
study = ot.Study(fname)
study.add("intersection", intersection)
study.save()
study = ot.Study(fname)
study.load()
intersection = ot.LevelSet()
study.fillObject("intersection", intersection)
os.remove(fname)
assert [1.0] not in intersection, "after save/load"
# check intersection/union at border
for op in ["Less", "Greater"]:
f1 = ot.SymbolicFunction(["x"], ["x"])
f2 = ot.SymbolicFunction(["x"], ["x"])
ls1 = ot.LevelSet(f1, eval(f"ot.{op}()"), 0.0)
ls2 = ot.LevelSet(f2, eval(f"ot.{op}()"), 0.0)
u1 = ls1.join(ls2)
i1 = ls1.intersect(ls2)
assert [0.0] not in i1, "!i1"
assert [0.0] not in u1, "!u1"
ls1 = ot.LevelSet(f1, eval(f"ot.{op}OrEqual()"), 0.0)
ls2 = ot.LevelSet(f2, eval(f"ot.{op}OrEqual()"), 0.0)
u2 = ls1.join(ls2)
i2 = ls1.intersect(ls2)
assert [0.0] in i2, "i2"
assert [0.0] in u2, "u2"
# check merge works
f1 = ot.SymbolicFunction(["x"], ["x"])
f2 = ot.SymbolicFunction(["x"], ["x+1"])
f3 = ot.SymbolicFunction(["x"], ["x+2"])
ls1 = ot.LevelSet(f1, ot.Less(), 0.0)
ls2 = ot.LevelSet(f2, ot.Less(), 0.0)
ls3 = ot.LevelSet(f3, ot.Less(), 0.0)
union = ls1.join(ls2).join(ls3)
intersection = ls1.intersect(ls2).intersect(ls3)
print("union x3", union)
print("intersection 3x", intersection)
x = [-3.0]
assert x in union, "union 3x"
assert x in intersection, "intersection 3x"
x = [3.0]
assert x not in union, "!union 3x"
assert x not in intersection, "!intersection 3x"
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