def test_optimization():
class ExampleOS(ClassWithOptimizableVariables):
def __init__(self):
super(ExampleOS, self).__init__()
self.X = OptimizableVariable(name="X",
variable_type="variable",
value=3.0)
self.Y = OptimizableVariable(name="Y",
variable_type="variable",
value=20.0)
self.Z = OptimizableVariable(name="Z",
variable_type="pickup",
functionobject=(FunctionObject(
"f = lambda x, y: x**2 + y**2",
["f"]), "f"),
args=(self.X, self.Y))
def testmerit(s):
# let x, y being on a circle of radius 5
return (s.X()**2 + s.Y()**2 - 5.**2)**2
def testmerit2(s):
# let x**2 + y**2 + z**2 be minimized with
# the pickup constraint z = x**2 + y**2
return s.X()**2 + s.Y()**2 + s.Z()**2
os = ExampleOS()
optimi = Optimizer(os,
testmerit,
backend=ScipyBackend(method="Nelder-Mead",
options={
"maxiter": 1000,
"disp": False
},
name="scipybackend"),
name="optimizer")
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, 25.0)
optimi.meritfunction = testmerit2
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, os.Z())
optimi.backend = Newton1DBackend(dx=1e-6, iterations=500)
optimi.meritfunction = testmerit
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, 25.0)
optimi.meritfunction = testmerit2
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, os.Z())
def test_optimization():
class ExampleOS(ClassWithOptimizableVariables):
def __init__(self):
super(ExampleOS, self).__init__()
self.X = OptimizableVariable(name="X", status="Variable", value=3.0)
self.Y = OptimizableVariable(name="Y", status="Variable", value=20.0)
self.Z = OptimizableVariable(name="Z", status="Pickup", \
function=lambda x, y: x**2 + y**2, \
args=(self.X, self.Y))
def testmerit(s):
# let x, y being on a circle of radius 5
return (s.X()**2 + s.Y()**2 - 5.**2)**2
def testmerit2(s):
# let x**2 + y**2 + z**2 be minimized with the pickup constraint z = x**2 + y**2
return s.X()**2 + s.Y()**2 + s.Z()**2
os = ExampleOS()
optimi = Optimizer(os, testmerit, backend=ScipyBackend(method='Nelder-Mead', options={'maxiter':1000, 'disp':False}))
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, 25.0)
optimi.meritfunction = testmerit2
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, os.Z())
optimi.backend = Newton1DBackend(dx=1e-6, iterations=500)
optimi.meritfunction = testmerit
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, 25.0)
optimi.meritfunction = testmerit2
optimi.run()
assert np.isclose(os.X()**2 + os.Y()**2, os.Z())
Update coordinate systems of optical system.
"""
my_s.rootcoordinatesystem.update()
# optimize
s.elements["stdelem"].surfaces["lens4front"].shape.curvature.to_variable()
s.elements["stdelem"].surfaces["lens4rear"].shape.curvature.to_variable()
s.elements["stdelem"].surfaces["lens4rear"].shape.curvature.\
to_pickup((FunctionObject("f = lambda x: -x"), "f"),
(s.elements["stdelem"].surfaces["lens4front"].shape.curvature,))
listOptimizableVariables(s, max_line_width=80)
optimi = Optimizer(s, meritfunction_step2, backend=ScipyBackend(),
updatefunction=updatefunction_allsteps, name="step2")
optimi.meritparameters["initialbundle"] = initialbundle_step1
s = optimi.run()
# draw system with last lens biconvex
s.draw2d(axarr[1], color="grey", vertices=50, plane_normal=pn, up=up)
r2 = s.seqtrace(bundle_step1(nrays=9), seq) # trace again
for r in r2:
r.draw2d(axarr[1], color="blue", plane_normal=pn, up=up)
# Step 3: colour, field, more variables
########################################
def bundles_step3(nrays=100, rpup=7.5, maxfield_deg=2.):
T0 = 20.
if len(sys.argv) == 4:
(Nt, T0) = (int(sys.argv[2]), float(sys.argv[3]))
opt_backend = SimulatedAnnealingBackend(
Nt=Nt, Tt=T0 * np.exp(-np.linspace(0, 10, 20)))
elif first_arg == "n":
dx = 1e-6
iterations = 100
if len(sys.argv) == 4:
(dx, iterations) = (float(sys.argv[2]), int(sys.argv[3]))
opt_backend = Newton1DBackend(dx=dx, iterations=iterations)
# pylint3 E1130: false positive
optimi = Optimizer(s,
meritfunctionrms,
backend=opt_backend,
updatefunction=osupdate)
optimi.logger.setLevel(logging.DEBUG)
s = optimi.run()
r2 = s.seqtrace(initialbundle, sysseq) # trace again
for r in r2:
r.draw2d(ax2, color="blue", plane_normal=pn, up=up)
listOptimizableVariables(s, filter_status='variable', max_line_width=80)
s.draw2d(ax2, color="grey", vertices=50, plane_normal=pn, up=up) # try phi=0.
# s.draw2d(ax, color="grey", inyzplane=False, vertices=50, plane_normal=pn, up=up) # try for phi=pi/4
osa.aim(500, divbundledict, wave=wavelength)
def benchmark(OpticalSystem,meritfunctionrms,updatefunction,methods):
"""
methods: 2D-Liste der Form: methods = [[name,methodparam1,methodparam2,...],...]
i.e. methods = [["Powell","penalty","penalty-lagrange"],["Nelder-Mead","penalty"]]
Achtung: methods out of scipy need the " at the beginning and the end -> ["Powell","penalty",...
ouer own methods doesnt need this -> e.g. [test_minimize_neldermead,"penalty",...
meritfunction = meritfunction you want to use
updatefunction = updatefunction you want to use
For NlOpt you have to do:
pip install nlopt --no-clean
"""
# All for Scipy-Methods:---------------------------------------------------- """
# Create a list with ProjectScipyBackend-Objects for all Methods:
listOptBackend = []
for i in range(len(methods)):
for j in range(len(methods[i])-1):
listOptBackend.append(ProjectScipyBackend(optimize_func=methods[i][0], \
methodparam=methods[i][j+1], \
options={'maxiter':100, 'xatol':1e-10, \
'fatol':1e-10, 'gtol':1e-10, \
'disp':True}))
# create a list to safe results:
header = ["Verfahren", "Pen/Lag", "MeritFinal", "Time [s]", "fEval","Iter", "xFinal", "Bound ok?"]
Result = [[] for i in range(len(listOptBackend)+1)]
Result[0].append(header)
for i in range(len(listOptBackend)):
Result[i+1].append(listOptBackend[i].optimize_func)
if (listOptBackend[i].methodparam == "standard"):
Result[i+1].append("None")
elif (listOptBackend[i].methodparam == "penalty"):
Result[i+1].append("Penalty")
elif (listOptBackend[i].methodparam == "penalty-lagrange"):
Result[i+1].append("Pen + Lag")
elif (listOptBackend[i].methodparam == "log"):
Result[i+1].append("Barrier-Met.")
# loop over all methods:
counter1 = 1
for backend in listOptBackend:
OS = deepcopy(OpticalSystem) # copy of OS for every method
optimi = Optimizer(OS,
meritfunctionrms,
backend=backend,
updatefunction=updatefunction)
# Update constraints:
backend.update_PSB(optimi)
# is done in upadate_PSB
"""
# Update parameter "bounds":
# needed for scipy-algos: "L-BFGS-B","TNC","SLSQP","trust-constr"
lb = np.empty([len(backend.bdry)/2])
ub = np.empty([len(backend.bdry)/2])
for i in range (len(backend.bdry)/2):
lb[i] = backend.bdry[2*i]
ub[i] = backend.bdry[2*i+1]
bound = scipy.optimize.Bounds(lb,ub)
backend.kwargs['bounds'] = bound
"""
bdry = backend.kwargs['bounds']
# Update Jacobi-Matrix for case methodparam == 1:
# (the other cases are treated in "project_minimize_backends")
def jacobian(x):
h = np.sqrt(np.finfo(float).eps)
func = optimi.MeritFunctionWrapper
grad = np.empty([len(x)])
E = np.eye(len(x))
for i in range (len(x)):
grad[i] = (func(x+h*E[i,:])-func(x-h*E[i,:])) / (2*h)
return grad
#backend.kwargs['jac'] = jacobian
"""
# Functions for jacobian and hessian for scipy.minimize function:
def jacobian(x):
eps = np.sqrt(np.finfo(float).eps)
func=optimi.MeritFunctionWrapper
grad = np.ones(len(x))
for i in range(len(x)):
x_neu1 = deepcopy(x)
x_neu2 = deepcopy(x)
x_neu1[i] = x_neu1[i] + eps
x_neu2[i] = x_neu2[i] - eps
grad[i] = (func(x_neu1)-func(x_neu2))/(2*eps)
return grad
def hessian(x):
eps = np.sqrt(np.finfo(float).eps)
func = optimi.MeritFunctionWrapper
hes = np.ones((len(x),len(x)))
for i in range(len(x)):
for j in range(len(x)):
x_neu1 = deepcopy(x)
x_neu2 = deepcopy(x)
x_neu3 = deepcopy(x)
x_neu1[i] += eps
x_neu1[j] += eps
x_neu2[i] += eps
x_neu3[j] += eps
hes[i,j] = (func(x_neu1)-func(x_neu2)-func(x_neu3)+func(x)) / eps**2
return hes
#temp = {"jac": jacobian, "hess": hessian} # add to options of backend
#met.options.update(temp)
"""
# start optimization run and messure the time:
start = time.time()
OS = optimi.run()
ende = time.time()
# save results in list "Result":
Result[counter1].append(backend.res.fun) # save final merit
Result[counter1].append(ende-start) # save time
Result[counter1].append(optimi.NoC) # number of calls of merit func
if (backend.methodparam == "standard"): # number Iterations
Result[counter1].append(backend.res.nit) # actual i do not know the nit by penalty and lagrange -> set to -1
else:
Result[counter1].append(-1)
Result[counter1].append(backend.res.x) # final x-value
# check if xfinal fulfills boundaries:
check = 0
for k in range (len(backend.res.x)):
if (backend.res.x[k] >= bdry.lb[k] and backend.res.x[k] <= bdry.ub[k]):
check += 0
else:
check += 1
if (check >= 1):
Result[counter1].append("no")
else:
Result[counter1].append("yes")
# Increment counter
counter1 += 1
# print Result:
print("====================================================================================================================================================")
print("Benchmark:")
print("Bei den penalty-Methoden kenne ich die Gesamte Iterationszahl nicht -> hier ist iter aktuell auf -1")
print("")
#print header
print("%60s %10s %10s %10s %10s %10s %10s %10s" % (header[0],header[1], \
header[2],header[3], \
header[4],header[5],header[6],header[7]))
print(" -----------------------------------------------------------------------------------------------------------------------------------------------")
for i in range(len(Result)-1):
# print entries for every backend
print("%60s %10s %10.5f %10.3f %10d %10d %10.3f %10s\n" % (Result[i+1][0],Result[i+1][1],Result[i+1][2],Result[i+1][3],Result[i+1][4],Result[i+1][5], \
Result[i+1][6][0], \
Result[i+1][7]))
# loop over all entries of res.x (without res.x[0], cause already printed above)
for j in range(len(backend.res.x)-1):
print("%126.3f\n" % Result[i+1][6][j+1])
print("====================================================================================================================================================")
rpaths = my_s.seqtrace(initialbundle_local, sysseq)
# other constructions lead to fill up of initial bundle with intersection
# values
# for glassy asphere only one path necessary
x = rpaths[0].raybundles[-1].x[-1, 0, :]
y = rpaths[0].raybundles[-1].x[-1, 1, :]
res = np.sum(x**2 + y**2)
return res
backsurf = s.elements["stdelem"].surfaces["back"]
backsurf.shape.params["curv"].to_variable()
backsurf.shape.params["cc"].to_variable()
# A2 not variable
backsurf.shape.params["A4"].to_variable()
backsurf.shape.params["A6"].to_variable()
opt_backend = ScipyBackend(method='Nelder-Mead', tol=1e-9)
optimi = Optimizer(s,
meritfunctionrms,
opt_backend,
name="Nelder-Mead Optimizer")
s = optimi.run()
r2 = s.seqtrace(initialbundle, sysseq)
draw(s, r2)
x = rpaths[0].raybundles[-1].x[-1, 0, :]
y = rpaths[0].raybundles[-1].x[-1, 1, :]
res = np.sum(x**2 + y**2) + 10. * math.exp(-len(x))
return res
#opt_backend = ScipyBackend(method='Nelder-Mead', options={'maxiter':1000, 'disp':True}, tol=1e-8)
#opt_backend = Newton1DBackend(dx=1e-6, iterations=100)
#opt_backend = ParticleSwarmBackend(c1=2.2, c2=2.1)
opt_backend = SimulatedAnnealingBackend(Nt=30,
Tt=20. *
np.exp(-np.linspace(0, 10, 20)))
optimi = Optimizer(s, \
meritfunctionrms, \
backend=opt_backend, \
updatefunction=osupdate)
optimi.logger.setLevel(logging.DEBUG)
s = optimi.run()
r2 = s.seqtrace(initialbundle, sysseq) # trace again
for r in r2:
r.draw2d(ax2, color="blue", plane_normal=pn, up=up)
listOptimizableVariables(s, filter_status='variable', maxcol=80)
s.draw2d(ax2, color="grey", vertices=50, plane_normal=pn,
up=up) # try for phi=0.
#s.draw2d(ax, color="grey", inyzplane=False, vertices=50, plane_normal=pn, up=up) # try for phi=pi/4