# Define residual functions
def residualFunction(params):
modelx = ot.ParametricFunction(model, [0, 1, 2], params)
return [modelx(x[i])[0] - y[i, 0] for i in range(m)]
def residualFunctionNoise(params):
modelx = ot.ParametricFunction(model, [0, 1, 2], params)
return [modelx(x[i])[0] - ynoise[i, 0] for i in range(m)]
# Definition of residual as ot.PythonFunction and optimization problem
residual = ot.PythonFunction(n, m, residualFunction)
residualNoise = ot.PythonFunction(n, m, residualFunctionNoise)
lsqProblem = ot.LeastSquaresProblem(residual)
lsqNoiseProblem = ot.LeastSquaresProblem(residualNoise)
startingPoint = [0.0, 0.0, 0.0]
### LSQ SOLVER
# Definition of Dlib solver, setting starting point
lsqAlgo = ot.Dlib(lsqProblem, "LSQ")
lsqAlgo.setStartingPoint(startingPoint)
lsqAlgo.run()
# Retrieving results
lsqResult = lsqAlgo.getResult()
printResults(lsqResult, "LSQ (without noise)")
# Same with noise
modelx = ot.ParametricFunction(model, [0, 1, 2], p)
return [modelx(x[i])[0] - y[i, 0] for i in range(m)]
residualFunction = ot.PythonFunction(n, m, residualFunction_py)
bounds = ot.Interval([0, 0, 0], [2.5, 8.0, 19])
for algoName in algoNames:
line_search = not (algoName in ['LEVENBERG_MARQUARDT', 'DOGLEG'])
for bound in [True, False]:
if bound and line_search:
# line search do not support bound constraints
continue
print('algoName=', algoName, 'bound=', bound)
problem = ot.LeastSquaresProblem(residualFunction)
if bound:
problem.setBounds(bounds)
startingPoint = [1.0] * n
algo = ot.Ceres(problem, algoName)
algo.setStartingPoint(startingPoint)
# algo.setProgressCallback(progress)
# algo.setStopCallback(stop)
algo.run()
result = algo.getResult()
x_star = result.getOptimalPoint()
print(result)
if bound:
assert x_star in bounds, "optimal point not in bounds"
else:
if not line_search:
p_ref = [2.8, 1.2, 0.5] # Reference a, b, c
modelx = ot.ParametricFunction(model, [0, 1, 2], p_ref)
# Generate reference sample (with normal noise)
y = np.multiply(modelx(x), np.random.normal(1.0, 0.05, m))
def residualFunction(params):
modelx = ot.ParametricFunction(model, [0, 1, 2], params)
return [modelx(x[i])[0] - y[i, 0] for i in range(m)]
# %%
# Definition of residual as ot.PythonFunction and optimization problem
residual = ot.PythonFunction(n, m, residualFunction)
lsqProblem = ot.LeastSquaresProblem(residual)
# %%
# Definition of Dlib solver, setting starting point
lsqAlgo = ot.Dlib(lsqProblem, "least_squares")
lsqAlgo.setStartingPoint([0.0, 0.0, 0.0])
lsqAlgo.run()
# %%
# Retrieve results
result = lsqAlgo.getResult()
print('x^ = ', result.getOptimalPoint())
print("f(x^) = ", result.getOptimalValue())
print("Iteration number: ", result.getIterationNumber())
print("Evaluation number: ", result.getEvaluationNumber())
