def fit(self):
"""
Run problem with DFO.
"""
if self.minimizer == 'dfogn':
self._soln = dfogn.solve(self.problem.eval_r, self._pinit)
elif self.minimizer == 'dfols':
self._soln = dfols.solve(self.problem.eval_r, self._pinit)
self._popt = self._soln.x
self._status = self._soln.flag
def fit(self):
"""
Run problem with DFO-GN.
"""
self.success = False
self._soln = dfogn.solve(self._prediction_error, self._pinit)
if (self._soln.flag == 0):
self.success = True
self._popt = self._soln.x
def runTest(self):
# n, m = 2, 2
x0 = np.array([-1.2, 1.0])
soln = dfogn.solve(rosenbrock, x0)
self.assertTrue(
array_compare(soln.x, np.array([1.0, 1.0]), thresh=1e-4),
"Wrong xmin")
self.assertTrue(
array_compare(soln.resid, rosenbrock(soln.x), thresh=1e-10),
"Wrong resid")
self.assertTrue(
array_compare(soln.jacobian,
rosenbrock_jacobian(soln.x),
thresh=2e-2), "Wrong Jacobian")
self.assertTrue(abs(soln.f) < 1e-10, "Wrong fmin")
def runTest(self):
n, m = 2, 5
np.random.seed(0) # (fixing random seed)
A = np.random.rand(m, n)
b = np.random.rand(m)
objfun = lambda x: np.dot(A, x) - b
xmin = np.linalg.lstsq(A, b)[0]
fmin = np.dot(objfun(xmin), objfun(xmin))
x0 = np.zeros((n, ))
soln = dfogn.solve(objfun, x0)
self.assertTrue(array_compare(soln.x, xmin, thresh=1e-2), "Wrong xmin")
self.assertTrue(
array_compare(soln.resid, objfun(soln.x), thresh=1e-10),
"Wrong resid")
self.assertTrue(array_compare(soln.jacobian, A, thresh=1e-2),
"Wrong Jacobian")
self.assertTrue(abs(soln.f - fmin) < 1e-4, "Wrong fmin")
def runTest(self):
# n, m = 2, 2
x0 = np.array([-1.2,
0.7]) # standard start point too close to upper bounds
lower = np.array([-2.0, -2.0])
upper = np.array([0.9, 0.9])
xmin = np.array([0.9, 0.81]) # approximate
fmin = np.dot(rosenbrock(xmin), rosenbrock(xmin))
soln = dfogn.solve(rosenbrock, x0, lower=lower, upper=upper)
print(soln.x)
self.assertTrue(array_compare(soln.x, xmin, thresh=1e-2), "Wrong xmin")
self.assertTrue(
array_compare(soln.resid, rosenbrock(soln.x), thresh=1e-10),
"Wrong resid")
self.assertTrue(
array_compare(soln.jacobian,
rosenbrock_jacobian(soln.x),
thresh=1e-2), "Wrong Jacobian")
self.assertTrue(abs(soln.f - fmin) < 1e-4, "Wrong fmin")
def do_parameter_fit(x0, datas, lsq_solver, model_solver, LARGE_V=50):
"""
Function to fit parameters given a starting point and datas.
Choice of which optimisation algorithm and which model to use.
"""
def prediction_error(x,
show_plots=True,
show_stars=True,
save_plot_data=False):
"""
Compare model to data and return array of differences
"""
# Rescale x
x = lower + (upper - lower) * x
# Initial SOCs
q0s = np.append([1], x[4:])
# Prepare dict
modelVs = {}
for i, name in enumerate(datas.keys()):
data = datas[name]
# Make dict of fitting parameters from x
pars = {
"epsnmax": x[0],
"epssmax": x[1],
"epspmax": x[0],
"cmax": 5.65,
"jref_n": x[2],
"jref_p": x[2] / 10,
"qinit": q0s[i],
}
# Shape preserving interpolation of current: do the hard work offline
interpclass = interp.PchipInterpolator(data["time"],
data["current"])
def Icircuit(t):
return interpclass(t)
# Load parameters
pars = Parameters(fit=pars,
Icircuit=Icircuit,
Ibar=np.max(Icircuit(data["time"])))
# Nondimensionalise time
t = data["time"] / pars.scales.time
# Run model
model = model_solver(t, pars, grid, Vonly=True)
model.dimensionalise(pars, grid)
# Take away resistance of the wires
model.Vcircuit -= x[3] * data["current"][:, np.newaxis]
# Remove NaNs
model.Vcircuit[np.isnan(model.Vcircuit)] = LARGE_V
# Store voltages
modelVs[name] = model.Vcircuit
# Plot data vs model
if show_plots:
plt.ion()
fig = plt.figure(1)
plt.clf()
for i, name in enumerate(datas.keys()):
plt.plot(
datas[name]["time"],
datas[name]["voltage"],
"o",
markersize=1,
color="C" + str(i),
)
plt.plot(datas[name]["time"],
modelVs[name],
color="C" + str(i),
label=name)
# plt.title('params={}'.format(x))
plt.xlabel("Time [h]")
plt.ylabel("Voltage [V]")
legend = plt.legend()
fig.canvas.flush_events()
time.sleep(0.01)
# Make vector of differences (including weights)
diffs = np.concatenate([
(data["voltage"] - modelVs[name][:, 0]) * data["weights"]
for name, data in datas.items()
])
# Show progress
# if show_stars:
# plt.figure(2)
# plt.plot(x, np.dot(diffs, diffs), 'rx')
# plt.pause(.01)
# Save plot data
if save_plot_data:
# Set linestyles
linestyles = {
"3A": "",
"2.5A": "",
"2A": "",
"1.5A": "",
"1A": "",
"0.5A": "",
}
with open(
"out/plot_calls/fits/{}_{}.txt".format(
lsq_solver, model_solver.__name__),
"w",
) as fit_plot_calls:
# Save data and model from each current
for i, name in enumerate(datas.keys()):
save_data(
"fits/{}/{}/{}_model".format(lsq_solver,
model_solver.__name__,
name),
datas[name]["time"],
modelVs[name],
fit_plot_calls,
linestyles[name],
n_coarse_points=100,
)
save_data(
"fits/{}/{}/{}_data".format(lsq_solver,
model_solver.__name__,
name),
datas[name]["time"],
datas[name]["voltage"],
fit_plot_calls,
linestyles[name],
n_coarse_points=100,
)
# Add legend (two commas to ignore the data entries)
fit_plot_calls.write(
("\\legend{{{!s}" + ", ,{!s}" * (len(datas.keys()) - 1) +
"}}\n").format(*tuple(datas.keys())))
return diffs
# Compute grid (doesn't depend on base parameters)
grid = Grid(10)
fit_currents = datas.keys()
# Set the bounds
lower = np.concatenate(
[np.array([0.0, 0.0, 0.01, 0.0]),
np.zeros(len(datas) - 1)])
upper = np.concatenate(
[np.array([1.0, 1.0, 1.0, 1.0]),
np.ones(len(datas) - 1)])
# Rescale x0 so that all fitting parameters go from 0 to 1
x0 = (x0 - lower) / (upper - lower)
# errs = np.array([])
# js = np.linspace(0.01,1,10)
# for j in js:
# diffs = prediction_error(j, show_plots=True, show_stars=False)
# errs = np.append(errs, np.dot(diffs, diffs))
# plt.figure(2)
# plt.plot(js, errs)
# plt.pause(0.01)
# Do curve fitting
print("Fit using {} on the {} model".format(lsq_solver,
model_solver.__name__))
print("-" * 60)
if lsq_solver in ["dfogn", "dfols"]:
# Set logging to INFO to view progress
logging.basicConfig(level=logging.INFO, format="%(message)s")
# Call and time DFO-GN or DFO-LS
start = time.time()
if lsq_solver == "dfogn":
soln = dfogn.solve(
prediction_error,
x0,
lower=np.zeros(len(x0)),
upper=np.ones(len(x0)),
rhoend=1e-5,
)
elif lsq_solver == "dfols":
soln = dfols.solve(
prediction_error,
x0,
bounds=(np.zeros(len(x0)), np.ones(len(x0))),
rhoend=1e-5,
)
soln_time = time.time() - start
# Scale x back to original scale
x = lower + (upper - lower) * soln.x
# Display output
print(" *** DFO-GN results *** ")
print("Solution xmin = %s" % str(x))
print("Objective value f(xmin) = %.10g" % soln.f)
print("Needed %g objective evaluations" % soln.nf)
print("Exit flag = %g" % soln.flag)
print(soln.msg)
# Save solution parameters
# save_output = {'y': True, 'n': False}[input('Save fitted params? (y/n): ')]
# if save_output:
# filename = "out/fits/dfogn_{}.txt".format(model_solver.__name__)
# np.savetxt(filename, lower+(upper-lower)*soln.x)
return (x, soln.f, soln_time)
elif lsq_solver == "scipy":
# Call and time scipy least squares
start = time.time()
soln = opt.least_squares(
prediction_error,
x0,
bounds=(np.zeros(len(x0)), np.ones(len(x0))),
method="trf",
jac="2-point",
diff_step=1e-5,
ftol=1e-4,
verbose=2,
)
soln_time = time.time() - start
# Scale x back to original scale
x = lower + (upper - lower) * soln.x
# Display output
print(" *** SciPy results *** ")
print("Solution xmin = %s" % str(x))
print("Objective value f(xmin) = %.10g" % (soln.cost * 2))
print("Needed %g objective evaluations" % soln.nfev)
print("Exit flag = %g" % soln.status)
print(soln.message)
# Save solution parameters
# save_output = {'y': True, 'n': False}[input('Save fitted params? (y/n): ')]
# if save_output:
# filename = "out/fits/scipy_{}.txt".format(model_solver.__name__)
# np.savetxt(filename, x)
return (x, soln.cost * 2, soln_time)
elif lsq_solver is None:
# Do nothing
diffs = prediction_error(x0)
return (x0, np.dot(diffs, diffs), 0)
# save plots (hacky!)
prediction_error(x, save_plot_data=True)
def rosenbrock_noisy(x):
return rosenbrock(x) * (1.0 + 1e-2 * np.random.normal(size=(2, )))
# Define the starting point
x0 = np.array([-1.2, 1.0])
np.random.seed(0)
print("Demonstrate noise in function evaluation:")
for i in range(5):
print("objfun(x0) = %s" % str(rosenbrock_noisy(x0)))
print("")
soln = dfogn.solve(rosenbrock_noisy, x0)
# Display output
print(" *** DFO-GN results *** ")
print("Solution xmin = %s" % str(soln.x))
print("Objective value f(xmin) = %.10g" % soln.f)
print("Needed %g objective evaluations" % soln.nf)
print("Residual vector = %s" % str(soln.resid))
print("Approximate Jacobian = %s" % str(soln.jacobian))
print("Exit flag = %g" % soln.flag)
print(soln.msg)
# Compare with a derivative-based solver
import scipy.optimize as opt
soln = opt.least_squares(rosenbrock_noisy, x0)
# http://support.sas.com/documentation/cdl/en/imlug/66112/HTML/default/viewer.htm#imlug_genstatexpls_sect004.htm
from __future__ import print_function
import math
import numpy as np
import dfogn
# Want to solve:
# x1 + x2 - x1*x2 + 2 = 0
# x1 * exp(-x2) - 1 = 0
def nonlinear_system(x):
return np.array(
[x[0] + x[1] - x[0] * x[1] + 2, x[0] * math.exp(-x[1]) - 1.0])
# Warning: if there are multiple solutions, which one
# DFO-GN returns will likely depend on x0!
x0 = np.array([0.1, -2.0])
soln = dfogn.solve(nonlinear_system, x0)
# Display output
print(" *** DFO-GN results *** ")
print("Solution xmin = %s" % str(soln.x))
print("Objective value f(xmin) = %.10g" % soln.f)
print("Needed %g objective evaluations" % soln.nf)
print("Residual vector = %s" % str(soln.resid))
print("Exit flag = %g" % soln.flag)
print(soln.msg)
# DFO-GN example: minimize the Rosenbrock function (with bounds)
from __future__ import print_function
import numpy as np
import dfogn
# Define the objective function
def rosenbrock(x):
return np.array([10.0 * (x[1] - x[0] ** 2), 1.0 - x[0]])
# Define the starting point
x0 = np.array([-1.2, 1.0])
# Define optional bound constraints (a <= x <= b)
a = np.array([-10.0, -10.0])
b = np.array([0.9, 0.85])
soln = dfogn.solve(rosenbrock, x0, lower=a, upper=b)
# Display output
print(" *** DFO-GN results *** ")
print("Solution xmin = %s" % str(soln.x))
print("Objective value f(xmin) = %.10g" % soln.f)
print("Needed %g objective evaluations" % soln.nf)
print("Residual vector = %s" % str(soln.resid))
print("Approximate Jacobian = %s" % str(soln.jacobian))
print("Exit flag = %g" % soln.flag)
print(soln.msg)
# DFO-GN example: minimize the Rosenbrock function
from __future__ import print_function
import numpy as np
import dfogn
# Define the objective function
def rosenbrock(x):
return np.array([10.0 * (x[1] - x[0]**2), 1.0 - x[0]])
# Define the starting point
x0 = np.array([-1.2, 1.0])
# For optional extra output details
# import logging
# logging.basicConfig(level=logging.INFO, format='%(message)s')
soln = dfogn.solve(rosenbrock, x0)
# Display output
print(" *** DFO-GN results *** ")
print("Solution xmin = %s" % str(soln.x))
print("Objective value f(xmin) = %.10g" % soln.f)
print("Needed %g objective evaluations" % soln.nf)
print("Residual vector = %s" % str(soln.resid))
print("Approximate Jacobian = %s" % str(soln.jacobian))
print("Exit flag = %g" % soln.flag)
print(soln.msg)
# Data fitting example
# https://uk.mathworks.com/help/optim/ug/lsqcurvefit.html#examples
from __future__ import print_function
import numpy as np
import dfogn
tdata = np.array([0.9, 1.5, 13.8, 19.8, 24.1, 28.2, 35.2, 60.3, 74.6, 81.3])
ydata = np.array(
[455.2, 428.6, 124.1, 67.3, 43.2, 28.1, 13.1, -0.4, -1.3, -1.5])
def prediction_error(x):
return ydata - x[0] * np.exp(x[1] * tdata)
x0 = np.array([100.0, -1.0])
upper = np.array([1e20, 0.0])
soln = dfogn.solve(prediction_error, x0, upper=upper)
# Display output
print(" *** DFO-GN results *** ")
print("Solution xmin = %s" % str(soln.x))
print("Objective value f(xmin) = %.10g" % soln.f)
print("Needed %g objective evaluations" % soln.nf)
print("Exit flag = %g" % soln.flag)
print(soln.msg)