def _leastSquaresFit(model, parameters, data, max_iterations=None, stopping_limit = 0.005):
"""General non-linear least-squares fit using the
Levenberg-Marquardt algorithm and automatic derivatives."""
n_param = len(parameters)
p = ()
i = 0
for param in parameters:
p = p + (_DerivVar(param, i),)
i = i + 1
id = num.identity(n_param)
l = 0.001
chi_sq, alpha = _chiSquare(model, p, data)
niter = 0
while 1:
delta = solveLinEq(alpha+l*num.diagonal(alpha)*id,-0.5*num.array(chi_sq[1]))
next_p = map(lambda a,b: a+b, p, delta)
next_chi_sq, next_alpha = _chiSquare(model, next_p, data)
if next_chi_sq > chi_sq:
l = 10.*l
else:
l = 0.1*l
if chi_sq[0] - next_chi_sq[0] < stopping_limit: break
p = next_p
chi_sq = next_chi_sq
alpha = next_alpha
niter = niter + 1
if max_iterations is not None and niter == max_iterations:
pass
return map(lambda p: p[0], next_p), next_chi_sq[0]
def _leastSquare(self, data, models, iterLimit=None, chiLimit=1e-3):
"""Least-square fitting. Adapted from the original code by Konrad Hinsen."""
normf = 100.0 / numpy.max(data)
data *= normf
params = [50.0] * len(models)
id = numpy.identity(len(params))
chisq, alpha = self._chiSquare(data, models, params)
l = 0.001
niter = 0
while True:
CHECK_FORCE_QUIT()
niter += 1
delta = solveLinEq(alpha + l * numpy.diagonal(alpha) * id,
-0.5 * numpy.array(chisq[1]))
next_params = list(map(lambda a, b: a + b, params, delta))
for x in range(len(next_params)):
if next_params[x] < 0.0:
next_params[x] = 0.0
next_chisq, next_alpha = self._chiSquare(data, models, next_params)
if next_chisq[0] > chisq[0]:
l = 5.0 * l
elif chisq[0] - next_chisq[0] < chiLimit:
break
else:
l = 0.5 * l
params = next_params
chisq = next_chisq
alpha = next_alpha
if iterLimit and niter == iterLimit:
break
next_params /= normf
return next_params
def _leastSquare(self, data, models, iterLimit=None, chiLimit=1e-3):
"""Least-square fitting. Adapted from the original code by Konrad Hinsen."""
normf = 100./numpy.max(data)
data *= normf
params = [50.] * len(models)
id = numpy.identity(len(params))
chisq, alpha = self._chiSquare(data, models, params)
l = 0.001
niter = 0
while True:
CHECK_FORCE_QUIT()
niter += 1
delta = solveLinEq(alpha+l*numpy.diagonal(alpha)*id,-0.5*numpy.array(chisq[1]))
next_params = map(lambda a,b: a+b, params, delta)
for x in range(len(next_params)):
if next_params[x] < 0.:
next_params[x] = 0.
next_chisq, next_alpha = self._chiSquare(data, models, next_params)
if next_chisq[0] > chisq[0]:
l = 5.*l
elif chisq[0] - next_chisq[0] < chiLimit:
break
else:
l = 0.5*l
params = next_params
chisq = next_chisq
alpha = next_alpha
if iterLimit and niter == iterLimit:
break
next_params /= normf
return next_params
def _leastSquaresFit(model, parameters, data, maxIterations=None, limit=1e-7):
"""General non-linear least-squares fit using the
Levenberg-Marquardt algorithm and automatic derivatives.
Originally developed by Konrad Hinsen.
"""
n_param = len(parameters)
p = ()
i = 0
for param in parameters:
p = p + (_DerivVar(param, i),)
i = i + 1
id = numpy.identity(n_param)
l = 0.001
chi_sq, alpha = _chiSquare(model, p, data)
niter = 0
while True:
niter += 1
delta = solveLinEq(
alpha + l * numpy.diagonal(alpha) * id, -0.5 * numpy.array(chi_sq[1])
)
next_p = list(map(lambda a, b: a + b, p, delta))
next_chi_sq, next_alpha = _chiSquare(model, next_p, data)
if next_chi_sq > chi_sq:
l = 10.0 * l
elif chi_sq[0] - next_chi_sq[0] < limit:
break
else:
l = 0.1 * l
p = next_p
chi_sq = next_chi_sq
alpha = next_alpha
if maxIterations and niter == maxIterations:
break
return [p[0] for p in next_p], next_chi_sq[0]
def _leastSquaresFit(model, parameters, data, maxIterations=None, limit=1e-7):
"""General non-linear least-squares fit using the
Levenberg-Marquardt algorithm and automatic derivatives.
Originally developed by Konrad Hinsen.
"""
n_param = len(parameters)
p = ()
i = 0
for param in parameters:
p = p + (_DerivVar(param, i),)
i = i + 1
id = numpy.identity(n_param)
l = 0.001
chi_sq, alpha = _chiSquare(model, p, data)
niter = 0
while True:
niter += 1
delta = solveLinEq(alpha + l * numpy.diagonal(alpha) * id, -0.5 * numpy.array(chi_sq[1]))
next_p = map(lambda a, b: a + b, p, delta)
next_chi_sq, next_alpha = _chiSquare(model, next_p, data)
if next_chi_sq > chi_sq:
l = 10.0 * l
elif chi_sq[0] - next_chi_sq[0] < limit:
break
else:
l = 0.1 * l
p = next_p
chi_sq = next_chi_sq
alpha = next_alpha
if maxIterations and niter == maxIterations:
break
return map(lambda p: p[0], next_p), next_chi_sq[0]