def _chiSquare_old(model, parameters, data):
n_param = len(parameters)
chi_sq = 0.
alpha = N.zeros((n_param, n_param))
for point in data:
sigma = 1
if len(point) == 3:
sigma = point[2]
f = model(parameters, point[0])
chi_sq = chi_sq + ((f-point[1])/sigma)**2
d = N.array(f[1])/sigma
alpha = alpha + d[:,N.NewAxis]*d
return chi_sq, alpha
def _chiSquare_old(model, parameters, data):
n_param = len(parameters)
chi_sq = 0.
alpha = N.zeros((n_param, n_param))
for point in data:
sigma = 1
if len(point) == 3:
sigma = point[2]
f = model(parameters, point[0])
chi_sq = chi_sq + ((f - point[1]) / sigma)**2
d = N.array(f[1]) / sigma
alpha = alpha + d[:, N.NewAxis] * d
return chi_sq, alpha
def _chiSquare(model, parameters, data):
# assume: data is a nx3 numpy array.
n_param = len(parameters)
chi_sq = 0.
alpha = N.zeros((n_param, n_param))
flist=model(parameters, data[:,0])
if data.shape[1]<3:
silist=np.ones(data.shape[0])
else:
silist=data[:,2]
if data.shape[0]==1:
flist=[flist]
for i in range(data.shape[0]):
f=flist[i]
sigma=silist[i]
#print(type(f))
#print(type(data))
chi_sq = chi_sq + ((f-data[i,1])/sigma)**2
d = N.array(f[1])/sigma
alpha = alpha + d[:,N.NewAxis]*d
return chi_sq, alpha
def _chiSquare(model, parameters, data):
# assume: data is a nx3 numpy array.
n_param = len(parameters)
chi_sq = 0.
alpha = N.zeros((n_param, n_param))
flist = model(parameters, data[:, 0])
if data.shape[1] < 3:
silist = np.ones(data.shape[0])
else:
silist = data[:, 2]
if data.shape[0] == 1:
flist = [flist]
for i in range(data.shape[0]):
f = flist[i]
sigma = silist[i]
#print(type(f))
#print(type(data))
chi_sq = chi_sq + ((f - data[i, 1]) / sigma)**2
d = N.array(f[1]) / sigma
alpha = alpha + d[:, N.NewAxis] * d
return chi_sq, alpha
def leastSquaresFit(model, parameters, data, max_iterations=None,
stopping_limit = 0.005):
"""General non-linear least-squares fit using the
X{Levenberg-Marquardt} algorithm and X{automatic differentiation}.
@param model: the function to be fitted. It will be called
with two parameters: the first is a tuple containing all fit
parameters, and the second is the first element of a data point (see
below). The return value must be a number. Since automatic
differentiation is used to obtain the derivatives with respect to the
parameters, the function may only use the mathematical functions known
to the module FirstDerivatives.
@type model: callable
@param parameters: a tuple of initial values for the
fit parameters
@type parameters: C{tuple} of numbers
@param data: a list of data points to which the model
is to be fitted. Each data point is a tuple of length two or
three. Its first element specifies the independent variables
of the model. It is passed to the model function as its first
parameter, but not used in any other way. The second element
of each data point tuple is the number that the return value
of the model function is supposed to match as well as possible.
The third element (which defaults to 1.) is the statistical
variance of the data point, i.e. the inverse of its statistical
weight in the fitting procedure.
@type data: C{list}
@returns: a list containing the optimal parameter values
and the chi-squared value describing the quality of the fit
@rtype: C{(list, float)}
"""
n_param = len(parameters)
p = ()
i = 0
for param in parameters:
p = p + (DerivVar(param, i),)
i = i + 1
id = N.identity(n_param)
l = 0.001
chi_sq, alpha = _chiSquare(model, p, data)
niter = 0
while 1:
delta = LA.solve_linear_equations(alpha+l*N.diagonal(alpha)*id,
-0.5*N.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:
#raise IterationCountExceededError
print('Max iterations reach. Returning values.')
break
return [p[0] for p in next_p], next_chi_sq[0]
def leastSquaresFit(model,
parameters,
data,
max_iterations=None,
stopping_limit=0.005):
"""General non-linear least-squares fit using the
X{Levenberg-Marquardt} algorithm and X{automatic differentiation}.
@param model: the function to be fitted. It will be called
with two parameters: the first is a tuple containing all fit
parameters, and the second is the first element of a data point (see
below). The return value must be a number. Since automatic
differentiation is used to obtain the derivatives with respect to the
parameters, the function may only use the mathematical functions known
to the module FirstDerivatives.
@type model: callable
@param parameters: a tuple of initial values for the
fit parameters
@type parameters: C{tuple} of numbers
@param data: a list of data points to which the model
is to be fitted. Each data point is a tuple of length two or
three. Its first element specifies the independent variables
of the model. It is passed to the model function as its first
parameter, but not used in any other way. The second element
of each data point tuple is the number that the return value
of the model function is supposed to match as well as possible.
The third element (which defaults to 1.) is the statistical
variance of the data point, i.e. the inverse of its statistical
weight in the fitting procedure.
@type data: C{list}
@returns: a list containing the optimal parameter values
and the chi-squared value describing the quality of the fit
@rtype: C{(list, float)}
"""
n_param = len(parameters)
p = ()
i = 0
for param in parameters:
p = p + (DerivVar(param, i), )
i = i + 1
id = N.identity(n_param)
l = 0.001
chi_sq, alpha = _chiSquare(model, p, data)
niter = 0
while 1:
delta = LA.solve_linear_equations(alpha + l * N.diagonal(alpha) * id,
-0.5 * N.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:
#raise IterationCountExceededError
print('Max iterations reach. Returning values.')
break
return [p[0] for p in next_p], next_chi_sq[0]
