was used only for yield surface fitting
This commit is contained in:
parent
1fcbc35611
commit
d1fa2a14dc
|
@ -221,263 +221,6 @@ class return_message():
|
||||||
return srepr(self.message)
|
return srepr(self.message)
|
||||||
|
|
||||||
|
|
||||||
def leastsqBound(func, x0, args=(), bounds=None, Dfun=None, full_output=0,
|
|
||||||
col_deriv=0, ftol=1.49012e-8, xtol=1.49012e-8,
|
|
||||||
gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None):
|
|
||||||
from scipy.optimize import _minpack
|
|
||||||
"""
|
|
||||||
Non-linear least square fitting (Levenberg-Marquardt method) with
|
|
||||||
bounded parameters.
|
|
||||||
the codes of transformation between int <-> ext refers to the work of
|
|
||||||
Jonathan J. Helmus: https://github.com/jjhelmus/leastsqbound-scipy
|
|
||||||
other codes refer to the source code of minpack.py:
|
|
||||||
|
|
||||||
An internal parameter list is used to enforce contraints on the fitting
|
|
||||||
parameters. The transfomation is based on that of MINUIT package.
|
|
||||||
please see: F. James and M. Winkler. MINUIT User's Guide, 2004.
|
|
||||||
|
|
||||||
bounds : list
|
|
||||||
(min, max) pairs for each parameter, use None for 'min' or 'max'
|
|
||||||
when there is no bound in that direction.
|
|
||||||
For example: if there are two parameters needed to be fitting, then
|
|
||||||
bounds is [(min1,max1), (min2,max2)]
|
|
||||||
|
|
||||||
This function is based on 'leastsq' of minpack.py, the annotation of
|
|
||||||
other parameters can be found in 'least_squares.py'.
|
|
||||||
"""
|
|
||||||
|
|
||||||
def _check_func(checker, argname, thefunc, x0, args, numinputs,
|
|
||||||
output_shape=None):
|
|
||||||
from numpy import shape
|
|
||||||
"""The same as that of minpack.py"""
|
|
||||||
res = np.atleast_1d(thefunc(*((x0[:numinputs],) + args)))
|
|
||||||
if (output_shape is not None) and (shape(res) != output_shape):
|
|
||||||
if (output_shape[0] != 1):
|
|
||||||
if len(output_shape) > 1:
|
|
||||||
if output_shape[1] == 1:
|
|
||||||
return shape(res)
|
|
||||||
msg = "%s: there is a mismatch between the input and output " \
|
|
||||||
"shape of the '%s' argument" % (checker, argname)
|
|
||||||
func_name = getattr(thefunc, '__name__', None)
|
|
||||||
if func_name:
|
|
||||||
msg += " '%s'." % func_name
|
|
||||||
else:
|
|
||||||
msg += "."
|
|
||||||
raise TypeError(msg)
|
|
||||||
if np.issubdtype(res.dtype, np.inexact):
|
|
||||||
dt = res.dtype
|
|
||||||
else:
|
|
||||||
dt = dtype(float)
|
|
||||||
return shape(res), dt
|
|
||||||
|
|
||||||
def _int2extGrad(p_int, bounds):
|
|
||||||
"""Calculate the gradients of transforming the internal (unconstrained) to external (constrained) parameter."""
|
|
||||||
grad = np.empty_like(p_int)
|
|
||||||
for i, (x, bound) in enumerate(zip(p_int, bounds)):
|
|
||||||
lower, upper = bound
|
|
||||||
if lower is None and upper is None: # No constraints
|
|
||||||
grad[i] = 1.0
|
|
||||||
elif upper is None: # only lower bound
|
|
||||||
grad[i] = x/np.sqrt(x*x + 1.0)
|
|
||||||
elif lower is None: # only upper bound
|
|
||||||
grad[i] = -x/np.sqrt(x*x + 1.0)
|
|
||||||
else: # lower and upper bounds
|
|
||||||
grad[i] = (upper - lower)*np.cos(x)/2.0
|
|
||||||
return grad
|
|
||||||
|
|
||||||
def _int2extFunc(bounds):
|
|
||||||
"""Transform internal parameters into external parameters."""
|
|
||||||
local = [_int2extLocal(b) for b in bounds]
|
|
||||||
|
|
||||||
def _transform_i2e(p_int):
|
|
||||||
p_ext = np.empty_like(p_int)
|
|
||||||
p_ext[:] = [i(j) for i, j in zip(local, p_int)]
|
|
||||||
return p_ext
|
|
||||||
return _transform_i2e
|
|
||||||
|
|
||||||
def _ext2intFunc(bounds):
|
|
||||||
"""Transform external parameters into internal parameters."""
|
|
||||||
local = [_ext2intLocal(b) for b in bounds]
|
|
||||||
|
|
||||||
def _transform_e2i(p_ext):
|
|
||||||
p_int = np.empty_like(p_ext)
|
|
||||||
p_int[:] = [i(j) for i, j in zip(local, p_ext)]
|
|
||||||
return p_int
|
|
||||||
return _transform_e2i
|
|
||||||
|
|
||||||
def _int2extLocal(bound):
|
|
||||||
"""Transform a single internal parameter to an external parameter."""
|
|
||||||
lower, upper = bound
|
|
||||||
if lower is None and upper is None: # no constraints
|
|
||||||
return lambda x: x
|
|
||||||
elif upper is None: # only lower bound
|
|
||||||
return lambda x: lower - 1.0 + np.sqrt(x*x + 1.0)
|
|
||||||
elif lower is None: # only upper bound
|
|
||||||
return lambda x: upper + 1.0 - np.sqrt(x*x + 1.0)
|
|
||||||
else:
|
|
||||||
return lambda x: lower + ((upper - lower)/2.0)*(np.sin(x) + 1.0)
|
|
||||||
|
|
||||||
def _ext2intLocal(bound):
|
|
||||||
"""Transform a single external parameter to an internal parameter."""
|
|
||||||
lower, upper = bound
|
|
||||||
if lower is None and upper is None: # no constraints
|
|
||||||
return lambda x: x
|
|
||||||
elif upper is None: # only lower bound
|
|
||||||
return lambda x: np.sqrt((x - lower + 1.0)**2 - 1.0)
|
|
||||||
elif lower is None: # only upper bound
|
|
||||||
return lambda x: np.sqrt((x - upper - 1.0)**2 - 1.0)
|
|
||||||
else:
|
|
||||||
return lambda x: np.arcsin((2.0*(x - lower)/(upper - lower)) - 1.0)
|
|
||||||
|
|
||||||
i2e = _int2extFunc(bounds)
|
|
||||||
e2i = _ext2intFunc(bounds)
|
|
||||||
|
|
||||||
x0 = np.asarray(x0).flatten()
|
|
||||||
n = len(x0)
|
|
||||||
|
|
||||||
if len(bounds) != n:
|
|
||||||
raise ValueError('the length of bounds is inconsistent with the number of parameters ')
|
|
||||||
|
|
||||||
if not isinstance(args, tuple):
|
|
||||||
args = (args,)
|
|
||||||
|
|
||||||
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
|
|
||||||
m = shape[0]
|
|
||||||
|
|
||||||
if n > m:
|
|
||||||
raise TypeError('Improper input: N=%s must not exceed M=%s' % (n, m))
|
|
||||||
if epsfcn is None:
|
|
||||||
epsfcn = np.finfo(dtype).eps
|
|
||||||
|
|
||||||
def funcWarp(x, *args):
|
|
||||||
return func(i2e(x), *args)
|
|
||||||
|
|
||||||
xi0 = e2i(x0)
|
|
||||||
|
|
||||||
if Dfun is None:
|
|
||||||
if maxfev == 0:
|
|
||||||
maxfev = 200*(n + 1)
|
|
||||||
retval = _minpack._lmdif(funcWarp, xi0, args, full_output, ftol, xtol,
|
|
||||||
gtol, maxfev, epsfcn, factor, diag)
|
|
||||||
else:
|
|
||||||
if col_deriv:
|
|
||||||
_check_func('leastsq', 'Dfun', Dfun, x0, args, n, (n, m))
|
|
||||||
else:
|
|
||||||
_check_func('leastsq', 'Dfun', Dfun, x0, args, n, (m, n))
|
|
||||||
if maxfev == 0:
|
|
||||||
maxfev = 100*(n + 1)
|
|
||||||
|
|
||||||
def DfunWarp(x, *args):
|
|
||||||
return Dfun(i2e(x), *args)
|
|
||||||
|
|
||||||
retval = _minpack._lmder(funcWarp, DfunWarp, xi0, args, full_output, col_deriv,
|
|
||||||
ftol, xtol, gtol, maxfev, factor, diag)
|
|
||||||
|
|
||||||
errors = {0: ["Improper input parameters.", TypeError],
|
|
||||||
1: ["Both actual and predicted relative reductions "
|
|
||||||
"in the sum of squares\n are at most %f" % ftol, None],
|
|
||||||
2: ["The relative error between two consecutive "
|
|
||||||
"iterates is at most %f" % xtol, None],
|
|
||||||
3: ["Both actual and predicted relative reductions in "
|
|
||||||
"the sum of squares\n are at most %f and the "
|
|
||||||
"relative error between two consecutive "
|
|
||||||
"iterates is at \n most %f" % (ftol, xtol), None],
|
|
||||||
4: ["The cosine of the angle between func(x) and any "
|
|
||||||
"column of the\n Jacobian is at most %f in "
|
|
||||||
"absolute value" % gtol, None],
|
|
||||||
5: ["Number of calls to function has reached "
|
|
||||||
"maxfev = %d." % maxfev, ValueError],
|
|
||||||
6: ["ftol=%f is too small, no further reduction "
|
|
||||||
"in the sum of squares\n is possible.""" % ftol,
|
|
||||||
ValueError],
|
|
||||||
7: ["xtol=%f is too small, no further improvement in "
|
|
||||||
"the approximate\n solution is possible." % xtol,
|
|
||||||
ValueError],
|
|
||||||
8: ["gtol=%f is too small, func(x) is orthogonal to the "
|
|
||||||
"columns of\n the Jacobian to machine "
|
|
||||||
"precision." % gtol, ValueError],
|
|
||||||
'unknown': ["Unknown error.", TypeError]}
|
|
||||||
|
|
||||||
info = retval[-1] # The FORTRAN return value
|
|
||||||
|
|
||||||
if info not in [1, 2, 3, 4] and not full_output:
|
|
||||||
if info in [5, 6, 7, 8]:
|
|
||||||
np.warnings.warn(errors[info][0], RuntimeWarning)
|
|
||||||
else:
|
|
||||||
try:
|
|
||||||
raise errors[info][1](errors[info][0])
|
|
||||||
except KeyError:
|
|
||||||
raise errors['unknown'][1](errors['unknown'][0])
|
|
||||||
|
|
||||||
mesg = errors[info][0]
|
|
||||||
x = i2e(retval[0])
|
|
||||||
|
|
||||||
if full_output:
|
|
||||||
grad = _int2extGrad(retval[0], bounds)
|
|
||||||
retval[1]['fjac'] = (retval[1]['fjac'].T / np.take(grad,
|
|
||||||
retval[1]['ipvt'] - 1)).T
|
|
||||||
cov_x = None
|
|
||||||
if info in [1, 2, 3, 4]:
|
|
||||||
from numpy.dual import inv
|
|
||||||
from numpy.linalg import LinAlgError
|
|
||||||
perm = np.take(np.eye(n), retval[1]['ipvt'] - 1, 0)
|
|
||||||
r = np.triu(np.transpose(retval[1]['fjac'])[:n, :])
|
|
||||||
R = np.dot(r, perm)
|
|
||||||
try:
|
|
||||||
cov_x = inv(np.dot(np.transpose(R), R))
|
|
||||||
except LinAlgError as inverror:
|
|
||||||
print(inverror)
|
|
||||||
pass
|
|
||||||
return (x, cov_x) + retval[1:-1] + (mesg, info)
|
|
||||||
else:
|
|
||||||
return (x, info)
|
|
||||||
|
|
||||||
def _general_function(params, ydata, xdata, function):
|
|
||||||
return function(xdata, *params) - ydata
|
|
||||||
def _weighted_general_function(params, ydata, xdata, function, weights):
|
|
||||||
return (function(xdata, *params) - ydata)*weights
|
|
||||||
|
|
||||||
def curve_fit_bound(f, xdata, ydata, p0=None, sigma=None, bounds=None, **kw):
|
|
||||||
"""Similar as 'curve_fit' in minpack.py."""
|
|
||||||
if p0 is None:
|
|
||||||
# determine number of parameters by inspecting the function
|
|
||||||
import inspect
|
|
||||||
args, varargs, varkw, defaults = inspect.getargspec(f)
|
|
||||||
if len(args) < 2:
|
|
||||||
msg = "Unable to determine number of fit parameters."
|
|
||||||
raise ValueError(msg)
|
|
||||||
if 'self' in args:
|
|
||||||
p0 = [1.0] * (len(args)-2)
|
|
||||||
else:
|
|
||||||
p0 = [1.0] * (len(args)-1)
|
|
||||||
|
|
||||||
if np.isscalar(p0):
|
|
||||||
p0 = np.array([p0])
|
|
||||||
|
|
||||||
args = (ydata, xdata, f)
|
|
||||||
if sigma is None:
|
|
||||||
func = _general_function
|
|
||||||
else:
|
|
||||||
func = _weighted_general_function
|
|
||||||
args += (1.0/np.asarray(sigma),)
|
|
||||||
|
|
||||||
return_full = kw.pop('full_output', False)
|
|
||||||
res = leastsqBound(func, p0, args=args, bounds = bounds, full_output=True, **kw)
|
|
||||||
(popt, pcov, infodict, errmsg, ier) = res
|
|
||||||
|
|
||||||
if ier not in [1, 2, 3, 4]:
|
|
||||||
msg = "Optimal parameters not found: " + errmsg
|
|
||||||
raise RuntimeError(msg)
|
|
||||||
|
|
||||||
if (len(ydata) > len(p0)) and pcov is not None:
|
|
||||||
s_sq = (func(popt, *args)**2).sum()/(len(ydata)-len(p0))
|
|
||||||
pcov = pcov * s_sq
|
|
||||||
else:
|
|
||||||
pcov = np.inf
|
|
||||||
|
|
||||||
return (popt, pcov, infodict, errmsg, ier) if return_full else (popt, pcov)
|
|
||||||
|
|
||||||
|
|
||||||
class ThreadPool:
|
class ThreadPool:
|
||||||
"""Pool of threads consuming tasks from a queue."""
|
"""Pool of threads consuming tasks from a queue."""
|
||||||
|
|
||||||
|
|
Loading…
Reference in New Issue