# -*- coding: UTF-8 no BOM -*-
# damask utility functions
import threading
import numpy as np
from optparse import OptionParser, Option
# -----------------------------
# Matlab like trigonometric functions that take and return angles in degrees.
# -----------------------------
for f in ['cos', 'sin', 'tan']:
exec('def %sd(deg): return (np.%s(np.deg2rad(deg)))'%(f,f))
exec('def a%sd(val): return (np.rad2deg(np.arc%s(val)))'%(f,f))
# -----------------------------
def gridLocation(idx,res):
# -----------------------------
return ( idx % res[0], \
( idx // res[0]) % res[1], \
( idx // res[0] // res[1]) % res[2] )
# -----------------------------
def gridIndex(location,res):
# -----------------------------
return ( location[0] % res[0] + \
( location[1] % res[1]) * res[0] + \
( location[2] % res[2]) * res[1] * res[0] )
# -----------------------------
class extendableOption(Option):
# -----------------------------
# used for definition of new option parser action 'extend', which enables to take multiple option arguments
# taken from online tutorial http://docs.python.org/library/optparse.html
ACTIONS = Option.ACTIONS + ("extend",)
STORE_ACTIONS = Option.STORE_ACTIONS + ("extend",)
TYPED_ACTIONS = Option.TYPED_ACTIONS + ("extend",)
ALWAYS_TYPED_ACTIONS = Option.ALWAYS_TYPED_ACTIONS + ("extend",)
def take_action(self, action, dest, opt, value, values, parser):
if action == "extend":
lvalue = value.split(",")
values.ensure_value(dest, []).extend(lvalue)
else:
Option.take_action(self, action, dest, opt, value, values, parser)
# -----------------------------
class backgroundMessage(threading.Thread):
# -----------------------------
def __init__(self):
threading.Thread.__init__(self)
self.message = ''
self.new_message = ''
self.counter = 0
self.symbols = ['- ', '\ ', '| ', '/ ']
self.waittime = 0.5
def __quit__(self):
length = len(self.message) + len(self.symbols[self.counter])
sys.stderr.write(chr(8)*length + ' '*length + chr(8)*length)
sys.stderr.write('')
def run(self):
while not threading.enumerate()[0]._Thread__stopped:
time.sleep(self.waittime)
self.update_message()
self.__quit__()
def set_message(self, new_message):
self.new_message = new_message
self.print_message()
def print_message(self):
length = len(self.message) + len(self.symbols[self.counter])
sys.stderr.write(chr(8)*length + ' '*length + chr(8)*length) # delete former message
sys.stderr.write(self.symbols[self.counter] + self.new_message) # print new message
self.message = self.new_message
def update_message(self):
self.counter = (self.counter + 1)%len(self.symbols)
self.print_message()
'''
Non-linear least square fitting (Levenberg-Marquardt method) with
the 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 refers to the source code of minpack.py:
..\Lib\site-packages\scipy\optimize\minpack.py
'''
from numpy import (array, arcsin, asarray, cos, dot, eye, empty_like,
isscalar,finfo, take, triu, transpose, sqrt, sin)
from scipy.optimize import _minpack
def _check_func(checker, argname, thefunc, x0, args, numinputs,
output_shape=None):
from numpy import atleast_1d, shape, issubdtype, dtype, inexact
'''
The same as that of minpack.py,
'''
res = 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 issubdtype(res.dtype, 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 (constained) parameter.
"""
grad = 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/sqrt(x*x + 1.0)
elif lower is None: # only upper bound
grad[i] = -x/sqrt(x*x + 1.0)
else: # lower and upper bounds
grad[i] = (upper - lower)*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 = 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 = 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 + sqrt(x*x + 1.0)
elif lower is None: # only upper bound
return lambda x: upper + 1.0 - sqrt(x*x + 1.0)
else:
return lambda x: lower + ((upper - lower)/2.0)*(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: sqrt((x - lower + 1.0)**2 - 1.0)
elif lower is None: # only upper bound
return lambda x: sqrt((x - upper - 1.0)**2 - 1.0)
else:
return lambda x: arcsin((2.0*(x - lower)/(upper - lower)) - 1.0)
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):
'''
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 'leastsq'.
..\Lib\site-packages\scipy\optimize\minpack.py
'''
i2e = _int2extFunc(bounds)
e2i = _ext2intFunc(bounds)
x0 = 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 = finfo(dtype).eps
# wrapped func
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)
# wrapped Dfun
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]:
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 / 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 = take(eye(n), retval[1]['ipvt'] - 1, 0)
r = triu(transpose(retval[1]['fjac'])[:n, :])
R = dot(r, perm)
try:
cov_x = inv(dot(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 isscalar(p0):
p0 = array([p0])
args = (ydata, xdata, f)
if sigma is None:
func = _general_function
else:
func = _weighted_general_function
args += (1.0/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 = inf
if return_full:
return popt, pcov, infodict, errmsg, ier
else:
return popt, pcov