462 lines
17 KiB
Python
462 lines
17 KiB
Python
# -*- coding: UTF-8 no BOM -*-
|
|
|
|
import sys,time,random,threading,os,subprocess,shlex
|
|
import numpy as np
|
|
from optparse import Option
|
|
|
|
class bcolors:
|
|
"""
|
|
ASCII Colors (Blender code)
|
|
|
|
https://svn.blender.org/svnroot/bf-blender/trunk/blender/build_files/scons/tools/bcolors.py
|
|
http://stackoverflow.com/questions/287871/print-in-terminal-with-colors-using-python
|
|
"""
|
|
|
|
HEADER = '\033[95m'
|
|
OKBLUE = '\033[94m'
|
|
OKGREEN = '\033[92m'
|
|
WARNING = '\033[93m'
|
|
FAIL = '\033[91m'
|
|
ENDC = '\033[0m'
|
|
BOLD = '\033[1m'
|
|
DIM = '\033[2m'
|
|
UNDERLINE = '\033[4m'
|
|
|
|
def disable(self):
|
|
self.HEADER = ''
|
|
self.OKBLUE = ''
|
|
self.OKGREEN = ''
|
|
self.WARNING = ''
|
|
self.FAIL = ''
|
|
self.ENDC = ''
|
|
self.BOLD = ''
|
|
self.UNDERLINE = ''
|
|
|
|
|
|
# -----------------------------
|
|
def srepr(arg,glue = '\n'):
|
|
"""Joins arguments as individual lines"""
|
|
if (not hasattr(arg, "strip") and
|
|
hasattr(arg, "__getitem__") or
|
|
hasattr(arg, "__iter__")):
|
|
return glue.join(str(x) for x in arg)
|
|
return arg if isinstance(arg,str) else repr(arg)
|
|
|
|
# -----------------------------
|
|
def croak(what, newline = True):
|
|
"""Writes formated to stderr"""
|
|
sys.stderr.write(srepr(what,glue = '\n') + ('\n' if newline else ''))
|
|
sys.stderr.flush()
|
|
|
|
# -----------------------------
|
|
def report(who = None,
|
|
what = None):
|
|
"""Reports script and file name"""
|
|
croak( (emph(who)+': ' if who is not None else '') + (what if what is not None else '') )
|
|
|
|
|
|
# -----------------------------
|
|
def report_geom(info,
|
|
what = ['grid','size','origin','homogenization','microstructures']):
|
|
"""Reports (selected) geometry information"""
|
|
output = {
|
|
'grid' : 'grid a b c: {}'.format(' x '.join(map(str,info['grid' ]))),
|
|
'size' : 'size x y z: {}'.format(' x '.join(map(str,info['size' ]))),
|
|
'origin' : 'origin x y z: {}'.format(' : '.join(map(str,info['origin']))),
|
|
'homogenization' : 'homogenization: {}'.format(info['homogenization']),
|
|
'microstructures' : 'microstructures: {}'.format(info['microstructures']),
|
|
}
|
|
for item in what: croak(output[item.lower()])
|
|
|
|
# -----------------------------
|
|
def emph(what):
|
|
"""Boldens string"""
|
|
return bcolors.BOLD+srepr(what)+bcolors.ENDC
|
|
|
|
# -----------------------------
|
|
def deemph(what):
|
|
"""Dims string"""
|
|
return bcolors.DIM+srepr(what)+bcolors.ENDC
|
|
|
|
# -----------------------------
|
|
def delete(what):
|
|
"""Dims string"""
|
|
return bcolors.DIM+srepr(what)+bcolors.ENDC
|
|
|
|
# -----------------------------
|
|
def execute(cmd,
|
|
streamIn = None,
|
|
wd = './'):
|
|
"""Executes a command in given directory and returns stdout and stderr for optional stdin"""
|
|
initialPath = os.getcwd()
|
|
os.chdir(wd)
|
|
process = subprocess.Popen(shlex.split(cmd),
|
|
stdout = subprocess.PIPE,
|
|
stderr = subprocess.PIPE,
|
|
stdin = subprocess.PIPE)
|
|
out,error = [i.replace("\x08","") for i in (process.communicate() if streamIn is None
|
|
else process.communicate(streamIn.read()))]
|
|
os.chdir(initialPath)
|
|
if process.returncode != 0: raise RuntimeError('{} failed with returncode {}'.format(cmd,process.returncode))
|
|
return out,error
|
|
|
|
|
|
def coordGridAndSize(coordinates):
|
|
"""Determines grid count and overall physical size along each dimension of an ordered array of coordinates"""
|
|
dim = coordinates.shape[1]
|
|
coords = [np.unique(coordinates[:,i]) for i in range(dim)]
|
|
mincorner = np.array(map(min,coords))
|
|
maxcorner = np.array(map(max,coords))
|
|
grid = np.array(map(len,coords),'i')
|
|
size = grid/np.maximum(np.ones(dim,'d'), grid-1.0) * (maxcorner-mincorner) # size from edge to edge = dim * n/(n-1)
|
|
size = np.where(grid > 1, size, min(size[grid > 1]/grid[grid > 1])) # spacing for grid==1 equal to smallest among other ones
|
|
return grid,size
|
|
|
|
# -----------------------------
|
|
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):
|
|
"""Reporting with animation to indicate progress"""
|
|
|
|
choices = {'bounce': ['_', 'o', 'O', '°', '‾', '‾', '°', 'O', 'o', '_'],
|
|
'spin': ['◜', '◝', '◞', '◟'],
|
|
'circle': ['◴', '◵', '◶', '◷'],
|
|
'hexagon': ['⬢', '⬣'],
|
|
'square': ['▖', '▘', '▝', '▗'],
|
|
'triangle': ['ᐊ', 'ᐊ', 'ᐃ', 'ᐅ', 'ᐅ', 'ᐃ'],
|
|
'amoeba': ['▖', '▏', '▘', '▔', '▝', '▕', '▗', '▁'],
|
|
'beat': ['▁', '▂', '▃', '▅', '▆', '▇', '▇', '▆', '▅', '▃', '▂'],
|
|
'prison': ['ᚋ', 'ᚌ', 'ᚍ', 'ᚏ', 'ᚎ', 'ᚍ', 'ᚌ', 'ᚋ'],
|
|
'breath': ['ᚐ', 'ᚑ', 'ᚒ', 'ᚓ', 'ᚔ', 'ᚓ', 'ᚒ', 'ᚑ', 'ᚐ'],
|
|
'pulse': ['·', '•', '●', '●', '•'],
|
|
'ant': ['⠁', '⠂', '⠐', '⠠', '⠄', '⡀', '⢀', '⠠', '⠄', '⠂', '⠐', '⠈'],
|
|
'juggle': ['꜈', '꜉', '꜊', '꜋', '꜌', '꜑', '꜐', '꜏', '꜍'],
|
|
# 'wobbler': ['▁', '◣', '▏', '◤', '▔', '◥', '▕', '◢'],
|
|
'grout': ['▁', '▏', '▔', '▕'],
|
|
'partner': ['⚬', '⚭', '⚮', '⚯', '⚮', '⚭'],
|
|
'classic': ['-', '\\', '|', '/',],
|
|
}
|
|
|
|
def __init__(self,symbol = None,wait = 0.1):
|
|
"""Sets animation symbol"""
|
|
super(backgroundMessage, self).__init__()
|
|
self._stop = threading.Event()
|
|
self.message = ''
|
|
self.new_message = ''
|
|
self.counter = 0
|
|
self.gap = ' '
|
|
self.symbols = self.choices[symbol if symbol in self.choices else random.choice(list(self.choices.keys()))]
|
|
self.waittime = wait
|
|
|
|
def __quit__(self):
|
|
"""Cleans output"""
|
|
length = len(self.symbols[self.counter] + self.gap + self.message)
|
|
sys.stderr.write(chr(8)*length + ' '*length + chr(8)*length)
|
|
sys.stderr.write('')
|
|
sys.stderr.flush()
|
|
|
|
def stop(self):
|
|
self._stop.set()
|
|
|
|
def stopped(self):
|
|
return self._stop.is_set()
|
|
|
|
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.symbols[self.counter] + self.gap + self.message)
|
|
sys.stderr.write(chr(8)*length + ' '*length + chr(8)*length + \
|
|
self.symbols[self.counter] + self.gap + self.new_message) # delete former and print new message
|
|
sys.stderr.flush()
|
|
self.message = self.new_message
|
|
|
|
def update_message(self):
|
|
self.counter = (self.counter + 1)%len(self.symbols)
|
|
self.print_message()
|
|
|
|
def animation(self,which = None):
|
|
return ''.join(self.choices[which]) if which in self.choices else ''
|
|
|
|
|
|
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 refers to the source code of minpack.py:
|
|
..\Lib\site-packages\scipy\optimize\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 'leastsq'.
|
|
..\Lib\site-packages\scipy\optimize\minpack.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)
|