460 lines
17 KiB
Python
460 lines
17 KiB
Python
# -*- coding: UTF-8 no BOM -*-
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import sys,time,random,threading,os,subprocess,shlex
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import numpy as np
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from optparse import Option
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class bcolors:
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"""
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ASCII Colors (Blender code)
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https://svn.blender.org/svnroot/bf-blender/trunk/blender/build_files/scons/tools/bcolors.py
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http://stackoverflow.com/questions/287871/print-in-terminal-with-colors-using-python
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"""
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HEADER = '\033[95m'
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OKBLUE = '\033[94m'
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OKGREEN = '\033[92m'
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WARNING = '\033[93m'
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FAIL = '\033[91m'
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ENDC = '\033[0m'
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BOLD = '\033[1m'
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DIM = '\033[2m'
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UNDERLINE = '\033[4m'
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def disable(self):
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self.HEADER = ''
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self.OKBLUE = ''
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self.OKGREEN = ''
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self.WARNING = ''
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self.FAIL = ''
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self.ENDC = ''
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self.BOLD = ''
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self.UNDERLINE = ''
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# -----------------------------
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def srepr(arg,glue = '\n'):
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"""Joins arguments as individual lines"""
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if (not hasattr(arg, "strip") and
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(hasattr(arg, "__getitem__") or
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hasattr(arg, "__iter__"))):
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return glue.join(str(x) for x in arg)
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return arg if isinstance(arg,str) else repr(arg)
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# -----------------------------
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def croak(what, newline = True):
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"""Writes formated to stderr"""
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sys.stderr.write(srepr(what,glue = '\n') + ('\n' if newline else ''))
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sys.stderr.flush()
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# -----------------------------
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def report(who = None,
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what = None):
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"""Reports script and file name"""
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croak( (emph(who)+': ' if who is not None else '') + (what if what is not None else '') )
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# -----------------------------
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def report_geom(info,
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what = ['grid','size','origin','homogenization','microstructures']):
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"""Reports (selected) geometry information"""
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output = {
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'grid' : 'grid a b c: {}'.format(' x '.join(list(map(str,info['grid' ])))),
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'size' : 'size x y z: {}'.format(' x '.join(list(map(str,info['size' ])))),
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'origin' : 'origin x y z: {}'.format(' : '.join(list(map(str,info['origin'])))),
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'homogenization' : 'homogenization: {}'.format(info['homogenization']),
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'microstructures' : 'microstructures: {}'.format(info['microstructures']),
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}
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for item in what: croak(output[item.lower()])
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# -----------------------------
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def emph(what):
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"""Boldens string"""
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return bcolors.BOLD+srepr(what)+bcolors.ENDC
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# -----------------------------
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def deemph(what):
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"""Dims string"""
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return bcolors.DIM+srepr(what)+bcolors.ENDC
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# -----------------------------
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def delete(what):
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"""Dims string"""
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return bcolors.DIM+srepr(what)+bcolors.ENDC
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# -----------------------------
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def execute(cmd,
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streamIn = None,
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wd = './'):
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"""Executes a command in given directory and returns stdout and stderr for optional stdin"""
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initialPath = os.getcwd()
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os.chdir(wd)
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process = subprocess.Popen(shlex.split(cmd),
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stdout = subprocess.PIPE,
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stderr = subprocess.PIPE,
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stdin = subprocess.PIPE)
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out,error = [i.replace(b"\x08",b"") for i in (process.communicate() if streamIn is None
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else process.communicate(streamIn.read()))]
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os.chdir(initialPath)
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if process.returncode != 0: raise RuntimeError('{} failed with returncode {}'.format(cmd,process.returncode))
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return out,error
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def coordGridAndSize(coordinates):
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"""Determines grid count and overall physical size along each dimension of an ordered array of coordinates"""
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dim = coordinates.shape[1]
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coords = [np.unique(coordinates[:,i]) for i in range(dim)]
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mincorner = np.array(list(map(min,coords)))
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maxcorner = np.array(list(map(max,coords)))
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grid = np.array(list(map(len,coords)),'i')
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size = grid/np.maximum(np.ones(dim,'d'), grid-1.0) * (maxcorner-mincorner) # size from edge to edge = dim * n/(n-1)
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size = np.where(grid > 1, size, min(size[grid > 1]/grid[grid > 1])) # spacing for grid==1 equal to smallest among other ones
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return grid,size
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# -----------------------------
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class extendableOption(Option):
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"""
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Used for definition of new option parser action 'extend', which enables to take multiple option arguments
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taken from online tutorial http://docs.python.org/library/optparse.html
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"""
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ACTIONS = Option.ACTIONS + ("extend",)
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STORE_ACTIONS = Option.STORE_ACTIONS + ("extend",)
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TYPED_ACTIONS = Option.TYPED_ACTIONS + ("extend",)
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ALWAYS_TYPED_ACTIONS = Option.ALWAYS_TYPED_ACTIONS + ("extend",)
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def take_action(self, action, dest, opt, value, values, parser):
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if action == "extend":
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lvalue = value.split(",")
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values.ensure_value(dest, []).extend(lvalue)
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else:
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Option.take_action(self, action, dest, opt, value, values, parser)
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# -----------------------------
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class backgroundMessage(threading.Thread):
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"""Reporting with animation to indicate progress"""
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choices = {'bounce': ['_', 'o', 'O', '°', '‾', '‾', '°', 'O', 'o', '_'],
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'spin': ['◜', '◝', '◞', '◟'],
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'circle': ['◴', '◵', '◶', '◷'],
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'hexagon': ['⬢', '⬣'],
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'square': ['▖', '▘', '▝', '▗'],
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'triangle': ['ᐊ', 'ᐊ', 'ᐃ', 'ᐅ', 'ᐅ', 'ᐃ'],
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'amoeba': ['▖', '▏', '▘', '▔', '▝', '▕', '▗', '▁'],
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'beat': ['▁', '▂', '▃', '▅', '▆', '▇', '▇', '▆', '▅', '▃', '▂'],
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'prison': ['ᚋ', 'ᚌ', 'ᚍ', 'ᚏ', 'ᚎ', 'ᚍ', 'ᚌ', 'ᚋ'],
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'breath': ['ᚐ', 'ᚑ', 'ᚒ', 'ᚓ', 'ᚔ', 'ᚓ', 'ᚒ', 'ᚑ', 'ᚐ'],
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'pulse': ['·', '•', '●', '●', '•'],
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'ant': ['⠁', '⠂', '⠐', '⠠', '⠄', '⡀', '⢀', '⠠', '⠄', '⠂', '⠐', '⠈'],
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'juggle': ['꜈', '꜉', '꜊', '꜋', '꜌', '꜑', '꜐', '꜏', '꜍'],
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# 'wobbler': ['▁', '◣', '▏', '◤', '▔', '◥', '▕', '◢'],
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'grout': ['▁', '▏', '▔', '▕'],
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'partner': ['⚬', '⚭', '⚮', '⚯', '⚮', '⚭'],
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'classic': ['-', '\\', '|', '/',],
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}
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def __init__(self,symbol = None,wait = 0.1):
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"""Sets animation symbol"""
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super(backgroundMessage, self).__init__()
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self._stop = threading.Event()
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self.message = ''
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self.new_message = ''
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self.counter = 0
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self.gap = ' '
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self.symbols = self.choices[symbol if symbol in self.choices else random.choice(list(self.choices.keys()))]
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self.waittime = wait
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def __quit__(self):
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"""Cleans output"""
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length = len(self.symbols[self.counter] + self.gap + self.message)
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sys.stderr.write(chr(8)*length + ' '*length + chr(8)*length)
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sys.stderr.write('')
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sys.stderr.flush()
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def stop(self):
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self._stop.set()
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def stopped(self):
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return self._stop.is_set()
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def run(self):
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while not threading.enumerate()[0]._Thread__stopped:
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time.sleep(self.waittime)
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self.update_message()
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self.__quit__()
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def set_message(self, new_message):
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self.new_message = new_message
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self.print_message()
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def print_message(self):
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length = len(self.symbols[self.counter] + self.gap + self.message)
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sys.stderr.write(chr(8)*length + ' '*length + chr(8)*length + \
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self.symbols[self.counter] + self.gap + self.new_message) # delete former and print new message
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sys.stderr.flush()
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self.message = self.new_message
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def update_message(self):
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self.counter = (self.counter + 1)%len(self.symbols)
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self.print_message()
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def animation(self,which = None):
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return ''.join(self.choices[which]) if which in self.choices else ''
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def leastsqBound(func, x0, args=(), bounds=None, Dfun=None, full_output=0,
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col_deriv=0, ftol=1.49012e-8, xtol=1.49012e-8,
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gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None):
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from scipy.optimize import _minpack
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"""
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Non-linear least square fitting (Levenberg-Marquardt method) with
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bounded parameters.
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the codes of transformation between int <-> ext refers to the work of
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Jonathan J. Helmus: https://github.com/jjhelmus/leastsqbound-scipy
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other codes refers to the source code of minpack.py:
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..\Lib\site-packages\scipy\optimize\minpack.py
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An internal parameter list is used to enforce contraints on the fitting
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parameters. The transfomation is based on that of MINUIT package.
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please see: F. James and M. Winkler. MINUIT User's Guide, 2004.
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bounds : list
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(min, max) pairs for each parameter, use None for 'min' or 'max'
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when there is no bound in that direction.
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For example: if there are two parameters needed to be fitting, then
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bounds is [(min1,max1), (min2,max2)]
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This function is based on 'leastsq' of minpack.py, the annotation of
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other parameters can be found in 'leastsq'.
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..\Lib\site-packages\scipy\optimize\minpack.py
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"""
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def _check_func(checker, argname, thefunc, x0, args, numinputs,
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output_shape=None):
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from numpy import shape
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"""The same as that of minpack.py"""
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res = np.atleast_1d(thefunc(*((x0[:numinputs],) + args)))
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if (output_shape is not None) and (shape(res) != output_shape):
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if (output_shape[0] != 1):
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if len(output_shape) > 1:
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if output_shape[1] == 1:
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return shape(res)
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msg = "%s: there is a mismatch between the input and output " \
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"shape of the '%s' argument" % (checker, argname)
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func_name = getattr(thefunc, '__name__', None)
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if func_name:
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msg += " '%s'." % func_name
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else:
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msg += "."
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raise TypeError(msg)
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if np.issubdtype(res.dtype, np.inexact):
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dt = res.dtype
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else:
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dt = dtype(float)
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return shape(res), dt
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def _int2extGrad(p_int, bounds):
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"""Calculate the gradients of transforming the internal (unconstrained) to external (constrained) parameter."""
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grad = np.empty_like(p_int)
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for i, (x, bound) in enumerate(zip(p_int, bounds)):
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lower, upper = bound
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if lower is None and upper is None: # No constraints
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grad[i] = 1.0
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elif upper is None: # only lower bound
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grad[i] = x/np.sqrt(x*x + 1.0)
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elif lower is None: # only upper bound
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grad[i] = -x/np.sqrt(x*x + 1.0)
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else: # lower and upper bounds
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grad[i] = (upper - lower)*np.cos(x)/2.0
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return grad
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def _int2extFunc(bounds):
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"""Transform internal parameters into external parameters."""
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local = [_int2extLocal(b) for b in bounds]
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def _transform_i2e(p_int):
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p_ext = np.empty_like(p_int)
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p_ext[:] = [i(j) for i, j in zip(local, p_int)]
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return p_ext
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return _transform_i2e
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def _ext2intFunc(bounds):
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"""Transform external parameters into internal parameters."""
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local = [_ext2intLocal(b) for b in bounds]
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def _transform_e2i(p_ext):
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p_int = np.empty_like(p_ext)
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p_int[:] = [i(j) for i, j in zip(local, p_ext)]
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return p_int
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return _transform_e2i
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def _int2extLocal(bound):
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"""Transform a single internal parameter to an external parameter."""
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lower, upper = bound
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if lower is None and upper is None: # no constraints
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return lambda x: x
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elif upper is None: # only lower bound
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return lambda x: lower - 1.0 + np.sqrt(x*x + 1.0)
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elif lower is None: # only upper bound
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return lambda x: upper + 1.0 - np.sqrt(x*x + 1.0)
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else:
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return lambda x: lower + ((upper - lower)/2.0)*(np.sin(x) + 1.0)
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def _ext2intLocal(bound):
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"""Transform a single external parameter to an internal parameter."""
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lower, upper = bound
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if lower is None and upper is None: # no constraints
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return lambda x: x
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elif upper is None: # only lower bound
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return lambda x: np.sqrt((x - lower + 1.0)**2 - 1.0)
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elif lower is None: # only upper bound
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return lambda x: np.sqrt((x - upper - 1.0)**2 - 1.0)
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else:
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return lambda x: np.arcsin((2.0*(x - lower)/(upper - lower)) - 1.0)
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i2e = _int2extFunc(bounds)
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e2i = _ext2intFunc(bounds)
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x0 = np.asarray(x0).flatten()
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n = len(x0)
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if len(bounds) != n:
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raise ValueError('the length of bounds is inconsistent with the number of parameters ')
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if not isinstance(args, tuple):
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args = (args,)
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shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
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m = shape[0]
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if n > m:
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raise TypeError('Improper input: N=%s must not exceed M=%s' % (n, m))
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if epsfcn is None:
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epsfcn = np.finfo(dtype).eps
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def funcWarp(x, *args):
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return func(i2e(x), *args)
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xi0 = e2i(x0)
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if Dfun is None:
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if maxfev == 0:
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maxfev = 200*(n + 1)
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retval = _minpack._lmdif(funcWarp, xi0, args, full_output, ftol, xtol,
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gtol, maxfev, epsfcn, factor, diag)
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else:
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if col_deriv:
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_check_func('leastsq', 'Dfun', Dfun, x0, args, n, (n, m))
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else:
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_check_func('leastsq', 'Dfun', Dfun, x0, args, n, (m, n))
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if maxfev == 0:
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maxfev = 100*(n + 1)
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def DfunWarp(x, *args):
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return Dfun(i2e(x), *args)
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retval = _minpack._lmder(funcWarp, DfunWarp, xi0, args, full_output, col_deriv,
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ftol, xtol, gtol, maxfev, factor, diag)
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errors = {0: ["Improper input parameters.", TypeError],
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1: ["Both actual and predicted relative reductions "
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"in the sum of squares\n are at most %f" % ftol, None],
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2: ["The relative error between two consecutive "
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"iterates is at most %f" % xtol, None],
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3: ["Both actual and predicted relative reductions in "
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"the sum of squares\n are at most %f and the "
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"relative error between two consecutive "
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"iterates is at \n most %f" % (ftol, xtol), None],
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4: ["The cosine of the angle between func(x) and any "
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"column of the\n Jacobian is at most %f in "
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"absolute value" % gtol, None],
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5: ["Number of calls to function has reached "
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"maxfev = %d." % maxfev, ValueError],
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6: ["ftol=%f is too small, no further reduction "
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"in the sum of squares\n is possible.""" % ftol,
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ValueError],
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7: ["xtol=%f is too small, no further improvement in "
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"the approximate\n solution is possible." % xtol,
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ValueError],
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8: ["gtol=%f is too small, func(x) is orthogonal to the "
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"columns of\n the Jacobian to machine "
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"precision." % gtol, ValueError],
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'unknown': ["Unknown error.", TypeError]}
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info = retval[-1] # The FORTRAN return value
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if info not in [1, 2, 3, 4] and not full_output:
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if info in [5, 6, 7, 8]:
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np.warnings.warn(errors[info][0], RuntimeWarning)
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else:
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try:
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raise errors[info][1](errors[info][0])
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except KeyError:
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raise errors['unknown'][1](errors['unknown'][0])
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mesg = errors[info][0]
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x = i2e(retval[0])
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if full_output:
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grad = _int2extGrad(retval[0], bounds)
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retval[1]['fjac'] = (retval[1]['fjac'].T / np.take(grad,
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retval[1]['ipvt'] - 1)).T
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cov_x = None
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if info in [1, 2, 3, 4]:
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from numpy.dual import inv
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from numpy.linalg import LinAlgError
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perm = np.take(np.eye(n), retval[1]['ipvt'] - 1, 0)
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r = np.triu(np.transpose(retval[1]['fjac'])[:n, :])
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R = np.dot(r, perm)
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try:
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cov_x = inv(np.dot(np.transpose(R), R))
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except LinAlgError as inverror:
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print(inverror)
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pass
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return (x, cov_x) + retval[1:-1] + (mesg, info)
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else:
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return (x, info)
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def _general_function(params, ydata, xdata, function):
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return function(xdata, *params) - ydata
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def _weighted_general_function(params, ydata, xdata, function, weights):
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return (function(xdata, *params) - ydata)*weights
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def curve_fit_bound(f, xdata, ydata, p0=None, sigma=None, bounds=None, **kw):
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"""Similar as 'curve_fit' in minpack.py"""
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if p0 is None:
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# determine number of parameters by inspecting the function
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import inspect
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args, varargs, varkw, defaults = inspect.getargspec(f)
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if len(args) < 2:
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msg = "Unable to determine number of fit parameters."
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raise ValueError(msg)
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if 'self' in args:
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p0 = [1.0] * (len(args)-2)
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else:
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p0 = [1.0] * (len(args)-1)
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if np.isscalar(p0):
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p0 = np.array([p0])
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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)
|