# -*- coding: UTF-8 no BOM -*- import sys,time,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""" if what is not None: 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 '') + '\n' ) # ----------------------------- def report_geom(info, what = ['grid','size','origin','homogenization','microstructures']): """Reports (selected) geometry information""" output = { 'grid' : 'grid a b c: {}'.format(' x '.join(list(map(str,info['grid' ])))), 'size' : 'size x y z: {}'.format(' x '.join(list(map(str,info['size' ])))), 'origin' : 'origin x y z: {}'.format(' : '.join(list(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 for i in (process.communicate() if streamIn is None else process.communicate(streamIn.read().encode('utf-8')))] out = out.decode('utf-8').replace('\x08','') error = error.decode('utf-8').replace('\x08','') 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(list(map(min,coords))) maxcorner = np.array(list(map(max,coords))) grid = np.array(list(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) # Print iterations progress # from https://gist.github.com/aubricus/f91fb55dc6ba5557fbab06119420dd6a def progressBar(iteration, total, prefix='', bar_length=50): """ Call in a loop to create terminal progress bar @params: iteration - Required : current iteration (Int) total - Required : total iterations (Int) prefix - Optional : prefix string (Str) bar_length - Optional : character length of bar (Int) """ fraction = iteration / float(total) if not hasattr(progressBar, "last_fraction"): # first call to function progressBar.start_time = time.time() progressBar.last_fraction = -1.0 remaining_time = ' n/a' else: if fraction <= progressBar.last_fraction or iteration == 0: # reset: called within a new loop progressBar.start_time = time.time() progressBar.last_fraction = -1.0 remaining_time = ' n/a' else: progressBar.last_fraction = fraction remainder = (total - iteration) * (time.time()-progressBar.start_time)/iteration remaining_time = '{: 3d}:'.format(int( remainder//3600)) + \ '{:02d}:'.format(int((remainder//60)%60)) + \ '{:02d}' .format(int( remainder %60)) filled_length = int(round(bar_length * fraction)) bar = '█' * filled_length + '░' * (bar_length - filled_length) sys.stderr.write('\r{} {} {}'.format(prefix, bar, remaining_time)), if iteration == total: sys.stderr.write('\n') sys.stderr.flush() 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)