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Best Python code snippet using tavern
bumps.py
Source:bumps.py 
1'''2===============================================3:mod:`gridcells.analysis.bumps` - bump tracking4===============================================5Classes and functions for processing data related to bump attractors.6Classes7-------8.. inheritance-diagram:: gridcells.analysis.bumps9 :parts: 210.. autosummary::11 MLFit12 MLFitList13 MLGaussianFit14 MLGaussianFitList15 SingleBumpPopulation16 SymmetricGaussianParams17Functions18---------19.. autosummary::20 fit_gaussian_tt21 fit_gaussian_bump_tt22 fit_maximum_lh23'''24from __future__ import absolute_import, division, print_function25import collections26import logging27import numpy as np28import scipy.optimize29from . import spikes30from ..core.common import Pair2D, twisted_torus_distance31LOGGER = logging.getLogger(__name__)32class SymmetricGaussianParams(object):33 '''Parameters for the symmetric Gaussian function.'''34 def __init__(self, amplitude, mu_x, mu_y, sigma, err2):35 self.A = amplitude36 self.mu_x = mu_x37 self.mu_y = mu_y38 self.sigma = sigma39 self.err2 = err240class MLFit(object):41 '''Maximum likelihood fit data holer.'''42 def __init__(self, mu, sigma2, ln_lh, err2):43 self.mu = mu44 self.sigma2 = sigma245 self.ln_lh = ln_lh46 self.err2 = err247class MLFitList(MLFit, collections.Sequence):48 '''A container for holding results of maximum likelihood fitting.49 Can be accessed as a Sequence object.50 '''51 def __init__(self, mu=None, sigma2=None, ln_lh=None, err2=None,52 times=None):53 if mu is None:54 mu = []55 if sigma2 is None:56 sigma2 = []57 if ln_lh is None:58 ln_lh = []59 if err2 is None:60 err2 = []61 if times is None:62 times = []63 super(MLFitList, self).__init__(mu, sigma2, ln_lh, err2)64 self.times = times65 if not self._consistent():66 raise ValueError('All input arguments mus have same length')67 def _consistent(self):68 '''Check if the data is consistent.'''69 return len(self.mu) == len(self.sigma2) and \70 len(self.mu) == len(self.ln_lh) and \71 len(self.mu) == len(self.err2) and \72 len(self.mu) == len(self.times)73 def __getitem__(self, key):74 return (MLFit(self.mu[key], self.sigma2[key], self.ln_lh[key],75 self.err2),76 self.times)77 def __len__(self):78 return len(self.mu)79 def append_data(self, d, t):80 '''`d` must be an instance of :class:`MLFit`'''81 if not isinstance(d, MLFit):82 raise TypeError('ML data must be an instance of MLFit')83 self.mu.append(d.mu)84 self.sigma2.append(d.sigma2)85 self.ln_lh.append(d.ln_lh)86 self.err2.append(d.err2)87 self.times.append(t)88class MLGaussianFit(SymmetricGaussianParams):89 '''Gaussian fit performed by applying maximum likelihood estimator.'''90 def __init__(self, amplitude, mu_x, mu_y, sigma, err2, ln_lh,91 lh_precision):92 super(MLGaussianFit, self).__init__(amplitude, mu_x, mu_y, sigma, err2)93 self.ln_lh = ln_lh94 self.lh_precision = lh_precision95class MLGaussianFitList(MLGaussianFit, collections.Sequence):96 '''A container for holding maximum likelihood Gaussian fits.97 Can be accessed as a Sequence.98 '''99 def __init__(self, amplitude=None, mu_x=None, mu_y=None, sigma=None,100 err2=None, ln_lh=None, lh_precision=None, times=None):101 if amplitude is None:102 amplitude = []103 if mu_x is None:104 mu_x = []105 if mu_y is None:106 mu_y = []107 if sigma is None:108 sigma = []109 if err2 is None:110 err2 = []111 if ln_lh is None:112 ln_lh = []113 if lh_precision is None:114 lh_precision = []115 if times is None:116 times = []117 super(MLGaussianFitList, self).__init__(amplitude, mu_x, mu_y, sigma,118 err2, ln_lh,119 lh_precision)120 self.times = times121 if not self._consistent():122 raise ValueError('All input arguments mus have same length')123 def _consistent(self):124 '''Check if the data is consistent.'''125 return \126 len(self.A) == len(self.mu_x) and \127 len(self.A) == len(self.mu_y) and \128 len(self.A) == len(self.sigma) and \129 len(self.A) == len(self.err2) and \130 len(self.A) == len(self.ln_lh) and \131 len(self.A) == len(self.lh_precision) and \132 len(self.A) == len(self.times)133 def append_data(self, d, t):134 '''`d` must be an instance of :class:`MLGaussianFit`'''135 if not isinstance(d, MLGaussianFit):136 raise TypeError('Data must be an instance of MLGaussianFit')137 self.A.append(d.A)138 self.mu_x.append(d.mu_x)139 self.mu_y.append(d.mu_y)140 self.sigma.append(d.sigma)141 self.err2.append(d.err2)142 self.ln_lh.append(d.ln_lh)143 self.lh_precision.append(d.lh_precision)144 self.times.append(t)145 def __getitem__(self, key):146 return MLGaussianFit(self.A[key],147 self.mu_x[key],148 self.mu_y[key],149 self.sigma[key],150 self.err2[key],151 self.ln_lh,152 self.lh_precision), \153 self.times[key]154 def __len__(self):155 return len(self.A) # All same length156def fit_gaussian_tt(sig_f, i):157 r'''Fit a 2D circular Gaussian function to a 2D signal using a maximum158 likelihood estimator.159 The Gaussian is not generic: :math:`\sigma_x = \sigma_y = \sigma`, i.e.160 it is circular only.161 The function fitted looks like this:162 .. math::163 f(\mathbf{X}) = |A| \exp\left\{\frac{-|\mathbf{X} -164 \mathbf{\mu}|^2}{2\sigma^2}\right\}165 where :math:`|\cdot|` is a distance metric on the twisted torus.166 Parameters167 ----------168 sig_f : np.ndarray169 A 2D array that specified the signal to fit the Gaussian onto. The170 dimensions of the torus will be inferred from the shape of `sig_f`:171 (dim.y, dim.x) = `sig_f.shape`.172 i : SymmetricGaussianParams173 Guassian initialisation parameters. The `err2` field will be ignored.174 Returns175 -------176 :class:`MLGaussianFit`177 Estimated values, together with maximum likelihood value and precision178 (inverse variance of noise: *NOT* of the fitted Gaussian).179 '''180 # Fit the Gaussian using least squares181 dim = Pair2D(sig_f.shape[1], sig_f.shape[0])182 X, Y = np.meshgrid( # pylint: disable=unbalanced-tuple-unpacking183 np.arange(dim.x, dtype=np.double),184 np.arange(dim.y, dtype=np.double))185 others = Pair2D(X.flatten(), Y.flatten())186 a = Pair2D(None, None)187 def gaussian_diff(x):188 '''Compute error.'''189 a.x = x[1] # mu_x190 a.y = x[2] # mu_y191 dist = twisted_torus_distance(a, others, dim)192 # A sigma193 # | |194 return (np.abs(x[0]) * np.exp(-dist ** 2 / 2. / x[3] ** 2) -195 sig_f.ravel())196 xest, _ = scipy.optimize.leastsq(gaussian_diff,197 np.array([i.A, i.mu_x, i.mu_y, i.sigma]))198 err2 = gaussian_diff(xest) ** 2199 # Remap the values modulo torus size200 xest[1] = xest[1] % dim.x201 xest[2] = xest[2] % dim.y202 # Compute the log-likelihood203 n = dim.x * dim.y204 aic_correction = 5 # Number of optimized parameters205 beta = 1.0 / (np.mean(err2))206 ln_lh = -beta / 2. * np.sum(err2) + \207 n / 2. * np.log(beta) - \208 n / 2. * np.log(2 * np.pi) - \209 aic_correction210 return MLGaussianFit(xest[0], xest[1], xest[2], xest[3], err2, ln_lh, beta)211def fit_gaussian_bump_tt(sig):212 '''Fit a 2D Gaussian onto a (potential) firing rate bump on the twisted213 torus.214 Parameters215 ----------216 sig : np.ndarray217 2D firing rate map to fit. Axis 0 is the Y position. This will be218 passed directly to :func:`~analysis.image.fit_gaussian_tt`.219 Returns220 -------221 :class:`analysis.image.MLGaussianFit`222 Estimated values of the fit.223 Notes224 -----225 The function initialises the Gaussian fitting parameters to a position at226 the maximum of `sig`.227 '''228 mu0_y, mu0_x = np.unravel_index(np.argmax(sig), sig.shape)229 a0 = sig[mu0_y, mu0_x]230 sigma0 = np.max(sig.shape) / 4.231 init = SymmetricGaussianParams(a0, mu0_x, mu0_y, sigma0, None)232 return fit_gaussian_tt(sig, init)233def fit_maximum_lh(sig):234 '''Fit a maximum likelihood solution under Gaussian noise.235 Parameters236 ----------237 sig : np.ndarray238 A vector containing the samples239 Returns240 fit : MLFit241 Maximum likelihood parameters242 '''243 sig = sig.flatten()244 mu = np.mean(sig)245 sigma2 = np.var(sig)246 err2 = (sig - mu) ** 2247 if sigma2 == 0:248 ln_lh = np.inf249 else:250 n = len(sig)251 aic_correction = 2252 ln_lh = -.5 / sigma2 * np.sum((sig - mu) ** 2) - \253 .5 * n * np.log(sigma2) - \254 .5 * n * np.log(2 * np.pi) - \255 aic_correction256 return MLFit(mu, sigma2, ln_lh, err2)257class SingleBumpPopulation(spikes.TwistedTorusSpikes):258 '''259 A population of neurons that is supposed to form a bump on a twisted torus.260 Parameters261 ----------262 senders : array_like263 A an array of neurons' IDs.264 times : array_like265 An array of spike times. Length must be the same as as <senders>.266 sheet_size : A pair267 A pair of X and Y dimensions of the torus.268 '''269 def __init__(self, senders, times, sheet_size):270 super(SingleBumpPopulation, self).__init__(senders, times, sheet_size)271 def _perform_fit(self, tstart, tend, dt, win_len, fit_callable, list_cls,272 full_err=True):273 '''Perform the fit given the requested ``fit_callable``.'''274 F, Ft = self.sliding_firing_rate(tstart, tend, dt, win_len)275 res = list_cls()276 for tIdx in range(len(Ft)):277 LOGGER.debug('%s:: fitting: %d/%d, %.3f/%.3f ',278 fit_callable.__name__, tIdx + 1, len(Ft), Ft[tIdx],279 Ft[-1])280 fit_params = fit_callable(F[:, :, tIdx])281 if not full_err:282 fit_params.err2 = np.sum(fit_params.err2)283 res.append_data(fit_params, Ft[tIdx])284 return res285 def bump_position(self, tstart, tend, dt, win_len, full_err=True):286 '''Estimate bump positions during the simulation time:287 1. Estimates population firing rate for each bin.288 2. Apply the bump position estimation procedure to each of the289 population activity items.290 Parameters291 ----------292 tstart, tend, dt, win_len : float293 Start and end time, time step, and window length. See also294 :meth:`~gridcells.analysis.spikes.PopulationSpikes.sliding_firing_rate`.295 full_err : bool296 If ``True``, save the full error of fit. Otherwise a sum only.297 Returns298 -------299 pos:list :class:`MLGaussianFitList`300 A list of fitted Gaussian parameters301 Notes302 -----303 This method uses the Maximum likelihood estimator to fit the Gaussian304 function (:meth:`~fit_gaussian_bump_tt`)305 '''306 return self._perform_fit(tstart, tend, dt, win_len,307 fit_gaussian_bump_tt, MLGaussianFitList,308 full_err=full_err)309 def uniform_fit(self, tstart, tend, dt, win_len, full_err=True):310 '''Estimate the mean firing rate using maximum likelihood estimator311 (:func:`~gridcells.analysis.image.fit_maximum_lh`)312 1. Uses :meth:`sliding_firing_rate`.313 2. Apply the estimator.314 Parameters315 ----------316 tstart, tend, dt, win_len317 As in :py:meth:`~analysis.spikes.sliding_firing_rate`.318 full_err : bool319 If ``True``, save the full error of fit. Otherwise a sum only.320 Returns321 -------322 MLFitList323 A list of fitted parameters.324 '''325 return self._perform_fit(tstart, tend, dt, win_len, fit_maximum_lh,...
art_misc.py
Source:art_misc.py
1#!/usr/bin/env python2# Copyright (C) 2002-2018 CERN for the benefit of the ATLAS collaboration3"""Miscellaneous functions."""4__author__ = "Tulay Cuhadar Donszelmann <tcuhadar@cern.ch>"5import concurrent.futures6import logging7import os8import shlex9import subprocess10import sys11from datetime import datetime12MODULE = "art.misc"13EOS_MGM_URL = 'root://eosatlas.cern.ch/'14KByte = 102415MByte = KByte * 102416GByte = MByte * 102417def set_log(kwargs):18 """Set the default log level and message format depending on --verbose or --quiet options."""19 level = logging.DEBUG if kwargs['verbose'] else logging.WARN if kwargs['quiet'] else logging.INFO20 log = logging.getLogger("art")21 log.setLevel(level)22 # create and attach new handler, disable propagation to root logger to avoid double messages23 handler = logging.StreamHandler(sys.stdout)24 format_string = "%(asctime)s %(name)15s.%(funcName)-15s %(levelname)8s %(message)s"25 date_format_string = None26 formatter = logging.Formatter(format_string, date_format_string)27 handler.setFormatter(formatter)28 log.addHandler(handler)29 log.propagate = False30def get_atlas_env():31 """Get all environment variables."""32 log = logging.getLogger(MODULE)33 try:34 nightly_release = os.environ['AtlasBuildBranch']35 project = os.environ['AtlasProject']36 platform = os.environ[project + '_PLATFORM']37 nightly_tag = os.environ['AtlasBuildStamp']38 return (nightly_release, project, platform, nightly_tag)39 except KeyError, e:40 log.critical("Environment variable not set %s", e)41 sys.exit(1)42def run_command(cmd, dir=None, shell=False, env=None, verbose=True):43 """44 Run the given command locally.45 The command runs as separate subprocesses for every piped command.46 Returns tuple of exit_code, output and err.47 """48 # leave at print for basic debugging, log sometimes lost49 start_time = datetime.now()50 if verbose:51 print "Execute:", cmd52 if "|" in cmd:53 cmd_parts = cmd.split('|')54 else:55 cmd_parts = []56 cmd_parts.append(cmd)57 i = 058 p = {}59 for cmd_part in cmd_parts:60 cmd_part = cmd_part.strip()61 if i == 0:62 p[i] = subprocess.Popen(shlex.split(cmd_part), stdin=None, stdout=subprocess.PIPE, stderr=subprocess.PIPE, cwd=dir, shell=shell, env=env)63 else:64 p[i] = subprocess.Popen(shlex.split(cmd_part), stdin=p[i - 1].stdout, stdout=subprocess.PIPE, stderr=subprocess.PIPE, cwd=dir, shell=shell, env=env)65 i = i + 166 (output, err) = p[i - 1].communicate()67 exit_code = p[0].wait()68 end_time = datetime.now()69 return (exit_code, str(output), str(err), cmd, start_time, end_time)70def run_command_parallel(cmd, nthreads, ncores, dir=None, shell=False, env=None, verbose=True):71 """72 Run the given command locally in parallel.73 The command runs as separate subprocesses for every piped command.74 Returns tuple of exit_code, output and err.75 """76 start_time = datetime.now()77 log = logging.getLogger(MODULE)78 ncores = min(ncores, nthreads)79 if env is None:80 env = os.environ.copy()81 env['ArtThreads'] = str(nthreads)82 env['ArtCores'] = str(ncores)83 # Results84 full_exit_code = 085 full_out = ''86 full_err = ''87 # Start88 env['ArtProcess'] = "start"89 (exit_code, out, err, command, start_time_start, end_time_start) = run_command(cmd, dir=dir, shell=shell, env=env, verbose=verbose)90 full_exit_code = full_exit_code if exit_code == 0 else exit_code91 full_out += "-+-art-process start out " + start_time_start.strftime('%Y-%m-%dT%H:%M:%S') + "\n"92 full_out += out93 full_out += "---art-process start out " + end_time_start.strftime('%Y-%m-%dT%H:%M:%S') + "\n"94 full_err += "-+-art-process start err " + start_time_start.strftime('%Y-%m-%dT%H:%M:%S') + "\n"95 full_err += err96 full_err += "---art-process start err " + end_time_start.strftime('%Y-%m-%dT%H:%M:%S') + "\n"97 log.info("Creating executor with cores: %d", ncores)98 executor = concurrent.futures.ThreadPoolExecutor(ncores)99 future_set = []100 # Processing101 log.info("Running threads: %d", nthreads)102 for index in range(nthreads):103 process_env = env.copy()104 process_env['ArtProcess'] = str(index)105 future_set.append(executor.submit(run_command, cmd, dir=dir, shell=shell, env=process_env, verbose=verbose))106 log.info("Waiting for threads to finish...")107 concurrent.futures.wait(future_set)108 for index, future in enumerate(future_set):109 (exit_code, out, err, command, start_time_process, end_time_process) = future.result()110 full_exit_code = full_exit_code if exit_code == 0 else exit_code111 full_out += "-+-art-process " + str(index) + " out " + start_time_process.strftime('%Y-%m-%dT%H:%M:%S') + "\n"112 full_out += out113 full_out += "---art-process " + str(index) + " out " + end_time_process.strftime('%Y-%m-%dT%H:%M:%S') + "\n"114 full_err += "-+-art-process " + str(index) + " err " + start_time_process.strftime('%Y-%m-%dT%H:%M:%S') + "\n"115 full_err += err116 full_err += "---art-process " + str(index) + " err " + end_time_process.strftime('%Y-%m-%dT%H:%M:%S') + "\n"117 # End118 env['ArtProcess'] = "end"119 (exit_code, out, err, command, start_time_end, end_time_end) = run_command(cmd, dir=dir, shell=shell, env=env, verbose=verbose)120 full_exit_code = full_exit_code if exit_code == 0 else exit_code121 full_out += "-+-art-process end out " + start_time_end.strftime('%Y-%m-%dT%H:%M:%S') + "\n"122 full_out += out123 full_out += "---art-process end out " + end_time_end.strftime('%Y-%m-%dT%H:%M:%S') + "\n"124 full_err += "-+-art-process end err " + start_time_end.strftime('%Y-%m-%dT%H:%M:%S') + "\n"125 full_err += err126 full_err += "---art-process end err " + end_time_end.strftime('%Y-%m-%dT%H:%M:%S') + "\n"127 end_time = datetime.now()128 return (full_exit_code, full_out, full_err, cmd, start_time, end_time)129def is_exe(path):130 """Return True if path is executable."""131 return os.path.isfile(path) and os.access(path, os.X_OK)132def make_executable(path):133 """Make file executable (chmod +x)."""134 mode = os.stat(path).st_mode135 mode |= (mode & 0o444) >> 2 # copy R bits to X136 os.chmod(path, mode)137def mkdir(path):138 """Make (missing) directories."""139 log = logging.getLogger(MODULE)140 if path.startswith('/eos'):141 mkdir_cmd = 'eos ' + EOS_MGM_URL + ' mkdir -p'142 else:143 mkdir_cmd = 'mkdir -p'144 if mkdir_cmd is not None:145 (exit_code, out, err, command, start_time, end_time) = run_command(' '.join((mkdir_cmd, path)))146 if exit_code != 0:147 log.error("Mkdir Error: %d %s %s", exit_code, out, err)148 return exit_code149 return 0150def ls(path):151 """List files in directroy."""152 if path.startswith('/eos'):153 ls_cmd = 'eos ' + EOS_MGM_URL + ' ls ' + path + '/'154 else:155 ls_cmd = 'ls ' + path + '/'156 (exit_code, out, err, command, start_time, end_time) = run_command(ls_cmd)157 if exit_code == 0:158 print out159 print err160 return exit_code161def cp(src, dst):162 """Copy files to directory."""163 log = logging.getLogger(MODULE)164 if dst.startswith('/eos'):165 # check which xrdcp we are running166 (exit_code, out, err, command, start_time, end_time) = run_command('which xrdcp')167 print out168 print err169 # check which version of xrdcp we are running170 (exit_code, out, err, command, start_time, end_time) = run_command('xrdcp --version')171 print out172 print err173 cmd = ' '.join(('xrdcp -f -N -r -p -v', src, EOS_MGM_URL + dst + '/'))174 else:175 cmd = ' '.join(('xrdcp -f -N -r -p -v', src, dst + '/'))176 # run the actual command177 log.info("Using: %s", cmd)178 (exit_code, exit_out, exit_err, command, start_time, end_time) = run_command(cmd)179 if exit_code != 0:180 log.error("COPY to DST Error: %d %s %s", exit_code, exit_out, exit_err)181 return exit_code182def count_files(path):183 """Count number of files."""184 log = logging.getLogger(MODULE)185 if path.startswith('/eos'):186 cmd = ' '.join(('eos', EOS_MGM_URL, 'find', path, '|', 'wc', '-l'))187 else:188 cmd = ' '.join(('find', path, '|', 'wc', '-l'))189 (exit_code, out, err, command, start_time, end_time) = run_command(cmd)190 if exit_code == 0:191 nFiles = int(out)192 return nFiles193 log.error("Error retrieving number of files on %s, %s", path, err)194 return -1195def touch(fname, times=None):196 """Touch a file."""197 with open(fname, 'a'):198 os.utime(fname, times)199def rm(fname):200 """Remove a file."""201 try:202 os.remove(fname)203 except OSError:204 pass205def which(program):206 """Show which program is actually found on the PATH."""207 fpath, fname = os.path.split(program)208 if fpath:209 if is_exe(program):210 return program211 else:212 for path in os.environ["PATH"].split(os.pathsep):213 path = path.strip('"')214 exe_file = os.path.join(path, program)215 if is_exe(exe_file):216 return exe_file217 return None218def memory(scale=1):219 """Return free memory."""...
ch4ex4.py
Source:ch4ex4.py
1# Example 4.42# Linearization3from pylab import*4# Clean up5clf()6# Obtain true solution using sympy if available7try:8 from sympy import dsolve, Derivative, symbols9 y, t = symbols("y t", function = True)10 y = dsolve(Derivative(y(t), t) + y(t)*(1 - y(t)), 0, ics={y(0): .5}).rhs11 print("y(t) =", y)12 true_solution = y.evalf(subs = {t:1.})13except ImportError:14 # suppy the true soln15 true_solution = 1./(exp(1.) + 1.)16# Setup schemes17# Linearized Trapeziodal method18lin_trap = lambda y, h: y + h*y*(y - 1.)/(1. - h*(y - 1./2.))19full_trap = lambda y, h: (2./h + 1. - sqrt((2./h + 1.)**2 - 4.*(2./h*y + y*(y - 1.))))/2.20# Collect Data21H = logspace(0., 2.7, 10).round()22STEPS = zeros(len(H))23LIN_ERR = zeros(len(H))24FULL_ERR = zeros(len(H))25for i in range(len(H)):26 N = H[i]27 h = 1./N28 yl = 1./2.29 yf = 1./2.30 for j in range(int(N)):31 yl = lin_trap(yl, h)32 yf = full_trap(yf, h)33 STEPS[i] = N34 LIN_ERR[i] = abs(yl - true_solution)35 FULL_ERR[i] = abs(yf - true_solution)36# Plot37figure(1); clf()38loglog(STEPS, LIN_ERR, "o-", mfc = "none", label = "Trapeziodal")39loglog(STEPS, FULL_ERR, "s-", mfc = "none", label = "Linearized Trapeziodal")40grid("on")41xlabel("N -- Number of Steps", fontsize = 14)42ylabel("Error", fontsize = 14)43legend(loc = 0)...
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