#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2020 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
"""Analyze pickled data demo.
Usage:
analyze_pickle.py histogram [--detailed=DETAILED_DATA] [--error-norm=NORM] REDUCED_DATA SAMPLES
analyze_pickle.py convergence [--detailed=DETAILED_DATA] [--error-norm=NORM] [--ndim=NDIM] REDUCED_DATA SAMPLES
analyze_pickle.py (-h | --help)
This demo loads a pickled reduced model, solves for random
parameters, estimates the reduction errors and then visualizes these
estimates. If the detailed model and the reductor are
also provided, the estimated error is visualized in comparison to
the real reduction error.
The needed data files are created by the thermal block demo, by
setting the '--pickle' option.
Arguments:
REDUCED_DATA File containing the pickled reduced model.
SAMPLES Number of parameter samples to test with.
Options:
--detailed=DETAILED_DATA File containing the high-dimensional model
and the reductor.
--error-norm=NORM Name of norm in which to compute the errors.
--ndim=NDIM Number of reduced basis dimensions for which to estimate
the error.
"""
import sys
import time
import numpy as np
import matplotlib.pyplot as plt
from docopt import docopt
from pymor.core.pickle import load
[docs]def _bins(start, stop, steps=100):
''' numpy has a quirk in unreleased master where logspace
might sometimes not return a 1d array
'''
bins = np.logspace(np.log10(start), np.log10(stop), steps)
if bins.shape == (steps,1):
bins = bins[:,0]
return bins
[docs]def analyze_pickle_histogram(args):
args['SAMPLES'] = int(args['SAMPLES'])
print('Loading reduced model ...')
rom, parameter_space = load(open(args['REDUCED_DATA'], 'rb'))
mus = parameter_space.sample_randomly(args['SAMPLES'])
us = []
for mu in mus:
print(f'Solving reduced for {mu} ... ', end='')
sys.stdout.flush()
us.append(rom.solve(mu))
print('done')
print()
if hasattr(rom, 'estimate'):
ests = []
for u, mu in zip(us, mus):
print(f'Estimating error for {mu} ... ', end='')
sys.stdout.flush()
ests.append(rom.estimate(u, mu=mu))
print('done')
if args['--detailed']:
print('Loading high-dimensional data ...')
fom, reductor = load(open(args['--detailed'], 'rb'))
errs = []
for u, mu in zip(us, mus):
print(f'Calculating error for {mu} ... ')
sys.stdout.flush()
err = fom.solve(mu) - reductor.reconstruct(u)
if args['--error-norm']:
errs.append(np.max(getattr(fom, args['--error-norm'] + '_norm')(err)))
else:
errs.append(np.max(err.l2_norm()))
print('done')
print()
try:
plt.style.use('ggplot')
except AttributeError:
pass # plt.style is only available in newer matplotlib versions
if hasattr(rom, 'estimate') and args['--detailed']:
# setup axes
left, width = 0.1, 0.65
bottom, height = 0.1, 0.65
bottom_h = left_h = left+width+0.02
rect_scatter = [left, bottom, width, height]
rect_histx = [left, bottom_h, width, 0.2]
rect_histy = [left_h, bottom, 0.2, height]
plt.figure(1, figsize=(8, 8))
axScatter = plt.axes(rect_scatter)
axHistx = plt.axes(rect_histx)
axHisty = plt.axes(rect_histy)
# scatter plot
total_min = min(np.min(ests), np.min(errs)) * 0.9
total_max = max(np.max(ests), np.max(errs)) * 1.1
axScatter.set_xscale('log')
axScatter.set_yscale('log')
axScatter.set_xlim([total_min, total_max])
axScatter.set_ylim([total_min, total_max])
axScatter.set_xlabel('errors')
axScatter.set_ylabel('estimates')
axScatter.plot([total_min, total_max], [total_min, total_max], 'r')
axScatter.scatter(errs, ests)
# plot histograms
x_hist, x_bin_edges = np.histogram(errs, bins=_bins(total_min, total_max))
axHistx.bar(x_bin_edges[1:], x_hist, width=x_bin_edges[:-1] - x_bin_edges[1:], color='blue')
y_hist, y_bin_edges = np.histogram(ests, bins=_bins(total_min, total_max))
axHisty.barh(y_bin_edges[1:], y_hist, height=y_bin_edges[:-1] - y_bin_edges[1:], color='blue')
axHistx.set_xscale('log')
axHisty.set_yscale('log')
axHistx.set_xticklabels([])
axHisty.set_yticklabels([])
axHistx.set_xlim(axScatter.get_xlim())
axHisty.set_ylim(axScatter.get_ylim())
axHistx.set_ylim([0, max(np.max(x_hist), np.max(y_hist))])
axHisty.set_xlim([0, max(np.max(x_hist), np.max(y_hist))])
plt.show()
elif hasattr(rom, 'estimate'):
total_min = np.min(ests) * 0.9
total_max = np.max(ests) * 1.1
hist, bin_edges = np.histogram(ests, bins=_bins(total_min, total_max))
plt.bar(bin_edges[1:], hist, width=bin_edges[:-1] - bin_edges[1:], color='blue')
plt.xlim([total_min, total_max])
plt.xscale('log')
plt.xlabel('estimated error')
plt.show()
elif args['--detailed']:
total_min = np.min(ests) * 0.9
total_max = np.max(ests) * 1.1
hist, bin_edges = np.histogram(errs, bins=_bins(total_min, total_max))
plt.bar(bin_edges[1:], hist, width=bin_edges[:-1] - bin_edges[1:], color='blue')
plt.xlim([total_min, total_max])
plt.xscale('log')
plt.xlabel('error')
plt.show()
else:
raise ValueError('Nothing to plot!')
[docs]def analyze_pickle_convergence(args):
args['SAMPLES'] = int(args['SAMPLES'])
print('Loading reduced model ...')
rom, parameter_space = load(open(args['REDUCED_DATA'], 'rb'))
if not args['--detailed']:
raise ValueError('High-dimensional data file must be specified.')
print('Loading high-dimensional data ...')
fom, reductor = load(open(args['--detailed'], 'rb'))
fom.enable_caching('disk')
dim = rom.solution_space.dim
if args['--ndim']:
dims = np.linspace(0, dim, args['--ndim'], dtype=np.int)
else:
dims = np.arange(dim + 1)
mus = parameter_space.sample_randomly(args['SAMPLES'])
ESTS = []
ERRS = []
T_SOLVES = []
T_ESTS = []
for N in dims:
rom = reductor.reduce(N)
print(f'N = {N:3} ', end='')
us = []
print('solve ', end='')
sys.stdout.flush()
start = time.time()
for mu in mus:
us.append(rom.solve(mu))
T_SOLVES.append((time.time() - start) * 1000. / len(mus))
print('estimate ', end='')
sys.stdout.flush()
if hasattr(rom, 'estimate'):
ests = []
start = time.time()
for u, mu in zip(us, mus):
# print('e', end='')
# sys.stdout.flush()
ests.append(rom.estimate(u, mu=mu))
ESTS.append(max(ests))
T_ESTS.append((time.time() - start) * 1000. / len(mus))
print('errors', end='')
sys.stdout.flush()
errs = []
for u, mu in zip(us, mus):
err = fom.solve(mu) - reductor.reconstruct(u)
if args['--error-norm']:
errs.append(np.max(getattr(fom, args['--error-norm'] + '_norm')(err)))
else:
errs.append(np.max(err.l2_norm()))
ERRS.append(max(errs))
print()
print()
try:
plt.style.use('ggplot')
except AttributeError:
pass # plt.style is only available in newer matplotlib versions
plt.subplot(1, 2, 1)
if hasattr(rom, 'estimate'):
plt.semilogy(dims, ESTS, label='max. estimate')
plt.semilogy(dims, ERRS, label='max. error')
plt.xlabel('dimension')
plt.legend()
plt.subplot(1, 2, 2)
plt.plot(dims, T_SOLVES, label='avg. solve time')
if hasattr(rom, 'estimate'):
plt.plot(dims, T_ESTS, label='avg. estimate time')
plt.xlabel('dimension')
plt.ylabel('milliseconds')
plt.legend()
plt.show()
[docs]def analyze_pickle_demo(args):
if args['histogram']:
analyze_pickle_histogram(args)
else:
analyze_pickle_convergence(args)
if __name__ == '__main__':
# parse arguments
args = docopt(__doc__)
# run demo
analyze_pickle_demo(args)