# matplotlib.rcParams.update({'font.size': 18})
# Source: docs.scipy.org/doc/scipy/reference/odr.html
def linear(b, x):
return b[0] * x + b[1]
mean = (2.5, 2.5)
cov = [[1.5, 0.3], [0.7, 1.5]]
data = np.random.multivariate_normal(mean, cov, 10)
x = [max(0.5, min(s[0], 4.5)) for s in data]
y = [max(0.5, min(s[1], 4.5)) for s in data]
odr_result = odr(linear, [0, 0], y, x, full_output=1)
m, b = odr_result[0]
m = round(m, 6)
b = round(b, 6)
f_odr = np.poly1d((m, b))
ols_result = linregress(x, y)
m, b = ols_result[0:2]
m = round(m, 6)
b = round(b, 6)
f_ols = np.poly1d((m, b))
r = [-1, 6]
fig = figure(figsize=(14, 7))
ax1 = fig.add_subplot(121)
def plot(args):
import os, os.path
import h5py
from matplotlib import pyplot as plt
import h5md._plot.label
from numpy import *
#from matplotlib import ticker
# import ssf
# import pycuda only if required
if args.cuda:
import pycuda.autoinit
make_cuda_kernels()
ax = plt.axes()
label = None
ax.axhline(y=1, color='black', lw=0.5)
ax.set_color_cycle(args.colors)
for (i, fn) in enumerate(args.input):
try:
f = h5py.File(fn, 'r')
except IOError:
raise SystemExit('failed to open HDF5 file: %s' % fn)
try:
try:
param = f['halmd' in f.keys() and 'halmd' or 'parameters'] # backwards compatibility
except KeyError:
param = None
# determine file type, prefer precomputed SSF data
ssf_path = 'structure/' + '/'.join(args.flavour) + '/static_structure_factor'
if ssf_path in f:
# load SSF from file
H5 = f[ssf_path]
q = H5['wavenumber'].__array__() # store in memory by conversion to NumPy array
S_q, S_q_err = load_ssf(H5, args)
elif 'structure/ssf/' + '/'.join(args.flavour) in f: # backwards compatibility
# load SSF from file
H5 = f['structure/ssf/' + '/'.join(args.flavour)]
q = f['structure/ssf/wavenumber'].__array__() # store in memory by conversion to NumPy array
S_q, S_q_err = load_ssf(H5, args)
elif 'trajectory' in f.keys() and param:
# compute SSF from trajectory data
H5 = f['trajectory/' + args.flavour[0]]
q, S_q = ssf_from_trajectory(H5['position'], param, args)
else:
raise SystemExit('Input file provides neither SSF data nor a trajectory')
# before closing the file, store attributes for later use
if param:
attrs = h5md._plot.label.attributes(param)
else:
attrs = {}
except IndexError:
raise SystemExit('invalid phase space sample offset')
except KeyError as what:
raise SystemExit(str(what) + '\nmissing simulation data in file: %s' % fn)
finally:
f.close()
if args.label:
label = args.label[i % len(args.label)] % attrs
elif args.legend or not args.small:
basename = os.path.splitext(os.path.basename(fn))[0]
label = r'%s' % basename.replace('_', r'\_')
if args.title:
title = args.title % attrs
c = args.colors[i % len(args.colors)]
ax.plot(q, S_q, '-', color=c, label=label)
if 'S_q_err' in locals():
ax.errorbar(q, S_q, S_q_err, fmt='o', color=c, markerfacecolor=c, markeredgecolor=c, markersize=2, linewidth=.5)
else:
ax.plot(q, S_q, 'o', markerfacecolor=c, markeredgecolor=c, markersize=2)
# optionally fit Ornstein-Zernike form
if args.fit_ornstein_zernike:
import scipy.odr as odr
density = attrs['density']
temperature = attrs['temperature']
idx, = where(q <= args.fit_limit)
kappa = mean(S_q[idx]) / density / temperature # initial guess
# result is a tuple (param, param_err, covariance_matrix)
param, param_err = odr.odr(
ornstein_zernike_log # fit model
, (kappa, 1) # initial parameter values (kappa, xi)
, S_q[idx], log(q[idx]) # data (y, x)
, extra_args=(density, temperature,), full_output=0
)[:2]
kappa, xi = abs(param)
kappa_err, xi_err = param_err
if args.verbose:
print 'Density: {0:g}'.format(density)
print 'Temperature: {0:g}'.format(temperature)
print 'Compressibility: {0:g} ± {1:g}'.format(kappa, kappa_err)
print 'Correlation length: {0:g} ± {1:g}'.format(xi, xi_err)
if args.axes == 'loglog' or args.axes == 'xlog':
xmin = args.xlim and args.xlim[0] or 0.01
x = logspace(log10(xmin), log10(3 * args.fit_limit), num=20)
else:
x = linspace(0, 3 * args.fit_limit, num=20)
y = ornstein_zernike((kappa, xi), x, density, temperature)
ax.plot(x, y, ':', color=c, linewidth=.8)
# write plot data to file
if args.dump:
f = open(args.dump, 'a')
print >>f, '# %s, sample %s' % (label.replace(r'\_', '_'), args.sample)
if 'S_q_err' in locals():
print >>f, '# q S_q S_q_err'
savetxt(f, array((q, S_q, S_q_err)).T)
else:
print >>f, '# q S_q'
savetxt(f, array((q, S_q)).T)
print >>f, '\n'
f.close()
# optionally plot power laws
if args.power_law:
p = reshape(args.power_law, (-1, 4))
for (pow_exp, pow_coeff, pow_xmin, pow_xmax) in p:
px = logspace(log10(pow_xmin), log10(pow_xmax), num=100)
py = pow_coeff * pow(px, pow_exp)
ax.plot(px, py, 'k--')
# adjust axis ranges
ax.axis('tight')
if args.xlim:
plt.setp(ax, xlim=args.xlim)
if args.ylim:
plt.setp(ax, ylim=args.ylim)
else:
plt.setp(ax, ylim=(0, plt.ylim()[1]))
# optionally plot with logarithmic scale(s)
if args.axes == 'xlog':
ax.set_xscale('log')
if args.axes == 'ylog':
ax.set_yscale('log')
if args.axes == 'loglog':
ax.set_xscale('log')
ax.set_yscale('log')
if args.legend or not args.small:
l = ax.legend(loc=args.legend)
l.legendPatch.set_alpha(0.7)
plt.xlabel(args.xlabel or r'Wavenumber $q\sigma$')
plt.ylabel(args.ylabel or r'Static structure factor $S(q)$')
if args.output is None:
plt.show()
else:
plt.savefig(args.output, dpi=args.dpi)
def wrap_odr(self, fun, p0, x, y, *args):
return odr.odr(fun, p0, y, x, extra_args=args)[0]
def plot(args):
from matplotlib import pyplot as plt
# import pycuda only if required
if args.cuda:
import pycuda.autoinit
make_cuda_kernels()
ax = plt.axes()
label = None
ax.axhline(y=1, color='black', lw=0.5)
ax.set_color_cycle(args.colors)
for (i, fn) in enumerate(args.input):
try:
f = tables.openFile(fn, mode='r')
except IOError:
raise SystemExit('failed to open HDF5 file: %s' % fn)
try:
H5 = f.root
param = H5.param
# determine file type, prefer precomputed SSF data
if 'structure' in H5._v_groups and 'ssf' in H5.structure._v_groups:
# load SSF from file
H5ssf = H5.structure.ssf._v_children[args.flavour or 'AA']
q = H5.structure.ssf.wavenumber[0]
S_q, S_q_err = load_ssf(H5ssf, args)
elif 'trajectory' in H5._v_groups:
# compute SSF from trajectory data
if args.flavour:
H5trj = H5.trajectory._v_children[args.flavour]
else:
H5trj = H5.trajectory
q, S_q = ssf_from_trajectory(H5trj, param, args)
else:
raise SystemExit('Input file provides neither SSF data nor a trajectory')
# before closing the file, store attributes for later use
attrs = mdplot.label.attributes(param)
except IndexError:
raise SystemExit('invalid phase space sample offset')
except tables.exceptions.NoSuchNodeError as what:
raise SystemExit(str(what) + '\nmissing simulation data in file: %s' % fn)
finally:
f.close()
if args.label:
label = args.label[i % len(args.label)] % attrs
elif args.legend or not args.small:
basename = os.path.splitext(os.path.basename(fn))[0]
label = r'%s' % basename.replace('_', r'\_')
if args.title:
title = args.title % attrs
c = args.colors[i % len(args.colors)]
ax.plot(q, S_q, '-', color=c, label=label)
if 'S_q_err' in locals():
ax.errorbar(q, S_q, S_q_err, fmt='o', color=c, markerfacecolor=c, markeredgecolor=c, markersize=2, linewidth=.5)
else:
ax.plot(q, S_q, 'o', markerfacecolor=c, markeredgecolor=c, markersize=2)
# optionally fit Ornstein-Zernike form
if args.fit_ornstein_zernike:
density = attrs['density']
temperature = attrs['temperature']
idx, = where(q <= args.fit_limit)
kappa = mean(S_q[idx]) / density / temperature # initial guess
# result is a tuple (param, param_err, covariance_matrix)
param, param_err = odr.odr(
ornstein_zernike_log # fit model
, (kappa, 1) # initial parameter values (kappa, xi)
, S_q[idx], log(q[idx]) # data (y, x)
, extra_args=(density, temperature,), full_output=0
)[:2]
kappa, xi = abs(param)
kappa_err, xi_err = param_err
if args.verbose:
print 'Density: {0:g}'.format(density)
print 'Temperature: {0:g}'.format(temperature)
print 'Compressibility: {0:g} ± {1:g}'.format(kappa, kappa_err)
print 'Correlation length: {0:g} ± {1:g}'.format(xi, xi_err)
if args.axes == 'loglog' or args.axes == 'xlog':
x = logspace(log10(args.xlim[0] or .01), log10(3 * args.fit_limit), num=20)
else:
x = linspace(0, 3 * args.fit_limit, num=20)
y = ornstein_zernike((kappa, xi), x, density, temperature)
ax.plot(x, y, ':', color=c, linewidth=.8)
# write plot data to file
if args.dump:
f = open(args.dump, 'a')
print >>f, '# %s, sample %s' % (label.replace(r'\_', '_'), args.sample)
if 'S_q_err' in locals():
print >>f, '# q S_q S_q_err'
savetxt(f, array((q, S_q, S_q_err)).T)
else:
print >>f, '# q S_q'
savetxt(f, array((q, S_q)).T)
print >>f, '\n'
f.close()
# optionally plot power laws
if args.power_law:
p = reshape(args.power_law, (-1, 4))
for (pow_exp, pow_coeff, pow_xmin, pow_xmax) in p:
px = logspace(log10(pow_xmin), log10(pow_xmax), num=100)
py = pow_coeff * pow(px, pow_exp)
ax.plot(px, py, 'k--')
# adjust axis ranges
ax.axis('tight')
if args.xlim:
plt.setp(ax, xlim=args.xlim)
if args.ylim:
plt.setp(ax, ylim=args.ylim)
else:
plt.setp(ax, ylim=(0, plt.ylim()[1]))
# optionally plot with logarithmic scale(s)
if args.axes == 'xlog':
ax.set_xscale('log')
if args.axes == 'ylog':
ax.set_yscale('log')
if args.axes == 'loglog':
ax.set_xscale('log')
ax.set_yscale('log')
if args.legend or not args.small:
l = ax.legend(loc=args.legend)
l.legendPatch.set_alpha(0.7)
plt.xlabel(args.xlabel or r'$\lvert\textbf{q}\rvert\sigma$')
plt.ylabel(args.ylabel or r'$S(\lvert\textbf{q}\rvert)$')
if args.output is None:
plt.show()
else:
plt.savefig(args.output, dpi=args.dpi)
def fit_line(points):
if len(points) < 2:
return False
elif len(points) == 2:
return Line(points[0], points[1])
else:
x = [p[0] for p in points]
y = [p[1] for p in points]
switched = False
if abs(x[0] - x[-1]) < abs(y[0] - y[-1]):
switched = True
x_temp = list(x)
x = list(y)
y = list(x_temp)
# print('Switched axes')
odr_result = odr(linear, [0, 0], y, x, full_output=1)
m, b = odr_result[0]
m = round(m, 6)
b = round(b, 6)
f = np.poly1d((m, b))
# if switched:
# print('ODR: x = {}y + {}'.format(m, b))
# else:
# print('ODR: y = {}x + {}'.format(m, b))
#
# stop_cond = odr_result[3]['info']
# if stop_cond < 1 or stop_cond > 3:
# print('Warning: ODR did not converge to a solution (stop condition {})'.format(stop_cond))
#
# ols_result = linregress(x, y)
# m, b = ols_result[0:2]
# m = round(m, 6)
# b = round(b, 6)
# f_ols = np.poly1d((m, b))
#
# if switched:
# print('OLS: x = {}y + {}'.format(m, b))
# else:
# print('OLS: y = {}x + {}'.format(m, b))
x1 = x[0]
x2 = x[-1]
if switched:
p1 = round(f(x1)), x1
p2 = round(f(x2)), x2
line = Line(p1, p2)
# pixels = line.pixels()
# x_temp = list(x)
# x = list(y)
# y = list(x_temp)
else:
p1 = x1, round(f(x1))
p2 = x2, round(f(x2))
line = Line(p1, p2)
# pixels = line.pixels()
# x_l = [p[0] for p in pixels]
# y_l = [p[1] for p in pixels]
#
# t_x = (min(x) - 1, max(x) + 1)
# t_y = (min(y) - 1, max(y) + 1)
# t = range(t_x[0], t_x[1] + 1, 1)
#
# plt.figure()
# ax = plt.gca()
# ax.plot(x, y, 'g', linewidth=3)
# ax.plot(x_l, y_l, 'b', linewidth=3)
# ax.plot(t, f(t), 'c--', linewidth=3)
# ax.plot(t, f_ols(t), 'r--', linewidth=3)
# ax.set_xlim(t_x)
# ax.set_ylim(t_y)
# plt.show()
return line
