def get_common_tangent(self, another_data, t0):
"""
共通接線を探す
"""
yp = None
xi = pylab.linspace(0, 0.3, 10001)
dxi = xi[1] - xi[0]
close_t0 = xi[np.searchsorted(xi, t0)]
y1 = pylab.stineman_interp(
xi, self['comp1'], self['corrected_g'], yp)
y2 = pylab.stineman_interp(
xi, another_data['comp1'], another_data['corrected_g'], yp)
def search_minimum(x):
x1, x2 = x
# print(y2[xi==x2])
# print(y1[xi==x2])
line = (y2[xi==x2]-y1[xi==x1])/(x2-x1)*(xi-x1) + y1[xi==x1]
delta1 = y1 - line
delta2 = y2 - line
return (xi[delta1 == delta1.min()],
xi[delta2 == delta2.min()])
a, b = xi[np.searchsorted(xi, close_t0-dxi)], xi[np.searchsorted(xi, close_t0+dxi)]
print(a, b)
print(xi[xi==a], xi[xi==b])
for i in range(10):
a, b = search_minimum((a, b))
print(a, b)
return a, b
def get_t0(self, another_data, range=(0, 1)):
"""
range 内の交点を探す
なければ None を return
"""
yp = None
xi = pylab.linspace(range[0], range[-1], 10000)
y1 = pylab.stineman_interp(xi, self['comp1'], self['collected_g'], yp)
y2 = pylab.stineman_interp(
xi, another_data['comp1'], another_data['collected_g'], yp)
delta = y1 - y2
# 最初に符号が反転する点を T0 とする
return xi[np.where((delta[0] * delta) < 0)][0], y1[np.where((delta[0] * delta) < 0)][0]
def plot_one(filename, name, axes):
field = 'Density'
print "opening " + filename
# open output and create ray
pf = load(filename)
ray = pf.h.ortho_ray(0, [0.5, 0.5])
# first interpolate the exact solution onto the ray
ray_exact = {
'x':
ray['x'],
'Density':
pylab.stineman_interp(ray['x'], exact['x'], exact['Density']),
'x-velocity':
pylab.stineman_interp(ray['x'], exact['x'], exact['x-velocity']),
'Pressure':
pylab.stineman_interp(ray['x'], exact['x'], exact['Pressure']),
'InternalEnergy':
pylab.stineman_interp(ray['x'], exact['x'], exact['InternalEnergy'])
}
# compute first order and max error norms
delta = ray['dx'] * abs(ray[field] - ray_exact[field])
norm = delta.sum()
maxnorm = abs(ray[field] - ray_exact[field]).max()
# rough computation of level for each point in ray (probably better way)
level = -pylab.log(ray['dx'] / ray['dx'][0]) / pylab.log(2.0)
# plot
ax = pylab.axes(axes)
pylab.axhline(0, color='k', linestyle='dotted')
pylab.plot(exact['x'], exact[field], c='black', linewidth=(1, ))
pylab.scatter(ray['x'], ray[field], c=level, s=8, linewidths=(0, ))
# Set axis (clunky)
pylab.axis([0, 0.999, 0, 1.1]) # for density
if axes[1] < 0.5:
pylab.xlabel('Position')
else:
ax.set_xticklabels([])
if axes[0] < 0.1:
pylab.ylabel(field)
else:
ax.set_yticklabels([])
error_label(name, norm, maxnorm, 0.41, 1.0)
def Stineman_interp_fit(x, y): #pylint: disable=C0103
"""
データ補間曲線
"""
yp = None #pylint: disable=C0103
xi = pylab.linspace(x[0], x[-1], 100) #pylint: disable=E1101,C0103
yi = pylab.stineman_interp(xi, x, y, yp) #pylint: disable=C0103
return xi, yi
def fit_interp(self, data_x, data_y, range=(0, 1), np=100):
"""
range 内のデータを interpolate して出力
"""
yp = None
xi = pylab.linspace(range[0], range[-1], np)
yi = pylab.stineman_interp(xi, data_x, data_y, yp)
return xi, yi
def interpol(x, y, start=None, end=None, step=None, num=None, kind='lin'):
from scipy import interpolate, exp, log10, linspace, logspace
from pylab import stineman_interp
from numpy import where
# check if it is a linear vector or a log one
if (x[1] - x[0]) * (1 - 0.01) <= x[2] - x[1] <= (x[1] - x[0]) * (1 + 0.01):
scale = 'lin'
else:
scale = 'log'
# set starting point of interpolation
# if it is not given
if start is None:
start = x[0]
# set ending point of interpolation
# if it is not given
if end is None:
end = x[-1]
# get stepsize / number of values of interpolation
# if the x vector should be logarithmic
if kind == 'log':
if start <= 0.0: start = x[where(x > 0.0)[0][0]]
if num is None:
if scale == 'log':
if step is None:
step = log10(x[2]) - log10(x[1])
num = 1 + (log10(end) - log10(start)) / step
else:
if step is None:
step = x[2] - x[1]
num = 1 + (end - start) / step
x1 = 10**(linspace(log10(start), log10(end), num))
# if the x vector should be linear
else: # linear
if num is None:
if scale == 'log':
if start <= 0.0: start = x[where(x > 0.0)[0][0]]
if step is None:
step = log10(x[2]) - log10(x[1])
num = 1 + (log10(end) - log10(start)) / step
else:
if step is None:
step = x[2] - x[1]
num = 1 + (end - start) / step
x1 = linspace(start, end, num)
# build a spline out of the x, y bvalues
#~ spline_coeffs=interpolate.splrep(x,y,s=0)
#~ # interpolate for new x vector
#~ y1=interpolate.splev(x1,spline_coeffs,der=0)
y2 = stineman_interp(x1, x, y)
#~ y2 = interpolate.splev(x1, interpolate.splrep(x, y, k=3))
#~ y2 = interpolate.interp1d(x,y)(x1)
return x1, y2 #~, y2
### extract an ortho_ray (1D solution vector)
ray = pf.h.ortho_ray(0, [0.5, 0.5])
### define fields vector
fields = ('Density', 'x-velocity', 'InternalEnergy', 'Pressure' )
### read exact solution
exact = pylab.csv2rec( exact_solution_filename, delimiter=' ', names=('x', 'Density', 'x-velocity', 'Pressure', 'InternalEnergy') )
### calculate difference norm
# first interpolate the exact solution onto the ray
ray_exact = {'x': ray['x'],
'Density': pylab.stineman_interp(ray['x'],exact['x'],exact['Density']),
'x-velocity': pylab.stineman_interp(ray['x'],exact['x'],exact['x-velocity']),
'Pressure': pylab.stineman_interp(ray['x'],exact['x'],exact['Pressure']),
'InternalEnergy': pylab.stineman_interp(ray['x'],exact['x'],exact['InternalEnergy'])}
# now calculate the norm (first order, since we're dealing with
# conservation laws)
norm = {}
maxnorm = {}
for f in fields:
delta = ray['dx'] * abs( ray[f] - ray_exact[f] )
norm[f] = delta.sum()
maxnorm[f] = delta.max()
def touch():
read_data = CVMCv1Parser.from_file('cv1.txt')
d = read_data.data[0]['data']
datax = d['comp1']
dataz = d['F'] * 8.31 / 1000
max_x = datax.max()
min_x = datax.min()
yp = None
xi = pylab.linspace(min_x, max_x, 20)
z1 = pylab.stineman_interp(xi, datax, dataz, yp)
points = []
for i, x in enumerate(xi):
fig = pylab.figure()
ax = fig.add_subplot(111)
ax.plot(datax, dataz, '+')
ax.plot(xi, z1, color='red', linewidth=2)
ax.axvline(x, color='black', linewidth=1)
Cursor(ax, vertOn=False, useblit=True, color='black', linewidth=1)
try:
p = pylab.ginput(n=1, timeout=2)
while p == []:
p = pylab.ginput(n=1, timeout=2)
print(x, p[0][1])
except KeyboardInterrupt:
print("そのまま利用します")
print(x, z1[i])
p = [[x, z1[i]]]
points.append(p[0][1])
pylab.close()
z2 = pylab.stineman_interp(datax, xi, points)
delta = (z2 - dataz)**2
sl = 5
# pylab.plot(datax, delta[delta < sl])
# pylab.show()
### interp
# z3 = pylab.stineman_interp(
# xi, datax[delta < sl], dataz[delta < sl])
# pylab.plot(datax, dataz, '+')
# pylab.plot(xi, z3)
# pylab.show()
### interp
err = make_err_func(hex_free_end)
opt = optimize.leastsq(err, [1, 1, 1, 1, 1, 1, 1],
args=(datax[delta<sl], dataz[delta<sl]))[0]
xi2 = pylab.linspace(min_x, max_x, 200)
fity = hex_free_end(opt, xi2)
pylab.plot((datax/(datax+0.5))[::5], (dataz/(datax+0.5))[::5], '+')
pylab.plot(xi2/(xi2+0.5), fity/(xi2+0.5), linewidth=2)
print(xi2/(xi2+0.5))
print(fity/(xi2+0.5))
# pylab.plot(datax, dataz, '+')
# pylab.plot(xi, fity, linewidth=2)
pylab.show()
lines = ''
for x, z in zip(datax[::5], dataz[::5]):
lines += '{0}\t{1}\n'.format(str(x/(x+0.5)), str(z/(x+0.5)))
with open('data.txt', 'w') as wfile:
wfile.write(lines)
lines = ''
for x, z in zip(xi2, fity):
lines += '{0}\t{1}\n'.format(str(x/(x+0.5)), str(z/(x+0.5)))
with open('fit.txt', 'w') as wfile:
wfile.write(lines)
def tospecdata(self, rate=None, method='fft', nugget=0.0, trunc=1e-5,
fast=True):
'''
Computes spectral density from the auto covariance function
Parameters
----------
rate = scalar, int
1,2,4,8...2^r, interpolation rate for f (default 1)
method : string
interpolation method 'stineman', 'linear', 'cubic', 'fft'
nugget : scalar, real
nugget effect to ensure that round off errors do not result in
negative spectral estimates. Good choice might be 10^-12.
trunc : scalar, real
truncates all spectral values where S/max(S) < trunc
0 <= trunc <1 This is to ensure that high frequency
noise is not added to the spectrum. (default 1e-5)
fast : bool
if True : zero-pad to obtain power of 2 length ACF (default)
otherwise no zero-padding of ACF, slower but more accurate.
Returns
--------
S : SpecData1D object
spectral density
NB! This routine requires that the covariance is evenly spaced
starting from zero lag. Currently only capable of 1D matrices.
Example:
>>> import wafo.spectrum.models as sm
>>> import numpy as np
>>> import scipy.signal as st
>>> import pylab
>>> L = 129
>>> t = np.linspace(0,75,L)
>>> R = np.zeros(L)
>>> win = st.parzen(41)
>>> R[0:21] = win[20:41]
>>> R0 = CovData1D(R,t)
>>> S0 = R0.tospecdata()
>>> Sj = sm.Jonswap()
>>> S = Sj.tospecdata()
>>> R2 = S.tocovdata()
>>> S1 = R2.tospecdata()
>>> abs(S1.data-S.data).max()
>>> S1.plot('r-')
>>> S.plot('b:')
>>> pylab.show()
>>> all(abs(S1.data-S.data)<1e-4)
See also
--------
spec2cov
datastructures
'''
dt = self.sampling_period()
# dt = time-step between data points.
acf, unused_ti = atleast_1d(self.data, self.args)
if self.lagtype in 't':
spectype = 'freq'
ftype = 'w'
else:
spectype = 'k1d'
ftype = 'k'
if rate is None:
rate = 1 # interpolation rate
else:
rate = 2 ** nextpow2(rate) # make sure rate is a power of 2
# add a nugget effect to ensure that round off errors
# do not result in negative spectral estimates
acf[0] = acf[0] + nugget
n = acf.size
# embedding a circulant vector and Fourier transform
nfft = 2 ** nextpow2(2 * n - 2) if fast else 2 * n - 2
if method == 'fft':
nfft *= rate
nf = nfft / 2 # number of frequencies
acf = r_[acf, zeros(nfft - 2 * n + 2), acf[n - 2:0:-1]]
Rper = (fft(acf, nfft).real).clip(0) # periodogram
RperMax = Rper.max()
Rper = where(Rper < trunc * RperMax, 0, Rper)
S = abs(Rper[0:(nf + 1)]) * dt / pi
w = linspace(0, pi / dt, nf + 1)
So = _wafospec.SpecData1D(S, w, type=spectype, freqtype=ftype)
So.tr = self.tr
So.h = self.h
So.norm = self.norm
if method != 'fft' and rate > 1:
So.args = linspace(0, pi / dt, nf * rate)
if method == 'stineman':
So.data = stineman_interp(So.args, w, S)
else:
intfun = interpolate.interp1d(w, S, kind=method)
So.data = intfun(So.args)
So.data = So.data.clip(0) # clip negative values to 0
return So
def tospecdata(self,
rate=None,
method='fft',
nugget=0.0,
trunc=1e-5,
fast=True):
'''
Computes spectral density from the auto covariance function
Parameters
----------
rate = scalar, int
1,2,4,8...2^r, interpolation rate for f (default 1)
method : string
interpolation method 'stineman', 'linear', 'cubic', 'fft'
nugget : scalar, real
nugget effect to ensure that round off errors do not result in
negative spectral estimates. Good choice might be 10^-12.
trunc : scalar, real
truncates all spectral values where S/max(S) < trunc
0 <= trunc <1 This is to ensure that high frequency
noise is not added to the spectrum. (default 1e-5)
fast : bool
if True : zero-pad to obtain power of 2 length ACF (default)
otherwise no zero-padding of ACF, slower but more accurate.
Returns
--------
S : SpecData1D object
spectral density
NB! This routine requires that the covariance is evenly spaced
starting from zero lag. Currently only capable of 1D matrices.
Example:
>>> import wafo.spectrum.models as sm
>>> import numpy as np
>>> import scipy.signal as st
>>> import pylab
>>> L = 129
>>> t = np.linspace(0,75,L)
>>> R = np.zeros(L)
>>> win = st.parzen(41)
>>> R[0:21] = win[20:41]
>>> R0 = CovData1D(R,t)
>>> S0 = R0.tospecdata()
>>> Sj = sm.Jonswap()
>>> S = Sj.tospecdata()
>>> R2 = S.tocovdata()
>>> S1 = R2.tospecdata()
>>> abs(S1.data-S.data).max() < 1e-4
True
S1.plot('r-')
S.plot('b:')
pylab.show()
See also
--------
spec2cov
datastructures
'''
dt = self.sampling_period()
# dt = time-step between data points.
acf, unused_ti = atleast_1d(self.data, self.args)
if self.lagtype in 't':
spectype = 'freq'
ftype = 'w'
else:
spectype = 'k1d'
ftype = 'k'
if rate is None:
rate = 1 # interpolation rate
else:
rate = 2**nextpow2(rate) # make sure rate is a power of 2
# add a nugget effect to ensure that round off errors
# do not result in negative spectral estimates
acf[0] = acf[0] + nugget
n = acf.size
# embedding a circulant vector and Fourier transform
nfft = 2**nextpow2(2 * n - 2) if fast else 2 * n - 2
if method == 'fft':
nfft *= rate
nf = nfft / 2 # number of frequencies
acf = r_[acf, zeros(nfft - 2 * n + 2), acf[n - 2:0:-1]]
Rper = (fft(acf, nfft).real).clip(0) # periodogram
RperMax = Rper.max()
Rper = where(Rper < trunc * RperMax, 0, Rper)
S = abs(Rper[0:(nf + 1)]) * dt / pi
w = linspace(0, pi / dt, nf + 1)
So = _wafospec.SpecData1D(S, w, type=spectype, freqtype=ftype)
So.tr = self.tr
So.h = self.h
So.norm = self.norm
if method != 'fft' and rate > 1:
So.args = linspace(0, pi / dt, nf * rate)
if method == 'stineman':
So.data = stineman_interp(So.args, w, S)
else:
intfun = interpolate.interp1d(w, S, kind=method)
So.data = intfun(So.args)
So.data = So.data.clip(0) # clip negative values to 0
return So
def Stineman_interp_fit(self, x, y):
yp = None
xi = pylab.linspace(x[0], x[-1], 100)
yi = pylab.stineman_interp(xi, x, y, yp)
return xi, yi
from pylab import figure, show, nx, linspace, stineman_interp x = linspace(0,2*nx.pi,20); y = nx.sin(x); yp = None xi = linspace(x[0],x[-1],100); yi = stineman_interp(xi,x,y,yp); fig = figure() ax = fig.add_subplot(111) ax.plot(x,y,'ro',xi,yi,'-b.') show()
from pylab import figure, show, nx, linspace, stineman_interp x = linspace(0, 2 * nx.pi, 20) y = nx.sin(x) yp = None xi = linspace(x[0], x[-1], 100) yi = stineman_interp(xi, x, y, yp) fig = figure() ax = fig.add_subplot(111) ax.plot(x, y, 'ro', xi, yi, '-b.') show()