def spectrum_2d(M, indices=None):
Fourier.compute_spectrum_2d(M, Dt=3) #smooth on 3 time step.
S_E = np.nanmean(M.S_E[..., indices], axis=2)
graphes.color_plot(M.kx, M.ky, S_E, log=True, fignum=1)
graphes.colorbar(label='$E_k$')
figs = graphes.legende('$k_x$ (mm)', '$k_y$ (mm)', 'Energy Spectrum (log)')
return figs
def fit_core_size(x, y, Z, fignum=1, display=False):
"""
Find the half width of a gaussian bump
INPUT
-----
x : 2d np array
spatial coordinates (columns)
y : 2d np array
spatial coordinates (lines)
Z : 2d np array
data to be fitted (typically vorticity field )
fignum : int
figure number for the output. Default 1
display : bool
OUTPUT
-----
a : float
parameter of the gaussian bump
center : 2 elements np array
center coordinates
"""
ny, nx = Z.shape
X, Y, data, center, factor = normalize(x, y, Z)
R, theta = Smath.cart2pol(X, Y)
a0 = 1
fun = gaussian
res = opt.minimize(distance_fit, a0, args=(fun, R, data))
cond = ((center[0] > 5) and (center[0] < nx - 5) and (center[1] > 5)
and (center[1] < ny - 5))
if cond:
a = np.sqrt(res.x)
else:
a = None
if display:
figs = {}
graphes.graph(R, factor * data, fignum=3, label='ko')
graphes.graph(R,
factor * gaussian(res.x, R),
label='r.',
fignum=fignum + 2)
graphes.set_axis(0, 20, 0, factor * 1.1)
figs.update(graphes.legende('r (mm)', 'Vorticity s^{-1})', ''))
graphes.cla(fignum=fignum)
graphes.color_plot(X, Y, factor * data, fignum=fignum + 3)
graphes.colorbar()
figs.update(
graphes.legende('X (mm)',
'Y (mm)',
'Vorticity',
display=False,
cplot=True))
return a, center, figs
else:
return a, center
def vfield(sigma, modes, fignum=1):
names = {
'sigma': sigma,
'n': modes
} #name:eval(name) for name in ['sigma','n','N_p']}# this piece of code does not work
t = distribution(sigma, modes)
B = 1.
n = 100
dx = 2 * B / n
x = np.arange(-B, B, dx)
y = 0.
z = np.arange(-B, B, dx)
P = np.asarray(np.meshgrid(x, y, z))
dim = P.shape
N = np.prod(dim[1:])
X = np.reshape(P[0, ...], (N, ))
Y = np.reshape(P[1, ...], (N, ))
Z = np.reshape(P[2, ...], (N, ))
Pos = [np.asarray([x0, y0, z0]) for x0, y0, z0 in zip(X, Y, Z)]
V = biot.velocity_from_line(t.paths, Pos, Gamma=1, d=3)
V_2d = np.reshape(V, (n, n, 3))
E = np.sum(np.power(V_2d, 2), axis=2)
subplot = [111]
fig, axes = panel.make(subplot, fignum=fignum)
fig.set_size_inches(10, 10)
graphes.color_plot(x, z, E, fignum=fignum, vmin=0, vmax=0, log=True)
c = graphes.colorbar()
figs = {}
figs.update(graphes.legende('X', 'Z', 'E'))
graphes.save_figs(figs,
prefix='Random_path/V_Distributions/Fields/',
suffix=suf(names),
dpi=300,
display=True,
frmt='png')
def time_average(M, indices=None):
figs = {}
fields, names, vmin, vmax, labels, units = std_fields()
for j, field in enumerate(fields):
Y = np.nanmean(getattr(M, field)[..., indices], axis=2)
graphes.color_plot(M.x,
M.y,
Y,
fignum=j + 1,
vmin=vmin[j] / 5,
vmax=vmax[j] / 5)
graphes.colorbar(label=names[j] + ' ' + units[j])
figs.update(
graphes.legende('X (mm)',
'Y (mm)',
'Time averaged ' + field,
cplot=True))
return figs
def positions(M,i,field='omega',display=False,sigma=1.,**kwargs):
"""
find the maximum position of the vortex core at a given instant, using the field specified in argument
"""
imin,imax,jmin,jmax,Zfilt,X,Y = position_index(M,i,field=field,display=display,sigma=sigma,**kwargs)
deltax_max,deltay_max = SubPix2DGauss(Zfilt/np.max(Zfilt),imax,jmax,SubPixOffset=0)
deltax_min,deltay_min = SubPix2DGauss(Zfilt/np.min(Zfilt),imin,jmin,SubPixOffset=0)
# print(deltax_max)
# print(deltax_min)
# print(deltay_min)
# print(deltax_max)
#if deltax_max == np.nan or deltax_min==np.nan:
# return np.nan,np.nan,np.nan,np.nan
#else:
xmin = X[imin,jmin]+deltax_min
xmax = X[imax,jmax]+deltax_max
ymin = Y[imin,jmin]-deltay_min
ymax = Y[imax,jmax]-deltay_max
# print(Zfilt.shape)
# print(Y.shape)
# print(X.shape)
if display:
graphes.color_plot(X[:,5:],Y[:,5:],Zfilt/np.min(Zfilt),**kwargs)
graphes.graph([xmin+10],[ymin],label='bo',**kwargs)
graphes.graph([xmax+10],[ymax],label='ro',**kwargs)
# graphes.color_plot(X[:,5:],Y[:,5:],Zfilt/np.max(Zfilt),fignum=2)
#input()
# t.append(M.t[i])
# Xmin.append(M.x[imin,jmin])
# Xmax.append(M.x[imax,jmax])
# Ymin.append(M.y[imin,jmin])
# Ymax.append(M.y[imax,jmax])
return xmin,xmax,ymin,ymax
def position_index(M,i,field='omega',display=True,sigma=1.,**kwargs):
dx = M.x[0,1]-M.x[0,0]
# x0 = M.x[0,5]
# y0 = M.y[0,0]
nx,ny,nt = M.shape()
crop=True
if crop:
lin = slice(0,nx)
col = slice(0,ny)
X = M.x[lin,col]
Y = M.y[lin,col]
Zfilt = smoothing(M,i,field=field,sigma=sigma)
if display:
graphes.color_plot(X,Y,Zfilt,**kwargs)
imax,jmax = np.unravel_index(np.argmax(Zfilt),Zfilt.shape)
imin,jmin = np.unravel_index(np.argmin(Zfilt),Zfilt.shape)
return imin,imax,jmin,jmax,Zfilt,X,Y
def example_2():
n = 100
N = 50
sigma = N / 5
i = round(N / 2)
j = round(N / 2)
X = np.asarray([math.exp(-(k - i)**2 / (2 * sigma**2)) for k in range(N)])
Y = np.asarray([math.exp(-(k - j)**2 / (2 * sigma**2)) for k in range(N)])
Y = np.reshape(X, (N, 1))
X = np.reshape(X, (1, N))
x = np.arange(N)
y = np.arange(N)
#generate
a_init = np.dot(Y, X)
i = np.floor(np.random.rand(n) * N)
j = np.floor(np.random.rand(n) * N)
a_dump = np.dot(Y, X)
for t in zip(i, j):
a_dump[t] = np.nan
graphes.color_plot(x, y, a_dump, fignum=1)
#remove NaN values
rm_nans([a_dump])
graphes.color_plot(x, y, a_dump, fignum=2)
graphes.color_plot(x, y, a_dump - a_init, fignum=3)
print(np.max(a_dump - a_init))
def vortex_maps(x, y, Z, dx=1, display_map=False):
dZ1 = strain_tensor.strain_tensor(Z, d=2) / dx
blist = np.arange(0.5, 6., 0.5)
b0 = 2.5
dZ2 = {}
for b in blist:
print('Compute vorticity with r=' + str(b))
dZ2[b] = strain_tensor.strain_tensor_C(Z, d=2, b=b) / dx
omega1, enstrophy2 = strain_tensor.vorticity(dZ1, d=2, norm=False)
omega2, enstrophy2 = strain_tensor.vorticity(dZ2[b0], d=2, norm=False)
eigen1 = strain_tensor.Lambda(dZ1, d=2)
eigen2 = strain_tensor.Lambda(dZ2[b0], d=2)
strain1 = np.sqrt(
np.power(eigen1['Lambda_0'], 2) + np.power(eigen1['Lambda_1'], 2))
strain2 = np.sqrt(
np.power(eigen2['Lambda_0'], 2) + np.power(eigen2['Lambda_1'], 2))
figs = {}
# dimensions = np.shape(omega1)
#graphes.hist(np.reshape(omega,np.prod(dimensions)),fignum=1)
#figs.update(graphes.legende('vorticity (s^-1)','PDF',''))
# graphes.set_axis(-2.5,2.5,0,40000)
n = 3
Xp1, Yp1 = np.meshgrid(x[n:-n], y[n:-n])
Xp2, Yp2 = np.meshgrid(x, y)
if display_map:
for i in range(2):
for j in range(2):
graphes.color_plot(Xp1,
Yp1,
dZ1[..., i, j],
fignum=i + j * 2 + 2)
graphes.colorbar()
title = 'dU_' + str(i) + '/x_' + str(j)
figs.update(graphes.legende('X', 'Y', title, cplot=True))
graphes.cla(6)
graphes.color_plot(Xp1, Yp1, -omega1, fignum=6)
graphes.colorbar()
figs.update(graphes.legende('X', 'Y', 'Vorticity', cplot=True))
graphes.color_plot(Xp1, Yp1, strain1, fignum=7)
graphes.colorbar()
figs.update(graphes.legende('X', 'Y', 'Strain', cplot=True))
#dissipation
dissipation1 = np.sum(np.power(dZ1, 2), axis=(2, 3))
graphes.color_plot(Xp1, Yp1, dissipation1, fignum=8)
graphes.colorbar()
figs.update(graphes.legende('X', 'Y', 'Dissipation', cplot=True))
i1 = Xp1.shape[0] // 2
i2 = Xp2.shape[0] // 2
Xp = Xp2[i2, :]
omega_th = profile_omega(Xp, sigma=2.)
graphes.graph(Xp1[i1, :], omega1[i1, :], label='b-', fignum=9)
graphes.graph(Xp2[i2, :], omega2[i2, :], label='k-', fignum=9)
graphes.graph(Xp, omega_th, label='r--', fignum=9)
graphes.legende('r', 'vorticity', 'Radial vorticity profile')
graphes.graph(Xp1[i1, :], strain1[i1, :], label='b.-', fignum=10)
graphes.graph(Xp2[i2, :], strain2[i2, :], label='k^-', fignum=10)
graphes.legende('r--', 'strain', 'Radial strain profile')
j2 = Xp2.shape[1] // 2
for b in blist:
omega2, enstrophy2 = strain_tensor.vorticity(dZ2[b], d=2, norm=False)
graphes.graph(Xp2[i2, :], omega2[i2, :], label='k-', fignum=11)
graphes.legende('r', 'vorticity',
'Radial vorticity profile, various b')
graphes.graph([b], [omega2[i2, j2]], label='k^', fignum=12)
graphes.legende('Circle radius r (in box unit)', 'max. vorticity',
'Influence of contour size')
print(Xp.shape)
print(Xp2.shape)
# graphes.color_plot(X,Y,R,fignum=3,vmin=0,vmax=10)
print(figs)
return figs
def display_fft_2d(kx, ky, S, fignum=1, vmin=1, vmax=7):
#display in logscale
S_log = np.log10(S)
c = graphes.color_plot(kx, ky, S_log, vmin=vmin, vmax=vmax, fignum=fignum)
graphes.clegende(c, '$E_k (a.u.)$')
def single(filename, display=False):
figs = {}
savedir = '/Users/stephane/Documents/Postdoc_Chicago/Process_data/Scripts/Samples/Smoothing/'
filesave, ext = os.path.splitext(filename)
filesave = filesave + '_processed.hdf5'
M = M_manip.load_Mdata_file(filename, data=True)
M.get('E')
M.get('omega')
nx, ny, nt = M.shape()
i = nt / 2
# display raw energy
if display:
graphes.plt.close('all')
graphes.Mplot(M, 'E', i, vmin=0, vmax=50000, fignum=1, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Energy without pre-processing',
cplot=True))
#Display raw vorticity
graphes.Mplot(M, 'omega', i, vmin=0, vmax=100, fignum=2, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity without pre-processing',
cplot=True))
graphes.save_figs(figs, savedir=savedir, prefix=M.Id.get_id())
graphes.Mplot(M, 'Ux', i, vmin=-200, vmax=200, fignum=3, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Ux after pre-processing',
cplot=True))
M = cdata.remove_spurious(M, borne=1.5)
M.get('E', force=True)
M.get('omega', force=True)
if display:
graphes.Mplot(M, 'E', i, vmin=0, vmax=50000, fignum=4, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Energy after pre-processing',
cplot=True))
#Display raw vorticity
graphes.Mplot(M, 'omega', i, vmin=0, vmax=100, fignum=5, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity after pre-processing',
cplot=True))
### Gaussian filter
omega_filt = track.smoothing(M, i, field='omega', sigma=2.5)
graphes.color_plot(M.x, M.y, omega_filt, vmin=0, vmax=100, fignum=6)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity after gaussian smoothing',
cplot=True))
graphes.save_figs(figs, savedir=savedir, prefix=M.Id.get_id())
### Gaussian filter
# omega_filt = filters.gaussian_filter(omega, sigma=2.)#[...,0]
# graphes.color_plot(x,y,omega_filt,vmin=0,vmax=50,fignum=5)
# graphes.plt.colorbar()
# figs.update(graphes.legende('$x$ (mm)','$y$ (mm)','Vorticity after gaussian smoothing',cplot=True))
# graphes.save_figs(figs,savedir=savedir)
to_hdf5.write(M, filename=filesave, key='Mdata')
def example(filename):
figs = {}
savedir = '/Users/stephane/Documents/Postdoc_Chicago/Process_data/Scripts/Example/Smoothing/'
M = M_manip.load_Mdata_file(filename, data=True)
M.get('E')
M.get('omega')
nx, ny, nt = M.shape()
x, y = M.x, M.y
i = nt / 2
# display raw energy
graphes.Mplot(M, 'E', i, vmin=0, vmax=50000, fignum=1, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Energy without pre-processing',
cplot=True))
#Display raw vorticity
graphes.Mplot(M, 'omega', i, vmin=0, vmax=80, fignum=2, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity without pre-processing',
cplot=True))
# Look for bada data point in amplitude
E = M.E[..., i]
tup, errors = cdata.rm_baddata(E, borne=2.)
xc = []
yc = []
for t in tup:
xc.append([x[t[0], t[1]]])
yc.append([y[t[0], t[1]]])
graphes.graph(xc, yc, label='ro', fignum=2)
print(figs)
graphes.save_figs(figs, savedir=savedir)
Ux, Uy = M.Ux[..., i], M.Uy[..., i]
#replace component of the velocity
Ux = cdata.replace_data(Ux, tup)[..., 0]
Uy = cdata.replace_data(Uy, tup)[..., 0]
U = np.transpose(np.asarray([Uy, Ux]), (1, 2, 0))
dU = strain.strain_tensor_C(U, b=2.)
omega, enstrophy = strain.vorticity(dU, d=2, norm=False)
E = Ux**2 + Uy**2
graphes.color_plot(x, y, omega, vmin=0, vmax=80, fignum=4)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity after pre-processing',
cplot=True))
graphes.color_plot(x, y, E, vmin=0, vmax=50000, fignum=3)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Energy after pre-processing',
cplot=True))
### Gaussian filter
omega_filt = filters.gaussian_filter(omega, sigma=2.) #[...,0]
graphes.color_plot(x, y, omega_filt, vmin=0, vmax=80, fignum=5)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity after gaussian smoothing',
cplot=True))
graphes.save_figs(figs, savedir=savedir)
