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csheet3d.py
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csheet3d.py
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import athena_read as ath
import matplotlib
import matplotlib.pyplot as plt
from matplotlib import gridspec
from mpl_toolkits.axes_grid1 import make_axes_locatable
import numpy as np
import cPickle as pickle
from my_colors import get_jhcolors
############################################
import matplotlib.gridspec as gridspec
import matplotlib.gridspec as gridspec
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
def plot_jhist(dv,ncells,jmax,jmaxnorm,diss,dissnorm,size,orient,theta,ntime,vsheet=False,size2=None):
nframe = 2
nplot = 3
matplotlib.rcParams['figure.figsize'] = (12, 12.0*nframe/nplot)
fig = plt.figure()
fraction=0.046;pad=0.04
gs = gridspec.GridSpec(2, 3)
# calc dissipation rate per sheet for normalization or weighted average
ncelltot= float(np.sum(np.array(ncells)))
diss_sheet = np.array(ncells)*np.array(diss)
disstot= float(np.sum(diss_sheet))
for i in np.arange(6):
if (i==0):
hdata = np.array(size)[:,0]
vmin=-2; vmax=0.5 #in log10
nbins = 100
xlab = r'$l/H$'
# modify to plot the aspect ratio: xi/lambda
hdata = np.array(size)[:,1]/np.array(size)[:,2]
vmin=-0.5; vmax=3.0 #in log10
nbins = 100
xlab = r'$\xi/\lambda$'
#
print 'non-weighted averaged (l,xi,lambda,aspect) = (',np.average(np.array(size)[:,0]),' ,',\
np.average(np.array(size)[:,1]),' ,',\
np.average(np.array(size)[:,2]),',',\
np.average(np.array(size)[:,1]/np.array(size)[:,2]),')'
print 'vol-weighted averaged (l,xi,lambda,aspect) = (',np.sum(np.array(size)[:,0]*np.array(ncells))/ncelltot,' ,',\
np.sum(np.array(size)[:,1]*np.array(ncells))/ncelltot,' ,',\
np.sum(np.array(size)[:,2]*np.array(ncells))/ncelltot,', ',\
np.sum(np.array(size)[:,1]/np.array(size)[:,2]*np.array(ncells))/ncelltot,')'
print 'dis-weighted averaged (l,xi,lambda,aspect) = (',np.sum(np.array(size)[:,0]*diss_sheet)/disstot,' ,',\
np.sum(np.array(size)[:,1]*diss_sheet)/disstot,' ,',\
np.sum(np.array(size)[:,2]*diss_sheet)/disstot,', ',\
np.sum(np.array(size)[:,1]/np.array(size)[:,2]*diss_sheet)/disstot,')'
index,coef=-3.2,1e-2
if (i==1):
hdata = np.array(size)[:,0]
vmin=-3;vmax=1
nbins = 100
xlab1 = r'$\xi$'
xlab =r'$l$'
xlab2 = r'$\lambda$'
hdata1 = np.array(size)[:,1]
hdata2 = np.array(size)[:,2]
index,coef=-3.0,1e-2
if size2:
print "reach size2 loop"
hdata3 = np.array(size2)[:,2]
if (i==2):
hdata = (theta)
vmin = np.log10(np.min(hdata))
vmax = np.log10(np.max(hdata))
nbins = 100
if vsheet:
xlab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
print 'average theta/E_nu = ', np.average(hdata)
else:
xlab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
print 'average theta/E_eta = ', np.average(hdata)
index,coef=-2.0,1e-5
if (i==3):
hdata = (np.array(jmaxnorm))
vmin = np.log10(2) #np.log10(np.min(hdata))
vmax = np.log10(20) #np.log10(np.max(hdata))
nbins=100
if vsheet:
xlab = r'$\omega_{max}/\omega_{rms}$'
print 'average w_max/w_rms = ',np.average(hdata)
else:
xlab = r'$j_{max}/j_{rms}$'
print 'average j_max/j_rms = ',np.average(hdata)
if (i==4):
hdata = np.array(dissnorm)
vmin = np.log10(5) #np.log10(np.min(hdata))
vmax = np.log10(50) #np.log10(np.max(hdata))
nbins = 100
if vsheet:
xlab = r'$\langle\varepsilon_{\nu,sh}\rangle_i /\langle\varepsilon_{\nu}\rangle$'
print 'average epsilon = ', np.average(hdata)
else:
xlab = r'$\langle\varepsilon_{\eta,sh}\rangle_i /\langle\varepsilon_{\eta}\rangle$'
print 'average epsilon = ', np.average(hdata)
if (i==5):
hdata = np.array(ncells)*dv #/((x[1]-x[0])**3)
#vmin = -3; vmax = 0
vmin = np.log10(np.min(hdata))
vmax = np.log10(np.max(hdata))
nbins = 100
xlab = r'$v_{sh}/V$'
print 'average volume fraction per sheet = ',np.average(hdata)/8.0
print 'dis-weighted average volume fraction per sheet = ',np.average(hdata*diss_sheet)\
/8.0/np.average(diss_sheet)
print 'average volume fraction for all sheets = ',np.sum(hdata)/float(ntime)/8.0
print 'time averaged number of current sheets = ', len(ncells)/float(ntime)
#print 'dis-weighted average volume fraction for all sheets = ',np.sum(hdata*diss_sheet)\
# /float(ntime)/8.0/(disstot)
hist, bins = np.histogram(hdata, bins=np.logspace(vmin,vmax,nbins),density=1)
center = 10**((np.log10(bins[:-1])+np.log10(bins[1:]))/2)
if (i==1):
hist1, bins1 = np.histogram(hdata1, bins=np.logspace(vmin,vmax,nbins),density=1)
hist2, bins2 = np.histogram(hdata2, bins=np.logspace(vmin,vmax,nbins),density=1)
if size2:
hist3, bins3 = np.histogram(hdata3, bins=np.logspace(vmin,vmax,nbins),density=1)
fig.add_subplot(gs[i])
if (i< 3):
plt.plot(center,hist,'k-',label=xlab)
#n, bins, patches = plt.hist(hdata, bins=np.logspace(vmin,vmax,nbins), \
# normed=1, facecolor='green', alpha=0.5,label=xlab)
if i==1:
plt.plot(center,hist1,'b-',label=xlab1)
plt.plot(center,hist2,'g-',label=xlab2)
#n, bins, patches = plt.hist(hdata1, bins=np.logspace(vmin,vmax,nbins), \
# normed=1, facecolor='blue', alpha=0.35,label=xlab1)
if size2:
plt.plot(center,hist3,'g--')
plt.legend(loc=1,fontsize=20)
xlab = r'$(l,\xi,\lambda)/H$'
#plt.text(vmin,7000,'total counts: '+str(len(hdata)),size=20,color='g')
plt.plot(center,coef*center**index,'k:')
else:
plt.plot(center,hist,'k-')
#n, bins, patches = plt.hist(hdata, bins=np.logspace(vmin,vmax,nbins), normed=1, facecolor='blue', alpha=0.5)
plt.xlabel(xlab,size=20)
plt.ylabel('probability density',size=20)
plt.xlim([10**vmin,10**vmax])
plt.gca().set_xscale("log")
plt.gca().set_yscale("log",nonposy='clip')
#if(i==5):
# plt.xlim([1e4,10**4.3])
plt.tight_layout()
## only use the following for the paper
def plot_jhist_2panel(dv,ncells,jmax,jmaxnorm,diss,dissnorm,size,orient,theta,ntime,vsheet=False,size2=None):
nframe = 2
nplot = 1
matplotlib.rcParams['figure.figsize'] = (8.0,4.0)
fig = plt.figure()
fraction=0.046;pad=0.04
gs = gridspec.GridSpec(nplot, nframe)
# calc dissipation rate per sheet for normalization or weighted average
ncelltot= float(np.sum(np.array(ncells)))
diss_sheet = np.array(ncells)*np.array(diss)
disstot= float(np.sum(diss_sheet))
for i in np.arange(2):
if (i==0):
hdata = np.array(size)[:,0]
vmin=-3;vmax=1
nbins = 100
xlab1 = r'$\xi$'
xlab =r'$l$'
xlab2 = r'$\lambda_2$'
hdata1 = np.array(size)[:,1]
hdata2 = np.array(size)[:,2]
index,coef=-3.0,1e-2
if size2:
print "reach size2 loop"
hdata3 = np.array(size2)[:,2]
xlab3 = r'$\lambda_1$'
if (i==1):
hdata = (theta)
vmin = np.log10(np.min(hdata))
vmax = np.log10(np.max(hdata))
nbins = 100
if vsheet:
xlab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
print 'average theta/E_nu = ', np.average(hdata)
else:
xlab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
print 'average theta/E_eta = ', np.average(hdata)
index,coef=-2.0,1e-5
hist, bins = np.histogram(hdata, bins=np.logspace(vmin,vmax,nbins),density=1)
center = 10**((np.log10(bins[:-1])+np.log10(bins[1:]))/2)
if (i==0):
hist1, bins1 = np.histogram(hdata1, bins=np.logspace(vmin,vmax,nbins),density=1)
hist2, bins2 = np.histogram(hdata2, bins=np.logspace(vmin,vmax,nbins),density=1)
if size2:
hist3, bins3 = np.histogram(hdata3, bins=np.logspace(vmin,vmax,nbins),density=1)
fig.add_subplot(gs[i])
if (i< 3):
plt.plot(center,hist,'k-',label=xlab)
#n, bins, patches = plt.hist(hdata, bins=np.logspace(vmin,vmax,nbins), \
# normed=1, facecolor='green', alpha=0.5,label=xlab)
if i==0:
plt.plot(center,hist1,'b-',label=xlab1)
if size2:
plt.plot(center,hist3,'r-',label=xlab3)
plt.plot(center,hist2,'g-',label=xlab2)
#n, bins, patches = plt.hist(hdata1, bins=np.logspace(vmin,vmax,nbins), \
# normed=1, facecolor='blue', alpha=0.35,label=xlab1)
plt.legend(loc=1,fontsize=20,handlelength=1.5,handletextpad=0.05)
xlab = r'$(l,\xi,\lambda)/H$'
#plt.text(vmin,7000,'total counts: '+str(len(hdata)),size=20,color='g')
plt.plot(center,coef*center**index,'k:')
else:
plt.plot(center,hist,'k-')
#n, bins, patches = plt.hist(hdata, bins=np.logspace(vmin,vmax,nbins), normed=1, facecolor='blue', alpha=0.5)
plt.xlabel(xlab,fontsize=20)
plt.ylabel('probability density',fontsize=20)
plt.xlim([10**vmin,10**vmax])
plt.gca().set_xscale("log")
plt.gca().set_yscale("log",nonposy='clip')
#if(i==5):
# plt.xlim([1e4,10**4.3])
plt.tight_layout()
def plot_jcorr(ncells,jmax,jmaxnorm,diss,dissnorm,size,orient,theta,disscut=4e-5,ntime=21,project=np.array([1,0,0]),cmap='jet',vsheet=False):
"""
plot the correlation between quantities within current sheet
"""
nframe = 3
nplot = 3
enlarge = 2
matplotlib.rcParams['figure.figsize'] = (10*enlarge, enlarge*8.0*nframe/nplot)
fig = plt.figure()
fraction=0.046;pad=0.04
gs = gridspec.GridSpec(nframe, nplot)
mask = (theta > disscut)
# calc dissipation rate per sheet for normalization or weighted average
ncelltot= float(np.sum(np.array(ncells)))
diss_sheet = np.array(ncells)*np.array(diss)
disstot= float(np.sum(diss_sheet))
for i in np.arange(9):
#######################################
# (1) orientation
#######################################
if (i==0):
vec2d = np.array(orient)[mask,0]#np.cross(np.array(orient)[mask,0],project)
hdata_x = vec2d[:,2]
hdata_y = vec2d[:,1]
xlab = r'$\hat{l}_x$'
ylab = r'$\hat{l}_y$'
xmin,xmax = -1,1
ymin,ymax = -1,1
vec2d = np.array(orient)[:,0]
vecnorm = np.average(vec2d,axis=0)
vecnorm /= np.linalg.norm(vecnorm)
print 'non-weighted averaged (\hat{l}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
vecnorm = np.average(np.array(ncells)*vec2d.T,axis=1)/ncelltot
vecnorm /= np.linalg.norm(vecnorm)
print 'vol-weighted averaged (\hat{l}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
vecnorm = np.average(diss_sheet*vec2d.T,axis=1)/disstot
vecnorm /= np.linalg.norm(vecnorm)
print 'dis-weighted averaged (\hat{l}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
if (i==1):
vec2d = np.array(orient)[mask,1]
hdata_x = vec2d[:,2]
hdata_y = vec2d[:,1]
xlab = r'$\hat{\xi}_x$'
ylab = r'$\hat{\xi}_y$'
xmin,xmax = -1,1
ymin,ymax = -1,1
vec2d = np.array(orient)[:,1]
vecnorm = np.average(vec2d,axis=0)
vecnorm /= np.linalg.norm(vecnorm)
print 'non-weighted averaged (\hat{xi}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
vecnorm = np.average(np.array(ncells)*vec2d.T,axis=1)/ncelltot
vecnorm /= np.linalg.norm(vecnorm)
print 'vol-weighted averaged (\hat{xi}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
vecnorm = np.average(diss_sheet*vec2d.T,axis=1)/disstot
vecnorm /= np.linalg.norm(vecnorm)
print 'dis-weighted averaged (\hat{xi}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
if (i==2):
vec2d = np.array(orient)[mask,2]
hdata_x = vec2d[:,2]
hdata_y = vec2d[:,1]
xlab = r'$\hat{\lambda}_x$'
ylab = r'$\hat{\lambda}_y$'
xmin,xmax = -1,1
ymin,ymax = -1,1
vec2d = np.array(orient)[:,2]
vecnorm = np.average(vec2d,axis=0)
vecnorm /= np.linalg.norm(vecnorm)
print 'non-weighted averaged (\hat{\lambda}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
vecnorm = np.average(np.array(ncells)*vec2d.T,axis=1)/ncelltot
vecnorm /= np.linalg.norm(vecnorm)
print 'vol-weighted averaged (\hat{\lambda}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
vecnorm = np.average(diss_sheet*vec2d.T,axis=1)/disstot
vecnorm /= np.linalg.norm(vecnorm)
print 'dis-weighted averaged (\hat{\lambda}) = (',vecnorm[2],' ,',\
vecnorm[1],' ,',\
vecnorm[0],')'
#######################################
# (2) 2d histogram of sheet dimensions
#######################################
if (i==3):
hdata_x = np.array(size)[:,0]
hdata_y = np.array(size)[:,1]
xlab = r'$l$'
ylab = r'$\xi$'
xmin,xmax = -2.7,1
ymin,ymax = -2.7,0
nbin = 100
if (i==4):
hdata_x = np.array(size)[:,0]
hdata_y = np.array(size)[:,2]
xlab = r'$l$'
ylab = r'$\lambda$'
xmin,xmax = -2.7,1
ymin,ymax = -2.7,0
nbin = 100
if (i==5):
hdata_x = np.array(size)[:,1]
hdata_y = np.array(size)[:,2]
xlab = r'$\xi$'
ylab = r'$\lambda$'
xmin,xmax = -2.7,1
ymin,ymax = -2.7,0
nbin = 100
# modify to plot the corr btw xi/lambda and lambda
hdata_x = np.array(size)[:,1]
hdata_y = np.array(size)[:,1]/np.array(size)[:,2]
xlab = r'$\xi$'
ylab = r'$\xi/\lambda$'
xmin,xmax = -3,1.
ymin,ymax = 0.0, 3. #-0.5,3.0
nbin = 100
#######################################
# (3) dissipation below
#######################################
if (i==6):
hdata_x = np.array(size)[:,0]
hdata_y = np.array(theta)
xlab = r'$l$'
if vsheet:
ylab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
else:
ylab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
ymin = np.log10(np.min(hdata_y))
ymax = np.log10(np.max(hdata_y))
xmin,xmax = -2.7,1
nbin = 100
if (i==7):
hdata_x = np.array(size)[:,1]
hdata_y = np.array(theta)
xlab = r'$\xi$'
if vsheet:
ylab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
else:
ylab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
ymin = np.log10(np.min(hdata_y))
ymax = np.log10(np.max(hdata_y))
xmin,xmax = -2.7,1
nbin = 100
# modify to plot corr btwn theta and aspect ratio
hdata_x = np.array(size)[:,1]/np.array(size)[:,2]
hdata_y = np.array(theta)
xlab = r'$\xi/\lambda$'
if vsheet:
ylab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
else:
ylab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
ymin = np.log10(np.min(hdata_y))
ymax = np.log10(np.max(hdata_y))
xmin,xmax = -0.5,2.5
nbin = 100
if (i==8):
hdata_x = np.array(size)[:,2]
hdata_y = np.array(theta)
xlab = r'$\lambda$'
if vsheet:
ylab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
else:
ylab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
ymin = np.log10(np.min(hdata_y))
ymax = np.log10(np.max(hdata_y))
xmin,xmax = -2.7,1
nbin = 100
if i !=-1:
fig.add_subplot(gs[i],aspect='equal')
else:
fig.add_subplot(gs[i])
if i<3:
plt.scatter(hdata_x,hdata_y,s=0.02, marker = '.' )
plt.ylim([ymin,ymax])
plt.xlim([xmin,xmax])
plt.xlabel(xlab,size=20)
plt.ylabel(ylab,size=20)
if i==0: # add tilt angle measured in Zhdankin paper -17.5degree
tilt = -17.5/180.*np.pi
rx,ry = 2.*np.sin(tilt),2.*np.cos(tilt)
plt.plot([rx,-rx],[ry,-ry],'k:')
elif i<6:
#plt.scatter(hdata_x,hdata_y,s=0.01,marker='.')
#hst are binned in the dissipation values (normalized with total dissipation)
hst,xe,ye = np.histogram2d(hdata_y,hdata_x,bins=(np.logspace(ymin,ymax,nbin),\
np.logspace(xmin,xmax,nbin)),\
weights=theta) #diss_sheet/disstot)
xx,yy = np.meshgrid(xe,ye)
loghst = np.log10(hst+1e-12)
plt.pcolormesh(yy,xx,np.transpose(loghst),vmin=-5,vmax=-1,cmap=cmap)
#vmax=np.max(loghst),cmap=cmap)
#print 'min/max of hst = ',np.min(loghst),np.max(loghst)
#print 'sum(hst) = ',np.sum(hst)
#print 'min/max of xe = ',np.min(xe),np.max(xe)
#print 'min/max of ye = ',np.min(ye),np.max(ye)
plt.colorbar(pad=pad,fraction=fraction*0.8)
plt.xscale("log")
plt.yscale("log")
plt.xlim([10**xmin,10**xmax])
plt.ylim([10**ymin,10**ymax])
plt.xlabel(xlab,size=20)
plt.ylabel(ylab,size=20)
if vsheet:
plt.title(r'$\theta_{\nu}/\mathcal{E}_{\nu}$',fontsize=15)
else:
plt.title(r'$\theta_{\eta}/\mathcal{E}_{\eta}$',fontsize=15)
if i==3:
index,coef=1.0,0.4
plt.plot(xe,coef*xe**index,'k:')
#plt.title(r'$\mathrm{Histogram\ of\ d_i:}$')
else:
hst,xe,ye = np.histogram2d(hdata_y,hdata_x,bins=[np.logspace(ymin,ymax,nbin),\
np.logspace(xmin,xmax,nbin)],\
normed=True)
xx,yy = np.meshgrid(xe,ye)
loghst = np.log10(hst+1e-12)
plt.pcolormesh(yy,xx,np.transpose(loghst),vmin=-3,vmax=9)
#print 'min/max of hst = ',np.min(loghst),np.max(loghst)
plt.colorbar(pad=pad,fraction=fraction)
plt.xscale("log")
plt.yscale("log")
plt.xlim([10**xmin,10**xmax])
plt.ylim([10**ymin,10**ymax])
plt.xlabel(xlab,size=20)
plt.ylabel(ylab,size=20)
plt.title(r'$\log$'+'(PDF)',fontsize=15)
if i==6:
index,coef=2.0,1.5e-3
plt.plot(ye,coef*ye**index,'k:')
plt.tight_layout()
# linear regression
#n_abovezero = np.min([len(hdata_x[hdata_x > 0]),len(hdata_y[hdata_y > 0])])
#clean_data = np.log10(np.array(zip(hdata_x[:n_abovezero],hdata_y[:n_abovezero])))
#print clean_data
#coeff = np.polyfit(clean_data[:,0], clean_data[:,1], 1)
#print coeff
#break
#yfit = 10**(coeff[0]*clean_data[:,0]+coeff[1])
#ax.plot(clean_data[:,0],yfit,'r-')
# use the following to generate the figure used in the paper
def plot_jcorr_4panel(ncells,jmax,jmaxnorm,diss,dissnorm,size,orient,theta,disscut=4e-5,ntime=21,project=np.array([1,0,0]),cmap='jet',vsheet=False):
"""
plot the correlation between quantities within current sheet
"""
nframe = 2
nplot = 2
enlarge = 1
matplotlib.rcParams['figure.figsize'] = (8*enlarge, enlarge*7.0*nframe/nplot)
fig = plt.figure()
fraction=0.046;pad=0.04
gs = gridspec.GridSpec(nframe, nplot)
mask = (theta > disscut)
# calc dissipation rate per sheet for normalization or weighted average
ncelltot= float(np.sum(np.array(ncells)))
diss_sheet = np.array(ncells)*np.array(diss)
disstot= float(np.sum(diss_sheet))
for i in np.arange(4):
#######################################
# (1) orientation
# (1) replace it with aspect ratio vs. xi
#######################################
if (i==2):
#vec2d = np.array(orient)[mask,0]#np.cross(np.array(orient)[mask,0],project)
#hdata_x = vec2d[:,2]
#hdata_y = vec2d[:,1]
#xlab = r'$\hat{l}_x$'
#ylab = r'$\hat{l}_y$'
#xmin,xmax = -1,1
#ymin,ymax = -1,1
# modify to plot the corr btw xi/lambda and lambda
hdata_x = np.array(size)[:,1]
hdata_y = np.array(size)[:,1]/np.array(size)[:,2]
xlab = r'$\xi$'
ylab = r'$\xi/\lambda$'
xmin,xmax = -3,1.
ymin,ymax = 0.0, 3. #-0.5,3.0
nbin = 100
#######################################
# (2) 2d histogram of sheet dimensions
#######################################
if (i==0):
hdata_x = np.array(size)[:,0]
hdata_y = np.array(size)[:,1]
xlab = r'$l$'
ylab = r'$\xi$'
xmin,xmax = -3.0,1.0 #2.7,1
ymin,ymax = -3.0,1.0 #-2.7,0
nbin = 100
if (i==1):
hdata_x = np.array(size)[:,0]
hdata_y = np.array(size)[:,2]
xlab = r'$l$'
ylab = r'$\lambda_2$'
xmin,xmax = -3.0,1.0 #-2.7,1
ymin,ymax = -3.0,-1.8 #-2.7,0
nbin = 100
#######################################
# (3) dissipation below
#######################################
if (i==3):
hdata_x = np.array(size)[:,0]
hdata_y = np.array(theta)
xlab = r'$l$'
if vsheet:
ylab = r'$\theta_{\nu}/\mathcal{E}_{\nu}$'
else:
ylab = r'$\theta_{\eta}/\mathcal{E}_{\eta}$'
ymin = np.log10(np.min(hdata_y))
ymax = np.log10(np.max(hdata_y))
xmin,xmax = -2.7,1
nbin = 100
#if i==2:
# fig.add_subplot(gs[i] ,aspect='equal')
#else:
fig.add_subplot(gs[i])
#if i==2:
# plt.scatter(hdata_x,hdata_y,s=0.03, marker = '.' )
# plt.ylim([ymin,ymax])
# plt.xlim([xmin,xmax])
# plt.xlabel(xlab,size=20)
# plt.ylabel(ylab,size=20)
# # add tilt angle measured in Zhdankin paper -17.5degree
# tilt = -17.5/180.*np.pi
# rx,ry = 2.*np.sin(tilt),2.*np.cos(tilt)
# plt.plot([rx,-rx],[ry,-ry],'k:')
#if i<2:
if i<3:
#plt.scatter(hdata_x,hdata_y,s=0.01,marker='.')
#hst are binned in the dissipation values (normalized with total dissipation)
hst,xe,ye = np.histogram2d(hdata_y,hdata_x,bins=(np.logspace(ymin,ymax,nbin),\
np.logspace(xmin,xmax,nbin)),\
weights=theta) #diss_sheet/disstot)
xx,yy = np.meshgrid(xe,ye)
loghst = np.log10(hst+1e-12)
plt.pcolormesh(yy,xx,np.transpose(loghst),vmin=-5,vmax=-1,cmap=cmap)
#vmax=np.max(loghst),cmap=cmap)
#print 'min/max of hst = ',np.min(loghst),np.max(loghst)
#print 'sum(hst) = ',np.sum(hst)
#print 'min/max of xe = ',np.min(xe),np.max(xe)
#print 'min/max of ye = ',np.min(ye),np.max(ye)
plt.colorbar(pad=pad,fraction=fraction)
plt.xscale("log")
plt.yscale("log")
plt.xlim([10**xmin,10**xmax])
plt.ylim([10**ymin,10**ymax])
plt.xlabel(xlab,size=20)
plt.ylabel(ylab,size=20)
if vsheet:
plt.title(r'$\theta_{\nu}/\mathcal{E}_{\nu}$',fontsize=15)
else:
plt.title(r'$\theta_{\eta}/\mathcal{E}_{\eta}$',fontsize=15)
if i==0:
index,coef=1.0,0.4
plt.plot(xe,coef*xe**index,'k:')
if i==1:
index,coef=1./3.,0.008
xe = 10**(np.linspace(-3.0,0.4,100))
plt.plot(xe,coef*xe**index,'k:')
index,coef=0.,0.0065
xe = 10**(np.linspace(-1.8,1.0,50))
plt.plot(xe,coef*xe**index,'k:')
if i==2:
index,coef=2./3.,85.
xe = 10**(np.linspace(-3.0,0.4,100))
plt.plot(xe,coef*xe**index,'k:')
index,coef=1.,160.
xe = 10**(np.linspace(-1.8,1.0,50))
plt.plot(xe,coef*xe**index,'k:')
#plt.title(r'$\mathrm{Histogram\ of\ d_i:}$')
if i==3:
hst,xe,ye = np.histogram2d(hdata_y,hdata_x,bins=[np.logspace(ymin,ymax,nbin),\
np.logspace(xmin,xmax,nbin)],\
normed=True)
xx,yy = np.meshgrid(xe,ye)
loghst = np.log10(hst+1e-12)
plt.pcolormesh(yy,xx,np.transpose(loghst),vmin=-3,vmax=9,cmap=cmap)
#print 'min/max of hst = ',np.min(loghst),np.max(loghst)
plt.colorbar(pad=pad,fraction=fraction)
plt.xscale("log")
plt.yscale("log")
plt.xlim([10**xmin,10**xmax])
plt.ylim([10**ymin,10**ymax])
plt.xlabel(xlab,size=20)
plt.ylabel(ylab,size=20)
plt.title(r'$\log$'+'(PDF)',fontsize=15)
index,coef=2.25,2.2e-3
plt.plot(ye,coef*ye**index,'k:')
plt.tight_layout()
# use the following to generate the figure used in the paper
def plot_jcorr_null(size,theta,size1,theta1,cmap1='hot_r',cmap='bone_r'):
"""
compare sheets with null and sheets w/o null
draw nonull sheets first then overlay with null sheets
then draw colorbar of these two..
"""
matplotlib.rcParams['figure.figsize'] = (5.5,5)
fig = plt.figure()
fraction=0.046;pad=0.04
hdata_x = np.array(size)[:,0]
hdata_y = np.array(size)[:,1]
xlab = r'$l$'
ylab = r'$\xi$'
xmin,xmax = -3.0,1.0 #2.7,1
ymin,ymax = -3.0,1.0 #-2.7,0
nbin = 100
# 1) plot all sheets
cs0 = plt.scatter(hdata_x,hdata_y,s=3,marker='s',color='b')
#hst are binned in the dissipation values (normalized with total dissipation)
#hst,xe,ye = np.histogram2d(hdata_y,hdata_x,bins=(np.logspace(ymin,ymax,nbin),\
# np.logspace(xmin,xmax,nbin)),\
# weights=theta) #diss_sheet/disstot)
#xx,yy = np.meshgrid(xe,ye)
#loghst = np.log10(hst+1e-12)
#cs1 = plt.pcolormesh(yy,xx,np.transpose(loghst),vmin=-8,vmax=-4,cmap=cmap)
#cbar1 = fig.colorbar(cs1,pad=pad,fraction=fraction,orientation='horizontal',ticks=[-6,-5,-4])
##plt.colorbar(cs1,pad=pad,fraction=fraction,orientation='horizontal',location='top')
#2) now plot the null sheets
hdata_x = np.array(size1)[:,0]
hdata_y = np.array(size1)[:,1]
hst,xe,ye = np.histogram2d(hdata_y,hdata_x,bins=(np.logspace(ymin,ymax,nbin),\
np.logspace(xmin,xmax,nbin)),\
weights=theta1) #diss_sheet/disstot)
xx,yy = np.meshgrid(xe,ye)
loghst = np.log10(hst+1e-12)
cs2 = plt.pcolormesh(yy,xx,np.transpose(loghst),vmin=-5,vmax=-1,alpha=0.8,cmap=cmap1)
#plt.colorbar(cs2,pad=pad,fraction=fraction,orientation='vertical')
cbar2 = fig.colorbar(cs2,pad=pad,fraction=fraction,orientation='vertical',ticks=[-5,-4,-3,-2,-1])
plt.xscale("log")
plt.yscale("log")
plt.xlim([10**xmin,10**xmax])
plt.ylim([10**ymin,10**ymax])
plt.xlabel(xlab,size=20)
plt.ylabel(ylab,size=20)
plt.title(r'$\theta_{\eta}/\mathcal{E}_{\eta}$',fontsize=20)
index,coef=1.0,0.4
plt.plot(xe,coef*xe**index,'k:')
plt.axes().set_aspect('equal')
# script to get big Epsilon normalized with total dissipation
def get_path(targname='x2y4z1r64pmre4000'):
direname='/tigress/jiming/reconnect/athena/bin/'
targname=targname+'/'
return direname+targname
def get_normtheta(targ,ts,te,tstride,eta=2.5e-4,vsheet=False,thick=False,null=False,wth=1):
direname = get_path(targ)
# 1. load the volume averaged data
if vsheet:
fname = direname+'Unstra.out2.wth.tab'
else:
fname = direname+'Unstra.out2.jth.tab'
dtype = np.dtype([('time', 'f8'), ('jth2', 'f8'),('jsh2','f8'),('jrms2','f8')])
ahist = np.loadtxt(fname, dtype=dtype, usecols=(0,1,2,3))
tt = ahist['time']
jrms2 = ahist['jrms2']
jsh2 = ahist['jsh2']
# pick out ts to te
istart,iend = 0,0
if wth==1:
for i in np.arange(len(tt)):
if ts == int(tt[i]):
istart = i
break
for i in np.arange(len(tt)):
if (te-1) == int(tt[i]):
iend = i
break
else: #wth=2 where rho\omega^2 is calc instead omega alone
for i in np.arange(len(tt)):
if ts == int(tt[i]):
istart = i
for i in np.arange(len(tt)):
if (te-1) == int(tt[i]):
iend = i
iend +=1
if iend==istart:
iend+=1
tt = tt[istart:iend]
jrms2 = jrms2[istart:iend]
jsh2 = jsh2[istart:iend]
jrms = np.sqrt(jrms2)
if vsheet:
print '<epsilon_{nu,sh}>/<epsilon_{nu}> = ',np.average(jsh2/jrms2)
else:
print '<epsilon_{eta,sh}>/<epsilon_{eta}> = ',np.average(jsh2/jrms2)
# 2. now load current sheets for each frame
# for each sheet we calc total dissipation
# and normalize it with jrms^2
if vsheet:
if wth == 1:
basename='vprop.'
appdname='.p'
else:
basename='vprop2.'
appdname='.p'
else:
basename='jprop.'
appdname='.p'
if thick:
basename='jprop_thick.'
if null:
basename='jprop_null.'
first_time = True
for i in np.arange(ts,te,tstride):
fname = direname+basename+str(i).zfill(5)+appdname
ncells,jmax,diss,size,orient = pickle.load( open(fname, "rb" ) )
if i != int(tt[i-ts]):
print 'at t = ',tt[i-ts]
return 0
else:
# sum(eta jsh^2)/ sum(eta jrms2) dissipation rate per sheet normalized
# with rms dissipation.equivalently it's theta normalized with
# instantaneous total dissipation (although the number of grid cells not included here)
diss =np.array(diss)/eta
ncells = np.array(ncells)
if first_time:
dissnorm = diss/jrms2[i-ts]
theta = diss*ncells/jrms2[i-ts]
jmaxnorm = np.array(jmax)/jrms[i-ts]
first_time = False
else:
dissnorm = np.hstack((dissnorm,diss/jrms2[i-ts]))
theta = np.hstack((theta,diss*ncells/jrms2[i-ts]))
jmaxnorm = np.hstack((jmaxnorm,np.array(jmax)/jrms[i-ts]))
# print 'at t = ',tt[i-ts]
# print 'jsh2 from pickled file: ',np.sum(diss*ncells)/float(np.sum(ncells))
# print 'jsh2 from tabulat file:',jsh2[i-ts]
# print 'jrms2 from tabulat file:',jrms2[i-ts]
return dissnorm,theta,jmaxnorm
# nbin = 100; nt = te-ts+1
# jth2 = np.zeros(nbin)
# cdfj2 = np.zeros(nbin)
# cdfvol = np.zeros(nbin)
# theta1 = get_normtheta('x2y4z1r64pm1re4000',50,51,1)
# theta2 = get_normtheta('x2y4z1r64pm1re4000',50,101,1)
def get_curl(fname='Unstra.out2.00008.athdf'):
"""load 3d bfield and calc the current density"""
# ---
def curl(vx,vy,vz,dx,dy,dz):
[dzvx,dyvx,dxvx] = np.gradient(vx)
[dzvy,dyvy,dxvy] = np.gradient(vy)
[dzvz,dyvz,dxvz] = np.gradient(vz)
j2 = (dyvz/dy-dzvy/dz)**2
j2 += (dzvx/dz-dxvz/dx)**2
j2 += (dxvy/dx-dyvx/dy)**2
return j2
# ---
#data=ath.athdf(fname,quantities=['B1','B2','B3'])
time,data=ath.athdf(fname,quantities=['Bcc1'])
bx = data['Bcc1']
time,data=ath.athdf(fname,quantities=['Bcc2'])
by = data['Bcc2']
time,data=ath.athdf(fname,quantities=['Bcc3'])
bz = data['Bcc3']
x = data['x1f'];y = data['x2f']; z = data['x3f']
dx = dz = x[1]-x[0]; dy = y[1]-y[0]
#j2 = curl(bx,by,bz,dx,dy,dz)
j2 = curl(bx,by,bz,dx,dy,dz)
time,data=ath.athdf(fname,quantities=['vel1'])
bx = data['vel1']
time,data=ath.athdf(fname,quantities=['vel2'])
by = data['vel2']
time,data=ath.athdf(fname,quantities=['vel3'])
bz = data['vel3']
time,data=ath.athdf(fname,quantities=['rho'])
d = data['rho']
#w2 = curl(bx,by,bz,dx,dy,dz)*data['rho']
w2 = curl(bx,by,bz,dx,dy,dz)*d
return time,x,y,z,j2,w2
def plot_3slice(input_data,xslice=512,yslice=504,zslice=256,dmin=0,dmax=100,cmap='OrRd',figsize_x=6,figsize_y=8,label=None):
tmp = input_data
matplotlib.rcParams['figure.figsize'] = (figsize_x, figsize_y)
matplotlib.rcParams['image.cmap'] = cmap
gs = gridspec.GridSpec(2, 2,width_ratios=[2, 1],height_ratios=[4, 1])
ax1 = plt.subplot(gs[0])
fig1 = plt.imshow(tmp[zslice,:,:],origin='lower',extent =[-1,1,-2,2],vmin=dmin,vmax=dmax)
plt.ylabel('y',fontsize=15)
ax2 = plt.subplot(gs[1])
fig2 = plt.imshow(np.transpose(tmp[:,:,xslice]),origin='lower',extent=[-0.5,0.5,-2,2],vmin=dmin,vmax=dmax)
ax3 = plt.subplot(gs[2])
fig3 = plt.imshow(tmp[:,yslice,:],origin='lower',extent=[-1,1,-0.5,0.5],vmin=dmin,vmax=dmax)
plt.ylabel('z',fontsize=15)
plt.xlabel('x',fontsize=15)
ax4 = plt.subplot(gs[3])
ax4.axis('off')
divider = make_axes_locatable(ax4)
cax = divider.append_axes("left", size="8%", pad=0.15)
ax1.tick_params(labelbottom='off')
ax2.tick_params(labelleft='off')
#ax2.get_yaxis().set_ticks([])
plt.colorbar(cax=cax)
if label != None:
ax3.text(1.8,0.08,label,fontsize=20,rotation=90)
plt.tight_layout()
def show_contour(x,y,input_data,dmin=0,dmax=100,cmap='OrRd',xspan=(0,0),yspan=(0,0),figsize_x=6,figsize_y=8,xlabel='x',ylabel='y'):
tmp = input_data
matplotlib.rcParams['figure.figsize'] = (figsize_x, figsize_y)
matplotlib.rcParams['image.cmap'] = cmap
#gs = gridspec.GridSpec(2, 2,width_ratios=[2, 1],height_ratios=[4, 1])
if xspan[0] == 0 and xspan[1] == 0:
xmin = -1; xmax=1
else:
xmin = xspan[0]; xmax=xspan[1]
if yspan[0] == 0 and yspan[1] == 0:
ymin = -2; ymax=2
else:
ymin = yspan[0]; ymax=yspan[1]
# reduce the img to required size
ids=np.abs(x-xmin).argmin()
ide=np.abs(x-xmax).argmin()
jds=np.abs(y-ymin).argmin()
jde=np.abs(y-ymax).argmin()
ndim = np.shape(tmp)
jde = jde if jde < ndim[0] else ndim[0]-1
ide = ide if ide < ndim[1] else ndim[1]-1
tmp = tmp[jds:jde,ids:ide]
fig1 = plt.imshow(tmp,origin='lower',extent =[xmin,xmax,ymin,ymax],vmin=dmin,vmax=dmax)
plt.ylabel(ylabel,fontsize=15)
plt.xlabel(xlabel,fontsize=15)
plt.colorbar(pad=0.05,fraction=0.05)
# plot 8-panels in x-z plane (jmag,bx,by,bz,wmag/rho,vx,dvy,vz)
def plot_8panel(t,x,y,j2u,w2u,b1,b2,b3,v1,v2,v3,d,xspan=(-1,1),yspan=(-0.5,0.5),yslice=502,step=10,nslice=1,isrho=False):
matplotlib.rcParams['figure.figsize'] = (15,40)
x1b = (x + 0.5*(x[1]-x[0]))[:-1]
x3b = (y + 0.5*(y[1]-y[0]))[:-1]
nx,nz = len(x1b),len(x3b)
count = 1
jmin,jmax = 0,5
bmin,bmax = -2,2
vmin,vmax = -1.5,1.5
rmin,rmax = 0,2
#xspan,yspan = (0.3,0.7),(-0.5,-0.1)
ncol,nrow = 4,22
left, width = .25, .5
bottom, height = .25, .5
right = left + width
top = bottom + height
cmap = 'seismic'
#yslice= 502
#step = 10
wu = np.sqrt(w2u)
wu /= np.average(wu)
ju = np.sqrt(j2u)
ju /= np.average(ju)
for i in (np.arange(nslice)-nslice/2):
ind = yslice+step*i
for nvar in np.arange(8): #// j2,vx,bx,by
cmap = 'seismic'
if nvar == 0:
var = ju[:,ind,:] #ysli(np.sqrt(j2u)/np.average(np.sqrt(j2u)))[:,yslice+step*i,:]
cmap = 'OrRd'
dmin,dmax = jmin,jmax
label = r'$|j|$'
elif nvar == 1:
var = b1[:,ind,:]
dmin,dmax = bmin,bmax
label = r'$B_x$'
elif nvar == 2:
var = b2[:,ind,:]
dmin,dmax = bmin,bmax
label = r'$B_y$'
elif nvar == 3:
var = b3[:,ind,:]
dmin,dmax = bmin,bmax
label = r'$B_z$'
elif nvar == 4:
if isrho:
var = d[:,ind,:]
dmin,dmax = rmin,rmax
label = r'$\rho$'
else:
var = wu[:,ind,:] #(np.sqrt(w2u)/np.average(np.sqrt(w2u)))[:,yslice+step*i,:]
cmap = 'OrRd'
dmin,dmax = jmin,jmax
label = r'$|\omega|$'
elif nvar == 5:
var = v1[:,ind,:]
dmin,dmax = vmin,vmax
label = r'$v_x$'
elif nvar == 6:
var = v2[:,ind,:]+1.5*1.0*np.array(np.tile(x1b,(nz,1)))
dmin,dmax = vmin,vmax
label = r'$\delta v_y$'
elif nvar == 7:
var = v3[:,ind,:]
dmin,dmax = vmin,vmax
label = r'$v_z$'
else:
print 'out plotting bound'
plt.subplot(nrow,ncol,count)
show_contour(x,y,var,dmin=dmin,dmax=dmax,xspan=xspan,yspan=yspan,cmap=cmap,xlabel='x',ylabel='z')
plt.text(xspan[1]-0.1,yspan[1]-0.05,label,fontsize=15)
if nvar > 0:
plt.tick_params(labelbottom='off')
plt.tick_params(labelleft='off')
count += 1
plt.tight_layout()
# plot 6-panels in x-z plane (jmag,bx,by,wmag/rho,vx,dvy)
def plot_6panel(t,x,y,j2u,w2u,b1,b2,v1,v2,d,xspan=(-1,1),yspan=(-0.5,0.5),yslice=502,nslice=1,isrho=False):
matplotlib.rcParams['figure.figsize'] = (10,3.5)
x1b = (x + 0.5*(x[1]-x[0]))[:-1]
x3b = (y + 0.5*(y[1]-y[0]))[:-1]