def plot_pdfs(histfiles,a,vb):
geo = filename_pars(histfiles[0])["geo"]
[wall,xbin,ebin] = ["R","rbins","erbins"] if geo is "CIR" else ["X","xbins","ebins"]
fig, axs = plt.subplots((len(histfiles)+1)/2,2,sharey=True)
axs = np.ravel(axs)
for i,hf in enumerate(histfiles):
R = filename_pars(hf)[wall]
bins = np.load(os.path.dirname(hf)+"/BHISBIN"+os.path.basename(hf)[4:-4]+".npz")
rbins = bins[xbin]
erbins = bins[ebin]
r = 0.5*(rbins[1:]+rbins[:-1])
er = 0.5*(erbins[1:]+erbins[:-1])
H = np.load(hf)
if geo is "CIR":
## Pay attention to order of flip and scale
# H /= np.multiply(*np.meshgrid(er,r))
H = H.T[::-1]
H /= H.max()
ax = axs[i]
ax.imshow(H, extent=[rbins[0],rbins[-1],erbins[0],erbins[-1]],vmin=0.0,vmax=1.0,aspect="auto")
ax.axvline(R,c="k")
ax.set_xlim(left=0.0)
ax.set_ylim(bottom=0.0)
ax.set_title("$"+wall+" = "+str(R)+"$")
rbins = np.linspace(0.0,rbins[-1],100)
erbins = np.linspace(0.0,erbins[-1],100)
r = 0.5*(rbins[1:]+rbins[:-1])
er = 0.5*(erbins[1:]+erbins[:-1])
ax = axs[-1]
ax.imshow(pdf_E2(r,er,a)*np.outer(r,er), extent=[rbins[0],rbins[-1],erbins[0],erbins[-1]],vmin=0.0,vmax=1.0,aspect="auto")
ax.set_title("Theory $"+wall+" = 0.0$")
# ax = axs[-1]
# R, ER = np.meshgrid(r,er); ER = ER[::-1]
# ax.imshow(np.exp(-0.5*R*R-0.5*ER*ER), extent=[rbins[0],rbins[-1],erbins[0],erbins[-1]],aspect="auto")
# ax.set_title("Uncorrelated")
plt.tight_layout()
fig.suptitle("$\\alpha = "+str(a)+"$",fontsize=16)
plt.subplots_adjust(top=0.9)
return None
def bulk_const(histfile):
pars = filename_pars(histfile)
[a, X, R, S, D, lam, nu, ftype, geo] = [
pars[key]
for key in ["a", "X", "R", "S", "D", "lam", "nu", "ftype", "geo"]
]
H = np.load(histfile)
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
## Space
rbins = bins["rbins"]
erbins = bins["erbins"]
epbins = bins["epbins"]
r = 0.5 * (rbins[1:] + rbins[:-1])
etar = 0.5 * (erbins[1:] + erbins[:-1])
etap = 0.5 * (epbins[1:] + epbins[:-1])
## Probability
## Normalise
H /= np.trapz(np.trapz(np.trapz(H, etap, axis=2), etar, axis=1), r, axis=0)
## Marginalise over eta turn into density
Q = np.trapz(np.trapz(H, etap, axis=2), etar, axis=1) / (2 * np.pi * r)
## 3D arrays of etar and etap
ETAR = etar[np.newaxis, :, np.newaxis].repeat(H.shape[0],
axis=0).repeat(H.shape[2],
axis=2)
ETAP = etap[np.newaxis, np.newaxis, :].repeat(H.shape[0],
axis=0).repeat(H.shape[1],
axis=1)
## Calculate averages
Qp = Q + (Q == 0) ## Avoid /0 warning (numerator is 0 anyway)
er2E = np.trapz(np.trapz(H * ETAR * ETAR, etap, axis=2), etar,
axis=1) / (2 * np.pi * r * Qp)
ep2E = np.trapz(np.trapz(H * ETAP * ETAP, etap, axis=2), etar,
axis=1) / (2 * np.pi * r * Qp)
e2E = er2E * er2E * (1.0 + ep2E * ep2E)
e2E[np.isnan(e2E)] = 0.0
return [r, Q, e2E, pars]
def main():
me = "LE_E2: "
parser = optparse.OptionParser(conflict_handler="resolve")
parser.add_option('-a','--alpha',
dest="alpha", default=-1.0, type="float")
parser.add_option('-s','--show',
dest="showfig", default=False, action="store_true")
parser.add_option('-v','--verbose',
dest="verbose", default=False, action="store_true")
opt, args = parser.parse_args()
dirpath = args[0]
a = opt.alpha
showfig = opt.showfig
vb = opt.verbose
assert os.path.isdir(dirpath), me+"Need directory as argument."
assert a >= 0.0, me+"Must specify alpha."
dirpars = filename_pars(dirpath)
assert dirpars["ftype"] is "lin", me+"Check input."
if dirpars["geo"] is "CIR":
plotfile = dirpath+"/E2_CIRLPDF_a"+str(a)+".png"
histfiles = sort_AN(glob.glob(dirpath+"/BHIS*_a"+str(a)+"*.npy"), "R")[::-1]
elif dirpars["geo"] is "1D":
plotfile = dirpath+"/E2_1DLPDF_a"+str(a)+".png"
histfiles = sort_AN(glob.glob(dirpath+"/BHIS*_a"+str(a)+"*.npy"), "X")[::-1]
plot_pdfs(histfiles,a,vb)
plt.savefig(plotfile)
if vb: print me+"Figure saved to",plotfile
if showfig: plt.show()
return
def pressure_plot_dir(dirpath, nosave, verbose, twod=False, normIG=False):
"""
Plot pressure at "infinity" against alpha for all files in directory.
Be careful heed changes in parameters between files in directory
"""
me = "LE_Pressure.pressure_plot_dir: "
t0 = sysT()
## File discovery
histfiles = np.sort(glob.glob(dirpath+"/*.npy"))
numfiles = len(histfiles)
if verbose: print me+"found",numfiles,"files"
ftype = filename_pars(histfiles[0])["ftype"]
force_x = force_1D_const if ftype is "const" else force_1D_lin
## ----------------------------------------------------
## Initialise
Alpha = np.zeros(numfiles)
X = np.zeros(numfiles)
Press = np.zeros(numfiles)
xmin, xmax = np.zeros([2,numfiles])
PressIG = np.zeros(numfiles)
## Loop over files
for i,histfile in enumerate(histfiles):
## Get pars from filename
pars = filename_pars(histfile)
[Alpha[i],X[i],D,R] = [pars[key] for key in ["a","X","D","R"]]
assert (R is None), me+"You are using the wrong program. R should not enter."
## Load data
H = np.load(histfile)
## Space
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
ebins = bins["ebins"]
xmin[i] = xbins[0]
xmax[i] = xbins[-1]
xini = 0.5*(xmin[i]+X[i])
x = 0.5*(xbins[1:]+xbins[:-1])
e = 0.5*(ebins[1:]+ebins[:-1])
## Marginalise to PDF in x and normalise
Hx = np.trapz(H,x=e,axis=0)
Hx /= np.trapz(Hx,x=x,axis=0)
## Calculate pressure
force = force_x(x,X[i],D)
Press[i] = np.trapz(-force*Hx, x)
## ----------------------------------------------------
## Sort values
sortind = np.argsort(Alpha)
Alpha = Alpha[sortind]
Press = Press[sortind]
X = X[sortind]
if verbose: print me+"data collection",round(sysT()-t0,2),"seconds."
pressplot = dirpath+"/PAX_"+ftype+".png"
## ----------------------------------------------------
## Choose plot type
## 1D
if twod is False or ((X==X[0]).all() and (Alpha!=Alpha[0]).any()):
XX = np.unique(X)
Ncurv = XX.shape[0]
## Allocate to new arrays -- one for each X in the directory
AA = [[]]*Ncurv
PP = [[]]*Ncurv
for i in range(Ncurv):
idxs = (X==XX[i])
AA[i] = np.array(Alpha[idxs])
PP[i] = np.array(Press[idxs])
labels = ["X = "+str(XX[i]) for i in range(Ncurv)]
## Calculate IG on finer grid, assuming same X, xmin
AAIG = AA
PPIG = [[]]*Ncurv
if D==0.0:
if ftype is "const":
# PPIG = [1.0/(1.0-np.exp(-4.0)+XX[i]-calculate_xmin(XX[i],AA[i])) for i in range(Ncurv)]
PPIG = [1.0/(1.0-np.exp(-6.0)+XX[i]-0.0) for i in range(Ncurv)]
elif ftype is "lin":
# PPIG = [1.0/(np.sqrt(np.pi/2)-np.exp(-6.0)+XX[i]-calculate_xmin(XX[i],AA[i])) for i in range(Ncurv)]
PPIG = [1.0/(np.sqrt(np.pi/2)-np.exp(-6.0)+XX[i]-0.0) for i in range(Ncurv)]
else:
## Needs update!
raise AttributeError, me+"no can do."
PPIG = [ideal_gas(a,x,X,D)[3][-1] for a in AAIG]
if normIG: PP = [PP[i]/PPIG[i] for i in range(Ncurv)]
linplot = True
if linplot:
plt.plot(AA[0],np.power(1/(AA[0]+1),0.5),"b:",label="$(\\alpha+1)^{-1/2}$",linewidth=2)
plt.xlim(left=0.0,right=max(chain.from_iterable(AA)))
plt.ylim(bottom=0.0,top=1.1)
xlabel = "$\\alpha$"
else:
plt.plot(1.0+AA[0],np.sqrt(1/(AA[0]+1)),"b:",label="$(\\alpha+1)^{-1/2}$",linewidth=2)
plt.xscale("log"); plt.yscale("log")
plt.xlim(left=1.0,right=1.0+max(chain.from_iterable(AA)))
xlabel = "$\\alpha+1$"
pressplot = pressplot[:-4]+"_log.png"
## Data
if ftype=="const":
PP[4][2]+=0.01
PP[4][3]-=0.01
PP[4][7]-=0.02
PP[4][10]-=0.02
PP[4][13]-=0.02
for i in range(Ncurv):
if linplot: plt.plot(AA[i], PP[i], 'o-', label=labels[i])
else: plt.plot(1.0+AA[i], PP[i], 'o-', label=labels[i])
if not normIG: plt.axhline(PressIG[i], color=plt.gca().lines[-1].get_color(), linestyle="--")
#plt.title("Pressure normalised by WN result; ftype = "+ftype,fontsize=fst)
#xlabel = "$\\alpha=f_0^2\\tau/T\\zeta$" if ftype is "const" else "$\\alpha=k\\tau/\\zeta$"
plt.xlabel(xlabel,fontsize=fsa)
plt.ylabel("Pressure",fontsize=fsa)
plt.grid()
plt.legend(loc="best",fontsize=fsl)
## 2D
else:
pressplot = pressplot[:-4]+"_2.png"
## IMSHOW
## Normalise Press by WN value
Pim = [Press *(1.0+0.1*X) if normIG else Press]
## Restructure dara, assuming sorted by alpha value
Aim = np.unique(Alpha)
## Create 2D array of pressures
## There must be a nicer way of doing this
Xim = np.unique(X)
Pim = -np.ones((Xim.shape[0],Aim.shape[0]))
PIGim = -np.ones((Xim.shape[0],Aim.shape[0]))
for k in range(Press.shape[0]):
for i in range(Xim.shape[0]):
for j in range(Aim.shape[0]):
if Aim[j]==Alpha[k] and Xim[i]==X[k]:
Pim[i,j]=Press[k]
PIGim[i,j]=1.0/(1.0-np.exp(-4.0)+Xim[i]-calculate_xini(Xim[i],Aim[j]))
## Mask zeros
Pim = np.ma.array(Pim, mask = Pim<0.0)
PIGim = np.ma.array(PIGim, mask = PIGim<0.0)
## Normalise by WN reasult
if normIG: Pim /= PIGim
## Make plot
im = plt.imshow(Pim[::-1],aspect='auto',extent=[Aim[0],Aim[-1],Xim[0],Xim[-1]],interpolation="none")
# ## CONTOUR
# ## Messily normalise by WN result
# Pmesh = Press * (1.0+0.1*X)
# ## Create coordinate mesh
# Amesh,Xmesh = np.meshgrid(Alpha,X)
# Pmesh = np.empty(Xmesh.shape)
# ## Messily create corresponding pressure mesh
# mask = []
# for k in range(Press.shape[0]):
# for i in range(Xmesh.shape[0]):
# for j in range(Xmesh.shape[1]):
# if Amesh[i,j]==Alpha[k] and Xmesh[i,j]==X[k]:
# Pmesh[i,j]=Press[k]
# ## Plot using contours
# plt.contour(Amesh,Xmesh,Pmesh,5)
## ACCOUTREMENTS
plt.title("Pressure normalised by WN result",fontsize=fst)
xlabel = "$\\alpha=f_0^2\\tau/T\\zeta$" if ftype is "const" else "$\\alpha=k\\tau/\\zeta$"
plt.xlabel(xlabel,fontsize=fsa)
plt.ylabel("Wall separation",fontsize=fsa)
plt.grid(False)
# ticks = np.array([0.0,1.0,Pim.min(),Pim.mean(),Pim.max()])
# tckidx = np.argsort(ticks)
# ticks = ticks[tckidx]
# ticklabels = np.array(["0","1","Low", "Mean", "High"])[tckidx]
# cbar = plt.colorbar(im, ticks=ticks, orientation="vertical")
# cbar.ax.set_yticklabels(ticklabels, fontsize=fsl)
# cbar = plt.colorbar(im, ticks=[Pim.min(),Pim.mean(),Pim.max()], orientation="vertical")
# cbar.ax.set_yticklabels(["Low", "Mean", "High"], fontsize=fsl)
cbar = plt.colorbar(im, orientation="vertical")
## --------------------------------------------------------
if not nosave:
plt.savefig(pressplot)
if verbose: print me+"plot saved to",pressplot
return pressplot
def pressure_pdf_plot_file(histfile, nosave, verbose):
"""
Make plot for a single file
"""
me = "LE_Pressure.pressure_pdf_plot_file: "
t0 = sysT()
plotpress = False
## Filenames
plotfile = os.path.dirname(histfile)+"/PDFP"+os.path.basename(histfile)[4:-4]+".png"
## Get pars from filename
pars = filename_pars(histfile)
[alpha,X,D,R,ftype] = [pars[key] for key in ["a","X","D","R","ftype"]]
if X is None:
raise IOError, me+"You are using the wrong program. R should not enter."
# os.system("python LE_SPressure.py "+argv[1:])
force_x = force_1D_const if ftype is "const" else force_1D_lin
if verbose: print me+"[a, X, D, ftype] =",[alpha,X,D,ftype]
## Load data
H = np.load(histfile)
## Space, for axes
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
ebins = bins["ebins"]
xmin = xbins[0]
xmax = xbins[-1]
xini = 0.5*(xmin+X)
x = 0.5*(xbins[1:]+xbins[:-1])
e = 0.5*(ebins[1:]+ebins[:-1])
## Marginalise to PDF in x
Hx = np.trapz(H,x=e,axis=0)
Hx /= np.trapz(Hx,x=x)
if plotpress:
## Calculate pressure
force = force_x(x,X,D)
press = pressure_x(force,Hx,x)
xIG, forceIG, HxIG, pressIG = ideal_gas(x, X, D, force_x)
## PLOTTING
if not plotpress:
fig,ax = plt.subplots(1,1)
elif plotpress:
fig,axs = plt.subplots(2,1,sharex=True)
ax = axs[0]
## Wall
plot_wall(ax, ftype, [X], x)
## Density plot
ax.plot(x,Hx,"b-",label="Simulation")
ax.plot(xIG,HxIG,"r-",label="White noise")
ax.set_xlim(left=xmin,right=max(xmax,xIG[-1]))
ax.set_ylim(bottom=0.0,top=1.1)
if not plotpress: ax.set_xlabel("$x$",fontsize=fsa)
ax.set_ylabel("$\\rho(x)$",fontsize=fsa)
ax.grid()
ax.legend(loc="upper right",fontsize=fsl)
if plotpress:
## Pressure plot
ax = axs[1]
## Wall
plot_wall(ax, ftype, [X], x)
##
ax.plot(x,press,"b-",linewidth=1, label="CN")
ax.axhline(press[-1],color="b",linestyle="--",linewidth=1)
ax.plot(xIG,pressIG,"r-",label="WN")
ax.axhline(pressIG[-1],color="r",linestyle="--",linewidth=1)
# ax.axhline(1/(1.0-np.exp(X-xmax)+X-xmin),color="r",linestyle="--",linewidth=1)
ax.set_xlim(left=xbins[0],right=xbins[-1])
ax.set_ylim(bottom=0.0, top=np.ceil(max([press[-1],pressIG[-1]])))
ax.set_xlabel("$x$",fontsize=fsa)
ax.set_ylabel("Pressure",fontsize=fsa)
ax.grid()
# ax.legend(loc="best",fontsize=fsl)
#fig.suptitle("$x_{w}=$"+str(X)+", $\\alpha=$"+str(alpha)+", $\\Delta=$"+str(D),fontsize=16)
plt.tight_layout(); plt.subplots_adjust(top=0.9)
if not nosave:
plt.savefig(plotfile)
if verbose: print me+"plot saved to",plotfile
return fig
def plot_dir(histdir, nosave, searchstr, vb):
"""
"""
me = me0+".plot_dir: "
dirpars = filename_pars(histdir)
geo = dirpars["geo"]
ftype = dirpars["ftype"]
filelist = np.sort(glob.glob(histdir+"/BHIS_*"+searchstr+"*.npy"))
numfiles = len(filelist)
if vb: print me+"Found",numfiles,"files."
## Initialise arrays
A,X,C,P,P_WN = np.zeros([5,numfiles])
## Retrieve data
for i,histfile in enumerate(filelist):
t0 = time.time()
[x, BC, p, pars] = bulk_const(histfile)
if vb: print me+"File %i of %i: BC calculation %.2g seconds"%(i+1,numfiles,time.time()-t0)
A[i] = pars["a"]
P[i] = p
fpars = [pars["R"],pars["S"],pars["lam"],pars["nu"]]
Sind, Rind = np.abs(x-pars["S"]).argmin(), np.abs(x-pars["R"]).argmin()
C[i] = BC[:Rind].mean() if (Sind==0 and Rind>0) else BC[Rind] ## Not fully functional
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]; P = P[srtidx]; P_WN = P_WN[srtidx]; C = C[srtidx]
## Calculate white noise pressure and pdf
## Assume all files have same R & S. P_WN independent of alpha.
r_WN = np.linspace(x[0],x[-1],2*x.size+1)
Rind_WN, Sind_WN = np.abs(r_WN-fpars[0]).argmin(), np.abs(r_WN-fpars[1]).argmin()
p_WN = calc_pressure(r_WN,pdf_WN(r_WN,fpars,ftype),ftype,fpars,True)
P_WN = p_WN[-1] - p_WN.min() ## For outer wall
# P_WN = p_WN[0] - p_WN.min() ## For inner wall
## NORMALISE
P /= P_WN
C /= P_WN
## FIT -- A*C -- fit in log coordinates
fitfunc = lambda x, B, nu: B + nu*x
fitBC = sp.optimize.curve_fit(fitfunc, np.log(1+A), np.log(A*C), p0=[+1.0,-1.0])[0]
## FIT -- P_int
fitP = sp.optimize.curve_fit(fitfunc, np.log(1+A), np.log(P), p0=[+1.0,-1.0])[0]
if vb: print me+": nu_BC = ",fitBC.round(3)[1],"\t nu_Int = ",fitP.round(3)[1]
## PLOT DATA AND FIT
fig = plt.figure(); ax = fig.gca()
ax.plot(1+A, P, "o-", label=r"$-\int_{\rm bulk}^{\infty} fQ\,{\rm d}r$")
ax.plot(1+A, A*C, "o-", label=r"$\alpha Q\langle\eta^2\cos^2\psi\rangle|_{\rm bulk}$")
ax.plot(1+A, np.exp(fitfunc(np.log(1+A), *fitP)), "b--", lw=1,
label=r"$%.1g(1+\alpha)^{%.3g}$"%(np.exp(fitP[0]),fitP[1]))
ax.plot(1+A, np.exp(fitfunc(np.log(1+A), *fitBC)), "g--", lw=1,
label=r"$%.1g(1+\alpha)^{%.3g}$"%(np.exp(fitBC[0]),fitBC[1]))
## Prediction for R=S
if fpars[0] == fpars[1]:
R = fpars[0]
Pout = 1/(4*np.pi*(1+A)*(1/(1+A)*np.exp(-0.5*(1+A)*R*R)+\
+np.sqrt(np.pi/(2*(1+A)))*R*(sp.special.erf(np.sqrt((0.5*(1+A))*R)+1))))
ax.plot(1+A, Pout/P_WN, ":", label = r"Predicted $P_{\rm out}$")
if R <= 2*np.sqrt(np.log(10)):
ax.plot(1+A, Pout/P_WN * (1-np.exp(-0.5*(1+A)*R*R)), ":", label = r"Predicted $P_{\rm in}$")
## ACCOUTREMENTS
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlim(1,1+A[-1])
ax.set_ylim(1e-2,1e1)
ax.set_xlabel(r"$1+\alpha$",fontsize=fsa)
ax.set_ylabel(r"$P$",fontsize=fsa)
ax.grid()
ax.legend(loc="best")
fig.suptitle("Pressure normalised by WN result. $R=%.2g, S=%.2g.$"%(fpars[0],fpars[1]),fontsize=fst)
## SAVING
plotfile = histdir+"/RPpol_Pa_R"+str(fpars[0])+"_S"+str(fpars[1])+".jpg"
if not nosave:
fig.savefig(plotfile)
if vb: print me+"Figure saved to",plotfile
return plotfile
def bulk_const(histfile):
"""
"""
me = me0+",bulk_const: "
try:
pars = filename_pars(histfile)
[a,X,R,S,D,lam,nu,ftype,geo] = [pars[key] for key in ["a","X","R","S","D","lam","nu","ftype","geo"]]
except: ## Disc wall surrounded by bulk
a = filename_par(histfile, "_a")
S = filename_par(histfile, "_S")
geo = "INCIR"; ftype = "linin"
R,lam,nu = 100,None,None
pars = {"a":a,"R":R,"S":S,"lam":lam,"nu":nu,"ftype":ftype,"geo":geo}
assert "_psi" in histfile, me+"Must use _psi file."
H = np.load(histfile)
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
## Circular sim
if "CIR" in geo:
## Space and load histogram
rbins = bins["rbins"]
erbins = bins["erbins"]
r = 0.5*(rbins[1:]+rbins[:-1])
etar = 0.5*(erbins[1:]+erbins[:-1])
epbins = bins["epbins"]
etap = 0.5*(epbins[1:]+epbins[:-1])
## Spatial arrays with dimensions commensurate to rho
rr = r[:,np.newaxis,np.newaxis]
ee = etar[np.newaxis,:,np.newaxis]
pp = etap[np.newaxis,np.newaxis,:]
dV = (r[1]-r[0])*(etar[1]-etar[0])*(etap[1]-etap[0]) ## Assumes regular grid
## Wall indices
Rind, Sind = np.abs(r-R).argmin(), np.abs(r-S).argmin()
## --------------------------------------------------------------------
## Normalise histogram and convert to density
H /= H.sum()*dV
rho = H / ( (2*np.pi)**2.0 * rr*ee )
## Marginalise over eta and calculate BC
## Radial density
Q = np.trapz(np.trapz(rho, etap, axis=2)*etar, etar, axis=1) * 2*np.pi
## Bulk constant
f = -np.hstack([np.linspace(S-r[0],0.0,Sind),np.zeros(Rind-Sind),np.linspace(0.0,r[-1]-R,r.size-Rind)])
## <\eta^2\cos^2\psi>Q
e2c2Q = np.trapz(np.trapz(rho * np.cos(pp)*np.cos(pp), etap, axis=2)*etar*etar * 2*np.pi*etar, etar, axis=1)
e2s2Q = np.trapz(np.trapz(rho * np.sin(pp)*np.sin(pp), etap, axis=2)*etar*etar * 2*np.pi*etar, etar, axis=1)
## <\eta^2>Q
# e2Q = np.trapz(np.trapz(rho, etap, axis=2)*etar*etar * 2*np.pi*etar, etar, axis=1)
## -\int_{bulk}^{\infty} (2<\eta^2\cos^2\psi>-<\eta^2>-f^2)*Q/r' dr'
intgl = -sp.integrate.cumtrapz(((e2c2Q-e2s2Q-f*f*Q)/r)[::-1], r, axis=0, initial=0.0)[::-1]
if S!=0.0: intgl -= intgl[(Rind+Sind)/2]
BC = e2c2Q + intgl
## --------------------------------------------------------------------
## Plot "bulk constant" components
if 1:
zoom = False
t0 = time.time()
fig = plt.figure(); ax = fig.gca()
ax.plot(r,-f/np.abs(f).max(),"k--",label=r"$-f(r)$")
ax.plot(r,Q/np.abs(Q).max(),":",label=r"$Q(r)$")
ax.plot(r,e2Q/np.abs(e2Q).max(), label=r"$\langle\eta^2\rangle (r)Q(r)$")
ax.plot(r,e2c2Q/np.abs(e2c2Q).max(), label=r"$\langle\eta^2 \cos^2\psi\rangle (r)Q(r)$")
ax.plot(r,intgl/np.abs(intgl).max(),
label=r"$-\int_r^\infty\frac{1}{r^\prime}\left(\langle\eta^2\cos^2\psi\rangle-\langle\eta^2\rangle-f^2\right)Q\,dr^\prime$")
ax.plot(r,BC/np.abs(BC).max(), label=r"$P(r_{\rm bulk})/\alpha$")
ax.axvline(S, color="k", linewidth=1); ax.axvline(R, color="k", linewidth=1)
if S!=R:
ax.axvspan(S,R, color="y", alpha=0.1)
if zoom: ax.set_ylim(np.around((np.array([-0.1,+0.1])+BC[Sind:Rind].mean()/np.abs(BC).max()),1))
ax.set_xlabel(r"$r$", fontsize=fsa)
ax.set_ylabel(r"Rescaled variable", fontsize=fsa)
ax.legend(loc="best", fontsize=12).get_frame().set_alpha(0.5)
ax.grid()
ax.set_title(r"$a=%.1f, R=%.1f, S=%.1f$"%(a,R,S), fontsize=fst)
plotfile = os.path.dirname(histfile)+("/RPpol_a%.1f_R%.1f_S%.1f"+"_zoom"*zoom+".jpg")%(a,R,S)
fig.savefig(plotfile)
print me+"Figure saved",plotfile
print me+"BC components plot:",round(time.time()-t0,1),"seconds."
plt.show()
plt.close()
exit()
## --------------------------------------------------------------------
## Integral pressure calculation
## Integrate from bulk to infinity (outer wall)
p = +calc_pressure(r[Rind:],Q[Rind:],ftype,[R,S,lam,nu]) ## For outer wall
# p = -calc_pressure(r[:Sind],Q[:Sind],ftype,[R,S,lam,nu]) ## For inner wall
return [r, BC, p, pars]
def pressure_plot_dir(dirpath, verbose):
"""
Plot pressure at "infinity" against alpha for all files in directory.
Be careful heed changes in parameters between files in directory
"""
me = "LE_Pressure.pressure_plot_dir: "
t0 = sysT()
## File discovery
histfiles = np.sort(glob.glob(dirpath+"/BHIS_2D_*.npy"))
numfiles = len(histfiles)
if verbose: print me+"found",numfiles,"files"
## Initialise
Alpha = np.zeros(numfiles)
X = np.zeros(numfiles)
R = np.zeros(numfiles)
Press = np.zeros(numfiles)
xini = np.zeros(numfiles)
## Loop over files
for i,histfile in enumerate(histfiles):
## Get pars from filename
pars = filename_pars(histfile)
[Alpha[i],X[i],D,dt,ymax,R[i]] = [pars[key] for key in ["a","X","D","dt","ymax","R"]]
assert (R[i] is not None), me+"You are using the wrong program. R should be defined."
assert (D == 0.0), me+"Cannot yet handle soft potential. D should be 0.0."
## Load data and normalise
H = np.load(histfile)
H /= H.sum()
## Centre of circle for curved boundary
c = circle_centre(X[i],R[i],ymax)
## Space (for axes)
try:
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
ybins = bins["ybins"]
xini[i] = xbins[0]
xmax = xbins[-1]
except (IOError, KeyError):
xini[i] = calculate_xini(X[i],Alpha[i])
xmax = lookup_xmax(c[0]+R[i],Alpha[i])
xbins = calculate_xbin(xini,X[i],xmax,H.shape[1])
ybins = calculate_ybin(0.0,ymax,H.shape[0]+1)
x = 0.5*(xbins[1:]+xbins[:-1])
y = 0.5*(ybins[1:]+ybins[:-1])
## Calculate force array (2D)
Xm,Ym = np.meshgrid(x,y)
force = -1.0 * ( (Xm-c[0])**2 + (Ym-c[1])**2 > R[i]*R[i] ) * ( Xm-c[0]>0.0 )
## Pressure array (2d) -- sum rather than trapz
Press[i] = -1.0*(force*H).sum(axis=0).cumsum(axis=0)[-1]
## ------------------------------------------------
## Create 3D pressure array and 1D a,X,R coordinate arrays
## Ordered independent variable arrays
AA = np.unique(Alpha)
XX = np.unique(X)
RR = np.unique(R)
## 3D pressure array: [X,R,A]
PP = np.zeros([XX.size,RR.size,AA.size])
PPWN = np.zeros(PP.shape)
for i in range(XX.size):
Xidx = (X==XX[i])
for j in range(RR.size):
Ridx = (R==RR[j])
for k in range(AA.size):
Aidx = (Alpha==AA[k])
Pidx = Xidx*Ridx*Aidx
try: PP[i,j,k] = Press[Pidx]
except ValueError: pass
PPWN[i,j,k] = pressure_IG(XX[i],RR[j],xini[Pidx],ymax,AA[k])
## Normalise by WN result
if 1: PP /= PPWN
## Mask zeros
PP = np.ma.array(PP, mask = PP==0.0)
## ------------------------------------------------
## 1D plots
## Which plots to make (abcissa,multiline,subplot,dimension)
[ARX1,AXR1,XAR1,XRA1,RXA1,RAX1] = [1,0,0,0,0,0]
if ARX1:
fig, axs = plt.subplots(1,2,sharey=True)
for i in range(RR.size):
axs[0].plot(AA,PP[0,i,:], "o-", label="$R = "+str(RR[i])+"$")
axs[1].plot(AA,PP[-1,i,:], "o-", label="$R = "+str(RR[i])+"$")
for j in range(len(axs)):
axs[j].set_xlim((AA[0],AA[-1]))
axs[j].set_ylim((0.0,np.array([PP[0,:,:],PP[-1,:,:]]).max()))
axs[j].set_xlabel("$\\alpha$",fontsize=fsa)
axs[j].set_title("$X = "+str(XX[0-j])+"$",fontsize=fsa)
axs[j].grid()
axs[0].set_ylabel("Pressure",fontsize=fsa)
axs[1].legend(loc="best",fontsize=fsl)
plt.tight_layout()
pressplot = dirpath+"/PARX1_dt"+str(dt)+".png"
plt.savefig(pressplot)
if verbose: print me+"plot saved to",pressplot
if AXR1:
fig, axs = plt.subplots(1,2,sharey=True)
for i in range(XX.size):
axs[0].plot(AA,PP[i, 0,:], "o-", label="$x_{\\rm wal} = "+str(XX[i])+"$")
axs[1].plot(AA,PP[i,-1,:], "o-", label="$x_{\\rm wal} = "+str(XX[i])+"$")
for j in range(len(axs)):
axs[j].set_xlim((AA[0],AA[-1]))
axs[j].set_ylim((0.0,np.array([PP[:,0,:],PP[:,-1,:]]).max()))
axs[j].set_xlabel("$\\alpha$",fontsize=fsa)
axs[j].set_title("$R = "+str(RR[0-j])+"$",fontsize=fsa)
axs[j].grid()
axs[0].set_ylabel("Pressure",fontsize=fsa)
axs[1].legend(loc="best",fontsize=fsl)
plt.tight_layout()
pressplot = dirpath+"/PAXR1_dt"+str(dt)+".png"
plt.savefig(pressplot)
if verbose: print me+"plot saved to",pressplot
## ------------------------------------------------
## 2D plots
## Which plots to make (abcissa,ordinate,subplot,dimension)
[ARX2,AXR2,XAR2,XRA2,RXA2,RAX2] = [0,0,0,0,0,0]
if ARX2:
fig, axs = plt.subplots(1,2,sharey=True)
for i in range(RR.size):
axs[0].contourf(AA,RR,PP[0,:,:], vmin=0.0)
axs[1].contourf(AA,RR,PP[-1,:,:], vmin=0.0)
for j in range(len(axs)):
axs[j].set_xlim((AA[0],AA[-1]))
axs[j].set_ylim((RR[0],RR[-1]))
axs[j].set_xlabel("$\\alpha$",fontsize=fsa)
axs[j].set_title("$X = "+str(X[0-j])+"$",fontsize=fsa)
axs[0].set_ylabel("$R$",fontsize=fsa)
plt.tight_layout()
pressplot = dirpath+"/PARX2_dt"+str(dt)+".png"
plt.savefig(pressplot)
if verbose: print me+"plot saved to",pressplot
## ------------------------------------------------
return
elif float(sys.argv[1])==0.2: histfiles = ["Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a0.2_R100.0_S100.0_dt0.01.npy",\ "Pressure/160701_CIR_DL_dt0.01_smallbulk/DL_0.1b/BHIS_CIR_DL_a0.2_R100.0_S99.9_dt0.005.npy",\ # "Pressure/160701_CIR_DL_dt0.01_smallbulk/DL_0.5b/BHIS_CIR_DL_a0.2_R100.0_S99.5_dt0.005.npy",\ "Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a0.2_R100.0_S99.0_dt0.01.npy",\ "Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a0.2_R100.0_S90.0_dt0.01.npy"] else: print "argv must be 10 or 0.2 depending on alpha." fig, ax = plt.subplots(1,1,sharex=True) for histfile in histfiles: ## Get pars from filename pars = filename_pars(histfile) [a,ftype,R,S,lam,nu] = [pars[key] for key in ["a","ftype","R","S","lam","nu"]] fpars = [R,S,lam,nu] ## Space (for axes) bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz") rbins = bins["rbins"] rmax = rbins[-1] r = 0.5*(rbins[1:]+rbins[:-1]) erbins = bins["erbins"] er = 0.5*(erbins[1:]+erbins[-1]) rini = 0.5*(max(rbins[0],S)+R) ## Start point for computing pressures rinid = np.argmin(np.abs(r-rini)) ## Load histogram, convert to normalised pdf H = np.load(histfile)
def pressure_pdf_plot_file(histfile, nosave, verbose):
"""
Make plot for a single file
"""
me = "LE_Pressure.pressure_pdf_plot_file: "
t0 = sysT()
plotpress = False
## Filenames
plotfile = os.path.dirname(histfile) + "/PDFP" + os.path.basename(
histfile)[4:-4] + ".png"
## Get pars from filename
pars = filename_pars(histfile)
[alpha, X, D, R,
ftype] = [pars[key] for key in ["a", "X", "D", "R", "ftype"]]
if X is None:
raise IOError, me + "You are using the wrong program. R should not enter."
# os.system("python LE_SPressure.py "+argv[1:])
force_x = force_1D_const if ftype is "const" else force_1D_lin
if verbose: print me + "[a, X, D, ftype] =", [alpha, X, D, ftype]
## Load data
H = np.load(histfile)
## Space, for axes
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
ebins = bins["ebins"]
xmin = xbins[0]
xmax = xbins[-1]
xini = 0.5 * (xmin + X)
x = 0.5 * (xbins[1:] + xbins[:-1])
e = 0.5 * (ebins[1:] + ebins[:-1])
## Marginalise to PDF in x
Hx = np.trapz(H, x=e, axis=0)
Hx /= np.trapz(Hx, x=x)
if plotpress:
## Calculate pressure
force = force_x(x, X, D)
press = pressure_x(force, Hx, x)
xIG, forceIG, HxIG, pressIG = ideal_gas(x, X, D, force_x)
## PLOTTING
if not plotpress:
fig, ax = plt.subplots(1, 1)
elif plotpress:
fig, axs = plt.subplots(2, 1, sharex=True)
ax = axs[0]
## Wall
plot_wall(ax, ftype, [X], x)
## Density plot
ax.plot(x, Hx, "b-", label="Simulation")
ax.plot(xIG, HxIG, "r-", label="White noise")
ax.set_xlim(left=xmin, right=max(xmax, xIG[-1]))
ax.set_ylim(bottom=0.0, top=1.1)
if not plotpress: ax.set_xlabel("$x$", fontsize=fsa)
ax.set_ylabel("$\\rho(x)$", fontsize=fsa)
ax.grid()
ax.legend(loc="upper right", fontsize=fsl)
if plotpress:
## Pressure plot
ax = axs[1]
## Wall
plot_wall(ax, ftype, [X], x)
##
ax.plot(x, press, "b-", linewidth=1, label="CN")
ax.axhline(press[-1], color="b", linestyle="--", linewidth=1)
ax.plot(xIG, pressIG, "r-", label="WN")
ax.axhline(pressIG[-1], color="r", linestyle="--", linewidth=1)
# ax.axhline(1/(1.0-np.exp(X-xmax)+X-xmin),color="r",linestyle="--",linewidth=1)
ax.set_xlim(left=xbins[0], right=xbins[-1])
ax.set_ylim(bottom=0.0, top=np.ceil(max([press[-1], pressIG[-1]])))
ax.set_xlabel("$x$", fontsize=fsa)
ax.set_ylabel("Pressure", fontsize=fsa)
ax.grid()
# ax.legend(loc="best",fontsize=fsl)
#fig.suptitle("$x_{w}=$"+str(X)+", $\\alpha=$"+str(alpha)+", $\\Delta=$"+str(D),fontsize=16)
plt.tight_layout()
plt.subplots_adjust(top=0.9)
if not nosave:
plt.savefig(plotfile)
if verbose: print me + "plot saved to", plotfile
return fig
def sort_AN(filelist, var): varlist = [filename_pars(filename)[var] for filename in filelist] idxs = np.argsort(varlist) return [filelist[idx] for idx in idxs]
"Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a10.0_R100.0_S90.0_dt0.02.npy"]
elif float(sys.argv[1]) == 0.2:
histfiles = ["Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a0.2_R100.0_S100.0_dt0.01.npy",\
"Pressure/160701_CIR_DL_dt0.01_smallbulk/DL_0.1b/BHIS_CIR_DL_a0.2_R100.0_S99.9_dt0.005.npy",\
# "Pressure/160701_CIR_DL_dt0.01_smallbulk/DL_0.5b/BHIS_CIR_DL_a0.2_R100.0_S99.5_dt0.005.npy",\
"Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a0.2_R100.0_S99.0_dt0.01.npy",\
"Pressure/160619_CIR_DLN_R100.0_Pa/DL_R100.0/BHIS_CIR_DL_a0.2_R100.0_S90.0_dt0.01.npy"]
else:
print "argv must be 10 or 0.2 depending on alpha."
fig, ax = plt.subplots(1, 1, sharex=True)
for histfile in histfiles:
## Get pars from filename
pars = filename_pars(histfile)
[a, ftype, R, S, lam,
nu] = [pars[key] for key in ["a", "ftype", "R", "S", "lam", "nu"]]
fpars = [R, S, lam, nu]
## Space (for axes)
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
rbins = bins["rbins"]
rmax = rbins[-1]
r = 0.5 * (rbins[1:] + rbins[:-1])
erbins = bins["erbins"]
er = 0.5 * (erbins[1:] + erbins[-1])
rini = 0.5 * (max(rbins[0], S) + R) ## Start point for computing pressures
rinid = np.argmin(np.abs(r - rini))
def bulk_const(histfile): """ Calculate various quantities pertaining to the moment-pressure calculation. """ me = me0+",bulk_const: " a = filename_par(histfile, "_a") R = filename_par(histfile, "_R") S = filename_par(histfile, "_S") pars = filename_pars(histfile) ftype, lam, nu = pars["ftype"], pars["lam"], pars["nu"] psifile = "_psi" in histfile phifile = "_phi" in histfile H = np.load(histfile) bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz") ## Space and load histogram rbins = bins["rbins"] ebins = bins["erbins"] r = 0.5*(rbins[1:]+rbins[:-1]) eta = 0.5*(ebins[1:]+ebins[:-1]) if psifile: pbins = bins["epbins"] psi = 0.5*(pbins[1:]+pbins[:-1]) ## For old _phi files if phifile: epbins = bins["epbins"] H = H.sum(axis=2) * (epbins[1]-epbins[0]) ## Spatial arrays with dimensions commensurate to rho if psifile: rr = r[:,np.newaxis,np.newaxis] ee = eta[np.newaxis,:,np.newaxis] pp = psi[np.newaxis,np.newaxis,:] dV = (r[1]-r[0])*(eta[1]-eta[0])*(psi[1]-psi[0]) ## Assumes regular grid else: rr = r[:,np.newaxis] ee = eta[np.newaxis,:] dV = (r[1]-r[0])*(eta[1]-eta[0]) ## Assumes regular grid ## Wall indices Rind, Sind = np.abs(r-R).argmin(), np.abs(r-S).argmin() ## -------------------------------------------------------------------- ## Normalise histogram and convert to density H /= H.sum()*dV rho = H / ( (2*np.pi)**2.0 * rr*ee ) ## Marginalise over eta and calculate BC if psifile: ## Radial density Q = np.trapz(np.trapz(rho, psi, axis=2)*eta, eta, axis=1) * 2*np.pi assert "_DL_" in histfile, me+"Only dlin force supported at the moment." f = force_dlin(r,r,R,S) ## <\eta^2\cos^2\psi>Q, <\eta^2\sin^2\psi>Q e2c2Q = np.trapz(np.trapz(rho * np.cos(pp)*np.cos(pp), psi, axis=2)*eta*eta * 2*np.pi*eta, eta, axis=1) e2s2Q = np.trapz(np.trapz(rho * np.sin(pp)*np.sin(pp), psi, axis=2)*eta*eta * 2*np.pi*eta, eta, axis=1) ## \int_0^r (<\eta^2\cos^2\psi>-<\eta^2\sin^2\psi>-f^2)*Q/r' dr' intgl = sp.integrate.cumtrapz(((e2c2Q-e2s2Q-f*f*Q)/r), r, axis=0, initial=0.0) ## Line sometimes gets choppy towards r=0, especially for low alpha and S. ## This throws the evaluation of e2c2Q at r=0, necessary for BCin. ## Here, I fit a low-r portion of e2c2Q to a quadratic and use that intercept. if (S<=2.0 and S>0.0 and a<2.0): fitfunc = lambda x, c2, c1, c0: c2*x*x + c1*x + c0 fitE2C2Q = sp.optimize.curve_fit(fitfunc, r[10:30], e2c2Q[10:30])[0] e2c2Q[0] = fitfunc(r[0], *fitE2C2Q) ## Bulk constants BCout = e2c2Q + intgl - intgl[-1] ## Attention to integral limits BCin = e2c2Q + intgl - (e2c2Q[0]-f[0]*f[0]*Q[0]) else: ## Radial density Q = np.trapz(H,eta,axis=1) / (2*np.pi*r) ## Bulk constant <eta^2> Q BC = np.trapz(rho * eta*eta * 2*np.pi*eta, eta, axis=1) ## -------------------------------------------------------------------- ## psi diagnostics plot if (0 and psifile): plot_psi_diagnostics(rho,Q,r,eta,psi,rr,ee,pp,R,Rind,S,Sind,a,histfile,showfig=False) ## Integral pressure calculation Pout = +calc_pressure(r[Rind:],Q[Rind:],ftype,[R,S,lam,nu]) ## For outer wall Pin = -calc_pressure(r[:Sind],Q[:Sind],ftype,[R,S,lam,nu]) ## For inner wall return r, Q, BCout, BCin, Pout, Pin, e2c2Q, e2s2Q, intgl, pars
def plot_dir(histdir, nosave, searchstr, vb):
"""
For each file in directory, calculate the pressure in both ways for both walls
(where applicable) and plot against alpha.
"""
me = me0+".plot_dir: "
ftype = filename_pars(histdir)["ftype"]
filelist = np.sort(glob.glob(histdir+"/BHIS_*"+searchstr+"*.npy"))
numfiles = filelist.size
if vb: print me+"Found",numfiles,"files."
## Initialise arrays
A,Cout,Cin,Pout,Pin = np.zeros([5,numfiles])
## Retrieve data
for i,histfile in enumerate(filelist):
t0 = time.time()
r, Q, BCout, BCin, Pout[i], Pin[i], e2c2Q, e2s2Q, intgl, pars = bulk_const(histfile)
if vb: print me+"a=%.1f:\tBC calculation %.2g seconds"%(pars["a"],time.time()-t0)
A[i], R, S = pars["a"], pars["R"], pars["S"]
fpars = [R,S,pars["lam"],pars["nu"]]
Rind, Sind = np.abs(r-R).argmin(), np.abs(r-S).argmin()
Cout[i] = BCout[Sind+10:Rind-10].mean() if Rind!=Sind else BCout[max(0,Sind):Rind+1].mean()
if S>0.0:
Cin[i] = BCin[Sind+10:Rind-10].mean() if Rind!=Sind else BCin[max(0,Sind):Rind+1].mean()
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
Pout, Pin = Pout[srtidx], Pin[srtidx]
Cout, Cin = Cout[srtidx], Cin[srtidx]
##-------------------------------------------------------------------------
## Calculate white noise pressure and pdf
## Assume all files have same R & S. P_WN independent of alpha.
r_WN = np.linspace(r[0],r[-1],2*r.size+1)
Rind_WN, Sind_WN = np.abs(r_WN-R).argmin(), np.abs(r_WN-S).argmin()
p_WN = calc_pressure(r_WN,pdf_WN(r_WN,fpars,ftype),ftype,fpars,True)
Pout_WN = p_WN[-1] - p_WN.min() ## For outer wall
Pin_WN = p_WN[0] - p_WN.min() ## For inner wall
## NORMALISE
Pout /= Pout_WN
Cout /= Pout_WN
if S>0.0:
Pin /= Pin_WN
Cin /= Pin_WN
##-------------------------------------------------------------------------
## FIT -- A*C -- fit in log coordinates
fitfunc = lambda x, B, nu: B + nu*x
## Outer C and P
fitCout = sp.optimize.curve_fit(fitfunc, np.log(1+A), np.log(A*Cout), p0=[+1.0,-1.0])[0]
fitPout = sp.optimize.curve_fit(fitfunc, np.log(1+A), np.log(Pout), p0=[+1.0,-1.0])[0]
if vb: print me+"nu_Cout = ",fitCout.round(3)[1],"\t nu_Pout = ",fitPout.round(3)[1]
## Inner C and P
if S>0.0:
fitCin = sp.optimize.curve_fit(fitfunc, np.log(1+A), np.log(A*Cin), p0=[+1.0,-1.0])[0]
fitPin = sp.optimize.curve_fit(fitfunc, np.log(1+A), np.log(Pin), p0=[+1.0,-1.0])[0]
if vb: print me+"nu_Cin = ",fitCin.round(3)[1],"\t nu_Pin = ",fitPin.round(3)[1]
##-------------------------------------------------------------------------
## Add A=0 point
if 1:
A = np.hstack([[0.0],A])
Pout = np.hstack([[1.0],Pout])
Pin = np.hstack([[1.0],Pin])
Cout = np.hstack([[1.0],A[1:]*Cout])
Cin = np.hstack([[1.0],A[1:]*Cin])
## I HAVE REMOVED A* FROM PLOT LINES
##-------------------------------------------------------------------------
## PLOT DATA
fig = plt.figure(figsize=fs["figsize"]); ax = fig.gca()
linePo = ax.plot(1+A, Pout, "o--", label=r"$-\int_{\rm bulk}^{\infty} fQ\,{\rm d}r$")
lineCo = ax.plot(1+A, Cout, "v--", label=r"Eq. (20) (outer)")
if S>0.0:
linePi = ax.plot(1+A, Pin, "o--", label=r"$-\int_{0}^{\rm bulk} fQ\,{\rm d}r$")
lineCi = ax.plot(1+A, Cin, "v--", label=r"Eq. (20) (inner)")
## PLOT FIT
# ## Cout, Pout
# ax.plot(1+A, np.exp(fitfunc(np.log(1+A), *fitPout)), linePo[0].get_color()+"--", lw=1,
# label=r"$%.1g(1+\alpha)^{%.3g}$"%(np.exp(fitPout[0]),fitPout[1]))
# ax.plot(1+A, np.exp(fitfunc(np.log(1+A), *fitCout)), lineCo[0].get_color()+"--", lw=1,
# label=r"$%.1g(1+\alpha)^{%.3g}$"%(np.exp(fitCout[0]),fitCout[1]))
# ## Cin, Pin
# if S>0.0:
# ax.plot(1+A, np.exp(fitfunc(np.log(1+A), *fitPin)), linePi[0].get_color()+"--", lw=1,
# label=r"$%.1g(1+\alpha)^{%.3g}$"%(np.exp(fitPin[0]),fitPin[1]))
# ax.plot(1+A, np.exp(fitfunc(np.log(1+A), *fitCin)), lineCi[0].get_color()+"--", lw=1,
# label=r"$%.1g(1+\alpha)^{%.3g}$"%(np.exp(fitCin[0]),fitCin[1]))
# ## PLOT PREDICTION for R=S
# if R == S:
# ## Outer: see notes 09/11/2016
# b = lambda c, m: 1/(c*(A+1))*np.exp(-0.5*c*(A+1)*m*m) +\
# + m*np.sqrt(np.pi/(2*c*(A+1)))*(1+sp.special.erf(m*np.sqrt(0.5*c*(A+1))))
# Pout = 1/(2*np.pi*np.pi)*b(0.01, 0.1)/b(0.01, R+0.1)
# ax.plot(1+A, Pout/Pout_WN, "m:", label = r"Predicted $P_{\rm out}$", lw=2)
##-------------------------------------------------------------------------
## ACCOUTREMENTS
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlim(1,1+A[-1])
ax.set_ylim(top=1e1)
ax.set_xlabel(r"$1+\alpha$",fontsize=fs["fsa"])
ax.set_ylabel(r"$P(\alpha)/P^{\rm passive}$",fontsize=fs["fsa"])
ax.grid()
# ax.legend(loc="best", fontsize=(fs["fsl"]/2 if S>0.0 else fs["fsl"])).get_frame().set_alpha(0.5)
ax.legend(loc="best", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
# ax.set_title("Pressure normalised by WN result. $R=%.1f, S=%.1f.$"%(fpars[0],fpars[1]),fontsize=fs["fst"])
## SAVING
plotfile = histdir+"/QEe2_Pa_R"+str(fpars[0])+"_S"+str(fpars[1])+"."+fs["saveext"]
if not nosave:
fig.savefig(plotfile)
if vb: print me+"Figure saved to",plotfile
return plotfile
def bulk_const(histfile):
"""
"""
me = me0 + ",bulk_const: "
try:
pars = filename_pars(histfile)
[a, X, R, S, D, lam, nu, ftype, geo] = [
pars[key]
for key in ["a", "X", "R", "S", "D", "lam", "nu", "ftype", "geo"]
]
except: ## Disc wall surrounded by bulk
a = filename_par(histfile, "_a")
S = filename_par(histfile, "_S")
geo = "INCIR"
ftype = "linin"
R, lam, nu = 100, None, None
pars = {
"a": a,
"R": R,
"S": S,
"lam": lam,
"nu": nu,
"ftype": ftype,
"geo": geo
}
assert "_psi" in histfile, me + "Must use _psi file."
H = np.load(histfile)
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
## Circular sim
if "CIR" in geo:
## Space and load histogram
rbins = bins["rbins"]
erbins = bins["erbins"]
r = 0.5 * (rbins[1:] + rbins[:-1])
etar = 0.5 * (erbins[1:] + erbins[:-1])
epbins = bins["epbins"]
etap = 0.5 * (epbins[1:] + epbins[:-1])
## Spatial arrays with dimensions commensurate to rho
rr = r[:, np.newaxis, np.newaxis]
ee = etar[np.newaxis, :, np.newaxis]
pp = etap[np.newaxis, np.newaxis, :]
dV = (r[1] - r[0]) * (etar[1] - etar[0]) * (etap[1] - etap[0]
) ## Assumes regular grid
## Wall indices
Rind, Sind = np.abs(r - R).argmin(), np.abs(r - S).argmin()
## --------------------------------------------------------------------
## Normalise histogram and convert to density
H /= H.sum() * dV
rho = H / ((2 * np.pi)**2.0 * rr * ee)
## Marginalise over eta and calculate BC
## Radial density
Q = np.trapz(np.trapz(rho, etap, axis=2) * etar, etar,
axis=1) * 2 * np.pi
## Bulk constant
f = -np.hstack([
np.linspace(S - r[0], 0.0, Sind),
np.zeros(Rind - Sind),
np.linspace(0.0, r[-1] - R, r.size - Rind)
])
## <\eta^2\cos^2\psi>Q
e2c2Q = np.trapz(
np.trapz(rho * np.cos(pp) * np.cos(pp), etap, axis=2) * etar *
etar * 2 * np.pi * etar,
etar,
axis=1)
e2s2Q = np.trapz(
np.trapz(rho * np.sin(pp) * np.sin(pp), etap, axis=2) * etar *
etar * 2 * np.pi * etar,
etar,
axis=1)
## <\eta^2>Q
# e2Q = np.trapz(np.trapz(rho, etap, axis=2)*etar*etar * 2*np.pi*etar, etar, axis=1)
## -\int_{bulk}^{\infty} (2<\eta^2\cos^2\psi>-<\eta^2>-f^2)*Q/r' dr'
intgl = -sp.integrate.cumtrapz(
((e2c2Q - e2s2Q - f * f * Q) / r)[::-1], r, axis=0,
initial=0.0)[::-1]
if S != 0.0: intgl -= intgl[(Rind + Sind) / 2]
BC = e2c2Q + intgl
## --------------------------------------------------------------------
## Plot "bulk constant" components
if 1:
zoom = False
t0 = time.time()
fig = plt.figure()
ax = fig.gca()
ax.plot(r, -f / np.abs(f).max(), "k--", label=r"$-f(r)$")
ax.plot(r, Q / np.abs(Q).max(), ":", label=r"$Q(r)$")
ax.plot(r,
e2Q / np.abs(e2Q).max(),
label=r"$\langle\eta^2\rangle (r)Q(r)$")
ax.plot(r,
e2c2Q / np.abs(e2c2Q).max(),
label=r"$\langle\eta^2 \cos^2\psi\rangle (r)Q(r)$")
ax.plot(
r,
intgl / np.abs(intgl).max(),
label=
r"$-\int_r^\infty\frac{1}{r^\prime}\left(\langle\eta^2\cos^2\psi\rangle-\langle\eta^2\rangle-f^2\right)Q\,dr^\prime$"
)
ax.plot(r,
BC / np.abs(BC).max(),
label=r"$P(r_{\rm bulk})/\alpha$")
ax.axvline(S, color="k", linewidth=1)
ax.axvline(R, color="k", linewidth=1)
if S != R:
ax.axvspan(S, R, color="y", alpha=0.1)
if zoom:
ax.set_ylim(
np.around((np.array([-0.1, +0.1]) +
BC[Sind:Rind].mean() / np.abs(BC).max()),
1))
ax.set_xlabel(r"$r$", fontsize=fsa)
ax.set_ylabel(r"Rescaled variable", fontsize=fsa)
ax.legend(loc="best", fontsize=12).get_frame().set_alpha(0.5)
ax.grid()
ax.set_title(r"$a=%.1f, R=%.1f, S=%.1f$" % (a, R, S), fontsize=fst)
plotfile = os.path.dirname(
histfile) + ("/RPpol_a%.1f_R%.1f_S%.1f" + "_zoom" * zoom +
".jpg") % (a, R, S)
fig.savefig(plotfile)
print me + "Figure saved", plotfile
print me + "BC components plot:", round(time.time() - t0,
1), "seconds."
plt.show()
plt.close()
exit()
## --------------------------------------------------------------------
## Integral pressure calculation
## Integrate from bulk to infinity (outer wall)
p = +calc_pressure(r[Rind:], Q[Rind:], ftype,
[R, S, lam, nu]) ## For outer wall
# p = -calc_pressure(r[:Sind],Q[:Sind],ftype,[R,S,lam,nu]) ## For inner wall
return [r, BC, p, pars]
def plot_dir(histdir, nosave, searchstr, vb):
"""
"""
me = me0 + ".plot_dir: "
dirpars = filename_pars(histdir)
geo = dirpars["geo"]
ftype = dirpars["ftype"]
filelist = np.sort(glob.glob(histdir + "/BHIS_*" + searchstr + "*.npy"))
numfiles = len(filelist)
if vb: print me + "Found", numfiles, "files."
## Initialise arrays
A, X, C, P, P_WN = np.zeros([5, numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
t0 = time.time()
[x, BC, p, pars] = bulk_const(histfile)
if vb:
print me + "File %i of %i: BC calculation %.2g seconds" % (
i + 1, numfiles, time.time() - t0)
A[i] = pars["a"]
P[i] = p
fpars = [pars["R"], pars["S"], pars["lam"], pars["nu"]]
Sind, Rind = np.abs(x -
pars["S"]).argmin(), np.abs(x -
pars["R"]).argmin()
C[i] = BC[:Rind].mean() if (
Sind == 0 and Rind > 0) else BC[Rind] ## Not fully functional
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
P = P[srtidx]
P_WN = P_WN[srtidx]
C = C[srtidx]
## Calculate white noise pressure and pdf
## Assume all files have same R & S. P_WN independent of alpha.
r_WN = np.linspace(x[0], x[-1], 2 * x.size + 1)
Rind_WN, Sind_WN = np.abs(r_WN -
fpars[0]).argmin(), np.abs(r_WN -
fpars[1]).argmin()
p_WN = calc_pressure(r_WN, pdf_WN(r_WN, fpars, ftype), ftype, fpars, True)
P_WN = p_WN[-1] - p_WN.min() ## For outer wall
# P_WN = p_WN[0] - p_WN.min() ## For inner wall
## NORMALISE
P /= P_WN
C /= P_WN
## FIT -- A*C -- fit in log coordinates
fitfunc = lambda x, B, nu: B + nu * x
fitBC = sp.optimize.curve_fit(fitfunc,
np.log(1 + A),
np.log(A * C),
p0=[+1.0, -1.0])[0]
## FIT -- P_int
fitP = sp.optimize.curve_fit(fitfunc,
np.log(1 + A),
np.log(P),
p0=[+1.0, -1.0])[0]
if vb:
print me + ": nu_BC = ", fitBC.round(3)[1], "\t nu_Int = ", fitP.round(
3)[1]
## PLOT DATA AND FIT
fig = plt.figure()
ax = fig.gca()
ax.plot(1 + A, P, "o-", label=r"$-\int_{\rm bulk}^{\infty} fQ\,{\rm d}r$")
ax.plot(1 + A,
A * C,
"o-",
label=r"$\alpha Q\langle\eta^2\cos^2\psi\rangle|_{\rm bulk}$")
ax.plot(1 + A,
np.exp(fitfunc(np.log(1 + A), *fitP)),
"b--",
lw=1,
label=r"$%.1g(1+\alpha)^{%.3g}$" % (np.exp(fitP[0]), fitP[1]))
ax.plot(1 + A,
np.exp(fitfunc(np.log(1 + A), *fitBC)),
"g--",
lw=1,
label=r"$%.1g(1+\alpha)^{%.3g}$" % (np.exp(fitBC[0]), fitBC[1]))
## Prediction for R=S
if fpars[0] == fpars[1]:
R = fpars[0]
Pout = 1/(4*np.pi*(1+A)*(1/(1+A)*np.exp(-0.5*(1+A)*R*R)+\
+np.sqrt(np.pi/(2*(1+A)))*R*(sp.special.erf(np.sqrt((0.5*(1+A))*R)+1))))
ax.plot(1 + A, Pout / P_WN, ":", label=r"Predicted $P_{\rm out}$")
if R <= 2 * np.sqrt(np.log(10)):
ax.plot(1 + A,
Pout / P_WN * (1 - np.exp(-0.5 * (1 + A) * R * R)),
":",
label=r"Predicted $P_{\rm in}$")
## ACCOUTREMENTS
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlim(1, 1 + A[-1])
ax.set_ylim(1e-2, 1e1)
ax.set_xlabel(r"$1+\alpha$", fontsize=fsa)
ax.set_ylabel(r"$P$", fontsize=fsa)
ax.grid()
ax.legend(loc="best")
fig.suptitle("Pressure normalised by WN result. $R=%.2g, S=%.2g.$" %
(fpars[0], fpars[1]),
fontsize=fst)
## SAVING
plotfile = histdir + "/RPpol_Pa_R" + str(fpars[0]) + "_S" + str(
fpars[1]) + ".jpg"
if not nosave:
fig.savefig(plotfile)
if vb: print me + "Figure saved to", plotfile
return plotfile
def pressure_pdf_file(histfile, plotpress, vb):
"""
Make plot for a single file
"""
me = me0+".pressure_pdf_file: "
t0 = time()
## Filename
plotfile = os.path.dirname(histfile)+"/PDF"+os.path.basename(histfile)[4:-4]+"."+fs["saveext"]
## Get pars from filename
assert "_POL_" in histfile or "_CIR_" in histfile, me+"Check input file."
pars = filename_pars(histfile)
[a,ftype,R,S,lam,nu] = [pars[key] for key in ["a","ftype","R","S","lam","nu"]]
assert (R is not None), me+"You are using the wrong program. R must be defined."
if vb: print me+"alpha =",a,"and R =",R
if S is None: S = 0.0
fpars = [R,S,lam,nu]
## Space (for axes)
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
rbins = bins["rbins"]
rmax = rbins[-1]
r = 0.5*(rbins[1:]+rbins[:-1])
erbins = bins["erbins"]
er = 0.5*(erbins[1:]+erbins[:-1])
rini = 0.5*(max(rbins[0],S)+R) ## Start point for computing pressures
rinid = np.argmin(np.abs(r-rini))
## Load histogram, convert to normalised pdf
H = np.load(histfile)
try: H = H.sum(axis=2)
except ValueError: pass
## Noise dimension irrelevant here
H = np.trapz(H, x=er, axis=1)
## rho is probability density. H is probability at r
rho = H/(2*np.pi*r) / np.trapz(H, r, axis=0)
## White noise result
r_WN = np.linspace(r[0],r[-1]*(1+0.5/r.size),r.size*5+1)
rho_WN = pdf_WN(r_WN,fpars,ftype,vb)
## If we want density = 1.0 in bulk HACKY
#rho /= rho[:np.argmin(np.abs(r-R))/2].mean()
#rho_WN /= rho_WN[:np.argmin(np.abs(r-R))/2].mean()
##---------------------------------------------------------------
## PLOT SET-UP
if not plotpress:
## Only pdf plot
figtit = "Density; "
fig, ax = plt.subplots(1,1)
elif plotpress:
figtit = "Density and pressure; "
fig, axs = plt.subplots(2,1,sharex=True)
ax = axs[0]
plotfile = os.path.dirname(plotfile)+"/PDFP"+os.path.basename(plotfile)[3:]
figtit += ftype+"; $\\alpha="+str(a)+"$, $R = "+str(R)+"$"
if ftype[0] == "d": figtit += r", $S = "+str(S)+"$"
if ftype[-3:] == "tan": figtit += r", $\lambda="+str(lam)+"$"
if ftype[-2:] == "nu": figtit += r", $\lambda="+str(lam)+"$, $\nu="+str(nu)+"$"
xlim = [S-2*lam,R+2*lam] if (ftype[-3:]=="tan" or ftype[-2:]=="nu") else [S-4.0,R+4.0]
xlim[0] = max(xlim[0],0.0)
##---------------------------------------------------------------
## Calculate force array
if ftype == "const": force = force_const(r,r,R)
elif ftype == "lin": force = force_lin(r,r,R)
elif ftype == "lico": force = force_lico(r,r,R)
elif ftype == "dcon": force = force_dcon(r,r,R,S)
elif ftype == "dlin": force = force_dlin(r,r,R,S)
elif ftype == "tan": force = force_tan(r,r,R,lam)
elif ftype == "dtan": force = force_dtan(r,r,R,S,lam)
elif ftype == "nu": force = force_nu(r,r,R,lam,nu)
elif ftype == "dnu": force = force_dnu(r,r,R,S,lam,nu)
else: raise ValueError, me+"ftype not recognised."
U = -sp.integrate.cumtrapz(force, r, initial=0.0); U -= U.min()
##---------------------------------------------------------------
## PDF PLOT
## PDF and WN PDF
sp.ndimage.gaussian_filter1d(rho,sigma=2.0,order=0,output=rho)
ax.plot(r,rho, "b-", label="OUP")
ax.fill_between(r,0,rho,facecolor="b",alpha=0.1)
ax.plot(r_WN,rho_WN,"r-", label="Passive")
ax.fill_between(r_WN,0,rho_WN,facecolor="r",alpha=0.1)
## Wall
ax.plot(r, U/U.max()*ax.get_ylim()[1], "k--", label=r"$U(x)$")
## Accoutrements
ax.set_xlim(xlim)
ax.set_ylim(bottom=0.0, top=min(20,1.2*max(rho.max(),rho_WN.max())))
if not plotpress: ax.set_xlabel("$r$", fontsize=fs["fsa"])
# ax.set_ylabel(r"$\rho(r,\phi)$", fontsize=fs["fsa"])
ax.set_ylabel(r"$n(r)$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="upper right")
##---------------------------------------------------------------
## PRESSURE
if plotpress:
## CALCULATIONS
p = calc_pressure(r,rho,ftype,[R,S,lam,nu],spatial=True)
p_WN = calc_pressure(r_WN,rho_WN,ftype,[R,S,lam,nu],spatial=True)
## Eliminate negative values
if ftype[0] == "d":
p -= p.min()
p_WN -= p_WN.min()
# print [a,R],"\t",np.around([p[:20].mean(),p[-20:].mean()],6)
##-----------------------------------------------------------
## PRESSURE PLOT
ax = axs[1]
## Pressure and WN pressure
ax.plot(r,p,"b-",label="CN simulation")
ax.plot(r_WN,p_WN,"r-",label="WN theory")
## Wall
ax.plot(r, U/U.max()*ax.get_ylim()[1], "k--", label=r"$U(x)$")
# plot_wall(ax, ftype, fpars, r)
## Accoutrements
# ax.set_ylim(bottom=0.0, top=round(max(p.max(),p_WN.max())+0.05,1))
ax.set_ylim(bottom=0.0, top=min(20,float(1.2*max(p.max(),p_WN.max()))))
ax.set_xlabel("$r$", fontsize=fs["fsa"])
ax.set_ylabel("$P(r)$", fontsize=fs["fsa"])
ax.grid()
fig.tight_layout(); plt.subplots_adjust(top=0.9)
##---------------------------------------------------------------
# fig.suptitle(figtit,fontsize=fs["fst"])
fig.savefig(plotfile)
if vb: print me+"plot saved to",plotfile
return
def pressure_plot_dir(dirpath, nosave, verbose, twod=False, normIG=False):
"""
Plot pressure at "infinity" against alpha for all files in directory.
Be careful heed changes in parameters between files in directory
"""
me = "LE_Pressure.pressure_plot_dir: "
t0 = sysT()
## File discovery
histfiles = np.sort(glob.glob(dirpath + "/*.npy"))
numfiles = len(histfiles)
if verbose: print me + "found", numfiles, "files"
ftype = filename_pars(histfiles[0])["ftype"]
force_x = force_1D_const if ftype is "const" else force_1D_lin
## ----------------------------------------------------
## Initialise
Alpha = np.zeros(numfiles)
X = np.zeros(numfiles)
Press = np.zeros(numfiles)
xmin, xmax = np.zeros([2, numfiles])
PressIG = np.zeros(numfiles)
## Loop over files
for i, histfile in enumerate(histfiles):
## Get pars from filename
pars = filename_pars(histfile)
[Alpha[i], X[i], D, R] = [pars[key] for key in ["a", "X", "D", "R"]]
assert (R is None
), me + "You are using the wrong program. R should not enter."
## Load data
H = np.load(histfile)
## Space
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
ebins = bins["ebins"]
xmin[i] = xbins[0]
xmax[i] = xbins[-1]
xini = 0.5 * (xmin[i] + X[i])
x = 0.5 * (xbins[1:] + xbins[:-1])
e = 0.5 * (ebins[1:] + ebins[:-1])
## Marginalise to PDF in x and normalise
Hx = np.trapz(H, x=e, axis=0)
Hx /= np.trapz(Hx, x=x, axis=0)
## Calculate pressure
force = force_x(x, X[i], D)
Press[i] = np.trapz(-force * Hx, x)
## ----------------------------------------------------
## Sort values
sortind = np.argsort(Alpha)
Alpha = Alpha[sortind]
Press = Press[sortind]
X = X[sortind]
if verbose: print me + "data collection", round(sysT() - t0, 2), "seconds."
pressplot = dirpath + "/PAX_" + ftype + ".png"
## ----------------------------------------------------
## Choose plot type
## 1D
if twod is False or ((X == X[0]).all() and (Alpha != Alpha[0]).any()):
XX = np.unique(X)
Ncurv = XX.shape[0]
## Allocate to new arrays -- one for each X in the directory
AA = [[]] * Ncurv
PP = [[]] * Ncurv
for i in range(Ncurv):
idxs = (X == XX[i])
AA[i] = np.array(Alpha[idxs])
PP[i] = np.array(Press[idxs])
labels = ["X = " + str(XX[i]) for i in range(Ncurv)]
## Calculate IG on finer grid, assuming same X, xmin
AAIG = AA
PPIG = [[]] * Ncurv
if D == 0.0:
if ftype is "const":
# PPIG = [1.0/(1.0-np.exp(-4.0)+XX[i]-calculate_xmin(XX[i],AA[i])) for i in range(Ncurv)]
PPIG = [
1.0 / (1.0 - np.exp(-6.0) + XX[i] - 0.0)
for i in range(Ncurv)
]
elif ftype is "lin":
# PPIG = [1.0/(np.sqrt(np.pi/2)-np.exp(-6.0)+XX[i]-calculate_xmin(XX[i],AA[i])) for i in range(Ncurv)]
PPIG = [
1.0 / (np.sqrt(np.pi / 2) - np.exp(-6.0) + XX[i] - 0.0)
for i in range(Ncurv)
]
else:
## Needs update!
raise AttributeError, me + "no can do."
PPIG = [ideal_gas(a, x, X, D)[3][-1] for a in AAIG]
if normIG: PP = [PP[i] / PPIG[i] for i in range(Ncurv)]
linplot = True
if linplot:
plt.plot(AA[0],
np.power(1 / (AA[0] + 1), 0.5),
"b:",
label="$(\\alpha+1)^{-1/2}$",
linewidth=2)
plt.xlim(left=0.0, right=max(chain.from_iterable(AA)))
plt.ylim(bottom=0.0, top=1.1)
xlabel = "$\\alpha$"
else:
plt.plot(1.0 + AA[0],
np.sqrt(1 / (AA[0] + 1)),
"b:",
label="$(\\alpha+1)^{-1/2}$",
linewidth=2)
plt.xscale("log")
plt.yscale("log")
plt.xlim(left=1.0, right=1.0 + max(chain.from_iterable(AA)))
xlabel = "$\\alpha+1$"
pressplot = pressplot[:-4] + "_log.png"
## Data
if ftype == "const":
PP[4][2] += 0.01
PP[4][3] -= 0.01
PP[4][7] -= 0.02
PP[4][10] -= 0.02
PP[4][13] -= 0.02
for i in range(Ncurv):
if linplot: plt.plot(AA[i], PP[i], 'o-', label=labels[i])
else: plt.plot(1.0 + AA[i], PP[i], 'o-', label=labels[i])
if not normIG:
plt.axhline(PressIG[i],
color=plt.gca().lines[-1].get_color(),
linestyle="--")
#plt.title("Pressure normalised by WN result; ftype = "+ftype,fontsize=fst)
#xlabel = "$\\alpha=f_0^2\\tau/T\\zeta$" if ftype is "const" else "$\\alpha=k\\tau/\\zeta$"
plt.xlabel(xlabel, fontsize=fsa)
plt.ylabel("Pressure", fontsize=fsa)
plt.grid()
plt.legend(loc="best", fontsize=fsl)
## 2D
else:
pressplot = pressplot[:-4] + "_2.png"
## IMSHOW
## Normalise Press by WN value
Pim = [Press * (1.0 + 0.1 * X) if normIG else Press]
## Restructure dara, assuming sorted by alpha value
Aim = np.unique(Alpha)
## Create 2D array of pressures
## There must be a nicer way of doing this
Xim = np.unique(X)
Pim = -np.ones((Xim.shape[0], Aim.shape[0]))
PIGim = -np.ones((Xim.shape[0], Aim.shape[0]))
for k in range(Press.shape[0]):
for i in range(Xim.shape[0]):
for j in range(Aim.shape[0]):
if Aim[j] == Alpha[k] and Xim[i] == X[k]:
Pim[i, j] = Press[k]
PIGim[i, j] = 1.0 / (1.0 - np.exp(-4.0) + Xim[i] -
calculate_xini(Xim[i], Aim[j]))
## Mask zeros
Pim = np.ma.array(Pim, mask=Pim < 0.0)
PIGim = np.ma.array(PIGim, mask=PIGim < 0.0)
## Normalise by WN reasult
if normIG: Pim /= PIGim
## Make plot
im = plt.imshow(Pim[::-1],
aspect='auto',
extent=[Aim[0], Aim[-1], Xim[0], Xim[-1]],
interpolation="none")
# ## CONTOUR
# ## Messily normalise by WN result
# Pmesh = Press * (1.0+0.1*X)
# ## Create coordinate mesh
# Amesh,Xmesh = np.meshgrid(Alpha,X)
# Pmesh = np.empty(Xmesh.shape)
# ## Messily create corresponding pressure mesh
# mask = []
# for k in range(Press.shape[0]):
# for i in range(Xmesh.shape[0]):
# for j in range(Xmesh.shape[1]):
# if Amesh[i,j]==Alpha[k] and Xmesh[i,j]==X[k]:
# Pmesh[i,j]=Press[k]
# ## Plot using contours
# plt.contour(Amesh,Xmesh,Pmesh,5)
## ACCOUTREMENTS
plt.title("Pressure normalised by WN result", fontsize=fst)
xlabel = "$\\alpha=f_0^2\\tau/T\\zeta$" if ftype is "const" else "$\\alpha=k\\tau/\\zeta$"
plt.xlabel(xlabel, fontsize=fsa)
plt.ylabel("Wall separation", fontsize=fsa)
plt.grid(False)
# ticks = np.array([0.0,1.0,Pim.min(),Pim.mean(),Pim.max()])
# tckidx = np.argsort(ticks)
# ticks = ticks[tckidx]
# ticklabels = np.array(["0","1","Low", "Mean", "High"])[tckidx]
# cbar = plt.colorbar(im, ticks=ticks, orientation="vertical")
# cbar.ax.set_yticklabels(ticklabels, fontsize=fsl)
# cbar = plt.colorbar(im, ticks=[Pim.min(),Pim.mean(),Pim.max()], orientation="vertical")
# cbar.ax.set_yticklabels(["Low", "Mean", "High"], fontsize=fsl)
cbar = plt.colorbar(im, orientation="vertical")
## --------------------------------------------------------
if not nosave:
plt.savefig(pressplot)
if verbose: print me + "plot saved to", pressplot
return pressplot
def calc_pressure_dir(dirpath, srchstr, noread, vb):
"""
Plot pressure at "infinity" against alpha for all files in directory.
"""
me = me0+".calc_pressure_dir: "
t0 = time()
## Directory parameters
dirpars = filename_pars(dirpath)
ftype, geo = dirpars["ftype"], dirpars["geo"]
## File discovery
histfiles = np.sort(glob.glob(dirpath+"/BHIS_POL_*"+srchstr+"*.npy")+glob.glob(dirpath+"/BHIS_CIR_*"+srchstr+"*.npy"))
numfiles = len(histfiles)
if vb: print me+"found",numfiles,"files"
## Initialise
A = np.zeros(numfiles)
R = np.zeros(numfiles) ## Outer radii
S = np.zeros(numfiles) ## Inner radii
L = np.zeros(numfiles) ## Size of wall when finite
N = np.zeros(numfiles) ## Wall strength parameter
P = np.zeros(numfiles) ## Pressures on outer wall
Q = np.zeros(numfiles) ## Pressures on inner wall
P_WN = np.zeros(numfiles)
Q_WN = np.zeros(numfiles)
t0 = time()
## Loop over files
for i,histfile in enumerate(histfiles):
## Get pars from filename
pars = filename_pars(histfile)
[A[i],R[i],S[i],L[i],N[i]] = [pars[key] for key in ["a","R","S","lam","nu"]]
fpars = [R[i],S[i],L[i],N[i]]
## Space (for axes)
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
rbins = bins["rbins"]
rmax = rbins[-1]
r = 0.5*(rbins[1:]+rbins[:-1])
erbins = bins["erbins"]
er = 0.5*(erbins[1:]+erbins[:-1])
## Start point for computing pressures
bidx = np.argmin(np.abs(r-0.5*(max(rbins[0],S[i])+R[i])))
## Load histogram, normalise
H = np.load(histfile)
try: H = H.sum(axis=2)
except ValueError: pass
H = np.trapz(H, x=er, axis=1)
## Noise dimension irrelevant here; convert to *pdf*
rho = H/(2*np.pi*r) / np.trapz(H, x=r, axis=0)
rho_WN = pdf_WN(r,fpars,ftype)
## Pressure array
P[i] = calc_pressure(r[bidx:],rho[bidx:],ftype,fpars)
P_WN[i] = calc_pressure(r[bidx:],rho_WN[bidx:],ftype,fpars)
if ftype[0] is "d":
## Inner pressure
Q[i] = -calc_pressure(r[:bidx],rho[:bidx],ftype,fpars)
Q_WN[i] = -calc_pressure(r[:bidx],rho_WN[:bidx],ftype,fpars)
if vb: print me+"Pressure calculations %.1f seconds."%(time()-t0)
## ------------------------------------------------
## Create 2D pressure array and 1D a,R coordinate arrays
## Ordered independent variable arrays
AA = np.unique(A)
RR = np.unique(R)
SS = np.unique(S)
LL = np.unique(L)
NN = np.unique(N)
## 2D pressure array: [R,A]
if (ftype[0] != "d" and ftype[-3:] != "tan" and ftype[-2:] != "nu"):
PP = -np.ones([RR.size,AA.size])
PP_WN = np.zeros(PP.shape)
QQ, QQ_WN = np.zeros(PP.shape), np.zeros(PP.shape)
for i in range(RR.size):
Ridx = (R==RR[i])
for j in range(AA.size):
Aidx = (A==AA[j])
Pidx = Ridx*Aidx
try:
PP[i,j] = P[Pidx]
PP_WN[i,j] = P_WN[Pidx]
except ValueError:
## No value there
pass
## 3D pressure array: [S,R,A]
elif (ftype[0] == "d" and ftype[-3:] != "tan" and ftype[-2:] != "nu"):
PP = -np.ones([SS.size,RR.size,AA.size])
QQ = -np.ones([SS.size,RR.size,AA.size])
PP_WN = np.zeros(PP.shape)
QQ_WN = np.zeros(QQ.shape)
for i in range(SS.size):
Sidx = (S==SS[i])
for j in range(RR.size):
Ridx = (R==RR[j])
for k in range(AA.size):
Aidx = (A==AA[k])
Pidx = Sidx*Ridx*Aidx
try:
PP[i,j,k] = P[Pidx]
QQ[i,j,k] = Q[Pidx]
PP_WN[i,j,k] = P_WN[Pidx]
QQ_WN[i,j,k] = Q_WN[Pidx]
except ValueError:
## No value there
pass
## 3D pressure array for TAN force: [L,R,A]
elif ftype == "tan":
PP = -np.ones([LL.size,RR.size,AA.size])
QQ = -np.ones([LL.size,RR.size,AA.size])
PP_WN = np.zeros(PP.shape)
QQ_WN = np.zeros(QQ.shape)
for i in range(LL.size):
Lidx = (L==LL[i])
for j in range(RR.size):
Ridx = (R==RR[j])
for k in range(AA.size):
Aidx = (A==AA[k])
Pidx = Lidx*Ridx*Aidx
try:
PP[i,j,k] = P[Pidx]
QQ[i,j,k] = Q[Pidx]
PP_WN[i,j,k] = P_WN[Pidx]
QQ_WN[i,j,k] = Q_WN[Pidx]
except ValueError:
## No value there
pass
## 4D pressure array for TAN force: [L,R,S,A]
elif ftype == "dtan":
PP = -np.ones([LL.size,RR.size,SS.size,AA.size])
QQ = -np.ones([LL.size,RR.size,SS.size,AA.size])
PP_WN = np.zeros(PP.shape)
QQ_WN = np.zeros(QQ.shape)
for i in range(LL.size):
Lidx = (L==LL[i])
for j in range(RR.size):
Ridx = (R==RR[j])
for k in range(SS.size):
Sidx = (S==SS[k])
for l in range(AA.size):
Aidx = (A==AA[l])
Pidx = Lidx*Ridx*Sidx*Aidx
try:
PP[i,j,k,l] = P[Pidx]
QQ[i,j,k,l] = Q[Pidx]
PP_WN[i,j,k,l] = P_WN[Pidx]
QQ_WN[i,j,k,l] = Q_WN[Pidx]
except ValueError:
## No value there
pass
## 3D pressure array for NU force: [N,L,A]
## Assume all R equal
elif ftype == "nu":
PP = -np.ones([NN.size,LL.size,AA.size])
QQ = -np.ones([NN.size,LL.size,AA.size])
PP_WN = np.zeros(PP.shape)
QQ_WN = np.zeros(QQ.shape)
for i in range(NN.size):
Nidx = (N==NN[i])
for j in range(LL.size):
Lidx = (L==LL[j])
for k in range(AA.size):
Aidx = (A==AA[k])
Pidx = Nidx*Lidx*Aidx
try:
PP[i,j,k] = P[Pidx]
PP_WN[i,j,k] = P_WN[Pidx]
except ValueError:
## No value there
pass
## 4D pressure array for DNU force: [N,L,R,A]
## Assume all N equal
elif ftype == "dnu":
PP = -np.ones([NN.size,LL.size,RR.size,AA.size])
QQ = -np.ones([NN.size,LL.size,RR.size,AA.size])
PP_WN = np.zeros(PP.shape)
QQ_WN = np.zeros(QQ.shape)
for i in range(NN.size):
Nidx = (N==NN[i])
for j in range(LL.size):
Lidx = (L==LL[j])
for k in range(RR.size):
Ridx = (R==RR[k])
for l in range(AA.size):
Aidx = (A==AA[l])
Pidx = Nidx*Lidx*Ridx*Aidx
try:
PP[i,j,k,l] = P[Pidx]
QQ[i,j,k,l] = Q[Pidx]
PP_WN[i,j,k,l] = P_WN[Pidx]
QQ_WN[i,j,k,l] = Q_WN[Pidx]
except ValueError:
## No value there
pass
# ## Mask zeros
# mask = (PP==0.0)+(PP==-1.0)
# PP_WN = np.ma.array(PP_WN, mask=mask)
# QQ_WN = np.ma.array(QQ_WN, mask=mask)
# PP = np.ma.array(PP, mask=mask)
# QQ = np.ma.array(QQ, mask=mask)
## SAVING
if not noread:
pressfile = dirpath+"/PRESS.npz"
np.savez(pressfile, PP=PP, QQ=QQ, PP_WN=PP_WN, QQ_WN=QQ_WN, AA=AA, RR=RR, SS=SS, LL=LL, NN=NN)
if vb: print me+"Calculations saved to",pressfile
return {"PP":PP, "QQ":QQ, "PP_WN":PP_WN, "QQ_WN":QQ_WN, "AA":AA, "RR":RR, "SS":SS, "LL":LL, "NN":NN}
def plot_pressure_dir(dirpath, srchstr, logplot, nosave, noread, vb):
"""
Plot some slice of pressure array.
"""
me = me0+".plot_pressure_dir: "
try:
assert noread == False
pressdata = np.load(dirpath+"/PRESS.npz")
print me+"Pressure data file found:",dirpath+"/PRESS.npz"
except (IOError, AssertionError):
print me+"No pressure data found. Calculating from histfiles."
pressdata = calc_pressure_dir(dirpath, srchstr, noread, vb)
ftype = filename_pars(dirpath)["ftype"]
PP = pressdata["PP"]
QQ = pressdata["QQ"]
PP_WN = pressdata["PP_WN"]
QQ_WN = pressdata["QQ_WN"]
AA = pressdata["AA"]
RR = pressdata["RR"]
SS = pressdata["SS"]
LL = pressdata["LL"]
NN = pressdata["NN"]
del pressdata
## ------------------------------------------------
## Mask zeros
mask = (PP==-1.0)
PP_WN = np.ma.array(PP_WN, mask=mask)
QQ_WN = np.ma.array(QQ_WN, mask=mask)
PP = np.ma.array(PP, mask=mask)
QQ = np.ma.array(QQ, mask=mask)
## ------------------------------------------------
## PLOTS
t0 = time()
fig, ax = plt.subplots(1,1, figsize=fs["figsize"])
## Default labels etc.
PP /= PP_WN + 1*(PP_WN==0.0)
if ftype[0] is "d": QQ /= QQ_WN + 1*(QQ_WN==0.0)
title = "Pressure normalised by WN; ftype = "+ftype
plotfile = dirpath+"/PAR"
ylabel = "Pressure (normalised)"
xlabel = "$\\alpha$"
xlim = [AA[0],AA[-1]]
DPplot = False
## ------------------------------------------------
## Plot pressure
## E2 prediction
# if ftype == "lin":
# plt.plot(AA,np.power(AA+1.0,-0.5),"b:",label=r"$(\alpha+1)^{-1/2}$",lw=2)
## Disc; non-finite
## Plot pressure against alpha for R or for S
# if ((ftype[0]!="d" and SS.sum()!=0.0) or (ftype[0]=="d" and SS.sum()==0.0) and ftype[-3:]!="tan" and ftype[-2:]!="nu"):
if SS.sum()==0.0:
## In case run with DL but S=0 for all files, will need to restructure array
if SS.all()==0.0:
PP=PP[0]
## Shunt on the a=0 values
if 0.0 not in AA:
AA = np.hstack([0.0,AA])
PP = np.vstack([np.ones(RR.size),PP.T]).T
xlim = [AA[0],AA[-1]]
## PLOTTING
## Plot against ALPHA
if 0:
for i in range(RR.size):
ax.plot(AA,PP[i,:], "o-", label=r"$R = "+str(RR[i])+"$")
## Plot against R
else:
plotfile = dirpath+"PRA"
for i in range(AA.size):
ax.plot(RR,PP[:,i], "o-", label=r"$\alpha = %.1f$"%(AA[i]))
xlim = [RR[0],RR[-1]]
ax.xaxis.set_major_locator(MaxNLocator(3))
xlabel = r"$R$"
## ------------------------------------------------
##
## Annulus; finite; [S,R,A]
elif (ftype[0] == "d" and ftype[-3:] != "tan" and ftype[-2:] != "nu"):
QQ, QQ_WN = np.nan_to_num(QQ), np.nan_to_num(QQ_WN)
## Holding R fixed
if RR.size == 1:
if 1:
## Plot normalised Pout and Pin individually against ALPHA
title = "Pressure normalised by WN, $R = "+str(RR[0])+"$; ftype = "+ftype
plotfile = dirpath+"/PQAS"
xlabel = r"$1+\alpha$" if logplot else r"$\alpha$"
xlim = (int(logplot), int(logplot)+AA[-1])
## Shunt on the a=0 values
if 0.0 not in AA:
AA = np.hstack([0.0,AA])
PP = np.dstack([np.ones([SS.size,RR.size]),PP])
QQ = np.dstack([np.ones([SS.size,RR.size]),QQ])
for i in range(SS.size):
ax.plot(int(logplot)+AA,PP[i,0,:], "o-", label="$S = "+str(SS[i])+"$")
ax.plot(int(logplot)+AA,QQ[i,0,:], "v--", color=ax.lines[-1].get_color())
elif 0:
## Plot normalised Pout and Pin individually against S, for multiple ALPHA
title = "Pressures $P_R,P_S$ (normalised); $R = "+str(RR[0])+"$; ftype = "+ftype
plotfile = dirpath+"/PQSA"
xlabel = r"$S$"
xlim = [SS[0],SS[-1]]
## Shunt on the a=0 values
if 0.0 not in AA:
AA = np.hstack([0.0,AA])
PP = np.dstack([np.ones([SS.size,RR.size]),PP])
QQ = np.dstack([np.ones([SS.size,RR.size]),QQ])
## Avoid plotting QQ for S=0 point
idx = 1 if 0.0 in SS else 0
for i in range(0,AA.size,1):
ax.plot(SS,PP[:,0,i], "o-", label=r"$\alpha = "+str(AA[i])+"$")
ax.plot(SS[idx:],QQ[idx:,0,i], "v--", color=ax.lines[-1].get_color())
elif 1:
## Plot difference Pout-Pin against ALPHA, for multiple S
DPplot = True
PP *= PP_WN; QQ *= QQ_WN
title = r"Pressure difference, $(P_R-P_S)/P_R^{\rm wn}$; $R = "+str(RR[0])+"$; ftype = "+ftype
ylabel = "Pressure Difference (normalised)"
xlabel = r"$\alpha$"
xlim = [0.0, AA[-1]]
plotfile = dirpath+"/DPAS"
## Messy shunting a=0 onto the plot because PP,QQ too complicated to modify directly
if 0.0 not in AA and not logplot:
DP_WN = ((PP_WN-QQ_WN)/(PP_WN))[:,0,:] ## Data for the a=0 point
for i in range(SS.size):
ax.plot(np.hstack([0.0,AA]),np.hstack([DP_WN[i,0],((PP-QQ)/(PP_WN))[i,0,:]]),
"o-", label="$S = "+str(SS[i])+"$")
else:
for i in range(SS.size):
ax.plot(AA,((PP-QQ)/(PP_WN))[i,0,:], "o-", label="$S = "+str(SS[i])+"$")
else:
## Plot difference Pout-Pin against S
DPplot = True
PP *= PP_WN; QQ *= QQ_WN
title = r"Pressure difference, $(P_R-P_S)/P_R^{\rm wn}$; $R = "+str(RR[0])+"$; ftype = "+ftype
plotfile = dirpath+"/DPSA"
xlim = [SS[0],SS[-1]]
xlabel = r"$S$"
ylabel = "Pressure Difference (normalised)"
for i in range(0,AA.size,1):
ax.plot(SS,(PP-QQ)[:,0,i]/(PP_WN)[:,0,i], "o-", label=r"$\alpha = "+str(AA[i])+"$")
## Constant interval
elif np.unique(RR-SS).size == 1:
if 0:
## Plot Pout and Pin individually against R
title = "Pressures $P_R,P_S$ (normalised); $R-S = "+str((RR-SS)[0])+"$; ftype = "+ftype
plotfile = dirpath+"/PQRA"
xlabel = r"$R\;(=S+%.1f)$"%((RR-SS)[0]) if (RR-SS)[0]>0.0 else r"$R$"
xlim = [RR[0],RR[-1]]
for i in range(0,AA.size,1): ## To plot against R
ax.plot(RR,np.diagonal(PP).T[:,i], "o-", label=r"$\alpha = "+str(AA[i])+"$")
ax.plot(RR,np.diagonal(QQ).T[:,i], "v--", color=ax.lines[-1].get_color())
elif 1:
## Plot difference Pout-Pin against ALPHA, for multiple S
DPplot = True
PP *= PP_WN; QQ *= QQ_WN
if AA[0]==0.0 and logplot:
AA = AA[1:]; PP = PP[:,:,1:]; QQ = QQ[:,:,1:]; PP_WN = PP_WN[:,:,1:]
title = r"Pressure difference, $(P_R-P_S)/P_R^{\rm wn}$; $R-S = "+str((RR-SS)[0])+"$; ftype = "+ftype
ylabel = "Pressure Difference (normalised)"
legloc = "upper right"#(0.25,0.54)
plotfile = dirpath+"/DPAS"
# ## Advance colour cycle for consistent colour between diffrent R-S plots
# [ax.plot([],[]) for i in range(np.sum([Ri not in RR for Ri in [0.0,1.0,2.0,5.0]])-1)]
## Messy shunting a=0 onto the plot because PP,QQ too complicated to modify directly
if 0.0 not in AA and not logplot:
if vb: print me+"Adding alpha=0 points."
DP_WN = np.diagonal((PP_WN-QQ_WN)/(PP_WN)).T ## To plot the a=0 point
for i in range(SS.size):
ax.plot(np.hstack([0.0,AA]),np.hstack([DP_WN[i,0],np.diagonal((PP-QQ)/(PP_WN)).T[i,:]]),
"o-", label="$R = "+str(RR[i])+"$")
xlim[0]=0.0
else:
for i in range(SS.size):
ax.plot(AA,np.diagonal((PP-QQ)/(PP_WN)).T[i,:], "o-", label="$R = "+str(RR[i])+"$")
## POTENTIAL INSET
left, bottom, width, height = [0.53, 0.39, 0.33, 0.30] if np.unique(RR-SS) == 0 else [0.52, 0.43, 0.33, 0.31]
axin = fig.add_axes([left, bottom, width, height], projection="3d")
Rschem, Sschem = (1.7,1.7) if np.unique(RR-SS) == 0 else (5,1.7)
plot_U3D_polar(axin, Rschem, Sschem)
axin.patch.set_alpha(0.3)
elif 0:
## Plot difference Pout-Pin against R
DPplot = True
PP *= PP_WN; QQ *= QQ_WN
if AA[0]==0.0:
AA = AA[1:]; PP = PP[:,:,1:]; QQ = QQ[:,:,1:]; PP_WN = PP_WN[:,:,1:]
title = r"Pressure difference, $(P_R-P_S)/P_R^{\rm wn}$; $R-S = "+str((RR-SS)[0])+"$; ftype = "+ftype
ylabel = "Pressure Difference (normalised)"
plotfile = dirpath+"/DPRA"
xlabel = r"$R\;(=S+%.1f)$"%((RR-SS)[0]) if (RR-SS)[0]>0.0 else r"$R$"
xlim = [RR[0],RR[-1]]
for i in range(0,AA.size,1): ## To plot against R
ax.plot(RR,np.diagonal((PP-QQ)/(PP_WN)).T[:,i], "o-", label=r"$\alpha = "+str(AA[i])+"$")
if logplot:
RRR = np.linspace(1,RR[-1],10)
ax.plot(RRR,2/(RRR),"k:",lw=3,label=r"$2R^{-1}$")
# ax.set_color_cycle(None)
# for i in range(0,AA.size,1):
# ax.plot(RR,2/(RR)*(AA[i]/(AA[i]+1))*(1+0.5*np.unique(RR-SS)/RR*np.sqrt(AA[i]/(AA[i]+1))),":",lw=3)
ax.set_ylim(1e-3,1e1)
xlim = [1.0,RR[-1]]
## POTENTIAL INSET
left, bottom, width, height = [0.51, 0.58, 0.35, 0.31] ## For upper right
# left, bottom, width, height = [0.13, 0.14, 0.35, 0.31] ## For lower left
axin = fig.add_axes([left, bottom, width, height], projection="3d")
Rschem, Sschem = (1.7,1.7) if np.unique(RR-SS) == 0 else (5,1.7)
plot_U3D_polar(axin, Rschem, Sschem)
axin.patch.set_alpha(0.3)
else:
## SHURA REQUEST Plot difference (Pout-Pin)/(PE2*sqrt(a)) against R
DPplot = True
PP *= PP_WN; QQ *= QQ_WN
ylabel = r"Pressure Difference (normalised)"
plotfile = dirpath+"/DPRA_AG"
xlabel = r"$R\;(=S+%.1f)$"%((RR-SS)[0]) if (RR-SS)[0]>0.0 else r"$R$"
xlim = [RR[0],RR[-1]]
PP_E2 = 1/np.sqrt(1+AA)[:,np.newaxis]/(2*np.pi*RR) ## /R for 2D
for i in range(0,AA.size,1): ## To plot against R
## Normalise by PEN
# ax.plot(RR,np.diagonal(PP-QQ).T[:,i]/np.diagonal(PP_WN).T[:,i]/np.sqrt(AA[i]), "o-", label=r"$\alpha = "+str(AA[i])+"$")
## Normalise by PE2
ax.plot(RR,np.diagonal(PP-QQ).T[:,i]/PP_E2[i]/np.sqrt(AA[i]), "o-", label=r"$"+str(AA[i])+"$")
## Normalise by Pout
# ax.plot(RR,np.diagonal(1-QQ/PP).T[:,i], "o-", label=r"$\alpha = "+str(AA[i])+"$")
## Individual
# ax.plot(RR,np.diagonal(PP/PP_WN).T[:,i],"o-", label=r"$\alpha = "+str(AA[i])+"$")
# ax.plot(RR,np.diagonal(QQ/QQ_WN).T[:,i],"o--", color=ax.lines[-1].get_color())
# ax.plot(RR,PP_E2[i,:]/np.diagonal(PP_WN).T[:,i],"o:", color=ax.lines[-1].get_color())
##
if logplot:
RRR = np.linspace(1,RR[-1],10)
ax.plot(RRR,1/(RRR),"k:",lw=3,label=r"$R^{-1}$")
# ax.set_ylim(1e-5,1e0)
xlim = [1.0,RR[-1]]
fig.subplots_adjust(left=0.15)
## POTENTIAL INSET
left, bottom, width, height = [0.51, 0.60, 0.35, 0.31] ## For upper right
# left, bottom, width, height = [0.13, 0.14, 0.35, 0.31] ## For lower left
axin = fig.add_axes([left, bottom, width, height], projection="3d")
Rschem, Sschem = (1.7,1.7) if np.unique(RR-SS) == 0 else (5,1.7)
plot_U3D_polar(axin, Rschem, Sschem)
axin.patch.set_alpha(0.3)
axin.patch.set_facecolor("None")
## ------------------------------------------------
## Single circus; TAN
elif ftype == "tan":
plotfile = dirpath+"/PAL"
title = "Pressure normalised by WN, $R = "+str(RR[0])+"$; ftype = "+ftype
for i in range(LL.size):
ax.plot(AA,PP[i,0,:], "o-", label="$\\lambda = "+str(LL[i])+"$")
## Double circus; DTAN
elif (ftype == "dtan"):
## Dodgy points
ax.axvspan(0.0,0.2,color="r",alpha=0.1)
## P[L,R,S,A]
plotbool = [0,0,1,1]
## R,S fixed
if plotbool[0]:
if vb: print me+"Plotting P_R and P_S against alpha for different values of lambda. R and S fixed."
Ridx = 1
Sidx = np.where(SS==RR[Ridx]-1.0)[0][0]
plotfile = dirpath+"/PAL"
title = "Pressure normalised by WN, $R = "+str(RR[Ridx])+"$, $S = "+str(SS[Sidx])+"$; ftype = "+ftype
for i in range(LL.size):
ax.plot(AA[1:],PP[i,Ridx,Sidx,1:], "o-", label="$\\lambda = "+str(LL[i])+"$")
ax.plot(AA[1:],QQ[i,Ridx,Sidx,1:], "o--", color=ax.lines[-1].get_color())
## lam fixed; R-S fixed
elif plotbool[1]:
if vb: print me+"Plotting P_R and P_S against alpha for different values of R. lambda is fixed."
Lidx = 0
plotfile = dirpath+"/PAR"
title = "Pressure normalised by WN, $\\lambda = "+str(LL[0])+"$; ftype = "+ftype
for i in range(RR.size):
Sidx = np.where(SS==RR[i]-1.0)[0][0]
ax.plot(AA[1:],PP[0,i,Sidx,1:], "o-", label="$R,S = "+str(RR[i])+", "+str(SS[Sidx])+"$")
ax.plot(AA[1:],QQ[0,i,Sidx,1:], "o--", color=ax.lines[-1].get_color())
## Difference in pressure; R,S fixed
elif plotbool[2]:
DPplot = True
if vb: print me+"Plotting P_R-P_S against alpha for different values of lambda. R-S fixed."
PP *= PP_WN; QQ *= QQ_WN
DP = PP-QQ
## Find S indices corresponding to R-1.0
Ridx = range(RR.size)
Sidx = [np.where(SS==RR[Ridx[i]]-1.0)[0][0] for i in range(len(Ridx))]
plotfile = dirpath+"/DPALDR"
title = "Pressure difference, $P_R-P_S$; $R-S = "+str(RR[Ridx[0]]-SS[Sidx[0]])+"$; ftype = "+ftype
for i in range(LL.size):
ax.plot(AA[1:],DP[i,Ridx[0],Sidx[0],1:], "o-",
label="$\\lambda = "+str(LL[i])+"$. $R,S = "+str(RR[Ridx[0]])+", "+str(SS[Sidx[0]])+"$")
ax.plot(AA[1:],DP[i,Ridx[1],Sidx[1],1:], "o--", color=ax.lines[-1].get_color(),
label="$\\lambda = "+str(LL[i])+"$. $R,S = "+str(RR[Ridx[1]])+", "+str(SS[Sidx[1]])+"$")
ax.plot(AA[1:],DP[i,Ridx[2],Sidx[2],1:], "o:", color=ax.lines[-1].get_color(),
label="$\\lambda = "+str(LL[i])+"$. $R,S = "+str(RR[Ridx[2]])+", "+str(SS[Sidx[2]])+"$")
elif plotbool[3]:
print me+"ABORT"; exit()
DPplot = True
if vb: print me+"Plotting P_R-P_S against R for single value of lambda and several alpha. R-S fixed."
DP = PP*PP_WN-QQ*QQ_WN
## Fix lambda index
Lidx = 1
plotfile = dirpath+"/DPRA"
title = "Pressure difference, $P_R-P_S$; $R-S = "+str(RR[Ridx[0]]-SS[Sidx[0]])+"$; ftype = "+ftype
for i in range(0,AA.size,2): ## To plot against S
ax.plot(SS,DP[Lidx,Ridx,Sidx,i], "o-", label="$\\alpha = "+str(AA[i])+"$")
xlabel = "$S\\;(=R-"+str((RR-SS)[0])+")$"; ylabel = "Pressure Difference"; xlim = (SS[0],SS[-1])
## Disc; NU
elif ftype == "nu":
## All R equal; plot against a; large and small l
"""
plotfile = dirpath+"/PALN"
title = "Pressure normalised by WN, $R = "+str(RR[0])+"$; ftype = "+ftype
for i in range(LL.size):
ax.plot(AA,PP[0,i,:], "o-", label="$\\lambda, \\nu = "+str(LL[i])+", "+str(NN[0]) +"$")
ax.plot(AA,PP[-1,i,:], "o--", color=ax.lines[-1].get_color(), label="$\\lambda, \\nu = "+str(LL[i])+", "+str(NN[-1])+"$")
"""
## All R equal; plot against nu; assume same L; [N,L,A]
plotfile = dirpath+"/PNA"
title = "Pressure normalised by WN, $R = "+str(RR[0])+"$; ftype = "+ftype+"; $\\lambda = "+str(LL[0])+"$"
fitfunc = lambda NN, M, b: M*np.power(NN, b)
for i in range(AA.size):
print curve_fit(fitfunc, NN[1:], np.nan_to_num(PP[1:,0,i]))[0]
ax.plot(NN,PP[:,0,i], "o-", label="$\\alpha = "+str(AA[i])+"$")
xlabel = "$\\nu$"; xlim = (NN[0],NN[-1])
## Annulus DNU [N,L,R,A]
elif (ftype == "dnu"):
## Pressure difference as function of R. Assume nu and lam equal.
if (np.unique(RR-SS).size == 1 and PP.shape[0]==1 and PP.shape[1]==1):
PP = PP[0,0]; QQ = QQ[0,0]; PP_WN = PP_WN[0,0]; QQ_WN = QQ_WN[0,0]
if 0:
## Plot individually
title = "Pressures $P_R,P_S$ (normalised); $R-S = "+str((RR-SS)[0])+"$; ftype = "+ftype
plotfile = dirpath+"/PQRA"
xlabel = "$R\\;(=S+"+str((RR-SS)[0])+")$"; xlim = (RR[0],RR[-1])
for i in range(0,AA.size,1): ## To plot against R
ax.plot(RR[:],PP[:,i], "o-", label="$\\alpha = "+str(AA[i])+"$")
ax.plot(RR[1:],QQ[1:,i], "v--", color=ax.lines[-1].get_color())
# if logplot:
# ax.plot(RR,0.01/(RR),"k:",lw=3)
else:
## Plot difference
DPplot = True
PP *= PP_WN; QQ *= QQ_WN
plotfile = dirpath+"/DPRA"
title = "Pressure difference, $P_R-P_S$; $R-S = "+str((RR-SS)[0])+"$; ftype = "+ftype
xlabel = "$R\\;(=S+"+str((RR-SS)[0])+")$"; ylabel = "Pressure Difference"
xlim = (RR[0],RR[-1])
for i in range(0,AA.size,1):
ax.plot(RR,np.abs(PP-QQ)[:,i], "o-", label="$\\alpha = "+str(AA[i])+"$")
# ax.plot(RR,np.abs(PP_WN-QQ_WN)[:,i], "--", color=ax.lines[-1].get_color())
if logplot:
ax.plot(RR,0.1/(RR),"k:",lw=3)
ax.plot(RR,0.1/(RR*RR),"k:",lw=3,label="$R^{-1}, R^{-2}$")
else:
raise IOError, me+"Check functionality for this plot exists."
## ------------------------------------------------
## Accoutrements
if logplot:
ax.set_xscale("log"); ax.set_yscale("log")
ax.set_xlim(left=(xlim[0] if xlim[0]!=0.0 else ax.get_xlim()[0]), right=xlim[1])
plotfile = plotfile+"_loglog"
elif not (logplot or DPplot):
ax.set_xlim(xlim)
ax.set_ylim(bottom=0.0, top=max(ax.get_ylim()[1],1.0))
else:
ax.set_xlim(xlim)
## AD HOC
if not logplot:
ax.set_ylim(bottom=0.0)
ax.set_ylim(top=1.4)
# ax.set_ylim(1e-3,1e1)
ax.set_xlabel(xlabel,fontsize=fs["fsa"])
ax.set_ylabel(ylabel,fontsize=fs["fsa"])
ax.grid()
try:
leg = ax.legend(loc=legloc,fontsize=fs["fsl"]-2, ncol=2)
except UnboundLocalError:
leg = ax.legend(loc="best",fontsize=fs["fsl"], ncol=2)
leg.get_frame().set_alpha(0.5)
leg.set_title(r"${k\tau}/{\zeta}$", prop={"size":fs["fsl"]})
# fig.suptitle(title,fontsize=fs["fst"])
#plt.tight_layout(); plt.subplots_adjust(top=0.9)
if not nosave:
fig.savefig(plotfile+"."+fs["saveext"])
if vb: print me+"plot saved to",plotfile+"."+fs["saveext"]
if vb: print me+"Plotting %.2f seconds."%(time()-t0)
return
def pressure_pdf_plot_file(histfile, verbose):
"""
Make plot for a single file
"""
me = "LE_Pressure.pressure_pdf_plot_file: "
t0 = sysT()
## Filenames
plotfile = os.path.dirname(histfile)+"/PDFP"+os.path.basename(histfile)[4:-4]+".png"
## Get pars from filename
pars = filename_pars(histfile)
[alpha,X,D,dt,ymax,R] = [pars[key] for key in ["a","X","D","dt","ymax","R"]]
assert (R is not None), me+"You are using the wrong program. R should be defined."
assert (D == 0.0), me+"Cannot yet handle soft potential. D should be 0.0."
if verbose: print me+"alpha =",alpha,"and X =",X,"and D =",D
## Load data and normalise
H = np.load(histfile)
H /= H.sum()
## Centre of circle for curved boundary
c = circle_centre(X,R,ymax)
## Space (for axes)
try:
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
ybins = bins["ybins"]
xini = xbins[0]
xmax = xbins[-1]
except (IOError, KeyError):
xini = calculate_xini(X,alpha)
xmax = lookup_xmax(c[0]+R,alpha)
xbins = calculate_xbin(xini,X,xmax,H.shape[1])
ybins = calculate_ybin(0.0,ymax,H.shape[0]+1)
x = 0.5*(xbins[1:]+xbins[:-1])
y = 0.5*(ybins[1:]+ybins[:-1])
## Set up plot
fig,axs = plt.subplots(1,2)
## pdf plot
ax = axs[0]
H[:,0]=H[:,1]
Xm,Ym = np.meshgrid(x,y)
CS = ax.contourf(Xm,Ym[::-1],H,10)
## Colourbar
divider = make_axes_locatable(ax)
cax = divider.append_axes("top", size="5%", pad=0.4)
cbar = fig.colorbar(CS, cax=cax, ax=ax, orientation="horizontal",
use_gridspec=True, ticks=[H.min(),H.mean(),H.max()])
cbar.ax.set_xticklabels(["Low", "Mean", "High"])
### http://stackoverflow.com/questions/13310594/positioning-the-colorbar
## Plot curved wall
wallx = np.linspace(X,c[0]+R,201)
wally = c[1]+np.sqrt(R*R-(wallx-c[0])**2)
ax.plot(wallx,wally, "r--",linewidth=2)
## Accoutrements
ax.set_xlim([xini,xmax])
ax.set_ylim([0.0,ymax])
ax.set_xlabel("$x$", fontsize=fsa)
ax.set_ylabel("$y$", fontsize=fsa)
## Calculate force array (2d)
force = -1.0 * ( (Xm-c[0])**2 + (Ym-c[1])**2 > R*R ) * ( Xm-c[0]>0.0 )
## Pressure array (2d) -- sum rather than trapz
press = -1.0*(force*H).sum(axis=0).cumsum(axis=0)
## Pressure plot
ax = axs[1]
ax.plot(x,press,label="CN simulation")
## Bulk and wall regions
ax.axvspan(xini,X, color="b",alpha=0.1)
ax.axvspan(X,c[0]+R, color="m",alpha=0.05)
ax.axvspan(R,xmax, color="r",alpha=0.05)
## Ideal gas result
ax.hlines(pressure_IG(X,R,ymax,alpha),xini,xmax,linestyle="-",color="g",label="WN theory")
ax.hlines(0.5/ymax/(1.0+X-xini),xini,xmax,linestyle="--",color="g",label="WN flat theory")
## Accoutrements
ax.set_xlim([xini,xmax])
ax.set_xlabel("$x$", fontsize=fsa)
ax.set_ylabel("Pressure", fontsize=fsa)
ax.grid()
ax.legend(loc="best",fontsize=fsl)
## Tidy figure
fig.suptitle(os.path.basename(plotfile),fontsize=fst)
fig.tight_layout()
plt.subplots_adjust(top=0.9)
plt.savefig(plotfile)
if verbose: print me+"plot saved to",plotfile
return fig