def plot_traj(x, ex, R, S, a, dt, totpts, vb):
"""
"""
me = "test_traj.plot_traj: "
fig = plt.figure()
ax = fig.gca()
cm = plt.get_cmap("GnBu")
## ------------------------------------------------------------------------
## LINE COLOUR
## Constant colour for each line segment of CH points
## Colour decays away and hits min value.
cm = plt.get_cmap("GnBu")
CH = int(a / dt / 20) ## Points in a colouring chunk
NCH = totpts / CH ## Total number of chunks
NCHC = 50 ## Number of coloured chunks, after which line is cmin
cmin = 0.3
## colourlist is linearly declining until NCHC chunks have been coloured, then constant colour
colourlist = [
cm(max(1. * (NCHC - i) / (NCHC - 1), cmin)) for i in range(NCHC)
] + [cm(cmin)] * (NCH - NCHC)
# colourlist = colourlist[::-1]
ax.set_prop_cycle("color", colourlist)
## ------------------------------------------------------------------------
## Plot segments
x = x[::-1]
ex = ex[::-1]
for i in range(x.shape[0] / CH):
ax.plot(x[i * CH:(i + 1) * CH + 1],
ex[i * CH:(i + 1) * CH + 1],
zorder=1)
## Plot wall
xfine = np.linspace(S - 3, R + 3, 100 * (R - S + 6) + 1)
ax.plot(xfine, -force_dlin([xfine, 0], R, S)[0], "k-")
ax.set_xlim(S - 2, R + 2)
ax.set_ylim(-3, +3)
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$\eta$")
ax.grid()
return fig
def plot_traj(x,ex,R,S,a,dt,totpts,vb):
"""
"""
me = "test_traj.plot_traj: "
fig = plt.figure(); ax = fig.gca()
cm = plt.get_cmap("GnBu")
## ------------------------------------------------------------------------
## LINE COLOUR
## Constant colour for each line segment of CH points
## Colour decays away and hits min value.
cm = plt.get_cmap("GnBu")
CH = int(a/dt/20) ## Points in a colouring chunk
NCH = totpts/CH ## Total number of chunks
NCHC = 50 ## Number of coloured chunks, after which line is cmin
cmin = 0.3
## colourlist is linearly declining until NCHC chunks have been coloured, then constant colour
colourlist = [cm(max(1.*(NCHC-i)/(NCHC-1),cmin)) for i in range(NCHC)] + [cm(cmin)]*(NCH-NCHC)
# colourlist = colourlist[::-1]
ax.set_prop_cycle("color", colourlist)
## ------------------------------------------------------------------------
## Plot segments
x=x[::-1]; ex=ex[::-1]
for i in range(x.shape[0]/CH):
ax.plot(x[i*CH:(i+1)*CH+1],ex[i*CH:(i+1)*CH+1],zorder=1)
## Plot wall
xfine = np.linspace(S-3,R+3,100*(R-S+6)+1)
ax.plot(xfine, -force_dlin([xfine,0],R,S)[0], "k-")
ax.set_xlim(S-2,R+2)
ax.set_ylim(-3,+3)
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$\eta$")
ax.grid()
return fig
def calc_mass_ratio(histdir, srchstr, noread, vb):
"""
Read in directory of files with inner and outer regions.
Compute mass in each region, take ratio.
Compare with integrated and calculated white noise result.
"""
me = me0 + ".calc_mass_ratio: "
t0 = time.time()
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histdir, me + "Functional only for Cartesian geometry."
assert "_DL_" not in histdir, me + "Must have interior region."
## File discovery
filelist = np.sort(glob.glob(histdir + "/BHIS_CAR_*" + srchstr + "*.npy"))
numfiles = len(filelist)
assert numfiles > 1, me + "Check input directory."
if vb: print me + "found", numfiles, "files"
##-------------------------------------------------------------------------
A, ML, MR = np.zeros([3, numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
## Assume R, S, T are same for all files
A[i] = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
try:
T = filename_par(histfile, "_T")
except ValueError:
T = -S
## Space
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
x = 0.5 * (xbins[1:] + xbins[:-1])
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
## Spatial density
Qx = H.sum(axis=2).sum(axis=1) / (H.sum() * (x[1] - x[0]))
## Mass on either side of cusp: data. Left, right.
if "_CL_" in histfile:
cuspind = np.abs(0.5 * (T + S) - x).argmin() ## Half-domain
elif "_ML_" in histfile:
cuspind = np.abs(0.5 * (T + S) - x).argmin()
elif "_NL_" in histfile:
cuspind = np.abs(S - x).argmin()
ML[i] = np.trapz(Qx[:cuspind], x[:cuspind])
MR[i] = np.trapz(Qx[cuspind:], x[cuspind:])
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
ML = ML[srtidx]
MR = MR[srtidx]
##-------------------------------------------------------------------------
## WN result from density solution
if "_DL_" in histfile: fx = force_dlin([x, 0], R, S)[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R, S, T)[0]
elif "_NL_" in histfile: fx = force_nlin([x, 0], R, S)[0]
else: raise IOError, me + "Force not recognised."
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
MLwn = np.trapz(Qx_WN[:cuspind], x[:cuspind])
MRwn = np.trapz(Qx_WN[cuspind:], x[cuspind:])
##-------------------------------------------------------------------------
## Add a=0 point
if 0.0 not in A:
A = np.hstack([0.0, A])
ML = np.hstack([MLwn, ML])
MR = np.hstack([MRwn, MR])
##-------------------------------------------------------------------------
### This might not be the cleanest thing to save...
## SAVING
if not noread:
massfile = histdir + "/MASS_" + srchstr + ".npz"
np.savez(massfile,
A=A,
ML=ML,
MR=MR,
MLwn=MLwn,
MRwn=MRwn,
x=x,
Qx_WN=Qx_WN,
R=R,
S=S,
T=T,
cuspind=cuspind)
if vb:
print me + "Calculations saved to", massfile
print me + "Calculation time %.1f seconds." % (time.time() - t0)
return {
"A": A,
"ML": ML,
"MR": MR,
"MLwn": MLwn,
"MRwn": MRwn,
"x": x,
"Qx_WN": Qx_WN,
"R": R,
"S": S,
"T": T,
"cuspind": cuspind
}
def plot_pdf1d(histfile, nosave, vb):
"""
Calculate Q(r) and q(eta) from file and plot.
"""
me = me0 + ".plot_pdf1d: "
t0 = time.time()
##-------------------------------------------------------------------------
## Filename pars
assert "_CAR_" in histfile, me + "Functional only for Cartesian geometry."
Casimir = "_CL_" in histfile or "_ML_" in histfile or "_NL_" in histfile
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
try:
T = filename_par(histfile, "_T")
except ValueError:
T = -S
doQfit = (R == S and "_DL_" in histfile)
plotq = int(False)
##-------------------------------------------------------------------------
## Space
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
exbins = bins["exbins"]
eybins = bins["eybins"]
x = 0.5 * (xbins[1:] + xbins[:-1])
etax = 0.5 * (exbins[1:] + exbins[:-1])
etay = 0.5 * (eybins[1:] + eybins[:-1])
## Wall indices
Rind, Sind = np.abs(x - R).argmin(), np.abs(x - S).argmin()
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
rho = H / (H.sum() * (x[1] - x[0]) * (etax[1] - etax[0]) *
(etay[1] - etay[0]))
## Spatial density
Qx = rho.sum(axis=2).sum(axis=1) * (etax[1] - etax[0]) * (etay[1] -
etay[0])
## Force density
qx = rho.sum(axis=2).sum(axis=0) * (x[1] - x[0]) * (etay[1] - etay[0])
qy = rho.sum(axis=1).sum(axis=0) * (x[1] - x[0]) * (etax[1] - etax[0])
##-------------------------------------------------------------------------
## Fit
gauss = lambda x, m, s2: 1 / np.sqrt(2 * np.pi * s2) * np.exp(-0.5 * (
x - m)**2 / s2)
if doQfit:
fitQx = sp.optimize.curve_fit(gauss, x, Qx, p0=[R,
1 / np.sqrt(1 + a)])[0]
##-------------------------------------------------------------------------
## PLOTTING
fig, axs = plt.subplots(1 + plotq, 1, figsize=fs["figsize"])
fig.canvas.set_window_title("1D PDFs")
## Set number of ticks
for ax in np.ravel([axs]):
ax.xaxis.set_major_locator(MaxNLocator(5))
ax.yaxis.set_major_locator(MaxNLocator(4))
##-------------------------------------------------------------------------
## Spatial density plot
ax = axs[0] if plotq else axs
## Data
ax.plot(x, Qx, label=r"OUP")
ax.fill_between(x, 0.0, Qx, color="b", alpha=0.1)
## Gaussian for spatial density
if doQfit:
ax.plot(x,
gauss(x, fitQx[0], 1 / (1 + a)),
"c-",
label=r"$G\left(\mu, \frac{1}{\alpha+1}\right)$")
## Potential and WN
if "_DC_" in histfile: fx = force_dcon([x, 0], R, S)[0]
elif "_DL_" in histfile: fx = force_dlin([x, 0], R, S)[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R, S, T)[0]
elif "_NL_" in histfile: fx = force_nlin([x, 0], R, S)[0]
else: raise IOError, me + "Force not recognised."
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
## Plot passive density
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
ax.plot(x, Qx_WN, "r-", label="Passive")
ax.fill_between(x, 0.0, Qx_WN, color="r", alpha=0.1)
## Plot potential
ax.plot(x, U / U.max() * ax.get_ylim()[1], "k--", label=r"$U(x)$")
## Indicate bulk
ax.axvline(S, c="k", lw=1)
ax.axvline(R, c="k", lw=1)
if T >= 0.0:
ax.axvspan(S, R, color="y", alpha=0.1)
ax.axvline(T, c="k", lw=1)
ax.axvspan(-R, T, color="y", alpha=0.1)
ax.axvline(-R, c="k", lw=1)
elif T < 0.0:
ax.axvline(-R, c="k", lw=1)
ax.set_xlim(left=x[0], right=x[-1])
ax.set_xlabel(r"$x$", fontsize=fs["fsa"])
ax.set_ylabel(r"$n(x)$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="upper right", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
if plotq:
## Force density plot
ax = axs[1]
## Data
ax.plot(etax, qx, label=r"Simulation $x$")
ax.plot(etay, qy, label=r"Simulation $y$")
## Gaussian
ax.plot(etax,
gauss(etax, 0.0, 1 / a),
"c-",
label=r"$G\left(0, \frac{1}{\alpha}\right)$")
ax.set_xlabel(r"$\eta$", fontsize=fs["fsa"])
ax.set_ylabel(r"$q(\eta)$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="upper right",
fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
fig.tight_layout()
fig.subplots_adjust(top=0.95)
title = r"PDFs in $r$ and $\eta$. $\alpha=%.1f, R=%.1f, S=%.1f$"%(a,R,S) if T<0.0\
else r"PDFs in $r$ and $\eta$. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.1f$"%(a,R,S,T)
else:
title = r"Spatial PDF. $\alpha=%.1f, R=%.1g, S=%.1g$"%(a,R,S) if T<0.0\
else r"Spatial PDF. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.f$"%(a,R,S,T)
# fig.suptitle(title, fontsize=fs["fst"])
if not nosave:
plotfile = os.path.dirname(histfile) + "/PDFxy1d" + os.path.basename(
histfile)[4:-4]
plotfile += "." + fs["saveext"]
fig.savefig(plotfile, format=fs["saveext"])
if vb: print me + "Figure saved to", plotfile
if vb: print me + "Execution time %.1f seconds." % (time.time() - t0)
return
HP = np.load(histfileP)
bP = np.load(os.path.dirname(histfileP)+"/BHISBIN"+os.path.basename(histfileP)[4:-4]+".npz")
HC = np.load(histfileC)
bC = np.load(os.path.dirname(histfileC)+"/BHISBIN"+os.path.basename(histfileC)[4:-4]+".npz")
r = 0.5*(bP["rbins"][1:]+bP["rbins"][:-1])
x = 0.5*(bC["xbins"][1:]+bC["xbins"][:-1])
## Spatial density
QP = HP.sum(axis=2).sum(axis=1) / (2*np.pi*r)
QP /= np.trapz(2*np.pi*r*QP, r)
QC = HC.sum(axis=2).sum(axis=1)
QC /= np.trapz(QC, x)
## Potential
if "_DL_" in histfileP: fx = force_dlin([x,0],R,S)[0]
elif "_CL_" in histfileP: fx = force_clin([x,0],R,S,T)[0]
elif "_ML_" in histfileP: fx = force_mlin([x,0],R,S,T)[0]
elif "_NL_" in histfileP: fx = force_nlin([x,0],R,S)[0]
else: raise IOError, me+"Force not recognised."
U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min()
## ------------------------------------------------------------------------
## 1D
if 1:
fig, axs = plt.subplots(1,1, figsize=(10,10))
ax = axs
ax.plot(r, QP/QP.max(), label=r"$n_{\rm rad}(r)$")
ax.plot(x, QC/QC.max(), label=r"$n_{\rm car}(x)$")
def main():
"""
"""
me = me0+".main: "
a = 1.0
timefac = 1.0
dt = 0.01
R = 2.0
S = 0.0
vb = True
fx = lambda x: force_dlin([x,0],R,S)[0]
outdir = "./Pressure/TRAJ_CAR_DL_a%.1f_R%.1f_S%.1f_t%.1f"%(a,R,S,timefac)
if not os.path.isdir(outdir):
os.mkdir(outdir)
print me+"Created directory",outdir
## ----------------------------------------------------------------
## SET UP CALCULATIONS
## Simulation time
tmax = 5e2*timefac
## Simulation limits
xmax = R+3.0
xmin = S-3.0
## Injection x coordinate
xini = 0.5*(S+R)
## Initial noise drawn from Gaussian
if a == 0.0: eIC = np.sqrt(2/dt)*np.random.normal(0.0, 1.0)
else: eIC = dt/np.sqrt(a)*np.random.normal(0.0, 1.0)
## Integration algorithm
x_step = lambda x, ex: eul(x, ex, fx, dt)
## ----------------------------------------------------------------
## SIMULATION
## Precompute exp(-t)
expmt = np.exp((np.arange(-10*a,dt,dt))/a)
x, ex = boundary_sim(xini, eIC, a, x_step, dt, tmax, expmt)
## Coarsen to speed up plotting
crsn = 5
if crsn>1:
x = x[::crsn]
ex = ex[::crsn]
## ----------------------------------------------------------------
## PLOT TRAJECTORY
## Number of steps per frame
nsteps = int(tmax/dt/crsn)
stride = 100/crsn ## Make a frame every stride timesteps
numf = nsteps/stride
## Loop over frames
for fnum in range(numf):
ti = time.time()
fig = plot_traj(x[:fnum*stride],ex[:fnum*stride],R,S,a,dt,x.shape[0],True)
## Save
plotfile = outdir+"/f%04d.png"%(fnum)
fig.savefig(plotfile)
plt.close()
if not fnum%10: print me+"Frame %04d/%04d saved. Time per file %.1f seconds."%(fnum,numf,time.time()-ti)
os.system("ffmpeg -r 10 -f image2 -s 1920x1080 -i f%04d.png -vcodec libx264 -crf 25 -pix_fmt yuv420p TRAJ_CAR_DL_a%.1f_R%.1f_S%.1f_t%.1f.mp4"%(a,R,S,t))
return
def calc_pressure_dir(histdir, srchstr, noread, vb):
"""
Calculate the pressure for all files in directory matching string.
The
"""
me = me0 + ".calc_pressure_dir: "
t0 = time.time()
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histdir, me + "Functional only for Cartesian geometry."
Casimir = "_DL_" not in histdir
## File discovery
filelist = np.sort(glob.glob(histdir + "/BHIS_CAR_*" + srchstr + "*.npy"))
numfiles = len(filelist)
assert numfiles > 1, me + "Check input directory."
if vb: print me + "found", numfiles, "files"
##-------------------------------------------------------------------------
A, R, S, T, PR, PS, PT, PU, PR_WN, PS_WN, PT_WN, PU_WN = np.zeros(
[12, numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
ti = time.time()
## Assuming R, S, T are same for all files
A[i] = filename_par(histfile, "_a")
R[i] = filename_par(histfile, "_R")
S[i] = filename_par(histfile, "_S")
try:
T[i] = filename_par(histfile, "_T")
except ValueError:
T[i] = -S[i]
## Space
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
x = 0.5 * (xbins[1:] + xbins[:-1])
## Wall indices
Rind, Sind, Tind = np.abs(x - R[i]).argmin(
), np.abs(x - S[i]).argmin() + 1, np.abs(x - T[i]).argmin()
STind = 0 if T[i] < 0.0 else (Sind + Tind) / 2
## Adjust indices for pressure calculation
if "_DC_" in histfile:
STind = 0
elif "_DL_" in histfile:
STind = 0
elif "_NL_" in histfile:
STind = Sind
Sind = Rind
Tind = x.size - Rind
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
## Spatial density
Qx = H.sum(axis=2).sum(axis=1) / (H.sum() * (x[1] - x[0]))
##-------------------------------------------------------------------------
## Choose force
if "_DC_" in histfile: fx = force_dcon([x, 0], R[i], S[i])[0]
elif "_DL_" in histfile: fx = force_dlin([x, 0], R[i], S[i])[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R[i], S[i], T[i])[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R[i], S[i], T[i])[0]
elif "_NL_" in histfile: fx = force_nlin([x, 0], R[i], S[i])[0]
else: raise IOError, me + "Force not recognised."
## Calculate integral pressure
PR[i] = -sp.integrate.trapz(fx[Rind:] * Qx[Rind:], x[Rind:])
PS[i] = +sp.integrate.trapz(fx[STind:Sind] * Qx[STind:Sind],
x[STind:Sind])
PT[i] = -sp.integrate.trapz(fx[Tind:STind] * Qx[Tind:STind],
x[Tind:STind])
if "_ML_" in histfile:
mRind = x.size - Rind ## Index of wall at x=-R
PU[i] = +sp.integrate.trapz(fx[:mRind] * Qx[:mRind], x[:mRind])
if vb:
print me + "a=%.1f:\tPressure calculation %.2g seconds" % (
A[i], time.time() - ti)
## Potential
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
## WN pressure
PR_WN[i] = -sp.integrate.trapz(fx[Rind:] * Qx_WN[Rind:], x[Rind:])
PS_WN[i] = +sp.integrate.trapz(fx[STind:Sind] * Qx_WN[STind:Sind],
x[STind:Sind])
if Casimir:
PT_WN[i] = -sp.integrate.trapz(fx[Tind:STind] * Qx_WN[Tind:STind],
x[Tind:STind])
if "_ML_" in histfile:
PU_WN[i] = +sp.integrate.trapz(fx[:mRind] * Qx_WN[:mRind],
x[:mRind])
##-------------------------------------------------------------------------
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
R, S, T = R[srtidx], S[srtidx], T[srtidx]
PR, PS, PT, PU = PR[srtidx], PS[srtidx], PT[srtidx], PU[srtidx]
PR_WN, PS_WN, PT_WN, PU_WN = PR_WN[srtidx], PS_WN[srtidx], PT_WN[
srtidx], PU_WN[srtidx]
## Normalise
PR /= PR_WN + (PR_WN == 0)
PS /= PS_WN + (PS_WN == 0)
if Casimir:
PT /= PT_WN + (PT_WN == 0)
if "_ML_" in histdir:
PU /= PU_WN + (PU_WN == 0)
##-------------------------------------------------------------------------
## SAVING
if not noread:
pressfile = histdir + "/PRESS_" + srchstr + ".npz"
np.savez(pressfile,
A=A,
R=R,
S=S,
T=T,
PR=PR,
PS=PS,
PT=PT,
PU=PU,
PR_WN=PR_WN,
PS_WN=PS_WN,
PT_WN=PT_WN,
PU_WN=PU_WN)
if vb:
print me + "Calculations saved to", pressfile
print me + "Calculation time %.1f seconds." % (time.time() - t0)
return {
"A": A,
"R": R,
"S": S,
"T": T,
"PR": PR,
"PS": PS,
"PT": PT,
"PU": PU,
"PR_WN": PR_WN,
"PS_WN": PS_WN,
"PT_WN": PT_WN,
"PU_WN": PU_WN
}
def calc_pressure_dir(histdir, srchstr, noread, vb):
"""
Calculate the pressure for all files in directory matching string.
The
"""
me = me0+".calc_pressure_dir: "
t0 = time.time()
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histdir, me+"Functional only for Cartesian geometry."
Casimir = "_DL_" not in histdir
## File discovery
filelist = np.sort(glob.glob(histdir+"/BHIS_CAR_*"+srchstr+"*.npy"))
numfiles = len(filelist)
assert numfiles>1, me+"Check input directory."
if vb: print me+"found",numfiles,"files"
##-------------------------------------------------------------------------
A, R, S, T, PR, PS, PT, PU, PR_WN, PS_WN, PT_WN, PU_WN = np.zeros([12,numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
ti = time.time()
## Assuming R, S, T are same for all files
A[i] = filename_par(histfile, "_a")
R[i] = filename_par(histfile, "_R")
S[i] = filename_par(histfile, "_S")
try:
T[i] = filename_par(histfile, "_T")
except ValueError:
T[i] = -S[i]
## Space
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
x = 0.5*(xbins[1:]+xbins[:-1])
## Wall indices
Rind, Sind, Tind = np.abs(x-R[i]).argmin(), np.abs(x-S[i]).argmin()+1, np.abs(x-T[i]).argmin()
STind = 0 if T[i]<0.0 else (Sind+Tind)/2
## Adjust indices for pressure calculation
if "_DC_" in histfile:
STind = 0
elif "_DL_" in histfile:
STind = 0
elif "_NL_" in histfile:
STind = Sind
Sind = Rind
Tind = x.size-Rind
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
## Spatial density
Qx = H.sum(axis=2).sum(axis=1) / (H.sum()*(x[1]-x[0]))
##-------------------------------------------------------------------------
## Choose force
if "_DC_" in histfile: fx = force_dcon([x,0],R[i],S[i])[0]
elif "_DL_" in histfile: fx = force_dlin([x,0],R[i],S[i])[0]
elif "_CL_" in histfile: fx = force_clin([x,0],R[i],S[i],T[i])[0]
elif "_ML_" in histfile: fx = force_mlin([x,0],R[i],S[i],T[i])[0]
elif "_NL_" in histfile: fx = force_nlin([x,0],R[i],S[i])[0]
else: raise IOError, me+"Force not recognised."
## Calculate integral pressure
PR[i] = -sp.integrate.trapz(fx[Rind:]*Qx[Rind:], x[Rind:])
PS[i] = +sp.integrate.trapz(fx[STind:Sind]*Qx[STind:Sind], x[STind:Sind])
PT[i] = -sp.integrate.trapz(fx[Tind:STind]*Qx[Tind:STind], x[Tind:STind])
if "_ML_" in histfile:
mRind = x.size-Rind ## Index of wall at x=-R
PU[i] = +sp.integrate.trapz(fx[:mRind]*Qx[:mRind], x[:mRind])
if vb: print me+"a=%.1f:\tPressure calculation %.2g seconds"%(A[i],time.time()-ti)
## Potential
U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
## WN pressure
PR_WN[i] = -sp.integrate.trapz(fx[Rind:]*Qx_WN[Rind:], x[Rind:])
PS_WN[i] = +sp.integrate.trapz(fx[STind:Sind]*Qx_WN[STind:Sind], x[STind:Sind])
if Casimir:
PT_WN[i] = -sp.integrate.trapz(fx[Tind:STind]*Qx_WN[Tind:STind], x[Tind:STind])
if "_ML_" in histfile:
PU_WN[i] = +sp.integrate.trapz(fx[:mRind]*Qx_WN[:mRind], x[:mRind])
##-------------------------------------------------------------------------
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
R, S, T = R[srtidx], S[srtidx], T[srtidx]
PR, PS, PT, PU = PR[srtidx], PS[srtidx], PT[srtidx], PU[srtidx]
PR_WN, PS_WN, PT_WN, PU_WN = PR_WN[srtidx], PS_WN[srtidx], PT_WN[srtidx], PU_WN[srtidx]
## Normalise
PR /= PR_WN + (PR_WN==0)
PS /= PS_WN + (PS_WN==0)
if Casimir:
PT /= PT_WN + (PT_WN==0)
if "_ML_" in histdir:
PU /= PU_WN + (PU_WN==0)
##-------------------------------------------------------------------------
## SAVING
if not noread:
pressfile = histdir+"/PRESS_"+srchstr+".npz"
np.savez(pressfile, A=A, R=R, S=S, T=T, PR=PR, PS=PS, PT=PT, PU=PU,
PR_WN=PR_WN, PS_WN=PS_WN, PT_WN=PT_WN, PU_WN=PU_WN)
if vb:
print me+"Calculations saved to",pressfile
print me+"Calculation time %.1f seconds."%(time.time()-t0)
return {"A":A,"R":R,"S":S,"T":T,"PR":PR,"PS":PS,"PT":PT,"PU":PU,
"PR_WN":PR_WN,"PS_WN":PS_WN,"PT_WN":PT_WN,"PU_WN":PU_WN}
def plot_pdf1d(histfile, nosave, vb):
"""
Calculate Q(r) and q(eta) from file and plot.
"""
me = me0+".plot_pdf1d: "
t0 = time.time()
##-------------------------------------------------------------------------
## Filename pars
assert "_CAR_" in histfile, me+"Functional only for Cartesian geometry."
Casimir = "_CL_" in histfile or "_ML_" in histfile or "_NL_" in histfile
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
try: T = filename_par(histfile, "_T")
except ValueError: T= -S
doQfit = (R==S and "_DL_" in histfile)
plotq = int(False)
##-------------------------------------------------------------------------
## Space
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
exbins = bins["exbins"]
eybins = bins["eybins"]
x = 0.5*(xbins[1:]+xbins[:-1])
etax = 0.5*(exbins[1:]+exbins[:-1])
etay = 0.5*(eybins[1:]+eybins[:-1])
## Wall indices
Rind, Sind = np.abs(x-R).argmin(), np.abs(x-S).argmin()
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
rho = H / (H.sum() * (x[1]-x[0])*(etax[1]-etax[0])*(etay[1]-etay[0]))
## Spatial density
Qx = rho.sum(axis=2).sum(axis=1) * (etax[1]-etax[0])*(etay[1]-etay[0])
## Force density
qx = rho.sum(axis=2).sum(axis=0) * (x[1]-x[0])*(etay[1]-etay[0])
qy = rho.sum(axis=1).sum(axis=0) * (x[1]-x[0])*(etax[1]-etax[0])
##-------------------------------------------------------------------------
## Fit
gauss = lambda x, m, s2: 1/np.sqrt(2*np.pi*s2)*np.exp(-0.5*(x-m)**2/s2)
if doQfit: fitQx = sp.optimize.curve_fit(gauss, x, Qx, p0=[R,1/np.sqrt(1+a)])[0]
##-------------------------------------------------------------------------
## PLOTTING
fig, axs = plt.subplots(1+plotq,1, figsize=fs["figsize"])
fig.canvas.set_window_title("1D PDFs")
## Set number of ticks
for ax in np.ravel([axs]):
ax.xaxis.set_major_locator(MaxNLocator(5))
ax.yaxis.set_major_locator(MaxNLocator(4))
##-------------------------------------------------------------------------
## Spatial density plot
ax = axs[0] if plotq else axs
## Data
ax.plot(x, Qx, label=r"OUP")
ax.fill_between(x, 0.0, Qx, color="b", alpha=0.1)
## Gaussian for spatial density
if doQfit:
ax.plot(x, gauss(x,fitQx[0],1/(1+a)), "c-", label=r"$G\left(\mu, \frac{1}{\alpha+1}\right)$")
## Potential and WN
if "_DC_" in histfile: fx = force_dcon([x,0],R,S)[0]
elif "_DL_" in histfile: fx = force_dlin([x,0],R,S)[0]
elif "_CL_" in histfile: fx = force_clin([x,0],R,S,T)[0]
elif "_ML_" in histfile: fx = force_mlin([x,0],R,S,T)[0]
elif "_NL_" in histfile: fx = force_nlin([x,0],R,S)[0]
else: raise IOError, me+"Force not recognised."
U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min()
## Plot passive density
Qx_WN = np.exp(-U)/np.trapz(np.exp(-U),x)
ax.plot(x, Qx_WN, "r-", label="Passive")
ax.fill_between(x, 0.0, Qx_WN, color="r", alpha=0.1)
## Plot potential
ax.plot(x, U/U.max()*ax.get_ylim()[1], "k--",label=r"$U(x)$")
## Indicate bulk
ax.axvline(S,c="k",lw=1)
ax.axvline(R,c="k",lw=1)
if T>=0.0:
ax.axvspan(S,R,color="y",alpha=0.1)
ax.axvline(T,c="k",lw=1)
ax.axvspan(-R,T,color="y",alpha=0.1)
ax.axvline(-R,c="k",lw=1)
elif T<0.0:
ax.axvline(-R,c="k",lw=1)
ax.set_xlim(left=x[0],right=x[-1])
ax.set_xlabel(r"$x$", fontsize=fs["fsa"])
ax.set_ylabel(r"$n(x)$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="upper right", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
if plotq:
## Force density plot
ax = axs[1]
## Data
ax.plot(etax, qx, label=r"Simulation $x$")
ax.plot(etay, qy, label=r"Simulation $y$")
## Gaussian
ax.plot(etax, gauss(etax,0.0,1/a), "c-", label=r"$G\left(0, \frac{1}{\alpha}\right)$")
ax.set_xlabel(r"$\eta$", fontsize=fs["fsa"])
ax.set_ylabel(r"$q(\eta)$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="upper right", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
fig.tight_layout()
fig.subplots_adjust(top=0.95)
title = r"PDFs in $r$ and $\eta$. $\alpha=%.1f, R=%.1f, S=%.1f$"%(a,R,S) if T<0.0\
else r"PDFs in $r$ and $\eta$. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.1f$"%(a,R,S,T)
else:
title = r"Spatial PDF. $\alpha=%.1f, R=%.1g, S=%.1g$"%(a,R,S) if T<0.0\
else r"Spatial PDF. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.f$"%(a,R,S,T)
# fig.suptitle(title, fontsize=fs["fst"])
if not nosave:
plotfile = os.path.dirname(histfile)+"/PDFxy1d"+os.path.basename(histfile)[4:-4]
plotfile += "."+fs["saveext"]
fig.savefig(plotfile, format=fs["saveext"])
if vb: print me+"Figure saved to",plotfile
if vb: print me+"Execution time %.1f seconds."%(time.time()-t0)
return
def plot_file(histfile, nosave, vb):
"""
"""
me = me0 + ".plot_file: "
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histfile, me + "Functional only for Cartesian geometry."
Casimir = "_CL_" in histfile or "_ML_" in histfile
## Get pars from filename
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
T = filename_par(histfile, "_T") if Casimir else -S
## Calculate quantities
x, Q, BC = bulk_const(histfile)[:3]
ex2 = BC / (Q + (Q == 0.0))
##-------------------------------------------------------------------------
## Potential
if "_DL_" in histfile: fx = force_dlin([x, 0], R, S)[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R, S, T)[0]
elif "_NL_" in histfile: fx = force_nlin([x, 0], R, S)[0]
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
##-------------------------------------------------------------------------
## Smooth
sp.ndimage.gaussian_filter1d(Q, 1.0, order=0, output=Q)
sp.ndimage.gaussian_filter1d(BC, 1.0, order=0, output=BC)
sp.ndimage.gaussian_filter1d(ex2, 1.0, order=0, output=ex2)
##-------------------------------------------------------------------------
## PLOT
fig, ax = plt.subplots(1, 1, figsize=fs["figsize"])
## Data
ax.plot(x, Q / Q.max(), label=r"$n(x)$", lw=2)
ax.plot(x, ex2 / ex2.max(), label=r"$\langle\eta_x^2\rangle(x)$", lw=2)
ax.plot(x, BC / BC.max(), label=r"$\langle\eta_x^2\rangle \cdot n$", lw=2)
ax.plot(x, U / U.max() * ax.get_ylim()[1], "k--", label=r"$U(x)$")
## Indicate bulk region
if "_DL_" in histfile:
ax.axvspan(S, R, color="yellow", alpha=0.2)
ax.axvline(S, c="k", lw=2)
ax.axvline(R, c="k", lw=2)
elif "_ML_" in histfile:
ax.axvspan(S, R, color="yellow", alpha=0.2)
ax.axvspan(-R, T, color="yellow", alpha=0.2)
ax.axvline(S, c="k", lw=2)
ax.axvline(R, c="k", lw=2)
ax.axvline(T, c="k", lw=2)
ax.axvline(-R, c="k", lw=2)
elif "_CL_" in histfile:
ax.axvspan(S, R, color="yellow", alpha=0.2)
ax.axvspan(0, T, color="yellow", alpha=0.2)
ax.axvline(S, c="k", lw=2)
ax.axvline(R, c="k", lw=2)
ax.axvline(T, c="k", lw=2)
ax.axvline(-R, c="k", lw=2)
##-------------------------------------------------------------------------
## ATTRIBUTES
ax.set_xlim(left=x[0], right=x[-1])
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
ax.set_xlabel("$x$", fontsize=fs["fsa"])
ax.set_ylabel("Rescaled variable", fontsize=fs["fsa"])
ax.grid()
legloc = [0.35, 0.25] if "_ML_" in histfile else [0.32, 0.67]
ax.legend(loc=legloc, fontsize=fs["fsl"]).get_frame().set_alpha(0.8)
title = r"Bulk Constant. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.1f$."%(a,R,S,T) if T>=0.0\
else r"Bulk Constant. $\alpha=%.1f, R=%.1f, S=%.1f$."%(a,R,S)
# fig.suptitle(title,fontsize=fs["fst"])
## SAVE
# ax.set_ylim(top=BC.max())
plotfile = os.path.dirname(histfile) + "/QEe2" + os.path.basename(
histfile)[4:-4] + "." + fs["saveext"]
if not nosave:
fig.savefig(plotfile)
if vb: print me + "Figure saved to", plotfile
##-------------------------------------------------------------------------
return plotfile
def plot_dir(histdir, srchstr, logplot, nosave, vb):
"""
For each file in directory, calculate the pressure in both ways for all walls
(where applicable) and plot against alpha.
"""
me = me0 + ".plot_dir: "
filelist = np.sort(glob.glob(histdir + "/BHIS_CAR_*" + srchstr + "*.npy"))
numfiles = filelist.size
if vb: print me + "Found", numfiles, "files."
## Initialise arrays
A, pR, pS, pT, PR, PS, PT = np.zeros([7, numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
Casimir = "_CL_" in histfile or "_ML_" in histfile or "_NL_" in histfile
## Get pars from filename
A[i] = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
T = filename_par(histfile, "_T") if Casimir else -S
## Calculate BC
x, Qx, BC = bulk_const(histfile)[:3]
## Wall indices
Rind, Sind, Tind = np.abs(x - R).argmin(), np.abs(
x - S).argmin(), np.abs(x - T).argmin()
STind = 0 if "_DL_" in histfile else (Tind + Sind) / 2
##---------------------------------------------------------------------
## Calculate pressure from BC
if "_DL_" in histfile:
BCsr = BC[Sind:Rind + 1].mean()
pR[i] = A[i] * BCsr
pS[i] = A[i] * BCsr
elif "_CL_" in histfile:
BCsr = BC[Sind:Rind + 1].mean()
BCts = BC[STind]
BC0t = BC[0:Tind + 1].mean()
pR[i] = A[i] * BCsr
pS[i] = A[i] * (BCsr - BCts)
pT[i] = A[i] * (BC0t - BCts)
elif "_ML_" in histfile:
BCsr = BC[Sind:Rind + 1].mean()
BCts = BC[STind]
BCrt = BC[x.size - Rind:Tind + 1].mean()
pR[i] = A[i] * BCsr
pS[i] = A[i] * (-BCsr + BCts)
pT[i] = A[i] * (-BCrt + BCts)
elif "_NL_" in histfile:
BCr = BC[Rind]
BCs = BC[Sind]
BCmr = BC[x.size - Rind]
pR[i] = A[i] * BCr
pS[i] = A[i] * (BCs - BCr)
pT[i] = A[i] * (BCs - BCmr)
##---------------------------------------------------------------------
## Calculate pressure from integral
## Choose force
if "_DL_" in histfile: fx = force_dlin([x, 0], R, S)[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R, S, T)[0]
elif "_NL_" in histfile: fx = force_nlin([x, 0], R, S)[0]
## Calculate integral pressure
PR[i] = -sp.integrate.trapz(fx[Rind:] * Qx[Rind:], x[Rind:])
PS[i] = +sp.integrate.trapz(fx[STind:Sind] * Qx[STind:Sind],
x[STind:Sind])
PT[i] = -sp.integrate.trapz(fx[Tind:STind] * Qx[Tind:STind],
x[Tind:STind])
##---------------------------------------------------------------------
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
pR, pS, pT = pR[srtidx], pS[srtidx], pT[srtidx]
PR, PS, PT = PR[srtidx], PS[srtidx], PT[srtidx]
##-------------------------------------------------------------------------
## Calculate white noise PDF and pressure -- assuming alpha is only varying parameter
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
PR_WN = -sp.integrate.trapz(fx[Rind:] * Qx_WN[Rind:], x[Rind:])
PS_WN = +sp.integrate.trapz(fx[STind:Sind] * Qx_WN[STind:Sind],
x[STind:Sind])
PT_WN = -sp.integrate.trapz(fx[Tind:STind] * Qx_WN[Tind:STind],
x[Tind:STind])
## Normalise
pR /= PR_WN
pS /= PS_WN
pT /= PT_WN
PR /= PR_WN
PS /= PS_WN
PT /= PT_WN
##-------------------------------------------------------------------------
## Add a=0 point
if 0.0 not in A:
nlin = np.unique(S).size
A = np.hstack([[0.0] * nlin, A])
pR = np.hstack([[1.0] * nlin, pR])
pS = np.hstack([[1.0] * nlin, pS])
PR = np.hstack([[1.0] * nlin, PR])
PS = np.hstack([[1.0] * nlin, PS])
##-------------------------------------------------------------------------
## PLOT DATA
fig, ax = plt.subplots(1, 1, figsize=fs["figsize"])
sty = ["-", "--", ":"]
A += int(logplot)
"""
lpR = ax.plot(A, pR, "o"+sty[0], label=r"BC pR")
lpS = ax.plot(A, pS, "o"+sty[1], c=ax.lines[-1].get_color(), label=r"BC pS")
if Casimir:
lpT = ax.plot(A, pT, "o"+sty[2], c=ax.lines[-1].get_color(), label=r"BC pT")
ax.plot(A, PR, "v"+sty[0], label=r"Int PR")
ax.plot(A, PS, "v"+sty[1], c=ax.lines[-1].get_color(), label=r"Int PS")
if Casimir:
ax.plot(A, PT, "v"+sty[2], c=ax.lines[-1].get_color(), label=r"Int PT")
"""
lpR = ax.plot(A,
0.5 * (pR + pS),
"o--",
label=r"$\alpha\left<\eta^2\right>n(x)|^{\rm bulk}$")
ax.plot(A, 0.5 * (PR + PS), "v--", label=r"$-\int f(x)n(x) {\rm d}x$")
##-------------------------------------------------------------------------
## ACCOUTREMENTS
if logplot:
ax.set_xscale("log")
ax.set_yscale("log")
xlim = (ax.get_xlim()[0], A[-1])
xlabel = r"$1+\alpha$"
else:
xlim = (0.0, A[-1])
xlabel = r"$\alpha$"
ax.set_xlim(xlim)
ax.set_ylim(1e-1, 1e+1)
ax.set_xlabel(xlabel, fontsize=fs["fsa"])
ax.set_ylabel(r"$P(\alpha)/P^{\rm passive}$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="best", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
title = "Pressure normalised by WN result. $R=%.1f, S=%.1f, T=%.1f.$"%(R,S,T) if T>=0.0\
else "Pressure normalised by WN result. $R=%.1f, S=%.1f.$"%(R,S)
# fig.suptitle(title,fontsize=fs["fst"])
## SAVING
plotfile = histdir+"/QEe2_Pa_R%.1f_S%.1f_T%.1f"%(R,S,T) if T>=0.0\
else histdir+"/QEe2_Pa_R%.1f_S%.1f"%(R,S)
plotfile += "_loglog" * logplot + "." + fs["saveext"]
if not nosave:
fig.savefig(plotfile)
if vb: print me + "Figure saved to", plotfile
return plotfile
def plot_current_1d(histfile, nosave, vb):
"""
"""
me = me0+".plot_current_1d: "
t0 = time.time()
##-------------------------------------------------------------------------
## Filename pars
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
T = filename_par(histfile, "_T")
##-------------------------------------------------------------------------
## Space
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
exbins = bins["exbins"]
x = 0.5*(xbins[1:]+xbins[:-1])
## Double space
x = np.hstack([-x[::-1],x])
etax = 0.5*(exbins[1:]+exbins[:-1])
X, ETAX = np.meshgrid(x,etax, indexing="ij")
## Wall indices
Rind, Sind = np.abs(x-R).argmin(), np.abs(x-S).argmin()
##-------------------------------------------------------------------------
## Force
if "_DL_" in histfile: fx = force_dlin([x,0],R,S)[0]
elif "_CL_" in histfile: fx = force_clin([x,0],R,S,T)[0]
elif "_ML_" in histfile: fx = force_mlin([x,0],R,S,T)[0]
else: raise IOError, me+"Force not recognised."
F = fx.repeat(etax.size).reshape([x.size,etax.size])
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
rho = H.sum(axis=2) / (H.sum() * (x[1]-x[0])*(etax[1]-etax[0]))
## Double space
rho = np.vstack([rho[::-1,::-1],rho])
## Currents
Jx = (F + ETAX)*rho
Jy = -1/a*ETAX*rho - 1/(a*a)*np.gradient(rho,etax[1]-etax[0])[1]
Vx, Vy = Jx/rho, Jy/rho
##-------------------------------------------------------------------------
## SMOOTHING
Vy = sp.ndimage.gaussian_filter(Vy, 2.0, order=0)
##-------------------------------------------------------------------------
## PLOTTING
plt.rcParams["image.cmap"] = "Greys"
fig, ax = plt.subplots(1,1, figsize=fs["figsize"])
fig.canvas.set_window_title("Current in x-eta")
##-------------------------------------------------------------------------
## Data
ax.contourf(x, etax, rho.T)
sx, se = 50, 5
# sx, se = 20, 2
ax.quiver(x[::sx], etax[::se], Vx.T[::se,::sx], Vy.T[::se,::sx] , scale=2, units='x', width=0.011*2)
## Indicate bulk
if 0:
ax.axvline(S,c="k",lw=1)
ax.axvline(R,c="k",lw=1)
## Set number of ticks
# ax.xaxis.set_major_locator(NullLocator()) #MaxNLocator(5)
# ax.yaxis.set_major_locator(NullLocator()) #MaxNLocator(4)
ax.set_xticks([-S,-0.5*(S+T),T,+0.5*(S+T),+S])
ax.set_xticklabels([""]*5)
ax.set_yticks([-0.5*(S+T),0.0,+0.5*(S+T)])
ax.set_yticklabels([""]*3)
# ax.set_xlim(left=x[0],right=x[-1])
ax.set_xlim(left=-S*2,right=S*2)
ax.set_xlabel(r"$x$", fontsize=fs["fsa"])
ax.set_ylabel(r"$\eta$", fontsize=fs["fsa"])
ax.grid()
# ax.legend(loc="upper right", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
## Add force line
if 1:
ax.plot(x, -fx, "k-", label=r"$-f(x)$")
ymax = min(3*fx.max(),etax.max())
ax.set_ylim(-ymax,ymax)
##-------------------------------------------------------------------------
## Add in BC line
if 1:
from LE_CBulkConst import bulk_const
x, Q, BC = bulk_const(histfile)
## Double space
x = np.hstack([-x[::-1],x])
Q = np.hstack([Q[::-1],Q])
BC = np.hstack([BC[::-1],BC])
ax.plot(x, (Q/Q.max())*0.5*ax.get_ylim()[1]+ax.get_ylim()[0], "b-", lw=4)
ax.plot(x, (BC/BC.max())*0.5*ax.get_ylim()[1]+ax.get_ylim()[0], "r-", lw=4)
ax2 = ax.twinx()
ax2.yaxis.set_major_locator(NullLocator())
ax2.set_ylabel(r"$n$ \& $\left<\eta^2\right>n$ \hfill")
ax2.yaxis.set_label_coords(-0.07,0.15)
# ax.yaxis.set_label_coords(-0.07,0.5)
##-------------------------------------------------------------------------
if not nosave:
plotfile = os.path.dirname(histfile)+"/Jxeta"+os.path.basename(histfile)[4:-4]
plotfile += "."+fs["saveext"]
fig.savefig(plotfile, format=fs["saveext"])
if vb: print me+"Figure saved to",plotfile
if vb: print me+"Execution time %.1f seconds."%(time.time()-t0)
return
HC = np.load(histfileC)
bC = np.load(
os.path.dirname(histfileC) + "/BHISBIN" +
os.path.basename(histfileC)[4:-4] + ".npz")
r = 0.5 * (bP["rbins"][1:] + bP["rbins"][:-1])
x = 0.5 * (bC["xbins"][1:] + bC["xbins"][:-1])
## Spatial density
QP = HP.sum(axis=2).sum(axis=1) / (2 * np.pi * r)
QP /= np.trapz(2 * np.pi * r * QP, r)
QC = HC.sum(axis=2).sum(axis=1)
QC /= np.trapz(QC, x)
## Potential
if "_DL_" in histfileP: fx = force_dlin([x, 0], R, S)[0]
elif "_CL_" in histfileP: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfileP: fx = force_mlin([x, 0], R, S, T)[0]
elif "_NL_" in histfileP: fx = force_nlin([x, 0], R, S)[0]
else: raise IOError, me + "Force not recognised."
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
## ------------------------------------------------------------------------
## 1D
if 1:
fig, axs = plt.subplots(1, 1, figsize=(10, 10))
ax = axs
ax.plot(r, QP / QP.max(), label=r"$n_{\rm rad}(r)$")
def main():
"""
"""
me = me0 + ".main: "
a = 1.0
timefac = 1.0
dt = 0.01
R = 2.0
S = 0.0
vb = True
fx = lambda x: force_dlin([x, 0], R, S)[0]
outdir = "./Pressure/TRAJ_CAR_DL_a%.1f_R%.1f_S%.1f_t%.1f" % (a, R, S,
timefac)
if not os.path.isdir(outdir):
os.mkdir(outdir)
print me + "Created directory", outdir
## ----------------------------------------------------------------
## SET UP CALCULATIONS
## Simulation time
tmax = 5e2 * timefac
## Simulation limits
xmax = R + 3.0
xmin = S - 3.0
## Injection x coordinate
xini = 0.5 * (S + R)
## Initial noise drawn from Gaussian
if a == 0.0: eIC = np.sqrt(2 / dt) * np.random.normal(0.0, 1.0)
else: eIC = dt / np.sqrt(a) * np.random.normal(0.0, 1.0)
## Integration algorithm
x_step = lambda x, ex: eul(x, ex, fx, dt)
## ----------------------------------------------------------------
## SIMULATION
## Precompute exp(-t)
expmt = np.exp((np.arange(-10 * a, dt, dt)) / a)
x, ex = boundary_sim(xini, eIC, a, x_step, dt, tmax, expmt)
## Coarsen to speed up plotting
crsn = 5
if crsn > 1:
x = x[::crsn]
ex = ex[::crsn]
## ----------------------------------------------------------------
## PLOT TRAJECTORY
## Number of steps per frame
nsteps = int(tmax / dt / crsn)
stride = 100 / crsn ## Make a frame every stride timesteps
numf = nsteps / stride
## Loop over frames
for fnum in range(numf):
ti = time.time()
fig = plot_traj(x[:fnum * stride], ex[:fnum * stride], R, S, a, dt,
x.shape[0], True)
## Save
plotfile = outdir + "/f%04d.png" % (fnum)
fig.savefig(plotfile)
plt.close()
if not fnum % 10:
print me + "Frame %04d/%04d saved. Time per file %.1f seconds." % (
fnum, numf, time.time() - ti)
os.system(
"ffmpeg -r 10 -f image2 -s 1920x1080 -i f%04d.png -vcodec libx264 -crf 25 -pix_fmt yuv420p TRAJ_CAR_DL_a%.1f_R%.1f_S%.1f_t%.1f.mp4"
% (a, R, S, t))
return
def calc_mass_ratio(histdir, srchstr, noread, vb):
"""
Read in directory of files with inner and outer regions.
Compute mass in each region, take ratio.
Compare with integrated and calculated white noise result.
"""
me = me0+".calc_mass_ratio: "
t0 = time.time()
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histdir, me+"Functional only for Cartesian geometry."
assert "_DL_" not in histdir, me+"Must have interior region."
## File discovery
filelist = np.sort(glob.glob(histdir+"/BHIS_CAR_*"+srchstr+"*.npy"))
numfiles = len(filelist)
assert numfiles>1, me+"Check input directory."
if vb: print me+"found",numfiles,"files"
##-------------------------------------------------------------------------
A, ML, MR = np.zeros([3,numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
## Assume R, S, T are same for all files
A[i] = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
try:
T = filename_par(histfile, "_T")
except ValueError:
T = -S
## Space
bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz")
xbins = bins["xbins"]
x = 0.5*(xbins[1:]+xbins[:-1])
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
## Spatial density
Qx = H.sum(axis=2).sum(axis=1) / (H.sum()*(x[1]-x[0]))
## Mass on either side of cusp: data. Left, right.
if "_CL_" in histfile: cuspind = np.abs(0.5*(T+S)-x).argmin() ## Half-domain
elif "_ML_" in histfile: cuspind = np.abs(0.5*(T+S)-x).argmin()
elif "_NL_" in histfile: cuspind = np.abs(S-x).argmin()
ML[i] = np.trapz(Qx[:cuspind],x[:cuspind])
MR[i] = np.trapz(Qx[cuspind:],x[cuspind:])
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
ML = ML[srtidx]; MR = MR[srtidx]
##-------------------------------------------------------------------------
## WN result from density solution
if "_DL_" in histfile: fx = force_dlin([x,0],R,S)[0]
elif "_CL_" in histfile: fx = force_clin([x,0],R,S,T)[0]
elif "_ML_" in histfile: fx = force_mlin([x,0],R,S,T)[0]
elif "_NL_" in histfile: fx = force_nlin([x,0],R,S)[0]
else: raise IOError, me+"Force not recognised."
U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
MLwn = np.trapz(Qx_WN[:cuspind],x[:cuspind])
MRwn = np.trapz(Qx_WN[cuspind:],x[cuspind:])
##-------------------------------------------------------------------------
## Add a=0 point
if 0.0 not in A:
A = np.hstack([0.0,A])
ML = np.hstack([MLwn,ML])
MR = np.hstack([MRwn,MR])
##-------------------------------------------------------------------------
### This might not be the cleanest thing to save...
## SAVING
if not noread:
massfile = histdir+"/MASS_"+srchstr+".npz"
np.savez(massfile, A=A, ML=ML, MR=MR, MLwn=MLwn, MRwn=MRwn, x=x, Qx_WN=Qx_WN, R=R, S=S, T=T, cuspind=cuspind)
if vb:
print me+"Calculations saved to",massfile
print me+"Calculation time %.1f seconds."%(time.time()-t0)
return {"A":A, "ML":ML, "MR":MR, "MLwn":MLwn, "MRwn":MRwn, "x":x, "Qx_WN":Qx_WN, "R":R, "S":S, "T":T, "cuspind":cuspind}
def plot_dir(histdir, srchstr, logplot, nosave, vb):
"""
For each file in directory, calculate the pressure in both ways for all walls
(where applicable) and plot against alpha.
"""
me = me0+".plot_dir: "
filelist = np.sort(glob.glob(histdir+"/BHIS_CAR_*"+srchstr+"*.npy"))
numfiles = filelist.size
if vb: print me+"Found",numfiles,"files."
## Initialise arrays
A, pR, pS, pT, PR, PS, PT = np.zeros([7,numfiles])
## Retrieve data
for i, histfile in enumerate(filelist):
Casimir = "_CL_" in histfile or "_ML_" in histfile or "_NL_" in histfile
## Get pars from filename
A[i] = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
T = filename_par(histfile, "_T") if Casimir else -S
## Calculate BC
x, Qx, BC = bulk_const(histfile)[:3]
## Wall indices
Rind, Sind, Tind = np.abs(x-R).argmin(), np.abs(x-S).argmin(), np.abs(x-T).argmin()
STind = 0 if "_DL_" in histfile else (Tind+Sind)/2
##---------------------------------------------------------------------
## Calculate pressure from BC
if "_DL_" in histfile:
BCsr = BC[Sind:Rind+1].mean()
pR[i] = A[i] * BCsr
pS[i] = A[i] * BCsr
elif "_CL_" in histfile:
BCsr = BC[Sind:Rind+1].mean()
BCts = BC[STind]
BC0t = BC[0:Tind+1].mean()
pR[i] = A[i] * BCsr
pS[i] = A[i] * (BCsr - BCts)
pT[i] = A[i] * (BC0t - BCts)
elif "_ML_" in histfile:
BCsr = BC[Sind:Rind+1].mean()
BCts = BC[STind]
BCrt = BC[x.size-Rind:Tind+1].mean()
pR[i] = A[i] * BCsr
pS[i] = A[i] * (-BCsr + BCts)
pT[i] = A[i] * (-BCrt + BCts)
elif "_NL_" in histfile:
BCr = BC[Rind]
BCs = BC[Sind]
BCmr = BC[x.size-Rind]
pR[i] = A[i] * BCr
pS[i] = A[i] * (BCs - BCr)
pT[i] = A[i] * (BCs - BCmr)
##---------------------------------------------------------------------
## Calculate pressure from integral
## Choose force
if "_DL_" in histfile: fx = force_dlin([x,0],R,S)[0]
elif "_CL_" in histfile: fx = force_clin([x,0],R,S,T)[0]
elif "_ML_" in histfile: fx = force_mlin([x,0],R,S,T)[0]
elif "_NL_" in histfile: fx = force_nlin([x,0],R,S)[0]
## Calculate integral pressure
PR[i] = -sp.integrate.trapz(fx[Rind:]*Qx[Rind:], x[Rind:])
PS[i] = +sp.integrate.trapz(fx[STind:Sind]*Qx[STind:Sind], x[STind:Sind])
PT[i] = -sp.integrate.trapz(fx[Tind:STind]*Qx[Tind:STind], x[Tind:STind])
##---------------------------------------------------------------------
## SORT BY ALPHA
srtidx = A.argsort()
A = A[srtidx]
pR, pS, pT = pR[srtidx], pS[srtidx], pT[srtidx]
PR, PS, PT = PR[srtidx], PS[srtidx], PT[srtidx]
##-------------------------------------------------------------------------
## Calculate white noise PDF and pressure -- assuming alpha is only varying parameter
U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U),x)
PR_WN = -sp.integrate.trapz(fx[Rind:]*Qx_WN[Rind:], x[Rind:])
PS_WN = +sp.integrate.trapz(fx[STind:Sind]*Qx_WN[STind:Sind], x[STind:Sind])
PT_WN = -sp.integrate.trapz(fx[Tind:STind]*Qx_WN[Tind:STind], x[Tind:STind])
## Normalise
pR /= PR_WN; pS /= PS_WN; pT /= PT_WN
PR /= PR_WN; PS /= PS_WN; PT /= PT_WN
##-------------------------------------------------------------------------
## Add a=0 point
if 0.0 not in A:
nlin = np.unique(S).size
A = np.hstack([[0.0]*nlin,A])
pR = np.hstack([[1.0]*nlin,pR])
pS = np.hstack([[1.0]*nlin,pS])
PR = np.hstack([[1.0]*nlin,PR])
PS = np.hstack([[1.0]*nlin,PS])
##-------------------------------------------------------------------------
## PLOT DATA
fig, ax = plt.subplots(1,1, figsize=fs["figsize"])
sty = ["-","--",":"]
A += int(logplot)
"""
lpR = ax.plot(A, pR, "o"+sty[0], label=r"BC pR")
lpS = ax.plot(A, pS, "o"+sty[1], c=ax.lines[-1].get_color(), label=r"BC pS")
if Casimir:
lpT = ax.plot(A, pT, "o"+sty[2], c=ax.lines[-1].get_color(), label=r"BC pT")
ax.plot(A, PR, "v"+sty[0], label=r"Int PR")
ax.plot(A, PS, "v"+sty[1], c=ax.lines[-1].get_color(), label=r"Int PS")
if Casimir:
ax.plot(A, PT, "v"+sty[2], c=ax.lines[-1].get_color(), label=r"Int PT")
"""
lpR = ax.plot(A, 0.5*(pR+pS), "o--", label=r"$\alpha\left<\eta^2\right>n(x)|^{\rm bulk}$")
ax.plot(A, 0.5*(PR+PS), "v--", label=r"$-\int f(x)n(x) {\rm d}x$")
##-------------------------------------------------------------------------
## ACCOUTREMENTS
if logplot:
ax.set_xscale("log"); ax.set_yscale("log")
xlim = (ax.get_xlim()[0],A[-1])
xlabel = r"$1+\alpha$"
else:
xlim = (0.0,A[-1])
xlabel = r"$\alpha$"
ax.set_xlim(xlim)
ax.set_ylim(1e-1,1e+1)
ax.set_xlabel(xlabel,fontsize=fs["fsa"])
ax.set_ylabel(r"$P(\alpha)/P^{\rm passive}$",fontsize=fs["fsa"])
ax.grid()
ax.legend(loc="best", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
title = "Pressure normalised by WN result. $R=%.1f, S=%.1f, T=%.1f.$"%(R,S,T) if T>=0.0\
else "Pressure normalised by WN result. $R=%.1f, S=%.1f.$"%(R,S)
# fig.suptitle(title,fontsize=fs["fst"])
## SAVING
plotfile = histdir+"/QEe2_Pa_R%.1f_S%.1f_T%.1f"%(R,S,T) if T>=0.0\
else histdir+"/QEe2_Pa_R%.1f_S%.1f"%(R,S)
plotfile += "_loglog"*logplot+"."+fs["saveext"]
if not nosave:
fig.savefig(plotfile)
if vb: print me+"Figure saved to",plotfile
return plotfile
def plot_current_1d(histfile, nosave, vb):
"""
"""
me = me0 + ".plot_current_1d: "
t0 = time.time()
##-------------------------------------------------------------------------
## Filename pars
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
T = filename_par(histfile, "_T")
##-------------------------------------------------------------------------
## Space
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
exbins = bins["exbins"]
x = 0.5 * (xbins[1:] + xbins[:-1])
## Double space
x = np.hstack([-x[::-1], x])
etax = 0.5 * (exbins[1:] + exbins[:-1])
X, ETAX = np.meshgrid(x, etax, indexing="ij")
## Wall indices
Rind, Sind = np.abs(x - R).argmin(), np.abs(x - S).argmin()
##-------------------------------------------------------------------------
## Force
if "_DL_" in histfile: fx = force_dlin([x, 0], R, S)[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R, S, T)[0]
else: raise IOError, me + "Force not recognised."
F = fx.repeat(etax.size).reshape([x.size, etax.size])
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
rho = H.sum(axis=2) / (H.sum() * (x[1] - x[0]) * (etax[1] - etax[0]))
## Double space
rho = np.vstack([rho[::-1, ::-1], rho])
## Currents
Jx = (F + ETAX) * rho
Jy = -1 / a * ETAX * rho - 1 / (a * a) * np.gradient(
rho, etax[1] - etax[0])[1]
Vx, Vy = Jx / rho, Jy / rho
##-------------------------------------------------------------------------
## SMOOTHING
Vy = sp.ndimage.gaussian_filter(Vy, 2.0, order=0)
##-------------------------------------------------------------------------
## PLOTTING
plt.rcParams["image.cmap"] = "Greys"
fig, ax = plt.subplots(1, 1, figsize=fs["figsize"])
fig.canvas.set_window_title("Current in x-eta")
##-------------------------------------------------------------------------
## Data
ax.contourf(x, etax, rho.T)
sx, se = 50, 5
# sx, se = 20, 2
ax.quiver(x[::sx],
etax[::se],
Vx.T[::se, ::sx],
Vy.T[::se, ::sx],
scale=2,
units='x',
width=0.011 * 2)
## Indicate bulk
if 0:
ax.axvline(S, c="k", lw=1)
ax.axvline(R, c="k", lw=1)
## Set number of ticks
# ax.xaxis.set_major_locator(NullLocator()) #MaxNLocator(5)
# ax.yaxis.set_major_locator(NullLocator()) #MaxNLocator(4)
ax.set_xticks([-S, -0.5 * (S + T), T, +0.5 * (S + T), +S])
ax.set_xticklabels([""] * 5)
ax.set_yticks([-0.5 * (S + T), 0.0, +0.5 * (S + T)])
ax.set_yticklabels([""] * 3)
# ax.set_xlim(left=x[0],right=x[-1])
ax.set_xlim(left=-S * 2, right=S * 2)
ax.set_xlabel(r"$x$", fontsize=fs["fsa"])
ax.set_ylabel(r"$\eta$", fontsize=fs["fsa"])
ax.grid()
# ax.legend(loc="upper right", fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
## Add force line
if 1:
ax.plot(x, -fx, "k-", label=r"$-f(x)$")
ymax = min(3 * fx.max(), etax.max())
ax.set_ylim(-ymax, ymax)
##-------------------------------------------------------------------------
## Add in BC line
if 1:
from LE_CBulkConst import bulk_const
x, Q, BC = bulk_const(histfile)
## Double space
x = np.hstack([-x[::-1], x])
Q = np.hstack([Q[::-1], Q])
BC = np.hstack([BC[::-1], BC])
ax.plot(x, (Q / Q.max()) * 0.5 * ax.get_ylim()[1] + ax.get_ylim()[0],
"b-",
lw=4)
ax.plot(x, (BC / BC.max()) * 0.5 * ax.get_ylim()[1] + ax.get_ylim()[0],
"r-",
lw=4)
ax2 = ax.twinx()
ax2.yaxis.set_major_locator(NullLocator())
ax2.set_ylabel(r"$n$ \& $\left<\eta^2\right>n$ \hfill")
ax2.yaxis.set_label_coords(-0.07, 0.15)
# ax.yaxis.set_label_coords(-0.07,0.5)
##-------------------------------------------------------------------------
if not nosave:
plotfile = os.path.dirname(histfile) + "/Jxeta" + os.path.basename(
histfile)[4:-4]
plotfile += "." + fs["saveext"]
fig.savefig(plotfile, format=fs["saveext"])
if vb: print me + "Figure saved to", plotfile
if vb: print me + "Execution time %.1f seconds." % (time.time() - t0)
return
def plot_file(histfile, nosave, vb):
"""
"""
me = me0+".plot_file: "
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histfile, me+"Functional only for Cartesian geometry."
Casimir = "_CL_" in histfile or "_ML_" in histfile
## Get pars from filename
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
T = filename_par(histfile, "_T") if Casimir else -S
## Calculate quantities
x, Q, BC = bulk_const(histfile)[:3]
ex2 = BC/(Q+(Q==0.0))
##-------------------------------------------------------------------------
## Potential
if "_DL_" in histfile: fx = force_dlin([x,0],R,S)[0]
elif "_CL_" in histfile: fx = force_clin([x,0],R,S,T)[0]
elif "_ML_" in histfile: fx = force_mlin([x,0],R,S,T)[0]
elif "_NL_" in histfile: fx = force_nlin([x,0],R,S)[0]
U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min()
##-------------------------------------------------------------------------
## Smooth
sp.ndimage.gaussian_filter1d(Q,1.0,order=0,output=Q)
sp.ndimage.gaussian_filter1d(BC,1.0,order=0,output=BC)
sp.ndimage.gaussian_filter1d(ex2,1.0,order=0,output=ex2)
##-------------------------------------------------------------------------
## PLOT
fig, ax = plt.subplots(1,1, figsize=fs["figsize"])
## Data
ax.plot(x, Q/Q.max(), label=r"$n(x)$",lw=2)
ax.plot(x, ex2/ex2.max(), label=r"$\langle\eta_x^2\rangle(x)$",lw=2)
ax.plot(x, BC/BC.max(), label=r"$\langle\eta_x^2\rangle \cdot n$",lw=2)
ax.plot(x, U/U.max()*ax.get_ylim()[1], "k--", label=r"$U(x)$")
## Indicate bulk region
if "_DL_" in histfile:
ax.axvspan(S,R, color="yellow",alpha=0.2)
ax.axvline(S, c="k",lw=2); ax.axvline(R, c="k",lw=2)
elif "_ML_" in histfile:
ax.axvspan(S,R, color="yellow",alpha=0.2)
ax.axvspan(-R,T, color="yellow",alpha=0.2)
ax.axvline(S, c="k",lw=2); ax.axvline(R, c="k",lw=2)
ax.axvline(T, c="k",lw=2); ax.axvline(-R, c="k",lw=2)
elif "_CL_" in histfile:
ax.axvspan(S,R, color="yellow",alpha=0.2)
ax.axvspan(0,T, color="yellow",alpha=0.2)
ax.axvline(S, c="k",lw=2); ax.axvline(R, c="k",lw=2)
ax.axvline(T, c="k",lw=2); ax.axvline(-R, c="k",lw=2)
##-------------------------------------------------------------------------
## ATTRIBUTES
ax.set_xlim(left=x[0],right=x[-1])
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
ax.set_xlabel("$x$",fontsize=fs["fsa"])
ax.set_ylabel("Rescaled variable",fontsize=fs["fsa"])
ax.grid()
legloc = [0.35,0.25] if "_ML_" in histfile else [0.32,0.67]
ax.legend(loc=legloc,fontsize=fs["fsl"]).get_frame().set_alpha(0.8)
title = r"Bulk Constant. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.1f$."%(a,R,S,T) if T>=0.0\
else r"Bulk Constant. $\alpha=%.1f, R=%.1f, S=%.1f$."%(a,R,S)
# fig.suptitle(title,fontsize=fs["fst"])
## SAVE
# ax.set_ylim(top=BC.max())
plotfile = os.path.dirname(histfile)+"/QEe2"+os.path.basename(histfile)[4:-4]+"."+fs["saveext"]
if not nosave:
fig.savefig(plotfile)
if vb: print me+"Figure saved to",plotfile
##-------------------------------------------------------------------------
return plotfile
def plot_pressure_file(histfile, nosave, vb): """ Plot spatial PDF Q(x) and spatially-varying pressure P(x). """ me = me0+".plot_pressure_file: " ##------------------------------------------------------------------------- ## Dir pars assert "_CAR_" in histfile, me+"Functional only for Cartesian geometry." Casimir = "_CL_" in histfile or "_ML_" in histfile or "_NL_" in histfile ##------------------------------------------------------------------------- ## Filename parameters a = filename_par(histfile, "_a") R = filename_par(histfile, "_R") S = filename_par(histfile, "_S") try: T = filename_par(histfile, "_T") except ValueError: T = -S ## Space bins = np.load(os.path.dirname(histfile)+"/BHISBIN"+os.path.basename(histfile)[4:-4]+".npz") xbins = bins["xbins"] x = 0.5*(xbins[1:]+xbins[:-1]) ## Wall indices Rind, Sind, Tind = np.abs(x-R).argmin(), np.abs(x-S).argmin(), np.abs(x-T).argmin() STind = (Sind+Tind)/2 ## Adjust indices for pressure calculation if "_DC_" in histfile: STind = 0 elif "_DL_" in histfile: STind = 0 elif "_NL_" in histfile: STind = Sind Sind = Rind Tind = x.size-Rind ##------------------------------------------------------------------------- ## Histogram H = np.load(histfile) ## Spatial density Qx = H.sum(axis=2).sum(axis=1) / (H.sum()*(x[1]-x[0])) ##------------------------------------------------------------------------- ## Choose force if "_DC_" in histfile: fx = force_dcon([x,0],R,S)[0] elif "_DL_" in histfile: fx = force_dlin([x,0],R[i],S[i])[0] elif "_CL_" in histfile: fx = force_clin([x,0],R,S,T)[0] elif "_ML_" in histfile: fx = force_mlin([x,0],R,S,T)[0] elif "_NL_" in histfile: fx = force_nlin([x,0],R,S)[0] else: raise IOError, me+"Force not recognised." ## Calculate integral pressure PR = -sp.integrate.cumtrapz(fx[Rind:]*Qx[Rind:], x[Rind:], initial=0.0) PS = -sp.integrate.cumtrapz(fx[STind:Sind+1]*Qx[STind:Sind+1], x[STind:Sind+1], initial=0.0); PS -= PS[-1] if Casimir: PT = -sp.integrate.cumtrapz(fx[Tind:STind+1]*Qx[Tind:STind+1], x[Tind:STind+1], initial=0.0) if x[0]<0: R2ind = x.size-Rind PR2 = -sp.integrate.cumtrapz(fx[:R2ind]*Qx[:R2ind], x[:R2ind], initial=0.0); PR2 -= PR2[-1] ##------------------------------------------------------------------------- ## Potential and WN U = -sp.integrate.cumtrapz(fx, x, initial=0.0); U -= U.min() Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x) ## WN pressure PR_WN = -sp.integrate.cumtrapz(fx[Rind:]*Qx_WN[Rind:], x[Rind:], initial=0.0) PS_WN = -sp.integrate.cumtrapz(fx[STind:Sind+1]*Qx_WN[STind:Sind+1], x[STind:Sind+1], initial=0.0); PS_WN -= PS_WN[-1] if Casimir: PT_WN = -sp.integrate.cumtrapz(fx[Tind:STind+1]*Qx_WN[Tind:STind+1], x[Tind:STind+1], initial=0.0) ##------------------------------------------------------------------------- ## PLOTTING fig, axs = plt.subplots(2,1, sharex=True, figsize=fs["figsize"]) if "_DL_" in histfile: legloc = "upper right" elif "_CL_" in histfile: legloc = "upper right" elif "_ML_" in histfile: legloc = "upper left" elif "_NL_" in histfile: legloc = "lower left" else: legloc = "best" ## Plot PDF ax = axs[0] lQ = ax.plot(x, Qx, lw=2, label=r"CN") ax.plot(x, Qx_WN, lQ[0].get_color()+":", lw=2, label="WN") ## Potential ax.plot(x, U/U.max()*ax.get_ylim()[1], "k--", lw=2, label=r"$U(x)$") ax.set_xlim((x[0],x[-1])) ax.set_ylim(bottom=0.0) ax.set_ylabel(r"$Q(x)$", fontsize=fs["fsa"]) ax.grid() ax.legend(loc=legloc, fontsize=fs["fsl"]).get_frame().set_alpha(0.5) ## Plot pressure ax = axs[1] lPR = ax.plot(x[Rind:], PR, lw=2, label=r"$P_R$") lPS = ax.plot(x[STind:Sind+1], PS, lw=2, label=r"$P_S$") if Casimir: lPT = ax.plot(x[Tind:STind+1], PT, lw=2, label=r"$P_T$") if x[0]<0: ax.plot(x[:R2ind], PR2, lPR[0].get_color()+"-", lw=2) ## WN result ax.plot(x[Rind:], PR_WN, lPR[0].get_color()+":", lw=2) ax.plot(x[STind:Sind+1], PS_WN, lPS[0].get_color()+":", lw=2) if Casimir: ax.plot(x[Tind:STind+1], PT_WN, lPT[0].get_color()+":", lw=2) if x[0]<0: ax.plot(x[:R2ind], PR_WN[::-1], lPR[0].get_color()+":", lw=2) ## Potential ax.plot(x, U/U.max()*ax.get_ylim()[1], "k--", lw=2)#, label=r"$U(x)$") ax.set_xlim((x[0],x[-1])) ax.set_ylim(bottom=0.0) ax.set_xlabel(r"$x$", fontsize=fs["fsa"]) ax.set_ylabel(r"$P(x)$", fontsize=fs["fsa"]) ax.grid() if Casimir: ax.legend(loc=legloc, fontsize=fs["fsl"]).get_frame().set_alpha(0.5) ##------------------------------------------------------------------------- fig.tight_layout() fig.subplots_adjust(top=0.90) title = r"Spatial PDF and Pressure. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.1f$"%(a,R,S,T) if T>=0.0\ else r"Spatial PDF and Pressure. $\alpha=%.1f, R=%.1f, S=%.1f$"%(a,R,S) fig.suptitle(title, fontsize=fs["fst"]) if not nosave: plotfile = os.path.dirname(histfile)+"/PDFP"+os.path.basename(histfile)[4:-4]+".jpg" fig.savefig(plotfile) if vb: print me+"Figure saved to",plotfile return
def plot_pressure_file(histfile, nosave, vb):
"""
Plot spatial PDF Q(x) and spatially-varying pressure P(x).
"""
me = me0 + ".plot_pressure_file: "
##-------------------------------------------------------------------------
## Dir pars
assert "_CAR_" in histfile, me + "Functional only for Cartesian geometry."
Casimir = "_CL_" in histfile or "_ML_" in histfile or "_NL_" in histfile
##-------------------------------------------------------------------------
## Filename parameters
a = filename_par(histfile, "_a")
R = filename_par(histfile, "_R")
S = filename_par(histfile, "_S")
try:
T = filename_par(histfile, "_T")
except ValueError:
T = -S
## Space
bins = np.load(
os.path.dirname(histfile) + "/BHISBIN" +
os.path.basename(histfile)[4:-4] + ".npz")
xbins = bins["xbins"]
x = 0.5 * (xbins[1:] + xbins[:-1])
## Wall indices
Rind, Sind, Tind = np.abs(x - R).argmin(), np.abs(x - S).argmin(), np.abs(
x - T).argmin()
STind = (Sind + Tind) / 2
## Adjust indices for pressure calculation
if "_DC_" in histfile:
STind = 0
elif "_DL_" in histfile:
STind = 0
elif "_NL_" in histfile:
STind = Sind
Sind = Rind
Tind = x.size - Rind
##-------------------------------------------------------------------------
## Histogram
H = np.load(histfile)
## Spatial density
Qx = H.sum(axis=2).sum(axis=1) / (H.sum() * (x[1] - x[0]))
##-------------------------------------------------------------------------
## Choose force
if "_DC_" in histfile: fx = force_dcon([x, 0], R, S)[0]
elif "_DL_" in histfile: fx = force_dlin([x, 0], R[i], S[i])[0]
elif "_CL_" in histfile: fx = force_clin([x, 0], R, S, T)[0]
elif "_ML_" in histfile: fx = force_mlin([x, 0], R, S, T)[0]
elif "_NL_" in histfile: fx = force_nlin([x, 0], R, S)[0]
else: raise IOError, me + "Force not recognised."
## Calculate integral pressure
PR = -sp.integrate.cumtrapz(fx[Rind:] * Qx[Rind:], x[Rind:], initial=0.0)
PS = -sp.integrate.cumtrapz(fx[STind:Sind + 1] * Qx[STind:Sind + 1],
x[STind:Sind + 1],
initial=0.0)
PS -= PS[-1]
if Casimir:
PT = -sp.integrate.cumtrapz(fx[Tind:STind + 1] * Qx[Tind:STind + 1],
x[Tind:STind + 1],
initial=0.0)
if x[0] < 0:
R2ind = x.size - Rind
PR2 = -sp.integrate.cumtrapz(
fx[:R2ind] * Qx[:R2ind], x[:R2ind], initial=0.0)
PR2 -= PR2[-1]
##-------------------------------------------------------------------------
## Potential and WN
U = -sp.integrate.cumtrapz(fx, x, initial=0.0)
U -= U.min()
Qx_WN = np.exp(-U) / np.trapz(np.exp(-U), x)
## WN pressure
PR_WN = -sp.integrate.cumtrapz(
fx[Rind:] * Qx_WN[Rind:], x[Rind:], initial=0.0)
PS_WN = -sp.integrate.cumtrapz(fx[STind:Sind + 1] * Qx_WN[STind:Sind + 1],
x[STind:Sind + 1],
initial=0.0)
PS_WN -= PS_WN[-1]
if Casimir:
PT_WN = -sp.integrate.cumtrapz(
fx[Tind:STind + 1] * Qx_WN[Tind:STind + 1],
x[Tind:STind + 1],
initial=0.0)
##-------------------------------------------------------------------------
## PLOTTING
fig, axs = plt.subplots(2, 1, sharex=True, figsize=fs["figsize"])
if "_DL_" in histfile: legloc = "upper right"
elif "_CL_" in histfile: legloc = "upper right"
elif "_ML_" in histfile: legloc = "upper left"
elif "_NL_" in histfile: legloc = "lower left"
else: legloc = "best"
## Plot PDF
ax = axs[0]
lQ = ax.plot(x, Qx, lw=2, label=r"CN")
ax.plot(x, Qx_WN, lQ[0].get_color() + ":", lw=2, label="WN")
## Potential
ax.plot(x, U / U.max() * ax.get_ylim()[1], "k--", lw=2, label=r"$U(x)$")
ax.set_xlim((x[0], x[-1]))
ax.set_ylim(bottom=0.0)
ax.set_ylabel(r"$Q(x)$", fontsize=fs["fsa"])
ax.grid()
ax.legend(loc=legloc, fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
## Plot pressure
ax = axs[1]
lPR = ax.plot(x[Rind:], PR, lw=2, label=r"$P_R$")
lPS = ax.plot(x[STind:Sind + 1], PS, lw=2, label=r"$P_S$")
if Casimir:
lPT = ax.plot(x[Tind:STind + 1], PT, lw=2, label=r"$P_T$")
if x[0] < 0:
ax.plot(x[:R2ind], PR2, lPR[0].get_color() + "-", lw=2)
## WN result
ax.plot(x[Rind:], PR_WN, lPR[0].get_color() + ":", lw=2)
ax.plot(x[STind:Sind + 1], PS_WN, lPS[0].get_color() + ":", lw=2)
if Casimir:
ax.plot(x[Tind:STind + 1], PT_WN, lPT[0].get_color() + ":", lw=2)
if x[0] < 0:
ax.plot(x[:R2ind], PR_WN[::-1], lPR[0].get_color() + ":", lw=2)
## Potential
ax.plot(x, U / U.max() * ax.get_ylim()[1], "k--",
lw=2) #, label=r"$U(x)$")
ax.set_xlim((x[0], x[-1]))
ax.set_ylim(bottom=0.0)
ax.set_xlabel(r"$x$", fontsize=fs["fsa"])
ax.set_ylabel(r"$P(x)$", fontsize=fs["fsa"])
ax.grid()
if Casimir:
ax.legend(loc=legloc, fontsize=fs["fsl"]).get_frame().set_alpha(0.5)
##-------------------------------------------------------------------------
fig.tight_layout()
fig.subplots_adjust(top=0.90)
title = r"Spatial PDF and Pressure. $\alpha=%.1f, R=%.1f, S=%.1f, T=%.1f$"%(a,R,S,T) if T>=0.0\
else r"Spatial PDF and Pressure. $\alpha=%.1f, R=%.1f, S=%.1f$"%(a,R,S)
fig.suptitle(title, fontsize=fs["fst"])
if not nosave:
plotfile = os.path.dirname(histfile) + "/PDFP" + os.path.basename(
histfile)[4:-4] + ".jpg"
fig.savefig(plotfile)
if vb: print me + "Figure saved to", plotfile
return
