def tail_plot(histfile, verbose):
"""
Plot tail PDF on log scale and make exponential fit
"""
me = "Tail.tail_plot: "
plotfile = os.path.splitext(histfile)[0] + "_t.png"
## Get alpha and X from filename
alpha, X, dt, ymax = filename_pars(histfile)
if verbose: print me + "alpha =", alpha, "and X =", X
## 2D histogram
H = np.load(histfile)
## Space -- bin edges and centres
ybins = np.linspace(-0.5, 0.5, H.shape[0] + 1)
y = 0.5 * (ybins[1:] + ybins[:-1])
xmin, xmax = 0.9 * X, lookup_xmax(X, alpha)
xbins = calculate_xbin(xmin, X, xmax, H.shape[1])[H.shape[1] / 2 - 1:]
x = 0.5 * (xbins[1:] + xbins[:-1])
## Interested in wall region
H = H[:, H.shape[1] / 2 - 1:]
## Marginalise
Hx = np.trapz(H, x=y, axis=0)
# Hx = H.sum(axis=0) * (y[1]-y[0]) ## Should be dot product with diffy
Hx = Hx[Hx != 0]
x = x[Hx != 0]
## Fit; throw away first portion of data
lm = Hx.shape[0] / 10
fit = np.polyfit(x[lm:], np.log(Hx[lm:]), 1)
fit_fn = np.poly1d(fit)
## White noise result
HxIG = np.exp(fit[1]) * np.exp(-alpha / dt * (x - X))
## Plot (x-X distance into wall)
plt.semilogy(x - X, Hx, label="Data")
plt.semilogy(x-X,np.exp(fit_fn(x)),"r--",\
label="$\exp["+str(round(fit[0]*dt/(alpha),1))+"\\frac{\\alpha}{dt}x]$")
## Plot IG result
plt.semilogy(x - X, HxIG, label="White noise")
plt.xlim(left=0.0)
plot_acco(plt.gca(),
title="Wall region, $\\alpha=" + str(alpha) + "$",
xlabel="Distance into wall region",
ylabel="PDF $p(x)$")
plt.savefig(plotfile)
if verbose: print me + "figure saved to", plotfile
return
def pressure_of_alpha(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_DeltaPressure.pressure_of_alpha: "
t0 = sysT()
## File discovery
histfiles = np.sort(glob.glob(dirpath + "/*.npy"))
numfiles = len(histfiles)
Alpha = np.zeros(numfiles)
Press = np.zeros(numfiles)
PressIG = np.zeros(numfiles)
## Loop over files
for i, filepath in enumerate(histfiles):
## Find alpha; assume all other pars stay the same
Alpha[i], X, D, dt, ymax = filename_pars(filepath)
## Load data
H = np.load(filepath)
## Space
xmin, xmax = 0.9 * X, lookup_xmax(X, Alpha[i])
ymax = 0.5
x = calculate_xbin(xmin, X, xmax, H.shape[1] - 1)
y = np.linspace(-ymax, ymax, H.shape[0])
## Marginalise to PDF in X
Hx = np.trapz(H, x=y, axis=0)
Hx /= np.trapz(Hx, x=x, axis=0)
## Calculate pressure
force = force_x(x, Alpha[i], X, 0.01)
Press[i] = np.trapz(-force * Hx, x) / dt
## Sort values
sortind = np.argsort(Alpha)
Alpha = Alpha[sortind]
Press = Press[sortind]
PressIG = PressIG[sortind]
if verbose:
print me + " pressure caclulation ", str(round(sysT() - t0,
2)), "seconds."
AlphaIG, PressIG = pressureIG_of_alpha(Alpha, Press, x, X, D, dt, verbose)
return [Alpha, Press, AlphaIG, PressIG, D]
def tail_plot(histfile, verbose):
"""
Plot tail PDF on log scale and make exponential fit
"""
me = "Tail.tail_plot: "
plotfile = os.path.splitext(histfile)[0]+"_t.png"
## Get alpha and X from filename
alpha, X, dt, ymax = filename_pars(histfile)
if verbose: print me+"alpha =",alpha,"and X =",X
## 2D histogram
H = np.load(histfile)
## Space -- bin edges and centres
ybins = np.linspace(-0.5,0.5,H.shape[0]+1)
y = 0.5*(ybins[1:]+ybins[:-1])
xmin, xmax = 0.9*X, lookup_xmax(X,alpha)
xbins = calculate_xbin(xmin,X,xmax,H.shape[1])[H.shape[1]/2-1:]
x = 0.5*(xbins[1:]+xbins[:-1])
## Interested in wall region
H = H[:,H.shape[1]/2-1:]
## Marginalise
Hx = np.trapz(H,x=y,axis=0)
# Hx = H.sum(axis=0) * (y[1]-y[0]) ## Should be dot product with diffy
Hx = Hx[Hx!=0]; x = x[Hx!=0]
## Fit; throw away first portion of data
lm=Hx.shape[0]/10
fit = np.polyfit(x[lm:],np.log(Hx[lm:]),1)
fit_fn = np.poly1d(fit)
## White noise result
HxIG = np.exp(fit[1])*np.exp(-alpha/dt*(x-X))
## Plot (x-X distance into wall)
plt.semilogy(x-X,Hx,label="Data")
plt.semilogy(x-X,np.exp(fit_fn(x)),"r--",\
label="$\exp["+str(round(fit[0]*dt/(alpha),1))+"\\frac{\\alpha}{dt}x]$")
## Plot IG result
plt.semilogy(x-X,HxIG,label="White noise")
plt.xlim(left=0.0)
plot_acco(plt.gca(),title="Wall region, $\\alpha="+str(alpha)+"$",
xlabel="Distance into wall region",ylabel="PDF $p(x)$")
plt.savefig(plotfile)
if verbose: print me+"figure saved to",plotfile
return
def pressure_of_alpha(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_DeltaPressure.pressure_of_alpha: " t0 = sysT() ## File discovery histfiles = np.sort(glob.glob(dirpath+"/*.npy")) numfiles = len(histfiles) Alpha = np.zeros(numfiles) Press = np.zeros(numfiles) PressIG = np.zeros(numfiles) ## Loop over files for i,filepath in enumerate(histfiles): ## Find alpha; assume all other pars stay the same Alpha[i], X, D, dt, ymax = filename_pars(filepath) ## Load data H = np.load(filepath) ## Space xmin,xmax = 0.9*X,lookup_xmax(X,Alpha[i]) ymax = 0.5 x = calculate_xbin(xmin,X,xmax,H.shape[1]-1) y = np.linspace(-ymax,ymax,H.shape[0]) ## Marginalise to PDF in X Hx = np.trapz(H,x=y,axis=0) Hx /= np.trapz(Hx,x=x,axis=0) ## Calculate pressure force = force_x(x,Alpha[i],X,0.01) Press[i] = np.trapz(-force*Hx, x)/dt ## Sort values sortind = np.argsort(Alpha) Alpha = Alpha[sortind]; Press = Press[sortind]; PressIG = PressIG[sortind] if verbose: print me+" pressure caclulation ",str(round(sysT()-t0,2)),"seconds." AlphaIG, PressIG = pressureIG_of_alpha(Alpha, Press, x,X,D,dt, verbose) return [Alpha, Press, AlphaIG, PressIG, D]
def main():
"""
NAME
LE_2DLBS.py
PURPOSE
Simulate coloured noise trajectories in 2D.
EXECUTION
FLAGS
-a --alpha 0.1 Slope of the potential
-X --wallpos 10.0 Position of wall
-D --Delta 0.0 Width of wall onset in units of X
-r --nruns 100 Number of runs for each (x0,y0)
-t --timefac 1.0 Multiply t_max by factor
-v --verbose False Print useful information to screen
-h --help False Print docstring and exit
-R --radius 1.0 Radius of wall curvature
--BC-impenetrable Change BC to impenetrable rather then periodic
--schematic Plot a schematic of the simulation space
--trajectory Output some trajectory plots
EXAMPLE
NOTES
BUGS
HISTORY
20 February 2016 Adapted from LE_LightBoundarySim.py
"""
me = "LE_2DLBS.main: "
t0 = time.time()
## ----------------------------------------------------------------
## INPUT OPTIONS
parser = optparse.OptionParser(conflict_handler="resolve")
parser.add_option('-a',
'--alpha',
dest="a",
default=0.1,
type="float",
help="The steepness of the potential.")
parser.add_option('-X', '--wallpos', dest="X", default=10.0, type="float")
parser.add_option('-D', '--Delta', dest="Delta", default=0.0, type="float")
parser.add_option('-r', '--nrun', dest="Nrun", default=100, type="int")
parser.add_option('--dt', dest="dt", default=0.01, type="float")
parser.add_option('-t',
'--timefac',
dest="timefac",
default=1.0,
type="float")
parser.add_option('-v',
'--verbose',
dest="vb",
default=False,
action="store_true",
help="Print useful information to screen.")
parser.add_option('-R', '--radius', dest="R", default=1.0, type="float")
parser.add_option('--BC-impenetrable',
dest="PBC",
default=True,
action="store_false")
parser.add_option('--schematic',
dest="schematic",
default=False,
action="store_true")
parser.add_option('--trajectory',
dest="traj",
default=False,
action="store_true")
parser.add_option('-v',
'--verbose',
dest="vb",
default=False,
action="store_true",
help="Print useful information to screen.")
parser.add_option('-h',
'--help',
dest="help",
default=False,
action="store_true",
help="Print docstring.")
opts, argv = parser.parse_args()
if opts.help:
print main.__doc__
return
a = opts.a
X = opts.X
Delta = opts.Delta
Nrun = opts.Nrun
global dt
dt = opts.dt
timefac = opts.timefac
vb = opts.vb
R = opts.R
schematic = opts.schematic
traj = opts.traj
PBC = opts.PBC
if Delta != 0.0:
print me + "WARNING: Resetting Delta = 0.0."
Delta = 0.0
if vb: print "\n==\n" + me + "Input parameters:\n\t", opts
## ----------------------------------------------------------------
## SETUP CALCULATIONS
## Simulation time
tmax = 5e2 * timefac
## Space: y, circle, x
ymax = 0.5
assert (R >= ymax), me + "The wall must enclose the volume."
if (vb and ymax <= 2 * a):
print me + "Warning: the width of the space is comparable to or smaller than the memory length-scale."
## Centre of circle for curved boundary
R2 = R * R
c = [X - np.sqrt(R2 - ymax * ymax), 0.0]
## Simulation limits
xmax = lookup_xmax(c[0] + R, a)
xmin = calculate_xmin(X, a) ## Simulation cutoff
## Injection x coordinate
xini = calculate_xini(X, a)
## Histogramming; bin edges
Nxbin = 200
Nybin = 50
xbins = calculate_xbin(xini, X, xmax, Nxbin)
ybins = calculate_ybin(0.0, ymax, Nybin + 1)
## Particles
Nparticles = 1 * len(ybins) * Nrun
## Initial noise drawn from Gaussian
eIC = np.random.normal(
0.0, 1.0 /
a, [Nparticles, 2
]) if a > 0.0 else 100 * (np.random.random([Nparticles, 2]) - 0.5)
## Centre of circle for curved boundary
R2 = R * R
c = [X - np.sqrt(R2 - ymax * ymax), 0.0]
## Filename; directory and file existence; readme
BCstr = "PBC" if PBC else "IBC"
hisdir = "Pressure/"+str(datetime.now().strftime("%y%m%d"))+\
"_2D_"+BCstr+"_r"+str(Nrun)+"_dt"+str(dt)+"/"
hisfile = "BHIS_2D_" + BCstr + "_a" + str(a) + "_X" + str(X) + "_R" + str(
R) + "_r" + str(Nrun) + "_dt" + str(dt)
binfile = "BHISBIN" + hisfile[4:]
filepath = hisdir + hisfile
check_path(filepath, vb)
create_readme(filepath, vb)
## Save bins
np.savez(hisdir + binfile, xbins=xbins, ybins=ybins)
## ----------------------------------------------------------------
## SCHEMATIC IMAGE
if schematic:
draw_schematic(xmin, xbins, ybins, c, R,
hisdir + "SCHM" + hisfile[4:] + ".png", True)
return
## ----------------------------------------------------------------
## SIMULATION
if vb: print me + "Computing", Nparticles, "trajectories."
## Precompute exp(-t/a^2)
expmt = np.exp(-np.arange(0, tmax, dt) /
(a * a)) if a > 0 else np.array([1.] + [0.] *
(int(tmax / dt) - 1))
## Initialise histogram in space
H = np.zeros((Nxbin, Nybin))
## Counter for noise initial conditions
i = 0
## Loop over initial coordinates
for yini in ybins:
## Perform several runs
for run in xrange(Nrun):
## x, y are coordinates as a function of time
x, y = boundary_sim((xini, yini), eIC[i], a, X, Delta, xmin, ymax,
R2, c, tmax, expmt, PBC,
(vb and run % 50 == 0))
if traj and run == 0:
plot_traj(x, y, xmin, X, xmax, ymax,
hisdir + "TRAJ" + str(i) + hisfile[4:] + ".png")
H += np.histogram2d(x, y, bins=[xbins, ybins], normed=False)[0]
i += 1
H = (H.T)[::-1]
## When normed=False, need to divide by the bin area
H /= np.outer(np.diff(ybins), np.diff(xbins))
## Normalise by number of particles
H /= Nparticles
save_data(filepath, H, vb)
if vb: print me + "execution time", round(time.time() - t0, 2), "seconds"
return filepath
def main():
"""
NAME
LE_2DLBS.py
PURPOSE
Simulate coloured noise trajectories in 2D.
EXECUTION
FLAGS
-a --alpha 0.1 Slope of the potential
-X --wallpos 10.0 Position of wall
-D --Delta 0.0 Width of wall onset in units of X
-r --nruns 100 Number of runs for each (x0,y0)
-t --timefac 1.0 Multiply t_max by factor
-v --verbose False Print useful information to screen
-h --help False Print docstring and exit
-R --radius 1.0 Radius of wall curvature
--BC-impenetrable Change BC to impenetrable rather then periodic
--schematic Plot a schematic of the simulation space
--trajectory Output some trajectory plots
EXAMPLE
NOTES
BUGS
HISTORY
20 February 2016 Adapted from LE_LightBoundarySim.py
"""
me = "LE_2DLBS.main: "
t0 = time.time()
## ----------------------------------------------------------------
## INPUT OPTIONS
parser = optparse.OptionParser(conflict_handler="resolve")
parser.add_option('-a','--alpha',
dest="a",default=0.1,type="float",
help="The steepness of the potential.")
parser.add_option('-X','--wallpos',
dest="X",default=10.0,type="float")
parser.add_option('-D','--Delta',
dest="Delta",default=0.0,type="float")
parser.add_option('-r','--nrun',
dest="Nrun",default=100,type="int")
parser.add_option('--dt',
dest="dt",default=0.01,type="float")
parser.add_option('-t','--timefac',
dest="timefac",default=1.0,type="float")
parser.add_option('-v','--verbose',
dest="vb",default=False,action="store_true",
help="Print useful information to screen.")
parser.add_option('-R','--radius',
dest="R",default=1.0,type="float")
parser.add_option('--BC-impenetrable',
dest="PBC",default=True,action="store_false")
parser.add_option('--schematic',
dest="schematic",default=False,action="store_true")
parser.add_option('--trajectory',
dest="traj",default=False,action="store_true")
parser.add_option('-v','--verbose',
dest="vb",default=False,action="store_true",
help="Print useful information to screen.")
parser.add_option('-h','--help',
dest="help",default=False,action="store_true",
help="Print docstring.")
opts, argv = parser.parse_args()
if opts.help: print main.__doc__; return
a = opts.a
X = opts.X
Delta = opts.Delta
Nrun = opts.Nrun
global dt; dt = opts.dt
timefac = opts.timefac
vb = opts.vb
R = opts.R
schematic = opts.schematic
traj = opts.traj
PBC = opts.PBC
if Delta!=0.0:
print me+"WARNING: Resetting Delta = 0.0."
Delta = 0.0
if vb: print "\n==\n"+me+"Input parameters:\n\t",opts
## ----------------------------------------------------------------
## SETUP CALCULATIONS
## Simulation time
tmax = 5e2*timefac
## Space: y, circle, x
ymax = 0.5
assert (R>=ymax), me+"The wall must enclose the volume."
if (vb and ymax<=2*a):
print me+"Warning: the width of the space is comparable to or smaller than the memory length-scale."
## Centre of circle for curved boundary
R2 = R*R
c = [X-np.sqrt(R2-ymax*ymax),0.0]
## Simulation limits
xmax = lookup_xmax(c[0]+R,a)
xmin = calculate_xmin(X,a) ## Simulation cutoff
## Injection x coordinate
xini = calculate_xini(X,a)
## Histogramming; bin edges
Nxbin = 200
Nybin = 50
xbins = calculate_xbin(xini,X,xmax,Nxbin)
ybins = calculate_ybin(0.0,ymax,Nybin+1)
## Particles
Nparticles = 1*len(ybins)*Nrun
## Initial noise drawn from Gaussian
eIC = np.random.normal(0.0,1.0/a,[Nparticles,2]) if a>0.0 else 100*(np.random.random([Nparticles,2])-0.5)
## Centre of circle for curved boundary
R2 = R*R
c = [X-np.sqrt(R2-ymax*ymax),0.0]
## Filename; directory and file existence; readme
BCstr = "PBC" if PBC else "IBC"
hisdir = "Pressure/"+str(datetime.now().strftime("%y%m%d"))+\
"_2D_"+BCstr+"_r"+str(Nrun)+"_dt"+str(dt)+"/"
hisfile = "BHIS_2D_"+BCstr+"_a"+str(a)+"_X"+str(X)+"_R"+str(R)+"_r"+str(Nrun)+"_dt"+str(dt)
binfile = "BHISBIN"+hisfile[4:]
filepath = hisdir+hisfile
check_path(filepath, vb)
create_readme(filepath, vb)
## Save bins
np.savez(hisdir+binfile,xbins=xbins,ybins=ybins)
## ----------------------------------------------------------------
## SCHEMATIC IMAGE
if schematic:
draw_schematic(xmin,xbins,ybins,c,R, hisdir+"SCHM"+hisfile[4:]+".png",True)
return
## ----------------------------------------------------------------
## SIMULATION
if vb: print me+"Computing",Nparticles,"trajectories."
## Precompute exp(-t/a^2)
expmt = np.exp(-np.arange(0,tmax,dt)/(a*a)) if a>0 else np.array([1.]+[0.]*(int(tmax/dt)-1))
## Initialise histogram in space
H = np.zeros((Nxbin,Nybin))
## Counter for noise initial conditions
i = 0
## Loop over initial coordinates
for yini in ybins:
## Perform several runs
for run in xrange(Nrun):
## x, y are coordinates as a function of time
x, y = boundary_sim((xini,yini), eIC[i], a, X,Delta, xmin,ymax,
R2,c, tmax,expmt, PBC, (vb and run%50==0))
if traj and run==0: plot_traj(x,y,xmin,X,xmax,ymax, hisdir+"TRAJ"+str(i)+hisfile[4:]+".png")
H += np.histogram2d(x,y,bins=[xbins,ybins],normed=False)[0]
i += 1
H = (H.T)[::-1]
## When normed=False, need to divide by the bin area
H /= np.outer(np.diff(ybins),np.diff(xbins))
## Normalise by number of particles
H /= Nparticles
save_data(filepath, H, vb)
if vb: print me+"execution time",round(time.time()-t0,2),"seconds"
return filepath
def plot_exp_alpha(dirpath, verbose):
"""
Plot exponents of fit in wall region against alphs
"""
me = "Tail.plot_exp_alpha: "
t0 = sysT()
## File discovery
histfiles = np.sort(glob.glob(dirpath + "/*1.npy"))
numfiles = len(histfiles)
if verbose: print me + "found", numfiles, "files"
## Assume all files have same X
start = histfiles[0].find("_X") + 2
X = float(histfiles[0][start:histfiles[0].find("_", start)])
if verbose: print me + "determined X=" + str(X)
## Outfile name
exponplot = dirpath + "/TailAlpha.png"
Alpha = np.zeros(numfiles + 1)
Expon = np.zeros(numfiles + 1)
## Loop over files
for i, filepath in enumerate(histfiles):
## Find alpha
start = filepath.find("_a") + 2
Alpha[i] = float(filepath[start:filepath.find("_", start)])
## Load data
H = np.load(filepath)
## Space
xmin, xmax = 0.9 * X, lookup_xmax(X, Alpha[i])
ymax = 0.5
x = calculate_xbin(xmin, X, xmax, H.shape[1] - 1)[H.shape[1] / 2 - 1:]
y = np.linspace(-ymax, ymax, H.shape[0])
H = H[:, H.shape[1] / 2 - 1:]
## Marginalise to PDF in x and eliminate zeroes
Hx = np.trapz(H, x=y, axis=0)
Hx = Hx[Hx != 0]
x = x[Hx != 0]
## Fit; throw away first portion of data
if Alpha[i] <= 0.2: lm = Hx.shape[0] / 6
else: lm = Hx.shape[0] / 10
fit = np.polyfit(x[lm:], np.log(Hx[lm:]), 1)
Expon[i] = fit[0]
## Sort values in increasing order
sortind = np.argsort(Alpha)
Alpha = Alpha[sortind]
Expon = Expon[sortind]
## Plotting
plt.plot(Alpha, Expon, "bo")
## Fit to parabola
coeff = np.transpose([Alpha * Alpha])
((a), _, _, _) = np.linalg.lstsq(coeff, Expon)
fit = np.poly1d([a, 0, 0])
plt.plot(Alpha, fit(Alpha), "r--", label=str(fit))
## This fit has nonzero intercept
# plt.plot(Alpha,np.poly1d(np.polyfit(Alpha,Expon,2))(Alpha),"r--")
plot_acco(
plt.gca(),
title=
"Wall region: exponential tail of PDF: $\\rho(x)\sim\exp[+m(x-X)]$",
xlabel="$\\alpha$",
ylabel="Exponent, $m$",
legloc="")
plt.savefig(exponplot)
if verbose: print me + "plot saved to", exponplot
return
def plot_exp_alpha(dirpath, verbose):
"""
Plot exponents of fit in wall region against alphs
"""
me = "Tail.plot_exp_alpha: "
t0 = sysT()
## File discovery
histfiles = np.sort(glob.glob(dirpath+"/*1.npy"))
numfiles = len(histfiles)
if verbose: print me+"found",numfiles,"files"
## Assume all files have same X
start = histfiles[0].find("_X") + 2
X = float(histfiles[0][start:histfiles[0].find("_",start)])
if verbose: print me+"determined X="+str(X)
## Outfile name
exponplot = dirpath+"/TailAlpha.png"
Alpha = np.zeros(numfiles+1)
Expon = np.zeros(numfiles+1)
## Loop over files
for i,filepath in enumerate(histfiles):
## Find alpha
start = filepath.find("_a") + 2
Alpha[i] = float(filepath[start:filepath.find("_",start)])
## Load data
H = np.load(filepath)
## Space
xmin,xmax = 0.9*X,lookup_xmax(X,Alpha[i])
ymax = 0.5
x = calculate_xbin(xmin,X,xmax,H.shape[1]-1)[H.shape[1]/2-1:]
y = np.linspace(-ymax,ymax,H.shape[0])
H = H[:,H.shape[1]/2-1:]
## Marginalise to PDF in x and eliminate zeroes
Hx = np.trapz(H,x=y,axis=0)
Hx = Hx[Hx!=0]; x = x[Hx!=0]
## Fit; throw away first portion of data
if Alpha[i]<=0.2: lm = Hx.shape[0]/6
else: lm=Hx.shape[0]/10
fit = np.polyfit(x[lm:],np.log(Hx[lm:]),1)
Expon[i] = fit[0]
## Sort values in increasing order
sortind = np.argsort(Alpha)
Alpha = Alpha[sortind]; Expon = Expon[sortind]
## Plotting
plt.plot(Alpha,Expon,"bo")
## Fit to parabola
coeff = np.transpose([Alpha*Alpha])
((a), _, _, _) = np.linalg.lstsq(coeff, Expon)
fit = np.poly1d([a, 0, 0])
plt.plot(Alpha,fit(Alpha),"r--",label=str(fit))
## This fit has nonzero intercept
# plt.plot(Alpha,np.poly1d(np.polyfit(Alpha,Expon,2))(Alpha),"r--")
plot_acco(plt.gca(), title="Wall region: exponential tail of PDF: $\\rho(x)\sim\exp[+m(x-X)]$",
xlabel="$\\alpha$", ylabel="Exponent, $m$", legloc="")
plt.savefig(exponplot)
if verbose: print me+"plot saved to",exponplot
return
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
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