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plot_loop.py
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plot_loop.py
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'''
Created on Jul 02, 2012
@author: mkraus
'''
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm, colors, gridspec
from matplotlib.ticker import MultipleLocator, FormatStrFormatter, ScalarFormatter
class PlotMHD2D(object):
'''
classdocs
'''
def __init__(self, diagnostics, nTime=0, nPlot=1):
'''
Constructor
'''
# plt.ion()
self.nrows = 2
self.ncols = 4
if nTime > 0 and nTime < diagnostics.nt:
self.nTime = nTime
else:
self.nTime = diagnostics.nt
self.iTime = 0
self.nPlot = nPlot
self.diagnostics = diagnostics
# self.L1_magnetic = np.zeros_like(diagnostics.tGrid)
# self.L1_velocity = np.zeros_like(diagnostics.tGrid)
#
# self.L2_magnetic = np.zeros_like(diagnostics.tGrid)
# self.L2_velocity = np.zeros_like(diagnostics.tGrid)
self.E_velocity = np.zeros_like(diagnostics.tGrid)
self.E_magnetic = np.zeros_like(diagnostics.tGrid)
self.energy = np.zeros_like(diagnostics.tGrid)
self.helicity = np.zeros_like(diagnostics.tGrid)
self.x = np.zeros(diagnostics.nx+1)
self.y = np.zeros(diagnostics.ny+1)
self.x[0:-1] = self.diagnostics.xGrid
self.x[ -1] = self.x[-2] + self.diagnostics.hx
self.y[0:-1] = self.diagnostics.yGrid
self.y[ -1] = self.y[-2] + self.diagnostics.hy
self.Bx = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.By = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.Vx = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.Vy = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.P = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.A = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.J = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.PB = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.B = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.V = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.divB = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
self.divV = np.zeros((diagnostics.nx+1, diagnostics.ny+1))
# set up figure/window size
self.figure = plt.figure(num=None, figsize=(16,9))
# set up plot margins
plt.subplots_adjust(hspace=1.75, wspace=0.25)
# plt.subplots_adjust(hspace=0.2, wspace=0.25)
plt.subplots_adjust(left=0.03, right=0.97, top=0.93, bottom=0.05)
# set up plot title
self.title = self.figure.text(0.5, 0.97, 't = 0.0' % (diagnostics.tGrid[self.iTime]), horizontalalignment='center')
# set up tick formatter
majorFormatter = ScalarFormatter(useOffset=False)
## -> limit to 1.1f precision
majorFormatter.set_powerlimits((-1,+1))
majorFormatter.set_scientific(True)
# add data for zero timepoint
self.add_timepoint()
# set up plots
self.axes = {}
self.conts = {}
self.cbars = {}
self.lines = {}
self.vecs = {}
self.update_boundaries()
# create subplots
gs = gridspec.GridSpec(20, 5)
self.gs = gs
self.axes["Bx"] = plt.subplot(gs[ 0: 4, 0])
self.axes["By"] = plt.subplot(gs[ 4: 8, 0])
self.axes["Vx"] = plt.subplot(gs[ 8:12, 0])
self.axes["Vy"] = plt.subplot(gs[12:16, 0])
self.axes["P"] = plt.subplot(gs[16:20, 0])
self.axes["Babs"] = plt.subplot(gs[ 0:10,1:3])
self.axes["Vabs"] = plt.subplot(gs[10:20,1:3])
self.axes["Emag"] = plt.subplot(gs[ 0: 5,3:5])
self.axes["Evel"] = plt.subplot(gs[ 5:10,3:5])
self.axes["E"] = plt.subplot(gs[10:15,3:5])
self.axes["H"] = plt.subplot(gs[15:20,3:5])
self.axes["Bx"].set_title('$B_{x} (x,y)$')
self.axes["By"].set_title('$B_{y} (x,y)$')
self.axes["Vx"].set_title('$V_{x} (x,y)$')
self.axes["Vy"].set_title('$V_{y} (x,y)$')
self.axes["P" ].set_title('$P (x,y)$')
self.axes["Babs"].set_title('$div \, V (x,y)$')
self.axes["Vabs"].set_title('$B (x,y)$')
self.conts["Bx"] = self.axes["Bx"].contourf(self.x, self.y, self.Bx.T, self.BxTicks, cmap=cm.jet, extend='both')
self.cbars["Bx"] = self.figure.colorbar(self.conts["Bx"], ax=self.axes["Bx"], orientation='vertical', ticks=self.BxTicks)#, format='%0.2E'
self.conts["By"] = self.axes["By"].contourf(self.x, self.y, self.By.T, self.ByTicks, cmap=cm.jet, extend='both')
self.cbars["By"] = self.figure.colorbar(self.conts["By"], ax=self.axes["By"], orientation='vertical', ticks=self.ByTicks)
self.conts["Vx"] = self.axes["Vx"].contourf(self.x, self.y, self.Vx.T, self.VxTicks, cmap=cm.jet, extend='both')
self.cbars["Vx"] = self.figure.colorbar(self.conts["Vx"], ax=self.axes["Vx"], orientation='vertical', ticks=self.VxTicks)
self.conts["Vy"] = self.axes["Vy"].contourf(self.x, self.y, self.Vy.T, self.VyTicks, cmap=cm.jet, extend='both')
self.cbars["Vy"] = self.figure.colorbar(self.conts["Vy"], ax=self.axes["Vy"], orientation='vertical', ticks=self.VyTicks)
self.conts["P" ] = self.axes["P"].contourf(self.x, self.y, self.P.T, self.PTicks, cmap=cm.jet, extend='both')
self.cbars["P" ] = self.figure.colorbar(self.conts["P"], ax=self.axes["P"], orientation='vertical', ticks=self.PTicks)
self.conts["Vabs"] = self.axes["Vabs"].contour(self.x, self.y, self.A.T, self.ATicks, cmap=cm.jet, extend='neither')
# self.conts["Babs"] = self.axes["Babs"].contourf(self.x, self.y, self.divV.T, self.divVTicks, cmap=cm.jet)
# self.cbars["Babs"] = self.figure.colorbar(self.conts["Babs"], ax=self.axes["Babs"], orientation='vertical', ticks=self.divVTicks)
# plt.subplot(self.gs[0:10,1:3])
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=1.2, arrowstyle='-', arrowsize=.01, minlength=.2, color='b')
# self.stream_xstart = np.linspace(0., 2., 25)
# self.stream_ystart = np.zeros(25)
# self.stream_ystart[7:19] = 2.
tStart, tEnd, xStart, xEnd = self.get_timerange()
self.lines["Emag" ], = self.axes["Emag" ].plot(self.diagnostics.tGrid[tStart:tEnd], self.E_magnetic [tStart:tEnd])
self.lines["Evel" ], = self.axes["Evel" ].plot(self.diagnostics.tGrid[tStart:tEnd], self.E_velocity [tStart:tEnd])
self.lines["E" ], = self.axes["E" ].plot(self.diagnostics.tGrid[tStart:tEnd], self.energy [tStart:tEnd])
self.lines["H" ], = self.axes["H" ].plot(self.diagnostics.tGrid[tStart:tEnd], self.helicity [tStart:tEnd])
self.axes["Emag"].set_title('$E_{B} (t)$')
self.axes["Evel"].set_title('$E_{V} (t)$')
if self.diagnostics.plot_energy:
self.axes["E"].set_title('$E (t)$')
else:
self.axes["E"].set_title('$(E-E_0) / E_0 (t)$')
if self.diagnostics.plot_helicity:
self.axes["H"].set_title('$H (t)$')
else:
self.axes["H"].set_title('$(H-H_0) / H_0 (t)$')
self.axes["Emag" ].set_xlim((xStart,xEnd))
self.axes["Evel" ].set_xlim((xStart,xEnd))
self.axes["E" ].set_xlim((xStart,xEnd))
self.axes["H" ].set_xlim((xStart,xEnd))
self.axes["Emag" ].yaxis.set_major_formatter(majorFormatter)
self.axes["Evel" ].yaxis.set_major_formatter(majorFormatter)
self.axes["E" ].yaxis.set_major_formatter(majorFormatter)
self.axes["H" ].yaxis.set_major_formatter(majorFormatter)
# switch off some ticks
plt.setp(self.axes["Bx" ].get_xticklabels(), visible=False)
plt.setp(self.axes["By" ].get_xticklabels(), visible=False)
plt.setp(self.axes["Vx" ].get_xticklabels(), visible=False)
plt.setp(self.axes["Vy" ].get_xticklabels(), visible=False)
plt.setp(self.axes["Babs" ].get_xticklabels(), visible=False)
plt.setp(self.axes["Emag" ].get_xticklabels(), visible=False)
plt.setp(self.axes["Evel" ].get_xticklabels(), visible=False)
plt.setp(self.axes["E" ].get_xticklabels(), visible=False)
self.update()
def update_boundaries(self):
Bmin = min(self.diagnostics.Bx.min(), self.diagnostics.By.min(), -self.diagnostics.Bx.max(), -self.diagnostics.By.max())
Bmax = max(self.diagnostics.Bx.max(), self.diagnostics.By.max(), -self.diagnostics.Bx.min(), -self.diagnostics.By.min())
# Bxmin = self.diagnostics.Bx.min()
# Bxmax = self.diagnostics.Bx.max()
#
# Bymin = self.diagnostics.By.min()
# Bymax = self.diagnostics.By.max()
#
# if Bxmin == Bxmax:
# Bxmin -= 1.
# Bxmax += 1.
#
# if Bymin == Bymax:
# Bymin -= 1.
# Bymax += 1.
self.BxTicks = np.linspace(Bmin, Bmax, 11, endpoint=True)
self.ByTicks = np.linspace(Bmin, Bmax, 11, endpoint=True)
# self.BxNorm = colors.Normalize(vmin=Bxmin, vmax=Bxmax)
# self.ByNorm = colors.Normalize(vmin=Bymin, vmax=Bymax)
Vmin = 2. * min(self.diagnostics.Vx.min(), self.diagnostics.Vy.min(), -self.diagnostics.Vx.max(), -self.diagnostics.Vy.max())
Vmax = 2. * max(self.diagnostics.Vx.max(), self.diagnostics.Vy.max(), -self.diagnostics.Vx.min(), -self.diagnostics.Vy.min())
# Vxmin = self.diagnostics.Vx.min()
# Vxmax = self.diagnostics.Vx.max()
#
# Vymin = self.diagnostics.Vy.min()
# Vymax = self.diagnostics.Vy.max()
divVmin = self.diagnostics.divV.min()
divVmax = self.diagnostics.divV.max()
if Vmin == Vmax:
Vmin -= 1.
Vmax += 1.
# if Vxmin == Vxmax:
# Vxmin -= 1.
# Vxmax += 1.
#
# if Vymin == Vymax:
# Vymin -= 1.
# Vymax += 1.
if divVmin == divVmax:
divVmin -= 0.1
divVmax += 0.1
self.VxTicks = np.linspace(Vmin, Vmax, 11, endpoint=True)
self.VyTicks = np.linspace(Vmin, Vmax, 11, endpoint=True)
self.divVTicks = np.linspace(divVmin, divVmax, 11, endpoint=True)
Pmin = min(self.diagnostics.e_magnetic.min(), -self.diagnostics.e_magnetic.max())
Pmax = min(self.diagnostics.e_magnetic.max(), -self.diagnostics.e_magnetic.min())
if Pmin == Pmax:
Pmin -= 1.
Pmax += 1.
self.PTicks = np.linspace(Pmin, Pmax, 11, endpoint=True)
Amin = min(self.diagnostics.A.min(), -self.diagnostics.A.max())
Amax = max(self.diagnostics.A.max(), -self.diagnostics.A.min())
Adif = Amax - Amin
# self.ATicks = np.linspace(Amin + 0.3 * Adif, Amax + 0.2 * Adif, 21, endpoint=True)
self.ATicks = np.linspace(Amin + 0.01 * Adif, Amax - 0.01 * Adif, 31)
def update(self, final=False):
if not (self.iTime == 1 or (self.iTime-1) % self.nPlot == 0 or self.iTime-1 == self.nTime):
return
# self.update_boundaries()
for ckey, cont in self.conts.items():
for coll in cont.collections:
self.axes[ckey].collections.remove(coll)
self.B [0:-1, 0:-1] = self.diagnostics.B [:,:]
self.B [ -1, 0:-1] = self.diagnostics.B [0,:]
self.B [ :, -1] = self.B[:,0]
self.Bx[0:-1, 0:-1] = self.diagnostics.Bx[:,:]
self.Bx[ -1, 0:-1] = self.diagnostics.Bx[0,:]
self.Bx[ :, -1] = self.Bx[:,0]
self.By[0:-1, 0:-1] = self.diagnostics.By[:,:]
self.By[ -1, 0:-1] = self.diagnostics.By[0,:]
self.By[ :, -1] = self.By[:,0]
self.divB[0:-1, 0:-1] = self.diagnostics.divB[:,:]
self.divB[ -1, 0:-1] = self.diagnostics.divB[0,:]
self.divB[ :, -1] = self.divB[:,0]
self.V [0:-1, 0:-1] = self.diagnostics.V [:,:]
self.V [ -1, 0:-1] = self.diagnostics.V [0,:]
self.V [ :, -1] = self.V[:,0]
self.Vx[0:-1, 0:-1] = self.diagnostics.Vx[:,:]
self.Vx[ -1, 0:-1] = self.diagnostics.Vx[0,:]
self.Vx[ :, -1] = self.Vx[:,0]
self.Vy[0:-1, 0:-1] = self.diagnostics.Vy[:,:]
self.Vy[ -1, 0:-1] = self.diagnostics.Vy[0,:]
self.Vy[ :, -1] = self.Vy[:,0]
self.divV[0:-1, 0:-1] = self.diagnostics.divV[:,:]
self.divV[ -1, 0:-1] = self.diagnostics.divV[0,:]
self.divV[ :, -1] = self.divV[:,0]
# self.P[0:-1, 0:-1] = self.diagnostics.P[:,:]
# self.P[ -1, 0:-1] = self.diagnostics.P[0,:]
# self.P[ :, -1] = self.P[:,0]
self.P[0:-1, 0:-1] = self.diagnostics.e_magnetic[:,:]
self.P[ -1, 0:-1] = self.diagnostics.e_magnetic[0,:]
self.P[ :, -1] = self.P[:,0]
self.A[0:-1, 0:-1] = self.diagnostics.A[:,:]
self.A[ -1, 0:-1] = self.diagnostics.A[0,:]
self.A[ :, -1] = self.A[:,0]
Pmin = min(self.diagnostics.e_magnetic.min(), -self.diagnostics.e_magnetic.max())
Pmax = max(self.diagnostics.e_magnetic.max(), -self.diagnostics.e_magnetic.min())
if Pmin == Pmax:
Pmin -= 1.
Pmax += 1.
self.PTicks = np.linspace(Pmin, Pmax, 11, endpoint=True)
self.conts["Bx"] = self.axes["Bx"].contourf(self.x, self.y, self.Bx.T, self.BxTicks, extend='both')
# self.cbars["Bx"] = self.figure.colorbar(self.conts["Bx"], ax=self.axes["Bx"], orientation='vertical', ticks=self.BxTicks)#, format='%0.2E'
self.conts["By"] = self.axes["By"].contourf(self.x, self.y, self.By.T, self.ByTicks, extend='both')
# self.cbars["By"] = self.figure.colorbar(self.conts["By"], ax=self.axes["By"], orientation='vertical', ticks=self.ByTicks)
self.conts["Vx"] = self.axes["Vx"].contourf(self.x, self.y, self.Vx.T, self.VxTicks, extend='both')
# self.cbars["Vx"] = self.figure.colorbar(self.conts["Vx"], ax=self.axes["Vx"], orientation='vertical', ticks=self.VxTicks)
self.conts["Vy"] = self.axes["Vy"].contourf(self.x, self.y, self.Vy.T, self.VyTicks, extend='both')
# self.cbars["Vy"] = self.figure.colorbar(self.conts["Vy"], ax=self.axes["Vy"], orientation='vertical', ticks=self.VyTicks)
# self.conts["P"] = self.axes["P"].contourf(self.x, self.y, self.P.T, self.PTicks, cmap=cm.jet, extend='both')
self.conts["P"] = self.axes["P"].contourf(self.x, self.y, self.P.T, self.PTicks, cmap=cm.jet, extend='both', ticks=self.PTicks)
# self.conts["Babs"] = self.axes["Babs"].contourf(self.x, self.y, self.divV.T, self.divVTicks, cmap=cm.jet)
# self.cbars["Babs"] = self.figure.colorbar(self.conts["Babs"], ax=self.axes["Babs"], orientation='vertical', ticks=self.divVTicks)
# stream_n = 19
# stream_res_fac = 10
# stream_density = stream_n / 30. * stream_res_fac
# self.stream_xstart = np.arange(stream_n, dtype=np.int) * stream_res_fac
# self.stream_ystart = np.zeros(stream_n, dtype=np.int)
#
# self.stream_xstart[0:5 ] -= 5
# self.stream_xstart[5:14] -= 1
# self.stream_xstart[14: ] += 3
### temporarily disabled
# self.axes["Babs"].clear()
# plt.subplot(self.gs[0:10,1:3])
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=1.2, arrowsize=0., color='b')
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=1., arrowsize=0., color='b')
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=1., color='b')
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=.8, arrowsize=0., color='b')
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=.72, arrowsize=0., color='b')
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, density=.6, arrowsize=0., color='b')
# plt.streamplot(self.x, self.y, self.Bx.T, self.By.T, xstart=self.stream_xstart[1:], ystart=self.stream_ystart[1:], density=stream_density, arrowsize=0., color='b')
# self.conts["Bx"] = self.axes["Bx"].contourf(self.x, self.y, self.Bx.T, self.BxTicks, cmap=cm.jet)
# self.conts["By"] = self.axes["By"].contourf(self.x, self.y, self.By.T, self.ByTicks, cmap=cm.jet)
# self.conts["Vx"] = self.axes["Vx"].contourf(self.x, self.y, self.Vx.T, self.VxTicks, cmap=cm.jet)
# self.conts["Vy"] = self.axes["Vy"].contourf(self.x, self.y, self.Vy.T, self.VyTicks, cmap=cm.jet)
# self.cbars["By"].set_clim(self.ByTicks[0], self.ByTicks[-1])
# self.cbars["By"].draw_all()
# self.cbars["Bx"].set_ticks(self.BxTicks)
# self.cbars["By"].set_ticks(self.ByTicks)
# self.cbars["Vx"].set_ticks(self.VxTicks)
# self.cbars["Vy"].set_ticks(self.VyTicks)
# self.cbars["Bx"].set_clim(vmin=self.BxTicks[0], vmax=self.BxTicks[-1])
# self.cbars["Bx"].draw_all()
#
# self.cbars["By"].set_clim(vmin=self.ByTicks[0], vmax=self.ByTicks[-1])
# self.cbars["By"].draw_all()
# self.conts["Babs"] = self.axes["Babs"].contourf(self.x, self.y, self.divV.T, self.divVTicks, cmap=cm.jet)
# self.cbars["Babs"].set_ticks(self.divVTicks)
# self.conts["Vabs"] = self.axes["Vabs"].contourf(self.x, self.y, self.divV.T, 10)
# if len(self.B[self.B == self.B[0,0]]) == len(self.B.ravel()):
# self.conts["Babs"] = self.axes["Babs"].contourf(, 10)
# else:
# self.conts["Babs"] = self.axes["Babs"].contour(self.x, self.y, self.B.T, 10)
#
# self.conts["Vabs"] = self.axes["Vabs"].contourf(self.x, self.y, self.V.T, 20)
# self.axes["Babs"].clear()
# plt.subplot(self.gs[0:2,1:3])
# streamplot(self.x, self.y, self.Bx.T, self.By.T, density=1.5, arrowsize=.5, color='b')
# self.axes["Babs"].clear()
# st_B = Streamlines(self.x, self.y, self.Bx.T, self.By.T, spacing=1)#, res=.25)
# st_B.plot(ax=self.axes["Babs"])
# self.axes["Vabs"].clear()
# plt.subplot(self.gs[2:4,1:3])
# streamplot(self.x, self.y, self.Vx.T, self.Vy.T, density=1, arrowsize=1, color='b')
### temporarily disabled
# self.axes["Vabs"].clear()
# self.axes["Vabs"].quiver(self.x[::2], self.y[::2], self.Bx.T[::2,::2], self.By.T[::2,::2])
# self.conts["Vabs"] = self.axes["Vabs"].contour(self.x, self.y, self.A.T, self.PTicks, cmap=cm.jet, extend='both', ticks=self.PTicks)
# self.conts["Vabs"] = self.axes["Vabs"].contour(self.x, self.y, self.A.T, 40)
# self.conts["Vabs"] = self.axes["Vabs"].contour(self.x, self.y, self.A.T, self.ATicks, cmap=cm.jet)
self.conts["Vabs"] = self.axes["Vabs"].contour(self.x, self.y, self.A.T, self.ATicks, extend='neither')
tStart, tEnd, xStart, xEnd = self.get_timerange()
self.lines["Emag"].set_xdata(self.diagnostics.tGrid[tStart:tEnd])
self.lines["Emag"].set_ydata(self.E_magnetic[tStart:tEnd])
self.axes ["Emag"].relim()
self.axes ["Emag"].autoscale_view()
self.axes ["Emag"].set_xlim((xStart,xEnd))
self.lines["Evel"].set_xdata(self.diagnostics.tGrid[tStart:tEnd])
self.lines["Evel"].set_ydata(self.E_velocity[tStart:tEnd])
self.axes ["Evel"].relim()
self.axes ["Evel"].autoscale_view()
self.axes ["Evel"].set_xlim((xStart,xEnd))
self.lines["E"].set_xdata(self.diagnostics.tGrid[tStart:tEnd])
self.lines["E"].set_ydata(self.energy[tStart:tEnd])
self.axes ["E"].relim()
self.axes ["E"].autoscale_view()
self.axes ["E"].set_xlim((xStart,xEnd))
self.lines["H"].set_xdata(self.diagnostics.tGrid[tStart:tEnd])
self.lines["H"].set_ydata(self.helicity[tStart:tEnd])
self.axes ["H"].relim()
self.axes ["H"].autoscale_view()
self.axes ["H"].set_xlim((xStart,xEnd))
plt.draw()
# self.figure.canvas.draw()
# self.figure.canvas.flush_events()
plt.show(block=final)
plt.pause(.001)
# return self.figure
def add_timepoint(self):
self.E_magnetic [self.iTime] = self.diagnostics.E_magnetic
self.E_velocity [self.iTime] = self.diagnostics.E_velocity
if self.diagnostics.plot_energy:
self.energy [self.iTime] = self.diagnostics.energy
else:
self.energy [self.iTime] = self.diagnostics.E_error
if self.diagnostics.plot_helicity:
self.helicity [self.iTime] = self.diagnostics.helicity
else:
self.helicity [self.iTime] = self.diagnostics.H_error
# self.L1_magnetic[self.iTime] = self.diagnostics.L1_magnetic_error
# self.L1_velocity[self.iTime] = self.diagnostics.L1_velocity_error
# self.L2_magnetic[self.iTime] = self.diagnostics.L2_magnetic_error
# self.L2_velocity[self.iTime] = self.diagnostics.L2_velocity_error
self.title.set_text('t = %1.2f' % (self.diagnostics.tGrid[self.iTime]))
self.iTime += 1
def get_timerange(self):
tStart = self.iTime - (self.nTime+1)
tEnd = self.iTime
if tStart < 0:
tStart = 0
xStart = self.diagnostics.tGrid[tStart]
xEnd = self.diagnostics.tGrid[tStart+self.nTime]
return tStart, tEnd, xStart, xEnd