def J_video(J, n, saveFile = None):
"""Given current density J, plot quiver animation"""
Jn = J[n]
def update_quiver(num,Q):
real_Jn = (Jn*np.e**(-1*1j*num/10.0)).real
Q.set_UVC(real_Jn[:,:,0], real_Jn[:,:,1])
return Q,
# py.quiver(Jn[:,:,0], Jn[:,:,1])
fig,ax = py.subplots(1,1)
im2 = draw_circle()
Q = ax.quiver(Jn[:,:,0], Jn[:,:,1],color='blue',scale=30000)
anim = animation.FuncAnimation(fig, update_quiver, fargs=(Q,), interval=10, blit = False)
if saveFile:
ani.save(saveFile)
py.title("Current Density")
py.figure(2)
x,y = np.meshgrid(np.arange(120), np.arange(120))
U = Jn[:,:,0].real
V = Jn[:,:,1].real
py.streamplot(x,y,U,V)
draw_circle()
py.show()
def main():
# For timing purposes
start = time.time()
pr = cProfile.Profile()
pr.enable()
# Ex 5.21
q1 = [0.05, 0.0]
q2 = [-0.05, 0.0]
a = -0.5
b = 0.5
num_squares = 100
x = np.linspace(a, b, num_squares)
xcoor, ycoor = np.meshgrid(x, x)
phi = np.zeros((num_squares, num_squares))
E = np.zeros((num_squares, num_squares))
for i in range(num_squares):
for j in range(num_squares):
r1 = np.sqrt((xcoor[i][j] - q1[0])**2 + (ycoor[i][j] - q1[1])**2)
r2 = np.sqrt((xcoor[i][j] - q2[0])**2 + (ycoor[i][j] - q2[1])**2)
phi[i][j] = (1 / 4 * np.pi * cons.epsilon_0) * (1 / r1 - 1 / r2)
plt.imshow(phi)
plt.title("electric potential of two particles")
plt.colorbar()
plt.show()
Ex, Ey = np.gradient(phi)
# Distance formula
def R(x, y):
return np.sqrt(x**2 + y**2)
# Potential for every point
q1x, q1y = xcoor - q1[0], ycoor - q1[1]
q2x, q2y = xcoor - q2[0], ycoor - q2[1]
# Electric field via partial derivative
h = 1e-5
def V(q, x, y):
return q * (1 / 4 * np.pi * cons.epsilon_0) * (1 / R(x, y))
vx1 = (V(1, (q1x + h / 2), q1y) - V(1, (q1x - h / 2), q1y)) / h
vy1 = (V(1, q1x, (q1y + h / 2)) - V(1, q1x, (q1y - h / 2))) / h
vx2 = (V(-1, (q2x + h / 2), q2y) - V(-1, (q2x - h / 2), q2y)) / h
vy2 = (V(-1, q2x, (q2y + h / 2)) - V(-1, q2x, (q2y - h / 2))) / h
Vx = vx1 + vx2
Vy = vy1 + vy2
streamplot(xcoor, ycoor, Vx, Vy, density=2.5, linewidth=0.5, arrowsize=0.8)
plt.title("Electric Field of a Dipole")
plt.show()
pr.disable()
# pr.print_stats(sort='time')
end = time.time()
print(f"Program took :{end - start} seconds to run")
def Bsf(self):
if not hasattr(self, 'Br'):
self.Bfeild()
pl.streamplot(self.r,
self.z,
self.Br.T,
self.Bz.T,
color=self.Br.T,
cmap=pl.cm.RdBu)
pl.clim([-1.5, 1.5])
def plot_streamlines(xin,yin):
x = np.linspace(xin[0], xin[-1], 64)
y = np.linspace(yin[0], yin[-1], 64)
X,Y = np.meshgrid(x,y)
relX = (X - xin[0]) / (xin[-1] - xin[0])
relY = (Y - xin[0]) / (yin[-1] - yin[0])
A = 2*pi
B = pi
U = 1 - 4 * np.cos(B*relY) * np.sin(A*relX)**2 * np.sin(B*relY)
V = 4 * np.cos(A*relX) * np.sin(B*relY)**2 * np.sin(A*relX)
S = np.sqrt(U*U + V*V)
pl.streamplot(X, Y, U, V,
linewidth=np.sqrt(S),
color="lightsteelblue",
density=1.1,
minlength=0.9,
arrowstyle='-')
def plot_B_streamlines(mi, mq, mu, imax, imin):
'''
Plotting B-field lines on top of Stokes I map
'''
import pylab as plt
import os
if np.shape(np.shape(mi))[0] == 1:
return print('********** NO PLOT: Maps must be 2D arrays ************'
), os.system('afplay /System/Library/Sounds/Sosumi.aiff')
nx = np.shape(mi)[0]
ny = np.shape(mi)[1]
x = np.linspace(0, nx - 1, nx)
y = np.linspace(0, ny - 1, ny)
xp = x
yp = y
y2, x2 = np.meshgrid(xp, yp, indexing='ij')
psi = -0.5 * np.arctan2(mu, mq)
x3 = np.cos(psi)
y3 = np.sin(psi)
plt.figure(10)
plt.contourf(mi,
levels=np.arange(imin, imax, (imax - imin) / 500.),
extent=[0, nx, 0, ny])
plt.colorbar()
plt.streamplot(x2,
y2,
x3,
y3,
density=[3, 3],
color='w',
arrowstyle='-',
linewidth=0.5)
plt.show()
return
import pylab, numpy as np import math xvalues, yvalues = pylab.meshgrid(np.arange(-4,4, 0.1), np.arange(-4,4,0.1)) vx = yvalues*np.cos(xvalues*yvalues) vy = xvalues*np.cos(xvalues*yvalues) pylab.streamplot(xvalues, yvalues, vx, vy) pylab.show()
np.set_printoptions(threshold='nan')
magU = np.sqrt(U*U+V*V)
cmap = py.cm.get_cmap('coolwarm')
lmax = 3.2 # (int(magU.max()*10) + 1.)/10
lev = np.linspace(0, lmax, 11)
CF = py.contourf(x, y, magU, cmap=cmap, levels=lev)
# streamplot version (need matplotlib 1.2.1, use only evenly grid)
from matplotlib.mlab import griddata
interp = 'linear' # 'nn'
N = 50
xi = np.linspace(0, 1, 2*N)
yi = np.linspace(0, .5, 4*N)
U = griddata(X0, Y0, U0, xi, yi, interp=interp)
V = griddata(X0, Y0, V0, xi, yi, interp=interp)
py.streamplot(xi, yi, U, V, color='k', density=0.89, minlength=.2, arrowstyle='->')
py.text(-.07, .4, r'$u_{i1}$', fontsize=10)
py.xlabel(r'$x$', labelpad=-3)
py.ylabel(r'$z$', labelpad=-3, rotation=0)
py.xlim(0,1)
py.ylim(0,0.5)
ax = py.axes()
ax.set_aspect('equal')
ax.set_yticks([0,0.5])
ax.set_xticks([0,1])
from mpl_toolkits.axes_grid1 import make_axes_locatable
divider = make_axes_locatable(py.axes())
cax = divider.append_axes("right", "5%", pad="5%")
py.colorbar(CF, cax=cax)
density.T,
100,
norm=colors.SymLogNorm(linthresh=density.max() / 20,
vmin=density_min,
vmax=density_max),
cmap='bwr')
# pl.colorbar()
pl.title(r'Time = ' + "%.2f" % (time_array[start_index + file_number]) +
" ps")
pl.streamplot(x[:, 0],
y[0, :],
j_x_m,
j_y_m,
density=2,
color='k',
linewidth=2.5,
arrowsize=3,
transform=rot + base)
pl.xlim([0, 5])
pl.ylim([-1.25, 0])
# print (j_x)
#radius = 0.1666
#theta = np.arange(0., 2*np.pi, 0.01)
#pl.plot(radius*np.cos(theta), radius*np.sin(theta), color = 'k', alpha = 0.3)
#pl.xlim([q1[0], q1[-1]])
#pl.ylim([q2[0], q2[-1]])
def View2D(g, option=0):
# plot and check the field
fig = figure(num=2, figsize=(16, 6))
# fig.suptitle('Efit Analysis', fontsize=20)
ax = subplot2grid((3, 3), (0, 0), colspan=1, rowspan=3)
nlev = 100
minf = np.min(g.psi)
maxf = np.max(g.psi)
levels = np.arange(
np.float(nlev)) * (maxf - minf) / np.float(nlev - 1) + minf
ax.contour(g.r, g.z, g.psi, levels=levels)
# ax.set_xlim([0,6])
ax.set_xlabel('R')
ax.set_ylabel('Z')
ax.yaxis.label.set_rotation('horizontal')
ax.set_aspect('equal')
# fig.suptitle('Efit Analysis', fontsize=20)
# title('Efit Analysis', fontsize=20)
text(0.5,
1.08,
'Efit Analysis',
horizontalalignment='center',
fontsize=20,
transform=ax.transAxes)
draw()
if option == 0: show(block=False)
plot(g.xlim, g.ylim, 'g-')
draw()
csb = contour(g.r, g.z, g.psi, levels=[g.sibdry])
clabel(
csb,
[g.sibdry], # label the level
inline=1,
fmt='%9.6f',
fontsize=14)
csb.collections[0].set_label('boundary')
# pl1=plot(g.rbdry,g.zbdry,'b-',marker='x', label='$\psi=$'+ np.str(g.sibdry))
# legend(bbox_to_anchor=(0., 1.05, 1., .105), loc='upper left')
draw()
# fig.set_tight_layout(True)
# show(block=False)
# Function fpol and qpsi are given between simagx (psi on the axis) and sibdry (
# psi on limiter or separatrix). So the toroidal field (fpol/R) and the q profile are within these boundaries
npsigrid = old_div(
np.arange(np.size(g.pres)).astype(float), (np.size(g.pres) - 1))
fpsi = np.zeros((2, np.size(g.fpol)), np.float64)
fpsi[0, :] = (g.simagx + npsigrid * (g.sibdry - g.simagx))
fpsi[1, :] = g.fpol
boundary = np.array([g.xlim, g.ylim])
rz_grid = Bunch(
nr=g.nx,
nz=g.ny, # Number of grid points
r=g.r[:, 0],
z=g.z[0, :], # R and Z as 1D arrays
simagx=g.simagx,
sibdry=g.sibdry, # Range of psi
psi=g.psi, # Poloidal flux in Weber/rad on grid points
npsigrid=npsigrid, # Normalised psi grid for fpol, pres and qpsi
fpol=g.fpol, # Poloidal current function on uniform flux grid
pres=g.pres, # Plasma pressure in nt/m^2 on uniform flux grid
qpsi=g.qpsi, # q values on uniform flux grid
nlim=g.nlim,
rlim=g.xlim,
zlim=g.ylim) # Wall boundary
critical = analyse_equil(g.psi, g.r[:, 0], g.z[0, :])
n_opoint = critical.n_opoint
n_xpoint = critical.n_xpoint
primary_opt = critical.primary_opt
inner_sep = critical.inner_sep
opt_ri = critical.opt_ri
opt_zi = critical.opt_zi
opt_f = critical.opt_f
xpt_ri = critical.xpt_ri
xpt_zi = critical.xpt_zi
xpt_f = critical.xpt_f
psi_inner = 0.6
psi_outer = 0.8,
nrad = 68
npol = 64
rad_peaking = [0.0]
pol_peaking = [0.0]
parweight = 0.0
boundary = np.array([rz_grid.rlim, rz_grid.zlim])
# Psi normalisation factors
faxis = critical.opt_f[critical.primary_opt]
fnorm = critical.xpt_f[critical.inner_sep] - critical.opt_f[
critical.primary_opt]
# From normalised psi, get range of f
f_inner = faxis + np.min(psi_inner) * fnorm
f_outer = faxis + np.max(psi_outer) * fnorm
fvals = radial_grid(nrad, f_inner, f_outer, 1, 1, [xpt_f[inner_sep]],
rad_peaking)
## Create a starting surface
#sind = np.int(nrad / 2)
#start_f = 0. #fvals[sind]
# Find where we have rational surfaces
# define an interpolation of psi(q)
psiq = np.arange(np.float(g.qpsi.size)) * (
g.sibdry - g.simagx) / np.float(g.qpsi.size - 1) + g.simagx
fpsiq = interpolate.interp1d(g.qpsi, psiq)
# Find how many rational surfaces we have within the boundary and locate x,y position of curves
nmax = g.qpsi.max().astype(int)
nmin = g.qpsi.min().astype(int)
nr = np.arange(nmin + 1, nmax + 1)
psi = fpsiq(nr)
cs = contour(g.r, g.z, g.psi, levels=psi)
labels = ['$q=' + np.str(x) + '$\n' for x in range(nr[0], nr[-1] + 1)]
for i in range(len(labels)):
cs.collections[i].set_label(labels[i])
style = ['--', ':', '--', ':', '-.']
# gca().set_color_cycle(col)
# proxy = [Rectangle((0,0),1,1, fc=col[:i+1])
# for pc in cs.collections]
#
# l2=legend(proxy, textstr[:i)
#
# gca().add_artist(l1)
x = []
y = []
for i in range(psi.size):
xx, yy = surface(cs, i, psi[i], opt_ri[primary_opt],
opt_zi[primary_opt], style, option)
x.append(xx)
y.append(yy)
#props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
#textstr = ['$q='+np.str(x)+'$\n' for x in range(psi.size)]
#
#ax.text(0.85, 1.15, ''.join(textstr), transform=ax.transAxes, fontsize=14,
#verticalalignment='top', bbox=props)
legend(bbox_to_anchor=(-.8, 1), loc='upper left', borderaxespad=0.)
draw()
#compute B - field
Bp = np.gradient(g.psi)
dr = old_div((np.max(g.r[:, 0]) - np.min(g.r[:, 0])), np.size(g.r[:, 0]))
dz = old_div((np.max(g.z[0, :]) - np.min(g.z[0, :])), np.size(g.z[0, :]))
dpsidr = Bp[0]
dpsidz = Bp[1]
Br = -dpsidz / dz / g.r
Bz = dpsidr / dr / g.r
Bprz = np.sqrt(Br * Br + Bz * Bz)
# plot Bp field
if option == 0:
sm = query_yes_no("Overplot vector field")
if sm == 1:
lw = 50 * Bprz / Bprz.max()
streamplot(
g.r.T,
g.z.T,
Br.T,
Bz.T,
color=Bprz,
linewidth=2,
cmap=cm.bone) #density =[.5, 1], color='k')#, linewidth=lw)
draw()
# plot toroidal field
ax = subplot2grid((3, 3), (0, 1), colspan=2, rowspan=1)
ax.plot(psiq, fpsi[1, :])
#ax.set_xlim([0,6])
#ax.set_xlabel('$\psi$')
ax.set_ylabel('$fpol$')
ax.yaxis.label.set_size(20)
#ax.xaxis.label.set_size(20)
ax.set_xticks([])
ax.yaxis.label.set_rotation('horizontal')
#ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 20
#props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
#ax.text(0.85, 0.95, '$B_t$', transform=ax.transAxes, fontsize=14,
# verticalalignment='top', bbox=props)
#
draw()
# plot pressure
ax = subplot2grid((3, 3), (1, 1), colspan=2, rowspan=1)
ax.plot(psiq, g.pres)
#ax.set_xlim([0,6])
#ax.set_xlabel('$\psi$')
ax.set_ylabel('$P$')
ax.yaxis.label.set_size(20)
#ax.xaxis.label.set_size(20)
ax.set_xticks([])
ax.yaxis.label.set_rotation('horizontal')
#ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 20
#props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
#ax.text(0.85, 0.95, '$B_t$', transform=ax.transAxes, fontsize=14,
# verticalalignment='top', bbox=props)
#
draw()
# plot qpsi
ax = subplot2grid((3, 3), (2, 1), colspan=2, rowspan=1)
ax.plot(psiq, g.qpsi)
ax.set_xlabel('$\psi$')
ax.set_ylabel('$q$')
ax.yaxis.label.set_rotation('horizontal')
ax.yaxis.label.set_size(20)
ax.xaxis.label.set_size(20)
ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 20
tick_params(\
axis='x', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='on', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
labelbottom='on')
draw()
# Compute and draw Jpar
#
# MU = 4.e-7*np.pi
#
# jpar0 = - Bxy * fprime / MU - Rxy*Btxy * dpdpsi / Bxy
#
# fig.set_tight_layout(True)
fig.subplots_adjust(left=0.2, top=0.9, hspace=0.1, wspace=0.5)
draw()
if option == 0: show(block=False)
if option != 0:
return Br, Bz, x, y, psi
print("spsolve() time = %1.6s" % (time.time() - start_time))
#==============================================================================
#==============================================================================
# Calculating the gradient of the solution
vx = -(Dx_2d * u.ravel()).reshape(Ny, Nx)
vy = -(Dy_2d * u.ravel()).reshape(Ny, Nx)
v = np.sqrt(vx**2 + vy**2)
#==============================================================================
#//////////////////////////////////////////////////////////////////////////////
#//////////////////////////////////////////////////////////////////////////////
#//////////////////////////////////////////////////////////////////////////////
#==============================================================================
# Plot solution
py.figure(figsize=(12, 7))
my_contourf(x, y, u, r'$u\,(x,y)$')
# Plotting the gradient
py.figure(figsize=(12, 7))
my_contourf(x, y, v, r'$|-\nabla u\,(x,y)|$', 'afmhot')
py.streamplot(x, y, vx, vy, color='w', density=1.2, linewidth=0.4)
# thin_factor = 10
# skip = (slice(None, None, thin_factor), slice(None, None, thin_factor))
# py.quiver(X[skip],Y[skip],vx[skip]/v[skip],vy[skip]/v[skip],color = 'w')
#==============================================================================
delta_n = density - np.mean(density)
pl.contourf(q1,
q2,
delta_n,
200,
norm=colors.SymLogNorm(linthresh=delta_n.max() / 20),
cmap='bwr',
transform=rot + base)
pl.streamplot(q1,
q2,
vel_drift_x,
vel_drift_y,
density=1.4 * l,
color='black',
linewidth=1,
arrowsize=1.5,
transform=rot + base)
pl.yticks([0, 5.])
pl.xticks([])
pl.xlim([q1[0], q1[-1]])
pl.ylim([q2[0], q2[-1]])
pl.gca().set_aspect('equal')
#pl.contourf(q1_meshgrid, q2_meshgrid, density.T, 100, cmap='bwr')
#pl.title(r'Time = ' + "%.2f"%(time_array[file_number]) + " ps")
pl.contourf(x,
y,
density.T,
100,
norm=MidpointNormalize(midpoint=0,
vmin=density_min,
vmax=density_max),
cmap='bwr')
pl.colorbar()
pl.title(r'Time = ' + "%.2f" % (time_array[start_index + file_number]) +
" ps")
pl.streamplot(x[:, 0],
y[0, :],
j_x,
j_y,
density=2,
color='k',
linewidth=0.7,
arrowsize=1)
# print (j_x)
pl.xlim([q1[0], q1[-1]])
pl.ylim([q2[0], q2[-1]])
pl.gca().set_aspect('equal')
pl.xlabel(r'$x\;(\mu \mathrm{m})$')
pl.ylabel(r'$y\;(\mu \mathrm{m})$')
#pl.suptitle('$\\tau_\mathrm{mc} = \infty$, $\\tau_\mathrm{mr} = \infty$')
pl.savefig('images/dump_' + '%06d' % (start_index + file_number) + '.png')
pl.clf()
def velocity_image(sim,
width="10 kpc",
vector_color='black',
edgecolor='black',
vector_resolution=40,
scale=None,
mode='quiver',
key_x=0.3,
key_y=0.9,
key_color='white',
key_length="100 km s**-1",
density=1.0,
**kwargs):
"""
Make an SPH image of the given simulation with velocity vectors overlaid on top.
For a description of additional keyword arguments see :func:`~pynbody.plot.sph.image`,
or see the `tutorial <http://pynbody.github.io/pynbody/tutorials/pictures.html#velocity-vectors>`_.
**Keyword arguments:**
*vector_color* (black): The color for the velocity vectors
*edgecolor* (black): edge color used for the lines - using a color
other than black for the *vector_color* and a black *edgecolor*
can result in poor readability in pdfs
*vector_resolution* (40): How many vectors in each dimension (default is 40x40)
*scale* (None): The length of a vector that would result in a displayed length of the
figure width/height.
*mode* ('quiver'): make a 'quiver' or 'stream' plot
*key_x* (0.3): Display x (width) position for the vector key (quiver mode only)
*key_y* (0.9): Display y (height) position for the vector key (quiver mode only)
*key_color* (white): Color for the vector key (quiver mode only)
*key_length* (100 km/s): Velocity to use for the vector key (quiver mode only)
*density* (1.0): Density of stream lines (stream mode only)
"""
subplot = kwargs.get('subplot', False)
if subplot:
p = subplot
else:
import matplotlib.pylab as p
vx = image(sim,
qty='vx',
width=width,
log=False,
resolution=vector_resolution,
noplot=True)
vy = image(sim,
qty='vy',
width=width,
log=False,
resolution=vector_resolution,
noplot=True)
key_unit = _units.Unit(key_length)
if isinstance(width, str) or issubclass(width.__class__, _units.UnitBase):
if isinstance(width, str):
width = _units.Unit(width)
width = width.in_units(sim['pos'].units, **sim.conversion_context())
width = float(width)
X, Y = np.meshgrid(
np.arange(-width / 2, width / 2, width / vector_resolution),
np.arange(-width / 2, width / 2, width / vector_resolution))
im = image(sim, width=width, **kwargs)
if mode == 'quiver':
if scale is None:
Q = p.quiver(X, Y, vx, vy, color=vector_color, edgecolor=edgecolor)
else:
Q = p.quiver(X,
Y,
vx,
vy,
scale=_units.Unit(scale).in_units(sim['vel'].units),
color=vector_color,
edgecolor=edgecolor)
p.quiverkey(Q,
key_x,
key_y,
key_unit.in_units(sim['vel'].units,
**sim.conversion_context()),
r"$\mathbf{" + key_unit.latex() + "}$",
labelcolor=key_color,
color=key_color,
fontproperties={'size': 16})
elif mode == 'stream':
Q = p.streamplot(X, Y, vx, vy, color=vector_color, density=density)
return im
import pylab as p
# Make an x,z grid
grid = np.linspace(-6,6,200)
x, z = np.meshgrid(grid,grid)
mu=4*np.pi # dipole strength (in z-direction)
# and the 2D cross section of the potential (scalar field)
phi = mu * z / (4 * np.pi * (x**2+z**2)**(3/2))
# End initialization
# Start contour plot
from matplotlib import colors
p.figure(figsize=(6,6))
heights = np.linspace(-0.6,0.6,7)
CS = p.contour(x,z,phi,heights,colors='k')
p.clabel(CS, inline=1, fontsize=10,fmt='%3.1f')
p.xlabel(r'$x$')
p.ylabel(r'$z$')
# End contour plot
# Start fieldline plot
Fx = mu / (4 * np.pi * (x**2+z**2)**(5/2)) * 2*x*z
Fz = mu / (4 * np.pi * (x**2+z**2)**(5/2)) * (z**2-x**2)
p.streamplot(x,z,Fx,Fz)
# End fieldline plot
CS = p.contour(x,z,phi,heights,colors='k')
p.clabel(CS, inline=1, fontsize=10,fmt='%3.1f')
p.savefig('dipole_fieldplot.png')
#p.show()
# contor grid
res = 0.4
xlim, zlim = ([-10,10], [-5,10])
dx, dz = (xlim[1]-xlim[0], zlim[1]-zlim[0])
nx, nz = (int(dx/res), int(dz/res))
x = np.linspace(xlim[0], xlim[1], nx)
z = np.linspace(zlim[0], zlim[1], nz)
xm, zm = np.meshgrid(x, z)
feild = np.zeros((nz,nx))
Bx = np.zeros((nz,nx))
Bz = np.zeros((nz,nx))
for i in range(nz):
for j in range(nx):
B = Bcoil(coil, [xm[i,j],zm[i,j]])
Bx[i,j] = B[0]
Bz[i,j] = B[2]
#feild[i,j] = B[2]#sum(B*B)**0.5
feild[i,j] = sum(B*B)**0.5
pl.figure(figsize=(12,12))
V = np.linspace(0,2,30)
#pl.contour(xm, zm, feild,V)
pl.plot(xm,zm,'k.')
pl.quiver(xm, zm, Bx, Bz)
pl.streamplot(xm, zm, Bx, Bz)
pl.axis('equal')
pl.xlim(xlim)
pl.ylim(zlim)
CS = py.contour(xi, yi, Fi, levels=levels, colors='k', linewidths=linewidth)
clabels = py.clabel(CS, levels,
inline=True,
use_clabeltext=True,
fmt='%g',
manual=labelpos,
fontsize=fontsize)
[ txt.set_backgroundcolor('white') for txt in clabels ]
[ txt.set_bbox(dict(facecolor='white', edgecolor='none', pad=0)) for txt in clabels ]
### Add a streamplot for the vector field
# NB: py.streamplot relies on evenly grid
if len(F.shape) > 1:
py.streamplot(xi, yi, Ui, Vi,
density=0.89,
minlength=.2,
arrowstyle='->',
color='k',
linewidth=1)
py.text(-.05, .4, r'$\displaystyle %s$' % args.latex)
py.xlabel(r'$x$', labelpad=-5)
py.ylabel(r'$y$', labelpad=-5, rotation=0)
py.xlim(xmin, xmax)
py.ylim(ymin, ymax)
ax = py.axes()
ax.set_aspect('equal')
ax.set_yticks([xmin, xmax])
ax.set_xticks([ymin, ymax])
py.tick_params(axis='both', direction='out')
py.savefig(args.pdffile, bbox_inches='tight', transparent=True)
import numpy as np
import pylab as pl
"""
A = np.array([[-1, 2], [2, -2]])
eig = np.linalg.eig(A)[0]
eigV = np.linalg.eig(A)[1]
x, y = np.meshgrid(np.arange(0, 3, 0.1), np.arange(0, 3, 0.1))
xv = -x + 2*y
yv = 2*x - 2*y
pl.streamplot(x, y, xv, yv)
pl.plot([0,0.7882], [0, 0.6154], 'r')
#######################
# LATER ON IN LECTURE #
#######################
from sympy import symbols, Matrix
a, b, c, d, x, y = symbols('a b c d x y')
# a, b, c, d > 0
dx = a*x - b*x*y
dy = -c*y + d*x*y
J = Matrix(
[[dx.diff(x), dx.diff(y)], # column 1
[dy.diff(x), dy.diff(y)]]) # column 2
density = density - density_bg
density_min = np.min(density)
density_max = np.max(density)
#plot_grid(x[::5, ::5], y[::5, ::5], alpha=0.5)
#pl.contourf(x, y, density.T, 100, cmap='bwr')
#pl.contourf(x, y, density.T, 100, norm=MidpointNormalize(midpoint=0, vmin=density_min, vmax=density_max), cmap='bwr')
#pl.contourf(x, y, density.T, 1000, norm=colors.DivergingNorm(vcenter=0, vmin=density_min, vmax=density_max), cmap='bwr')
#pl.colorbar()
#pl.title(r'Time = ' + "%.2f"%(time_array[start_index+file_number]) + " ps")
pl.streamplot(x[:, 0],
y[0, :],
vel_drift_x,
vel_drift_y,
density=4.,
color='k',
linewidth=1.5,
arrowsize=1.2)
#pl.xlim([q1[0], q1[-1]])
#pl.ylim([q2[0], q2[-1]])
pl.xlim([0.5, 1.5])
pl.ylim([q2[0], 0.625])
pl.gca().spines['right'].set_visible(False)
pl.gca().spines['top'].set_visible(False)
pl.gca().spines['bottom'].set_visible(False)
pl.gca().spines['left'].set_visible(False)
M = X.max()
X = np.reshape(X,(N,N)) * L/M
Y = np.reshape(Y,(N,N)) * L/M
x,y = X[0,:], Y[:,0]
U = np.reshape(U/rho,(N,N)) / k
V = np.reshape(V/rho,(N,N)) / k
return U,V,x,y
data = py.loadtxt(sys.argv[2]).T
U,V,x,y = load_data()
magU = np.sqrt(U*U+V*V)
cmap = py.cm.get_cmap('coolwarm')
CF = py.contourf(x, y, magU, cmap=cmap)
py.colorbar(CF, use_gridspec=True)
# streamplot version (need matplotlib 1.2.1, use only evenly grid)
py.streamplot(x, y, U, V, color='k', density=.8, minlength=.4)
py.text(-.06, .37, r'$\displaystyle\frac{u_i}k$', fontsize=11)
py.xlabel(r'$x$', labelpad=-5)
py.ylabel(r'$z$', labelpad=-5, rotation=0)
py.xlim(0,0.5)
py.ylim(0,0.5)
ax = py.axes()
ax.set_aspect('equal')
ax.set_yticks([0,0.5])
ax.set_xticks([0,0.5])
py.tick_params(axis='both', direction='out')
py.savefig(sys.argv[3], bbox_inches='tight')
def velocity_image(sim,
width="10 kpc",
vector_color='black',
edgecolor='black',
quiverkey_bg_color=None,
vector_resolution=40,
scale=None,
mode='quiver',
key_x=0.3,
key_y=0.9,
key_color='white',
key_length="100 km s**-1",
quiverkey=True,
density=1.0,
vector_qty='vel',
**kwargs):
"""
Make an SPH image of the given simulation with velocity vectors overlaid on top.
For a description of additional keyword arguments see :func:`~pynbody.plot.sph.image`,
or see the `tutorial <http://pynbody.github.io/pynbody/tutorials/pictures.html#velocity-vectors>`_.
**Keyword arguments:**
*vector_color* (black): The color for the velocity vectors
*edgecolor* (black): edge color used for the lines - using a color
other than black for the *vector_color* and a black *edgecolor*
can result in poor readability in pdfs
*vector_resolution* (40): How many vectors in each dimension (default is 40x40)
*quiverkey_bg_color* (none): The color for the legend (scale) background
*scale* (None): The length of a vector that would result in a displayed length of the
figure width/height.
*mode* ('quiver'): make a 'quiver' or 'stream' plot
*key_x* (0.3): Display x (width) position for the vector key (quiver mode only)
*key_y* (0.9): Display y (height) position for the vector key (quiver mode only)
*key_color* (white): Color for the vector key (quiver mode only)
*key_length* (100 km/s): Velocity to use for the vector key (quiver mode only)
*density* (1.0): Density of stream lines (stream mode only)
*quiverkey* (True): Whether or not to inset the key
*vector_qty* ('vel'): The name of the vector field to plot
"""
subplot = kwargs.get('subplot', False)
av_z = kwargs.get('av_z', None)
if subplot:
p = subplot
else:
import matplotlib.pylab as p
vx_name, vy_name, _ = sim._array_name_ND_to_1D(vector_qty)
vx = image(sim,
qty=vx_name,
width=width,
log=False,
resolution=vector_resolution,
noplot=True,
av_z=av_z)
vy = image(sim,
qty=vy_name,
width=width,
log=False,
resolution=vector_resolution,
noplot=True,
av_z=av_z)
key_unit = _units.Unit(key_length)
if isinstance(width, str) or issubclass(width.__class__, _units.UnitBase):
if isinstance(width, str):
width = _units.Unit(width)
width = width.in_units(sim['pos'].units, **sim.conversion_context())
width = float(width)
pixel_size = width / vector_resolution
X, Y = np.meshgrid(
np.arange(-width / 2 + pixel_size / 2, width / 2 + pixel_size / 2,
pixel_size),
np.arange(-width / 2 + pixel_size / 2, width / 2 + pixel_size / 2,
pixel_size))
im = image(sim, width=width, **kwargs)
if mode == 'quiver':
if scale is None:
Q = p.quiver(X, Y, vx, vy, color=vector_color, edgecolor=edgecolor)
else:
Q = p.quiver(X,
Y,
vx,
vy,
scale=_units.Unit(scale).in_units(sim['vel'].units),
color=vector_color,
edgecolor=edgecolor)
if quiverkey:
qk = p.quiverkey(Q,
key_x,
key_y,
key_unit.in_units(sim['vel'].units,
**sim.conversion_context()),
r"$\mathbf{" + key_unit.latex() + "}$",
labelcolor=key_color,
color=key_color,
fontproperties={'size': 24})
if quiverkey_bg_color is not None:
qk.text.set_backgroundcolor(quiverkey_bg_color)
elif mode == 'stream':
Q = p.streamplot(X, Y, vx, vy, color=vector_color, density=density)
# RS - if a axis object is passed in, use the right limit call
if subplot:
p.set_xlim(-width / 2, width / 2)
p.set_ylim(-width / 2, width / 2)
else:
p.xlim(-width / 2, width / 2)
p.ylim(-width / 2, width / 2)
return im
r = np.linspace(rlim[0], rlim[1], nr)
z = np.linspace(zlim[0], zlim[1], nz)
rm, zm = np.meshgrid(r, z)
Br = np.zeros((nz, nr))
Bz = np.zeros((nz, nr))
Bmag = np.zeros((nz, nr))
for i in range(nz):
for j in range(nr):
B = Bcoil(mu_o, coil, [rm[i, j], zm[i, j]])
Br[i, j] = B[0]
Bz[i, j] = B[1]
Bmag[i, j] = sum(B * B)**0.5
V = np.linspace(0, 10, 30)
pl.streamplot(rm, zm, Br, Bz, density=[2 * nr / 25, 2 * nz / 25])
pl.contour(rm, zm, Bmag, levels=[5 * np.min(Bmag)])
pl.axis('equal')
pl.xlim(rlim)
pl.ylim(zlim)
if I > 0:
plasma_dir = 'pos'
elif I == 0:
plasma_dir = 'off'
else:
plasma_dir = 'neg'
#pl.savefig(fig_path+config+'_flux_conv_'+plasma_dir+'.png', dpi=300)
fig = pl.figure(figsize=(9, 12))
ax = fig.add_subplot(111)
mu = lagrange_multipliers[:, :, 0]
mu_ee = lagrange_multipliers[:, :, 1]
T_ee = lagrange_multipliers[:, :, 2]
vel_drift_x = lagrange_multipliers[:, :, 3]
vel_drift_y = lagrange_multipliers[:, :, 4]
print(vel_drift_x.shape)
print(density.shape)
pl.contourf(q1_meshgrid, q2_meshgrid, density.T, 100, cmap='bwr')
pl.title(r'Time = ' + "%.2f" % (time_array[file_number]) + " ps")
pl.streamplot(q1,
q2,
vel_drift_x,
vel_drift_y,
density=2,
color='k',
linewidth=0.7,
arrowsize=1)
pl.xlim([q1[0], q1[-1]])
pl.ylim([q2[0], q2[-1]])
pl.gca().set_aspect('equal')
pl.xlabel(r'$x\;(\mu \mathrm{m})$')
pl.ylabel(r'$y\;(\mu \mathrm{m})$')
pl.suptitle('$\\tau_\mathrm{mc} = 0.2$ ps, $\\tau_\mathrm{mr} = 1.0$ ps')
pl.savefig('images/dump_' + '%06d' % file_number + '.png')
pl.clf()
ax = fig.gca()
if value == 'Density':
data = rawData[:,:,0,t]
if value == 'Velocity':
Vx = rawData[:,:,2,t]/rawData[:,:,0,t] # x velocity
Vy = rawData[:,:,1,t]/rawData[:,:,0,t] # y velocity (seem reversed cause of poor definitions in earlier code
data = np.sqrt(Vx*Vx+Vy*Vy) #total speed
# print data
X, Y = np.linspace(-0.5,0.5,Nx), np.linspace(0,5,Ny) ## CHANGE THIS MANUALLY FOR DIFFERENT SYSTEMS so far
if value =='Density':
plt.imshow(data, origin = 'lower',cmap = colormap)
if value == 'Velocity':
plt.streamplot(X, Y, Vx, Vy ,color='k', linewidth=2)
plt.tick_params(labelsize=tickSize)
plt.title(title, fontsize = titleSize)
if value == 'Density':
plt.xlabel('X Cell Number', fontsize = labelSize)
plt.ylabel('Y Cell Number', fontsize = labelSize)
plt.xlim([3,Nx-2])
plt.ylim([3,Ny-2])
m = cm.ScalarMappable(cmap= colormap)
m.set_array(data)
plt.colorbar(m)
if value == 'Velocity':
plt.xlabel('X Position', fontsize = labelSize)
plt.ylabel('Y Position', fontsize = labelSize)
plt.xlim([min(X),max(X)])
plt.ylim([min(Y),max(Y)])
def velocity_image(sim, width="10 kpc", vector_color='black', edgecolor='black', quiverkey_bg_color=None,
vector_resolution=40, scale=None, mode='quiver', key_x=0.3, key_y=0.9,
key_color='white', key_length="100 km s**-1", quiverkey=True, density=1.0, **kwargs):
"""
Make an SPH image of the given simulation with velocity vectors overlaid on top.
For a description of additional keyword arguments see :func:`~pynbody.plot.sph.image`,
or see the `tutorial <http://pynbody.github.io/pynbody/tutorials/pictures.html#velocity-vectors>`_.
**Keyword arguments:**
*vector_color* (black): The color for the velocity vectors
*edgecolor* (black): edge color used for the lines - using a color
other than black for the *vector_color* and a black *edgecolor*
can result in poor readability in pdfs
*vector_resolution* (40): How many vectors in each dimension (default is 40x40)
*quiverkey_bg_color* (none): The color for the legend (scale) background
*scale* (None): The length of a vector that would result in a displayed length of the
figure width/height.
*mode* ('quiver'): make a 'quiver' or 'stream' plot
*key_x* (0.3): Display x (width) position for the vector key (quiver mode only)
*key_y* (0.9): Display y (height) position for the vector key (quiver mode only)
*key_color* (white): Color for the vector key (quiver mode only)
*key_length* (100 km/s): Velocity to use for the vector key (quiver mode only)
*density* (1.0): Density of stream lines (stream mode only)
*quiverkey* (True): Whether or not to inset the key
"""
subplot = kwargs.get('subplot', False)
av_z = kwargs.get('av_z',None)
if subplot:
p = subplot
else:
import matplotlib.pylab as p
vx = image(sim, qty='vx', width=width, log=False,
resolution=vector_resolution, noplot=True,av_z=av_z)
vy = image(sim, qty='vy', width=width, log=False,
resolution=vector_resolution, noplot=True,av_z=av_z)
key_unit = _units.Unit(key_length)
if isinstance(width, str) or issubclass(width.__class__, _units.UnitBase):
if isinstance(width, str):
width = _units.Unit(width)
width = width.in_units(sim['pos'].units, **sim.conversion_context())
width = float(width)
X, Y = np.meshgrid(np.arange(-width / 2, width / 2, width / vector_resolution),
np.arange(-width / 2, width / 2, width / vector_resolution))
im = image(sim, width=width, **kwargs)
if mode == 'quiver':
if scale is None:
Q = p.quiver(X, Y, vx, vy, color=vector_color, edgecolor=edgecolor)
else:
Q = p.quiver(X, Y, vx, vy, scale=_units.Unit(scale).in_units(
sim['vel'].units), color=vector_color, edgecolor=edgecolor)
if quiverkey:
qk = p.quiverkey(Q, key_x, key_y, key_unit.in_units(sim['vel'].units, **sim.conversion_context()),
r"$\mathbf{" + key_unit.latex() + "}$", labelcolor=key_color, color=key_color, fontproperties={'size': 24})
if quiverkey_bg_color is not None:
qk.text.set_backgroundcolor(quiverkey_bg_color)
elif mode == 'stream' :
Q = p.streamplot(X, Y, vx, vy, color=vector_color, density=density)
return im
def View2D(g, option=0):
# plot and check the field
fig = figure(num=2, figsize=(16, 6))
# fig.suptitle('Efit Analysis', fontsize=20)
ax = subplot2grid((3, 3), (0, 0), colspan=1, rowspan=3)
nlev = 100
minf = np.min(g.psi)
maxf = np.max(g.psi)
levels = np.arange(np.float(nlev)) * (maxf - minf) / np.float(nlev - 1) + minf
ax.contour(g.r, g.z, g.psi, levels=levels)
# ax.set_xlim([0,6])
ax.set_xlabel("R")
ax.set_ylabel("Z")
ax.yaxis.label.set_rotation("horizontal")
ax.set_aspect("equal")
# fig.suptitle('Efit Analysis', fontsize=20)
# title('Efit Analysis', fontsize=20)
text(0.5, 1.08, "Efit Analysis", horizontalalignment="center", fontsize=20, transform=ax.transAxes)
draw()
if option == 0:
show(block=False)
plot(g.xlim, g.ylim, "g-")
draw()
csb = contour(g.r, g.z, g.psi, levels=[g.sibdry])
clabel(csb, [g.sibdry], inline=1, fmt="%9.6f", fontsize=14) # label the level
csb.collections[0].set_label("boundary")
# pl1=plot(g.rbdry,g.zbdry,'b-',marker='x', label='$\psi=$'+ np.str(g.sibdry))
# legend(bbox_to_anchor=(0., 1.05, 1., .105), loc='upper left')
draw()
# fig.set_tight_layout(True)
# show(block=False)
# Function fpol and qpsi are given between simagx (psi on the axis) and sibdry (
# psi on limiter or separatrix). So the toroidal field (fpol/R) and the q profile are within these boundaries
npsigrid = old_div(np.arange(np.size(g.pres)).astype(float), (np.size(g.pres) - 1))
fpsi = np.zeros((2, np.size(g.fpol)), np.float64)
fpsi[0, :] = g.simagx + npsigrid * (g.sibdry - g.simagx)
fpsi[1, :] = g.fpol
boundary = np.array([g.xlim, g.ylim])
rz_grid = Bunch(
nr=g.nx,
nz=g.ny, # Number of grid points
r=g.r[:, 0],
z=g.z[0, :], # R and Z as 1D arrays
simagx=g.simagx,
sibdry=g.sibdry, # Range of psi
psi=g.psi, # Poloidal flux in Weber/rad on grid points
npsigrid=npsigrid, # Normalised psi grid for fpol, pres and qpsi
fpol=g.fpol, # Poloidal current function on uniform flux grid
pres=g.pres, # Plasma pressure in nt/m^2 on uniform flux grid
qpsi=g.qpsi, # q values on uniform flux grid
nlim=g.nlim,
rlim=g.xlim,
zlim=g.ylim,
) # Wall boundary
critical = analyse_equil(g.psi, g.r[:, 0], g.z[0, :])
n_opoint = critical.n_opoint
n_xpoint = critical.n_xpoint
primary_opt = critical.primary_opt
inner_sep = critical.inner_sep
opt_ri = critical.opt_ri
opt_zi = critical.opt_zi
opt_f = critical.opt_f
xpt_ri = critical.xpt_ri
xpt_zi = critical.xpt_zi
xpt_f = critical.xpt_f
psi_inner = 0.6
psi_outer = (0.8,)
nrad = 68
npol = 64
rad_peaking = [0.0]
pol_peaking = [0.0]
parweight = 0.0
boundary = np.array([rz_grid.rlim, rz_grid.zlim])
# Psi normalisation factors
faxis = critical.opt_f[critical.primary_opt]
fnorm = critical.xpt_f[critical.inner_sep] - critical.opt_f[critical.primary_opt]
# From normalised psi, get range of f
f_inner = faxis + np.min(psi_inner) * fnorm
f_outer = faxis + np.max(psi_outer) * fnorm
fvals = radial_grid(nrad, f_inner, f_outer, 1, 1, [xpt_f[inner_sep]], rad_peaking)
## Create a starting surface
# sind = np.int(nrad / 2)
# start_f = 0. #fvals[sind]
# Find where we have rational surfaces
# define an interpolation of psi(q)
psiq = np.arange(np.float(g.qpsi.size)) * (g.sibdry - g.simagx) / np.float(g.qpsi.size - 1) + g.simagx
fpsiq = interpolate.interp1d(g.qpsi, psiq)
# Find how many rational surfaces we have within the boundary and locate x,y position of curves
nmax = g.qpsi.max().astype(int)
nmin = g.qpsi.min().astype(int)
nr = np.arange(nmin + 1, nmax + 1)
psi = fpsiq(nr)
cs = contour(g.r, g.z, g.psi, levels=psi)
labels = ["$q=" + np.str(x) + "$\n" for x in range(nr[0], nr[-1] + 1)]
for i in range(len(labels)):
cs.collections[i].set_label(labels[i])
style = ["--", ":", "--", ":", "-."]
# gca().set_color_cycle(col)
# proxy = [Rectangle((0,0),1,1, fc=col[:i+1])
# for pc in cs.collections]
#
# l2=legend(proxy, textstr[:i)
#
# gca().add_artist(l1)
x = []
y = []
for i in range(psi.size):
xx, yy = surface(cs, i, psi[i], opt_ri[primary_opt], opt_zi[primary_opt], style, option)
x.append(xx)
y.append(yy)
# props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# textstr = ['$q='+np.str(x)+'$\n' for x in range(psi.size)]
#
# ax.text(0.85, 1.15, ''.join(textstr), transform=ax.transAxes, fontsize=14,
# verticalalignment='top', bbox=props)
legend(bbox_to_anchor=(-0.8, 1), loc="upper left", borderaxespad=0.0)
draw()
# compute B - field
Bp = np.gradient(g.psi)
dr = old_div((np.max(g.r[:, 0]) - np.min(g.r[:, 0])), np.size(g.r[:, 0]))
dz = old_div((np.max(g.z[0, :]) - np.min(g.z[0, :])), np.size(g.z[0, :]))
dpsidr = Bp[0]
dpsidz = Bp[1]
Br = -dpsidz / dz / g.r
Bz = dpsidr / dr / g.r
Bprz = np.sqrt(Br * Br + Bz * Bz)
# plot Bp field
if option == 0:
sm = query_yes_no("Overplot vector field")
if sm == 1:
lw = 50 * Bprz / Bprz.max()
streamplot(
g.r.T, g.z.T, Br.T, Bz.T, color=Bprz, linewidth=2, cmap=cm.bone
) # density =[.5, 1], color='k')#, linewidth=lw)
draw()
# plot toroidal field
ax = subplot2grid((3, 3), (0, 1), colspan=2, rowspan=1)
ax.plot(psiq, fpsi[1, :])
# ax.set_xlim([0,6])
# ax.set_xlabel('$\psi$')
ax.set_ylabel("$fpol$")
ax.yaxis.label.set_size(20)
# ax.xaxis.label.set_size(20)
ax.set_xticks([])
ax.yaxis.label.set_rotation("horizontal")
# ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 20
# props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# ax.text(0.85, 0.95, '$B_t$', transform=ax.transAxes, fontsize=14,
# verticalalignment='top', bbox=props)
#
draw()
# plot pressure
ax = subplot2grid((3, 3), (1, 1), colspan=2, rowspan=1)
ax.plot(psiq, g.pres)
# ax.set_xlim([0,6])
# ax.set_xlabel('$\psi$')
ax.set_ylabel("$P$")
ax.yaxis.label.set_size(20)
# ax.xaxis.label.set_size(20)
ax.set_xticks([])
ax.yaxis.label.set_rotation("horizontal")
# ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 20
# props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# ax.text(0.85, 0.95, '$B_t$', transform=ax.transAxes, fontsize=14,
# verticalalignment='top', bbox=props)
#
draw()
# plot qpsi
ax = subplot2grid((3, 3), (2, 1), colspan=2, rowspan=1)
ax.plot(psiq, g.qpsi)
ax.set_xlabel("$\psi$")
ax.set_ylabel("$q$")
ax.yaxis.label.set_rotation("horizontal")
ax.yaxis.label.set_size(20)
ax.xaxis.label.set_size(20)
ax.xaxis.labelpad = 10
ax.yaxis.labelpad = 20
tick_params(
axis="x", # changes apply to the x-axis
which="both", # both major and minor ticks are affected
bottom="on", # ticks along the bottom edge are off
top="off", # ticks along the top edge are off
labelbottom="on",
)
draw()
# Compute and draw Jpar
#
# MU = 4.e-7*np.pi
#
# jpar0 = - Bxy * fprime / MU - Rxy*Btxy * dpdpsi / Bxy
#
# fig.set_tight_layout(True)
fig.subplots_adjust(left=0.2, top=0.9, hspace=0.1, wspace=0.5)
draw()
if option == 0:
show(block=False)
if option != 0:
return Br, Bz, x, y, psi
density_min = np.min(density)
density_max = np.max(density)
ground_indices = y[0, :] < 0.25
# Ground the right contact
#density = density - np.mean(density[ground_indices, -1])
#plot_grid(x[::5, ::5], y[::5, ::5], alpha=0.5)
#pl.contourf(x, y, density.T, 100, cmap='bwr')
pl.contourf(x, y, density.T, 100, norm=MidpointNormalize(midpoint=0, vmin=density_min, vmax=density_max), cmap='bwr')
pl.title(r'Time = ' + "%.2f"%(time_array[start_index+file_number]) + " ps")
#pl.colorbar()
pl.streamplot(x[:, 0], y[0, :],
vel_drift_x, vel_drift_y,
density=2., color='k',
linewidth=0.7, arrowsize=1
)
#pl.axvline(1.5, color = 'k', ls = '--')
#pl.axvline(3.5, color = 'k', ls = '--')
pl.axvspan(4.8, 4.9, color = 'k', alpha = 0.3)
#pl.axvspan(3.45, 3.55, color = 'k', alpha = 0.5)
pl.xlim([0, 2])
pl.ylim([0, 1.5])
pl.gca().set_aspect('equal')
pl.xlabel(r'$x\;(\mu \mathrm{m})$')
pl.ylabel(r'$y\;(\mu \mathrm{m})$')
# pl.suptitle('$\\tau_\mathrm{mc} = \infty$, $\\tau_\mathrm{mr} = \infty$')
plot.coil_loc()
pl.plot(r,z,'b-x')
pl.axis('equal')
# contor grid
res = 0.4
xlim, zlim = ([3,14], [-11,5])
dx, dz = (xlim[1]-xlim[0], zlim[1]-zlim[0])
nx, nz = (int(dx/res), int(dz/res))
x = np.linspace(xlim[0], xlim[1], nx)
z = np.linspace(zlim[0], zlim[1], nz)
xm, zm = np.meshgrid(x, z)
feild = np.zeros((nz,nx))
Bx = np.zeros((nz,nx))
Bz = np.zeros((nz,nx))
for i in range(nz):
for j in range(nx):
B = Bcoil(mu_o, coil, [xm[i,j],0,zm[i,j]])
Bx[i,j] = B[0]
Bz[i,j] = B[2]
feild[i,j] = sum(B*B)**0.5
V = np.linspace(0,10,30)
pl.streamplot(xm, zm, Bx, Bz, density = [2*nx/25,2*nz/25])
pl.axis('equal')
pl.xlim(xlim)
pl.ylim(zlim)
