def panel_plot(plot_data, fname='panel.pdf'):
set_rc_params(tickfs=30)
levels = np.linspace(-0.05, 1.15, 25)
fig, axarr = plt.subplots(2,
2,
figsize=(20, 14),
sharex='col',
sharey='row')
field2pos = {'gh': (0, 0), 'cb': (0, 1), 'ccb': (1, 1), 'sc': (1, 0)}
field2title = {
'gh': '(a) Gaussian hills',
'cb': '(b) cosine bells',
'ccb': "(d) 'correlated' cosine bells",
'sc': '(c) slotted cylinders'
}
for f in plot_data.keys():
field = np.transpose(plot_data[f])
ny, nx = field.shape
cmap = plt.get_cmap('terrain')
i = field2pos[f]
p = axarr[i].contourf(field, levels=levels, zorder=1, cmap=cmap)
axarr[i].contour(field, levels=levels, zorder=1, cmap=cmap)
axarr[i].set_title(field2title[f], fontsize=30, y=1.02)
for ax in axarr.flatten():
ax.set_xticks(
[0, (nx - 1) / 4, (nx - 1) / 2, 3 * (nx - 1) / 4, nx - 1])
ax.set_xticklabels(
[r'$0$', r'$\pi$/2', r'$\pi$', r'$3\pi/2$', r'$2\pi$'])
ax.set_yticks([0, (ny + 0.5) / 2, ny - 1])
ax.set_yticklabels([r'$-\pi/2$', r'$0$', r'$\pi/2$'])
ax.grid(color='w', lw=2, linestyle=':')
plt.subplots_adjust(bottom=0.2)
cbaxes = fig.add_axes([0.1, 0.1, 0.8, 0.02])
plt.colorbar(p, cax=cbaxes, ticks=levels[1:-1:2], orientation='horizontal')
#plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname, bbox_inches='tight')
def conv_plot(plot_data, ord_data, fname = 'fig.pdf'):
set_rc_params()
fs = 45
lab2ls = {'Mp3' : 'ks-', 'Mp3cc' : 'bo-', 'Mg3No' : 'gD-', 'Mg2No' : 'r^-'}
lab2dsh = {'Mp3' : [], 'Mp3cc' : [6, 1], 'Mg3No' : [1, 1], 'Mg2No' : [6, 1, 1 ,1]}
fig, axarr = plt.subplots(1, 1, figsize=(14,12))
plots = {}
for x, y, opt in plot_data:
zo = 2.0
lab = opt2lab[opt]
if lab == 'Mg3No':
zo = 2.1
p, = axarr.loglog(x, y, lab2ls[lab], label = lab, lw = 6, ms = 16, dashes = lab2dsh[lab], zorder = zo)
plots[lab] = p
for x, y, x0, y0, t, a in ord_data:
axarr.loglog(x, y, color = 'gray', lw = 6)
axarr.text(x0, y0, t, rotation = a, size = 28, backgroundcolor = 'w', zorder=2.1)
axarr.xaxis.set_ticks(plot_data[0][0])
axarr.xaxis.set_tick_params(direction = 'in')
axarr.yaxis.set_tick_params(direction = 'in')
axarr.minorticks_off()
axarr.get_xaxis().set_major_formatter(ScalarFormatter())
axarr.set_xlabel('$N$', fontsize = fs)
axarr.set_ylabel('$\ell_2$ error norm', fontsize = fs)
labels = list(range(len(plots.keys())))
for lab in plots.keys():
labels[lab2pos[lab]] = lab
handles = [plots[lab] for lab in labels]
l = axarr.legend(handles, labels, fontsize=fs, numpoints=1, edgecolor = 'k', framealpha = 1.0, loc = 3, handlelength = 2.5)
l.get_frame().set_linewidth(3)
axarr.grid(color = 'k', lw = 2, linestyle = ':')
plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname)
def panel_plot(plot_data, fname = 'panel.pdf'):
set_rc_params(tickfs = 30)
levels = np.linspace(-0.05, 1.15, 25)
fig, axarr = plt.subplots(2, 2, figsize=(20, 14), sharex = 'col', sharey = 'row')
field2pos = {'gh' : (0, 0), 'cb' : (0, 1), 'ccb' : (1, 1), 'sc' : (1, 0) }
field2title = {'gh' : '(a) Gaussian hills',
'cb' : '(b) cosine bells',
'ccb' : "(d) 'correlated' cosine bells",
'sc' : '(c) slotted cylinders'}
for f in plot_data.keys():
field = np.transpose(plot_data[f])
ny, nx = field.shape
cmap = plt.get_cmap('terrain')
i = field2pos[f]
p = axarr[i].contourf(field, levels = levels, zorder = 1, cmap = cmap)
axarr[i].contour(field, levels = levels, zorder = 1, cmap = cmap)
axarr[i].set_title(field2title[f], fontsize = 30, y = 1.02)
for ax in axarr.flatten():
ax.set_xticks([0, (nx - 1) / 4, (nx - 1) / 2, 3 * (nx - 1) / 4, nx - 1])
ax.set_xticklabels([r'$0$', r'$\pi$/2', r'$\pi$', r'$3\pi/2$', r'$2\pi$'])
ax.set_yticks([0, (ny+0.5) / 2, ny - 1])
ax.set_yticklabels([r'$-\pi/2$', r'$0$', r'$\pi/2$'])
ax.grid(color = 'w', lw = 2, linestyle = ':')
plt.subplots_adjust(bottom=0.2)
cbaxes = fig.add_axes([0.1, 0.1, 0.8, 0.02])
plt.colorbar(p, cax = cbaxes, ticks = levels[1:-1:2], orientation = 'horizontal')
#plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname, bbox_inches='tight')
def panel_plot(geo_data, field_data, opt, time, ny, fname):
set_rc_params(onlytex=True)
nx, ny = geo_data[ny]['g'].shape
X = geo_data[ny]['di'] * np.arange(nx)
Y = geo_data[ny]['dj'] * (np.arange(ny) + 0.5) - pi / 2
# extend Y values to cover the poles
Y = np.concatenate([[-pi / 2], Y, [pi / 2]])
X, Y = np.meshgrid(X, Y, indexing='ij')
init = asolution(0.0, X, Y)
asol = asolution(float(time), X, Y)
nsol = field_data[ny][opt][time]['psi']
nsol = np.concatenate([np.zeros((nx, 1)), nsol, np.zeros((nx, 1))], axis=1)
errf = nsol - asol
panel_fields = {'init': init, 'asol': asol, 'nsol': nsol, 'errf': errf}
XI, YI, XN, YN = transform_iso_coord(X, Y)
for pf in panel_fields:
panel_fields[pf] = transform_iso_field(panel_fields[pf], X, Y)
levels = [0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6]
colors = [
'white', 'slateblue', 'indigo', 'mediumblue', 'blue', 'darkolivegreen',
'olive', 'lawngreen', 'yellowgreen', 'darkorange', 'red', 'firebrick'
]
err_levels = [-0.021, -0.015, -0.009, -0.003, 0.003, 0.009, 0.015, 0.021]
err_colors = [
'slateblue', 'blue', 'indigo', 'white', 'darkorange', 'red',
'firebrick'
]
fig, axarr = plt.subplots(2, 2, figsize=(15, 12))
for ax in axarr.flatten():
ax.axis('off')
ax.contour(XI,
YI,
XN,
levels=xlevels,
linewidths=(0.5, ),
colors=('k', ),
linestyles=('dashed', ))
ax.contour(XI,
YI,
YN,
levels=ylevels,
linewidths=(0.5, ),
colors=('k', ),
linestyles=('dashed', ))
p = axarr[0, 0].contourf(XI,
YI,
panel_fields['init'],
levels=levels,
colors=colors)
cb1 = fig.colorbar(p, ax=axarr[0, 0], ticks=levels[1:-1])
p = axarr[0, 1].contourf(XI,
YI,
panel_fields['asol'],
levels=levels,
colors=colors)
cb2 = fig.colorbar(p, ax=axarr[0, 1], ticks=levels[1:-1])
p = axarr[1, 1].contourf(XI,
YI,
panel_fields['nsol'],
levels=levels,
colors=colors)
cb3 = fig.colorbar(p, ax=axarr[1, 1], ticks=levels[1:-1])
p = axarr[1, 0].contourf(XI,
YI,
panel_fields['errf'],
levels=err_levels,
colors=err_colors)
cb4 = fig.colorbar(p, ax=axarr[1, 0], ticks=err_levels[1:-1])
for cb in [cb1, cb2, cb3, cb4]:
ticklabs = cb.ax.get_yticklabels()
cb.ax.tick_params(labelsize=16)
axarr[0, 0].set_title('(a) Initial condition', y=1.02, fontsize=30)
axarr[0, 1].set_title(r'(b) Exact solution $t = 12$ days',
y=1.02,
fontsize=30)
axarr[1, 0].set_title(r'(c) Difference $t = 12$ days', y=1.02, fontsize=30)
axarr[1, 1].set_title(r'(d) Numerical solution $t = 12$ days',
y=1.02,
fontsize=30)
cb4.ax.set_yticklabels(ticklabs, ha='right')
cb4.ax.yaxis.set_tick_params(pad=50)
plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname, transparent=True)
def panel_plot(geo_data, field_data, opt, time, ny, fname):
set_rc_params(onlytex = True)
nx, ny = geo_data[ny]['g'].shape
X = geo_data[ny]['di'] * np.arange(nx)
Y = geo_data[ny]['dj'] * (np.arange(ny) + 0.5) - pi / 2
# extend Y values to cover the poles
Y = np.concatenate([[-pi / 2], Y, [pi / 2]])
X, Y = np.meshgrid(X, Y, indexing ='ij')
init = asolution(0.0, X, Y)
asol = asolution(float(time), X, Y)
nsol = field_data[ny][opt][time]['psi']
nsol = np.concatenate([np.zeros((nx, 1)), nsol, np.zeros((nx, 1))], axis = 1)
errf = nsol - asol
panel_fields = {'init' : init, 'asol' : asol, 'nsol' : nsol, 'errf' : errf}
XI, YI, XN, YN = transform_iso_coord(X, Y)
for pf in panel_fields:
panel_fields[pf] = transform_iso_field(panel_fields[pf], X, Y)
levels = [0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6]
colors = ['white',
'slateblue',
'indigo',
'mediumblue',
'blue',
'darkolivegreen',
'olive',
'lawngreen',
'yellowgreen',
'darkorange',
'red',
'firebrick'
]
err_levels = [-0.021, -0.015, -0.009, -0.003, 0.003, 0.009, 0.015, 0.021]
err_colors = [
'slateblue',
'blue',
'indigo',
'white',
'darkorange',
'red',
'firebrick'
]
fig, axarr = plt.subplots(2, 2, figsize = (15, 12))
for ax in axarr.flatten():
ax.axis('off')
ax.contour(XI, YI, XN, levels = xlevels, linewidths = (0.5,), colors = ('k',), linestyles = ('dashed',))
ax.contour(XI, YI, YN, levels = ylevels, linewidths = (0.5,), colors = ('k',), linestyles = ('dashed',))
p = axarr[0, 0].contourf(XI, YI, panel_fields['init'], levels = levels, colors = colors)
cb1 = fig.colorbar(p, ax = axarr[0, 0], ticks = levels[1:-1])
p = axarr[0, 1].contourf(XI, YI, panel_fields['asol'], levels = levels, colors = colors)
cb2 = fig.colorbar(p, ax = axarr[0, 1], ticks = levels[1:-1])
p = axarr[1, 1].contourf(XI, YI, panel_fields['nsol'], levels = levels, colors = colors)
cb3 = fig.colorbar(p, ax = axarr[1, 1], ticks = levels[1:-1])
p = axarr[1, 0].contourf(XI, YI, panel_fields['errf'], levels = err_levels, colors = err_colors)
cb4 = fig.colorbar(p, ax = axarr[1, 0], ticks = err_levels[1:-1])
for cb in [cb1, cb2, cb3, cb4]:
ticklabs = cb.ax.get_yticklabels()
cb.ax.tick_params(labelsize=16)
axarr[0, 0].set_title('(a) Initial condition', y = 1.02, fontsize = 30)
axarr[0, 1].set_title(r'(b) Exact solution $t = 12$ days', y = 1.02, fontsize = 30)
axarr[1, 0].set_title(r'(c) Difference $t = 12$ days', y = 1.02, fontsize = 30)
axarr[1, 1].set_title(r'(d) Numerical solution $t = 12$ days', y = 1.02, fontsize = 30)
cb4.ax.set_yticklabels(ticklabs,ha='right')
cb4.ax.yaxis.set_tick_params(pad=50)
plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname, transparent = True)
def plot_mixing(field_data, mixing_diags, ny, fname = 'mixing.pdf'):
set_rc_params()
matplotlib.rcParams['text.latex.preamble']=[r"\usepackage{amsmath}"]
plt.clf()
fig, axarr = plt.subplots(2, 2, sharex='col', sharey = 'row', figsize=(14, 12))
c = 'red'
s = 1
marker = '.'
edgecolor = 'r'
fs = 22
lw = 2
x = np.linspace(xmin, xmax)
for opt in field_data[ny]:
cb, ccb = field_data[ny][opt]['2.5']['cb'].flatten(), field_data[ny][opt]['2.5']['ccb'].flatten()
lab = opt2lab[opt]
lab2num = {'Mp3' : (0, 1), 'Mp3cc' : (0, 0), 'Mg2No' : (1, 0), 'Mg3No' : (1, 1)}
num = lab2num[lab]
axarr[num].scatter(cb, ccb, c = c, s = s, marker = marker, edgecolor = edgecolor, rasterized = True)
axarr[num].plot(x, corr_func(x), 'k-', lw = lw)
axarr[num].plot(x, ymin * x / x, 'k-', lw = lw)
axarr[num].plot(xmax * x / x, np.linspace(ymax, ymin), 'k-', lw = lw)
axarr[num].plot(x, line_func(x), 'k-', lw = lw)
axarr[num].set_ylim([0, 1])
axarr[num].set_xlim([0, 1.1])
axarr[num].set_title(lab, fontsize = fs + 8, y = 1.02)
if (num not in [(0, 0), (0, 1)]):
axarr[num].set_xlabel('$\\chi$', fontsize = fs+2)
if (num not in [(1, 1), (0, 1)]):
axarr[num].set_ylabel('$\\xi$', fontsize = fs+2)
axarr[num].xaxis.set_tick_params(direction = 'in', top = True, labelsize = 20)
axarr[num].xaxis.set_ticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
#if (num in [(1, 0), (1, 1)]):
axarr[num].yaxis.set_ticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
axarr[num].yaxis.set_tick_params(direction = 'in', right = True, labelsize = 20)
axarr[num].minorticks_off()
axarr[num].grid()
lr, lu, lo = mixing_diags[ny][opt]
expformat = '{} \\times 10^{{{}}}'
lrs = '{:.2e}'.format(lr)
l_r_d, l_r_e = (lrs[0:4], int(lrs[5:]))
lus = '{:.2e}'.format(lu)
l_u_d, l_u_e = lus[0:4], int(lus[5:])
if lo != 0:
los = '{:.2e}'.format(lo)
lo = (los[0:4], int(los[5:]))
loformat = expformat
else:
lo = (lo,)
loformat = '{:g}'
test2 = (
'''\\begin{{{{align}}}}'''
'''l_r &= {l_r_format}\\\\'''
'''l_u &= {l_u_format}\\\\'''
'''l_o &= {l_o_format}\\\\'''
'''\\end{{{{align}}}}'''
)
test = test2.format(l_r_format = expformat,
l_u_format = expformat,
l_o_format = loformat)
axarr[num].text(0.1,
0.05,
test.format(l_r_d, l_r_e, l_u_d, l_u_e, *lo),
size = 28,
multialignment = 'left'
)
plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname)
def plot_mixing(field_data, mixing_diags, ny, fname='mixing.pdf'):
set_rc_params()
matplotlib.rcParams['text.latex.preamble'] = [r"\usepackage{amsmath}"]
plt.clf()
fig, axarr = plt.subplots(2,
2,
sharex='col',
sharey='row',
figsize=(14, 12))
c = 'red'
s = 1
marker = '.'
edgecolor = 'r'
fs = 22
lw = 2
x = np.linspace(xmin, xmax)
for opt in field_data[ny]:
cb, ccb = field_data[ny][opt]['2.5']['cb'].flatten(
), field_data[ny][opt]['2.5']['ccb'].flatten()
lab = opt2lab[opt]
lab2num = {
'Mp3': (0, 1),
'Mp3cc': (0, 0),
'Mg2No': (1, 0),
'Mg3No': (1, 1)
}
num = lab2num[lab]
axarr[num].scatter(cb,
ccb,
c=c,
s=s,
marker=marker,
edgecolor=edgecolor,
rasterized=True)
axarr[num].plot(x, corr_func(x), 'k-', lw=lw)
axarr[num].plot(x, ymin * x / x, 'k-', lw=lw)
axarr[num].plot(xmax * x / x, np.linspace(ymax, ymin), 'k-', lw=lw)
axarr[num].plot(x, line_func(x), 'k-', lw=lw)
axarr[num].set_ylim([0, 1])
axarr[num].set_xlim([0, 1.1])
axarr[num].set_title(lab, fontsize=fs + 8, y=1.02)
if (num not in [(0, 0), (0, 1)]):
axarr[num].set_xlabel('$\\chi$', fontsize=fs + 2)
if (num not in [(1, 1), (0, 1)]):
axarr[num].set_ylabel('$\\xi$', fontsize=fs + 2)
axarr[num].xaxis.set_tick_params(direction='in',
top=True,
labelsize=20)
axarr[num].xaxis.set_ticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
#if (num in [(1, 0), (1, 1)]):
axarr[num].yaxis.set_ticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
axarr[num].yaxis.set_tick_params(direction='in',
right=True,
labelsize=20)
axarr[num].minorticks_off()
axarr[num].grid()
lr, lu, lo = mixing_diags[ny][opt]
expformat = '{} \\times 10^{{{}}}'
lrs = '{:.2e}'.format(lr)
l_r_d, l_r_e = (lrs[0:4], int(lrs[5:]))
lus = '{:.2e}'.format(lu)
l_u_d, l_u_e = lus[0:4], int(lus[5:])
if lo != 0:
los = '{:.2e}'.format(lo)
lo = (los[0:4], int(los[5:]))
loformat = expformat
else:
lo = (lo, )
loformat = '{:g}'
test2 = ('''\\begin{{{{align}}}}'''
'''l_r &= {l_r_format}\\\\'''
'''l_u &= {l_u_format}\\\\'''
'''l_o &= {l_o_format}\\\\'''
'''\\end{{{{align}}}}''')
test = test2.format(l_r_format=expformat,
l_u_format=expformat,
l_o_format=loformat)
axarr[num].text(0.1,
0.05,
test.format(l_r_d, l_r_e, l_u_d, l_u_e, *lo),
size=28,
multialignment='left')
plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname)
def conv_plot(plot_data, ord_data, fname='fig.pdf'):
set_rc_params()
fs = 45
lab2ls = {'Mp3': 'ks-', 'Mp3cc': 'bo-', 'Mg3No': 'gD-', 'Mg2No': 'r^-'}
lab2dsh = {
'Mp3': [],
'Mp3cc': [6, 1],
'Mg3No': [1, 1],
'Mg2No': [6, 1, 1, 1]
}
fig, axarr = plt.subplots(1, 1, figsize=(14, 12))
plots = {}
for x, y, opt in plot_data:
zo = 2.0
lab = opt2lab[opt]
if lab == 'Mg3No':
zo = 2.1
p, = axarr.loglog(x,
y,
lab2ls[lab],
label=lab,
lw=6,
ms=16,
dashes=lab2dsh[lab],
zorder=zo)
plots[lab] = p
for x, y, x0, y0, t, a in ord_data:
axarr.loglog(x, y, color='gray', lw=6)
axarr.text(x0,
y0,
t,
rotation=a,
size=28,
backgroundcolor='w',
zorder=2.1)
axarr.xaxis.set_ticks(plot_data[0][0])
axarr.xaxis.set_tick_params(direction='in')
axarr.yaxis.set_tick_params(direction='in')
axarr.minorticks_off()
axarr.get_xaxis().set_major_formatter(ScalarFormatter())
axarr.set_xlabel('$N$', fontsize=fs)
axarr.set_ylabel('$\ell_2$ error norm', fontsize=fs)
labels = list(range(len(plots.keys())))
for lab in plots.keys():
labels[lab2pos[lab]] = lab
handles = [plots[lab] for lab in labels]
l = axarr.legend(handles,
labels,
fontsize=fs,
numpoints=1,
edgecolor='k',
framealpha=1.0,
loc=3,
handlelength=2.5)
l.get_frame().set_linewidth(3)
axarr.grid(color='k', lw=2, linestyle=':')
plt.tight_layout(pad=1., w_pad=5., h_pad=1)
plt.savefig(fname)