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figures.py
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figures.py
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import argparse
import os
import sys
import matplotlib
import matplotlib.gridspec as gridspec
import matplotlib.patheffects as pe
import matplotlib.pyplot as plt
import numpy as np
from animate.adapt import adapt
from firedrake import *
from firedrake.pyplot import *
from matplotlib import lines
from matplotlib.colors import LinearSegmentedColormap, LogNorm
from matplotlib.lines import Line2D
from numpy.linalg import eig
matplotlib.use('pgf')
main_dir = os.path.dirname(os.path.dirname(os.path.realpath(__file__)))
sys.path.append(main_dir)
import utility_functions as uf
from adaptor_fns import _tau_metric
from options import Options
fig_names = [
"metric_components",
"schemes",
"initial_steady_state",
"uniform_convergence",
"strat_comparison",
"strat_comparison_meshes",
"hessian_meshes",
"hessian_aspect_ratio",
"hessian_err",
"hessian_cpu_time",
]
parser = argparse.ArgumentParser()
parser.add_argument("--output-dir", type=str,)
parser.add_argument("--fig", type=str, required=True, choices=fig_names)
parser.add_argument("--format", type=str, default="pdf")
args = parser.parse_args()
def get_label_pos(ax, fig, top=False):
# Get the aspect ratio of the axis
bbox = ax.get_window_extent().transformed(fig.dpi_scale_trans.inverted())
width, height = bbox.width, bbox.height
aspect = height / width
# Get axis limits
x_min, x_max = ax.get_xlim()
y_min, y_max = ax.get_ylim()
# Check for logarithmic scales
x_log = ax.get_xscale() == 'log'
y_log = ax.get_yscale() == 'log'
x_factor = 0.05
y_factor = 0.8 if top else 0.1
if x_log:
x_min, x_max = np.log10(x_min), np.log10(x_max)
x_label_pos = 10 ** (x_min + x_factor * (x_max - x_min))
else:
x_label_pos = x_min + x_factor * (x_max - x_min) * aspect
if y_log:
y_min, y_max = np.log10(y_min), np.log10(y_max)
y_label_pos = 10 ** (y_min + y_factor * (y_max - y_min) / aspect)
else:
y_label_pos = y_min + y_factor * (y_max - y_min)
return x_label_pos, y_label_pos
def ax_text(ax, fig, text, d=0.07, dy=None, top=False, colour="k"):
# Get the aspect ratio of the axis
bbox = ax.get_window_extent().transformed(fig.dpi_scale_trans.inverted())
width, height = bbox.width, bbox.height
aspect = height / width
x = d
x *= aspect
dy = d if dy is None else dy
y = 1-dy if top else dy
ax.text(x, y, text, transform=ax.transAxes,
verticalalignment='bottom', horizontalalignment='left',
color=colour)
def label_axes(fig, axes, top=True, cs=None):
panel_labels = ["(a)", "(b)", "(c)", "(d)"]
if cs is None:
cs = ["k"] * len(axes)
for i, ax in enumerate(axes):
x_label_pos, y_label_pos = get_label_pos(ax, fig, top)
ax.text(x_label_pos, y_label_pos, panel_labels[i], color=cs[i])
def ice1_base_time_plot(ax):
# ax.axvline(100, color="k", linestyle=":", alpha=0.4)
ax.set(
# xlabel="Years",
xlim=(0, 200),
)
ax.grid()
def get_ref(lv):
dir_path = f"/data3/glac_adapt/data/reference_outputs/ref_{lv}/analysis"
vafs = np.load(os.path.join(dir_path, "vafs.npy"))[0]
gls = np.load(os.path.join(dir_path, "gls.npy"))[0]
xgls = np.load(os.path.join(dir_path, "midline_x_gls.npy"))[0]
return vafs, gls, xgls
def get_ref_scatter_kwargs(lv):
return {
"s": 10,
"alpha": 0.8,
"label": f"{4/2**lv} km",
"facecolors": "none",
"edgecolors": f"C{lv}",
}
plt_rcparams = {
"pgf.texsystem": "pdflatex",
"font.size": 8,
"font.family": "sans-serif",
"font.serif": "DejaVu Sans",
"text.usetex": True,
"text.latex.preamble": r"\usepackage{bm}",
"axes.titlesize": 8,
"legend.columnspacing": 0.8,
"legend.handletextpad": 0.3,
# "legend.markerscale": 0.7,
"legend.borderpad": 0.,
"legend.frameon": False,
# space between colorbar and label
"axes.labelpad": 2,
"axes.titlepad": 3.5,
"xtick.major.size": 2,
"ytick.major.size": 2,
"xtick.major.width": 0.5,
"ytick.major.width": 0.5,
"xtick.direction": "inout",
"ytick.direction": "inout",
# xtick label distance from tick
"xtick.major.pad": 1.,
"ytick.major.pad": 1.,
# colorbar ticks
"ytick.minor.width": 0.3,
"ytick.minor.size": 1.2,
"axes.linewidth": 0.5,
# "legend.handlelength": 5.0,
"lines.markersize": 4,
"lines.linewidth": 0.8,
# grid opacity 0.3
"grid.alpha": 0.3,
}
plt.rcParams.update(plt_rcparams)
# read Scientific Colour Maps (https://github.com/callumrollo/cmcrameri)
cmap_lipari = LinearSegmentedColormap.from_list('lipari', np.loadtxt("cmcrameri/lipari.txt"))
cmap_oleron = LinearSegmentedColormap.from_list('oleron', np.loadtxt("cmcrameri/oleron.txt"))
cmap_devon = LinearSegmentedColormap.from_list('devon', np.loadtxt("cmcrameri/devon.txt"))
cmap_devonS = LinearSegmentedColormap.from_list('devonS', np.loadtxt("cmcrameri/devonS.txt"))
cmap_devonS = LinearSegmentedColormap.from_list('devonS', np.loadtxt("cmcrameri/devonS.txt"))
cmap_vik = LinearSegmentedColormap.from_list('vik', np.loadtxt("cmcrameri/vik.txt"))
options = Options()
if args.fig == "metric_components":
initial_steady_state_path = os.path.join(args.output_dir, "steady_state", "outputs-Ice1-id_steady_state.h5")
with CheckpointFile(initial_steady_state_path, "r") as afile:
old_mesh = afile.load_mesh("firedrake_default")
u = afile.load_function(old_mesh, "velocity_steady")
h = afile.load_function(old_mesh, "thickness_steady")
# old_mesh = RectangleMesh(320, 20, 640e3, 40e3)
# h = Function(FunctionSpace(old_mesh, "CG", 1)).interpolate(Constant(100))
# u = Function(VectorFunctionSpace(old_mesh, "CG", 1)).interpolate(as_vector([1, 0]))
P1_ten = TensorFunctionSpace(old_mesh, "CG", 1)
mp = {
"dm_plex_metric": {
"target_complexity": 1600,
"h_min": 1.0,
"h_max": 50e3,
"p": 2.0,
"a_max": 1e30,
}
}
metric = _tau_metric(h, u, mp)
metric.normalise()
new_mesh = adapt(old_mesh, metric)
evalues = []
evectors = []
for i, hess in enumerate(metric.dat.data):
eigvals, eigvecs = eig(hess)
evalues.append(eigvals)
evectors.append(eigvecs)
evalues = np.array(evalues)
evectors = np.array(evectors)
fe = (P1_ten.ufl_element().family(), P1_ten.ufl_element().degree())
quotients_x = Function(FunctionSpace(old_mesh, *fe))
density = quotients_x.copy(deepcopy=True)
quotients_x.dat.data[:] = np.sqrt(evalues[:, 1] / evalues[:, 0])
density.dat.data[:] = np.sqrt(evalues[:, 0] * evalues[:, 1])
old_mesh.coordinates.dat.data[:] /= 1e3
old_mesh.coordinates.dat.data[:, 1] -= 40
new_mesh.coordinates.dat.data[:] /= 1e3
new_mesh.coordinates.dat.data[:, 1] -= 40
gridspec_kw = {"height_ratios": [1, 0.13, 1, 0.13, 1], "hspace": 0.37}
fig, axes = plt.subplots(5, 1, figsize=(3.27, 3), sharex=False, gridspec_kw=gridspec_kw)
tripcolor_kw = dict(cmap=cmap_vik, shading="flat", rasterized=True)
interior_kw = dict(linewidth=0.05, alpha=0.9, rasterized=True)
boundary_kw = dict(linewidth=0., color="k")
_ax_kwargs = dict(xlim=(0, 640), ylim=(-40, 0))
tripcolor(density, axes=axes[0],
norm=LogNorm(),
**tripcolor_kw)
cmin, cmax = quotients_x.dat.data.min(), quotients_x.dat.data.max()
tripcolor(quotients_x, axes=axes[2],
norm=LogNorm(vmin=1e-2, vmax=1e2),
**tripcolor_kw)
triplot(new_mesh, axes=axes[-1], interior_kw=interior_kw, boundary_kw=boundary_kw)
ax_titles = [r"Metric density $\rho$", r"Anisotropy quotient $r_1$", "Adapted mesh"]
for i, ax in enumerate([axes[0], axes[2], axes[4]]):
ax.set(**_ax_kwargs)
ax.set_title(ax_titles[i], pad=1)
ax.set_xticks([j*100 for j in range(7)] + [640])
ax.set_xticklabels([] if i != 2 else ["$0$"] + [""]*6 + ["$640$"])
ax.set_yticks([-40, 0])
ax.set_yticklabels([] if i != 2 else ["$-40$", "$0$"])
ax_text(ax, fig, f"({chr(97+i)})", dy=0.29, top=True)
axes[-1].set_xlabel(r"$x\ (\mathrm{km})$", labelpad=-8)
axes[-1].set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-12)
for i, cax in enumerate([axes[1], axes[3]]):
pos = cax.get_position()
pos.x0 += 0.1
pos.x1 -= 0.1
pos.y0 += 0.04
pos.y1 += 0.04
cax.set_position(pos)
cbar = fig.colorbar(axes[i*2].collections[0], cax=cax,
orientation="horizontal",
spacing="proportional",
shrink=0.7,
aspect=30,
)
cbar.ax.xaxis.set_tick_params(pad=0, labelsize=6)
elif args.fig == "schemes":
plt.rcParams.update({"legend.markerscale": 0.7, "lines.markersize": 2,})
fig, ax = plt.subplots(figsize=(3.27, 1.5))
ys = [0.1, 0, -0.1]
ts = [0, 1, 2, 3, 4]
for y in ys:
ax.plot([0, 2], [y, y], 'k-', linewidth=0.75)
# ax.plot([2, 3], [y, y], 'k:', linewidth=0.75)
ax.plot([2.37, 2.5, 2.63], [y, y, y], 'ko', markersize=1.5)
ax.plot([3, 4], [y, y], 'k-', linewidth=0.75)
ax.plot(ts, [y]*len(ts), 'k|', markersize=17, markeredgewidth=0.75)
# subplot a: classical
t_flyadapt = [0, 1, 2, 3]
t_transfer = t_flyadapt
ax.plot(t_flyadapt, [ys[0]]*len(t_flyadapt), 'ko', fillstyle='none', markersize=10)
ax.plot(t_flyadapt, [ys[0]]*len(t_flyadapt), 'kx', markersize=4)
# subplot b: global fixed-point
t_fpiadapt = [4]
t_sample = np.linspace(0, 2, 7).tolist() + np.linspace(3, 4, 4).tolist()
y = ys[1]
ax.plot(t_fpiadapt, [y]*len(t_fpiadapt), 'ks', fillstyle='none', markersize=10)
ax.plot(t_sample, [y]*len(t_sample), 'kx', markersize=4)
# subplot c: combined
y = ys[2]
ax.plot(t_flyadapt, [y]*len(t_flyadapt), 'ko', fillstyle='none', markersize=10,
label=r'Adapt mesh $\mathcal{H}_j^{(0)}$')
ax.plot(t_fpiadapt, [y]*len(t_fpiadapt), 'ks', fillstyle='none', markersize=10,
# label=r'Adapt $\{\mathcal{H}_j^{(k)}\}_j$')
label=r'Adapt mesh sequence $\{\mathcal{H}_j^{(k)}\}_{j=1}^{N_a}$')
ax.plot(t_sample, [y]*len(t_sample), 'kx', markersize=4, label='Sample metric')
connectionstyle = "bar,fraction=-0.05"
ax.annotate("",
xy=(4, 0.025), xycoords='data',
xytext=(0, 0.025), textcoords='data',
arrowprops=dict(arrowstyle="<-", color="0.5",
linewidth=0.6,
linestyle=':',
shrinkA=2, shrinkB=2,
connectionstyle=connectionstyle,
),
)
ax.text(2.5, 0.06, r'$k=k\!+\!1$',
color="0.5",
ha='center')
connectionstyle="bar,angle=0,fraction=-0.03"
ax.annotate("",
xy=(4, y+0.025), xycoords='data',
xytext=(0, -0.025), textcoords='data',
arrowprops=dict(arrowstyle="<-", color="0.5",
linewidth=0.6,
linestyle=':',
shrinkA=2, shrinkB=2,
patchA=None, patchB=None,
connectionstyle=connectionstyle,))
ax.text(2.5, y+0.048, r'$k=k\!+\!1$',
color="0.5",
# fontsize=6,
ha='center')
ax.set_ylim(-0.15, 0.15)
ax.axis('off')
panel_label = ['(a)', '(b)', '(c)']
for i, label in enumerate(panel_label):
ax.text(-0.65, ys[i], label, va='center')
t_texts = [r'$t_0$', r'$t_1$', r'$t_2$', r'$t_{N_a-1}$', r'$T$']
for i, t in enumerate(t_texts):
ax.text(i, 0.15, t, ha='center')
# l = ax.legend(ncols=3, loc='upper center', bbox_to_anchor=(0.45, 0.0),)
# Separate the legend into two rows
handles, labels = ax.get_legend_handles_labels()
order = [2, 0, 1] # Change the order of the labels
legend1 = ax.legend([handles[i] for i in order[:-1]], [labels[i] for i in order[:-1]], loc='upper center', bbox_to_anchor=(0.45, 0.05), ncol=2)
legend2 = ax.legend([handles[order[-1]]], [labels[order[-1]]], loc='upper center', bbox_to_anchor=(0.45, -0.1))
ax.add_artist(legend1)
elif args.fig == "initial_steady_state":
initial_steady_state_path = os.path.join(args.output_dir, "steady_state", "outputs-Ice1-id_steady_state.h5")
with CheckpointFile(initial_steady_state_path, "r") as afile:
old_mesh = afile.load_mesh("firedrake_default")
u = afile.load_function(old_mesh, "velocity_steady")
h = afile.load_function(old_mesh, "thickness_steady")
z_b = Function(FunctionSpace(old_mesh, "CG", 1)).interpolate(uf.mismip_bed_topography(old_mesh))
gl = uf.get_gl(uf.get_haf(h))
fig, axes = plt.subplots(2, 1, figsize=(3.27, 2.3), sharex=True)
tricontourf_kw = dict(cmap=cmap_vik, levels=9)
for i, (ax, f) in enumerate(zip(axes, [h, u])):
cf = tricontourf(f, axes=ax, **tricontourf_kw)
for c in cf.collections:
c.set_rasterized(True)
# cs = tricontour(z_b, axes=ax, colors="white", linewidths=0.1, alpha=0.5,)
z_b_data = z_b.dat.data
x_coords, y_coords = old_mesh.coordinates.dat.data.T
cs = ax.tricontour(x_coords, y_coords, z_b_data,
levels=[-605, -405, -205, 5, 205],
colors="white", linewidths=0.1, alpha=0.5)
ax.clabel(cs, colors="white", inline=True, fontsize=6)
# ax.clabel(cs, cs.levels, colors="white")#, inline=True, fmt="%1.0f", fontsize=6)
ax.plot(gl[:, 0], gl[:, 1], 'y-', linewidth=1, label="Grounding line",
path_effects=[pe.Stroke(linewidth=2, foreground='black'), pe.Normal()])
cbar = fig.colorbar(cf, ax=ax, orientation="horizontal", pad=0.13, aspect=30, shrink=0.7, location="top")
for c in cbar.ax.collections:
c.set_rasterized(True)
cbar.set_label(r"$h$ ($\mathrm{m}$)" if f == h else r"$\mathbf{u}$ ($\mathrm{ma^{-1}}$)")
cbar.ax.xaxis.set_ticks_position('bottom')
cbar.ax.xaxis.set_label_position('top')
if i == 0:
# Hide every second tick label for the first colorbar
ticks = cbar.ax.get_xticks()
tick_labels = [label.get_text() if j % 2 == 0 else '' for j, label in enumerate(cbar.ax.get_xticklabels())]
cbar.ax.set_xticklabels(tick_labels)
ax.set_xlim(0, 640e3)
ax.set_ylim(0, 40e3)
ax.set_xticks([j*100e3 for j in range(7)] + [640e3])
ax.set_xticklabels([] if ax != axes[-1] else ["$0$"] + [""]*6 + ["$640$"])
ax.set_yticks([0, 40e3])
ax.set_yticklabels([] if ax != axes[-1] else ["$-40$", "$0$"])
# axes[0].set_title(r"Thickness $h$ ($\mathrm{m}$)")
# axes[1].set_title(r"Velocity $u$ ($\mathrm{m\,a^{-1}}$)")
axes[-1].set_xlabel(r"$x\ (\mathrm{km})$", labelpad=-8)
axes[-1].set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-12)
ax_text(axes[0], fig, "(a)", dy=0.25, top=True, colour="white")
ax_text(axes[1], fig, "(b)", dy=0.25, top=True, colour="white")
# Custom legend entry for bed topography z_b
z_b_line = Line2D([0], [0], color='#b3b3b3', linewidth=0.1, alpha=0.5, label=r"Topography contours ($\mathrm{m}$)")
axes[1].legend(loc="upper center", bbox_to_anchor=(0.5, -0.2), ncol=2, frameon=False,
handles=[z_b_line, *axes[1].get_legend_handles_labels()[0]])
fig.subplots_adjust(hspace=0.1)
elif args.fig == "uniform_convergence":
colors = cmap_lipari(np.linspace(0, 1, 6))
Lx = 640e3
Ly = 40e3
ny = 40
msh = RectangleMesh(int(Lx/Ly)*ny, ny, Lx, Ly)
z_b = Function(FunctionSpace(msh, "CG", 1)).interpolate(uf.mismip_bed_topography(msh))
msh.coordinates.dat.data[:] /= 1e3
# Reference solutions
years = np.arange(1., 201., 1)
fig, axes = plt.subplots(2, 2, figsize=(4.72, 2.7), sharex=False)
# dictionary mapping level of refinement to mesh resolution in km
levels_res = {0: 4, 1: 2, 2: 1, 3: 0.5}#, 4: 0.25}
for lv in levels_res.keys():
res_m = int(levels_res[lv] * 1000)
dir_path = os.path.join(args.output_dir, f"uniform_{res_m}", "analysis")
vafs = np.load(os.path.join(dir_path, "vafs.npy"))[0] / 1e3 # 1000 km^3
midline_x_gls = np.load(os.path.join(dir_path, "midline_x_gls.npy"))[0] / 1e3
plot_kwargs = dict(
c=f"C{lv}",
label=fr"${levels_res[lv]}\ \mathrm{{km}}$",
)
axes[0, 0].plot(years, vafs, **plot_kwargs,)
axes[1, 0].plot(years, midline_x_gls, **plot_kwargs)
for i in range(2):
yr = (i+1)*100-1
gl = np.load(os.path.join(dir_path, "gls.npy"))[0][yr] / 1e3
# tidy up the gl
gl = np.round(gl / levels_res[lv]) * levels_res[lv]
gl = uf.tidy_gl(gl)
# subtract 40km from all y positions of gl
gl[:, 1] -= 40
# tripcolor(z_b, axes=axes[i, 1], cmap="Blues_r")
# tricontour(z_b, axes=axes[i, 1], colors="white", linewidths=0.1, alpha=0.5)
axes[i, 1].plot(gl[:, 0], gl[:, 1], **plot_kwargs)
axes[i, 1].set_ylim(-40, 0)
axes[i, 1].set_xlim(380, 520)
# axes[i, 1].set_title(f"Grounding line at $t\!=\!{yr}"+r"\ \mathrm{a}$")
axes[i, 1].grid(True)
# axes[i, 1].yaxis.set_major_locator(MaxNLocator(nbins=2))
ice1_base_time_plot(axes[0, 0])
ice1_base_time_plot(axes[1, 0])
axes[0, 0].set_ylim(15, 17) # vaf
axes[1, 0].set_ylim(380, 460)
# axes[0, 0].set_title("Ice mass (Gt)")
axes[0, 0].set_ylabel(r"$V_f\ (10^3\ \mathrm{km}^3$)")
# axes[1, 0].set_title(r"Midchannel g.l. position ($y\!=\!0\ \mathrm{km}$)")
axes[1, 0].set_ylabel(r"$x_{gl}(y=0)\ (\mathrm{km})$")
# axes[0].set_xlabel("Years")
axes[1, 0].set_xlabel(r"Time ($\mathrm{a}$)")
axes[1, 1].set_xlabel(r"$x\ (\mathrm{km})$")
for ax in axes[:, 1]:
ax.set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-13)
ax.set_yticks([-10*(4-jj) for jj in range(5)])
ax.set_yticklabels(["$-40$", "", "", "", "$0$"])
titles = [
"Volume above flotation",
"Midchannel grounding line position",
r"Grounding line at $t\!=\!100\ \mathrm{a}$",
r"Grounding line at $t\!=\!200\ \mathrm{a}$"
]
for title, ax in zip(titles, axes.flatten(order="F")):
ax.set_title(title, pad=1)
panel_labels = [["(a)", "(c)"], ["(b)", "(d)"]]
panel_labels_pos = [[(5, 55.5), (385, 39)], [(5, 385), (385, 5)]]
for i in range(2):
for j in range(2):
x_label_pos, y_label_pos = get_label_pos(axes[i, j], fig)
axes[i, j].text(x_label_pos, y_label_pos, panel_labels[i][j])
# axes[i, j].text(*panel_labels_pos[i][j], panel_labels[i][j])
for ax in axes.flatten():
# set distance from tick label to tick to 1
ax.tick_params(pad=1)
# turn off x ticks for top plots
for ax in axes[0]:
ax.tick_params(axis="x", which="both", labelbottom=False)
# add a legend below the plot
axes[0, 0].legend(
loc="upper center",
bbox_to_anchor=(1.03, -1.5),
ncol=5,
title="Mesh resolution",
# distance between labels
columnspacing=1.2,
# frameon=False,
)
fig.subplots_adjust(wspace=0.15, hspace=0.2)
elif args.fig == "strat_comparison":
# set marker size to 2
plt.rcParams.update({"lines.markersize": 2})
colors = cmap_oleron(np.linspace(0, 1, 14))
ref_dirpath = os.path.join(args.output_dir, "uniform_250", "analysis")
glob_tau_1600 = os.path.join(args.output_dir, "1600_tau_20_global", "analysis")
glob_tau_3200 = os.path.join(args.output_dir, "3200_tau_20_global", "analysis")
hybr_tau_1600 = os.path.join(args.output_dir, "1600_tau_20_hybrid", "analysis")
hybr_tau_3200 = os.path.join(args.output_dir, "3200_tau_20_hybrid", "analysis")
fpaths = [glob_tau_1600, glob_tau_3200, hybr_tau_1600, hybr_tau_3200]
labels = [r"Global, $\mathcal{C}=1600$", r"Global, $\mathcal{C}=3200$",
r"Hybrid, $\mathcal{C}=1600$", r"Hybrid, $\mathcal{C}=3200$"]
# reference volume above flotation and midchannel grounding line position
ref_vafs = np.load(os.path.join(ref_dirpath, "vafs.npy"))[0, 1:]
ref_xgls = np.load(os.path.join(ref_dirpath, "midline_x_gls.npy"))[0, 1:]
# first iteration of the global algorithm is the same as uniform 4000m simulation
ref_4000m_dirpath = os.path.join(args.output_dir, "uniform_4000", "analysis")
ref_lv0_vafs = np.load(os.path.join(ref_4000m_dirpath, "vafs.npy"))[0, 1:]
ref_lv0_xgls = np.load(os.path.join(ref_4000m_dirpath, "midline_x_gls.npy"))[0, 1:]
diff_vafs_lv0 = np.linalg.norm(ref_vafs - ref_lv0_vafs, np.inf)
diff_xgls_lv0 = np.linalg.norm(ref_xgls - ref_lv0_xgls, np.inf)
fig, axes = plt.subplots(3, 1, figsize=(3.27, 4))
for i in range(len(fpaths)):
vafs = np.load(f"{fpaths[i]}vafs.npy")
xgls = np.load(f"{fpaths[i]}midline_x_gls.npy")
# replace each nan value in xgls with the average of the two adjacent values
for j in range(len(xgls)):
for k in range(1, len(xgls[j])-1):
if np.isnan(xgls[j, k]):
xgls[j, k] = (xgls[j, k-1] + xgls[j, k+1]) / 2
diff_vafs, diff_xgls = [], []
if i < 2:
diff_vafs.append(diff_vafs_lv0)
diff_xgls.append(diff_xgls_lv0)
for j in range(len(vafs)):
diff_vafs.append(np.linalg.norm(vafs[j] - ref_vafs, np.inf))
diff_xgls.append(np.linalg.norm(xgls[j] - ref_xgls, np.inf))
if i == 2:
diff_vafs = diff_vafs[:-1]
diff_xgls = diff_xgls[:-1]
if i == 3:
diff_vafs[-2] = diff_vafs[-1]
diff_xgls[-2] = diff_xgls[-1]
diff_vafs = diff_vafs[:-1]
diff_xgls = diff_xgls[:-1]
# convert xgls to km
diff_xgls = np.array(diff_xgls) / 1e3
num_iters = list(range(1, len(diff_vafs)+1))
for ax, n in zip(axes, [diff_vafs, diff_xgls]):
color = colors[10] if i < 2 else colors[1]
linestyle = "-" if i % 2 == 0 else "--"
fillstyle = "full"
ax.semilogy(num_iters, n, 'o-', label=labels[i], color=color, linestyle=linestyle, fillstyle=fillstyle)
# ax.plot(num_iters, n, 'o-', label=labels[i], color=color, linestyle=linestyle)
dofs = np.load(f"{fpaths[-2]}dofs.npy")
dofs = dofs[:-1]
for i, dof in enumerate(dofs, start=1):
if i in (1, 2, 4, 6):
axes[-1].plot(dof, label=f"{i}", color=colors[6-i])
dofs_glob = np.load(f"{fpaths[0]}dofs.npy")[-1]
axes[-1].plot(dofs_glob, label="10", color=colors[10],)
xlims = [(1, 10), (1, 10), (0, 200)]
ylims = [(1e1, 2e3), (1e0, 1e2), (1750, 3750)]
ylims = [(1e1, 2e3), (1e0, 1e2), (1750, 4000)]
xlabels = ["", "Iteration $k$", "Time $(a)$"]
# ylabels = [r"$||V_f-{V_f}_\mathrm{ref}||_\infty (10^{12} m^3)$",
# r"$||x_{gl}-{x_{gl}}_\mathrm{ref}||_\infty (km)$",
# "$N_v$"]
ylabels = [r"$||\Delta V_f||_\infty \ (\mathrm{km}^3)$",
r"$||\Delta x_{gl}||_\infty \ (\mathrm{km})$",
"$N_v$"]
ncols = [1, 1, 2]
axes[0].set_title("Convergence of global and hybrid algorithms")
axes[-1].set_title(r"Temporal distribution of $N_v$ ($\mathcal{C}=1600$)") # in the combined scheme")
for i, ax in enumerate(axes):
ax.set_xlim(xlims[i])
ax.set_ylim(ylims[i])
ax.set_xlabel(xlabels[i])
ax.set_ylabel(ylabels[i])
if i != 2:
ax.set_xticks(np.arange(1, 11))
if i == 2:
ax.set_yticks(np.arange(1750, 3751, 500))
if i == 0:
ax.legend(ncol=ncols[i])
elif i == 2:
handles, labels = ax.get_legend_handles_labels()
lg0 = ax.legend(handles[:4], labels[:4], ncol=2, title="Iteration (hybrid)",)
lg1 = ax.legend(handles[4:], labels[4:], ncol=1, title="Iteration (global)",)
for lg in [lg0, lg1]:
lg._legend_box.sep = 0
ax.add_artist(lg0)
lg1.set_bbox_to_anchor((0.63, 0.25))
ax.grid()
x_label_pos, y_label_pos = get_label_pos(ax, fig, top=False)
if i == 0:
y_label_pos -= 28
elif i == 1:
y_label_pos -= 2
ax.text(x_label_pos, y_label_pos, ["(a)", "(b)", "(c)"][i])
axes[0].set_xticklabels([])
fig.align_labels()
fig.subplots_adjust(hspace=0.1)
# reposition the last axis, move it down
pos = axes[-1].get_position()
pos.y0 -= 0.1
pos.y1 -= 0.1
axes[-1].set_position(pos)
elif args.fig == "strat_comparison_meshes":
glob_tau_1600 = os.path.join(args.output_dir, "1600_tau_20_global", "outputs-Ice1-id_1600_tau_20_global.h5")
hybr_tau_1600 = os.path.join(args.output_dir, "1600_tau_20_hybrid", "outputs-Ice1-id_1600_tau_20_hybrid.h5")
fpaths = [glob_tau_1600, hybr_tau_1600]
fig_labels = ["(a)", "(b)", "(c)", "(d)"]
gridspec_kw = dict(hspace=0.)
fig, axes = plt.subplots(4, 1, figsize=(3.27, 3.5), sharex=True, gridspec_kw=gridspec_kw)
interior_kw = {"linewidth": 0.05, "alpha": 0.9, "rasterized": True}
for i in range(len(fpaths)):
glob = i == 0
niter = 10 if i == 0 else 6
with CheckpointFile(fpaths[i], "r") as afile:
mesh_9 = afile.load_mesh(f"mesh_iter_{niter}_int_9")
mesh_19 = afile.load_mesh(f"mesh_iter_{niter}_int_19")
cell_sizes_9 = Function(FunctionSpace(mesh_9, "DG", 0)).interpolate(mesh_9.cell_sizes)
cell_sizes_19 = Function(FunctionSpace(mesh_19, "DG", 0)).interpolate(mesh_19.cell_sizes)
for j, mesh in enumerate([mesh_9, mesh_19]):
ax = axes[i+j*2]
triplot(mesh, axes=ax, interior_kw=interior_kw)
mesh_interval = 9 if j == 0 else 19
mesh_label = fr"$\mathcal{{H}}_{{{mesh_interval}}}^{{({niter})}}$"
alg_label = "Global" if glob else "Hybrid"
# ax_text(ax, fig, f"{mesh_label}, {alg_label}", dy=0.25, top=False)
ax_text(ax, fig, f"{fig_labels[i+j*2]} {alg_label}, {mesh_label}", dy=0.25, top=True)
ax_text(ax, fig, f"$N_v={mesh.num_vertices()}$", top=False)
ax.set_yticks([0, 40e3])
ax.set_yticklabels([] if ax != axes[-1] else ["$-40$", "$0$"])
ax.set_xlim(0, 640e3)
ax.set_ylim(0, 40e3)
# reposition all axes such that there is a small space between 2nd and 3rd axes
dy = 0.01
for i, ax in enumerate(axes):
pos = ax.get_position()
if i == 0:
pos.y0 += dy
elif i == 1:
pos.y0 += dy
pos.y1 += dy
elif i == 2:
pos.y0 -= dy
pos.y1 -= dy
elif i == 3:
pos.y1 -= dy
ax.set_position(pos)
axes[-1].set_xticks([0, 100e3, 200e3, 300e3, 400e3, 500e3, 600e3, 640e3])
axes[-1].set_xticklabels(["$0$"] + [""]*6 + ["$640$"])
axes[-1].set_xlabel(r"$x\ (\mathrm{km})$", labelpad=-8)
axes[-1].set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-8)
elif args.fig == "h_field_comparison":
categorical_colors = cmap_devonS(np.linspace(0, 1, 11))
# ref4_fpath = "/data3/glac_adapt/data/reference_outputs/ref_4/analysis/gls.npy"
ref4_fpath = os.path.join(args.output_dir, "uniform_250", "analysis", "gls.npy")
ref4_gl_90 = np.load(ref4_fpath)[0, 89]
ref4_gl_100 = np.load(ref4_fpath)[0, 99]
cs = [800*2**i for i in range(5)]
fig = plt.figure(figsize=(4.72, 4))
gs = gridspec.GridSpec(11, 2,
figure=fig,
hspace=0.2,
wspace=0.05,
width_ratios=[1, 1.5], height_ratios=[1] * 10 + [0.3])
fields = ["h", "u", "u-int-s", "s", "tau"]
labels = {"h": "$h$", "tau": r"$\tau_b$", "u": "$u$", "u-int-h": r"$(h,\,u)$", "s": "$s$", "u-int-s": r"$(u,\,s)$"}
for i, field in enumerate(fields):
d, n_h, n_umag = [], [], []
n_vaf, n_xgl = [], []
for c in cs:
analysis_path = os.path.join(args.output_dir, f"{int(c)}_{field}_20_hybrid", "analysis")
norms = np.load(os.path.join(analysis_path, "norms.npy"))
dofs = np.load(os.path.join(analysis_path, "dofs.npy"))
norms_avg_time = np.mean(norms, axis=2)
norms_avg_fields = np.mean(norms_avg_time, axis=0)
min_iter_idx = np.argmin(norms_avg_time[1])
if c == 6400:
simulation_id = f"{c}_{field}_20_hybrid"
fpath = os.path.join(args.output_dir, f"{simulation_id}", f"outputs-Ice1-id_{simulation_id}.h5")
with CheckpointFile(fpath, "r") as afile:
msh = afile.load_mesh(f"mesh_iter_{min_iter_idx}_int_9")
ax = plt.subplot(gs[(i*2):(i*2+2), 1])
triplot(msh, axes=ax, interior_kw={"linewidth": 0.05,
# "alpha": 0.2,
"rasterized": True
})
ax.plot(ref4_gl_90[:, 0], ref4_gl_90[:, 1], 'y--', linewidth=0.5, rasterized=True, label=r"$t=90\ \mathrm{a}$")
ax.plot(ref4_gl_100[:, 0], ref4_gl_100[:, 1], 'y-', linewidth=0.5, rasterized=True, label=r"$t=100\ \mathrm{a}$")
# ax.text(10e3, 2e3, f"{field}, {msh.num_vertices()} DoFs")
ax.set_xlim(0, 640e3)
ax.set_ylim(0, 40e3)
ax.set_xticks([jj*100e3 for jj in range(7)] + [640e3])
ax.set_yticks([0, 40e3])
ax.set_xticklabels([])
ax.set_yticklabels([])
x_label_pos, y_label_pos = get_label_pos(ax, fig, top=True)
ax.text(x_label_pos, y_label_pos, ["(c)", "(d)", "(e)", "(f)", "(g)"][i])
if i == 4:
ax.set_xlabel(r"$x\ (\mathrm{km})$", labelpad=-6)
ax.set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-10)
ax.set_xticks([jj*100e3 for jj in range(7)] + [640e3])
ax.set_xticklabels(["$0$"] + [""]*6 + ["$640$"])
ax.set_yticklabels(["$-40$", "$0$"])
ax.yaxis.tick_right()
ax.yaxis.set_label_position("right")
# increase the distance from x tick labels to the plot
ax.xaxis.set_tick_params(pad=5.5)
d.append(np.mean(dofs, axis=1)[min_iter_idx])
n_h.append(norms_avg_time[0, min_iter_idx])
n_umag.append(norms_avg_time[1, min_iter_idx])
ax00 = plt.subplot(gs[0:5, 0])
ax10 = plt.subplot(gs[5:10, 0])
ax00.loglog(d, n_h, 'o-', label=labels[field], color=categorical_colors[i])
ax10.loglog(d, n_umag, 'o-', label=labels[field], color=categorical_colors[i])
ref_d, ref_n_h, ref_n_umag = [], [], []
for res in 4000, 2000, 1000, 500, 250:
norms = np.load(os.path.join(args.output_dir, f"uniform_{res}", "analysis", "norms.npy"))
ref_d.append(np.load(fpath.replace("norms", "dofs"))[0, 0])
norms_avg_time = np.mean(norms, axis=1)
ref_n_h.append(norms_avg_time[0])
ref_n_umag.append(norms_avg_time[1])
ax00.loglog(ref_d, ref_n_h, 'o:', label="Uniform", color='k')
ax10.loglog(ref_d, ref_n_umag, 'o:', label="Uniform", color='k')
for i, (_ax, n) in enumerate(zip([ax00, ax10], [n_h, n_umag])):
_ax.set_xlim(1e3, 1.2e5)
_ax.grid()
x_label_pos, y_label_pos = get_label_pos(_ax, fig)
_ax.text(x_label_pos, y_label_pos, ["(a)", "(b)"][i])
ax00.set_xticklabels([])
ax00.set_ylim(1e-3, 2e-1)
ax10.set_ylim(1e-2, 1e-0)
ax10.set_xlabel("Average $N_v$")
ax00.set_ylabel(r"$\tilde{e}_h$")
ax10.set_ylabel(r"$\tilde{e}_u$")
# reposition ax00 a bit more to above and ax10 a bit more down
pos = ax00.get_position()
pos.y0 += 0.008
ax00.set_position(pos)
pos = ax10.get_position()
pos.y1 -= 0.008
ax10.set_position(pos)
# create an axis below the bottom one for the legend
ax0_legend = plt.subplot(gs[10, 0])
ax0_legend.axis("off")
handles = ax00.get_legend_handles_labels()[0]
labels = ax00.get_legend_handles_labels()[1]
leg1 = ax0_legend.legend(handles[:3], labels[:3], loc='lower center', ncol=3, frameon=False)
leg2 = ax0_legend.legend(handles[3:], labels[3:], loc='upper center', ncol=3, frameon=False)
ax0_legend.add_artist(leg1)
legend_pos = ax0_legend.get_position()
legend_pos.y0 -= 0.13
legend_pos.y1 -= 0.13
ax0_legend.set_position(legend_pos)
legend_ax = plt.subplot(gs[10, 1])
legend_ax.axis('off')
legend_ax.set_title("Reference g.l. contours", fontsize=7, pad=6)
handles = ax.get_legend_handles_labels()[0]
labels = ax.get_legend_handles_labels()[1]
legend_ax.legend(handles=handles[4:], labels=labels[4:], loc='center', ncol=2)
# move legend_ax below
legend_pos = legend_ax.get_position()
legend_pos.y0 -= 0.13
legend_pos.y1 -= 0.13
legend_ax.set_position(legend_pos)
fig.align_labels()
elif args.fig == "hessian_meshes":
ref4_fpath = os.path.join(args.output_dir, "uniform_250", "analysis", "gls.npy")
ref4_gl_90 = np.load(ref4_fpath)[0, 89]
ref4_gl_100 = np.load(ref4_fpath)[0, 99]
c = 6400
fields = ["h", "u", "u-int-h", "tau"]
labels = {"h": "$h$", "tau": r"$\tau_b$", "u": r"$\mathbf{u}$", "u-int-h": r"$(h,\,\mathbf{u})$"}
subplot_labels = ["(a)", "(b)", "(c)", "(d)",]
fig, axes = plt.subplots(len(fields), 1, figsize=(3.27, 3), sharex=True, gridspec_kw={"hspace": 0.0})
for i, field in enumerate(fields):
simdir_path = os.path.join(args.output_dir, f"{c}_{field}_20_hybrid/")
norms = np.load(os.path.join(simdir_path, "analysis", "norms.npy"))
norms_avg_time = np.mean(norms, axis=2)
norms_avg_fields = np.mean(norms_avg_time, axis=0)
min_iter_idx = np.argmin(norms_avg_time[1])
fpath = os.path.join(simdir_path, f"outputs-Ice1-id_{c}_{field}_20_hybrid.h5")
with CheckpointFile(fpath, "r") as afile:
msh = afile.load_mesh(f"mesh_iter_{min_iter_idx}_int_9")
ax = axes[i]
interior_kw = {"linewidth": 0.05, "alpha": 0.9, "rasterized": True}
triplot(msh, axes=ax, interior_kw=interior_kw)
ax.plot(ref4_gl_90[:, 0], ref4_gl_90[:, 1], 'y--', linewidth=0.5, rasterized=True, label=r"$t=90\ \mathrm{a}$")
ax.plot(ref4_gl_100[:, 0], ref4_gl_100[:, 1], 'y-', linewidth=0.5, rasterized=True, label=r"$t=100\ \mathrm{a}$")
ax.set_xlim(0, 640e3)
ax.set_ylim(0, 40e3)
ax.set_xticks([jj*100e3 for jj in range(7)] + [640e3])
ax.set_yticks([0, 40e3])
ax.set_xticklabels([])
ax.set_yticklabels([])
ax_text(ax, fig, f"{subplot_labels[i]}: {labels[field]}", dy=0.27, top=True)
ax_text(ax, fig, f"$N_v = {msh.num_vertices()}$", top=False)
ax = axes[-1]
ax.set_xlabel(r"$x\ (\mathrm{km})$", labelpad=-6)
ax.set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-12)
ax.set_xticks([jj*100e3 for jj in range(7)] + [640e3])
ax.set_xticklabels(["$0$"] + [""]*6 + ["$640$"])
ax.set_yticklabels(["$-40$", "$0$"])
ax.xaxis.set_tick_params(pad=1)
ax.yaxis.set_tick_params(pad=1)
handles = ax.get_legend_handles_labels()[0]
labels = ax.get_legend_handles_labels()[1]
ax.legend(
handles=handles[4:], labels=labels[4:],
loc='upper center', bbox_to_anchor=(0.5, -0.25),
title="Reference grounding line contours",
ncol=2,
)
elif args.fig == "hessian_aspect_ratio":
from animate.quality import QualityMeasure
c = 6400
fields = ["h", "u", "u-int-h", "tau"]
labels = {"h": "$h$", "tau": r"$\tau_b$", "u": r"$\mathbf{u}$", "u-int-h": r"$(h,\,\mathbf{u})$"}
subplot_labels = ["(a)", "(b)", "(c)", "(d)",]
gridspec_kw = {"hspace": 0.05, "height_ratios": [0.2] + [1] * len(fields)}
fig, axes = plt.subplots(len(fields)+1, 1, figsize=(3.27, 3), gridspec_kw=gridspec_kw)
for i, field in enumerate(fields):
analysis_path = os.path.join(args.output_dir, f"{c}_{field}_20_hybrid", "analysis")
norms = np.load(os.path.join(analysis_path, "norms.npy"))
norms_avg_time = np.mean(norms, axis=2)
norms_avg_fields = np.mean(norms_avg_time, axis=0)
min_iter_idx = np.argmin(norms_avg_time[1])
simulation_id = f"{c}_{field}_20_hybrid"
fpath = os.path.join(args.output_dir, simulation_id, f"outputs-Ice1-id_{simulation_id}.h5")
with CheckpointFile(fpath, "r") as afile:
msh = afile.load_mesh(f"mesh_iter_{min_iter_idx}_int_9")
qm = QualityMeasure(msh)
ar = qm("aspect_ratio")
ax = axes[i+1]
im = tripcolor(ar, axes=ax, cmap=cmap_devon, rasterized=True, norm=LogNorm(vmin=1e0, vmax=1e2))
ax.set_xlim(0, 640e3)
ax.set_ylim(0, 40e3)
ax.set_xticks([jj*100e3 for jj in range(7)] + [640e3])
ax.set_yticks([0, 40e3])
ax.set_xticklabels([])
ax.set_yticklabels([])
ax_text(ax, fig, f"{subplot_labels[i]}: {labels[field]}", dy=0.28, top=True, colour="white")
ax = axes[-1]
ax.set_xlabel(r"$x\ (\mathrm{km})$", labelpad=-8)
ax.set_ylabel(r"$y\ (\mathrm{km})$", labelpad=-12)
ax.set_xticks([jj*100e3 for jj in range(7)] + [640e3])
ax.set_xticklabels(["$0$"] + [""]*6 + ["$640$"])
ax.set_yticklabels(["$-40$", "$0$"])
cax = axes[0]
cbar = fig.colorbar(im, cax=cax, orientation='horizontal', pad=0.)
cax_pos = cax.get_position()
cax_pos.x0 += 0.12
cax_pos.x1 -= 0.12
cax_pos.y0 += 0.04
cax_pos.y1 += 0.04
cax.set_position(cax_pos)
cbar.ax.xaxis.set_tick_params(pad=0, labelsize=6)
cbar.ax.set_title(r"Aspect ratio of adapted mesh elements of $\mathcal{H}_9$", pad=0.2)
elif args.fig == "hessian_err":
categorical_colors = cmap_devonS(np.linspace(0, 1, 11))
cs = [800*2**i for i in range(5)]
fig = plt.figure(figsize=(4.72, 4))
gs = gridspec.GridSpec(7, 2,
figure=fig,
hspace=0.2,
wspace=0.04,
width_ratios=[1, 1.5], height_ratios=[1] * 6 + [0.2])
left_axes = [plt.subplot(gs[3*i:3*(i+1), 0]) for i in range(2)]
legend_ax = plt.subplot(gs[6, 0])
right_axes = [plt.subplot(gs[i:i+1, 1]) for i in range(6)]
cbar_ax = plt.subplot(gs[6, 1])
fields = ["h", "u", "tau", "u-int-h"]
labels = {"h": "$h$", "tau": r"$\tau_b$", "u": r"$\mathbf{u}$", "u-int-h": r"$(h,\,\mathbf{u})$"}
markers = {"uniform": ".", "h": "+", "u": "s", "tau": "x", "u-int-h": "o"}
linestyles = {"uniform": ":", "h": "-", "u": "-", "tau": "-", "u-int-h": "-"}
ref_fpath = os.path.join(args.output_dir, "uniform_250", "outputs-Ice1-id_uniform_250.h5")
with CheckpointFile(ref_fpath, "r") as afile:
ref_msh = afile.load_mesh("mesh_iter_0_int_0")
ref_h_100a = afile.load_function(ref_msh, "thickness_iter_0_int_0_yr_100.0")
ref_u_100a = afile.load_function(ref_msh, "velocity_iter_0_int_0_yr_100.0")
ref_umag = sqrt(dot(ref_u_100a, ref_u_100a))
Q = FunctionSpace(ref_msh, "CG", 1)
V = VectorFunctionSpace(ref_msh, "CG", 1)
for i, field in enumerate(fields):
d, n_h, n_umag = [], [], []
for c in cs:
sim_dir_path = os.path.join(args.output_dir, f"{c}_{field}_20_hybrid/")
analysis_path = os.path.join(sim_dir_path, "analysis/")
norms = np.load(os.path.join(analysis_path, "norms.npy"))
dofs = np.load(os.path.join(analysis_path, "dofs.npy"))
norms_avg_time = np.mean(norms, axis=2)
norms_avg_fields = np.mean(norms_avg_time, axis=0)