def __init__(self, *args, **kwargs):
# Init grid
super().__init__(*args, **kwargs)
# Gridded properties
self.Gridded = DotDict(
K=np.ones((2, *self.shape)), # permeability in x&y dirs.
por=np.ones(self.shape), # porosity
)
self.Fluid = DotDict(
vw=1.0,
vo=1.0, # Viscosities
swc=0.0,
sor=0.0, # Irreducible saturations
)
def TPFA(self, K, q):
"""Two-point flux-approximation (TPFA) of Darcy:
diffusion w/ nonlinear coefficient K.
"""
# Compute transmissibilities by harmonic averaging.
L = K**(-1)
TX = np.zeros((self.Nx + 1, self.Ny))
TY = np.zeros((self.Nx, self.Ny + 1)) # noqa
TX[1:-1, :] = 2 * self.hy / self.hx / (L[0, :-1, :] + L[0, 1:, :])
TY[:, 1:-1] = 2 * self.hx / self.hy / (L[1, :, :-1] + L[1, :, 1:])
# Assemble TPFA discretization matrix.
x1 = TX[:-1, :].ravel()
x2 = TX[1:, :].ravel()
y1 = TY[:, :-1].ravel()
y2 = TY[:, 1:].ravel()
# Setup linear system
DiagVecs = [-x2, -y2, y1 + y2 + x1 + x2, -y1, -x1] # noqa
DiagIndx = [-self.Ny, -1, 0, 1, self.Ny] # noqa
# Coerce system to be SPD (ref article, page 13).
DiagVecs[2][0] += np.sum(self.Gridded.K[:, 0, 0])
A = self.spdiags(DiagVecs, DiagIndx)
# Solve
# u = np.linalg.solve(A.A, q) # direct dense solver
u = spsolve(A.tocsr(), q) # direct sparse solver
# u, _info = cg(A, q) # conjugate gradient
# Could also try scipy.linalg.solveh_banded which, according to
# https://scicomp.stackexchange.com/a/30074 uses the Thomas algorithm,
# as recommended by Aziz and Settari ("Petro. Res. simulation").
# NB: stackexchange also mentions that solve_banded does not work well
# when the band offsets large, i.e. higher-dimensional problems.
# Extract fluxes
P = u.reshape(self.shape)
V = DotDict(
x=np.zeros((self.Nx + 1, self.Ny)),
y=np.zeros((self.Nx, self.Ny + 1)), # noqa
)
V.x[1:-1, :] = (P[:-1, :] - P[1:, :]) * TX[1:-1, :]
V.y[:, 1:-1] = (P[:, :-1] - P[:, 1:]) * TY[:, 1:-1]
return P, V
def init(fignum, stats, key0, plot_u, E, P, **kwargs):
xx, yy, mu, _, tseq = \
stats.xx, stats.yy, stats.mu, stats.spread, stats.HMM.tseq
# Set parameters (kwargs takes precedence over params_orig)
p = DotDict(
**{kw: kwargs.get(kw, val)
for kw, val in params_orig.items()})
# Lag settings:
has_w = hasattr(stats, 'w')
if p.Tplot == 0:
K_plot = 1
else:
T_lag, K_lag, a_lag = validate_lag(p.Tplot, tseq)
K_plot = comp_K_plot(K_lag, a_lag, plot_u)
# Extend K_plot forther for adding blanks in resampling (PartFilt):
if has_w:
K_plot += a_lag
# Dimension settings
if not p.dims:
p.dims = arange(M)
if not p.labels:
p.labels = ["$x_%d$" % d for d in p.dims]
assert len(p.dims) == M
# Set up figure, axes
fig, _ = place.freshfig(fignum, figsize=(5, 5))
ax = plt.subplot(111, projection='3d' if is_3d else None)
ax.set_facecolor('w')
ax.set_title("Phase space trajectories")
# Tune plot
for ind, (s, i, t) in enumerate(zip(p.labels, p.dims, "xyz")):
viz.set_ilim(ax, ind,
*viz.stretch(*viz.xtrema(xx[:, i]), 1 / p.zoom))
eval("ax.set_%slabel('%s')" % (t, s))
# Allocate
d = DotDict() # data arrays
h = DotDict() # plot handles
s = DotDict() # scatter handles
if E is not None:
d.E = RollingArray((K_plot, len(E), M))
h.E = []
if P is not None:
d.mu = RollingArray((K_plot, M))
if True:
d.x = RollingArray((K_plot, M))
if list(p.obs_inds) == list(p.dims):
d.y = RollingArray((K_plot, M))
# Plot tails (invisible coz everything here is nan, for the moment).
if 'E' in d:
h.E += [
ax.plot(*xn, **p.ens_props)[0]
for xn in np.transpose(d.E, [1, 2, 0])
]
if 'mu' in d:
h.mu = ax.plot(*d.mu.T, 'b', lw=2)[0]
if True:
h.x = ax.plot(*d.x.T, 'k', lw=3)[0]
if 'y' in d:
h.y = ax.plot(*d.y.T, 'g*', ms=14)[0]
# Scatter. NB: don't init with nan's coz it's buggy
# (wrt. get_color() and _offsets3d) since mpl 3.1.
if 'E' in d:
s.E = ax.scatter(*E.T[p.dims],
s=3**2,
c=[hn.get_color() for hn in h.E])
if 'mu' in d:
s.mu = ax.scatter(*ones(M), s=8**2, c=[h.mu.get_color()])
if True:
s.x = ax.scatter(*ones(M),
s=14**2,
c=[h.x.get_color()],
marker=(5, 1),
zorder=99)
def update(key, E, P):
k, ko, faus = key
show_y = 'y' in d and ko is not None
def update_tail(handle, newdata):
handle.set_data(newdata[:, 0], newdata[:, 1])
if is_3d:
handle.set_3d_properties(newdata[:, 2])
def update_sctr(handle, newdata):
if is_3d:
handle._offsets3d = juggle_axes(*newdata.T, 'z')
else:
handle.set_offsets(newdata)
EE = duplicate_with_blanks_for_resampled(E, p.dims, key, has_w)
# Roll data array
ind = k if plot_u else ko
for Ens in EE: # If E is duplicated, so must the others be.
if 'E' in d:
d.E.insert(ind, Ens)
if True:
d.x.insert(ind, xx[k, p.dims])
if 'y' in d:
d.y.insert(ind, yy[ko, :] if show_y else nan * ones(M))
if 'mu' in d:
d.mu.insert(ind, mu[key][p.dims])
# Update graph
update_sctr(s.x, d.x[[-1]])
update_tail(h.x, d.x)
if 'y' in d:
update_tail(h.y, d.y)
if 'mu' in d:
update_sctr(s.mu, d.mu[[-1]])
update_tail(h.mu, d.mu)
else:
update_sctr(s.E, d.E[-1])
for n in range(len(E)):
update_tail(h.E[n], d.E[:, n, :])
update_alpha(key, stats, h.E, s.E)
return
return update
def init(fignum, stats, key0, plot_u, E, P, **kwargs):
xx, yy, mu, spread, tseq = \
stats.xx, stats.yy, stats.mu, stats.spread, stats.HMM.tseq
# Set parameters (kwargs takes precedence over params_orig)
p = DotDict(
**{kw: kwargs.get(kw, val)
for kw, val in params_orig.items()})
# Lag settings:
T_lag, K_lag, a_lag = validate_lag(p.Tplot, tseq)
K_plot = comp_K_plot(K_lag, a_lag, plot_u)
# Extend K_plot forther for adding blanks in resampling (PartFilt):
has_w = hasattr(stats, 'w')
if has_w:
K_plot += a_lag
# Chose marginal dims to plot
if not p.dims:
Nx = min(10, xx.shape[-1])
DimsX = linspace_int(xx.shape[-1], Nx)
else:
Nx = len(p.dims)
DimsX = p.dims
# Pre-process obs dimensions
# Rm inds of obs if not in DimsX
iiY = [i for i, m in enumerate(p.obs_inds) if m in DimsX]
# Rm obs_inds if not in DimsX
DimsY = [m for i, m in enumerate(p.obs_inds) if m in DimsX]
# Get dim (within y) of each x
DimsY = [DimsY.index(m) if m in DimsY else None for m in DimsX]
Ny = len(iiY)
# Set up figure, axes
fig, axs = place.freshfig(fignum,
figsize=(5, 7),
nrows=Nx,
sharex=True)
if Nx == 1:
axs = [axs]
# Tune plots
axs[0].set_title("Marginal time series")
for ix, (m, ax) in enumerate(zip(DimsX, axs)):
# ax.set_ylim(*viz.stretch(*viz.xtrema(xx[:, m]), 1/p.zoomy))
if not p.labels:
ax.set_ylabel("$x_{%d}$" % m)
else:
ax.set_ylabel(p.labels[ix])
axs[-1].set_xlabel('Time (t)')
plot_pause(0.05)
plt.tight_layout()
# Allocate
d = DotDict() # data arrays
h = DotDict() # plot handles
# Why "if True" ? Just to indent the rest of the line...
if True:
d.t = RollingArray((K_plot, ))
if True:
d.x = RollingArray((K_plot, Nx))
h.x = []
if True:
d.y = RollingArray((K_plot, Ny))
h.y = []
if E is not None:
d.E = RollingArray((K_plot, len(E), Nx))
h.E = []
if P is not None:
d.mu = RollingArray((K_plot, Nx))
h.mu = []
if P is not None:
d.s = RollingArray((K_plot, 2, Nx))
h.s = []
# Plot (invisible coz everything here is nan, for the moment).
for ix, (_m, iy, ax) in enumerate(zip(DimsX, DimsY, axs)):
if True:
h.x += ax.plot(d.t, d.x[:, ix], 'k')
if iy != None:
h.y += ax.plot(d.t, d.y[:, iy], 'g*', ms=10)
if 'E' in d:
h.E += [ax.plot(d.t, d.E[:, :, ix], **p.ens_props)]
if 'mu' in d:
h.mu += ax.plot(d.t, d.mu[:, ix], 'b')
if 's' in d:
h.s += [ax.plot(d.t, d.s[:, :, ix], 'b--', lw=1)]
def update(key, E, P):
k, ko, faus = key
EE = duplicate_with_blanks_for_resampled(E, DimsX, key, has_w)
# Roll data array
ind = k if plot_u else ko
for Ens in EE: # If E is duplicated, so must the others be.
if 'E' in d:
d.E.insert(ind, Ens)
if 'mu' in d:
d.mu.insert(ind, mu[key][DimsX])
if 's' in d:
d.s.insert(
ind, mu[key][DimsX] + [[1], [-1]] * spread[key][DimsX])
if True:
d.t.insert(ind, tseq.tt[k])
if True:
d.y.insert(
ind, yy[ko, iiY] if ko is not None else nan * ones(Ny))
if True:
d.x.insert(ind, xx[k, DimsX])
# Update graphs
for ix, (_m, iy, ax) in enumerate(zip(DimsX, DimsY, axs)):
sliding_xlim(ax, d.t, T_lag, True)
if True:
h.x[ix].set_data(d.t, d.x[:, ix])
if iy != None:
h.y[iy].set_data(d.t, d.y[:, iy])
if 'mu' in d:
h.mu[ix].set_data(d.t, d.mu[:, ix])
if 's' in d:
[h.s[ix][b].set_data(d.t, d.s[:, b, ix]) for b in [0, 1]]
if 'E' in d:
[
h.E[ix][n].set_data(d.t, d.E[:, n, ix])
for n in range(len(E))
]
if 'E' in d:
update_alpha(key, stats, h.E[ix])
# TODO 3: fixup. This might be slow?
# In any case, it is very far from tested.
# Also, relim'iting all of the time is distracting.
# Use d_ylim?
if 'E' in d:
lims = d.E
elif 'mu' in d:
lims = d.mu
lims = np.array(viz.xtrema(lims[..., ix]))
if lims[0] == lims[1]:
lims += [-.5, +.5]
ax.set_ylim(*viz.stretch(*lims, 1 / p.zoomy))
return
return update
def init(fignum, stats, key0, plot_u, E, P, **kwargs):
xx, yy, mu = stats.xx, stats.yy, stats.mu
# Set parameters (kwargs takes precedence over params_orig)
p = DotDict(
**{kw: kwargs.get(kw, val)
for kw, val in params_orig.items()})
if not p.dims:
M = xx.shape[-1]
p.dims = arange(M)
else:
M = len(p.dims)
# Make periodic wrapper
ii, wrap = viz.setup_wrapping(M, p.periodicity)
# Set up figure, axes
fig, ax = place.freshfig(fignum, figsize=(8, 5))
fig.suptitle("1d amplitude plot")
# Nans
nan1 = wrap(nan * ones(M))
if E is None and p.conf_mult is None:
p.conf_mult = 2
# Init plots
if p.conf_mult:
lines_s = ax.plot(ii,
nan1,
"b-",
lw=1,
label=(str(p.conf_mult) + r'$\sigma$ conf'))
lines_s += ax.plot(ii, nan1, "b-", lw=1)
line_mu, = ax.plot(ii, nan1, 'b-', lw=2, label='DA mean')
else:
nanE = nan * ones((stats.xp.N, M))
lines_E = ax.plot(ii,
wrap(nanE[0]),
**p.ens_props,
lw=1,
label='Ensemble')
lines_E += ax.plot(ii, wrap(nanE[1:]).T, **p.ens_props, lw=1)
# Truth, Obs
(line_x, ) = ax.plot(ii, nan1, 'k-', lw=3, label='Truth')
if p.obs_inds is not None:
p.obs_inds = np.asarray(p.obs_inds)
(line_y, ) = ax.plot(p.obs_inds,
nan * p.obs_inds,
'g*',
ms=5,
label='Obs')
# Tune plot
ax.set_ylim(*viz.xtrema(xx))
ax.set_xlim(viz.stretch(ii[0], ii[-1], 1))
# Xticks
xt = ax.get_xticks()
xt = xt[abs(xt % 1) < 0.01].astype(int) # Keep only the integer ticks
xt = xt[xt >= 0]
xt = xt[xt < len(p.dims)]
ax.set_xticks(xt)
ax.set_xticklabels(p.dims[xt])
ax.set_xlabel('State index')
ax.set_ylabel('Value')
ax.legend(loc='upper right')
text_t = ax.text(0.01,
0.01,
format_time(None, None, None),
transform=ax.transAxes,
family='monospace',
ha='left')
# Init visibility (must come after legend):
if p.obs_inds is not None:
line_y.set_visible(False)
def update(key, E, P):
k, ko, faus = key
if p.conf_mult:
sigma = mu[key] + p.conf_mult * stats.spread[key] * [[1], [-1]]
lines_s[0].set_ydata(wrap(sigma[0, p.dims]))
lines_s[1].set_ydata(wrap(sigma[1, p.dims]))
line_mu.set_ydata(wrap(mu[key][p.dims]))
else:
for n, line in enumerate(lines_E):
line.set_ydata(wrap(E[n, p.dims]))
update_alpha(key, stats, lines_E)
line_x.set_ydata(wrap(xx[k, p.dims]))
text_t.set_text(format_time(k, ko, stats.HMM.tseq.tt[k]))
if 'f' in faus:
if p.obs_inds is not None:
line_y.set_ydata(yy[ko])
line_y.set_zorder(5)
line_y.set_visible(True)
if 'u' in faus:
if p.obs_inds is not None:
line_y.set_visible(False)
return
return update
for the default configuration.
"""
import os
from pathlib import Path
import matplotlib as mpl
import yaml
from mpl_tools import is_using_interactive_backend
from struct_tools import DotDict
##################################
# Load configurations
##################################
dapper_dir = Path(__file__).absolute().parent
rc = DotDict()
rc.loaded_from = []
for d in [dapper_dir, "~", "~/.config", "."]:
d = Path(d).expanduser().absolute()
for prefix in [".", ""]:
f = d / (prefix+"dpr_config.yaml")
if f.is_file():
dct = yaml.load(open(f), Loader=yaml.SafeLoader)
rc.loaded_from.append(str(f))
if dct:
if d == dapper_dir:
rc.update(dct)
else:
for k in dct:
if k in rc:
rc[k] = dct[k]
def default_styles(coord, baseline_legends=False):
"""Quick and dirty (but somewhat robust) styling."""
style = DotDict(ms=8)
style.label = make_label(coord)
if coord.da_method == "Climatology":
style.ls = ":"
style.c = "k"
if not baseline_legends:
style.label = None
elif coord.da_method == "OptInterp":
style.ls = ":"
style.c = .7*np.ones(3)
style.label = "Opt. Interp."
if not baseline_legends:
style.label = None
elif coord.da_method == "Var3D":
style.ls = ":"
style.c = .5*np.ones(3)
style.label = "3D-Var"
if not baseline_legends:
style.label = None
elif coord.da_method == "EnKF":
style.marker = "*"
style.c = "C1"
elif coord.da_method == "PartFilt":
style.marker = "X"
style.c = "C2"
else:
style.marker = "."
return style