# -*- coding: utf-8 -*-
"""
Module for animating solutions in 1D.
Can also save them but requieres ffmpeg package
see save_animation method.
"""
import numpy as nm
from os.path import join as pjoin
from glob import glob
from matplotlib import animation
from matplotlib import pyplot as plt
from matplotlib import colors
from sfepy.discrete.fem.meshio import MeshioLibIO
from sfepy.discrete.fem.mesh import Mesh
# This would still use some refactoring so it is more flexible
__author__ = 'tomas_zitka'
ffmpeg_path = '' # for saving animations
[docs]
def head(l):
"""
Maybe get head of the list.
Parameters
----------
l : indexable
Returns
-------
head : first element in l or None is l is empty
"""
if l:
return l[0]
else:
return None
[docs]
def animate1D_dgsol(Y, X, T, ax=None, fig=None, ylims=None, labs=None,
plott=None, delay=None):
"""Animates solution of 1D problem into current figure.
Keep reference to returned animation object otherwise
it is discarded
Parameters
----------
Y :
solution, array |T| x |X| x n, where n is dimension of the solution
X :
space interval discetization
T :
time interval discretization
ax :
specify axes to plot to (Default value = None)
fig :
specifiy figure to plot to (Default value = None)
ylims :
limits for y axis, default are 10% offsets of Y extremes
labs :
labels to use for parts of the solution (Default value = None)
plott :
plot type - how to plot data: tested plot, step (Default value = None)
delay :
(Default value = None)
Returns
-------
anim
the animation object, keep it to see the animation, used for savig too
"""
ax, fig, time_text = setup_axis(X, Y, ax, fig, ylims)
if not isinstance(Y, nm.ndarray):
Y = nm.stack(Y, axis=2)
lines = setup_lines(ax, Y.shape, labs, plott)
def animate(i):
ax.legend()
time_text.set_text("t= {0:3.2f} / {1:3.3}".format(T[i], T[-1]))
# from sfepy.base.base import debug;
# debug()
if len(Y.shape) > 2:
for ln, l in enumerate(lines):
l.set_data(X, Y[i].swapaxes(0, 1)[ln])
return tuple(lines) + (time_text,)
# https://stackoverflow.com/questions/20624408/matplotlib-animating-multiple-lines-and-text
else:
lines.set_data(X, Y[i])
return lines, time_text
if delay is None:
delay = int(nm.round(2000 * (T[-1] - T[0]) / len(T)))
anim = animation.FuncAnimation(fig, animate, frames=len(T), interval=delay,
blit=True, repeat=True, repeat_delay=250)
return anim
[docs]
def setup_axis(X, Y, ax=None, fig=None, ylims=None):
"""Setup axis, including timer for animation or snaps
Parameters
----------
X :
space disctretization to get limits
Y :
solution to get limits
ax :
ax where to put everything, if None current axes are used (Default value = None)
fig :
fig where to put everything, if None current figure is used (Default value = None)
ylims :
custom ylims, if None y axis limits are calculated from Y (Default value = None)
Returns
-------
ax
fig
time_text
object to fill in text
"""
if ax is None:
fig = plt.gcf()
ax = plt.gca()
if ylims is None:
lowery = nm.min(Y) - nm.min(Y) / 10
uppery = nm.max(Y) + nm.max(Y) / 10
else:
lowery = ylims[0]
uppery = ylims[1]
ax.set_ylim(lowery, uppery)
ax.set_xlim(X[0], X[-1])
time_text = ax.text(X[0] + nm.sign(X[0]) * X[0] / 10,
uppery - uppery / 10,
'empty', fontsize=15)
return ax, fig, time_text
[docs]
def setup_lines(ax, Yshape, labs, plott):
"""Sets up artist for animation or solution snaps
Parameters
----------
ax :
axes to use for artist
Yshape : tuple
shape of the solution array
labs : list
labels for the solution
plott : str ("steps" or "plot")
type of plot to use
Returns
-------
lines
"""
if plott is None:
plott = ax.plot
else:
plott = ax.__getattribute__(plott)
if len(Yshape) > 2:
lines = [plott([], [], lw=2)[0] for foo in range(Yshape[2])]
for i, l in enumerate(lines):
if labs is None:
l.set_label("q" + str(i + 1) + "(x, t)")
else:
l.set_label(labs[i])
else:
lines, = plott([], [], lw=2)
if labs is None:
lines.set_label("q(x, t)")
else:
lines.set_label(labs)
return lines
[docs]
def save_animation(anim, filename):
"""Saves animation as .mp4, requires ffmeg package
Parameters
----------
anim :
animation object
filename :
name of the file, without the .mp4 ending
"""
plt.rcParams['animation.ffmpeg_path'] = ffmpeg_path
writer = animation.FFMpegWriter(fps=24)
anim.save(filename + ".mp4", writer=writer)
[docs]
def sol_frame(Y, X, T, t0=.5, ax=None, fig=None, ylims=None, labs=None, plott=None):
"""Creates snap of solution at specified time frame t0, basically gets one
frame from animate1D_dgsol, but colors wont be the same :-(
Parameters
----------
Y :
solution, array |T| x |X| x n, where n is dimension of the solution
X :
space interval discetization
T :
time interval discretization
t0 :
time to take snap at (Default value = .5)
ax :
specify axes to plot to (Default value = None)
fig :
specifiy figure to plot to (Default value = None)
ylims :
limits for y axis, default are 10% offsets of Y extremes
labs :
labels to use for parts of the solution (Default value = None)
plott :
plot type - how to plot data: tested plot, step (Default value = None)
Returns
-------
fig
"""
ax, fig, time_text = setup_axis(X, Y, ax, fig, ylims)
if not isinstance(Y, nm.ndarray):
Y = nm.stack(Y, axis=2)
lines = setup_lines(ax, Y.shape, labs, plott)
nt0 = nm.abs(T - t0).argmin()
ax.legend()
time_text.set_text("t= {0:3.2f} / {1:3.3}".format(T[nt0], T[-1]))
if len(Y.shape) > 2:
for ln, l in enumerate(lines):
l.set_data(X, Y[nt0].swapaxes(0, 1)[ln])
else:
lines.set_data(X, Y[nt0])
return fig
[docs]
def save_sol_snap(Y, X, T, t0=.5, filename=None, name=None,
ylims=None, labs=None, plott=None):
"""Wrapper for sol_frame, saves the frame to file specified.
Parameters
----------
name :
name of the solution e.g. name of the solver used (Default value = None)
filename :
name of the file, overrides automatic generation (Default value = None)
Y :
solution, array |T| x |X| x n, where n is dimension of the solution
X :
space interval discetization
T :
time interval discretization
t0 :
time to take snap at (Default value = .5)
ylims :
limits for y axis, default are 10% offsets of Y extremes
labs :
labels to use for parts of the solution (Default value = None)
plott :
plot type - how to plot data: tested plot, step (Default value = None)
Returns
-------
fig
"""
if filename is None:
filename = "{0}_solsnap{1:3.2f}-{2:3.3}".format(name, t0, T[-1]).replace(".", "_")
if name is None:
name = "unknown_solver"
filename = "{0}_solsnap{1:3.2f}-{2:3.3}".format(name, t0, T[-1]).replace(".", "_")
filename = pjoin("semestralka", "figs", filename)
fig = plt.figure(filename)
snap1 = sol_frame(Y, X, T, t0=t0, ylims=ylims, labs=labs, plott=None)
if not isinstance(Y, nm.ndarray):
plt.plot(X, Y[0][0], label="q(x, 0)")
else:
if len(Y.shape) > 2:
plt.plot(X, Y[0, :, 0], label="q(x, 0)")
else:
plt.plot(X, Y[0, :], label="q(x, 0)")
plt.legend()
snap1.savefig(filename)
return fig
[docs]
def plotsXT(Y1, Y2, YE, extent, lab1=None, lab2=None, lab3=None):
"""Plots Y1 and Y2 to one axes and YE to the second axes,
Y1 and Y2 are presumed to be two solutions and YE their error
Parameters
----------
Y1 :
solution 1, shape = (space nodes, time nodes)
Y2 :
solution 2, shape = (space nodes, time nodes)
YE :
soulutio 1 - soulution 2||
extent :
imshow extent
lab1 :
(Default value = None)
lab2 :
(Default value = None)
lab3 :
(Default value = None)
"""
# >> Plot contours
cmap1 = plt.cm.get_cmap("bwr")
cmap1.set_bad('white')
# cmap2 = plt.cm.get_cmap("BrBG")
# cmap2.set_bad('white')
bounds = nm.arange(-1, 1, .05)
norm1 = colors.BoundaryNorm(bounds, cmap1.N)
# norm2 = colors.BoundaryNorm(bounds, cmap2.N)
fig, (ax1, ax2, ax3) = plt.subplots(nrows=1, ncols=3, sharey=True)
fig.suptitle("X-T plane plot")
if lab1 is not None:
ax1.set(title=lab1)
c1 = ax1.imshow(Y1, extent=extent,
cmap=cmap1, norm=norm1,
interpolation='none',
origin='lower')
ax1.grid()
if lab2 is not None:
ax2.set(title=lab2)
c2 = ax2.imshow(Y2, extent=extent,
cmap=cmap1, norm=norm1,
interpolation='none',
origin='lower')
ax2.grid()
if lab3 is not None:
ax3.set(title=lab3)
c3 = ax3.imshow(YE, extent=extent,
cmap="bwr", norm=norm1,
interpolation='none',
origin='lower')
ax3.grid()
fig.colorbar(c3, ax=[ax1, ax2, ax3])
[docs]
def load_state_1D_vtk(name):
"""Load one VTK file containing state in time
Parameters
----------
name : str
Returns
-------
coors : ndarray
u : ndarray
"""
from sfepy.discrete.fem.meshio import MeshioLibIO
io = MeshioLibIO(name)
coors = io.read(Mesh()).coors[:, 0, None]
data = io.read_data(step=0)
var_name = head([k for k in data.keys() if "_modal" in k])[:-1]
if var_name is None:
print("File {} does not contain modal data.".format(name))
return
porder = len([k for k in data.keys() if var_name in k])
u = nm.zeros((porder, coors.shape[0] - 1, 1, 1))
for ii in range(porder):
u[ii, :, 0, 0] = data[var_name+'{}'.format(ii)].data
return coors, u
[docs]
def load_1D_vtks(fold, name):
"""Reads series of .vtk files and crunches them into form
suitable for plot10_DG_sol.
Attempts to read modal cell data for variable mod_data. i.e.
``?_modal{i}``, where i is number of modal DOF
Resulting solution data have shape:
``(order, nspace_steps, ntime_steps, 1)``
Parameters
----------
fold :
folder where to look for files
name :
used in ``{name}.i.vtk, i = 0,1, ... tns - 1``
Returns
-------
coors : ndarray
mod_data : ndarray
solution data
"""
files = glob(pjoin(fold, name) + ".[0-9]*")
if len(files) == 0: # no multiple time steps, try loading single file
print("No files {} found in {}".format(pjoin(fold, name) + ".[0-9]*", fold))
print("Trying {}".format(pjoin(fold, name) + ".vtk"))
files = glob(pjoin(fold, name) + ".vtk")
if files:
return load_state_1D_vtk(files[0])
else:
print("Nothing found.")
return
io = MeshioLibIO(files[0])
coors = io.read(Mesh()).coors[:, 0, None]
data = io.read_data(step=0)
var_name = head([k for k in data.keys() if "_modal" in k])[:-1]
if var_name is None:
print("File {} does not contain modal data.".format(files[0]))
return
porder = len([k for k in data.keys() if var_name in k])
tn = len(files)
nts = sorted([int(f.split(".")[-2]) for f in files])
digs = len(files[0].split(".")[-2])
full_name_form = ".".join((pjoin(fold, name), ("{:0" + str(digs) + "d}"), "vtk"))
mod_data = nm.zeros((porder, coors.shape[0] - 1, tn, 1))
for i, nt in enumerate(nts):
io = MeshioLibIO(full_name_form.format(nt))
# parameter "step" does nothing, but is obligatory
data = io.read_data(step=0)
for ii in range(porder):
mod_data[ii, :, i, 0] = data[var_name+'{}'.format(ii)].data
return coors, mod_data
[docs]
def animate_1D_DG_sol(coors, t0, t1, u,
tn=None, dt=None,
ic=lambda x: 0.0, exact=lambda x, t: 0,
delay=None, polar=False):
"""Animates solution to 1D problem produced by DG:
1. animates DOF values in elements as steps
2. animates reconstructed solution with discontinuities
Parameters
----------
coors :
coordinates of the mesh
t0 : float
starting time
t1 : float
final time
u :
vectors of DOFs, for each order one, shape(u) = (order, nspace_steps, ntime_steps, 1)
ic :
analytical initial condition, optional (Default value = lambda x: 0.0)
tn :
number of time steps to plot, starting at 0, if None and dt is not None run animation through
all time steps, spaced dt within [t0, tn] (Default value = None)
dt :
time step size, if None and tn is not None computed as (t1- t0) / tn otherwise set to 1
if dt and tn are both None, t0 and t1 are ignored and solution is animated as if in time 0 ... ntime_steps (Default value = None)
exact :
(Default value = lambda x)
t: 0 :
delay :
(Default value = None)
polar :
(Default value = False)
Returns
-------
anim_dofs : animation object of DOFs,
anim_recon : animation object of reconstructed solution
"""
# Setup space coordinates
XN = coors[-1]
X1 = coors[0]
Xvol = XN - X1
X = (coors[1:] + coors[:-1]) / 2
XS = nm.linspace(X1, XN, 500)[:, None]
if polar: # setup polar coorinates
coors *= 2*nm.pi
X *= 2*nm.pi
XS *= 2*nm.pi
# Setup times
if tn is not None and dt is not None:
T = nm.array(nm.cumsum(nm.ones(tn) * dt))
elif tn is not None:
T, dt = nm.linspace(t0, t1, tn, retstep=True)
elif dt is not None:
tn = int(nm.ceil(float(t1 - t0) / dt))
T = nm.linspace(t0, t1, tn)
else:
T = nm.arange(nm.shape(u)[2])
n_nod = len(coors)
n_el_nod = nm.shape(u)[0]
# prepend u[:, 0, ...] to all time frames for plotting step in left corner
u_step = nm.append(u[:, 0:1, :, 0], u[:, :, :, 0], axis=1)
# Plot DOFs directly
figs = plt.figure()
if polar:
axs = plt.subplot(111, projection='polar')
axs.set_theta_direction('clockwise')
else:
axs = plt.subplot(111)
# Plot mesh
axs.vlines(coors[:, 0], ymin=0, ymax=.5, colors="grey")
axs.vlines((X1, XN), ymin=0, ymax=.5, colors="k")
axs.vlines(X, ymin=0, ymax=.3, colors="grey", linestyles="--")
axs.plot([X1, XN], [1, 1], 'k')
# Plot IC and its sampling
for i in range(n_el_nod):
c0 = axs.plot(X, u[i, :, 0, 0],
label="IC-{}".format(i),
marker=".", ls="")[0].get_color()
# c1 = plt.plot(X, u[1, :, 0, 0], label="IC-1", marker=".", ls="")[0].get_color()
# # plt.plot(coors, .1*alones(n_nod), marker=".", ls="")
axs.step(coors[1:], u[i, :, 0, 0], color=c0)
# plt.step(coors[1:], u[1, :, 0, 0], color=c1)
# plt.plot(coors[1:], sic[1, :], label="IC-1", color=c1)
if ic is not None:
ics = ic(XS)
axs.plot(nm.squeeze(XS), nm.squeeze(ics), label="IC-ex")
# Animate sampled solution DOFs directly
anim_dofs = animate1D_dgsol(u_step.T, coors, T, axs, figs,
ylims=[-1, 2],
plott="step",
delay=delay)
if not polar:
axs.set_xlim(coors[0] - .1 * Xvol, coors[-1] + .1 * Xvol)
axs.legend(loc="upper left")
axs.set_title("Sampled solution")
# Plot reconstructed solution
figr = plt.figure()
if polar:
axr = plt.subplot(111, projection='polar')
axr.set_theta_direction('clockwise')
else:
axr = plt.subplot(111)
# Plot mesh
axr.vlines(coors[:, 0], ymin=0, ymax=.5, colors="grey")
axr.vlines((X1, XN), ymin=0, ymax=.5, colors="k")
axr.vlines(X, ymin=0, ymax=.3, colors="grey", linestyles="--")
axr.plot([X1, XN], [1, 1], 'k')
# Plot discontinuously!
# (order, space_steps, t_steps, 1)
ww, xx = reconstruct_legendre_dofs(coors, tn, u)
# plt.vlines(xx, ymin=0, ymax=.3, colors="green")
# plot reconstructed IC
axr.plot(xx, ww[:, 0], label="IC")
# get exact solution values
if exact is not None:
exact_vals = exact(xx, T)[..., None]
labs = ["q{}(x,t)".format(i) for i in range(ww.shape[-1])] + ["exact"]
ww = nm.concatenate((ww, exact_vals), axis=-1)
else:
labs = None
# Animate reconstructed solution
anim_recon = animate1D_dgsol(ww.swapaxes(0, 1), xx, T, axr, figr,
ylims=[-1, 2],
labs=labs,
delay=delay)
if not polar:
axr.set_xlim(coors[0] - .1 * Xvol, coors[-1] + .1 * Xvol)
axr.legend(loc="upper left")
axr.set_title("Reconstructed solution")
# sol_frame(u[:, :, :, 0].T, nm.append(coors, coors[-1]), T, t0=0., ylims=[-1, 1], plott="step")
plt.show()
return anim_dofs, anim_recon
[docs]
def plot1D_legendre_dofs(coors, dofss, fun=None):
"""Plots values of DOFs as steps
Parameters
----------
coors :
coordinates of nodes of the mesh
dofss :
iterable of different projections' DOFs into legendre space
fun :
analytical function to plot (Default value = None)
"""
X = (coors[1:] + coors[:-1]) / 2
plt.figure("DOFs for function fun")
plt.gcf().clf()
for ii, dofs in enumerate(dofss):
for i in range(dofs.shape[1]):
c0 = plt.plot(X, dofs[:, i], label="fun-{}dof-{}".format(ii, i), marker=".", ls="")[0].get_color()
# # plt.plot(coors, .1*alones(n_nod), marker=".", ls="")
plt.step(coors[1:], dofs[:, i], color=c0)
# plt.plot(coors[1:], sic[1, :], label="IC-1", color=c1)
if fun is not None:
xs = nm.linspace(nm.min(coors), nm.max(coors), 500)[:, None]
plt.plot(xs, fun(xs), label="fun-ex")
plt.legend()
# plt.show()
[docs]
def reconstruct_legendre_dofs(coors, tn, u):
"""Creates solution and coordinates vector which when plotted as
plot(xx, ww)
represent solution reconstructed from DOFs in Legendre poly space at
cell borders.
Works only as linear interpolation between cell boundary points
Parameters
----------
coors :
coors of nodes of the mesh
u :
vectors of DOFs, for each order one,
shape(u) = (order, nspace_steps, ntime_steps, 1)
tn :
number of time steps to reconstruct,
if None all steps are reconstructed
Returns
-------
ww : ndarray
solution values vector, shape is (3 * nspace_steps - 1, ntime_steps, 1),
xx : ndarray
corresponding coordinates vector, shape is (3 * nspace_steps - 1, 1)
"""
XN = coors[-1]
X1 = coors[0]
n_nod = len(coors) - 1
if tn is None:
tn = nm.shape(u)[2]
n_el_nod = nm.shape(u)[0]
ww = nm.zeros((3 * n_nod - 1, tn, 1))
for i in range(n_el_nod):
ww[0:-1:3] = ww[0:-1:3] + (-1)**i * u[i, :, :] # left edges of elements
ww[1::3] = ww[1::3] + u[i, :, :] # right edges of elements
# NaNs ensure plotting of discontinuities at element borders
ww[2::3, :] = nm.NaN
# nodes for plotting reconstructed solution
xx = nm.zeros((3 * n_nod - 1, 1))
xx[0] = X1
xx[-1] = XN
# the ending is still a bit odd, but hey, it works!
xx[1:-1] = nm.repeat(coors[1:-1], 3)[:, None]
return ww, xx