"""Plot sound fields etc."""
from __future__ import division
import matplotlib.pyplot as plt
from matplotlib.patches import PathPatch
from matplotlib.path import Path
from matplotlib.collections import PatchCollection
from mpl_toolkits import axes_grid1
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from . import util
from . import defs
def _register_cmap_clip(name, original_cmap, alpha):
"""Create a color map with "over" and "under" values."""
from matplotlib.colors import LinearSegmentedColormap
cdict = plt.cm.datad[original_cmap]
cmap = LinearSegmentedColormap(name, cdict)
cmap.set_over([alpha * c + 1 - alpha for c in cmap(1.0)[:3]])
cmap.set_under([alpha * c + 1 - alpha for c in cmap(0.0)[:3]])
plt.cm.register_cmap(cmap=cmap)
# The 'coolwarm' colormap is based on the paper
# "Diverging Color Maps for Scientific Visualization" by Kenneth Moreland
# http://www.sandia.gov/~kmorel/documents/ColorMaps/
_register_cmap_clip('coolwarm_clip', 'coolwarm', 0.7)
def _register_cmap_transparent(name, color):
"""Create a color map from a given color to transparent."""
from matplotlib.colors import colorConverter, LinearSegmentedColormap
red, green, blue = colorConverter.to_rgb(color)
cdict = {'red': ((0, red, red), (1, red, red)),
'green': ((0, green, green), (1, green, green)),
'blue': ((0, blue, blue), (1, blue, blue)),
'alpha': ((0, 0, 0), (1, 1, 1))}
cmap = LinearSegmentedColormap(name, cdict)
plt.cm.register_cmap(cmap=cmap)
_register_cmap_transparent('blacktransparent', 'black')
[docs]def virtualsource_2d(xs, ns=None, type='point', ax=None):
"""Draw position/orientation of virtual source."""
xs = np.asarray(xs)
ns = np.asarray(ns)
if ax is None:
ax = plt.gca()
if type == 'point':
vps = plt.Circle(xs, .05, edgecolor='k', facecolor='k')
ax.add_artist(vps)
for n in range(1, 3):
vps = plt.Circle(xs, .05+n*0.05, edgecolor='k', fill=False)
ax.add_artist(vps)
elif type == 'plane':
ns = 0.2 * ns
ax.arrow(xs[0], xs[1], ns[0], ns[1], head_width=0.05,
head_length=0.1, fc='k', ec='k')
[docs]def reference_2d(xref, size=0.1, ax=None):
"""Draw reference/normalization point."""
xref = np.asarray(xref)
if ax is None:
ax = plt.gca()
ax.plot((xref[0]-size, xref[0]+size), (xref[1]-size, xref[1]+size), 'k-')
ax.plot((xref[0]-size, xref[0]+size), (xref[1]+size, xref[1]-size), 'k-')
[docs]def secondarysource_2d(x0, n0, grid=None):
"""Simple plot of secondary source locations."""
x0 = np.asarray(x0)
n0 = np.asarray(n0)
ax = plt.gca()
# plot only secondary sources inside simulated area
if grid is not None:
x0, n0 = _visible_secondarysources_2d(x0, n0, grid)
# plot symbols
for x00 in x0:
ss = plt.Circle(x00[0:2], .05, edgecolor='k', facecolor='k')
ax.add_artist(ss)
[docs]def loudspeaker_2d(x0, n0, a0=0.5, size=0.08, show_numbers=False, grid=None,
ax=None):
"""Draw loudspeaker symbols at given locations and angles.
Parameters
----------
x0 : (N, 3) array_like
Loudspeaker positions.
n0 : (N, 3) or (3,) array_like
Normal vector(s) of loudspeakers.
a0 : float or (N,) array_like, optional
Weighting factor(s) of loudspeakers.
size : float, optional
Size of loudspeakers in metres.
show_numbers : bool, optional
If ``True``, loudspeaker numbers are shown.
grid : triple of numpy.ndarray, optional
If specified, only loudspeakers within the `grid` are shown.
ax : Axes object, optional
The loudspeakers are plotted into this
:class:`~matplotlib.axes.Axes` object or -- if not specified --
into the current axes.
"""
x0 = util.asarray_of_rows(x0)
n0 = util.asarray_of_rows(n0)
a0 = util.asarray_1d(a0).reshape(-1, 1)
# plot only secondary sources inside simulated area
if grid is not None:
x0, n0 = _visible_secondarysources_2d(x0, n0, grid)
# normalized coordinates of loudspeaker symbol (see IEC 60617-9)
codes, coordinates = zip(*(
(Path.MOVETO, [-0.62, 0.21]),
(Path.LINETO, [-0.31, 0.21]),
(Path.LINETO, [0, 0.5]),
(Path.LINETO, [0, -0.5]),
(Path.LINETO, [-0.31, -0.21]),
(Path.LINETO, [-0.62, -0.21]),
(Path.CLOSEPOLY, [0, 0]),
(Path.MOVETO, [-0.31, 0.21]),
(Path.LINETO, [-0.31, -0.21]),
))
coordinates = np.column_stack([coordinates, np.zeros(len(coordinates))])
coordinates *= size
patches = []
for x00, n00 in util.broadcast_zip(x0, n0):
# rotate and translate coordinates
R = util.rotation_matrix([1, 0, 0], n00)
transformed_coordinates = np.inner(coordinates, R) + x00
patches.append(PathPatch(Path(transformed_coordinates[:, :2], codes)))
# add collection of patches to current axis
p = PatchCollection(patches, edgecolor='0', facecolor=np.tile(1 - a0, 3))
if ax is None:
ax = plt.gca()
ax.add_collection(p)
if show_numbers:
for idx, (x00, n00) in enumerate(util.broadcast_zip(x0, n0)):
x, y = x00[:2] - 1.2 * size * n00[:2]
ax.text(x, y, idx + 1, horizontalalignment='center',
verticalalignment='center')
def _visible_secondarysources_2d(x0, n0, grid):
"""Determine secondary sources which lie within `grid`."""
x, y = util.as_xyz_components(grid[:2])
idx = np.where((x0[:, 0] > x.min()) & (x0[:, 0] < x.max()) &
(x0[:, 1] > y.min()) & (x0[:, 1] < x.max()))
idx = np.squeeze(idx)
return x0[idx, :], n0[idx, :]
[docs]def loudspeaker_3d(x0, n0, a0=None, w=0.08, h=0.08):
"""Plot positions and normals of a 3D secondary source distribution."""
fig = plt.figure(figsize=(15, 15))
ax = fig.add_subplot(111, projection='3d')
ax.quiver(x0[:, 0], x0[:, 1], x0[:, 2], n0[:, 0],
n0[:, 1], n0[:, 2], length=0.1)
plt.xlabel('x (m)')
plt.ylabel('y (m)')
plt.title('Secondary Sources')
fig.show()
[docs]def soundfield(p, grid, xnorm=None, cmap='coolwarm_clip', vmin=-2.0, vmax=2.0,
xlabel=None, ylabel=None, colorbar=True, colorbar_kwargs={},
ax=None, **kwargs):
"""Two-dimensional plot of sound field.
Parameters
----------
p : array_like
Sound pressure values (or any other scalar quantity if you
like). If the values are complex, the imaginary part is
ignored.
Typically, `p` is two-dimensional with a shape of `(Ny, Nx)`,
`(Nz, Nx)` or `(Nz, Ny)`. This is the case if
:func:`sfs.util.xyz_grid` was used with a single number for `z`,
`y` or `x`, respectively.
However, `p` can also be three-dimensional with a shape of `(Ny,
Nx, 1)`, `(1, Nx, Nz)` or `(Ny, 1, Nz)`. This is the case if
:func:`numpy.meshgrid` was used with a scalar for `z`, `y` or
`x`, respectively (and of course with the default
``indexing='xy'``).
.. note:: If you want to plot a single slice of a pre-computed
"full" 3D sound field, make sure that the slice still
has three dimensions (including one singleton
dimension). This way, you can use the original `grid`
of the full volume without changes.
This works because the grid component corresponding to
the singleton dimension is simply ignored.
grid : triple or pair of numpy.ndarray
The grid that was used to calculate `p`, see
:func:`sfs.util.xyz_grid`. If `p` is two-dimensional, but
`grid` has 3 components, one of them must be scalar.
xnorm : array_like, optional
Coordinates of a point to which the sound field should be
normalized before plotting. If not specified, no normalization
is used. See :func:`sfs.util.normalize`.
Returns
-------
AxesImage
See :func:`matplotlib.pyplot.imshow`.
Other Parameters
----------------
xlabel, ylabel : str
Overwrite default x/y labels. Use ``xlabel=''`` and
``ylabel=''`` to remove x/y labels. The labels can be changed
afterwards with :func:`matplotlib.pyplot.xlabel` and
:func:`matplotlib.pyplot.ylabel`.
colorbar : bool, optional
If ``False``, no colorbar is created.
colorbar_kwargs : dict, optional
Further colorbar arguments, see :func:`add_colorbar`.
ax : Axes, optional
If given, the plot is created on `ax` instead of the current
axis (see :func:`matplotlib.pyplot.gca`).
cmap, vmin, vmax, **kwargs
All further parameters are forwarded to
:func:`matplotlib.pyplot.imshow`.
See Also
--------
sfs.plot.level
"""
p = np.asarray(p)
grid = util.as_xyz_components(grid)
# normalize sound field wrt xnorm
if xnorm is not None:
p = util.normalize(p, grid, xnorm)
if p.ndim == 3:
if p.shape[2] == 1:
p = p[:, :, 0] # first axis: y; second axis: x
plotting_plane = 'xy'
elif p.shape[1] == 1:
p = p[:, 0, :].T # first axis: z; second axis: y
plotting_plane = 'yz'
elif p.shape[0] == 1:
p = p[0, :, :].T # first axis: z; second axis: x
plotting_plane = 'xz'
else:
raise ValueError("If p is 3D, one dimension must have length 1")
elif len(grid) == 3:
if grid[2].ndim == 0:
plotting_plane = 'xy'
elif grid[1].ndim == 0:
plotting_plane = 'xz'
elif grid[0].ndim == 0:
plotting_plane = 'yz'
else:
raise ValueError(
"If p is 2D and grid is 3D, one grid component must be scalar")
else:
# 2-dimensional case
plotting_plane = 'xy'
if plotting_plane == 'xy':
x, y = grid[[0, 1]]
elif plotting_plane == 'xz':
x, y = grid[[0, 2]]
elif plotting_plane == 'yz':
x, y = grid[[1, 2]]
if ax is None:
ax = plt.gca()
im = ax.imshow(np.real(p), cmap=cmap, origin='lower',
extent=[x.min(), x.max(), y.min(), y.max()],
vmax=vmax, vmin=vmin, **kwargs)
if xlabel is None:
xlabel = plotting_plane[0] + ' / m'
if ylabel is None:
ylabel = plotting_plane[1] + ' / m'
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
if colorbar:
add_colorbar(im, **colorbar_kwargs)
return im
[docs]def level(p, grid, xnorm=None, power=False, cmap=None, vmax=3, vmin=-50,
**kwargs):
"""Two-dimensional plot of level (dB) of sound field.
Takes the same parameters as :func:`sfs.plot.soundfield`.
Other Parameters
----------------
power : bool, optional
See :func:`sfs.util.db`.
"""
# normalize before converting to dB!
if xnorm is not None:
p = util.normalize(p, grid, xnorm)
L = util.db(p, power=power)
return soundfield(L, grid=grid, xnorm=None, cmap=cmap,
vmax=vmax, vmin=vmin, **kwargs)
[docs]def particles(x, trim=None, ax=None, xlabel='x (m)', ylabel='y (m)',
edgecolor='', **kwargs):
"""Plot particle positions as scatter plot"""
XX, YY = [np.real(c) for c in x[:2]]
if trim is not None:
xmin, xmax, ymin, ymax = trim
idx = np.where((XX > xmin) & (XX < xmax) & (YY > ymin) & (YY < ymax))
XX = XX[idx]
YY = YY[idx]
if ax is None:
ax = plt.gca()
ax.scatter(XX, YY, edgecolor=edgecolor, **kwargs)
if xlabel:
ax.set_xlabel(xlabel)
if ylabel:
ax.set_ylabel(ylabel)
[docs]def vectors(v, grid, cmap='blacktransparent', headlength=3, headaxislength=2.5,
ax=None, clim=None, **kwargs):
"""Plot a vector field in the xy plane.
Parameters
----------
v : triple or pair of array_like
x, y and optionally z components of vector field. The z
components are ignored.
If the values are complex, the imaginary parts are ignored.
grid : triple or pair of array_like
The grid that was used to calculate `v`, see
:func:`sfs.util.xyz_grid`. Any z components are ignored.
Returns
-------
Quiver
See :func:`matplotlib.pyplot.quiver`.
Other Parameters
----------------
ax : Axes, optional
If given, the plot is created on `ax` instead of the current
axis (see :func:`matplotlib.pyplot.gca`).
clim : pair of float, optional
Limits for the scaling of arrow colors.
See :func:`matplotlib.pyplot.quiver`.
cmap, headlength, headaxislength, **kwargs
All further parameters are forwarded to
:func:`matplotlib.pyplot.quiver`.
"""
v = util.as_xyz_components(v[:2]).apply(np.real)
X, Y = util.as_xyz_components(grid[:2])
speed = np.linalg.norm(v)
with np.errstate(invalid='ignore'):
U, V = v.apply(np.true_divide, speed)
if ax is None:
ax = plt.gca()
if clim is None:
v_ref = 1 / (defs.rho0 * defs.c) # reference particle velocity
clim = 0, 2 * v_ref
return ax.quiver(X, Y, U, V, speed, cmap=cmap, pivot='mid', units='xy',
angles='xy', headlength=headlength,
headaxislength=headaxislength, clim=clim, **kwargs)
[docs]def add_colorbar(im, aspect=20, pad=0.5, **kwargs):
"""Add a vertical color bar to a plot.
Parameters
----------
im : ScalarMappable
The output of :func:`sfs.plot.soundfield`,
:func:`sfs.plot.level` or any other
:class:`matplotlib.cm.ScalarMappable`.
aspect : float, optional
Aspect ratio of the colorbar. Strictly speaking, since the
colorbar is vertical, it's actually the inverse of the aspect
ratio.
pad : float, optional
Space between image plot and colorbar, as a fraction of the
width of the colorbar.
.. note:: The `pad` argument of
:meth:`matplotlib.figure.Figure.colorbar` has a
slightly different meaning ("fraction of original
axes")!
\**kwargs
All further arguments are forwarded to
:meth:`matplotlib.figure.Figure.colorbar`.
See Also
--------
matplotlib.pyplot.colorbar
"""
ax = im.axes
divider = axes_grid1.make_axes_locatable(ax)
width = axes_grid1.axes_size.AxesY(ax, aspect=1/aspect)
pad = axes_grid1.axes_size.Fraction(pad, width)
current_ax = plt.gca()
cax = divider.append_axes("right", size=width, pad=pad)
plt.sca(current_ax)
return ax.figure.colorbar(im, cax=cax, orientation='vertical', **kwargs)