# http://pyrocko.org - GPLv3
#
# The Pyrocko Developers, 21st Century
# ---|P------/S----------~Lg----------
# python 2/3
from __future__ import absolute_import
from math import pi as PI
import logging
import numpy as num
from matplotlib.collections import PatchCollection
from matplotlib.patches import Polygon
from matplotlib.transforms import Transform
from matplotlib.colors import LinearSegmentedColormap
from pyrocko import moment_tensor as mtm
from pyrocko.util import num_full
logger = logging.getLogger('pyrocko.plot.beachball')
NA = num.newaxis
_view_south = num.array([[0, 0, -1],
[0, 1, 0],
[1, 0, 0]])
_view_north = _view_south.T
_view_east = num.array([[1, 0, 0],
[0, 0, -1],
[0, 1, 0]])
_view_west = _view_east.T
[docs]class BeachballError(Exception):
pass
def vnorm(points):
return num.sqrt(num.sum(points**2, axis=1))
def clean_poly(points):
if not num.all(points[0, :] == points[-1, :]):
points = num.vstack((points, points[0:1, :]))
dupl = num.concatenate(
(num.all(points[1:, :] == points[:-1, :], axis=1), [False]))
points = points[num.logical_not(dupl)]
return points
def close_poly(points):
if not num.all(points[0, :] == points[-1, :]):
points = num.vstack((points, points[0:1, :]))
return points
def circulation(points, axis):
# assert num.all(points[:, axis] >= 0.0) or num.all(points[:, axis] <= 0.0)
points2 = points[:, ((axis+2) % 3, (axis+1) % 3)].copy()
points2 *= 1.0 / num.sqrt(1.0 + num.abs(points[:, axis]))[:, num.newaxis]
result = -num.sum(
(points2[1:, 0] - points2[:-1, 0]) *
(points2[1:, 1] + points2[:-1, 1]))
result -= (points2[0, 0] - points2[-1, 0]) \
* (points2[0, 1] + points2[-1, 1])
return result
def spoly_cut(l_points, axis=0, nonsimple=True, arcres=181):
dphi = 2.*PI / (2*arcres)
# cut sub-polygons and gather crossing point information
crossings = []
snippets = {}
for ipath, points in enumerate(l_points):
if not num.all(points[0, :] == points[-1, :]):
points = num.vstack((points, points[0:1, :]))
# get upward crossing points
iup = num.where(num.logical_and(points[:-1, axis] <= 0.,
points[1:, axis] > 0.))[0]
aup = - points[iup, axis] / (points[iup+1, axis] - points[iup, axis])
pup = points[iup, :] + aup[:, num.newaxis] * (points[iup+1, :] -
points[iup, :])
phiup = num.arctan2(pup[:, (axis+2) % 3], pup[:, (axis+1) % 3])
for i in range(len(iup)):
crossings.append((phiup[i], ipath, iup[i], 1, pup[i], [1, -1]))
# get downward crossing points
idown = num.where(num.logical_and(points[:-1, axis] > 0.,
points[1:, axis] <= 0.))[0]
adown = - points[idown+1, axis] / (points[idown, axis] -
points[idown+1, axis])
pdown = points[idown+1, :] + adown[:, num.newaxis] * (
points[idown, :] - points[idown+1, :])
phidown = num.arctan2(pdown[:, (axis+2) % 3], pdown[:, (axis+1) % 3])
for i in range(idown.size):
crossings.append(
(phidown[i], ipath, idown[i], -1, pdown[i], [1, -1]))
icuts = num.sort(num.concatenate((iup, idown)))
for i in range(icuts.size-1):
snippets[ipath, icuts[i]] = (
ipath, icuts[i+1], points[icuts[i]+1:icuts[i+1]+1])
if icuts.size:
points_last = num.concatenate((
points[icuts[-1]+1:],
points[:icuts[0]+1]))
snippets[ipath, icuts[-1]] = (ipath, icuts[0], points_last)
else:
snippets[ipath, 0] = (ipath, 0, points)
crossings.sort()
# assemble new sub-polygons
current = snippets.pop(list(snippets.keys())[0])
outs = [[]]
while True:
outs[-1].append(current[2])
for i, c1 in enumerate(crossings):
if c1[1:3] == current[:2]:
direction = -1 * c1[3]
break
else:
if not snippets:
break
current = snippets.pop(list(snippets.keys())[0])
outs.append([])
continue
while True:
i = (i + direction) % len(crossings)
if crossings[i][3] == direction and direction in crossings[i][-1]:
break
c2 = crossings[i]
c2[-1].remove(direction)
phi1 = c1[0]
phi2 = c2[0]
if direction == 1:
if phi1 > phi2:
phi2 += PI * 2.
if direction == -1:
if phi1 < phi2:
phi2 -= PI * 2.
n = int(abs(phi2 - phi1) / dphi) + 2
phis = num.linspace(phi1, phi2, n)
cpoints = num.zeros((n, 3))
cpoints[:, (axis+1) % 3] = num.cos(phis)
cpoints[:, (axis+2) % 3] = num.sin(phis)
cpoints[:, axis] = 0.0
outs[-1].append(cpoints)
try:
current = snippets[c2[1:3]]
del snippets[c2[1:3]]
except KeyError:
if not snippets:
break
current = snippets.pop(list(snippets.keys())[0])
outs.append([])
# separate hemispheres, force polygons closed, remove duplicate points
# remove polygons with less than 3 points (4, when counting repeated
# endpoint)
outs_upper = []
outs_lower = []
for out in outs:
if out:
out = clean_poly(num.vstack(out))
if out.shape[0] >= 4:
if num.sum(out[:, axis]) > 0.0:
outs_upper.append(out)
else:
outs_lower.append(out)
if nonsimple and (
len(crossings) == 0 or
len(outs_upper) == 0 or
len(outs_lower) == 0):
# check if we are cutting between holes
need_divider = False
if outs_upper:
candis = sorted(
outs_upper, key=lambda out: num.min(out[:, axis]))
if circulation(candis[0], axis) > 0.0:
need_divider = True
if outs_lower:
candis = sorted(
outs_lower, key=lambda out: num.max(out[:, axis]))
if circulation(candis[0], axis) < 0.0:
need_divider = True
if need_divider:
phi1 = 0.
phi2 = PI*2.
n = int(abs(phi2 - phi1) / dphi) + 2
phis = num.linspace(phi1, phi2, n)
cpoints = num.zeros((n, 3))
cpoints[:, (axis+1) % 3] = num.cos(phis)
cpoints[:, (axis+2) % 3] = num.sin(phis)
cpoints[:, axis] = 0.0
outs_upper.append(cpoints)
outs_lower.append(cpoints[::-1, :])
return outs_lower, outs_upper
def numpy_rtp2xyz(rtp):
r = rtp[:, 0]
theta = rtp[:, 1]
phi = rtp[:, 2]
vecs = num.empty(rtp.shape, dtype=num.float64)
vecs[:, 0] = r*num.sin(theta)*num.cos(phi)
vecs[:, 1] = r*num.sin(theta)*num.sin(phi)
vecs[:, 2] = r*num.cos(theta)
return vecs
def numpy_xyz2rtp(xyz):
x, y, z = xyz[:, 0], xyz[:, 1], xyz[:, 2]
vecs = num.empty(xyz.shape, dtype=num.float64)
vecs[:, 0] = num.sqrt(x**2+y**2+z**2)
vecs[:, 1] = num.arctan2(num.sqrt(x**2+y**2), z)
vecs[:, 2] = num.arctan2(y, x)
return vecs
def circle_points(aphi, sign=1.0):
vecs = num.empty((aphi.size, 3), dtype=num.float64)
vecs[:, 0] = num.cos(sign*aphi)
vecs[:, 1] = num.sin(sign*aphi)
vecs[:, 2] = 0.0
return vecs
def eig2gx(eig, arcres=181):
aphi = num.linspace(0., 2.*PI, arcres)
ep, en, et, vp, vn, vt = eig
mt_sign = num.sign(ep + en + et)
groups = []
for (pt_name, pt_sign) in [('P', -1.), ('T', 1.)]:
patches = []
patches_lower = []
patches_upper = []
lines = []
lines_lower = []
lines_upper = []
for iperm, (va, vb, vc, ea, eb, ec) in enumerate([
(vp, vn, vt, ep, en, et),
(vt, vp, vn, et, ep, en)]): # (vn, vt, vp, en, et, ep)]):
perm_sign = [-1.0, 1.0][iperm]
to_e = num.vstack((vb, vc, va))
from_e = to_e.T
poly_es = []
polys = []
for sign in (-1., 1.):
xphi = perm_sign*pt_sign*sign*aphi
denom = eb*num.cos(xphi)**2 + ec*num.sin(xphi)**2
if num.any(denom == 0.):
continue
Y = -ea/denom
if num.any(Y < 0.):
continue
xtheta = num.arctan(num.sqrt(Y))
rtp = num.empty(xphi.shape+(3,), dtype=num.float64)
rtp[:, 0] = 1.
if sign > 0:
rtp[:, 1] = xtheta
else:
rtp[:, 1] = PI - xtheta
rtp[:, 2] = xphi
poly_e = numpy_rtp2xyz(rtp)
poly = num.dot(from_e, poly_e.T).T
poly[:, 2] -= 0.001
poly_es.append(poly_e)
polys.append(poly)
if polys:
polys_lower, polys_upper = spoly_cut(polys, 2, arcres=arcres)
lines.extend(polys)
lines_lower.extend(polys_lower)
lines_upper.extend(polys_upper)
if poly_es:
for aa in spoly_cut(poly_es, 0, arcres=arcres):
for bb in spoly_cut(aa, 1, arcres=arcres):
for cc in spoly_cut(bb, 2, arcres=arcres):
for poly_e in cc:
poly = num.dot(from_e, poly_e.T).T
poly[:, 2] -= 0.001
polys_lower, polys_upper = spoly_cut(
[poly], 2, nonsimple=False, arcres=arcres)
patches.append(poly)
patches_lower.extend(polys_lower)
patches_upper.extend(polys_upper)
if not patches:
if mt_sign * pt_sign == 1.:
patches_lower.append(circle_points(aphi, -1.0))
patches_upper.append(circle_points(aphi, 1.0))
lines_lower.append(circle_points(aphi, -1.0))
lines_upper.append(circle_points(aphi, 1.0))
groups.append((
pt_name,
patches, patches_lower, patches_upper,
lines, lines_lower, lines_upper))
return groups
def extr(points):
pmean = num.mean(points, axis=0)
return points + pmean*0.05
def draw_eigenvectors_mpl(eig, axes):
vp, vn, vt = eig[3:]
for lab, v in [('P', vp), ('N', vn), ('T', vt)]:
sign = num.sign(v[2]) + (v[2] == 0.0)
axes.plot(sign*v[1], sign*v[0], 'o', color='black')
axes.text(sign*v[1], sign*v[0], ' '+lab)
def project(points, projection='lambert'):
points_out = points[:, :2].copy()
if projection == 'lambert':
factor = 1.0 / num.sqrt(1.0 + points[:, 2])
elif projection == 'stereographic':
factor = 1.0 / (1.0 + points[:, 2])
elif projection == 'orthographic':
factor = None
else:
raise BeachballError(
'invalid argument for projection: %s' % projection)
if factor is not None:
points_out *= factor[:, num.newaxis]
return points_out
def inverse_project(points, projection='lambert'):
points_out = num.zeros((points.shape[0], 3))
rsqr = points[:, 0]**2 + points[:, 1]**2
if projection == 'lambert':
points_out[:, 2] = 1.0 - rsqr
points_out[:, 1] = num.sqrt(2.0 - rsqr) * points[:, 1]
points_out[:, 0] = num.sqrt(2.0 - rsqr) * points[:, 0]
elif projection == 'stereographic':
points_out[:, 2] = - (rsqr - 1.0) / (rsqr + 1.0)
points_out[:, 1] = 2.0 * points[:, 1] / (rsqr + 1.0)
points_out[:, 0] = 2.0 * points[:, 0] / (rsqr + 1.0)
elif projection == 'orthographic':
points_out[:, 2] = num.sqrt(num.maximum(1.0 - rsqr, 0.0))
points_out[:, 1] = points[:, 1]
points_out[:, 0] = points[:, 0]
else:
raise BeachballError(
'invalid argument for projection: %s' % projection)
return points_out
def deco_part(mt, mt_type='full', view='top'):
assert view in ('top', 'north', 'south', 'east', 'west'),\
'Allowed views are top, north, south, east and west'
mt = mtm.as_mt(mt)
if view == 'top':
pass
elif view == 'north':
mt = mt.rotated(_view_north)
elif view == 'south':
mt = mt.rotated(_view_south)
elif view == 'east':
mt = mt.rotated(_view_east)
elif view == 'west':
mt = mt.rotated(_view_west)
if mt_type == 'full':
return mt
res = mt.standard_decomposition()
m = dict(
dc=res[1][2],
deviatoric=res[3][2])[mt_type]
return mtm.MomentTensor(m=m)
def choose_transform(axes, size_units, position, size):
if size_units == 'points':
transform = FixedPointOffsetTransform(
axes.transData,
axes.figure.dpi_scale_trans,
position)
if size is None:
size = 12.
size = size * 0.5 / 72.
position = (0., 0.)
elif size_units == 'data':
transform = axes.transData
if size is None:
size = 1.0
size = size * 0.5
elif size_units == 'axes':
transform = axes.transAxes
if size is None:
size = 1.
size = size * .5
else:
raise BeachballError(
'invalid argument for size_units: %s' % size_units)
position = num.asarray(position, dtype=num.float64)
return transform, position, size
def mt2beachball(
mt,
beachball_type='deviatoric',
position=(0., 0.),
size=None,
color_t='red',
color_p='white',
edgecolor='black',
linewidth=2,
projection='lambert',
view='top'):
position = num.asarray(position, dtype=num.float64)
size = size or 1
mt = deco_part(mt, beachball_type, view)
eig = mt.eigensystem()
if eig[0] == 0. and eig[1] == 0. and eig[2] == 0:
raise BeachballError('eigenvalues are zero')
data = []
for (group, patches, patches_lower, patches_upper,
lines, lines_lower, lines_upper) in eig2gx(eig):
if group == 'P':
color = color_p
else:
color = color_t
for poly in patches_upper:
verts = project(poly, projection)[:, ::-1] * size + \
position[NA, :]
data.append((verts, color, color, 1.0))
for poly in lines_upper:
verts = project(poly, projection)[:, ::-1] * size + \
position[NA, :]
data.append((verts, 'none', edgecolor, linewidth))
return data
[docs]def plot_beachball_mpl(
mt, axes,
beachball_type='deviatoric',
position=(0., 0.),
size=None,
zorder=0,
color_t='red',
color_p='white',
edgecolor='black',
linewidth=2,
alpha=1.0,
arcres=181,
decimation=1,
projection='lambert',
size_units='points',
view='top'):
'''
Plot beachball diagram to a Matplotlib plot
:param mt: :py:class:`pyrocko.moment_tensor.MomentTensor` object or an
array or sequence which can be converted into an MT object
:param beachball_type: ``'deviatoric'`` (default), ``'full'``, or ``'dc'``
:param position: position of the beachball in data coordinates
:param size: diameter of the beachball either in points or in data
coordinates, depending on the ``size_units`` setting
:param zorder: (passed through to matplotlib drawing functions)
:param color_t: color for compressional quadrants (default: ``'red'``)
:param color_p: color for extensive quadrants (default: ``'white'``)
:param edgecolor: color for lines (default: ``'black'``)
:param linewidth: linewidth in points (default: ``2``)
:param alpha: (passed through to matplotlib drawing functions)
:param projection: ``'lambert'`` (default), ``'stereographic'``, or
``'orthographic'``
:param size_units: ``'points'`` (default) or ``'data'``, where the
latter causes the beachball to be projected in the plots data
coordinates (axes must have an aspect ratio of 1.0 or the
beachball will be shown distorted when using this).
:param view: View the beachball from ``top``, ``north``, ``south``,
``east`` or ``west``. Useful for to show beachballs in cross-sections.
Default is ``top``.
'''
transform, position, size = choose_transform(
axes, size_units, position, size)
mt = deco_part(mt, beachball_type, view)
eig = mt.eigensystem()
if eig[0] == 0. and eig[1] == 0. and eig[2] == 0:
raise BeachballError('eigenvalues are zero')
data = []
for (group, patches, patches_lower, patches_upper,
lines, lines_lower, lines_upper) in eig2gx(eig, arcres):
if group == 'P':
color = color_p
else:
color = color_t
# plot "upper" features for lower hemisphere, because coordinate system
# is NED
for poly in patches_upper:
verts = project(poly, projection)[:, ::-1] * size + position[NA, :]
if alpha == 1.0:
data.append(
(verts[::decimation], color, color, linewidth))
else:
data.append(
(verts[::decimation], color, 'none', 0.0))
for poly in lines_upper:
verts = project(poly, projection)[:, ::-1] * size + position[NA, :]
data.append(
(verts[::decimation], 'none', edgecolor, linewidth))
patches = []
for (path, facecolor, edgecolor, linewidth) in data:
patches.append(Polygon(
xy=path, facecolor=facecolor,
edgecolor=edgecolor,
linewidth=linewidth,
alpha=alpha))
collection = PatchCollection(
patches, zorder=zorder, transform=transform, match_original=True)
axes.add_artist(collection)
return collection
def mts2amps(mts, projection, beachball_type, grid_resolution=200, mask=True,
view='top'):
n_balls = len(mts)
nx = grid_resolution
ny = grid_resolution
x = num.linspace(-1., 1., nx)
y = num.linspace(-1., 1., ny)
vecs2 = num.zeros((nx * ny, 2), dtype=num.float64)
vecs2[:, 0] = num.tile(x, ny)
vecs2[:, 1] = num.repeat(y, nx)
ii_ok = vecs2[:, 0]**2 + vecs2[:, 1]**2 <= 1.0
amps = num_full(nx * ny, num.nan, dtype=num.float64)
amps[ii_ok] = 0.
for mt in mts:
mt = deco_part(mt, beachball_type, view)
ep, en, et, vp, vn, vt = mt.eigensystem()
vecs3_ok = inverse_project(vecs2[ii_ok, :], projection)
to_e = num.vstack((vn, vt, vp))
vecs_e = num.dot(to_e, vecs3_ok.T).T
rtp = numpy_xyz2rtp(vecs_e)
atheta, aphi = rtp[:, 1], rtp[:, 2]
amps_ok = ep * num.cos(atheta)**2 + (
en * num.cos(aphi)**2 + et * num.sin(aphi)**2) * num.sin(atheta)**2
if mask:
amps_ok[amps_ok > 0] = 1.
amps_ok[amps_ok < 0] = 0.
amps[ii_ok] += amps_ok
return num.reshape(amps, (ny, nx)) / n_balls, x, y
[docs]def plot_fuzzy_beachball_mpl_pixmap(
mts, axes,
best_mt=None,
beachball_type='deviatoric',
position=(0., 0.),
size=None,
zorder=0,
color_t='red',
color_p='white',
edgecolor='black',
best_color='red',
linewidth=2,
alpha=1.0,
projection='lambert',
size_units='data',
grid_resolution=200,
method='imshow',
view='top'):
'''
Plot fuzzy beachball from a list of given MomentTensors
:param mts: list of
:py:class:`pyrocko.moment_tensor.MomentTensor` object or an
array or sequence which can be converted into an MT object
:param best_mt: :py:class:`pyrocko.moment_tensor.MomentTensor` object or
an array or sequence which can be converted into an MT object
of most likely or minimum misfit solution to extra highlight
:param best_color: mpl color for best MomentTensor edges,
polygons are not plotted
See plot_beachball_mpl for other arguments
'''
if size_units == 'points':
raise BeachballError(
'size_units="points" not supported in '
'plot_fuzzy_beachball_mpl_pixmap')
transform, position, size = choose_transform(
axes, size_units, position, size)
amps, x, y = mts2amps(
mts,
grid_resolution=grid_resolution,
projection=projection,
beachball_type=beachball_type,
mask=True,
view=view)
ncolors = 256
cmap = LinearSegmentedColormap.from_list(
'dummy', [color_p, color_t], N=ncolors)
levels = num.linspace(0, 1., ncolors)
if method == 'contourf':
axes.contourf(
position[0] + y * size, position[1] + x * size, amps.T,
levels=levels,
cmap=cmap,
transform=transform,
zorder=zorder,
alpha=alpha)
elif method == 'imshow':
axes.imshow(
amps.T,
extent=(
position[0] + y[0] * size,
position[0] + y[-1] * size,
position[1] - x[0] * size,
position[1] - x[-1] * size),
cmap=cmap,
transform=transform,
zorder=zorder-0.1,
alpha=alpha)
else:
assert False, 'invalid `method` argument'
# draw optimum edges
if best_mt is not None:
best_amps, bx, by = mts2amps(
[best_mt],
grid_resolution=grid_resolution,
projection=projection,
beachball_type=beachball_type,
mask=False)
axes.contour(
position[0] + by * size, position[1] + bx * size, best_amps.T,
levels=[0.],
colors=[best_color],
linewidths=linewidth,
transform=transform,
zorder=zorder,
alpha=alpha)
phi = num.linspace(0., 2 * PI, 361)
x = num.cos(phi)
y = num.sin(phi)
axes.plot(
position[0] + x * size, position[1] + y * size,
linewidth=linewidth,
color=edgecolor,
transform=transform,
zorder=zorder,
alpha=alpha)
def plot_beachball_mpl_construction(
mt, axes,
show='patches',
beachball_type='deviatoric',
view='top'):
mt = deco_part(mt, beachball_type, view)
eig = mt.eigensystem()
for (group, patches, patches_lower, patches_upper,
lines, lines_lower, lines_upper) in eig2gx(eig):
if group == 'P':
color = 'blue'
lw = 1
else:
color = 'red'
lw = 1
if show == 'patches':
for poly in patches_upper:
px, py, pz = poly.T
axes.plot(*extr(poly).T, color=color, lw=lw, alpha=0.5)
if show == 'lines':
for poly in lines_upper:
px, py, pz = poly.T
axes.plot(*extr(poly).T, color=color, lw=lw, alpha=0.5)
def plot_beachball_mpl_pixmap(
mt, axes,
beachball_type='deviatoric',
position=(0., 0.),
size=None,
zorder=0,
color_t='red',
color_p='white',
edgecolor='black',
linewidth=2,
alpha=1.0,
projection='lambert',
size_units='data',
view='top'):
if size_units == 'points':
raise BeachballError(
'size_units="points" not supported in plot_beachball_mpl_pixmap')
transform, position, size = choose_transform(
axes, size_units, position, size)
mt = deco_part(mt, beachball_type, view)
ep, en, et, vp, vn, vt = mt.eigensystem()
amps, x, y = mts2amps(
[mt], projection, beachball_type, grid_resolution=200, mask=False)
axes.contourf(
position[0] + y * size, position[1] + x * size, amps.T,
levels=[-num.inf, 0., num.inf],
colors=[color_p, color_t],
transform=transform,
zorder=zorder,
alpha=alpha)
axes.contour(
position[0] + y * size, position[1] + x * size, amps.T,
levels=[0.],
colors=[edgecolor],
linewidths=linewidth,
transform=transform,
zorder=zorder,
alpha=alpha)
phi = num.linspace(0., 2 * PI, 361)
x = num.cos(phi)
y = num.sin(phi)
axes.plot(
position[0] + x * size, position[1] + y * size,
linewidth=linewidth,
color=edgecolor,
transform=transform,
zorder=zorder,
alpha=alpha)
if __name__ == '__main__':
import sys
import os
import matplotlib.pyplot as plt
from pyrocko import model
args = sys.argv[1:]
data = []
for iarg, arg in enumerate(args):
if os.path.exists(arg):
events = model.load_events(arg)
for ev in events:
if not ev.moment_tensor:
logger.warn('no moment tensor given for event')
continue
data.append((ev.name, ev.moment_tensor))
else:
vals = list(map(float, arg.split(',')))
mt = mtm.as_mt(vals)
data.append(('%i' % (iarg+1), mt))
n = len(data)
ncols = 1
while ncols**2 < n:
ncols += 1
nrows = ncols
fig = plt.figure()
axes = fig.add_subplot(1, 1, 1, aspect=1.)
axes.axison = False
axes.set_xlim(-0.05 - ncols, ncols + 0.05)
axes.set_ylim(-0.05 - nrows, nrows + 0.05)
for ibeach, (name, mt) in enumerate(data):
irow = ibeach // ncols
icol = ibeach % ncols
plot_beachball_mpl(
mt, axes,
position=(icol*2-ncols+1, -irow*2+nrows-1),
size_units='data')
axes.annotate(
name,
xy=(icol*2-ncols+1, -irow*2+nrows-2),
xycoords='data',
xytext=(0, 0),
textcoords='offset points',
verticalalignment='center',
horizontalalignment='center',
rotation=0.)
plt.show()
