def bubblematerial(c=1, N=20, dt=0.05, gridpoints=100, plotoutput=True):
""" Calculate first arrival times for a wave travelling through NicolasBubble using a wavefront method
that is then interpolated onto a grid
Args:
c: baseline wave speed
N: number of points to put on initial wavefront
dt: timestep (the wavefront implementation uses forward Euler)
gridpoints: number of points to resolve on the grid
plotoutput: whether to display output
Returns:
A 2D array containing the first arrival times at the points on the grid
"""
bounds = [[0, 1], [0, 1]] # The x-axis and y-axis bounds for the domain
npoints = [gridpoints, gridpoints] # The number of points to (eventually) resolve in the grid
speed = NicolasBubble()
if plotoutput:
pom.output2dfn(bounds, speed, npoints, show=False) # plot the speed function
slowness = lambda x: 1 / speed(x)
gradslowness = prw.gradient(slowness, 1e-6) # A very crude numerical gradient
# These two lines would initialise a plane wave entering the domain
# x0 = np.vstack((np.linspace(0,1,N), np.zeros(N))).T
# p0 = np.vstack((np.zeros(N), np.ones(N))).T
# These three lines initialise a source
angles = np.linspace(-1e-2, math.pi + 1e-2, N)
p0 = np.vstack((np.cos(angles), np.sin(angles))).T
x0 = np.array([0.5, 0]) + dt * p0
# Perform the wavefront tracking
wfs, idxs = prw.wavefront(x0, p0, slowness, gradslowness, dt, 1.25 / c, 0.1)
if plotoutput:
erw.plotwavefront(wfs, idxs, bounds) # plot the wavefronts
# Use SciPy's interpolation (which doesn't work well when there are multiple arrival times)
# phasefn = interpolatephase(wfs, dt)
# pom.output2dfn(bounds, phasefn, npoints, show=False, type='contour')
# Home-brew interpolation:
sp = pug.StructuredPoints(np.array(bounds).T, npoints) # Define the points onto which we're going to interpolate
initialbox = [[0.4, 0], [0.6, 0.1]] # The vertices of a box that contain (some of) the first wave front
pointinfo = prw.StructuredPointInfo(
sp, sp.getPoints(initialbox)[0]
) # Obtain the indices of the points that are in the initial box
h = np.max((sp.upper - sp.lower) / sp.npoints) # The (maximum) grid spacing
_, phases = prw.nodesToDirsAndPhases(
wfs, idxs, pointinfo, lookback=int(math.ceil(h / (c * dt)))
) # perform the interpolation
firstphase = (
np.array([p[0] if len(p) > 0 else -1 for p in phases]) * dt
) # We only care about the first phase found per point
# pom.image(firstphase, (M+1,M+1), np.array(bounds))
if plotoutput:
pom.contour(pointinfo.points, firstphase, npoints)
return firstphase.reshape(npoints)
def testGradient(self):
N = 10
f = lambda x: x[:,0]**2 + x[:,1]**2
x = np.random.rand(N,2)
g = prw.gradient(f, 1E-7)
gx = g(x)
self.assertEquals(gx.shape, (N,2))
np.testing.assert_almost_equal(gx, x * 2)
def linearmaterial():
N = 50
speed = lambda x: 1 + x[:,0]
slowness = lambda x: 1 / speed(x)
gradslowness = prw.gradient(slowness, 1E-6)
x0 = np.vstack((np.linspace(0,1,N), np.zeros(N))).T
p0 = np.vstack((np.zeros(N), np.ones(N))).T
wfs, idxs = prw.wavefront(x0, p0, slowness, gradslowness, 0.05, 1.5, 1)
plotwavefront(wfs, idxs)
def hump(c = 1, yc = 0.3, yr = 0.1, alpha = 0.3):
def slowness(x):
yparabola = (x[:,1] - yc)**2 / (yr**2) - 1
return (1 + (yparabola < 0) * yparabola * (-alpha))*c
return slowness, prw.gradient(slowness, 1E-6)
# 8:impbd}
#bnddata={7:pcbd.dirichlet(g),
# 8:pcbd.dirichlet(g)}
bounds=np.array([[0,1],[0,1]],dtype='d')
npoints=np.array([500,500])
npw = 15
quadpoints = 8
pdeg = 2
c = 1
N = 20
slow = w.GaussianBubble(c)
gradslow = prw.gradient(slow, 1E-6)
#speed = Recip(slow)
speed = lambda p: 1.0/slow(p)
#slow, gradslow = w.hump(c,0.2,0.1,0.3)
#entityton = {6:1}
x0 = np.vstack((np.linspace(0,1,N),np.zeros(N))).T
p0 = np.vstack((np.zeros(N),np.ones(N))).T
wavefronts, forwardidxs = prw.wavefront(x0, p0, slow, gradslow, 0.1, 1.6/c, 0.1)
# Original basis:
pw = pcbv.PlaneWaveVariableN(pcb.uniformdirs(2,npw))
# Polynomials only:
poly = pcbr.ReferenceBasisRule(pcbr.Dubiner(pdeg))
