DeSitterConstantHeavisideGyratonNullTetrad(
np.array([0, 0, r * np.exp(x * 1j), r * np.exp(-x * 1j)]))
for x in np.linspace(0, 2 * np.pi * (N - 1) / N, num=N)
]
initvels = [
DeSitterConstantHeavisideGyratonNullTetrad(-v0 / g(v0, v0, x0, lmb), True)
for x0 in initpos
]
wave = GeneralLambdaGyratonSolution(lmb, chi, _h, _hz, mu)
static_plotter = StaticGeodesicPlotter(labels2d=["$U$", "$V$"])
dynamic_plotter = PlotlyDynamicPlotter(["x", "y", "U"],
aspectratio=[1, 1, 1],
showSpikes=False,
bgcolor="#ccffeb",
fontsize=30,
ticks=True,
tick_fontsize=15)
dynamic_plotter2 = PlotlyDynamicPlotter(["x", "y", "V"],
aspectratio=[1, 1, 1],
showSpikes=False,
bgcolor="#ccffeb",
fontsize=30,
ticks=True,
tick_fontsize=15)
dynamic_plotter3 = PlotlyDynamicPlotter(["x", "z", "t"],
aspectratio=[1, 1, 1],
showSpikes=False,
bgcolor="#ccffeb",
fontsize=30,
np.exp(-1j * phi)]))
for phi in np.linspace(0, 2 * np.pi, num=NU)
]
#u0 = [np.array([1, 1, 0, 0]) for phi in np.linspace(0, 2*np.pi * (N-1.) / N, num=N)]
u0 = [np.array([1, 0, 0, 0]) for phi in np.linspace(-2, 2, num=NU)]
initvels = [DeSitterNullTetrad(x, dif=True)
for x in u0] #Can be generalized to different initial 4-vels
wave = HottaTanakaSolution(lmb, mu) #Generate spacetime with wave
ds = Solution()
plotter = PlotlyDynamicPlotter(title=r"$\text{Hotta Tanaka solution, }\mu=" +
str(mu) + ", \lambda=" + str(lmb) + "$",
aspectratio=[1, 1, 1],
labels=["Z4", "Z1", "Z0"],
xrange=[-20, 20],
yrange=[-20, 20],
zrange=[-20, 20]) #Init 3D plotter
# For each init pos generate geodesic (splitted)
for x0, u0, geonum in zip(initpos, initvels, range(0, len(initpos))):
a = wave.generate_geodesic(x0,
u0, (-4, 2),
max_step=0.1,
christoffelParams=[lmb])
trajm, trajp = a[0]
tm, tp = a[1]
#trajp, tp = ds.generate_geodesic(x0, u0, (-20, 20), max_step=0.4, christoffelParams=[lmb])
color = "#{:06x}".format(random.randint(0, 0xFFFFFF)).upper()
lab = ["x", "y", "U"]
convertFunction = toGyraUVxy
plotName = "AS/ASMatterHearth"
staticplotter = StaticGeodesicPlotter(
labels2d=[r"$\mathcal{U}$", r"$\mathcal{V}$"],
labelsize=16,
aspect='auto',
figsize=(6, 2.1))
for m, i in zip(mu, range(len(mu))):
wave = AichelburgSexlSolution(m)
plotter = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1],
labels=lab,
xrange=[-6, 6],
yrange=[-6, 6],
zrange=[-1, 2],
bgcolor="#ccffeb",
fontsize=30)
staticplotter2 = StaticGeodesicPlotter(labels2d=["x", "z"],
labelsize=30,
aspect='auto',
figsize=(12, 6))
staticplotter2.ax.plot([0, 0], [-5, 5], "k-")
for x0, u0, geonum in zip(initpos, initvels, range(0, len(initpos))):
a = wave.generate_geodesic(x0,
u0, (-1.3, 3),
max_step=0.2,
mu = n / 2.
sigma = mu / 2.
return (gaussian((i + add) % n, mu, sigma), 0.1, (1.-gaussian((i + add) % n, mu, sigma)))
N = 14
initu = np.array([1, 0, 0, 0])
initp = [DeSitterNullTetrad(np.array([0, x/np.pi - 1, 1.5+0j, 1.5+0j])) for x in np.linspace(0, 2 * np.pi, num=N) if np.abs(x) > 0.3]
initv = [DeSitterNullTetrad(initu, dif=True) for x in np.linspace(0, 2 * np.pi, num=N) if np.abs(x) > 0.3]
wave = HottaTanakaSolution(lmb, mu)
statplotterUV = StaticGeodesicPlotter(labels2d=[r"$\mathcal{V}$", r"$\mathcal{U}$"], aspect="auto", ticks=True, tick_labelsize=14)
statplotterxU = StaticGeodesicPlotter(labels2d=[r"$x$", r"$\mathcal{U}$"], aspect="auto", ticks=True, tick_labelsize=14)
dynplotterxyU = PlotlyDynamicPlotter(labels=["x", "y", "U"], showSpikes=False, aspectratio=[1, 1, 1], bgcolor="#ccffeb", fontsize=30, ticks=True, tick_fontsize=15)
dynplotterZ2Z3Z4 = PlotlyDynamicPlotter(labels=["Z2", "Z3", "Z4"], showSpikes=False, aspectratio=[1, 1, 1], bgcolor="#ccffeb", fontsize=30, ticks=True, tick_fontsize=15)
dynplotterZ0Z2Z4 = PlotlyDynamicPlotter(labels=["Z4", "Z1", "Z0"], showSpikes=False, aspectratio=[1, 1, 1], bgcolor="#ccffeb", fontsize=30, ticks=True, tick_fontsize=15)
for x0, u0, geonum in zip(initp, initv, range(0, len(initp))):
#fr = -quadratic(geonum, (len(initp)-1)/2., 0.5/len(initp), 0.6)
#to = quadratic(geonum, (len(initp)-1)/2., 0.7/len(initp), 1)
fr, to = -1 - 1 / (geonum+1), 1
print("Integrating geo {} form {} to {}".format(geonum, fr, to))
print("Initial conditions are: x = {} ;u = {}".format(x0.x, u0.x))
a = wave.generate_geodesic(x0, u0, (fr, to), max_step=0.005, christoffelParams=[lmb], verbose=True)
trajm, trajp = a[0]
tm, tp = a[1]
color = genRGB(geonum+0.5, len(initp))
#UV plot
statplotterUV.plot(toConformalUVxy(trajm), xc=1, yc=0)
def H_z(x, arg):
return -2 * arg[0] * (x[2])
plot = [2, 3, 1]
lab = ["x", "y", "V"]
convertFunction = toGyraUVxy
plot2 = [2, 3, 0]
lab2 = ["x", "y", "U"]
convertFunction2 = toGyraUVxy
plotName = "xsqr_ysqr/x_xsqr_ysqr_solution"
plotter = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1], labels=lab,
xrange=[-10, 10], yrange=[-10, 10], zrange=[-4, 15], bgcolor="#ccffeb")
plotter2 = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1], labels=lab2,
xrange=[-10, 10], yrange=[-10, 10], zrange=[-4, 15], bgcolor="#ccffeb")
wave1 = GeneralMinkowskiRefractionSolution(H, H_z, .2)
wave2 = GeneralGyratonicRefractionSolution(H, H_z, chi[0], .2) #Generate spacetime with wave
plotterg = []
plotterg2 = []
for chival in chi:
plotterg.append(PlotlyDynamicPlotter(title="", aspectratio=[1, 1, 1], labels=lab, xrange=[-10, 10], yrange=[-10, 10], zrange=[-4, 13], bgcolor="#ccffeb"))
plotterg2.append(PlotlyDynamicPlotter(title="", aspectratio=[1, 1, 1], labels=lab2, xrange=[-10, 10], yrange=[-10, 10], zrange=[-4, 13], bgcolor="#ccffeb"))
from grimpulsivewaves.plotting import PlotlyDynamicPlotter
import numpy as np
rs = 1
def toCartNaive(x):
return list(map(lambda x:[x[0],
x[1] * np.sin(x[2]) * np.cos(x[3]),
x[1] * np.sin(x[2]) * np.sin(x[3]),
x[1] * np.cos(x[2])], x))
def metric(x, u, rs):
return -(1-rs/x[1]) * u[0] * u[0] + 1/(1-rs/x[1]) * u[1] * u[1] + x[1]*x[1] * (u[2] * u[2] + np.sin(x[2])**2 * u[3] * u[3])
initpos = [SchwarzschildCoordinates(np.array([0, 3, np.pi/2, 0])), SchwarzschildCoordinates(np.array([0, 6, np.pi/2, 0])), SchwarzschildCoordinates(np.array([0, 0.95, np.pi/2, 0]))]
initvel = [SchwarzschildCoordinates(np.array([1, 0, 0, 0]), dif=True), SchwarzschildCoordinates(np.array([1, 0, 0.052, 0]), dif=True), SchwarzschildCoordinates(np.array([0.1, 0.3, 0.5, 0]), dif=True)]
gen = Solution()
plotterRTphi = PlotlyDynamicPlotter(labels=["x", "z", "t"], aspectratio=[1, 1, 1], bgcolor="#ccffeb", fontsize=30)
for x0, u0n, geonum in zip(initpos, initvel, range(len(initvel))):
norm = metric(x0, u0n, rs)
u0 = (u0n / norm) if norm < 0 else u0n
print(norm)
pos, t = gen.generate_geodesic(x0, u0, (0, 400), christoffelParams=[rs], max_step=0.1)
plotterRTphi.plotTrajectory3D(toCartNaive(pos), t=t, xc=1, yc=3, zc=0, color="rgb(" + str(255 - geonum * 80) + "," + str(geonum * 80) + ",0)")
plotterRTphi.export_html("schw.html")
# ACTUAL CODE HERE PROCEED WITH CAUTION (please)
iposg = [DeSitterConstantHeavisideGyratonNullTetrad(x) for x in initpos]
ivel0 = [DeSitterNullTetrad(x, True) for x in initvels]
ivelg = [DeSitterConstantHeavisideGyratonNullTetrad(x, True) for x in initvels]
waveGENG = GeneralLambdaGyratonSolution(lmb, chi, H1, H1Z)
waveGEN0 = LambdaGeneralSolution(lmb, H1, H1Z)
plotter0 = PlotlyDynamicPlotter(title=r"",
aspectratio=[1, 1, 1],
labels=lab,
xrange=[-5, 5],
yrange=[-5, 5],
zrange=[-5, 5],
showSpikes=True,
bgcolor="#d1f1ff")
plotterG = PlotlyDynamicPlotter(title=r"",
aspectratio=[1, 1, 1],
labels=lab,
xrange=[-5, 5],
yrange=[-5, 5],
zrange=[-5, 5],
showSpikes=True,
bgcolor="#d1f1ff")
if plotHyperboloids:
plotter0.plotHyperboloid(-3. / 2., (-5, 5),
sigma = mu / 2.
return [
gaussian((i + add) % n, mu, sigma) * 255., 0.,
(1. - gaussian((i + add) % n, mu, sigma)) * 255.
]
plot = [2, 3, 0]
lab = ["x", "y", "U"]
convertFunction = toGyraUVxy
plotName = "AS/ASRingGyraNull"
plotter = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1],
labels=lab,
xrange=[-10, 10],
yrange=[-10, 10],
zrange=[-4, 15],
bgcolor="#ccffeb")
plotterg = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1],
labels=lab,
xrange=[-10, 10],
yrange=[-10, 10],
zrange=[-4, 13],
bgcolor="#ccffeb")
plotterg2 = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1],
labels=lab,
lmb = -1.0
initpos = [DeSitterNullTetrad(np.array([0, theta, 0j, 0j])) for theta in np.linspace(-.2, .2, num=N)]
surps = [] #surpress
#u0 = [np.array([1, 1, 0, 0]) for phi in np.linspace(0, 2*np.pi * (N-1.) / N, num=N)]
u0 = [np.array([0.1, 0, 0, 0]) for theta in np.linspace(-2, 2, num=N)]
initvels = [DeSitterNullTetrad(x, dif=True) for x in u0] #Can be generalized to different initial 4-vels
wave = LambdaGeneralSolution(lmb, H, H_z) #Generate spacetime with wave
plotter = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1], labels=["Z4", "Z1", "Z0"],
xrange=[-4.5, 4.5], yrange=[-4.5, 4.5], zrange=[-4.5, 4.5], showSpikes=True, bgcolor="#d1f1ff") #Init 3D plotter
plotter.plotHyperboloid(lmb, (-2.5, 2.5), opacity=0.2, color="rgb(181,0,136)", drawImpulse=True, showlegend=True)
plotter2 = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1], labels=["Z4", "Z1", "Z0"],
xrange=[-4.5, 4.5], yrange=[-4.5, 4.5], zrange=[-4.5, 4.8], showSpikes=True, bgcolor="#d1f1ff") #Init 3D plotter
plotter2.plotCutAndPasteHyperboloid(1., lmb, (-2.5, 2.5), opacity=0.2, color="rgb(181,0,136)", drawImpulse=True, showlegend=True)
# For each init pos generate geodesic (splitted)
for x0, u0, geonum in zip(initpos, initvels, range(0, len(initpos))):
a = wave.generate_geodesic(x0, u0, (-30, 30), max_step=0.1, christoffelParams=[lmb], rtol=1e-7, atol=1e-9)
trajm, trajp = a[0]
sigma = mu / 2.
return [gaussian((i + add) % n, mu, sigma) * 255., 0., (1.-gaussian((i + add) % n, mu, sigma)) * 255.]
plot = [2, 3, 0]
lab = ["x", "y", "U"]
convertFunction = toGyraUVxy
plotName = "Multipole/DipoleTimelike"
for b1 in bu1:
staticplotter = StaticGeodesicPlotter(labels2d=[r"$\mathcal{U}$", r"$\mathcal{V}$"], labelsize=16, aspect='auto',
figsize=(6, 2.1))
for m, i in zip(mu, range(len(mu))):
wave = GeneralMinkowskiRefractionSolution(H, H_z, m, b1)
plotter = PlotlyDynamicPlotter(title="",
aspectratio=[1, 1, 1], labels=lab,
xrange=[-xran, xran], yrange=[-yran, yran], zrange=zran,
bgcolor="#ccffeb", fontsize=30)
staticplotter2 = StaticGeodesicPlotter(labels2d=["x", "z"], labelsize=30, aspect='auto',
figsize=(12, 6))
staticplotter2.ax.plot([0, 0], [-5, 5], "k-")
for x0, u0, geonum in zip(initpos, initvels, range(0, len(initpos))):
a = wave.generate_geodesic(x0, u0, (-3, 6), max_step=0.2, verbose=False)
trajm, trajp = a[0]
tm, tp = a[1]
rgb = genRGB(geonum, len(initpos), 8)
rgb2 = genRGB(geonum, 2*len(initpos), len(initpos))