def minimal():
'''
A minimal working example to perform a BH binary inspiral
**Run using**
import precession.test
precession.test.minimal()
'''
t0 = time.time()
q = 0.75 # Mass ratio
chi1 = 0.5 # Primary's spin magnitude
chi2 = 0.95 # Secondary's spin magnitude
print "Take a BH binary with q=%.2f, chi1=%.2f and chi2=%.2f" % (q, chi1,
chi2)
sep = numpy.logspace(10, 1, 10) # Output separations
t1 = numpy.pi / 3. # Spin orientations at r_vals[0]
t2 = 2. * numpy.pi / 3.
dp = numpy.pi / 4.
M, m1, m2, S1, S2 = precession.get_fixed(q, chi1, chi2)
t1v, t2v, dpv = precession.evolve_angles(t1, t2, dp, sep, q, S1, S2)
print "Perform BH binary inspiral"
print "log10(r/M) \t theta1 \t theta2 \t deltaphi"
for r, t1, t2, dp in zip(numpy.log10(sep), t1v, t2v, dpv):
print "%.0f \t\t %.3f \t\t %.3f \t\t %.3f" % (r, t1, t2, dp)
t = time.time() - t0
print "Executed in %.3fs" % t
def test():
t0 = time.time()
q = 0.75 # Mass ratio
chi1 = 0.5 # Primary’s spin magnitude
chi2 = 0.95 # Secondary’s spin magnitude
print("Take a BH binary with q=%.2f, chi1=%.2f and ,→ chi2=%.2f" %
(q, chi1, chi2))
sep = numpy.logspace(10, 1, 10) # Output separations
t1 = numpy.pi / 3. # Spin orientations at r_vals[0]
t2 = 2. * numpy.pi / 3.
dp = numpy.pi / 4.
M, m1, m2, S1, S2 = precession.get_fixed(q, chi1, chi2)
freq = [rtof(s, M) for s in sep]
print(ftor(20, M))
t1v, t2v, dpv = precession.evolve_angles(t1, t2, dp, sep, q, S1, S2)
print("Perform BH binary inspiral")
print("log10(r/M) \t freq(Hz) \t theta1 \t theta2 \t deltaphi")
for r, f, t1, t2, dp in zip(numpy.log10(sep), freq, t1v, t2v, dpv):
print("%.0f \t\t %.3f \t\t %.3f \t\t %.3f \t\t %.3f" %
(r, f, t1, t2, dp))
t = time.time() - t0
print("Executed in %.3fs" % t)
def timing():
'''
This examples compare the numerical performance of `precession.orbit_angles`
and `precession.evolve_angles`. Computation is performed twice, first using
all the available CPUs and then explicitely disabling the code
parallelization.
**Run using**
import precession.test
precession.test.timing()
'''
BHsample = [] # Construct a sample of BH binaries
N = 100
for i in range(N):
q = random.uniform(0, 1)
chi1 = random.uniform(0, 1)
chi2 = random.uniform(0, 1)
M, m1, m2, S1, S2 = precession.get_fixed(q, chi1, chi2)
t1 = random.uniform(0, numpy.pi)
t2 = random.uniform(0, numpy.pi)
dp = random.uniform(0, 2. * numpy.pi)
BHsample.append([q, S1, S2, t1, t2, dp])
q_vals, S1_vals, S2_vals, t1i_vals, t2i_vals, dpi_vals = zip(
*BHsample) # Traspose python list
ri = 1e4 * M # Initial separation
rf = 10 * M # Final separation
r_vals = [ri, rf] # Intermediate output separations not needed here
print " *Integrating a sample of N=%.0f BH binaries from ri=%.0f to rf=%.0f using %.0f CPUs*" % (
N, ri, rf, multiprocessing.cpu_count()
) # Parallel computation used by default
t0 = time.time()
precession.orbit_angles(t1i_vals, t2i_vals, dpi_vals, r_vals, q_vals,
S1_vals, S2_vals)
t = time.time() - t0
print "Orbit-averaged: parallel integrations\n\t total time t=%.3fs\n\t time per binary t/N=%.3fs" % (
t, t / N)
t0 = time.time()
precession.evolve_angles(t1i_vals, t2i_vals, dpi_vals, r_vals, q_vals,
S1_vals, S2_vals)
t = time.time() - t0
print "Precession-averaged: parallel integrations\n\t total time t=%.3fs\n\t time per binary t/N=%.3fs" % (
t, t / N)
precession.empty_temp() # Remove previous checkpoints
precession.CPUs = 1 # Force serial computation
print " *Integrating a sample of N=%.0f BH binaries from ri=%.0f to rf=%.0f using %.0f CPU*" % (
len(BHsample), ri, rf, precession.CPUs)
t0 = time.time()
precession.orbit_angles(t1i_vals, t2i_vals, dpi_vals, r_vals, q_vals,
S1_vals, S2_vals)
t = time.time() - t0
print "Orbit-averaged: serial integrations\n\t total time t=%.3fs\n\t time per binary t/N=%.3fs" % (
t, t / N)
t0 = time.time()
precession.evolve_angles(t1i_vals, t2i_vals, dpi_vals, r_vals, q_vals,
S1_vals, S2_vals)
t = time.time() - t0
print "Precession-averaged: serial integrations\n\t total time t=%.3fs\n\t time per binary t/N=%.3fs" % (
t, t / N)
precession.empty_temp() # Remove previous checkpoints
def PNwrappers():
'''
Wrappers of the PN integrators. Here we show how to perform orbit-averaged,
precession-averaged and hybrid PN inspirals using the various wrappers
implemented in the code. We also show how to estimate the final mass, spin
and recoil of the BH remnant following a merger.
**Run using**
import precession.test
precession.test.PNwrappers()
'''
q = 0.9 # Mass ratio. Must be q<=1.
chi1 = 0.5 # Primary spin. Must be chi1<=1
chi2 = 0.5 # Secondary spin. Must be chi2<=1
print "We study a binary with\n\tq=%.3f, chi1=%.3f, chi2=%.3f" % (q, chi1,
chi2)
M, m1, m2, S1, S2 = precession.get_fixed(q, chi1,
chi2) # Total-mass units M=1
ri = 1000 * M # Initial separation.
rf = 10. * M # Final separation.
rt = 100. * M # Intermediate separation for hybrid evolution.
r_vals = numpy.logspace(numpy.log10(ri), numpy.log10(rf),
10) # Output requested
t1i = numpy.pi / 4.
t2i = numpy.pi / 4.
dpi = numpy.pi / 4. # Initial configuration
xii, Ji, Si = precession.from_the_angles(t1i, t2i, dpi, q, S1, S2, ri)
print "Configuration at ri=%.0f\n\t(xi,J,S)=(%.3f,%.3f,%.3f)\n\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (
ri, xii, Ji, Si, t1i, t2i, dpi)
print " *Orbit-averaged evolution*"
print "Evolution ri=%.0f --> rf=%.0f" % (ri, rf)
Jf, xif, Sf = precession.orbit_averaged(Ji, xii, Si, r_vals, q, S1, S2)
print "\t(xi,J,S)=(%.3f,%.3f,%.3f)" % (xif[-1], Jf[-1], Sf[-1])
t1f, t2f, dpf = precession.orbit_angles(t1i, t2i, dpi, r_vals, q, S1, S2)
print "\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (t1f[-1], t2f[-1],
dpf[-1])
Jvec, Lvec, S1vec, S2vec, Svec = precession.Jframe_projection(
xii, Si, Ji, q, S1, S2, ri)
Lxi, Lyi, Lzi = Lvec
S1xi, S1yi, S1zi = S1vec
S2xi, S2yi, S2zi = S2vec
Lx, Ly, Lz, S1x, S1y, S1z, S2x, S2y, S2z = precession.orbit_vectors(
Lxi, Lyi, Lzi, S1xi, S1yi, S1zi, S2xi, S2yi, S2zi, r_vals, q)
print "\t(Lx,Ly,Lz)=(%.3f,%.3f,%.3f)\n\t(S1x,S1y,S1z)=(%.3f,%.3f,%.3f)\n\t(S2x,S2y,S2z)=(%.3f,%.3f,%.3f)" % (
Lx[-1], Ly[-1], Lz[-1], S1x[-1], S1y[-1], S1z[-1], S2x[-1], S2y[-1],
S2z[-1])
print " *Precession-averaged evolution*"
print "Evolution ri=%.0f --> rf=%.0f" % (ri, rf)
Jf = precession.evolve_J(xii, Ji, r_vals, q, S1, S2)
print "\t(xi,J,S)=(%.3f,%.3f,-)" % (xii, Jf[-1])
t1f, t2f, dpf = precession.evolve_angles(t1i, t2i, dpi, r_vals, q, S1, S2)
print "\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (t1f[-1], t2f[-1],
dpf[-1])
print "Evolution ri=%.0f --> infinity" % ri
kappainf = precession.evolve_J_backwards(xii, Jf[-1], rf, q, S1, S2)
print "\tkappainf=%.3f" % kappainf
Jf = precession.evolve_J_infinity(xii, kappainf, r_vals, q, S1, S2)
print "Evolution infinity --> rf=%.0f" % rf
print "\tJ=%.3f" % Jf[-1]
print " *Hybrid evolution*"
print "Prec.Av. infinity --> rt=%.0f & Orb.Av. rt=%.0f --> rf=%.0f" % (
rt, rt, rf)
t1f, t2f, dpf = precession.hybrid(xii, kappainf, r_vals, q, S1, S2, rt)
print "\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (t1f[-1], t2f[-1],
dpf[-1])
print " *Properties of the BH remnant*"
Mfin = precession.finalmass(t1f[-1], t2f[-1], dpf[-1], q, S1, S2)
print "\tM_f=%.3f" % Mfin
chifin = precession.finalspin(t1f[-1], t2f[-1], dpf[-1], q, S1, S2)
print "\tchi_f=%.3f, S_f=%.3f" % (chifin, chifin * Mfin**2)
vkick = precession.finalkick(t1f[-1], t2f[-1], dpf[-1], q, S1, S2)
print "\tvkick=%.5f" % (vkick) # Geometrical units c=1
