def simrv(time, flux, strad = 1.0, nmed = 11, nlin = 5, \
kvc = 0.0, phi0 = None, f = None, doplot = False):
'''Simulate RV time series given photometric time series. Assumes
input flux array has already been normalised & smoothed, but does
very light smoothing (nmed=nbin=5 by default)'''
ln = scipy.isnan(flux)
npt = len(time)
phi = filter.filt1d(flux, 1, nlin)
# phi = signal.medfilt(flux, nmed)
# phi = scipy.copy(flux)
if doplot == True:
ee = dofig(1, 1, 3)
ax1 = doaxes(ee, 1, 3, 0, 0)
pylab.plot(time, flux, 'k.')
pylab.plot(time, phi, 'r-')
pylab.ylabel('Norm. flux')
dt = (time[1:] - time[:npt-1])
dts = dt * DAY2S
tout = time[:npt-1] + 0.5 * dt
phidot = (phi[1:] - phi[:npt-1]) / dts
if doplot == True:
ax2 = doaxes(ee, 1, 3, 0, 1, sharex = ax1)
pylab.plot(tout, phidot, 'k.')
pylab.ylabel('Flux. der.')
phidot = filter.filt1d(phidot, 1, nlin)
if doplot == True:
pylab.plot(tout, phidot, 'r-')
lf = scipy.isfinite(phi)
phimin = min(phi[lf])
phimax = max(phi[lf])
med, sig = filter.medsig(phi)
if phi0 == None:
phi0 = phimax + sig
if f == None:
f = (phi0 - phimin) / phi0
print phimin, phimax, sig, phi0, f
rstar = strad * RSUN
print rstar / f
if f < 1e-6:
rvout = tout - tout
else:
rvout = - phidot/phi0 * (1 - phi[:npt-1] / phi0) * rstar / f
if kvc != 0:
rvout += (1 - phi[:npt-1] / phi0)**2 * kvc / f
rvout[ln[0:npt-1]] = scipy.nan
if doplot == True:
ax3 = doaxes(ee, 1, 3, 0, 2, sharex = ax1)
pylab.plot(tout, 1 - phi[:npt-1] / phi0)
# pylab.plot(tout, rvout, 'r-')
pylab.ylabel('RV (m/s)')
pylab.xlabel('time (days)')
pylab.xlim(time.min(), time.max())
return tout, rvout
def rv_noise(time, tau = 0.5, ninit = 10):
npt = len(time)
# Burn-in section
dt = 2.3 * tau / float(ninit)
tinit = (scipy.arange(ninit) + 1) * dt
tsim = scipy.append(time[0] - tinit[::-1], time)
nsim = len(tsim)
# Instead of Gaussian white noise, to simulate effects of moon and
# such like, each point in the "WGN" component is drawn from a
# distribution with a different sigma each night, where the sigma itself is
# drawn from a powerlaw distribution between 1 and 10
wt = pylab.normal(0, 1, nsim)
ye = scipy.ones(nsim)
nights = scipy.fix(tsim)
unights = scipy.unique(nights)
nnights = len(unights)
sigma = 10.0 ** (scipy.rand(nnights))**4
for i in scipy.arange(nnights):
l = scipy.where(nights == unights[i])[0]
if l.any():
wt[l] *= sigma[i]
ye[l] = sigma[i]
# Now apply MA model with exponentially decaying correlation
ysim = scipy.copy(wt)
for i in scipy.arange(nsim):
j = i - 1
coeff = 1.0
while (j > 0) * (coeff > 0.1):
dt = tsim[i] - tsim[j]
coeff = scipy.exp(-dt/tau)
ysim[i] += coeff * wt[j]
j -= 1
# Discard burn-in and globally re-scale before returning
yout = ysim[ninit:]
eout = ye[ninit:]
med, sig = filter.medsig(yout)
yout /= sig
eout /= sig
return yout, eout