11.5.2.4. astroML.time_series.generate_damped_RW¶
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astroML.time_series.generate_damped_RW(t_rest, tau=300.0, z=2.0, xmean=0, SFinf=0.3, random_state=None)[source]¶ Generate a damped random walk light curve
This uses a damped random walk model to generate a light curve similar to that of a QSO [1].
- Parameters
- t_restarray_like
rest-frame time. Should be in increasing order
- taufloat
relaxation time
- zfloat
redshift
- xmeanfloat (optional)
mean value of random walk; default=0
- SFinffloat (optional
Structure function at infinity; default=0.3
- random_stateNone, int, or np.random.RandomState instance (optional)
random seed or random number generator
- Returns
- xndarray
the sampled values corresponding to times t_rest
Notes
The differential equation is (with t = time/tau):
dX = -X(t) * dt + sigma * sqrt(tau) * e(t) * sqrt(dt) + b * tau * dt
where e(t) is white noise with zero mean and unit variance, and
Xmean = b * tau SFinf = sigma * sqrt(tau / 2)
so
dX(t) = -X(t) * dt + sqrt(2) * SFint * e(t) * sqrt(dt) + Xmean * dt
References