a ߙfbeI@sdZddlZddlZddlmZddlmZgdZdddZ Gd d d Z Gd d d e Z Gd dde Z Gddde Z dS)ug Bayesian Blocks for Time Series Analysis ======================================== Dynamic programming algorithm for solving a piecewise-constant model for various datasets. This is based on the algorithm presented in Scargle et al 2013 [1]_. This code was ported from the astroML project [2]_. Applications include: - finding an optimal histogram with adaptive bin widths - finding optimal segmentation of time series data - detecting inflection points in the rate of event data The primary interface to these routines is the :func:`bayesian_blocks` function. This module provides fitness functions suitable for three types of data: - Irregularly-spaced event data via the :class:`Events` class - Regularly-spaced event data via the :class:`RegularEvents` class - Irregularly-spaced point measurements via the :class:`PointMeasures` class For more fine-tuned control over the fitness functions used, it is possible to define custom :class:`FitnessFunc` classes directly and use them with the :func:`bayesian_blocks` routine. One common application of the Bayesian Blocks algorithm is the determination of optimal adaptive-width histogram bins. This uses the same fitness function as for irregularly-spaced time series events. The easiest interface for creating Bayesian Blocks histograms is the :func:`astropy.stats.histogram` function. References ---------- .. [1] https://ui.adsabs.harvard.edu/abs/2013ApJ...764..167S .. [2] https://www.astroml.org/ https://github.com//astroML/astroML/ .. [3] Bellman, R.E., Dreyfus, S.E., 1962. Applied Dynamic Programming. Princeton University Press, Princeton. https://press.princeton.edu/books/hardcover/9780691651873/applied-dynamic-programming .. [4] Bellman, R., Roth, R., 1969. Curve fitting by segmented straight lines. J. Amer. Statist. Assoc. 64, 1079–1084. https://www.tandfonline.com/doi/abs/10.1080/01621459.1969.10501038 N) signature)AstropyUserWarning) FitnessFuncEvents RegularEvents PointMeasuresbayesian_blockseventscKsdtttd}|||}t|tur>t|tr>|fi|}nt|trN|}ntd| |||S)u Compute optimal segmentation of data with Scargle's Bayesian Blocks This is a flexible implementation of the Bayesian Blocks algorithm described in Scargle 2013 [1]_. Parameters ---------- t : array-like data times (one dimensional, length N) x : array-like, optional data values sigma : array-like or float, optional data errors fitness : str or object the fitness function to use for the model. If a string, the following options are supported: - 'events' : binned or unbinned event data. Arguments are ``gamma``, which gives the slope of the prior on the number of bins, or ``ncp_prior``, which is :math:`-\ln({\tt gamma})`. - 'regular_events' : non-overlapping events measured at multiples of a fundamental tick rate, ``dt``, which must be specified as an additional argument. Extra arguments are ``p0``, which gives the false alarm probability to compute the prior, or ``gamma``, which gives the slope of the prior on the number of bins, or ``ncp_prior``, which is :math:`-\ln({\tt gamma})`. - 'measures' : fitness for a measured sequence with Gaussian errors. Extra arguments are ``p0``, which gives the false alarm probability to compute the prior, or ``gamma``, which gives the slope of the prior on the number of bins, or ``ncp_prior``, which is :math:`-\ln({\tt gamma})`. In all three cases, if more than one of ``p0``, ``gamma``, and ``ncp_prior`` is chosen, ``ncp_prior`` takes precedence over ``gamma`` which takes precedence over ``p0``. Alternatively, the fitness parameter can be an instance of :class:`FitnessFunc` or a subclass thereof. **kwargs : any additional keyword arguments will be passed to the specified :class:`FitnessFunc` derived class. Returns ------- edges : ndarray array containing the (N+1) edges defining the N bins Examples -------- .. testsetup:: >>> np.random.seed(12345) Event data: >>> t = np.random.normal(size=100) >>> edges = bayesian_blocks(t, fitness='events', p0=0.01) Event data with repeats: >>> t = np.random.normal(size=100) >>> t[80:] = t[:20] >>> edges = bayesian_blocks(t, fitness='events', p0=0.01) Regular event data: >>> dt = 0.05 >>> t = dt * np.arange(1000) >>> x = np.zeros(len(t)) >>> x[np.random.randint(0, len(t), len(t) // 10)] = 1 >>> edges = bayesian_blocks(t, x, fitness='regular_events', dt=dt) Measured point data with errors: >>> t = 100 * np.random.random(100) >>> x = np.exp(-0.5 * (t - 50) ** 2) >>> sigma = 0.1 >>> x_obs = np.random.normal(x, sigma) >>> edges = bayesian_blocks(t, x_obs, sigma, fitness='measures') References ---------- .. [1] Scargle, J et al. (2013) https://ui.adsabs.harvard.edu/abs/2013ApJ...764..167S .. [2] Bellman, R.E., Dreyfus, S.E., 1962. Applied Dynamic Programming. Princeton University Press, Princeton. https://press.princeton.edu/books/hardcover/9780691651873/applied-dynamic-programming .. [3] Bellman, R., Roth, R., 1969. Curve fitting by segmented straight lines. J. Amer. Statist. Assoc. 64, 1079–1084. https://www.tandfonline.com/doi/abs/10.1080/01621459.1969.10501038 See Also -------- astropy.stats.histogram : compute a histogram using bayesian blocks )r Zregular_eventsZmeasuresz fitness parameter not understood) rrrgettype issubclassr isinstance ValueErrorfit)txsigmafitnesskwargsZ FITNESS_DICTZfitfuncrr?r@rArr) __classcell__rrrFrrsrcs6eZdZdZd fdd ZfddZdd ZZS) raBayesian blocks fitness for regular events This is for data which has a fundamental "tick" length, so that all measured values are multiples of this tick length. In each tick, there are either zero or one counts. Parameters ---------- dt : float tick rate for data p0 : float, optional False alarm probability, used to compute the prior on :math:`N_{\rm blocks}` (see eq. 21 of Scargle 2013). If gamma is specified, p0 is ignored. ncp_prior : float, optional If specified, use the value of ``ncp_prior`` to compute the prior as above, using the definition :math:`{\tt ncp\_prior} = -\ln({\tt gamma})`. If ``ncp_prior`` is specified, ``gamma`` and ``p0`` are ignored. rNcs||_t|||dSr)dtrCr)rrIrrrrFrrrszRegularEvents.__init__cs>t|||\}}}t|dk|dkBs4td|||fS)Nrr z*Regular events must have only 0 and 1 in x)rCr)r!allrrErFrrr)szRegularEvents.validate_inputcCst||j}||}d}t|d|kr4tdtd|}d||dk<d||dk<|t|||t|S)Ng:0yE>r z3regular events: N/M > 1. Is the time step correct?r)rIr!rDwarningswarnrr,)rr8r9ZM_kZN_over_MZepsZone_m_NMrrrrs   zRegularEvents.fitness)rNN)r>r?r@rArr)rrHrrrFrrs rcs6eZdZdZd fdd ZddZfdd ZZS) ra!Bayesian blocks fitness for point measures Parameters ---------- p0 : float, optional False alarm probability, used to compute the prior on :math:`N_{\rm blocks}` (see eq. 21 of Scargle 2013). If gamma is specified, p0 is ignored. ncp_prior : float, optional If specified, use the value of ``ncp_prior`` to compute the prior as above, using the definition :math:`{\tt ncp\_prior} = -\ln({\tt gamma})`. If ``ncp_prior`` is specified, ``gamma`` and ``p0`` are ignored. rNcst|||dSr)rCrrrFrrrszPointMeasures.__init__cCs||d|S)Nr+r)rr4r6rrrrszPointMeasures.fitnesscs |durtdt|||S)Nz&x must be specified for point measures)rrCr)rErFrrr) szPointMeasures.validate_input)rNN)r>r?r@rArrr)rHrrrFrrsr)NNr )rArKZnumpyr!inspectrZastropy.utils.exceptionsr__all__rrrrrrrrrs+   tr$0