U d{j3?@sdZddlmZddlZddlmZddZddZ d d Z d d Z d dZ d5ddZ d6ddZd7ddZd8ddZd9ddZd:ddZd;ddZdd$d%Ze d?d&d'Zd@d)d*ZdAd+d,ZdBd-d.Zeeeeed/ZdCd1d2Zeeeeed/ZdDd3d4ZdS)Ez Utilities for computing periodogram statistics. This is an internal module; users should access this functionality via the ``false_alarm_probability`` and ``false_alarm_level`` methods of the ``astropy.timeseries.LombScargle`` API. wrapsN)unitscCs$|dk r||dS|SdSN)sumvaldyr v/var/www/html/bwave/python/venv/lib/python3.8/site-packages/astropy/timeseries/periodograms/lombscargle/_statistics.py _weighted_sumsr cCs0|dkr|St||tt|j|SdSN)Zmeanr npZonesshaperr r r _weighted_meansrcCst|d|t||dSr)rrr r r _weighted_varsrcCs<ddlm}td|t||d||ddS)Nr)gammalnr)Z scipy.specialrrsqrtexp)Nrr r r _gamma"s rcstfdd}|S)Ncs0t|}tfdd|jD|jS)Ncsg|]}|fqSr r ).0xi)argsfunckwargsr r -sz>vectorize_first_argument..new_func..)rasarrayarrayZflatZreshaper)xrrr)rrr new_func*s z*vectorize_first_argument..new_funcr)rr#r r"r vectorize_first_argument)sr$rcCst|}||dkrtd||}|dkr:t| S|dkr^d|d|d|dS|dkrd|d|d|dS|d krd|td||Std |d d S) aProbability density function for Lomb-Scargle periodogram Compute the expected probability density function of the periodogram for the null hypothesis - i.e. data consisting of Gaussian noise. Parameters ---------- z : array-like The periodogram value. N : int The number of data points from which the periodogram was computed. normalization : {'standard', 'model', 'log', 'psd'} The periodogram normalization. dH, dK : int, optional The number of parameters in the null hypothesis and the model. Returns ------- pdf : np.ndarray The expected probability density function. Notes ----- For normalization='psd', the distribution can only be computed for periodograms constructed with errors specified. All expressions used here are adapted from Table 1 of Baluev 2008 [1]_. References ---------- .. [1] Baluev, R.V. MNRAS 385, 1279 (2008) rDegrees of freedom != 2psdstandard?rmodellognormalization='' is not recognizedNrrNotImplementedErrorr ValueErrorzr normalizationdHdKNkr r r pdf_single2s   r8cCst|}||dkrtd||}|dkr:t| S|dkrRd|d|S|dkrjd|d|S|d krtd||Std |d d S) a%Single-frequency false alarm probability for the Lomb-Scargle periodogram This is equal to 1 - cdf, where cdf is the cumulative distribution. The single-frequency false alarm probability should not be confused with the false alarm probability for the largest peak. Parameters ---------- z : array-like The periodogram value. N : int The number of data points from which the periodogram was computed. normalization : {'standard', 'model', 'log', 'psd'} The periodogram normalization. dH, dK : int, optional The number of parameters in the null hypothesis and the model. Returns ------- false_alarm_probability : np.ndarray The single-frequency false alarm probability. Notes ----- For normalization='psd', the distribution can only be computed for periodograms constructed with errors specified. All expressions used here are adapted from Table 1 of Baluev 2008 [1]_. References ---------- .. [1] Baluev, R.V. MNRAS 385, 1279 (2008) rr&r'r(rr)r*r+r,r-r.Nr/r2r r r fap_singlecs!   r9c Cst|}||dkrtd||}tjdd|dkrTt| W5QRS|dkrxd|d|W5QRS|dkrd |d |W5QRS|d krd |t|W5QRStd |d W5QRXdS)a*Single-frequency inverse false alarm probability This function computes the periodogram value associated with the specified single-frequency false alarm probability. This should not be confused with the false alarm level of the largest peak. Parameters ---------- fap : array-like The false alarm probability. N : int The number of data points from which the periodogram was computed. normalization : {'standard', 'model', 'log', 'psd'} The periodogram normalization. dH, dK : int, optional The number of parameters in the null hypothesis and the model. Returns ------- z : np.ndarray The periodogram power corresponding to the single-peak false alarm probability. Notes ----- For normalization='psd', the distribution can only be computed for periodograms constructed with errors specified. All expressions used here are adapted from Table 1 of Baluev 2008 [1]_. References ---------- .. [1] Baluev, R.V. MNRAS 385, 1279 (2008) rr&ignoredivider'r(rr*r,r-r.N)rrr0errstater,r1)faprr4r5r6r7r r r inv_fap_singles"  rAcCsdt|||||dS)aCumulative distribution for the Lomb-Scargle periodogram Compute the expected cumulative distribution of the periodogram for the null hypothesis - i.e. data consisting of Gaussian noise. Parameters ---------- z : array-like The periodogram value. N : int The number of data points from which the periodogram was computed. normalization : {'standard', 'model', 'log', 'psd'} The periodogram normalization. dH, dK : int, optional The number of parameters in the null hypothesis and the model. Returns ------- cdf : np.ndarray The expected cumulative distribution function. Notes ----- For normalization='psd', the distribution can only be computed for periodograms constructed with errors specified. All expressions used here are adapted from Table 1 of Baluev 2008 [1]_. References ---------- .. [1] Baluev, R.V. MNRAS 385, 1279 (2008) r)r4r5r6)r9)r3rr4r5r6r r r cdf_singles rBr(cCs0t|}||} ||} t||} tdtj| } || } t|}|dkrj| t| t|S|dkrt| | d|d| dtd| |S|dkrt| | d|d| td| |S|dkrt| | td|| dt| td|St d |d S) z=tau factor for estimating Davies bound (Baluev 2008, Table 1)r'r(rr)r*r+r,znormalization=N) lenrrrpirrrsinhr0)Zfmaxtyr r4r5r6rZNHZNKZDtZTeffWr r r tau_daviess.  2. rLc Csjt|}t|t|}||}t|||d} tjdd&t|t|  W5QRSQRXdS)zFFalse Alarm Probability based on estimated number of indep frequenciesr4r:r;N)rDmaxminr9rr?expm1log1p) rGrHrIrJr r4rTN_efffap_sr r r fap_naive s rUc Csht|}t|}t|t|}||}tjdd ttd|| } W5QRXt| ||S)z:Inverse FAP based on estimated number of indep frequenciesr:r;r) rrrDrNrOr?rPr,rA) r@rHrIrJr r4rrRrSrTr r r inv_fap_naives $rVc Cs2t|}t|||d}t||||||d}||S)zRDavies upper-bound to the false alarm probability (Eqn 5 of Baluev 2008) rM)rDr9rL) rGrHrIrJr r4rrTtaur r r fap_davies%srXc s`ddlm}|||||f}tf|}fdd} |j| ||dd} | jsZtd| jS)z!Inverse of the davies upper-boundroptimizecst|f|Sr)rXr3rpr r 7z inv_fap_davies..lmrmethod&inv_fap_baluev did not converge for p=ZscipyrZrVrootsuccessr1r! r]rHrIrJr r4rZrZz0rresr r\r inv_fap_davies0s  ricCsBt|t||}t||||||d}t|  |t| S)zTAlias-free approximation to false alarm probability (Eqn 6 of Baluev 2008) rM)r9rDrLrrPr)rGrHrIrJr r4rTrWr r r fap_baluev>srjc s`ddlm}|||||f}tf|}fdd} |j| ||dd} | jsZtd| jS)z.Inverse of the Baluev alias-free approximationrrYcst|f|Sr)rjr[r\r r r^Qr_z inv_fap_baluev..r`rarcrdrgr r\r inv_fap_baluevJs  rkcCsddlm}tj|}g} t|D]\} |dt|t|} |||| |dkrT|n|| |d} | j|d\} }| | q$t | } | | S)z5Generate a sequence of bootstrap estimates of the maxr) LombScarglerNrM)Zmaximum_frequency)corermrrandomZ default_rngrangeZintegersrDZ autopowerappendrNuZQuantitysort)rIrJr rHr4 random_seedZ n_bootstraprmrngZ power_max_sZls_bootfreqpowerr r r _bootstrap_maxXs     rzc Cs,t|||||||}dt||t|S)z1Bootstrap estimate of the false alarm probabilityr)rzrZ searchsortedrD) rGrHrIrJr r4 n_bootstrapsrtpmaxr r r fap_bootstraplsr}c CsPt|}t|||||||}|ttd|t|tdt|dS)z9Bootstrap estimate of the inverse false alarm probabilityrr)rrrzZclipfloorrDZastypeint) r@rHrIrJr r4r{rtr|r r r inv_fap_bootstrapus r)singleZnaiveZdaviesbaluevZ bootstraprcCsT|dkrt|t||S|tkr.td|t|}|psb   1 2 5 #      6