IR-eC?dZddlmZddlZddlmZdZdZ dZ dZ d Z d d Z d d Zd dZd dZd!dZd"dZd"dZd"dZe d"dZd"dZe d"dZd#dZ d$dZ d$dZeeeeedZ d%dZeeeeedZ d&dZdS)'z 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)unitscb|||dzz S|SN)sumvaldys Wlib/python3.11/site-packages/astropy/timeseries/periodograms/lombscargle/_statistics.py _weighted_sumrs/ ~b!e   """wwyyc||St||ttj|j|z SN)meanrnponesshaper s r _weighted_meanrs@ zxxzzS"%% bgci6H6H"(M(MMMrcPt|dz|t||dzz Sr)rr s r _weighted_varrs* #q&" % %sB(?(?1(D DDrcddlm}tjd|z tj||dz ||dz dz z zS)Nr)gammalnr) scipy.specialrrsqrtexp)Nrs r _gammar "sZ%%%%%% 71q5>>BF771q5>>GGQUaK4H4H#HII IIrc<tfd}|S)Nctj|}tjfd|jD|jS)Nc(g|]}|gRiSr$).0xiargsfunckwargss r z>vectorize_first_argument..new_func..-s3DDDrb24222622DDDr)rasarrayarrayflatreshaper)xr'r)r(s ``r new_funcz*vectorize_first_argument..new_func*sO JqMMxDDDDDDQVDDDEEMMagVVVrr)r(r0s` r vectorize_first_argumentr1)s8 4[[WWWW[W Orrcttj|}||z dkrtd||z }|dkrtj| S|dkrd|zd|z d|zdz zzS|dkrd|zd|zd|zdz zzS|d kr d|ztjd|z|zzSt d |d ) 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 recognizedrr+NotImplementedErrorr ValueErrorzr normalizationdHdKNks r pdf_singlerF2s@ 1 A Bw!||!";<<< RBvqbzz * $ $Rx1q5cBhl333 ' ! !Rx1q5dRi!m444 %  Rx"&Q////M=MMMNNNrcDtj|}||z dkrtd||z }|dkrtj| S|dkr d|z d|zzS|dkr d|zd|zzS|d krtjd|z|zSt d |d ) 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) rr4r5r6rr7r8r9r:r;r<r=r@s r fap_singlerHcsB 1 A Bw!||!";<<< RBvqbzz * $ $A38$$ ' ! !A4"9%% %  vdRi!m$$$M=MMMNNNrctj|}||z dkrtd||z }tjd5|dkr!tj| cdddS|dkrd|d|z zz cdddS|d krd |d |z zzcdddS|d kr&d |z tj|zcdddSt d |d#1swxYwYdS)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) rr4ignoredivider5Nr6rr8r:r;r<)rr+r>errstater:r?)faprrBrCrDrEs r inv_fap_singlerQsD *S//C Bw!||!";<<< RB H % % % S S E ! !F3KK< S S S S S S S Sj ( (sq2v& S S S S S S S S g % %R(( S S S S S S S Se # #7RVC[[( S S S S S S S SQ}QQQRR R S S S S S S S S S Ss*C(/C( C()C(C((C,/C,c0dt|||||z S)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)rBrCrD)rH)rArrBrCrDs r cdf_singlerSs#@ z!QmrJJJ JJrr6c t|}||z } ||z } t||} tjdtjz| z} || z} tj|}|dkr-| tj| ztj|zS|dkrtau factor for estimating Davies bound (Baluev 2008, Table 1).r5r6rr7r8r9r:znormalization=) lenrrrpir+rr sinhr>)Zfmaxtyr rBrCrDrNHNKDtTeffWs r tau_daviesrbs AA RB RB q"  B 71ru9r> " "D t A 1 A261"::~ ** * $ $bzzA~QC26N ;;bgcBhQRl>S>SSS ' ! !bzzA~QD2I 66rA9N9NNN %   2JJ fTAXc*++ ,gb2737+++,, - ""B="B"BCCCrc@t|}t|t|z }||z}t|||} t jd5t j|t j| z cdddS#1swxYwYdS)zGFalse Alarm Probability based on estimated number of indep frequencies.rBrJrKN)rVmaxminrHrrOexpm1log1p) rYrZr[r\r rBrTN_efffap_ss r fap_naiverl s AA AQA 1HE q!= 9 9 9E H % % %335&!1!11222333333333333333333s+BBBcftj|}t|}t|t |z }||z}tjd5tjtjd|z |z  } dddn #1swxYwYt| ||S)z;Inverse FAP based on estimated number of indep frequencies.rJrKrN) rr+rVrerfrOrgr:rQ) rPrZr[r\r rBrrirjrks r inv_fap_naiverns *S//C AA AQA 1HE H % % %33"&S//E1222333333333333333 %M 2 22s.BBBcxt|}t|||}t||||||}||zS)zSDavies upper-bound to the false alarm probability. (Eqn 5 of Baluev 2008) rd)rVrHrb) rYrZr[r\r rBrrktaus r fap_daviesrq%sG AA q!= 9 9 9E QaBm D D DC 3;rcddlm}|||||f}tg|R}fd} || ||d} | jst d| jS)z"Inverse of the davies upper-bound.roptimizec$t|g|Rz Sr)rqrAr'ps r z inv_fap_davies..7Jq0400014rlmr'method&inv_fap_baluev did not converge for p=scipyrtrnrootsuccessr?r/ rwrZr[r\r rBrtr'z0r(ress ` r inv_fap_daviesr0 !QM *D q 4 B 4 4 4 4D --btD- 9 9C ;GE!EEFFF 5Lrct|t||}t||||||}tj|  |tj| zzS)zUAlias-free approximation to false alarm probability. (Eqn 6 of Baluev 2008) rd)rHrVrbrrgr)rYrZr[r\r rBrkrps r fap_baluevr>s] q#a&&- 0 0E QaBm D D DC HcTNN?URVSD\\1 11rcddlm}|||||f}tg|R}fd} || ||d} | jst d| jS)z/Inverse of the Baluev alias-free approximation.rrsc$t|g|Rz Sr)rrvs r rxz inv_fap_baluev..Qryrrzr{r}r~rs ` r inv_fap_baluevrJrrcddlm}tj|}g} t |D]} |dt|t|} |||| ||n|| |} | |\} }| | tj | } | | S)z6Generate a sequence of bootstrap estimates of the max.r) LombScarglerNrd)maximum_frequency)corerrrandom default_rngrangeintegersrV autopowerappendreuQuantitysort)r[r\r rZrB random_seed n_bootstraprrng power_max_sls_bootfreqpowers r _bootstrap_maxrXs!!!!!! )   , ,CI ;  && LLCFFCFF + ++ qt2:RR2a5    ''$'?? e%%%% 9%%I NN rc |t|||||||}dtj||t|z z S)z2Bootstrap estimate of the false alarm probability.r)rr searchsortedrV) rYrZr[r\r rB n_bootstrapsrpmaxs r fap_bootstraprls? !QD-l S SD rtQ''#d))3 33rc &tj|}t|||||||}|tjtjd|z t |ztdt |dz S)z:Bootstrap estimate of the inverse false alarm probability.rr)rr+rclipfloorrVastypeint) rPrZr[r\r rBrrrs r inv_fap_bootstraprusu *S//C !QD-l S SD !c'SYY!677>>sCCQD TU VV WWr)singlenaivedaviesbaluev bootstraprc|dkrt|t||S|tvrtd|t|}|pi}|||||||fi|S)a$Compute the approximate false alarm probability for periodogram peaks Z. This gives an estimate of the false alarm probability for the largest value in a periodogram, based on the null hypothesis of non-varying data with Gaussian noise. The true probability cannot be computed analytically, so each method available here is an approximation to the true value. Parameters ---------- Z : array-like The periodogram value. fmax : float The maximum frequency of the periodogram. t, y, dy : array-like The data times, values, and errors. normalization : {'standard', 'model', 'log', 'psd'}, optional The periodogram normalization. method : {'baluev', 'davies', 'naive', 'bootstrap'}, optional The approximation method to use. method_kwds : dict, optional Additional method-specific keywords. Returns ------- false_alarm_probability : np.ndarray The false alarm probability. Notes ----- For normalization='psd', the distribution can only be computed for periodograms constructed with errors specified. See Also -------- false_alarm_level : compute the periodogram level for a particular fap References ---------- .. [1] Baluev, R.V. MNRAS 385, 1279 (2008) rUnrecognized method: )rHrVMETHODSr?)rYrZr[r\r rBr| method_kwdss r false_alarm_probabilityrsV!SVV]333 w  999::: V_F#K 6!T1a] B Bk B BBrc|dkrt|t||S|tvrtd|t|}|pi}|||||||fi|S)a2Compute the approximate periodogram level given a false alarm probability. This gives an estimate of the periodogram level corresponding to a specified false alarm probability for the largest peak, assuming a null hypothesis of non-varying data with Gaussian noise. The true level cannot be computed analytically, so each method available here is an approximation to the true value. Parameters ---------- p : array-like The false alarm probability (0 < p < 1). fmax : float The maximum frequency of the periodogram. t, y, dy : arrays The data times, values, and errors. normalization : {'standard', 'model', 'log', 'psd'}, optional The periodogram normalization. method : {'baluev', 'davies', 'naive', 'bootstrap'}, optional The approximation method to use. method_kwds : dict, optional Additional method-specific keywords. Returns ------- z : np.ndarray The periodogram level. Notes ----- For normalization='psd', the distribution can only be computed for periodograms constructed with errors specified. See Also -------- false_alarm_probability : compute the fap for a given periodogram level References ---------- .. [1] Baluev, R.V. MNRAS 385, 1279 (2008) rr)rQrV INV_METHODSr?)rwrZr[r\r rBr|rs r false_alarm_levelrsXaQ777 { " "999:::  F#K 6!T1a] B Bk B BBr)rr2)r6rr2)r6)r)r6rN)r6rN)rN)__doc__ functoolsrnumpyrastropyrrrrrr r1rFrHrQrSrbrlrnrqrrrrrrrrrrr$rr rsvNNNEEEJJJ.O.O.O.Ob/O/O/O/Od2S2S2S2Sj K K K KFDDDD< 3 3 3 3 3 3 3 3     2 2 2 2    *QU4444SWXXXX    OS2C2C2C2Cl "  DH3C3C3C3C3C3Cr