IR-e0ddlmZddlZdZd dZd d ZdS) ) factorialNcPdt|dz zS)z Find the bit (i.e. power of 2) immediately greater than or equal to N Note: this works for numbers up to 2 ** 64. Roughly equivalent to int(2 ** np.ceil(np.log2(N))). )int bit_length)Ns alib/python3.11/site-packages/astropy/timeseries/periodograms/lombscargle/implementations/utils.pybitceilr s% AE %%'' ''c ~ttjtj||\}}|*t tj|d|zzdz}tj||j}|dzdk}tj ||| t||||||}}tj ||dzz td||z }|tj ||z tj |ddtjfz dz}t|dz }t!|D]H} | dkr || | |z z z}||dz | z z} tj || |||| z zz I|S)a Extirpolate the values (x, y) onto an integer grid range(N), using lagrange polynomial weights on the M nearest points. Parameters ---------- x : array-like array of abscissas y : array-like array of ordinates N : int number of integer bins to use. For best performance, N should be larger than the maximum of x M : int number of adjoining points on which to extirpolate. Returns ------- yN : ndarray N extirpolated values associated with range(N) Examples -------- >>> rng = np.random.default_rng(0) >>> x = 100 * rng.random(20) >>> y = np.sin(x) >>> y_hat = extirpolate(x, y) >>> x_hat = np.arange(len(y_hat)) >>> f = lambda x: np.sin(x / 10) >>> np.allclose(np.sum(y * f(x)), np.sum(y_hat * f(x_hat))) True Notes ----- This code is based on the C implementation of spread() presented in Numerical Recipes in C, Second Edition (Press et al. 1989; p.583). Ng?r)dtyper)mapnpravelbroadcast_arraysrmaxzerosraddatastypeclipprodarangenewaxisrrange) xyrMresultintegersilo numerator denominatorjinds r extirpolater(sL rx,Q22 3 3DAqy q C!G#a' ( (Xaqw ' ' 'F1uzHFIIfak((--q{;;; hY<H9qA '1qAv:%%c**Aq1u 5 5CBGAGbill111bj=&AA1EEEIAE""K 1XXFF q55 1A; &KQUQY  &#yK1s7,CDEEEE Mr rTc `||z}||z}|dkrtdttjtj||\}}|r#t |}|dkrtdt ||z} |} |dkr-|tjdtj z|z|| z zz}|| z | z|z| z} t| || |} tj | d|} | dkrD||tj |zz}| tjdtj z| z|zz} | | jz}| | jz}n||tj |zz}tj|tjdtj z|z|ddtjfz}tj|tjdtj z|z|ddtjfz}||fS)aCompute (approximate) trigonometric sums for a number of frequencies. This routine computes weighted sine and cosine sums:: S_j = sum_i { h_i * sin(2 pi * f_j * t_i) } C_j = sum_i { h_i * cos(2 pi * f_j * t_i) } Where f_j = freq_factor * (f0 + j * df) for the values j in 1 ... N. The sums can be computed either by a brute force O[N^2] method, or by an FFT-based O[Nlog(N)] method. Parameters ---------- t : array-like array of input times h : array-like array weights for the sum df : float frequency spacing N : int number of frequency bins to return f0 : float, optional The low frequency to use freq_factor : float, optional Factor which multiplies the frequency use_fft : bool if True, use the approximate FFT algorithm to compute the result. This uses the FFT with Press & Rybicki's Lagrangian extirpolation. oversampling : int (default = 5) oversampling freq_factor for the approximation; roughly the number of time samples across the highest-frequency sinusoid. This parameter contains the trade-off between accuracy and speed. Not referenced if use_fft is False. Mfft : int The number of adjacent points to use in the FFT approximation. Not referenced if use_fft is False. Returns ------- S, C : ndarray summation arrays for frequencies f = df * np.arange(1, N + 1) rzdf must be positivezMfft must be positivey@Nr) ValueErrorrrrrrr minexppir(fftifftrrealimagdotcosrsin)thdfrf0 freq_factor oversamplinguse_fftMfftNfftt0tnormgridfftgridfCSs r trig_sumrFRsV+B+B Qww./// rx,Q22 3 3DAq@4yy 199455 5q<'(( UUWW 66BF2:?a"f5666Ab&D2%-5!T400&++d##BQB' 77R")A,,&&A rvb25j2o122 2G 7<  7<  bill" " F1bfQY]Qqqq"*}-==>> ? ? F1bfQY]Qqqq"*}-==>> ? ? a4Kr )Nr )rrr)Tr )mathrnumpyrr r(rFr r rJso(((@@@@FMMMMMMr