B î&]\i#ã@s¤ddlmZmZmZddlZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZddlmZmZmZddlmZdddd d gZdd d „Zd d „Zdd„Zdd„ZdS)é)ÚdivisionÚprint_functionÚabsolute_importN) ÚarangeÚarrayÚasarrayÚ atleast_1dÚintcÚintegerÚisscalarÚ issubdtypeÚtakeÚuniqueÚwhere)ÚfftshiftÚ ifftshiftÚfftfreq)Ú bisect_leftrrrÚrfftfreqÚ next_fast_lençð?cCs@t |¡}|dkrtd|ƒ‚td|dtddt||ƒS)a›DFT sample frequencies (for usage with rfft, irfft). The returned float array contains the frequency bins in cycles/unit (with zero at the start) given a window length `n` and a sample spacing `d`:: f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n) if n is even f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n) if n is odd Parameters ---------- n : int Window length. d : scalar, optional Sample spacing. Default is 1. Returns ------- out : ndarray The array of length `n`, containing the sample frequencies. Examples -------- >>> from scipy import fftpack >>> sig = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) >>> sig_fft = fftpack.rfft(sig) >>> n = sig_fft.size >>> timestep = 0.1 >>> freq = fftpack.rfftfreq(n, d=timestep) >>> freq array([ 0. , 1.25, 1.25, 2.5 , 2.5 , 3.75, 3.75, 5. ]) rz5n = %s is not valid. n must be a nonnegative integer.é)Údtypeé)ÚoperatorÚindexÚ ValueErrorrÚintÚfloat)ÚnÚd©r!ú3lib/python3.7/site-packages/scipy/fftpack/helper.pyr s " cCsîd}t|ƒ}|dkr|S||d@s(|S||dkrB|t||ƒStdƒ}d}xŽ||krÜ|}x\||kr¸| | }d|d ¡}||}||kr–|S||kr¢|}|d9}||kr^|Sq^W||krÆ|}|d9}||krP|SqPW||krê|}|S) aà Find the next fast size of input data to `fft`, for zero-padding, etc. SciPy's FFTPACK has efficient functions for radix {2, 3, 4, 5}, so this returns the next composite of the prime factors 2, 3, and 5 which is greater than or equal to `target`. (These are also known as 5-smooth numbers, regular numbers, or Hamming numbers.) Parameters ---------- target : int Length to start searching from. Must be a positive integer. Returns ------- out : int The first 5-smooth number greater than or equal to `target`. Notes ----- .. versionadded:: 0.18.0 Examples -------- On a particular machine, an FFT of prime length takes 133 ms: >>> from scipy import fftpack >>> min_len = 10007 # prime length is worst case for speed >>> a = np.random.randn(min_len) >>> b = fftpack.fft(a) Zero-padding to the next 5-smooth length reduces computation time to 211 us, a speedup of 630 times: >>> fftpack.helper.next_fast_len(min_len) 10125 >>> b = fftpack.fft(a, 10125) Rounding up to the next power of 2 is not optimal, taking 367 us to compute, 1.7 times as long as the 5-smooth size: >>> b = fftpack.fft(a, 16384) )©éé é é ééééééééé é$é(é-é0é2é6é<é@éHéKéPéQéZé`édéléxé}é€é‡éé–é é¢é´éÀéÈéØéáéðéóéúéii i,i@iDihiwi€ii•i°iÂiàiæiôiii@iXiqi€iˆi£iÐiÙiîii i*i`i„iÀiÌièii8iei€i°i¿iâiiiFi i²iÜii@iTiÀiiSi€i˜iÐiéiipi‹iÊi i` i~ iÄ i i iŒ i@ id i¸ i i5 i€ i¨ i/ i€ ii=i¦ii0i iÒiiàii”iiÀiüiˆii@iiùi€iÈipi»iijiiPi¡i^ii iziLii`i@i¤i iÀ!i,"i(#i$iŸ$i€%iø%i'éréÿÿÿÿÚinfréé)rrrÚ bit_length)ÚtargetZhamsÚmatchZp5Zp35ZquotientZp2ÚNr!r!r"r6s>-     cCs¸t|ƒ}|dk}|dk}|r,t|jtd}nt|ƒ}|jdkrH| t¡}|jdksZtdƒ‚t|j t ƒsntdƒ‚t |dk||j|ƒ}|jdkr°|  ¡|jks¨|  ¡dkr°tdƒ‚|jdkrÒt|ƒj|jkrÒtdƒ‚|sàt|ƒ}n8t|ƒrötgtd}n"|r t|jtd}n t|j|ƒ}|jdkr.| t¡}|jdkrBtd ƒ‚t|j t ƒsXtd ƒ‚|j|jkrntd ƒ‚t |d kt|jƒ||ƒ}|jdkr°|dk ¡r°td  |¡ƒ‚||fS)aHandle shape and axes arguments for n-dimensional transforms. Returns the shape and axes in a standard form, taking into account negative values and checking for various potential errors. Parameters ---------- x : array_like The input array. shape : int or array_like of ints or None The shape of the result. If both `shape` and `axes` (see below) are None, `shape` is ``x.shape``; if `shape` is None but `axes` is not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``. If `shape` is -1, the size of the corresponding dimension of `x` is used. axes : int or array_like of ints or None Axes along which the calculation is computed. The default is over all axes. Negative indices are automatically converted to their positive counterpart. Returns ------- shape : array The shape of the result. It is a 1D integer array. axes : array The shape of the result. It is a 1D integer array. N)rrrz2when given, axes values must be a scalar or vectorz(when given, axes values must be integersz$axes exceeds dimensionality of inputzall axes must be uniquez3when given, shape values must be a scalar or vectorz)when given, shape values must be integerszBwhen given, axes and shape arguments have to be of the same lengthrRz-invalid number of data points ({0}) specified)rrÚndimr rÚsizeZastyperr rr rÚmaxÚminrÚshaper rr ÚanyÚformat)Úxr^ÚaxesZnoshapeÚnoaxesr!r!r"Ú_init_nd_shape_and_axessJ    $      rdcCs8|dk}t|||ƒ\}}|s0|| ¡}| ¡||fS)aHandle and sort shape and axes arguments for n-dimensional transforms. This is identical to `_init_nd_shape_and_axes`, except the axes are returned in sorted order and the shape is reordered to match. Parameters ---------- x : array_like The input array. shape : int or array_like of ints or None The shape of the result. If both `shape` and `axes` (see below) are None, `shape` is ``x.shape``; if `shape` is None but `axes` is not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``. If `shape` is -1, the size of the corresponding dimension of `x` is used. axes : int or array_like of ints or None Axes along which the calculation is computed. The default is over all axes. Negative indices are automatically converted to their positive counterpart. Returns ------- shape : array The shape of the result. It is a 1D integer array. axes : array The shape of the result. It is a 1D integer array. N)rdZargsortÚsort)rar^rbrcr!r!r"Ú_init_nd_shape_and_axes_sortedðs  rf)r)Z __future__rrrrZnumpyrrrrr r r r r rrZnumpy.fft.helperrrrZbisectrÚ__all__rrrdrfr!r!r!r"Ús4  *gS