ó î&]\c@`sàddlmZmZmZddlZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZddlmZmZmZddlmZdddd d gZd d „Zd „Zd„Zd„ZdS(i(tdivisiontprint_functiontabsolute_importN( tarangetarraytasarrayt atleast_1dtintctintegertisscalart issubdtypettaketuniquetwhere(tfftshiftt ifftshifttfftfreq(t bisect_leftRRRtrfftfreqt next_fast_lengð?cC`sWtj|ƒ}|dkr.td|ƒ‚ntd|ddtƒdt||ƒS(s›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. ]) is5n = %s is not valid. n must be a nonnegative integer.itdtypei(toperatortindext ValueErrorRtinttfloat(tntd((s3lib/python2.7/site-packages/scipy/fftpack/helper.pyR s "  c©C`sDd±}t|ƒ}|dªkr"|S||d«@s4|S||d¬krU|t||ƒStd­ƒ}d«}xÁ||kr*|}xy||kr÷| | }d®|d«jƒ}||}||krÅ|S||krÚ|}n|d¯9}||kr|SqW||kr |}n|d°9}||krj|SqjW||kr@|}n|S(²sà 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) ii i i iiiiiiiii i$i(i-i0i2i6i<i@iHiKiPiQiZi`idilixi}i€i‡ii–i i¢i´iÀiÈiØiáiðióiúiii i,i@iDihiwi€ii•i°iÂiàiæiôiii@iXiqi€iˆi£iÐiÙiîii i*i`i„iÀiÌièii8iei€i°i¿iâiiiFi i²iÜii@iTiÀiiSi€i˜iÐiéiipi‹iÊi i` i~ iÄ i i iŒ i@ id i¸ i i5 i€ i¨ i/ i€ ii=i¦ii0i iÒiiàii”iiÀiüiˆii@iiùi€iÈipi»iijiiPi¡i^ii iziLii`i@i¤i iÀ!i,"i(#i$iŸ$i€%iø%i'iiiÿÿÿÿtinfiii(©ii i i iiiiiiiii i$i(i-i0i2i6i<i@iHiKiPiQiZi`idilixi}i€i‡ii–i i¢i´iÀiÈiØiáiðióiúiii 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'(RRRt bit_length(ttargetthamstmatchtp5tp35tquotienttp2tN((s3lib/python2.7/site-packages/scipy/fftpack/helper.pyR6sX-                cC`s—t|ƒ}|d k}|d k}|rBt|jdtƒ}n t|ƒ}|jdkro|jtƒ}n|jdkstdƒ‚nt |j t ƒs®tdƒ‚nt |dk||j|ƒ}|jdkr|j ƒ|jks|jƒdkrtdƒ‚n|jdkrHt|ƒj|jkrHtdƒ‚n|s]t|ƒ}nQt|ƒr~tgdtƒ}n0|rœt|jdtƒ}nt|j|ƒ}|jdkrÏ|jtƒ}n|jdkrítdƒ‚nt |j t ƒstd ƒ‚n|j|jkr/td ƒ‚nt |d kt|jƒ||ƒ}|jdkr|dkjƒrtd j|ƒƒ‚n||fS(sHandle 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. Riis2when given, axes values must be a scalar or vectors(when given, axes values must be integerss$axes exceeds dimensionality of inputsall axes must be uniques3when given, shape values must be a scalar or vectors)when given, shape values must be integerssBwhen given, axes and shape arguments have to be of the same lengthiÿÿÿÿs-invalid number of data points ({0}) specifiedN(RtNoneRtndimRRtsizetastypeRR RRR tmaxtminR tshapeR RR tanytformat(txR,taxestnoshapetnoaxes((s3lib/python2.7/site-packages/scipy/fftpack/helper.pyt_init_nd_shape_and_axessJ    6' %!cC`sQ|dk}t|||ƒ\}}|sG||jƒ}|jƒn||fS(sHandle 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(R&R3targsorttsort(R/R,R0R2((s3lib/python2.7/site-packages/scipy/fftpack/helper.pyt_init_nd_shape_and_axes_sortedðs   (t __future__RRRRtnumpyRRRRRRR R R R R tnumpy.fft.helperRRRtbisectRt__all__RRR3R6(((s3lib/python2.7/site-packages/scipy/fftpack/helper.pyts L * g S