ÿØÿàJFIFÿþ ÿÛC       ÿÛC ÿÀÿÄÿÄ"#QrÿÄÿÄ&1!A"2qQaáÿÚ ?Øy,æ/3JæݹÈ߲؋5êXw²±ÉyˆR”¾I0ó2—PI¾IÌÚiMö¯–þrìN&"KgX:Šíµ•nTJnLK„…@!‰-ý ùúmë;ºgµŒ&ó±hw’¯Õ@”Ü— 9ñ-ë.²1<yà‚¹ïQÐU„ہ?.’¦èûbß±©Ö«Âw*VŒ) `$‰bØԟ’ëXÖ-ËTÜíGÚ3ð«g Ÿ§¯—Jx„–’U/ÂÅv_s(Hÿ@TñJÑãõçn­‚!ÈgfbÓc­:él[ðQe 9ÀPLbÃãCµm[5¿ç'ªjglå‡Ûí_§Úõl-;"PkÞÞÁQâ¼_Ñ^¢SŸx?"¸¦ùY騐ÒOÈ q’`~~ÚtËU¹CڒêV  I1Áß_ÿÙ ]c+@`s ddlmZmZmZddlZddlZddlZddlZddlZddl Z ddl j j ZddlmZmZmZmZddl mZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(ddl)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5ddl6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=ddl>m?Z?m@Z@ddlAmBZBd d lCmDZDdd lEmFZFmGZGmHZHmIZImJZJmKZLmMZNdd l)mOZPdd lQmRZRddlSmTZTejUddkrheVZWddlXZYn ddlYZYddddddddddddddddd d!d"d#d$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8d9d:g+ZZd dd fd;Z[d<Z\d=Z]d>Z^d?Z_d@Z`dAZadBZbdCZcdDZdieddE6ebdF6ecdG6e`dH6eadI6e^dJ6e_dK6ZedLefegefefdMZhdLefegefdNZiefefegdOZjefefdPZkdQZlddRZmdSdTZndUZod dVdWZpefefefdXZKddYZqe*dVdZZrd[Zsd\d]ZteDd^Zud_Zvd`ZwefexdaZydbZzdcj{ezZ|ddj{e|Z}dej{e}Z~dfj{e~ZdgZdhZdiZdjZdkZd efdlYZefexegefefefdmZefexe je jdnZdoZdpZdqZdrZdsdtdudvdwdxdydzd{d|d}d~ddddddddddddddddddgZdddddddddddddddddddddddddgZdZdZdZdZdZdZdZdZefefegegdZefefegdZefefegdegdZefefegdegdZefddVdZdZdZefdZefdZefdZdS(i(tdivisiontabsolute_importtprint_functionN(tlinspacet atleast_1dt atleast_2dt transpose(tonestzerostaranget concatenatetarraytasarrayt asanyarraytemptyt empty_liketndarraytaroundtfloortceilttaketdottwheretintptintegertisscalartabsolutet AxisError( tpitmultiplytaddtarctan2t frompyfunctcost less_equaltsqrttsintmodtexptlog10(traveltnonzerotsortt partitiontmeantanytsum(t typecodestnumber(tdiagi(t deprecate(t_insertt add_docstringtdigitizetbincounttnormalize_axis_indextinterptinterp_complex(t_add_newdoc_ufunc(tlong(t basestringitselectt piecewiset trim_zerostcopytiterablet percentiletdifftgradienttangletunwrapt sort_complextdisptfliptrot90textracttplacet vectorizetasarray_chkfinitetaveraget histogramt histogramddR6R5tcovtcorrcoeftmsorttmediantsincthammingthanningtbartletttblackmantkaiserttrapzti0t add_newdocR4tmeshgridtdeletetinserttappendR8tadd_newdoc_ufunccC`st|}t|dkr-tdnt|}|d|dksnt|d|d|jkr}tdn|d|jks|d|j ks|d|jks|d|j krtdj||jn|d;}|dkr|S|dkr.tt||d|dStd|j}||d||d||d<||d<|dkrt t||d|Stt |||dSdS( s Rotate an array by 90 degrees in the plane specified by axes. Rotation direction is from the first towards the second axis. .. versionadded:: 1.12.0 Parameters ---------- m : array_like Array of two or more dimensions. k : integer Number of times the array is rotated by 90 degrees. axes: (2,) array_like The array is rotated in the plane defined by the axes. Axes must be different. Returns ------- y : ndarray A rotated view of `m`. See Also -------- flip : Reverse the order of elements in an array along the given axis. fliplr : Flip an array horizontally. flipud : Flip an array vertically. Notes ----- rot90(m, k=1, axes=(1,0)) is the reverse of rot90(m, k=1, axes=(0,1)) rot90(m, k=1, axes=(1,0)) is equivalent to rot90(m, k=-1, axes=(0,1)) Examples -------- >>> m = np.array([[1,2],[3,4]], int) >>> m array([[1, 2], [3, 4]]) >>> np.rot90(m) array([[2, 4], [1, 3]]) >>> np.rot90(m, 2) array([[4, 3], [2, 1]]) >>> m = np.arange(8).reshape((2,2,2)) >>> np.rot90(m, 1, (1,2)) array([[[1, 3], [0, 2]], [[5, 7], [4, 6]]]) islen(axes) must be 2.iisAxes must be different.s*Axes={} out of range for array of ndim={}.iN( ttupletlent ValueErrorR RtndimtformatRIR R(tmtktaxest axes_list((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRJ6s*7  5''     " cC`st|dst|}ntdg|j}ytddd||>> A = np.arange(8).reshape((2,2,2)) >>> A array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> flip(A, 0) array([[[4, 5], [6, 7]], [[0, 1], [2, 3]]]) >>> flip(A, 1) array([[[2, 3], [0, 1]], [[6, 7], [4, 5]]]) >>> A = np.random.randn(3,4,5) >>> np.all(flip(A,2) == A[:,:,::-1,...]) True Rgis5axis=%i is invalid for the %i-dimensional input arrayN(thasattrR tslicetNoneRgt IndexErrorRfRd(Ritaxistindexer((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRIs= cC`s'yt|Wntk r"tSXtS(sw Check whether or not an object can be iterated over. Parameters ---------- y : object Input object. Returns ------- b : bool Return ``True`` if the object has an iterator method or is a sequence and ``False`` otherwise. Examples -------- >>> np.iterable([1, 2, 3]) True >>> np.iterable(2) False (titert TypeErrortFalsetTrue(ty((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRAs  cC`s|jtj|jS(s~ Square root histogram bin estimator. Bin width is inversely proportional to the data size. Used by many programs for its simplicity. Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. (tptptnpR#tsize(tx((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_hist_bin_sqrtscC`s|jtj|jdS(s Sturges histogram bin estimator. A very simplistic estimator based on the assumption of normality of the data. This estimator has poor performance for non-normal data, which becomes especially obvious for large data sets. The estimate depends only on size of the data. Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. g?(RxRytlog2Rz(R{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_hist_bin_sturgesscC`s|jd|jdS(sI Rice histogram bin estimator. Another simple estimator with no normality assumption. It has better performance for large data than Sturges, but tends to overestimate the number of bins. The number of bins is proportional to the cube root of data size (asymptotically optimal). The estimate depends only on size of the data. Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. g@g?igUUUUUU?(RxRz(R{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_hist_bin_ricescC`s'dtjd|jdtj|S(s Scott histogram bin estimator. The binwidth is proportional to the standard deviation of the data and inversely proportional to the cube root of data size (asymptotically optimal). Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. g8@g?g?g@gUUUUUU?(RyRRztstd(R{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_hist_bin_scott5scC`s|jdkrtjd|jd|jd|jd}tj|}|dkr|tj|}tj|||tj|d|tj|}|jdtj|jtjdtj ||SndS(s Doane's histogram bin estimator. Improved version of Sturges' formula which works better for non-normal data. See stats.stackexchange.com/questions/55134/doanes-formula-for-histogram-binning Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. ig@g?ig( RzRyR#RR,t true_dividetpowerRxR}R(R{tsg1tsigmattemptg1((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_hist_bin_doaneJs0 #cC`s4tjtj|ddg}d||jdS(sB The Freedman-Diaconis histogram bin estimator. The Freedman-Diaconis rule uses interquartile range (IQR) to estimate binwidth. It is considered a variation of the Scott rule with more robustness as the IQR is less affected by outliers than the standard deviation. However, the IQR depends on fewer points than the standard deviation, so it is less accurate, especially for long tailed distributions. If the IQR is 0, this function returns 1 for the number of bins. Binwidth is inversely proportional to the cube root of data size (asymptotically optimal). Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. iKig@gg@gUUUUUUտ(RytsubtractRBRz(R{tiqr((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt _hist_bin_fdls!cC`stt|t|S(s Histogram bin estimator that uses the minimum width of the Freedman-Diaconis and Sturges estimators. The FD estimator is usually the most robust method, but its width estimate tends to be too large for small `x`. The Sturges estimator is quite good for small (<1000) datasets and is the default in the R language. This method gives good off the shelf behaviour. Parameters ---------- x : array_like Input data that is to be histogrammed, trimmed to range. May not be empty. Returns ------- h : An estimate of the optimal bin width for the given data. See Also -------- _hist_bin_fd, _hist_bin_sturges (tminRR~(R{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_hist_bin_autostautotdoanetfdtricetscottR#tsturgesi c C`skt|}|dk r]t|}tj|j|jkrNtdn|j}n|j}|dkr|jdkrd\}}q|jd|j d}}n#g|D]}|d^q\}}||krtdntj tj ||gs"tdn||krE|d8}|d7}nt |t r:|tkrxtdj|n|dk rtd n|} |dk r||k} | ||kM} tjj| s|| } qn| jdkrd }q:t|| } | r1ttj||| }q:d }n|dkr[tjtj} n |j} d } t|stj|r|d krtd n|dk rtj|jtjptj|jtj rt|||d d t}qnt|s#tj|| }|||}t|||d d t}xtdt || D]}|||| !}|dkrd}n|||| !}||k} | ||kM} tjj| s|| }|dk r|| }qn|j!t"}||}||9}|j!tj}|||kcd 8<|||k}||cd 8<|||d k||d k@}||cd 7<| j#dkr|j$tj%|d|j$d|7_$|j&tj%|d|j&d|7_&q`|tj%|d|d|j!| 7}q`W|}nt|}tj|d |d kr[tdntj|j| }|dkrxJtdt || D]T}t'|||| !}|tj(|j)|d d|j)|ddf7}qWnt*dd| }xtdt || D]}|||| !}|||| !}tj+|}||}||}tj,|g|j-f}tj(|j)|d d|j)|ddf}|||7}qWtj.|}|dk r'|rt*tj.|t"}|||j/|fS||fSn@|r]t*tj.|t"}|||j/|fS||fSdS(sQ" Compute the histogram of a set of data. Parameters ---------- a : array_like Input data. The histogram is computed over the flattened array. bins : int or sequence of scalars or str, optional If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths. .. versionadded:: 1.11.0 If `bins` is a string from the list below, `histogram` will use the method chosen to calculate the optimal bin width and consequently the number of bins (see `Notes` for more detail on the estimators) from the data that falls within the requested range. While the bin width will be optimal for the actual data in the range, the number of bins will be computed to fill the entire range, including the empty portions. For visualisation, using the 'auto' option is suggested. Weighted data is not supported for automated bin size selection. 'auto' Maximum of the 'sturges' and 'fd' estimators. Provides good all around performance. 'fd' (Freedman Diaconis Estimator) Robust (resilient to outliers) estimator that takes into account data variability and data size. 'doane' An improved version of Sturges' estimator that works better with non-normal datasets. 'scott' Less robust estimator that that takes into account data variability and data size. 'rice' Estimator does not take variability into account, only data size. Commonly overestimates number of bins required. 'sturges' R's default method, only accounts for data size. Only optimal for gaussian data and underestimates number of bins for large non-gaussian datasets. 'sqrt' Square root (of data size) estimator, used by Excel and other programs for its speed and simplicity. range : (float, float), optional The lower and upper range of the bins. If not provided, range is simply ``(a.min(), a.max())``. Values outside the range are ignored. The first element of the range must be less than or equal to the second. `range` affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within `range`, the bin count will fill the entire range including portions containing no data. normed : bool, optional This keyword is deprecated in NumPy 1.6.0 due to confusing/buggy behavior. It will be removed in NumPy 2.0.0. Use the ``density`` keyword instead. If ``False``, the result will contain the number of samples in each bin. If ``True``, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that this latter behavior is known to be buggy with unequal bin widths; use ``density`` instead. weights : array_like, optional An array of weights, of the same shape as `a`. Each value in `a` only contributes its associated weight towards the bin count (instead of 1). If `density` is True, the weights are normalized, so that the integral of the density over the range remains 1. density : bool, optional If ``False``, the result will contain the number of samples in each bin. If ``True``, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability *mass* function. Overrides the ``normed`` keyword if given. Returns ------- hist : array The values of the histogram. See `density` and `weights` for a description of the possible semantics. bin_edges : array of dtype float Return the bin edges ``(length(hist)+1)``. See Also -------- histogramdd, bincount, searchsorted, digitize Notes ----- All but the last (righthand-most) bin is half-open. In other words, if `bins` is:: [1, 2, 3, 4] then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which *includes* 4. .. versionadded:: 1.11.0 The methods to estimate the optimal number of bins are well founded in literature, and are inspired by the choices R provides for histogram visualisation. Note that having the number of bins proportional to :math:`n^{1/3}` is asymptotically optimal, which is why it appears in most estimators. These are simply plug-in methods that give good starting points for number of bins. In the equations below, :math:`h` is the binwidth and :math:`n_h` is the number of bins. All estimators that compute bin counts are recast to bin width using the `ptp` of the data. The final bin count is obtained from ``np.round(np.ceil(range / h))`. 'Auto' (maximum of the 'Sturges' and 'FD' estimators) A compromise to get a good value. For small datasets the Sturges value will usually be chosen, while larger datasets will usually default to FD. Avoids the overly conservative behaviour of FD and Sturges for small and large datasets respectively. Switchover point is usually :math:`a.size \approx 1000`. 'FD' (Freedman Diaconis Estimator) .. math:: h = 2 \frac{IQR}{n^{1/3}} The binwidth is proportional to the interquartile range (IQR) and inversely proportional to cube root of a.size. Can be too conservative for small datasets, but is quite good for large datasets. The IQR is very robust to outliers. 'Scott' .. math:: h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}} The binwidth is proportional to the standard deviation of the data and inversely proportional to cube root of ``x.size``. Can be too conservative for small datasets, but is quite good for large datasets. The standard deviation is not very robust to outliers. Values are very similar to the Freedman-Diaconis estimator in the absence of outliers. 'Rice' .. math:: n_h = 2n^{1/3} The number of bins is only proportional to cube root of ``a.size``. It tends to overestimate the number of bins and it does not take into account data variability. 'Sturges' .. math:: n_h = \log _{2}n+1 The number of bins is the base 2 log of ``a.size``. This estimator assumes normality of data and is too conservative for larger, non-normal datasets. This is the default method in R's ``hist`` method. 'Doane' .. math:: n_h = 1 + \log_{2}(n) + \log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}}) g_1 = mean[(\frac{x - \mu}{\sigma})^3] \sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}} An improved version of Sturges' formula that produces better estimates for non-normal datasets. This estimator attempts to account for the skew of the data. 'Sqrt' .. math:: n_h = \sqrt n The simplest and fastest estimator. Only takes into account the data size. Examples -------- >>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3]) (array([0, 2, 1]), array([0, 1, 2, 3])) >>> np.histogram(np.arange(4), bins=np.arange(5), density=True) (array([ 0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4])) >>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3]) (array([1, 4, 1]), array([0, 1, 2, 3])) >>> a = np.arange(5) >>> hist, bin_edges = np.histogram(a, density=True) >>> hist array([ 0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5]) >>> hist.sum() 2.4999999999999996 >>> np.sum(hist * np.diff(bin_edges)) 1.0 .. versionadded:: 1.11.0 Automated Bin Selection Methods example, using 2 peak random data with 2000 points: >>> import matplotlib.pyplot as plt >>> rng = np.random.RandomState(10) # deterministic random data >>> a = np.hstack((rng.normal(size=1000), ... rng.normal(loc=5, scale=2, size=1000))) >>> plt.hist(a, bins='auto') # arguments are passed to np.histogram >>> plt.title("Histogram with 'auto' bins") >>> plt.show() s(weights should have the same shape as a.igg?s/max must be larger than min in range parameter.srange parameter must be finite.g?s"{0} not a valid estimator for binssMAutomated estimation of the number of bins is not supported for weighted dataiis$`bins` should be a positive integer.tendpointtctweightst minlengthis!bins must increase monotonically.tlefttrighttdtypeN(gg?(0R RoRyR-tshapeRfR(RzRtmaxtalltisfinitet isinstanceR<t_hist_bin_selectorsRhRtt logical_andtreducetintRRRRARtcan_casttdoubletcomplexRRvRR RetastypetfloattkindtrealR6timagR*tr_t searchsortedR targsortR tcumsumRCR.(tatbinstrangetnormedRtdensitytmntmxtmitbtkeeptwidthtntypetBLOCKtntnormt bin_edgestittmp_attmp_wt tmp_a_datatindicest decrementt incrementtsatzerot sorting_indextswtcwt bin_indextdb((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRPs      $#                 $"             "    cC`sy|j\}}Wn5ttfk rJt|j}|j\}}nXt|t}|d g}|d g} |d k rt|}ny+t |} | |krtdnWnt k r||g}nX|d krM|dkrt |} t |} qt t|jdt} t t|jdt} nntjtj|sttdnt |} t |} x,t|D]} || \| | <| | } t |t}|| d|| <|| | j"|}qW||}n|j|dkjr~t+d n||fS(sQ Compute the multidimensional histogram of some data. Parameters ---------- sample : array_like The data to be histogrammed. It must be an (N,D) array or data that can be converted to such. The rows of the resulting array are the coordinates of points in a D dimensional polytope. bins : sequence or int, optional The bin specification: * A sequence of arrays describing the bin edges along each dimension. * The number of bins for each dimension (nx, ny, ... =bins) * The number of bins for all dimensions (nx=ny=...=bins). range : sequence, optional A sequence of lower and upper bin edges to be used if the edges are not given explicitly in `bins`. Defaults to the minimum and maximum values along each dimension. normed : bool, optional If False, returns the number of samples in each bin. If True, returns the bin density ``bin_count / sample_count / bin_volume``. weights : (N,) array_like, optional An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`. Weights are normalized to 1 if normed is True. If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray The multidimensional histogram of sample x. See normed and weights for the different possible semantics. edges : list A list of D arrays describing the bin edges for each dimension. See Also -------- histogram: 1-D histogram histogram2d: 2-D histogram Examples -------- >>> r = np.random.randn(100,3) >>> H, edges = np.histogramdd(r, bins = (5, 8, 4)) >>> H.shape, edges[0].size, edges[1].size, edges[2].size ((5, 8, 4), 6, 9, 5) sFThe dimension of bins must be equal to the dimension of the sample x.isrange parameter must be finite.g?is;Element at index %s in `bins` should be a positive integer.iRsOFound bin edge of size <= 0. Did you specify `bins` withnon-monotonic sequence?NiisInternal Shape Error(,RtAttributeErrorRfRtTRRRoR ReRtRRRR RRRRyRRR t issubdtypeRtinexactRRRCR-R5tisinfR'RRtreshapeRtprodR6R*RztswapaxesRnR.t RuntimeError(tsampleRRRRtNtDtnbintedgestdedgestMtsmintsmaxRtedge_dttNcounttmindifftdecimaltnot_smaller_than_edgeton_edgethisttnitxyt flatcountRtjtcoretsR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRQ=s4         !     /"  +$) , !    cC`stj|}|d krI|j|}|jj|j|j}nttj|}t|jjtjtj frtj |j|jd}ntj |j|j}|j |j kr\|d krt dn|j dkrt dn|j d|j |kr#tdntj||j dd |j }|jd|}n|jd|d |}tj|d krtd ntj||d |j||}|r|j |j krtj||j j}n||fS|Sd S(s Compute the weighted average along the specified axis. Parameters ---------- a : array_like Array containing data to be averaged. If `a` is not an array, a conversion is attempted. axis : None or int or tuple of ints, optional Axis or axes along which to average `a`. The default, axis=None, will average over all of the elements of the input array. If axis is negative it counts from the last to the first axis. .. versionadded:: 1.7.0 If axis is a tuple of ints, averaging is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before. weights : array_like, optional An array of weights associated with the values in `a`. Each value in `a` contributes to the average according to its associated weight. The weights array can either be 1-D (in which case its length must be the size of `a` along the given axis) or of the same shape as `a`. If `weights=None`, then all data in `a` are assumed to have a weight equal to one. returned : bool, optional Default is `False`. If `True`, the tuple (`average`, `sum_of_weights`) is returned, otherwise only the average is returned. If `weights=None`, `sum_of_weights` is equivalent to the number of elements over which the average is taken. Returns ------- average, [sum_of_weights] : array_type or double Return the average along the specified axis. When returned is `True`, return a tuple with the average as the first element and the sum of the weights as the second element. The return type is `Float` if `a` is of integer type, otherwise it is of the same type as `a`. `sum_of_weights` is of the same type as `average`. Raises ------ ZeroDivisionError When all weights along axis are zero. See `numpy.ma.average` for a version robust to this type of error. TypeError When the length of 1D `weights` is not the same as the shape of `a` along axis. See Also -------- mean ma.average : average for masked arrays -- useful if your data contains "missing" values Examples -------- >>> data = range(1,5) >>> data [1, 2, 3, 4] >>> np.average(data) 2.5 >>> np.average(range(1,11), weights=range(10,0,-1)) 4.0 >>> data = np.arange(6).reshape((3,2)) >>> data array([[0, 1], [2, 3], [4, 5]]) >>> np.average(data, axis=1, weights=[1./4, 3./4]) array([ 0.75, 2.75, 4.75]) >>> np.average(data, weights=[1./4, 3./4]) Traceback (most recent call last): ... TypeError: Axis must be specified when shapes of a and weights differ. tf8s;Axis must be specified when shapes of a and weights differ.is81D weights expected when shapes of a and weights differ.is5Length of weights not compatible with specified axis.iRqRgs(Weights sum to zero, can't be normalizedN(i(RyR RoR,RttypeRzt issubclassRtbool_t result_typeRRtRgRft broadcast_toRR.R-tZeroDivisionErrorRR@(RRqRtreturnedtavgtscltwgtt result_dtype((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyROs<Q !    $ % cC`sWt|d|d|}|jjtdkrStj|j rStdn|S(sTConvert the input to an array, checking for NaNs or Infs. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. Success requires no NaNs or Infs. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major (C-style) or column-major (Fortran-style) memory representation. Defaults to 'C'. Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray. If `a` is a subclass of ndarray, a base class ndarray is returned. Raises ------ ValueError Raises ValueError if `a` contains NaN (Not a Number) or Inf (Infinity). See Also -------- asarray : Create and array. asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array. If all elements are finite ``asarray_chkfinite`` is identical to ``asarray``. >>> a = [1, 2] >>> np.asarray_chkfinite(a, dtype=float) array([1., 2.]) Raises ValueError if array_like contains Nans or Infs. >>> a = [1, 2, np.inf] >>> try: ... np.asarray_chkfinite(a) ... except ValueError: ... print('ValueError') ... ValueError RtordertAllFloats#array must not contain infs or NaNs(R RtcharR/RyRRRf(RRR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRNs <, cO`sUt|}t|}t|sKt|dtpGt|dt rt| r|jdkr|jdkrg|D]}|g^q}}q|g}nt|dt }t|}t }|jdkr|d}t }n||dkrt jj|dd} |jdkr7t j|| g}neg|D]}t|dt ^q>}|d} x%td|D]} | || O} qvW|j| |d7}nt|j|j} x{t|D]m} || } t| tjs| | || = 0``. >>> x = np.linspace(-2.5, 2.5, 6) >>> np.piecewise(x, [x < 0, x >= 0], [-1, 1]) array([-1., -1., -1., 1., 1., 1.]) Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for ``x >= 0``. >>> np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x]) array([ 2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) Apply the same function to a scalar value. >>> y = -2 >>> np.piecewise(y, [y < 0, y >= 0], [lambda x: -x, lambda x: x]) array(2) iiRRqN(R ReRRtlistRRzRgR tboolRuRoRvRyt logical_orRtvstackR RRbRRRt collectionstCallabletsqueeze(R{tcondlisttfunclisttargstkwtn2RRtzerodttotlistRjRwtitemtvals((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR>sDW  +    %   !c C`s0t|t|kr'tdnt|dkr`tjdtddtj|d Sg|D]}tj|^qg}|jtj|tj|}tj |}tj |}t }xt t|D]l}||}|j j tjk rtj|j tjr;||jt||>> x = np.arange(10) >>> condlist = [x<3, x>5] >>> choicelist = [x, x**2] >>> np.select(condlist, choicelist) array([ 0, 1, 2, 0, 0, 0, 36, 49, 64, 81]) s7list of cases must be same length as list of conditionsisIselect with an empty condition list is not possibleand will be deprecatedt stacklevelis6invalid entry in choicelist: should be boolean ndarraysselect condlists containing integer ndarrays is deprecated and will be removed in the future. Use `.astype(bool)` to convert to bools.iiNR((ReRftwarningstwarntDeprecationWarningRyR RbRtbroadcast_arraysRuRRRRRRRRRvRgRtfulltziptcopyto( Rt choicelisttdefaulttchoiceRtdeprecated_intsRtcondtmsgt result_shapetresult((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR=FsB&   "  !tKcC`st|d|dtS(s Return an array copy of the given object. Parameters ---------- a : array_like Input data. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :meth:`ndarray.copy` are very similar, but have different default values for their order= arguments.) Returns ------- arr : ndarray Array interpretation of `a`. Notes ----- This is equivalent to: >>> np.array(a, copy=True) #doctest: +SKIP Examples -------- Create an array x, with a reference y and a copy z: >>> x = np.array([1, 2, 3]) >>> y = x >>> z = np.copy(x) Note that, when we modify x, y changes, but not z: >>> x[0] = 10 >>> x[0] == y[0] True >>> x[0] == z[0] False RR@(R Rv(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR@s,cO`sgtj|}|j}|jdd!}|d!krKtt|}ntj||}t |}t |}|dkrdg|}n|dkrtj|ddkr||}n||krt |}xt |D]\}} tj| dkrqn$tj| dkr3t dnt | |j ||kr_t dntj| } | | dkjr| d} n| ||>> f = np.array([1, 2, 4, 7, 11, 16], dtype=np.float) >>> np.gradient(f) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ]) >>> np.gradient(f, 2) array([ 0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ]) Spacing can be also specified with an array that represents the coordinates of the values F along the dimensions. For instance a uniform spacing: >>> x = np.arange(f.size) >>> np.gradient(f, x) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ]) Or a non uniform one: >>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=np.float) >>> np.gradient(f, x) array([ 1. , 3. , 3.5, 6.7, 6.9, 2.5]) For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction: >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float)) [array([[ 2., 2., -1.], [ 2., 2., -1.]]), array([[ 1. , 2.5, 4. ], [ 1. , 1. , 1. ]])] In this example the spacing is also specified: uniform for axis=0 and non uniform for axis=1 >>> dx = 2. >>> y = [1., 1.5, 3.5] >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float), dx, y) [array([[ 1. , 1. , -0.5], [ 1. , 1. , -0.5]]), array([[ 2. , 2. , 2. ], [ 2. , 1.7, 0.5]])] It is possible to specify how boundaries are treated using `edge_order` >>> x = np.array([0, 1, 2, 3, 4]) >>> f = x**2 >>> np.gradient(f, edge_order=1) array([ 1., 2., 4., 6., 7.]) >>> np.gradient(f, edge_order=2) array([-0., 2., 4., 6., 8.]) The `axis` keyword can be used to specify a subset of axes of which the gradient is calculated >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float), axis=0) array([[ 2., 2., -1.], [ 2., 2., -1.]]) Notes ----- Assuming that :math:`f\in C^{3}` (i.e., :math:`f` has at least 3 continuous derivatives) and let be :math:`h_{*}` a non homogeneous stepsize, the spacing the finite difference coefficients are computed by minimising the consistency error :math:`\eta_{i}`: .. math:: \eta_{i} = f_{i}^{\left(1\right)} - \left[ \alpha f\left(x_{i}\right) + \beta f\left(x_{i} + h_{d}\right) + \gamma f\left(x_{i}-h_{s}\right) \right] By substituting :math:`f(x_{i} + h_{d})` and :math:`f(x_{i} - h_{s})` with their Taylor series expansion, this translates into solving the following the linear system: .. math:: \left\{ \begin{array}{r} \alpha+\beta+\gamma=0 \\ -\beta h_{d}+\gamma h_{s}=1 \\ \beta h_{d}^{2}+\gamma h_{s}^{2}=0 \end{array} \right. The resulting approximation of :math:`f_{i}^{(1)}` is the following: .. math:: \hat f_{i}^{(1)} = \frac{ h_{s}^{2}f\left(x_{i} + h_{d}\right) + \left(h_{d}^{2} - h_{s}^{2}\right)f\left(x_{i}\right) - h_{d}^{2}f\left(x_{i}-h_{s}\right)} { h_{s}h_{d}\left(h_{d} + h_{s}\right)} + \mathcal{O}\left(\frac{h_{d}h_{s}^{2} + h_{s}h_{d}^{2}}{h_{d} + h_{s}}\right) It is worth noting that if :math:`h_{s}=h_{d}` (i.e., data are evenly spaced) we find the standard second order approximation: .. math:: \hat f_{i}^{(1)}= \frac{f\left(x_{i+1}\right) - f\left(x_{i-1}\right)}{2h} + \mathcal{O}\left(h^{2}\right) With a similar procedure the forward/backward approximations used for boundaries can be derived. References ---------- .. [1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics (Texts in Applied Mathematics). New York: Springer. .. [2] Durran D. R. (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. New York: Springer. .. [3] Fornberg B. (1988) Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, Mathematics of Computation 51, no. 184 : 699-706. `PDF `_. Rqig?is&distances must be either scalars or 1dsGwhen 1d, distances must match the length of the corresponding dimensionsinvalid number of argumentst edge_orders%"{}" are not valid keyword arguments.s", "is)'edge_order' greater than 2 not supportedtftdtFRRiRtdatetimet timedeltatint64slShape of array too small to calculate a numerical gradient, at least (edge_order + 1) elements are required.Riig@ggig?gg?N(RRR RRiR(RRi(RyR RgtpopRoRdRt_nxtnormalize_axis_tupleReRt enumerateRfRRCRRtRhtjointkeysRnRRtnametreplacetviewRRRRb(RtvarargstkwargsRRktlen_axesRtdxRt distancestdiffxRtoutvalstslice1tslice2tslice3tslice4totypeRwRqtouttuniform_spacingtdx1tdx2RRRRtdx_0tdx_n((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRDs     %              % *           *    *  icC`s|dkr|S|dkr5tdt|nt|}|j}tdg|}tdg|}tdd||>> u8_arr = np.array([1, 0], dtype=np.uint8) >>> np.diff(u8_arr) array([255], dtype=uint8) >>> u8_arr[1,...] - u8_arr[0,...] array(255, np.uint8) If this is not desirable, then the array should be cast to a larger integer type first: >>> i16_arr = u8_arr.astype(np.int16) >>> np.diff(i16_arr) array([-1], dtype=int16) Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.diff(x) array([ 1, 2, 3, -7]) >>> np.diff(x, n=2) array([ 1, 1, -10]) >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]]) >>> np.diff(x) array([[2, 3, 4], [5, 1, 2]]) >>> np.diff(x, axis=0) array([[-1, 2, 0, -2]]) is#order must be non-negative but got iiRqN(RftreprR RgRnRoRdRC(RRRqtndR4R5((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRC8s C       #c C`stj|}tj|r0t}tj}nt}tj}|dkrt|t t t fr||g||||j St|tj r|jdkr||g||||j S||||||Sn|dkrtdnt|}d}d}t}t|t t t fr>t}|g}ntj|dtj}tj|dtj}tj|d|}|jdks|jdkrtdn|jd|jdkrtdn||}||}tj|} || }|| }tj|d|||dd!|f}tj|d||dd!f}|rz||||||S||||||j SdS( s One-dimensional linear interpolation. Returns the one-dimensional piecewise linear interpolant to a function with given values at discrete data-points. Parameters ---------- x : array_like The x-coordinates of the interpolated values. xp : 1-D sequence of floats The x-coordinates of the data points, must be increasing if argument `period` is not specified. Otherwise, `xp` is internally sorted after normalizing the periodic boundaries with ``xp = xp % period``. fp : 1-D sequence of float or complex The y-coordinates of the data points, same length as `xp`. left : optional float or complex corresponding to fp Value to return for `x < xp[0]`, default is `fp[0]`. right : optional float or complex corresponding to fp Value to return for `x > xp[-1]`, default is `fp[-1]`. period : None or float, optional A period for the x-coordinates. This parameter allows the proper interpolation of angular x-coordinates. Parameters `left` and `right` are ignored if `period` is specified. .. versionadded:: 1.10.0 Returns ------- y : float or complex (corresponding to fp) or ndarray The interpolated values, same shape as `x`. Raises ------ ValueError If `xp` and `fp` have different length If `xp` or `fp` are not 1-D sequences If `period == 0` Notes ----- Does not check that the x-coordinate sequence `xp` is increasing. If `xp` is not increasing, the results are nonsense. A simple check for increasing is:: np.all(np.diff(xp) > 0) Examples -------- >>> xp = [1, 2, 3] >>> fp = [3, 2, 0] >>> np.interp(2.5, xp, fp) 1.0 >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp) array([ 3. , 3. , 2.5 , 0.56, 0. ]) >>> UNDEF = -99.0 >>> np.interp(3.14, xp, fp, right=UNDEF) -99.0 Plot an interpolant to the sine function: >>> x = np.linspace(0, 2*np.pi, 10) >>> y = np.sin(x) >>> xvals = np.linspace(0, 2*np.pi, 50) >>> yinterp = np.interp(xvals, x, y) >>> import matplotlib.pyplot as plt >>> plt.plot(x, y, 'o') [] >>> plt.plot(xvals, yinterp, '-x') [] >>> plt.show() Interpolation with periodic x-coordinates: >>> x = [-180, -170, -185, 185, -10, -5, 0, 365] >>> xp = [190, -190, 350, -350] >>> fp = [5, 10, 3, 4] >>> np.interp(x, xp, fp, period=360) array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75]) Complex interpolation >>> x = [1.5, 4.0] >>> xp = [2,3,5] >>> fp = [1.0j, 0, 2+3j] >>> np.interp(x, xp, fp) array([ 0.+1.j , 1.+1.5j]) isperiod must be a non-zero valueRis!Data points must be 1-D sequencess$fp and xp are not of the same lengthiN(RyR t iscomplexobjtcompiled_interp_complext complex128tcompiled_interptfloat64RoRRRR0R RRgRftabsRvRuRRR ( R{txptfpRRtperiodt interp_funct input_dtypet return_arraytasort_xp((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR8sL_   !       +#cC`so|rdt}nd}t|}t|jjtjrR|j}|j}n d}|}t |||S(s Return the angle of the complex argument. Parameters ---------- z : array_like A complex number or sequence of complex numbers. deg : bool, optional Return angle in degrees if True, radians if False (default). Returns ------- angle : ndarray or scalar The counterclockwise angle from the positive real axis on the complex plane, with dtype as numpy.float64. See Also -------- arctan2 absolute Examples -------- >>> np.angle([1.0, 1.0j, 1+1j]) # in radians array([ 0. , 1.57079633, 0.78539816]) >>> np.angle(1+1j, deg=True) # in degrees 45.0 ig?i( RR RRRR%tcomplexfloatingRRR(tztdegtfacttzimagtzreal((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyREs     c C`st|}|j}t|d|}td d g|}tdd ||>> phase = np.linspace(0, np.pi, num=5) >>> phase[3:] += np.pi >>> phase array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) >>> np.unwrap(phase) array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) RqiiRiR@RRN( R RgRCRnRoR%RR%RRFR RvR( tptdiscontRqR@tddR4tddmodt ph_correcttup((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRFKs)  ' "cC`st|dt}|jt|jjtjs|jjdkrS|j dS|jjdkrr|j dS|j dSn|SdS(s Sort a complex array using the real part first, then the imaginary part. Parameters ---------- a : array_like Input array Returns ------- out : complex ndarray Always returns a sorted complex array. Examples -------- >>> np.sort_complex([5, 3, 6, 2, 1]) array([ 1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j]) >>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j]) array([ 1.+2.j, 2.-1.j, 3.-3.j, 3.-2.j, 3.+5.j]) R@tbhBHR tgtGRN( R RvR*RRRR%RNRR(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRGs   tfbcC`sd}|j}d|krLx+|D] }|dkr;Pq%|d}q%Wnt|}d|krx8|dddD] }|dkrPqx|d}qxWn|||!S(s3 Trim the leading and/or trailing zeros from a 1-D array or sequence. Parameters ---------- filt : 1-D array or sequence Input array. trim : str, optional A string with 'f' representing trim from front and 'b' to trim from back. Default is 'fb', trim zeros from both front and back of the array. Returns ------- trimmed : 1-D array or sequence The result of trimming the input. The input data type is preserved. Examples -------- >>> a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0)) >>> np.trim_zeros(a) array([1, 2, 3, 0, 2, 1]) >>> np.trim_zeros(a, 'b') array([0, 0, 0, 1, 2, 3, 0, 2, 1]) The input data type is preserved, list/tuple in means list/tuple out. >>> np.trim_zeros([0, 1, 2, 0]) [1, 2] iR gitBNi(tupperRe(tfiltttrimtfirstRtlast((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR?s!       cC`syX|j}|jdkr"|S|jttg|d|d kf}||SWn*tk rtt|}t|SXdS(sW This function is deprecated. Use numpy.lib.arraysetops.unique() instead. iiiN( tflattenRzR*R RvRtsortedtsetR (R{ttmptidxtitems((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pytuniques  #  cC`s&tjt|tt|dS(s Return the elements of an array that satisfy some condition. This is equivalent to ``np.compress(ravel(condition), ravel(arr))``. If `condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``. Note that `place` does the exact opposite of `extract`. Parameters ---------- condition : array_like An array whose nonzero or True entries indicate the elements of `arr` to extract. arr : array_like Input array of the same size as `condition`. Returns ------- extract : ndarray Rank 1 array of values from `arr` where `condition` is True. See Also -------- take, put, copyto, compress, place Examples -------- >>> arr = np.arange(12).reshape((3, 4)) >>> arr array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> condition = np.mod(arr, 3)==0 >>> condition array([[ True, False, False, True], [False, False, True, False], [False, True, False, False]], dtype=bool) >>> np.extract(condition, arr) array([0, 3, 6, 9]) If `condition` is boolean: >>> arr[condition] array([0, 3, 6, 9]) i(R%RR(R)(t conditiontarr((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRKs0cC`sFt|tjs6tdjdt|jnt|||S(s Change elements of an array based on conditional and input values. Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that `place` uses the first N elements of `vals`, where N is the number of True values in `mask`, while `copyto` uses the elements where `mask` is True. Note that `extract` does the exact opposite of `place`. Parameters ---------- arr : ndarray Array to put data into. mask : array_like Boolean mask array. Must have the same size as `a`. vals : 1-D sequence Values to put into `a`. Only the first N elements are used, where N is the number of True values in `mask`. If `vals` is smaller than N, it will be repeated, and if elements of `a` are to be masked, this sequence must be non-empty. See Also -------- copyto, put, take, extract Examples -------- >>> arr = np.arange(6).reshape(2, 3) >>> np.place(arr, arr>2, [44, 55]) >>> arr array([[ 0, 1, 2], [44, 55, 44]]) s,argument 1 must be numpy.ndarray, not {name}R*(RRyRRtRhRt__name__R3(RltmaskR ((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRL s$ cC`sQ|dkrtj}n|r2|jd|n|jd||jdS(s7 Display a message on a device. Parameters ---------- mesg : str Message to display. device : object Device to write message. If None, defaults to ``sys.stdout`` which is very similar to ``print``. `device` needs to have ``write()`` and ``flush()`` methods. linefeed : bool, optional Option whether to print a line feed or not. Defaults to True. Raises ------ AttributeError If `device` does not have a ``write()`` or ``flush()`` method. Examples -------- Besides ``sys.stdout``, a file-like object can also be used as it has both required methods: >>> from StringIO import StringIO >>> buf = StringIO() >>> np.disp('"Display" in a file', device=buf) >>> buf.getvalue() '"Display" in a file\n' s%s s%sN(Rotsyststdouttwritetflush(tmesgtdevicetlinefeed((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRHI s   s\w+s(?:{0:}(?:,{0:})*)?s\({}\)s{0:}(?:,{0:})*s ^{0:}->{0:}$cC`sGtjt|s*tdj|ntd|jdDS(ss Parse string signatures for a generalized universal function. Arguments --------- signature : string Generalized universal function signature, e.g., ``(m,n),(n,p)->(m,p)`` for ``np.matmul``. Returns ------- Tuple of input and output core dimensions parsed from the signature, each of the form List[Tuple[str, ...]]. s not a valid gufunc signature: {}cs`sF|]<}gtjt|D]}ttjt|^qVqdS(N(tretfindallt _ARGUMENTRdt_DIMENSION_NAME(t.0targ_listtarg((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pys ss->(Rvtmatcht _SIGNATURERfRhRdtsplit(t signature((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_parse_gufunc_signature{ s  cC`s|s dSt|}|j|krAtd|j|fn|j| }xft||D]U\}}||kr|||krtd||||fqq_||| s(Rd(RRtlist_of_core_dimsR((RsJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_calculate_shapes scC`s5t|||}tdt||D}|S(s/Helper for creating output arrays in vectorize.cs`s*|] \}}tj|d|VqdS(RN(RyR(RzRR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pys s(RRdR(RRRtdtypestshapestarrays((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_create_arrays s cB`sJeZdZdddeddZdZdZdZdZ RS(sC vectorize(pyfunc, otypes=None, doc=None, excluded=None, cache=False, signature=None) Generalized function class. Define a vectorized function which takes a nested sequence of objects or numpy arrays as inputs and returns an single or tuple of numpy array as output. The vectorized function evaluates `pyfunc` over successive tuples of the input arrays like the python map function, except it uses the broadcasting rules of numpy. The data type of the output of `vectorized` is determined by calling the function with the first element of the input. This can be avoided by specifying the `otypes` argument. Parameters ---------- pyfunc : callable A python function or method. otypes : str or list of dtypes, optional The output data type. It must be specified as either a string of typecode characters or a list of data type specifiers. There should be one data type specifier for each output. doc : str, optional The docstring for the function. If `None`, the docstring will be the ``pyfunc.__doc__``. excluded : set, optional Set of strings or integers representing the positional or keyword arguments for which the function will not be vectorized. These will be passed directly to `pyfunc` unmodified. .. versionadded:: 1.7.0 cache : bool, optional If `True`, then cache the first function call that determines the number of outputs if `otypes` is not provided. .. versionadded:: 1.7.0 signature : string, optional Generalized universal function signature, e.g., ``(m,n),(n)->(m)`` for vectorized matrix-vector multiplication. If provided, ``pyfunc`` will be called with (and expected to return) arrays with shapes given by the size of corresponding core dimensions. By default, ``pyfunc`` is assumed to take scalars as input and output. .. versionadded:: 1.12.0 Returns ------- vectorized : callable Vectorized function. Examples -------- >>> def myfunc(a, b): ... "Return a-b if a>b, otherwise return a+b" ... if a > b: ... return a - b ... else: ... return a + b >>> vfunc = np.vectorize(myfunc) >>> vfunc([1, 2, 3, 4], 2) array([3, 4, 1, 2]) The docstring is taken from the input function to `vectorize` unless it is specified: >>> vfunc.__doc__ 'Return a-b if a>b, otherwise return a+b' >>> vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`') >>> vfunc.__doc__ 'Vectorized `myfunc`' The output type is determined by evaluating the first element of the input, unless it is specified: >>> out = vfunc([1, 2, 3, 4], 2) >>> type(out[0]) >>> vfunc = np.vectorize(myfunc, otypes=[np.float]) >>> out = vfunc([1, 2, 3, 4], 2) >>> type(out[0]) The `excluded` argument can be used to prevent vectorizing over certain arguments. This can be useful for array-like arguments of a fixed length such as the coefficients for a polynomial as in `polyval`: >>> def mypolyval(p, x): ... _p = list(p) ... res = _p.pop(0) ... while _p: ... res = res*x + _p.pop(0) ... return res >>> vpolyval = np.vectorize(mypolyval, excluded=['p']) >>> vpolyval(p=[1, 2, 3], x=[0, 1]) array([3, 6]) Positional arguments may also be excluded by specifying their position: >>> vpolyval.excluded.add(0) >>> vpolyval([1, 2, 3], x=[0, 1]) array([3, 6]) The `signature` argument allows for vectorizing functions that act on non-scalar arrays of fixed length. For example, you can use it for a vectorized calculation of Pearson correlation coefficient and its p-value: >>> import scipy.stats >>> pearsonr = np.vectorize(scipy.stats.pearsonr, ... signature='(n),(n)->(),()') >>> pearsonr([[0, 1, 2, 3]], [[1, 2, 3, 4], [4, 3, 2, 1]]) (array([ 1., -1.]), array([ 0., 0.])) Or for a vectorized convolution: >>> convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)') >>> convolve(np.eye(4), [1, 2, 1]) array([[ 1., 2., 1., 0., 0., 0.], [ 0., 1., 2., 1., 0., 0.], [ 0., 0., 1., 2., 1., 0.], [ 0., 0., 0., 1., 2., 1.]]) See Also -------- frompyfunc : Takes an arbitrary Python function and returns a ufunc Notes ----- The `vectorize` function is provided primarily for convenience, not for performance. The implementation is essentially a for loop. If `otypes` is not specified, then a call to the function with the first argument will be used to determine the number of outputs. The results of this call will be cached if `cache` is `True` to prevent calling the function twice. However, to implement the cache, the original function must be wrapped which will slow down subsequent calls, so only do this if your function is expensive. The new keyword argument interface and `excluded` argument support further degrades performance. References ---------- .. [1] NumPy Reference, section `Generalized Universal Function API `_. c C`sD||_||_||_d|_|dkr?|j|_n ||_t|trx|D],}|tdkr^t d|fq^q^WnXt |rdj g|D]}t j |j^q}n|dk rt dn||_|dkr t}nt||_|dk r7t||_n d|_dS(NtAllsInvalid otype specified: %stsInvalid otype specification(tpyfunctcacheRRot_ufunct__doc__RtstrR/RfRAR(R%RRtotypesRftexcludedRt_in_and_out_core_dims( tselfRRtdocRRRRR{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt__init__w s,        1     c `sj} r)| r)j}|}nt|}gD]}||kr<|^q<gt|D]}||krg|^qgt|fd}gD]}||^q}|jgD]}|^qjd|d|S(s Return arrays with the results of `pyfunc` broadcast (vectorized) over `args` and `kwargs` not in `excluded`. c`s[x(tD]\}}||| ss?cannot call `vectorize` on size 0 inputs unless `otypes` is setic`srjS|SdS(N(R$(R(t_cacheR(sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_func s iRN(RfRRoReRRR R tbuiltinsR-tflatRRRdR(RRR( RRRRtnouttufuncR|tinputstoutputsRt_k((RRsJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_get_ufunc_and_otypes s2   "      /c C`s|jdk r$|j||}n|s6|}n|jd|d|\}}g|D]$}t|dtdtdt^q[}||}|jdkrt|dtdtd|d}nFt gt ||D]*\} } t| dtdtd| ^q}|S( s1Vectorized call to `func` over positional `args`.RRR@tsubokRiiN( RRot_vectorize_call_with_signatureRR RuRvtobjectRRdR( RRRtresRRRRRR{tt((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR s . %@c`s|j\}}t|t|krLtdt|t|fntd|D}t||\}t||}gt||D]$\}}tj||dt ^q}d } |j } t|} x@tj |D]/|fd|D} t | tr+t| nd} | | krVtd| | fn| dkrn| f} n| d krx-t| |D]\}}t||qW| d krg| D]}t|j^q} nt||| } nx't| | D]\}}|| sRc3`s|]}|VqdS(N((RzR|(tindex(sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pys  sis8wrong number of outputs from pyfunc: expected %r, got %rs?cannot call `vectorize` on size 0 inputs unless `otypes` is setc3`s(|]}|D]}|kVq qdS(N((RztdimsR(R(sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pys < ssYcannot call `vectorize` with a signature including new output dimensions on size 0 inputsiN(RReRtRdRRRRyRRvRoRtndindexRRfRR RRRR-(RRRRtoutput_core_dimsRt input_shapesR|RRRRtresultst n_resultsRRtoutput((RRsJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR sR  7  !     %     N( Rmt __module__RRoRuRRRRR(((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRM s   = cC`sm|dk r-|t|kr-tdntj|}|jdkrZtdn|dkr~tj|tj}nEtj|}|jdkrtdntj||tj}t|ddd|}| r|j ddkr|j }n|j ddkr-tjgj ddS|dk rt|d t ddd|}| r}|j ddkr}|j }ntj ||f}n|dkr|dkrd}qd}nd} |dk rtj|dtj}tj|tj|kstd n|jdkr4td n|j d|j dkr]td nt|dkr~td n|} n|dk r5tj|dtj}|jdkrtdn|j d|j dkrtdnt|dkrtdn| dkr(|} q5| |9} nt|ddd| dt\} } | d} | dkr|j d|} nJ|dkr| } n5|dkr| |} n| |t| || } | dkrtjdtddd} n|| dddf8}| dkr*|j } n || j } t|| j}|dtj| 9}|jS(s Estimate a covariance matrix, given data and weights. Covariance indicates the level to which two variables vary together. If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`, then the covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance of :math:`x_i`. See the notes for an outline of the algorithm. Parameters ---------- m : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of `m` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below. y : array_like, optional An additional set of variables and observations. `y` has the same form as that of `m`. rowvar : bool, optional If `rowvar` is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : bool, optional Default normalization (False) is by ``(N - 1)``, where ``N`` is the number of observations given (unbiased estimate). If `bias` is True, then normalization is by ``N``. These values can be overridden by using the keyword ``ddof`` in numpy versions >= 1.5. ddof : int, optional If not ``None`` the default value implied by `bias` is overridden. Note that ``ddof=1`` will return the unbiased estimate, even if both `fweights` and `aweights` are specified, and ``ddof=0`` will return the simple average. See the notes for the details. The default value is ``None``. .. versionadded:: 1.5 fweights : array_like, int, optional 1-D array of integer freguency weights; the number of times each observation vector should be repeated. .. versionadded:: 1.10 aweights : array_like, optional 1-D array of observation vector weights. These relative weights are typically large for observations considered "important" and smaller for observations considered less "important". If ``ddof=0`` the array of weights can be used to assign probabilities to observation vectors. .. versionadded:: 1.10 Returns ------- out : ndarray The covariance matrix of the variables. See Also -------- corrcoef : Normalized covariance matrix Notes ----- Assume that the observations are in the columns of the observation array `m` and let ``f = fweights`` and ``a = aweights`` for brevity. The steps to compute the weighted covariance are as follows:: >>> w = f * a >>> v1 = np.sum(w) >>> v2 = np.sum(w * a) >>> m -= np.sum(m * w, axis=1, keepdims=True) / v1 >>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2) Note that when ``a == 1``, the normalization factor ``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)`` as it should. Examples -------- Consider two variables, :math:`x_0` and :math:`x_1`, which correlate perfectly, but in opposite directions: >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T >>> x array([[0, 1, 2], [2, 1, 0]]) Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance matrix shows this clearly: >>> np.cov(x) array([[ 1., -1.], [-1., 1.]]) Note that element :math:`C_{0,1}`, which shows the correlation between :math:`x_0` and :math:`x_1`, is negative. Further, note how `x` and `y` are combined: >>> x = [-2.1, -1, 4.3] >>> y = [3, 1.1, 0.12] >>> X = np.vstack((x,y)) >>> print(np.cov(X)) [[ 11.71 -4.286 ] [ -4.286 2.14413333]] >>> print(np.cov(x, y)) [[ 11.71 -4.286 ] [ -4.286 2.14413333]] >>> print(np.cov(x)) 11.71 sddof must be integerism has more than 2 dimensionssy has more than 2 dimensionstndminRiiR@sfweights must be integers'cannot handle multidimensional fweightss,incompatible numbers of samples and fweightssfweights cannot be negatives'cannot handle multidimensional aweightss,incompatible numbers of samples and aweightssaweights cannot be negativeRqRRs!Degrees of freedom <= 0 for sliceR gNg?(RoRRfRyR RgRRER RRRRuRRRRRtRR-RORvR.R RtRuntimeWarningRtconjR(RiRwtrowvartbiastddoftfweightstaweightsRtXtwRtw_sumRQtX_TR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRRH sr                      $             cC`s |tjk s|tjk r7tjdtddnt|||}yt|}Wntk rq||SXt|j }||dddf}||dddf}tj |j ddd|j tj |rtj |j ddd|j n|S(s Return Pearson product-moment correlation coefficients. Please refer to the documentation for `cov` for more detail. The relationship between the correlation coefficient matrix, `R`, and the covariance matrix, `C`, is .. math:: R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } } The values of `R` are between -1 and 1, inclusive. Parameters ---------- x : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of `x` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below. y : array_like, optional An additional set of variables and observations. `y` has the same shape as `x`. rowvar : bool, optional If `rowvar` is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : _NoValue, optional Has no effect, do not use. .. deprecated:: 1.10.0 ddof : _NoValue, optional Has no effect, do not use. .. deprecated:: 1.10.0 Returns ------- R : ndarray The correlation coefficient matrix of the variables. See Also -------- cov : Covariance matrix Notes ----- Due to floating point rounding the resulting array may not be Hermitian, the diagonal elements may not be 1, and the elements may not satisfy the inequality abs(a) <= 1. The real and imaginary parts are clipped to the interval [-1, 1] in an attempt to improve on that situation but is not much help in the complex case. This function accepts but discards arguments `bias` and `ddof`. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy. s/bias and ddof have no effect and are deprecatedR iNiiR9(Ryt_NoValueR RRRRR1RfR#RRotclipRAR(R{RwRRRRRtstddev((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRS s:   "cC`s~|dkrtgS|dkr/tdtStd|}ddtdt||ddtdt||dS(s Return the Blackman window. The Blackman window is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, hamming, hanning, kaiser Notes ----- The Blackman window is defined as .. math:: w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M) Most references to the Blackman window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. It is known as a "near optimal" tapering function, almost as good (by some measures) as the kaiser window. References ---------- Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471. Examples -------- >>> np.blackman(12) array([ -1.38777878e-17, 3.26064346e-02, 1.59903635e-01, 4.14397981e-01, 7.36045180e-01, 9.67046769e-01, 9.67046769e-01, 7.36045180e-01, 4.14397981e-01, 1.59903635e-01, 3.26064346e-02, -1.38777878e-17]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.blackman(51) >>> plt.plot(window) [] >>> plt.title("Blackman window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Blackman window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() iigzG?g?g@g{Gz?g@(R RRR R!R(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRZl s Z    cC`s{|dkrtgS|dkr/tdtStd|}tt||ddd||ddd||dS(s Return the Bartlett window. The Bartlett window is very similar to a triangular window, except that the end points are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : array The triangular window, with the maximum value normalized to one (the value one appears only if the number of samples is odd), with the first and last samples equal to zero. See Also -------- blackman, hamming, hanning, kaiser Notes ----- The Bartlett window is defined as .. math:: w(n) = \frac{2}{M-1} \left( \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right| \right) Most references to the Bartlett window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. Note that convolution with this window produces linear interpolation. It is also known as an apodization (which means"removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. The fourier transform of the Bartlett is the product of two sinc functions. Note the excellent discussion in Kanasewich. References ---------- .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", Biometrika 37, 1-16, 1950. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal Processing", Prentice-Hall, 1999, pp. 468-471. .. [4] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 429. Examples -------- >>> np.bartlett(12) array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636, 0.18181818, 0. ]) Plot the window and its frequency response (requires SciPy and matplotlib): >>> from numpy.fft import fft, fftshift >>> window = np.bartlett(51) >>> plt.plot(window) [] >>> plt.title("Bartlett window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Bartlett window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() iig@(R RRR RR"(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRY s b    cC`s`|dkrtgS|dkr/tdtStd|}ddtdt||dS(sa Return the Hanning window. The Hanning window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray, shape(M,) The window, with the maximum value normalized to one (the value one appears only if `M` is odd). See Also -------- bartlett, blackman, hamming, kaiser Notes ----- The Hanning window is defined as .. math:: w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 The Hanning was named for Julius von Hann, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window. Most references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 106-108. .. [3] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. Examples -------- >>> np.hanning(12) array([ 0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037, 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249, 0.07937323, 0. ]) Plot the window and its frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.hanning(51) >>> plt.plot(window) [] >>> plt.title("Hann window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of the Hann window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() iig?g@(R RRR R!R(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRX8 s \    cC`s`|dkrtgS|dkr/tdtStd|}ddtdt||dS(sQ Return the Hamming window. The Hamming window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, blackman, hanning, kaiser Notes ----- The Hamming window is defined as .. math:: w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 The Hamming was named for R. W. Hamming, an associate of J. W. Tukey and is described in Blackman and Tukey. It was recommended for smoothing the truncated autocovariance function in the time domain. Most references to the Hamming window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. Examples -------- >>> np.hamming(12) array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909, 0.15302337, 0.08 ]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.hamming(51) >>> plt.plot(window) [] >>> plt.title("Hamming window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Hamming window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() iigHzG?gq= ףp?g@(R RRR R!R(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRW s Z    g4!\Tg}b3g0 Kg5dMv;p>g"c쑾g$>g'doҾgY(X?>gZY&+g|t(?gRBguZ?gI ^qga?g!Ng-Ί>?g-4pKgw?gWӿg*5N?gT`g0fFVg!g["d,->gmրVX>gna>g+A>gRx?gI墌k?g b?cC`s^|d}d}x?tdt|D](}|}|}|||||}q&Wd||S(Nigig?(RRe(R{R tb0tb1Rtb2((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_chbevl=s cC`st|t|ddtS(Ng@i(R&Rt_i0A(R{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_i0_1IscC`s)t|td|dtt|S(Ng@@g@(R&Rt_i0BR#(R{((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyt_i0_2MscC`s~t|j}t|}|dk}|| ||<|dk}t||||<|}t||||<|jS(s0 Modified Bessel function of the first kind, order 0. Usually denoted :math:`I_0`. This function does broadcast, but will *not* "up-cast" int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below). Parameters ---------- x : array_like, dtype float or complex Argument of the Bessel function. Returns ------- out : ndarray, shape = x.shape, dtype = x.dtype The modified Bessel function evaluated at each of the elements of `x`. Raises ------ TypeError: array cannot be safely cast to required type If argument consists exclusively of int dtypes. See Also -------- scipy.special.iv, scipy.special.ive Notes ----- We use the algorithm published by Clenshaw [1]_ and referenced by Abramowitz and Stegun [2]_, for which the function domain is partitioned into the two intervals [0,8] and (8,inf), and Chebyshev polynomial expansions are employed in each interval. Relative error on the domain [0,30] using IEEE arithmetic is documented [3]_ as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000). References ---------- .. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in *National Physical Laboratory Mathematical Tables*, vol. 5, London: Her Majesty's Stationery Office, 1962. .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 379. http://www.math.sfu.ca/~cbm/aands/page_379.htm .. [3] http://kobesearch.cpan.org/htdocs/Math-Cephes/Math/Cephes.html Examples -------- >>> np.i0([0.]) array(1.0) >>> np.i0([0., 1. + 2j]) array([ 1.00000000+0.j , 0.18785373+0.64616944j]) ig @(RR@RRRR(R{Rwtindtind2((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR]Qs6   cC`s}ddlm}|dkr,tjdgStd|}|dd}||td|||d|t|S(s Return the Kaiser window. The Kaiser window is a taper formed by using a Bessel function. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. beta : float Shape parameter for window. Returns ------- out : array The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, blackman, hamming, hanning Notes ----- The Kaiser window is defined as .. math:: w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}} \right)/I_0(\beta) with .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2}, where :math:`I_0` is the modified zeroth-order Bessel function. The Kaiser was named for Jim Kaiser, who discovered a simple approximation to the DPSS window based on Bessel functions. The Kaiser window is a very good approximation to the Digital Prolate Spheroidal Sequence, or Slepian window, which is the transform which maximizes the energy in the main lobe of the window relative to total energy. The Kaiser can approximate many other windows by varying the beta parameter. ==== ======================= beta Window shape ==== ======================= 0 Rectangular 5 Similar to a Hamming 6 Similar to a Hanning 8.6 Similar to a Blackman ==== ======================= A beta value of 14 is probably a good starting point. Note that as beta gets large, the window narrows, and so the number of samples needs to be large enough to sample the increasingly narrow spike, otherwise NaNs will get returned. Most references to the Kaiser window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285. John Wiley and Sons, New York, (1966). .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 177-178. .. [3] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function Examples -------- >>> np.kaiser(12, 14) array([ 7.72686684e-06, 3.46009194e-03, 4.65200189e-02, 2.29737120e-01, 5.99885316e-01, 9.45674898e-01, 9.45674898e-01, 5.99885316e-01, 2.29737120e-01, 4.65200189e-02, 3.46009194e-03, 7.72686684e-06]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.kaiser(51, 14) >>> plt.plot(window) [] >>> plt.title("Kaiser window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Kaiser window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() i(R]ig?g@(t numpy.dualR]RyR R R#R(RtbetaR]Rtalpha((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR[s w cC`s9tj|}tt|dkd|}t||S(s Return the sinc function. The sinc function is :math:`\sin(\pi x)/(\pi x)`. Parameters ---------- x : ndarray Array (possibly multi-dimensional) of values for which to to calculate ``sinc(x)``. Returns ------- out : ndarray ``sinc(x)``, which has the same shape as the input. Notes ----- ``sinc(0)`` is the limit value 1. The name sinc is short for "sine cardinal" or "sinus cardinalis". The sinc function is used in various signal processing applications, including in anti-aliasing, in the construction of a Lanczos resampling filter, and in interpolation. For bandlimited interpolation of discrete-time signals, the ideal interpolation kernel is proportional to the sinc function. References ---------- .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html .. [2] Wikipedia, "Sinc function", http://en.wikipedia.org/wiki/Sinc_function Examples -------- >>> x = np.linspace(-4, 4, 41) >>> np.sinc(x) array([ -3.89804309e-17, -4.92362781e-02, -8.40918587e-02, -8.90384387e-02, -5.84680802e-02, 3.89804309e-17, 6.68206631e-02, 1.16434881e-01, 1.26137788e-01, 8.50444803e-02, -3.89804309e-17, -1.03943254e-01, -1.89206682e-01, -2.16236208e-01, -1.55914881e-01, 3.89804309e-17, 2.33872321e-01, 5.04551152e-01, 7.56826729e-01, 9.35489284e-01, 1.00000000e+00, 9.35489284e-01, 7.56826729e-01, 5.04551152e-01, 2.33872321e-01, 3.89804309e-17, -1.55914881e-01, -2.16236208e-01, -1.89206682e-01, -1.03943254e-01, -3.89804309e-17, 8.50444803e-02, 1.26137788e-01, 1.16434881e-01, 6.68206631e-02, 3.89804309e-17, -5.84680802e-02, -8.90384387e-02, -8.40918587e-02, -4.92362781e-02, -3.89804309e-17]) >>> plt.plot(x, np.sinc(x)) [] >>> plt.title("Sinc Function") >>> plt.ylabel("Amplitude") >>> plt.xlabel("X") >>> plt.show() It works in 2-D as well: >>> x = np.linspace(-4, 4, 401) >>> xx = np.outer(x, x) >>> plt.imshow(np.sinc(xx)) ig#B ;(RyR RRR$(R{Rw((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRVsJcC`s)t|dtdt}|jd|S(sk Return a copy of an array sorted along the first axis. Parameters ---------- a : array_like Array to be sorted. Returns ------- sorted_array : ndarray Array of the same type and shape as `a`. See Also -------- sort Notes ----- ``np.msort(a)`` is equivalent to ``np.sort(a, axis=0)``. RR@i(R RvR*(RR((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRTbs c K`sBtj|}|jdd}|dk rt|j}|j}tj||}x|D]}d||>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.median(a) 3.5 >>> np.median(a, axis=0) array([ 6.5, 4.5, 2.5]) >>> np.median(a, axis=1) array([ 7., 2.]) >>> m = np.median(a, axis=0) >>> out = np.zeros_like(m) >>> np.median(a, axis=0, out=m) array([ 6.5, 4.5, 2.5]) >>> m array([ 6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.median(b, axis=1, overwrite_input=True) array([ 7., 2.]) >>> assert not np.all(a==b) >>> b = a.copy() >>> np.median(b, axis=None, overwrite_input=True) 3.5 >>> assert not np.all(a==b) RRqR9toverwrite_inputN(Rt_medianR(RRqR9RtkeepdimsRRj((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRUs Q c C`stj|}|dkr'|j}n |j|}|ddkra|d}|d|g}n|ddg}tj|jtjr|jdn|r|dkr|j }|j |q|j |d||}nt ||d|}|jdkr|j S|dkr'd}nt dg|j }|j|d} |j|ddkrt | | d||>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.percentile(a, 50) 3.5 >>> np.percentile(a, 50, axis=0) array([[ 6.5, 4.5, 2.5]]) >>> np.percentile(a, 50, axis=1) array([ 7., 2.]) >>> np.percentile(a, 50, axis=1, keepdims=True) array([[ 7.], [ 2.]]) >>> m = np.percentile(a, 50, axis=0) >>> out = np.zeros_like(m) >>> np.percentile(a, 50, axis=0, out=out) array([[ 6.5, 4.5, 2.5]]) >>> m array([[ 6.5, 4.5, 2.5]]) >>> b = a.copy() >>> np.percentile(b, 50, axis=1, overwrite_input=True) array([ 7., 2.]) >>> assert not np.all(a == b) RR@RtqRqR9Rt interpolationiN( R RyRERvRt _percentileRgRRe( RRRqR9RRRRRj((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRBCsl! cC`st|}|jdkr.t}|d}nt}|jdkrxt|jD]E}||dksy||dkrtdn||cd>> np.trapz([1,2,3]) 4.0 >>> np.trapz([1,2,3], x=[4,6,8]) 8.0 >>> np.trapz([1,2,3], dx=2) 8.0 >>> a = np.arange(6).reshape(2, 3) >>> a array([[0, 1, 2], [3, 4, 5]]) >>> np.trapz(a, axis=0) array([ 1.5, 2.5, 3.5]) >>> np.trapz(a, axis=1) array([ 2., 8.]) iiRqig@N( R RoRgRCRRRnR.RfRyR RR( RwR{R0RqRRR@R4R5tret((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR\Ls,>      ' *cC`sytt|ti|g|}t|trLt||jn}t|trtt||d|djnGt|trx5|D]*}tt||d|djqWnWnnXdS(s Adds documentation to obj which is in module place. If doc is a string add it to obj as a docstring If doc is a tuple, then the first element is interpreted as an attribute of obj and the second as the docstring (method, docstring) If doc is a list, then each element of the list should be a sequence of length two --> [(method1, docstring1), (method2, docstring2), ...] This routine never raises an error. This routine cannot modify read-only docstrings, as appear in new-style classes or built-in functions. Because this routine never raises an error the caller must check manually that the docstrings were changed. iiN( tgetattrt __import__tglobalsRRR4tstripRdR(RLtobjRtnewtval((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR^s$' /c O`sgt|}|jdt}|jdt}|jdd}|rhtdt|dfn|d krtdnd|}gt|D]8\}}tj |j || d||d ^q} |dkr|d krd|d | d_ d|d | d _ n|s;tj d t| } n|rcg| D]}|j ^qH} n| S(s Return coordinate matrices from coordinate vectors. Make N-D coordinate arrays for vectorized evaluations of N-D scalar/vector fields over N-D grids, given one-dimensional coordinate arrays x1, x2,..., xn. .. versionchanged:: 1.9 1-D and 0-D cases are allowed. Parameters ---------- x1, x2,..., xn : array_like 1-D arrays representing the coordinates of a grid. indexing : {'xy', 'ij'}, optional Cartesian ('xy', default) or matrix ('ij') indexing of output. See Notes for more details. .. versionadded:: 1.7.0 sparse : bool, optional If True a sparse grid is returned in order to conserve memory. Default is False. .. versionadded:: 1.7.0 copy : bool, optional If False, a view into the original arrays are returned in order to conserve memory. Default is True. Please note that ``sparse=False, copy=False`` will likely return non-contiguous arrays. Furthermore, more than one element of a broadcast array may refer to a single memory location. If you need to write to the arrays, make copies first. .. versionadded:: 1.7.0 Returns ------- X1, X2,..., XN : ndarray For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` , return ``(N1, N2, N3,...Nn)`` shaped arrays if indexing='ij' or ``(N2, N1, N3,...Nn)`` shaped arrays if indexing='xy' with the elements of `xi` repeated to fill the matrix along the first dimension for `x1`, the second for `x2` and so on. Notes ----- This function supports both indexing conventions through the indexing keyword argument. Giving the string 'ij' returns a meshgrid with matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing. In the 2-D case with inputs of length M and N, the outputs are of shape (N, M) for 'xy' indexing and (M, N) for 'ij' indexing. In the 3-D case with inputs of length M, N and P, outputs are of shape (N, M, P) for 'xy' indexing and (M, N, P) for 'ij' indexing. The difference is illustrated by the following code snippet:: xv, yv = np.meshgrid(x, y, sparse=False, indexing='ij') for i in range(nx): for j in range(ny): # treat xv[i,j], yv[i,j] xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy') for i in range(nx): for j in range(ny): # treat xv[j,i], yv[j,i] In the 1-D and 0-D case, the indexing and sparse keywords have no effect. See Also -------- index_tricks.mgrid : Construct a multi-dimensional "meshgrid" using indexing notation. index_tricks.ogrid : Construct an open multi-dimensional "meshgrid" using indexing notation. Examples -------- >>> nx, ny = (3, 2) >>> x = np.linspace(0, 1, nx) >>> y = np.linspace(0, 1, ny) >>> xv, yv = np.meshgrid(x, y) >>> xv array([[ 0. , 0.5, 1. ], [ 0. , 0.5, 1. ]]) >>> yv array([[ 0., 0., 0.], [ 1., 1., 1.]]) >>> xv, yv = np.meshgrid(x, y, sparse=True) # make sparse output arrays >>> xv array([[ 0. , 0.5, 1. ]]) >>> yv array([[ 0.], [ 1.]]) `meshgrid` is very useful to evaluate functions on a grid. >>> x = np.arange(-5, 5, 0.1) >>> y = np.arange(-5, 5, 0.1) >>> xx, yy = np.meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x,y,z) R@tsparsetindexingRs2meshgrid() got an unexpected keyword argument '%s'itijs.Valid values for `indexing` are 'xy' and 'ij'.iiiR(RR(i(i(ii(ii(ReR$RvRuRtRRfR'RyR RRRR@( txiR.Rgtcopy_RRts0RR{R((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR_s*f    H"cC`sd }t|tk r<y |j}Wq<tk r8q<Xnt|}|j}|jjrcdnd}|d kr|dkr|j }n|j}d}n|dkrt j dt dd|r||S|j d |Snt||}td g|}|j|}t|j}t|tr4|j|\} } } t| | | } t| } | dkr|r||j d |S|j d |Sn| dkr| } | d} | dd} n||c| 8>> mask = np.ones(len(arr), dtype=bool) >>> mask[[0,2,4]] = False >>> result = arr[mask,...] Is equivalent to `np.delete(arr, [0,2,4], axis=0)`, but allows further use of `mask`. Examples -------- >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) >>> arr array([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]]) >>> np.delete(arr, 1, 0) array([[ 1, 2, 3, 4], [ 9, 10, 11, 12]]) >>> np.delete(arr, np.s_[::2], 1) array([[ 2, 4], [ 6, 8], [10, 12]]) >>> np.delete(arr, [1,3,5], None) array([ 1, 3, 5, 7, 8, 9, 10, 11, 12]) R tCiiis\in the future the special handling of scalars will be removed from delete and raise an errorR iRRNspin the future insert will treat boolean arrays and array-likes as boolean index instead of casting it to integers2index %i is out of bounds for axis %i with size %it same_kindsPusing a non-integer array as obj in delete will result in an error in the futurescin the future out of bounds indices will raise an error instead of being ignored by `numpy.delete`.sEin the future negative indices will not be ignored by `numpy.delete`.('RoRRt__array_wrap__RR RgtflagstfncR(R RRR@R7RnRRRRRReRRRRRuRyt FutureWarningRRRR;RR RpRzRR(RlRRqtwrapRgtarrordertslobjRtnewshapetstarttstoptsteptxrtnumtodelRtslobj2Rt_objt inside_boundstpositive_indices((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyR`Qs:                           "            cC`sd}t|tk r<y |j}Wq<tk r8q<Xnt|}|j}|jjrcdnd}|dkr|dkr|j }n|j}|d}nd|dkrt j dt dd|j d|}||d <|r||S|Snt||}tdg|}|j|}t|j} t|trjt|j|itd 6} ndtj|} | jtkrt j d tdd| jt} n| jdkrtd n| jdkr`| j} | | ks| |krtd |||fn| dkr7| |7} nt|dt d|jd |j}| jdkrtj!|d||jd}n|j|} | |c| 7>> a = np.array([[1, 1], [2, 2], [3, 3]]) >>> a array([[1, 1], [2, 2], [3, 3]]) >>> np.insert(a, 1, 5) array([1, 5, 1, 2, 2, 3, 3]) >>> np.insert(a, 1, 5, axis=1) array([[1, 5, 1], [2, 5, 2], [3, 5, 3]]) Difference between sequence and scalars: >>> np.insert(a, [1], [[1],[2],[3]], axis=1) array([[1, 1, 1], [2, 2, 2], [3, 3, 3]]) >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1), ... np.insert(a, [1], [[1],[2],[3]], axis=1)) True >>> b = a.flatten() >>> b array([1, 1, 2, 2, 3, 3]) >>> np.insert(b, [2, 2], [5, 6]) array([1, 1, 5, 6, 2, 2, 3, 3]) >>> np.insert(b, slice(2, 4), [5, 6]) array([1, 1, 5, 2, 6, 2, 3, 3]) >>> np.insert(b, [2, 2], [7.13, False]) # type casting array([1, 1, 7, 0, 2, 2, 3, 3]) >>> x = np.arange(8).reshape(2, 4) >>> idx = (1, 3) >>> np.insert(x, idx, 999, axis=1) array([[ 0, 999, 1, 2, 999, 3], [ 4, 999, 5, 6, 999, 7]]) R Riis\in the future the special handling of scalars will be removed from insert and raise an errorR iR.Rsrin the future insert will treat boolean arrays and array-likes as a boolean index instead of casting it to integersDindex array argument obj to insert must be one dimensional or scalars2index %i is out of bounds for axis %i with size %iR@RRsPusing a non-integer array as obj in insert will result in an error in the futureRt mergesortN('RoRRRRR RgRRR(R RRR@R7RnRRRR RRRyR RRRRRfRzR RpRuRRRReRR(RlRtvaluesRqRRgRR RR!RRtnumnewRR'Rtold_mask((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRasX             "     $#   "        cC`sht|}|dkrR|jdkr6|j}nt|}|jd}nt||fd|S(s Append values to the end of an array. Parameters ---------- arr : array_like Values are appended to a copy of this array. values : array_like These values are appended to a copy of `arr`. It must be of the correct shape (the same shape as `arr`, excluding `axis`). If `axis` is not specified, `values` can be any shape and will be flattened before use. axis : int, optional The axis along which `values` are appended. If `axis` is not given, both `arr` and `values` are flattened before use. Returns ------- append : ndarray A copy of `arr` with `values` appended to `axis`. Note that `append` does not occur in-place: a new array is allocated and filled. If `axis` is None, `out` is a flattened array. See Also -------- insert : Insert elements into an array. delete : Delete elements from an array. Examples -------- >>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]]) array([1, 2, 3, 4, 5, 6, 7, 8, 9]) When `axis` is specified, `values` must have the correct shape. >>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0) array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0) Traceback (most recent call last): ... ValueError: arrays must have same number of dimensions iRqN(R RoRgR(R (RlR,Rq((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pyRbs.   (t __future__RRRRtoperatorRvRoR tnumpyRytnumpy.core.numericRtnumericR%t numpy.coreRRRRRRR R R R R RRRRRRRRRRRRRRtnumpy.core.umathRRRRR R!R"R#R$R%R&R'tnumpy.core.fromnumericR(R)R*R+R,R-R.tnumpy.core.numerictypesR/R0tnumpy.lib.twodim_baseR1RR2tnumpy.core.multiarrayR3R4R5R6R7R8RDR9RBR:Rct numpy.compatR;tnumpy.compat.py3kR<t version_infotxrangeRt __builtin__Rt__all__RJRIRAR|R~RRRRRRRoRuRPRQRORNR>R=R@RDRCRERFRGR?RjRKRLRvRHRyRht_CORE_DIMENSION_LISTRxt_ARGUMENT_LISTR~RRRRRRRMRRRRSRZRYRXRWRRRRRR]R[RVRTRRURRBRR\R^R_R`RaRb(((sJ/opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/function_base.pytsB      "R44 W H      "      ~C g 1 [V .7 $ 3 3 ++  "   j S b j d d     C  O  6X7x[ #