a BCCf@sddlZddlmZmZddlZddlmZddlm Z gdZ e ddZ dd d Z e d d Z dddZe ddZddZd ddZddZddZd!ddZddZdS)"N)catch_warnings simplefilter)index) namedtuple)binned_statisticbinned_statistic_2dbinned_statistic_ddBinnedStatisticResult) statistic bin_edges binnumbermean c Cs|z t|}Wnty"d}Yn0|dkr:t|tg}|durTt|dkrT|g}t|g||||\}}}t||d|S)a Compute a binned statistic for one or more sets of data. This is a generalization of a histogram function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values (or set of values) within each bin. Parameters ---------- x : (N,) array_like A sequence of values to be binned. values : (N,) array_like or list of (N,) array_like The data on which the statistic will be computed. This must be the same shape as `x`, or a set of sequences - each the same shape as `x`. If `values` is a set of sequences, the statistic will be computed on each independently. statistic : string or callable, optional The statistic to compute (default is 'mean'). The following statistics are available: * 'mean' : compute the mean of values for points within each bin. Empty bins will be represented by NaN. * 'std' : compute the standard deviation within each bin. This is implicitly calculated with ddof=0. * 'median' : compute the median of values for points within each bin. Empty bins will be represented by NaN. * 'count' : compute the count of points within each bin. This is identical to an unweighted histogram. `values` array is not referenced. * 'sum' : compute the sum of values for points within each bin. This is identical to a weighted histogram. * 'min' : compute the minimum of values for points within each bin. Empty bins will be represented by NaN. * 'max' : compute the maximum of values for point within each bin. Empty bins will be represented by NaN. * function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error. bins : int or sequence of scalars, 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. Values in `x` that are smaller than lowest bin edge are assigned to bin number 0, values beyond the highest bin are assigned to ``bins[-1]``. If the bin edges are specified, the number of bins will be, (nx = len(bins)-1). range : (float, float) or [(float, float)], optional The lower and upper range of the bins. If not provided, range is simply ``(x.min(), x.max())``. Values outside the range are ignored. Returns ------- statistic : array The values of the selected statistic in each bin. bin_edges : array of dtype float Return the bin edges ``(length(statistic)+1)``. binnumber: 1-D ndarray of ints Indices of the bins (corresponding to `bin_edges`) in which each value of `x` belongs. Same length as `values`. A binnumber of `i` means the corresponding value is between (bin_edges[i-1], bin_edges[i]). See Also -------- numpy.digitize, numpy.histogram, binned_statistic_2d, binned_statistic_dd 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:: 0.11.0 Examples -------- >>> import numpy as np >>> from scipy import stats >>> import matplotlib.pyplot as plt First some basic examples: Create two evenly spaced bins in the range of the given sample, and sum the corresponding values in each of those bins: >>> values = [1.0, 1.0, 2.0, 1.5, 3.0] >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2) BinnedStatisticResult(statistic=array([4. , 4.5]), bin_edges=array([1., 4., 7.]), binnumber=array([1, 1, 1, 2, 2])) Multiple arrays of values can also be passed. The statistic is calculated on each set independently: >>> values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]] >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2) BinnedStatisticResult(statistic=array([[4. , 4.5], [8. , 9. ]]), bin_edges=array([1., 4., 7.]), binnumber=array([1, 1, 1, 2, 2])) >>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean', ... bins=3) BinnedStatisticResult(statistic=array([1., 2., 4.]), bin_edges=array([1., 2., 3., 4.]), binnumber=array([1, 2, 1, 2, 3])) As a second example, we now generate some random data of sailing boat speed as a function of wind speed, and then determine how fast our boat is for certain wind speeds: >>> rng = np.random.default_rng() >>> windspeed = 8 * rng.random(500) >>> boatspeed = .3 * windspeed**.5 + .2 * rng.random(500) >>> bin_means, bin_edges, binnumber = stats.binned_statistic(windspeed, ... boatspeed, statistic='median', bins=[1,2,3,4,5,6,7]) >>> plt.figure() >>> plt.plot(windspeed, boatspeed, 'b.', label='raw data') >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5, ... label='binned statistic of data') >>> plt.legend() Now we can use ``binnumber`` to select all datapoints with a windspeed below 1: >>> low_boatspeed = boatspeed[binnumber == 0] As a final example, we will use ``bin_edges`` and ``binnumber`` to make a plot of a distribution that shows the mean and distribution around that mean per bin, on top of a regular histogram and the probability distribution function: >>> x = np.linspace(0, 5, num=500) >>> x_pdf = stats.maxwell.pdf(x) >>> samples = stats.maxwell.rvs(size=10000) >>> bin_means, bin_edges, binnumber = stats.binned_statistic(x, x_pdf, ... statistic='mean', bins=25) >>> bin_width = (bin_edges[1] - bin_edges[0]) >>> bin_centers = bin_edges[1:] - bin_width/2 >>> plt.figure() >>> plt.hist(samples, bins=50, density=True, histtype='stepfilled', ... alpha=0.2, label='histogram of data') >>> plt.plot(x, x_pdf, 'r-', label='analytical pdf') >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=2, ... label='binned statistic of data') >>> plt.plot((binnumber - 0.5) * bin_width, x_pdf, 'g.', alpha=0.5) >>> plt.legend(fontsize=10) >>> plt.show() Nr)len TypeErrornpasarrayfloatrr ) xvaluesr binsrangeNmediansedges binnumbersrY/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/stats/_binned_statistic.pyrs     rBinnedStatistic2dResult)r Zx_edgeZy_edger Fc Csz t|}Wnty"d}Yn0|dkrL|dkrLt|t}} || g}t||g|||||d\} } } t| | d| d| S)a9 Compute a bidimensional binned statistic for one or more sets of data. This is a generalization of a histogram2d function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values (or set of values) within each bin. Parameters ---------- x : (N,) array_like A sequence of values to be binned along the first dimension. y : (N,) array_like A sequence of values to be binned along the second dimension. values : (N,) array_like or list of (N,) array_like The data on which the statistic will be computed. This must be the same shape as `x`, or a list of sequences - each with the same shape as `x`. If `values` is such a list, the statistic will be computed on each independently. statistic : string or callable, optional The statistic to compute (default is 'mean'). The following statistics are available: * 'mean' : compute the mean of values for points within each bin. Empty bins will be represented by NaN. * 'std' : compute the standard deviation within each bin. This is implicitly calculated with ddof=0. * 'median' : compute the median of values for points within each bin. Empty bins will be represented by NaN. * 'count' : compute the count of points within each bin. This is identical to an unweighted histogram. `values` array is not referenced. * 'sum' : compute the sum of values for points within each bin. This is identical to a weighted histogram. * 'min' : compute the minimum of values for points within each bin. Empty bins will be represented by NaN. * 'max' : compute the maximum of values for point within each bin. Empty bins will be represented by NaN. * function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error. bins : int or [int, int] or array_like or [array, array], optional The bin specification: * the number of bins for the two dimensions (nx = ny = bins), * the number of bins in each dimension (nx, ny = bins), * the bin edges for the two dimensions (x_edge = y_edge = bins), * the bin edges in each dimension (x_edge, y_edge = bins). If the bin edges are specified, the number of bins will be, (nx = len(x_edge)-1, ny = len(y_edge)-1). range : (2,2) array_like, optional The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be considered outliers and not tallied in the histogram. expand_binnumbers : bool, optional 'False' (default): the returned `binnumber` is a shape (N,) array of linearized bin indices. 'True': the returned `binnumber` is 'unraveled' into a shape (2,N) ndarray, where each row gives the bin numbers in the corresponding dimension. See the `binnumber` returned value, and the `Examples` section. .. versionadded:: 0.17.0 Returns ------- statistic : (nx, ny) ndarray The values of the selected statistic in each two-dimensional bin. x_edge : (nx + 1) ndarray The bin edges along the first dimension. y_edge : (ny + 1) ndarray The bin edges along the second dimension. binnumber : (N,) array of ints or (2,N) ndarray of ints This assigns to each element of `sample` an integer that represents the bin in which this observation falls. The representation depends on the `expand_binnumbers` argument. See `Notes` for details. See Also -------- numpy.digitize, numpy.histogram2d, binned_statistic, binned_statistic_dd Notes ----- Binedges: 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. `binnumber`: This returned argument assigns to each element of `sample` an integer that represents the bin in which it belongs. The representation depends on the `expand_binnumbers` argument. If 'False' (default): The returned `binnumber` is a shape (N,) array of linearized indices mapping each element of `sample` to its corresponding bin (using row-major ordering). Note that the returned linearized bin indices are used for an array with extra bins on the outer binedges to capture values outside of the defined bin bounds. If 'True': The returned `binnumber` is a shape (2,N) ndarray where each row indicates bin placements for each dimension respectively. In each dimension, a binnumber of `i` means the corresponding value is between (D_edge[i-1], D_edge[i]), where 'D' is either 'x' or 'y'. .. versionadded:: 0.11.0 Examples -------- >>> from scipy import stats Calculate the counts with explicit bin-edges: >>> x = [0.1, 0.1, 0.1, 0.6] >>> y = [2.1, 2.6, 2.1, 2.1] >>> binx = [0.0, 0.5, 1.0] >>> biny = [2.0, 2.5, 3.0] >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny]) >>> ret.statistic array([[2., 1.], [1., 0.]]) The bin in which each sample is placed is given by the `binnumber` returned parameter. By default, these are the linearized bin indices: >>> ret.binnumber array([5, 6, 5, 9]) The bin indices can also be expanded into separate entries for each dimension using the `expand_binnumbers` parameter: >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny], ... expand_binnumbers=True) >>> ret.binnumber array([[1, 1, 1, 2], [1, 2, 1, 1]]) Which shows that the first three elements belong in the xbin 1, and the fourth into xbin 2; and so on for y. rr)expand_binnumbersr)rrrrrrr ) ryrr rrr!rZxedgesZyedgesrrrrrrrs    rBinnedStatisticddResultcCsLt|rd|8| ddt|d}t?||S)aE Compute a multidimensional binned statistic for a set of data. This is a generalization of a histogramdd function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values within each bin. Parameters ---------- sample : array_like Data to histogram passed as a sequence of N arrays of length D, or as an (N,D) array. values : (N,) array_like or list of (N,) array_like The data on which the statistic will be computed. This must be the same shape as `sample`, or a list of sequences - each with the same shape as `sample`. If `values` is such a list, the statistic will be computed on each independently. statistic : string or callable, optional The statistic to compute (default is 'mean'). The following statistics are available: * 'mean' : compute the mean of values for points within each bin. Empty bins will be represented by NaN. * 'median' : compute the median of values for points within each bin. Empty bins will be represented by NaN. * 'count' : compute the count of points within each bin. This is identical to an unweighted histogram. `values` array is not referenced. * 'sum' : compute the sum of values for points within each bin. This is identical to a weighted histogram. * 'std' : compute the standard deviation within each bin. This is implicitly calculated with ddof=0. If the number of values within a given bin is 0 or 1, the computed standard deviation value will be 0 for the bin. * 'min' : compute the minimum of values for points within each bin. Empty bins will be represented by NaN. * 'max' : compute the maximum of values for point within each bin. Empty bins will be represented by NaN. * function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error. bins : sequence or positive int, optional The bin specification must be in one of the following forms: * 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. expand_binnumbers : bool, optional 'False' (default): the returned `binnumber` is a shape (N,) array of linearized bin indices. 'True': the returned `binnumber` is 'unraveled' into a shape (D,N) ndarray, where each row gives the bin numbers in the corresponding dimension. See the `binnumber` returned value, and the `Examples` section of `binned_statistic_2d`. binned_statistic_result : binnedStatisticddResult Result of a previous call to the function in order to reuse bin edges and bin numbers with new values and/or a different statistic. To reuse bin numbers, `expand_binnumbers` must have been set to False (the default) .. versionadded:: 0.17.0 Returns ------- statistic : ndarray, shape(nx1, nx2, nx3,...) The values of the selected statistic in each two-dimensional bin. bin_edges : list of ndarrays A list of D arrays describing the (nxi + 1) bin edges for each dimension. binnumber : (N,) array of ints or (D,N) ndarray of ints This assigns to each element of `sample` an integer that represents the bin in which this observation falls. The representation depends on the `expand_binnumbers` argument. See `Notes` for details. See Also -------- numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d Notes ----- Binedges: All but the last (righthand-most) bin is half-open in each dimension. 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. `binnumber`: This returned argument assigns to each element of `sample` an integer that represents the bin in which it belongs. The representation depends on the `expand_binnumbers` argument. If 'False' (default): The returned `binnumber` is a shape (N,) array of linearized indices mapping each element of `sample` to its corresponding bin (using row-major ordering). If 'True': The returned `binnumber` is a shape (D,N) ndarray where each row indicates bin placements for each dimension respectively. In each dimension, a binnumber of `i` means the corresponding value is between (bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'. .. versionadded:: 0.11.0 Examples -------- >>> import numpy as np >>> from scipy import stats >>> import matplotlib.pyplot as plt >>> from mpl_toolkits.mplot3d import Axes3D Take an array of 600 (x, y) coordinates as an example. `binned_statistic_dd` can handle arrays of higher dimension `D`. But a plot of dimension `D+1` is required. >>> mu = np.array([0., 1.]) >>> sigma = np.array([[1., -0.5],[-0.5, 1.5]]) >>> multinormal = stats.multivariate_normal(mu, sigma) >>> data = multinormal.rvs(size=600, random_state=235412) >>> data.shape (600, 2) Create bins and count how many arrays fall in each bin: >>> N = 60 >>> x = np.linspace(-3, 3, N) >>> y = np.linspace(-3, 4, N) >>> ret = stats.binned_statistic_dd(data, np.arange(600), bins=[x, y], ... statistic='count') >>> bincounts = ret.statistic Set the volume and the location of bars: >>> dx = x[1] - x[0] >>> dy = y[1] - y[0] >>> x, y = np.meshgrid(x[:-1]+dx/2, y[:-1]+dy/2) >>> z = 0 >>> bincounts = bincounts.ravel() >>> x = x.ravel() >>> y = y.ravel() >>> fig = plt.figure() >>> ax = fig.add_subplot(111, projection='3d') >>> with np.errstate(divide='ignore'): # silence random axes3d warning ... ax.bar3d(x, y, z, dx, dy, bincounts) Reuse bin numbers and bin edges with new values: >>> ret2 = stats.binned_statistic_dd(data, -np.arange(600), ... binned_statistic_result=ret, ... statistic='mean') )r mediancountsumstdminmaxzinvalid statistic z contains non-finite values.r-zQThe number of `values` elements must match the length of each `sample` dimension.zEThe dimension of bins must be equal to the dimension of the sample x.Ncsg|]}t|dqS)r)r.0irrr Kz'binned_statistic_dd..csg|]}t|qSr)rdiffr2r5rrr6Mr7dtyper r/rr.r,T)Z return_indexZ return_countsrrr0r1ignore)invalidzInternal Shape Error)@callable ValueErrorrr isinstanceintrisfiniteallshapeAttributeErrorZ atleast_2dTrlistr _bin_edges _bin_numbersr arraybuiltinsrr result_typeZfloat64emptyprodr fillnanr+Znonzeror/sqrtZconjr%ZarangeZnewaxisr.r,ZlexsortuniquefloorZastypeceilr0Zargsortr1ZerrstaterrRuntimeWarning Exceptionr$Z complex128_calc_binned_statisticZreshapeappendtuplesliceZ unravel_indexany RuntimeErrorr#)#samplerr rrr!Zbinned_statistic_resultZ known_statsDlenNdimZ input_shapeVdimZVlenMnbindedgesrrLresultZ flatcountr(vvZflatsumdeltar/r4_jcountsmidZmid_aZmid_brnullcorerr5rrxs!                  "           L      rc Cspt|}t|D]V}t||||}|D]>}|t||} t| r\t|s\td| |||f<q*qdS)Nz'The statistic function returns complex )rrRrKr_create_binned_datarJr$r?) r` bin_numbersrdr stat_funcunique_bin_numbersrebin_mapr4statrrrrWs rWcCsJt}|D] }g||<q tt|D]}||||||fq&|S)zd Create hashmap of bin ids to values in bins key: bin number value: list of binned data )dictrKrrrX)rnrprrerqr4rrrrms  rmc Cs|j\}}t|t}|dg}|dg}|durhtt|jddt}tt|jddt} nt ||krt dt |d|dt|}t|} t |D]V} || d|| dkrt d |dkrd | dd nd || \|| <| | <qt t |D]8} || | | kr|| d || <| | d | | <qt|jtjrd|jnt} t |D]} t|| r|| d || <tj|| | | || d| d|| <n(t|| | || <t || d|| <t|| || <qrt|}|||fS)z Create edge arrays Nr)Zaxiszrange given for z dimensions; z requiredrz!In {}range, start must be <= stopz dimension z of g?rr9)rDrrMrAZ atleast_1drJr0rr1rr?rKrformatZ issubdtyper:ZfloatingZisscalarZlinspacerr8) r]rrr^r_rbrrcZsminZsmaxr4Z edges_dtyperrrrHsN         rHc sj\}}fddt|D}t|D]}||}|dkrJtdtt| d} tdd|f|dktdd|f| t|d| k@d} ||| d8<q*t ||} | S) zECompute the bin number each sample falls into, in each dimension cs(g|] }tdd|f|qS)N)rZdigitizer2rr]rrr6sz _bin_numbers..rz.The smallest edge difference is numerically 0.Nr;r) rDrr0r?rArlog10whereZaroundZravel_multi_index) r]rbrrcr^r_ZsampBinr4Z dedges_mindecimalZon_edgerrrvrrIs&     rI)r rN)r rNF)r rNFN)NN)rKwarningsrrnumpyroperatorr collectionsr__all__r rr rr#r+rrWrmrHrIrrrrsB   / &  :  5