# scipy/scipy

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 import numpy as np def binned_statistic(x, values, statistic='mean', bins=10, range=None): """ Compute a binned statistic for a set 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 within each bin. Parameters ---------- x : array_like A sequence of values to be binned. values : array_like The values on which the statistic will be computed. This must be the same shape as x. 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. * 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. range : (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. binnumber : ndarray, 1d, int This assigns to each observation an integer that represents the bin in which this observation falls. Array has the same length as values. 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)``. 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. Examples -------- >>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean', ... bins=3) (array([ 1., 2., 4.]), array([ 1., 2., 3., 4.]), array([1, 2, 1, 2, 3])) >>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean', bins=3) (array([ 1., 2., 4.]), array([ 1., 2., 3., 4.]), array([1, 2, 1, 2, 3])) See Also -------- np.histogram, binned_statistic_2d, binned_statistic_dd """ try: N = len(bins) except TypeError: N = 1 if N != 1: bins = [np.asarray(bins, float)] medians, edges, xy = binned_statistic_dd([x], values, statistic, bins, range) return medians, edges[0], xy def binned_statistic_2d(x, y, values, statistic='mean', bins=10, range=None): """ Compute a bidimensional binned statistic for a set 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 within each bin. Parameters ---------- x : array_like A sequence of values to be binned along the first dimension. y : array_like A sequence of values to be binned along the second dimension. values : array_like The values on which the statistic will be computed. This must be the same shape as x. 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. * 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_edges=y_edges=bins), * the bin edges in each dimension (x_edges, y_edges = bins). range : array_like, shape(2,2), 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. Returns ------- statistic : ndarray, shape(nx, ny) The values of the selected statistic in each two-dimensional bin xedges : ndarray, shape(nx + 1,) The bin edges along the first dimension. yedges : ndarray, shape(ny + 1,) The bin edges along the second dimension. binnumber : ndarray, 1d, int This assigns to each observation an integer that represents the bin in which this observation falls. Array has the same length as values. See Also -------- np.histogram2d, binned_statistic, binned_statistic_dd """ # This code is based on np.histogram2d try: N = len(bins) except TypeError: N = 1 if N != 1 and N != 2: xedges = yedges = np.asarray(bins, float) bins = [xedges, yedges] medians, edges, xy = binned_statistic_dd([x, y], values, statistic, bins, range) return medians, edges[0], edges[1], xy def binned_statistic_dd(sample, values, statistic='mean', bins=10, range=None): """ 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 D arrays of length N, or as an (N,D) array. values : array_like The values on which the statistic will be computed. This must be the same shape as x. 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. * 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 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 explicitely in `bins`. Defaults to the minimum and maximum values along each dimension. Returns ------- statistic : ndarray, shape(nx1, nx2, nx3,...) The values of the selected statistic in each two-dimensional bin edges : list of ndarrays A list of D arrays describing the (nxi + 1) bin edges for each dimension binnumber : ndarray, 1d, int This assigns to each observation an integer that represents the bin in which this observation falls. Array has the same length as values. See Also -------- np.histogramdd, binned_statistic, binned_statistic_2d """ if type(statistic) == str: if statistic not in ['mean', 'median', 'count', 'sum', 'std']: raise ValueError('unrecognized statistic "%s"' % statistic) elif callable(statistic): pass else: raise ValueError("statistic not understood") # This code is based on np.histogramdd try: # Sample is an ND-array. N, D = sample.shape except (AttributeError, ValueError): # Sample is a sequence of 1D arrays. sample = np.atleast_2d(sample).T N, D = sample.shape nbin = np.empty(D, int) edges = D * [None] dedges = D * [None] try: M = len(bins) if M != D: raise AttributeError('The dimension of bins must be equal ' 'to the dimension of the sample x.') except TypeError: bins = D * [bins] # Select range for each dimension # Used only if number of bins is given. if range is None: smin = np.atleast_1d(np.array(sample.min(0), float)) smax = np.atleast_1d(np.array(sample.max(0), float)) else: smin = np.zeros(D) smax = np.zeros(D) for i in np.arange(D): smin[i], smax[i] = range[i] # Make sure the bins have a finite width. for i in np.arange(len(smin)): if smin[i] == smax[i]: smin[i] = smin[i] - .5 smax[i] = smax[i] + .5 # Create edge arrays for i in np.arange(D): if np.isscalar(bins[i]): nbin[i] = bins[i] + 2 # +2 for outlier bins edges[i] = np.linspace(smin[i], smax[i], nbin[i] - 1) else: edges[i] = np.asarray(bins[i], float) nbin[i] = len(edges[i]) + 1 # +1 for outlier bins dedges[i] = np.diff(edges[i]) nbin = np.asarray(nbin) # Compute the bin number each sample falls into. Ncount = {} for i in np.arange(D): Ncount[i] = np.digitize(sample[:, i], edges[i]) # Using digitize, values that fall on an edge are put in the right bin. # For the rightmost bin, we want values equal to the right # edge to be counted in the last bin, and not as an outlier. for i in np.arange(D): # Rounding precision decimal = int(-np.log10(dedges[i].min())) + 6 # Find which points are on the rightmost edge. on_edge = np.where(np.around(sample[:, i], decimal) == np.around(edges[i][-1], decimal))[0] # Shift these points one bin to the left. Ncount[i][on_edge] -= 1 # Compute the sample indices in the flattened statistic matrix. ni = nbin.argsort() xy = np.zeros(N, int) for i in np.arange(0, D - 1): xy += Ncount[ni[i]] * nbin[ni[i + 1:]].prod() xy += Ncount[ni[-1]] result = np.empty(nbin.prod(), float) if statistic == 'mean': result.fill(np.nan) flatcount = np.bincount(xy, None) flatsum = np.bincount(xy, values) a = flatcount.nonzero() result[a] = flatsum[a] / flatcount[a] elif statistic == 'std': result.fill(0) flatcount = np.bincount(xy, None) flatsum = np.bincount(xy, values) flatsum2 = np.bincount(xy, values ** 2) a = flatcount.nonzero() result[a] = np.sqrt(flatsum2[a] / flatcount[a] - (flatsum[a] / flatcount[a]) ** 2) elif statistic == 'count': result.fill(0) flatcount = np.bincount(xy, None) a = np.arange(len(flatcount)) result[a] = flatcount elif statistic == 'sum': result.fill(0) flatsum = np.bincount(xy, values) a = np.arange(len(flatsum)) result[a] = flatsum elif statistic == 'median': result.fill(np.nan) for i in np.unique(xy): result[i] = np.median(values[xy == i]) elif callable(statistic): old = np.seterr(invalid='ignore') try: null = statistic([]) except: null = np.nan np.seterr(**old) result.fill(null) for i in np.unique(xy): result[i] = statistic(values[xy == i]) # Shape into a proper matrix result = result.reshape(np.sort(nbin)) for i in np.arange(nbin.size): j = ni.argsort()[i] result = result.swapaxes(i, j) ni[i], ni[j] = ni[j], ni[i] # Remove outliers (indices 0 and -1 for each dimension). core = D * [slice(1, -1)] result = result[core] if (result.shape != nbin - 2).any(): raise RuntimeError('Internal Shape Error') return result, edges, xy
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