diff options
Diffstat (limited to 'numpy/lib/function_base.py')
| -rw-r--r-- | numpy/lib/function_base.py | 886 |
1 files changed, 49 insertions, 837 deletions
diff --git a/numpy/lib/function_base.py b/numpy/lib/function_base.py index 498853d32..391c47a06 100644 --- a/numpy/lib/function_base.py +++ b/numpy/lib/function_base.py @@ -39,12 +39,14 @@ if sys.version_info[0] < 3: else: import builtins +# needed in this module for compatibility +from numpy.lib.histograms import histogram, histogramdd __all__ = [ 'select', 'piecewise', 'trim_zeros', 'copy', 'iterable', 'percentile', 'diff', 'gradient', 'angle', 'unwrap', 'sort_complex', 'disp', 'flip', 'rot90', 'extract', 'place', 'vectorize', 'asarray_chkfinite', 'average', - 'histogram', 'histogramdd', 'bincount', 'digitize', 'cov', 'corrcoef', + 'bincount', 'digitize', 'cov', 'corrcoef', 'msort', 'median', 'sinc', 'hamming', 'hanning', 'bartlett', 'blackman', 'kaiser', 'trapz', 'i0', 'add_newdoc', 'add_docstring', 'meshgrid', 'delete', 'insert', 'append', 'interp', 'add_newdoc_ufunc' @@ -241,806 +243,6 @@ def iterable(y): return True -def _hist_bin_sqrt(x): - """ - 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. - """ - return x.ptp() / np.sqrt(x.size) - - -def _hist_bin_sturges(x): - """ - 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. - """ - return x.ptp() / (np.log2(x.size) + 1.0) - - -def _hist_bin_rice(x): - """ - 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. - """ - return x.ptp() / (2.0 * x.size ** (1.0 / 3)) - - -def _hist_bin_scott(x): - """ - 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. - """ - return (24.0 * np.pi**0.5 / x.size)**(1.0 / 3.0) * np.std(x) - - -def _hist_bin_doane(x): - """ - 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. - """ - if x.size > 2: - sg1 = np.sqrt(6.0 * (x.size - 2) / ((x.size + 1.0) * (x.size + 3))) - sigma = np.std(x) - if sigma > 0.0: - # These three operations add up to - # g1 = np.mean(((x - np.mean(x)) / sigma)**3) - # but use only one temp array instead of three - temp = x - np.mean(x) - np.true_divide(temp, sigma, temp) - np.power(temp, 3, temp) - g1 = np.mean(temp) - return x.ptp() / (1.0 + np.log2(x.size) + - np.log2(1.0 + np.absolute(g1) / sg1)) - return 0.0 - - -def _hist_bin_fd(x): - """ - 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. - """ - iqr = np.subtract(*np.percentile(x, [75, 25])) - return 2.0 * iqr * x.size ** (-1.0 / 3.0) - - -def _hist_bin_auto(x): - """ - 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 - """ - # There is no need to check for zero here. If ptp is, so is IQR and - # vice versa. Either both are zero or neither one is. - return min(_hist_bin_fd(x), _hist_bin_sturges(x)) - - -# Private dict initialized at module load time -_hist_bin_selectors = {'auto': _hist_bin_auto, - 'doane': _hist_bin_doane, - 'fd': _hist_bin_fd, - 'rice': _hist_bin_rice, - 'scott': _hist_bin_scott, - 'sqrt': _hist_bin_sqrt, - 'sturges': _hist_bin_sturges} - - -def histogram(a, bins=10, range=None, normed=False, weights=None, - density=None): - r""" - 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() - - """ - a = asarray(a) - if weights is not None: - weights = asarray(weights) - if weights.shape != a.shape: - raise ValueError( - 'weights should have the same shape as a.') - weights = weights.ravel() - a = a.ravel() - - # Do not modify the original value of range so we can check for `None` - if range is None: - if a.size == 0: - # handle empty arrays. Can't determine range, so use 0-1. - first_edge, last_edge = 0.0, 1.0 - else: - first_edge, last_edge = a.min() + 0.0, a.max() + 0.0 - else: - first_edge, last_edge = [mi + 0.0 for mi in range] - if first_edge > last_edge: - raise ValueError( - 'max must be larger than min in range parameter.') - if not np.all(np.isfinite([first_edge, last_edge])): - raise ValueError( - 'range parameter must be finite.') - if first_edge == last_edge: - first_edge -= 0.5 - last_edge += 0.5 - - # density overrides the normed keyword - if density is not None: - normed = False - - # parse the overloaded bins argument - n_equal_bins = None - bin_edges = None - - if isinstance(bins, basestring): - bin_name = bins - # if `bins` is a string for an automatic method, - # this will replace it with the number of bins calculated - if bin_name not in _hist_bin_selectors: - raise ValueError( - "{!r} is not a valid estimator for `bins`".format(bin_name)) - if weights is not None: - raise TypeError("Automated estimation of the number of " - "bins is not supported for weighted data") - # Make a reference to `a` - b = a - # Update the reference if the range needs truncation - if range is not None: - keep = (a >= first_edge) - keep &= (a <= last_edge) - if not np.logical_and.reduce(keep): - b = a[keep] - - if b.size == 0: - n_equal_bins = 1 - else: - # Do not call selectors on empty arrays - width = _hist_bin_selectors[bin_name](b) - if width: - n_equal_bins = int(np.ceil((last_edge - first_edge) / width)) - else: - # Width can be zero for some estimators, e.g. FD when - # the IQR of the data is zero. - n_equal_bins = 1 - - elif np.ndim(bins) == 0: - try: - n_equal_bins = operator.index(bins) - except TypeError: - raise TypeError( - '`bins` must be an integer, a string, or an array') - if n_equal_bins < 1: - raise ValueError('`bins` must be positive, when an integer') - - elif np.ndim(bins) == 1: - bin_edges = np.asarray(bins) - if np.any(bin_edges[:-1] > bin_edges[1:]): - raise ValueError( - '`bins` must increase monotonically, when an array') - - else: - raise ValueError('`bins` must be 1d, when an array') - - del bins - - # compute the bins if only the count was specified - if n_equal_bins is not None: - bin_edges = linspace( - first_edge, last_edge, n_equal_bins + 1, endpoint=True) - - # Histogram is an integer or a float array depending on the weights. - if weights is None: - ntype = np.dtype(np.intp) - else: - ntype = weights.dtype - - # We set a block size, as this allows us to iterate over chunks when - # computing histograms, to minimize memory usage. - BLOCK = 65536 - - # The fast path uses bincount, but that only works for certain types - # of weight - simple_weights = ( - weights is None or - np.can_cast(weights.dtype, np.double) or - np.can_cast(weights.dtype, complex) - ) - - if n_equal_bins is not None and simple_weights: - # Fast algorithm for equal bins - # We now convert values of a to bin indices, under the assumption of - # equal bin widths (which is valid here). - - # Initialize empty histogram - n = np.zeros(n_equal_bins, ntype) - - # Pre-compute histogram scaling factor - norm = n_equal_bins / (last_edge - first_edge) - - # We iterate over blocks here for two reasons: the first is that for - # large arrays, it is actually faster (for example for a 10^8 array it - # is 2x as fast) and it results in a memory footprint 3x lower in the - # limit of large arrays. - for i in arange(0, len(a), BLOCK): - tmp_a = a[i:i+BLOCK] - if weights is None: - tmp_w = None - else: - tmp_w = weights[i:i + BLOCK] - - # Only include values in the right range - keep = (tmp_a >= first_edge) - keep &= (tmp_a <= last_edge) - if not np.logical_and.reduce(keep): - tmp_a = tmp_a[keep] - if tmp_w is not None: - tmp_w = tmp_w[keep] - tmp_a_data = tmp_a.astype(float) - tmp_a = tmp_a_data - first_edge - tmp_a *= norm - - # Compute the bin indices, and for values that lie exactly on - # last_edge we need to subtract one - indices = tmp_a.astype(np.intp) - indices[indices == n_equal_bins] -= 1 - - # The index computation is not guaranteed to give exactly - # consistent results within ~1 ULP of the bin edges. - decrement = tmp_a_data < bin_edges[indices] - indices[decrement] -= 1 - # The last bin includes the right edge. The other bins do not. - increment = ((tmp_a_data >= bin_edges[indices + 1]) - & (indices != n_equal_bins - 1)) - indices[increment] += 1 - - # We now compute the histogram using bincount - if ntype.kind == 'c': - n.real += np.bincount(indices, weights=tmp_w.real, - minlength=n_equal_bins) - n.imag += np.bincount(indices, weights=tmp_w.imag, - minlength=n_equal_bins) - else: - n += np.bincount(indices, weights=tmp_w, - minlength=n_equal_bins).astype(ntype) - else: - # Compute via cumulative histogram - cum_n = np.zeros(bin_edges.shape, ntype) - if weights is None: - for i in arange(0, len(a), BLOCK): - sa = sort(a[i:i+BLOCK]) - cum_n += np.r_[sa.searchsorted(bin_edges[:-1], 'left'), - sa.searchsorted(bin_edges[-1], 'right')] - else: - zero = array(0, dtype=ntype) - for i in arange(0, len(a), BLOCK): - tmp_a = a[i:i+BLOCK] - tmp_w = weights[i:i+BLOCK] - sorting_index = np.argsort(tmp_a) - sa = tmp_a[sorting_index] - sw = tmp_w[sorting_index] - cw = np.concatenate(([zero], sw.cumsum())) - bin_index = np.r_[sa.searchsorted(bin_edges[:-1], 'left'), - sa.searchsorted(bin_edges[-1], 'right')] - cum_n += cw[bin_index] - - n = np.diff(cum_n) - - if density: - db = array(np.diff(bin_edges), float) - return n/db/n.sum(), bin_edges - elif normed: - # deprecated, buggy behavior. Remove for NumPy 2.0.0 - db = array(np.diff(bin_edges), float) - return n/(n*db).sum(), bin_edges - else: - return n, bin_edges - - -def histogramdd(sample, bins=10, range=None, normed=False, weights=None): - """ - 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) - - """ - - try: - # Sample is an ND-array. - N, D = sample.shape - except (AttributeError, ValueError): - # Sample is a sequence of 1D arrays. - sample = atleast_2d(sample).T - N, D = sample.shape - - nbin = empty(D, int) - edges = D*[None] - dedges = D*[None] - if weights is not None: - weights = asarray(weights) - - try: - M = len(bins) - if M != D: - raise ValueError( - 'The dimension of bins must be equal to the dimension of the ' - ' sample x.') - except TypeError: - # bins is an integer - bins = D*[bins] - - # Select range for each dimension - # Used only if number of bins is given. - if range is None: - # Handle empty input. Range can't be determined in that case, use 0-1. - if N == 0: - smin = zeros(D) - smax = ones(D) - else: - smin = atleast_1d(array(sample.min(0), float)) - smax = atleast_1d(array(sample.max(0), float)) - else: - if not np.all(np.isfinite(range)): - raise ValueError( - 'range parameter must be finite.') - smin = zeros(D) - smax = zeros(D) - for i in arange(D): - smin[i], smax[i] = range[i] - - # Make sure the bins have a finite width. - for i in arange(len(smin)): - if smin[i] == smax[i]: - smin[i] = smin[i] - .5 - smax[i] = smax[i] + .5 - - # avoid rounding issues for comparisons when dealing with inexact types - if np.issubdtype(sample.dtype, np.inexact): - edge_dt = sample.dtype - else: - edge_dt = float - # Create edge arrays - for i in arange(D): - if isscalar(bins[i]): - if bins[i] < 1: - raise ValueError( - "Element at index %s in `bins` should be a positive " - "integer." % i) - nbin[i] = bins[i] + 2 # +2 for outlier bins - edges[i] = linspace(smin[i], smax[i], nbin[i]-1, dtype=edge_dt) - else: - edges[i] = asarray(bins[i], edge_dt) - nbin[i] = len(edges[i]) + 1 # +1 for outlier bins - dedges[i] = diff(edges[i]) - if np.any(np.asarray(dedges[i]) <= 0): - raise ValueError( - "Found bin edge of size <= 0. Did you specify `bins` with" - "non-monotonic sequence?") - - nbin = asarray(nbin) - - # Handle empty input. - if N == 0: - return np.zeros(nbin-2), edges - - # Compute the bin number each sample falls into. - Ncount = {} - for i in arange(D): - Ncount[i] = 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 arange(D): - # Rounding precision - mindiff = dedges[i].min() - if not np.isinf(mindiff): - decimal = int(-log10(mindiff)) + 6 - # Find which points are on the rightmost edge. - not_smaller_than_edge = (sample[:, i] >= edges[i][-1]) - on_edge = (around(sample[:, i], decimal) == - around(edges[i][-1], decimal)) - # Shift these points one bin to the left. - Ncount[i][nonzero(on_edge & not_smaller_than_edge)[0]] -= 1 - - # Flattened histogram matrix (1D) - # Reshape is used so that overlarge arrays - # will raise an error. - hist = zeros(nbin, float).reshape(-1) - - # Compute the sample indices in the flattened histogram matrix. - ni = nbin.argsort() - xy = zeros(N, int) - for i in arange(0, D-1): - xy += Ncount[ni[i]] * nbin[ni[i+1:]].prod() - xy += Ncount[ni[-1]] - - # Compute the number of repetitions in xy and assign it to the - # flattened histmat. - if len(xy) == 0: - return zeros(nbin-2, int), edges - - flatcount = bincount(xy, weights) - a = arange(len(flatcount)) - hist[a] = flatcount - - # Shape into a proper matrix - hist = hist.reshape(sort(nbin)) - for i in arange(nbin.size): - j = ni.argsort()[i] - hist = hist.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)] - hist = hist[core] - - # Normalize if normed is True - if normed: - s = hist.sum() - for i in arange(D): - shape = ones(D, int) - shape[i] = nbin[i] - 2 - hist = hist / dedges[i].reshape(shape) - hist /= s - - if (hist.shape != nbin - 2).any(): - raise RuntimeError( - "Internal Shape Error") - return hist, edges - - def average(a, axis=None, weights=None, returned=False): """ Compute the weighted average along the specified axis. @@ -2034,7 +1236,8 @@ def interp(x, xp, fp, left=None, right=None, period=None): >>> np.interp(x, xp, fp, period=360) array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75]) - Complex interpolation + Complex interpolation: + >>> x = [1.5, 4.0] >>> xp = [2,3,5] >>> fp = [1.0j, 0, 2+3j] @@ -2333,7 +1536,7 @@ def extract(condition, arr): >>> condition array([[ True, False, False, True], [False, False, True, False], - [False, True, False, False]], dtype=bool) + [False, True, False, False]]) >>> np.extract(condition, arr) array([0, 3, 6, 9]) @@ -2942,7 +2145,7 @@ def cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, .. versionadded:: 1.5 fweights : array_like, int, optional - 1-D array of integer freguency weights; the number of times each + 1-D array of integer frequency weights; the number of times each observation vector should be repeated. .. versionadded:: 1.10 @@ -3993,7 +3196,7 @@ def _ureduce(a, func, **kwargs): Input array or object that can be converted to an array. func : callable Reduction function capable of receiving a single axis argument. - It is is called with `a` as first argument followed by `kwargs`. + It is called with `a` as first argument followed by `kwargs`. kwargs : keyword arguments additional keyword arguments to pass to `func`. @@ -4188,27 +3391,24 @@ def percentile(a, q, axis=None, out=None, ---------- a : array_like Input array or object that can be converted to an array. - q : float in range of [0,100] (or sequence of floats) - Percentile to compute, which must be between 0 and 100 inclusive. - axis : {int, sequence of int, None}, optional + q : array_like of float + Percentile or sequence of percentiles to compute, which must be between + 0 and 100 inclusive. + axis : {int, tuple of int, None}, optional Axis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened - version of the array. A sequence of axes is supported since - version 1.9.0. + version of the array. + + .. versionchanged:: 1.9.0 + A tuple of axes is supported out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional - If True, then allow use of memory of input array `a` - calculations. The input array will be modified by the call to - `percentile`. This will save memory when you do not need to - preserve the contents of the input array. In this case you - should not make any assumptions about the contents of the input - `a` after this function completes -- treat it as undefined. - Default is False. If `a` is not already an array, this parameter - will have no effect as `a` will be converted to an array - internally regardless of the value of this parameter. + If True, then allow the input array `a` to be modified by intermediate + calculations, to save memory. In this case, the contents of the input + `a` after this function completes is undefined. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'} This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points @@ -4243,7 +3443,9 @@ def percentile(a, q, axis=None, out=None, See Also -------- - mean, median, nanpercentile + mean + median : equivalent to ``percentile(..., 50)`` + nanpercentile Notes ----- @@ -4285,8 +3487,17 @@ def percentile(a, q, axis=None, out=None, >>> assert not np.all(a == b) """ - q = array(q, dtype=np.float64, copy=True) - r, k = _ureduce(a, func=_percentile, q=q, axis=axis, out=out, + q = np.true_divide(q, 100.0) # handles the asarray for us too + if not _quantile_is_valid(q): + raise ValueError("Percentiles must be in the range [0, 100]") + return _quantile_unchecked( + a, q, axis, out, overwrite_input, interpolation, keepdims) + + +def _quantile_unchecked(a, q, axis=None, out=None, overwrite_input=False, + interpolation='linear', keepdims=False): + """Assumes that q is in [0, 1], and is an ndarray""" + r, k = _ureduce(a, func=_quantile_ureduce_func, q=q, axis=axis, out=out, overwrite_input=overwrite_input, interpolation=interpolation) if keepdims: @@ -4295,8 +3506,21 @@ def percentile(a, q, axis=None, out=None, return r -def _percentile(a, q, axis=None, out=None, - overwrite_input=False, interpolation='linear', keepdims=False): +def _quantile_is_valid(q): + # avoid expensive reductions, relevant for arrays with < O(1000) elements + if q.ndim == 1 and q.size < 10: + for i in range(q.size): + if q[i] < 0.0 or q[i] > 1.0: + return False + else: + # faster than any() + if np.count_nonzero(q < 0.0) or np.count_nonzero(q > 1.0): + return False + return True + + +def _quantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False, + interpolation='linear', keepdims=False): a = asarray(a) if q.ndim == 0: # Do not allow 0-d arrays because following code fails for scalar @@ -4305,19 +3529,7 @@ def _percentile(a, q, axis=None, out=None, else: zerod = False - # avoid expensive reductions, relevant for arrays with < O(1000) elements - if q.size < 10: - for i in range(q.size): - if q[i] < 0. or q[i] > 100.: - raise ValueError("Percentiles must be in the range [0,100]") - q[i] /= 100. - else: - # faster than any() - if np.count_nonzero(q < 0.) or np.count_nonzero(q > 100.): - raise ValueError("Percentiles must be in the range [0,100]") - q /= 100. - - # prepare a for partioning + # prepare a for partitioning if overwrite_input: if axis is None: ap = a.ravel() |