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diff --git a/venv/lib/python3.9/site-packages/numpy/ma/extras.py b/venv/lib/python3.9/site-packages/numpy/ma/extras.py new file mode 100644 index 00000000..41bce0f2 --- /dev/null +++ b/venv/lib/python3.9/site-packages/numpy/ma/extras.py @@ -0,0 +1,2045 @@ +""" +Masked arrays add-ons. + +A collection of utilities for `numpy.ma`. + +:author: Pierre Gerard-Marchant +:contact: pierregm_at_uga_dot_edu +:version: $Id: extras.py 3473 2007-10-29 15:18:13Z jarrod.millman $ + +""" +__all__ = [ + 'apply_along_axis', 'apply_over_axes', 'atleast_1d', 'atleast_2d', + 'atleast_3d', 'average', 'clump_masked', 'clump_unmasked', 'column_stack', + 'compress_cols', 'compress_nd', 'compress_rowcols', 'compress_rows', + 'count_masked', 'corrcoef', 'cov', 'diagflat', 'dot', 'dstack', 'ediff1d', + 'flatnotmasked_contiguous', 'flatnotmasked_edges', 'hsplit', 'hstack', + 'isin', 'in1d', 'intersect1d', 'mask_cols', 'mask_rowcols', 'mask_rows', + 'masked_all', 'masked_all_like', 'median', 'mr_', 'ndenumerate', + 'notmasked_contiguous', 'notmasked_edges', 'polyfit', 'row_stack', + 'setdiff1d', 'setxor1d', 'stack', 'unique', 'union1d', 'vander', 'vstack', + ] + +import itertools +import warnings + +from . import core as ma +from .core import ( + MaskedArray, MAError, add, array, asarray, concatenate, filled, count, + getmask, getmaskarray, make_mask_descr, masked, masked_array, mask_or, + nomask, ones, sort, zeros, getdata, get_masked_subclass, dot, + mask_rowcols + ) + +import numpy as np +from numpy import ndarray, array as nxarray +from numpy.core.multiarray import normalize_axis_index +from numpy.core.numeric import normalize_axis_tuple +from numpy.lib.function_base import _ureduce +from numpy.lib.index_tricks import AxisConcatenator + + +def issequence(seq): + """ + Is seq a sequence (ndarray, list or tuple)? + + """ + return isinstance(seq, (ndarray, tuple, list)) + + +def count_masked(arr, axis=None): + """ + Count the number of masked elements along the given axis. + + Parameters + ---------- + arr : array_like + An array with (possibly) masked elements. + axis : int, optional + Axis along which to count. If None (default), a flattened + version of the array is used. + + Returns + ------- + count : int, ndarray + The total number of masked elements (axis=None) or the number + of masked elements along each slice of the given axis. + + See Also + -------- + MaskedArray.count : Count non-masked elements. + + Examples + -------- + >>> import numpy.ma as ma + >>> a = np.arange(9).reshape((3,3)) + >>> a = ma.array(a) + >>> a[1, 0] = ma.masked + >>> a[1, 2] = ma.masked + >>> a[2, 1] = ma.masked + >>> a + masked_array( + data=[[0, 1, 2], + [--, 4, --], + [6, --, 8]], + mask=[[False, False, False], + [ True, False, True], + [False, True, False]], + fill_value=999999) + >>> ma.count_masked(a) + 3 + + When the `axis` keyword is used an array is returned. + + >>> ma.count_masked(a, axis=0) + array([1, 1, 1]) + >>> ma.count_masked(a, axis=1) + array([0, 2, 1]) + + """ + m = getmaskarray(arr) + return m.sum(axis) + + +def masked_all(shape, dtype=float): + """ + Empty masked array with all elements masked. + + Return an empty masked array of the given shape and dtype, where all the + data are masked. + + Parameters + ---------- + shape : int or tuple of ints + Shape of the required MaskedArray, e.g., ``(2, 3)`` or ``2``. + dtype : dtype, optional + Data type of the output. + + Returns + ------- + a : MaskedArray + A masked array with all data masked. + + See Also + -------- + masked_all_like : Empty masked array modelled on an existing array. + + Examples + -------- + >>> import numpy.ma as ma + >>> ma.masked_all((3, 3)) + masked_array( + data=[[--, --, --], + [--, --, --], + [--, --, --]], + mask=[[ True, True, True], + [ True, True, True], + [ True, True, True]], + fill_value=1e+20, + dtype=float64) + + The `dtype` parameter defines the underlying data type. + + >>> a = ma.masked_all((3, 3)) + >>> a.dtype + dtype('float64') + >>> a = ma.masked_all((3, 3), dtype=np.int32) + >>> a.dtype + dtype('int32') + + """ + a = masked_array(np.empty(shape, dtype), + mask=np.ones(shape, make_mask_descr(dtype))) + return a + + +def masked_all_like(arr): + """ + Empty masked array with the properties of an existing array. + + Return an empty masked array of the same shape and dtype as + the array `arr`, where all the data are masked. + + Parameters + ---------- + arr : ndarray + An array describing the shape and dtype of the required MaskedArray. + + Returns + ------- + a : MaskedArray + A masked array with all data masked. + + Raises + ------ + AttributeError + If `arr` doesn't have a shape attribute (i.e. not an ndarray) + + See Also + -------- + masked_all : Empty masked array with all elements masked. + + Examples + -------- + >>> import numpy.ma as ma + >>> arr = np.zeros((2, 3), dtype=np.float32) + >>> arr + array([[0., 0., 0.], + [0., 0., 0.]], dtype=float32) + >>> ma.masked_all_like(arr) + masked_array( + data=[[--, --, --], + [--, --, --]], + mask=[[ True, True, True], + [ True, True, True]], + fill_value=1e+20, + dtype=float32) + + The dtype of the masked array matches the dtype of `arr`. + + >>> arr.dtype + dtype('float32') + >>> ma.masked_all_like(arr).dtype + dtype('float32') + + """ + a = np.empty_like(arr).view(MaskedArray) + a._mask = np.ones(a.shape, dtype=make_mask_descr(a.dtype)) + return a + + +#####-------------------------------------------------------------------------- +#---- --- Standard functions --- +#####-------------------------------------------------------------------------- +class _fromnxfunction: + """ + Defines a wrapper to adapt NumPy functions to masked arrays. + + + An instance of `_fromnxfunction` can be called with the same parameters + as the wrapped NumPy function. The docstring of `newfunc` is adapted from + the wrapped function as well, see `getdoc`. + + This class should not be used directly. Instead, one of its extensions that + provides support for a specific type of input should be used. + + Parameters + ---------- + funcname : str + The name of the function to be adapted. The function should be + in the NumPy namespace (i.e. ``np.funcname``). + + """ + + def __init__(self, funcname): + self.__name__ = funcname + self.__doc__ = self.getdoc() + + def getdoc(self): + """ + Retrieve the docstring and signature from the function. + + The ``__doc__`` attribute of the function is used as the docstring for + the new masked array version of the function. A note on application + of the function to the mask is appended. + + Parameters + ---------- + None + + """ + npfunc = getattr(np, self.__name__, None) + doc = getattr(npfunc, '__doc__', None) + if doc: + sig = self.__name__ + ma.get_object_signature(npfunc) + doc = ma.doc_note(doc, "The function is applied to both the _data " + "and the _mask, if any.") + return '\n\n'.join((sig, doc)) + return + + def __call__(self, *args, **params): + pass + + +class _fromnxfunction_single(_fromnxfunction): + """ + A version of `_fromnxfunction` that is called with a single array + argument followed by auxiliary args that are passed verbatim for + both the data and mask calls. + """ + def __call__(self, x, *args, **params): + func = getattr(np, self.__name__) + if isinstance(x, ndarray): + _d = func(x.__array__(), *args, **params) + _m = func(getmaskarray(x), *args, **params) + return masked_array(_d, mask=_m) + else: + _d = func(np.asarray(x), *args, **params) + _m = func(getmaskarray(x), *args, **params) + return masked_array(_d, mask=_m) + + +class _fromnxfunction_seq(_fromnxfunction): + """ + A version of `_fromnxfunction` that is called with a single sequence + of arrays followed by auxiliary args that are passed verbatim for + both the data and mask calls. + """ + def __call__(self, x, *args, **params): + func = getattr(np, self.__name__) + _d = func(tuple([np.asarray(a) for a in x]), *args, **params) + _m = func(tuple([getmaskarray(a) for a in x]), *args, **params) + return masked_array(_d, mask=_m) + + +class _fromnxfunction_args(_fromnxfunction): + """ + A version of `_fromnxfunction` that is called with multiple array + arguments. The first non-array-like input marks the beginning of the + arguments that are passed verbatim for both the data and mask calls. + Array arguments are processed independently and the results are + returned in a list. If only one array is found, the return value is + just the processed array instead of a list. + """ + def __call__(self, *args, **params): + func = getattr(np, self.__name__) + arrays = [] + args = list(args) + while len(args) > 0 and issequence(args[0]): + arrays.append(args.pop(0)) + res = [] + for x in arrays: + _d = func(np.asarray(x), *args, **params) + _m = func(getmaskarray(x), *args, **params) + res.append(masked_array(_d, mask=_m)) + if len(arrays) == 1: + return res[0] + return res + + +class _fromnxfunction_allargs(_fromnxfunction): + """ + A version of `_fromnxfunction` that is called with multiple array + arguments. Similar to `_fromnxfunction_args` except that all args + are converted to arrays even if they are not so already. This makes + it possible to process scalars as 1-D arrays. Only keyword arguments + are passed through verbatim for the data and mask calls. Arrays + arguments are processed independently and the results are returned + in a list. If only one arg is present, the return value is just the + processed array instead of a list. + """ + def __call__(self, *args, **params): + func = getattr(np, self.__name__) + res = [] + for x in args: + _d = func(np.asarray(x), **params) + _m = func(getmaskarray(x), **params) + res.append(masked_array(_d, mask=_m)) + if len(args) == 1: + return res[0] + return res + + +atleast_1d = _fromnxfunction_allargs('atleast_1d') +atleast_2d = _fromnxfunction_allargs('atleast_2d') +atleast_3d = _fromnxfunction_allargs('atleast_3d') + +vstack = row_stack = _fromnxfunction_seq('vstack') +hstack = _fromnxfunction_seq('hstack') +column_stack = _fromnxfunction_seq('column_stack') +dstack = _fromnxfunction_seq('dstack') +stack = _fromnxfunction_seq('stack') + +hsplit = _fromnxfunction_single('hsplit') + +diagflat = _fromnxfunction_single('diagflat') + + +#####-------------------------------------------------------------------------- +#---- +#####-------------------------------------------------------------------------- +def flatten_inplace(seq): + """Flatten a sequence in place.""" + k = 0 + while (k != len(seq)): + while hasattr(seq[k], '__iter__'): + seq[k:(k + 1)] = seq[k] + k += 1 + return seq + + +def apply_along_axis(func1d, axis, arr, *args, **kwargs): + """ + (This docstring should be overwritten) + """ + arr = array(arr, copy=False, subok=True) + nd = arr.ndim + axis = normalize_axis_index(axis, nd) + ind = [0] * (nd - 1) + i = np.zeros(nd, 'O') + indlist = list(range(nd)) + indlist.remove(axis) + i[axis] = slice(None, None) + outshape = np.asarray(arr.shape).take(indlist) + i.put(indlist, ind) + res = func1d(arr[tuple(i.tolist())], *args, **kwargs) + # if res is a number, then we have a smaller output array + asscalar = np.isscalar(res) + if not asscalar: + try: + len(res) + except TypeError: + asscalar = True + # Note: we shouldn't set the dtype of the output from the first result + # so we force the type to object, and build a list of dtypes. We'll + # just take the largest, to avoid some downcasting + dtypes = [] + if asscalar: + dtypes.append(np.asarray(res).dtype) + outarr = zeros(outshape, object) + outarr[tuple(ind)] = res + Ntot = np.product(outshape) + k = 1 + while k < Ntot: + # increment the index + ind[-1] += 1 + n = -1 + while (ind[n] >= outshape[n]) and (n > (1 - nd)): + ind[n - 1] += 1 + ind[n] = 0 + n -= 1 + i.put(indlist, ind) + res = func1d(arr[tuple(i.tolist())], *args, **kwargs) + outarr[tuple(ind)] = res + dtypes.append(asarray(res).dtype) + k += 1 + else: + res = array(res, copy=False, subok=True) + j = i.copy() + j[axis] = ([slice(None, None)] * res.ndim) + j.put(indlist, ind) + Ntot = np.product(outshape) + holdshape = outshape + outshape = list(arr.shape) + outshape[axis] = res.shape + dtypes.append(asarray(res).dtype) + outshape = flatten_inplace(outshape) + outarr = zeros(outshape, object) + outarr[tuple(flatten_inplace(j.tolist()))] = res + k = 1 + while k < Ntot: + # increment the index + ind[-1] += 1 + n = -1 + while (ind[n] >= holdshape[n]) and (n > (1 - nd)): + ind[n - 1] += 1 + ind[n] = 0 + n -= 1 + i.put(indlist, ind) + j.put(indlist, ind) + res = func1d(arr[tuple(i.tolist())], *args, **kwargs) + outarr[tuple(flatten_inplace(j.tolist()))] = res + dtypes.append(asarray(res).dtype) + k += 1 + max_dtypes = np.dtype(np.asarray(dtypes).max()) + if not hasattr(arr, '_mask'): + result = np.asarray(outarr, dtype=max_dtypes) + else: + result = asarray(outarr, dtype=max_dtypes) + result.fill_value = ma.default_fill_value(result) + return result +apply_along_axis.__doc__ = np.apply_along_axis.__doc__ + + +def apply_over_axes(func, a, axes): + """ + (This docstring will be overwritten) + """ + val = asarray(a) + N = a.ndim + if array(axes).ndim == 0: + axes = (axes,) + for axis in axes: + if axis < 0: + axis = N + axis + args = (val, axis) + res = func(*args) + if res.ndim == val.ndim: + val = res + else: + res = ma.expand_dims(res, axis) + if res.ndim == val.ndim: + val = res + else: + raise ValueError("function is not returning " + "an array of the correct shape") + return val + + +if apply_over_axes.__doc__ is not None: + apply_over_axes.__doc__ = np.apply_over_axes.__doc__[ + :np.apply_over_axes.__doc__.find('Notes')].rstrip() + \ + """ + + Examples + -------- + >>> a = np.ma.arange(24).reshape(2,3,4) + >>> a[:,0,1] = np.ma.masked + >>> a[:,1,:] = np.ma.masked + >>> a + masked_array( + data=[[[0, --, 2, 3], + [--, --, --, --], + [8, 9, 10, 11]], + [[12, --, 14, 15], + [--, --, --, --], + [20, 21, 22, 23]]], + mask=[[[False, True, False, False], + [ True, True, True, True], + [False, False, False, False]], + [[False, True, False, False], + [ True, True, True, True], + [False, False, False, False]]], + fill_value=999999) + >>> np.ma.apply_over_axes(np.ma.sum, a, [0,2]) + masked_array( + data=[[[46], + [--], + [124]]], + mask=[[[False], + [ True], + [False]]], + fill_value=999999) + + Tuple axis arguments to ufuncs are equivalent: + + >>> np.ma.sum(a, axis=(0,2)).reshape((1,-1,1)) + masked_array( + data=[[[46], + [--], + [124]]], + mask=[[[False], + [ True], + [False]]], + fill_value=999999) + """ + + +def average(a, axis=None, weights=None, returned=False, *, + keepdims=np._NoValue): + """ + Return the weighted average of array over the given axis. + + Parameters + ---------- + a : array_like + Data to be averaged. + Masked entries are not taken into account in the computation. + axis : int, optional + Axis along which to average `a`. If None, averaging is done over + the flattened array. + weights : array_like, optional + The importance that each element has in the computation of the average. + 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. The 1-D calculation is:: + + avg = sum(a * weights) / sum(weights) + + The only constraint on `weights` is that `sum(weights)` must not be 0. + returned : bool, optional + Flag indicating whether a tuple ``(result, sum of weights)`` + should be returned as output (True), or just the result (False). + Default is False. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the original `a`. + *Note:* `keepdims` will not work with instances of `numpy.matrix` + or other classes whose methods do not support `keepdims`. + + .. versionadded:: 1.23.0 + + Returns + ------- + average, [sum_of_weights] : (tuple of) scalar or MaskedArray + 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 `np.float64` + if `a` is of integer type and floats smaller than `float64`, or the + input data-type, otherwise. If returned, `sum_of_weights` is always + `float64`. + + Examples + -------- + >>> a = np.ma.array([1., 2., 3., 4.], mask=[False, False, True, True]) + >>> np.ma.average(a, weights=[3, 1, 0, 0]) + 1.25 + + >>> x = np.ma.arange(6.).reshape(3, 2) + >>> x + masked_array( + data=[[0., 1.], + [2., 3.], + [4., 5.]], + mask=False, + fill_value=1e+20) + >>> avg, sumweights = np.ma.average(x, axis=0, weights=[1, 2, 3], + ... returned=True) + >>> avg + masked_array(data=[2.6666666666666665, 3.6666666666666665], + mask=[False, False], + fill_value=1e+20) + + With ``keepdims=True``, the following result has shape (3, 1). + + >>> np.ma.average(x, axis=1, keepdims=True) + masked_array( + data=[[0.5], + [2.5], + [4.5]], + mask=False, + fill_value=1e+20) + """ + a = asarray(a) + m = getmask(a) + + # inspired by 'average' in numpy/lib/function_base.py + + if keepdims is np._NoValue: + # Don't pass on the keepdims argument if one wasn't given. + keepdims_kw = {} + else: + keepdims_kw = {'keepdims': keepdims} + + if weights is None: + avg = a.mean(axis, **keepdims_kw) + scl = avg.dtype.type(a.count(axis)) + else: + wgt = asarray(weights) + + if issubclass(a.dtype.type, (np.integer, np.bool_)): + result_dtype = np.result_type(a.dtype, wgt.dtype, 'f8') + else: + result_dtype = np.result_type(a.dtype, wgt.dtype) + + # Sanity checks + if a.shape != wgt.shape: + if axis is None: + raise TypeError( + "Axis must be specified when shapes of a and weights " + "differ.") + if wgt.ndim != 1: + raise TypeError( + "1D weights expected when shapes of a and weights differ.") + if wgt.shape[0] != a.shape[axis]: + raise ValueError( + "Length of weights not compatible with specified axis.") + + # setup wgt to broadcast along axis + wgt = np.broadcast_to(wgt, (a.ndim-1)*(1,) + wgt.shape, subok=True) + wgt = wgt.swapaxes(-1, axis) + + if m is not nomask: + wgt = wgt*(~a.mask) + wgt.mask |= a.mask + + scl = wgt.sum(axis=axis, dtype=result_dtype, **keepdims_kw) + avg = np.multiply(a, wgt, + dtype=result_dtype).sum(axis, **keepdims_kw) / scl + + if returned: + if scl.shape != avg.shape: + scl = np.broadcast_to(scl, avg.shape).copy() + return avg, scl + else: + return avg + + +def median(a, axis=None, out=None, overwrite_input=False, keepdims=False): + """ + Compute the median along the specified axis. + + Returns the median of the array elements. + + Parameters + ---------- + a : array_like + Input array or object that can be converted to an array. + axis : int, optional + Axis along which the medians are computed. The default (None) is + to compute the median along a flattened version of the array. + 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 will be cast if necessary. + overwrite_input : bool, optional + If True, then allow use of memory of input array (a) for + calculations. The input array will be modified by the call to + median. This will save memory when you do not need to preserve + the contents of the input array. Treat the input as undefined, + but it will probably be fully or partially sorted. Default is + False. Note that, if `overwrite_input` is True, and the input + is not already an `ndarray`, an error will be raised. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the input array. + + .. versionadded:: 1.10.0 + + Returns + ------- + median : ndarray + A new array holding the result is returned unless out is + specified, in which case a reference to out is returned. + Return data-type is `float64` for integers and floats smaller than + `float64`, or the input data-type, otherwise. + + See Also + -------- + mean + + Notes + ----- + Given a vector ``V`` with ``N`` non masked values, the median of ``V`` + is the middle value of a sorted copy of ``V`` (``Vs``) - i.e. + ``Vs[(N-1)/2]``, when ``N`` is odd, or ``{Vs[N/2 - 1] + Vs[N/2]}/2`` + when ``N`` is even. + + Examples + -------- + >>> x = np.ma.array(np.arange(8), mask=[0]*4 + [1]*4) + >>> np.ma.median(x) + 1.5 + + >>> x = np.ma.array(np.arange(10).reshape(2, 5), mask=[0]*6 + [1]*4) + >>> np.ma.median(x) + 2.5 + >>> np.ma.median(x, axis=-1, overwrite_input=True) + masked_array(data=[2.0, 5.0], + mask=[False, False], + fill_value=1e+20) + + """ + if not hasattr(a, 'mask'): + m = np.median(getdata(a, subok=True), axis=axis, + out=out, overwrite_input=overwrite_input, + keepdims=keepdims) + if isinstance(m, np.ndarray) and 1 <= m.ndim: + return masked_array(m, copy=False) + else: + return m + + return _ureduce(a, func=_median, keepdims=keepdims, axis=axis, out=out, + overwrite_input=overwrite_input) + + +def _median(a, axis=None, out=None, overwrite_input=False): + # when an unmasked NaN is present return it, so we need to sort the NaN + # values behind the mask + if np.issubdtype(a.dtype, np.inexact): + fill_value = np.inf + else: + fill_value = None + if overwrite_input: + if axis is None: + asorted = a.ravel() + asorted.sort(fill_value=fill_value) + else: + a.sort(axis=axis, fill_value=fill_value) + asorted = a + else: + asorted = sort(a, axis=axis, fill_value=fill_value) + + if axis is None: + axis = 0 + else: + axis = normalize_axis_index(axis, asorted.ndim) + + if asorted.shape[axis] == 0: + # for empty axis integer indices fail so use slicing to get same result + # as median (which is mean of empty slice = nan) + indexer = [slice(None)] * asorted.ndim + indexer[axis] = slice(0, 0) + indexer = tuple(indexer) + return np.ma.mean(asorted[indexer], axis=axis, out=out) + + if asorted.ndim == 1: + idx, odd = divmod(count(asorted), 2) + mid = asorted[idx + odd - 1:idx + 1] + if np.issubdtype(asorted.dtype, np.inexact) and asorted.size > 0: + # avoid inf / x = masked + s = mid.sum(out=out) + if not odd: + s = np.true_divide(s, 2., casting='safe', out=out) + s = np.lib.utils._median_nancheck(asorted, s, axis) + else: + s = mid.mean(out=out) + + # if result is masked either the input contained enough + # minimum_fill_value so that it would be the median or all values + # masked + if np.ma.is_masked(s) and not np.all(asorted.mask): + return np.ma.minimum_fill_value(asorted) + return s + + counts = count(asorted, axis=axis, keepdims=True) + h = counts // 2 + + # duplicate high if odd number of elements so mean does nothing + odd = counts % 2 == 1 + l = np.where(odd, h, h-1) + + lh = np.concatenate([l,h], axis=axis) + + # get low and high median + low_high = np.take_along_axis(asorted, lh, axis=axis) + + def replace_masked(s): + # Replace masked entries with minimum_full_value unless it all values + # are masked. This is required as the sort order of values equal or + # larger than the fill value is undefined and a valid value placed + # elsewhere, e.g. [4, --, inf]. + if np.ma.is_masked(s): + rep = (~np.all(asorted.mask, axis=axis, keepdims=True)) & s.mask + s.data[rep] = np.ma.minimum_fill_value(asorted) + s.mask[rep] = False + + replace_masked(low_high) + + if np.issubdtype(asorted.dtype, np.inexact): + # avoid inf / x = masked + s = np.ma.sum(low_high, axis=axis, out=out) + np.true_divide(s.data, 2., casting='unsafe', out=s.data) + + s = np.lib.utils._median_nancheck(asorted, s, axis) + else: + s = np.ma.mean(low_high, axis=axis, out=out) + + return s + + +def compress_nd(x, axis=None): + """Suppress slices from multiple dimensions which contain masked values. + + Parameters + ---------- + x : array_like, MaskedArray + The array to operate on. If not a MaskedArray instance (or if no array + elements are masked), `x` is interpreted as a MaskedArray with `mask` + set to `nomask`. + axis : tuple of ints or int, optional + Which dimensions to suppress slices from can be configured with this + parameter. + - If axis is a tuple of ints, those are the axes to suppress slices from. + - If axis is an int, then that is the only axis to suppress slices from. + - If axis is None, all axis are selected. + + Returns + ------- + compress_array : ndarray + The compressed array. + """ + x = asarray(x) + m = getmask(x) + # Set axis to tuple of ints + if axis is None: + axis = tuple(range(x.ndim)) + else: + axis = normalize_axis_tuple(axis, x.ndim) + + # Nothing is masked: return x + if m is nomask or not m.any(): + return x._data + # All is masked: return empty + if m.all(): + return nxarray([]) + # Filter elements through boolean indexing + data = x._data + for ax in axis: + axes = tuple(list(range(ax)) + list(range(ax + 1, x.ndim))) + data = data[(slice(None),)*ax + (~m.any(axis=axes),)] + return data + + +def compress_rowcols(x, axis=None): + """ + Suppress the rows and/or columns of a 2-D array that contain + masked values. + + The suppression behavior is selected with the `axis` parameter. + + - If axis is None, both rows and columns are suppressed. + - If axis is 0, only rows are suppressed. + - If axis is 1 or -1, only columns are suppressed. + + Parameters + ---------- + x : array_like, MaskedArray + The array to operate on. If not a MaskedArray instance (or if no array + elements are masked), `x` is interpreted as a MaskedArray with + `mask` set to `nomask`. Must be a 2D array. + axis : int, optional + Axis along which to perform the operation. Default is None. + + Returns + ------- + compressed_array : ndarray + The compressed array. + + Examples + -------- + >>> x = np.ma.array(np.arange(9).reshape(3, 3), mask=[[1, 0, 0], + ... [1, 0, 0], + ... [0, 0, 0]]) + >>> x + masked_array( + data=[[--, 1, 2], + [--, 4, 5], + [6, 7, 8]], + mask=[[ True, False, False], + [ True, False, False], + [False, False, False]], + fill_value=999999) + + >>> np.ma.compress_rowcols(x) + array([[7, 8]]) + >>> np.ma.compress_rowcols(x, 0) + array([[6, 7, 8]]) + >>> np.ma.compress_rowcols(x, 1) + array([[1, 2], + [4, 5], + [7, 8]]) + + """ + if asarray(x).ndim != 2: + raise NotImplementedError("compress_rowcols works for 2D arrays only.") + return compress_nd(x, axis=axis) + + +def compress_rows(a): + """ + Suppress whole rows of a 2-D array that contain masked values. + + This is equivalent to ``np.ma.compress_rowcols(a, 0)``, see + `compress_rowcols` for details. + + See Also + -------- + compress_rowcols + + """ + a = asarray(a) + if a.ndim != 2: + raise NotImplementedError("compress_rows works for 2D arrays only.") + return compress_rowcols(a, 0) + + +def compress_cols(a): + """ + Suppress whole columns of a 2-D array that contain masked values. + + This is equivalent to ``np.ma.compress_rowcols(a, 1)``, see + `compress_rowcols` for details. + + See Also + -------- + compress_rowcols + + """ + a = asarray(a) + if a.ndim != 2: + raise NotImplementedError("compress_cols works for 2D arrays only.") + return compress_rowcols(a, 1) + + +def mask_rows(a, axis=np._NoValue): + """ + Mask rows of a 2D array that contain masked values. + + This function is a shortcut to ``mask_rowcols`` with `axis` equal to 0. + + See Also + -------- + mask_rowcols : Mask rows and/or columns of a 2D array. + masked_where : Mask where a condition is met. + + Examples + -------- + >>> import numpy.ma as ma + >>> a = np.zeros((3, 3), dtype=int) + >>> a[1, 1] = 1 + >>> a + array([[0, 0, 0], + [0, 1, 0], + [0, 0, 0]]) + >>> a = ma.masked_equal(a, 1) + >>> a + masked_array( + data=[[0, 0, 0], + [0, --, 0], + [0, 0, 0]], + mask=[[False, False, False], + [False, True, False], + [False, False, False]], + fill_value=1) + + >>> ma.mask_rows(a) + masked_array( + data=[[0, 0, 0], + [--, --, --], + [0, 0, 0]], + mask=[[False, False, False], + [ True, True, True], + [False, False, False]], + fill_value=1) + + """ + if axis is not np._NoValue: + # remove the axis argument when this deprecation expires + # NumPy 1.18.0, 2019-11-28 + warnings.warn( + "The axis argument has always been ignored, in future passing it " + "will raise TypeError", DeprecationWarning, stacklevel=2) + return mask_rowcols(a, 0) + + +def mask_cols(a, axis=np._NoValue): + """ + Mask columns of a 2D array that contain masked values. + + This function is a shortcut to ``mask_rowcols`` with `axis` equal to 1. + + See Also + -------- + mask_rowcols : Mask rows and/or columns of a 2D array. + masked_where : Mask where a condition is met. + + Examples + -------- + >>> import numpy.ma as ma + >>> a = np.zeros((3, 3), dtype=int) + >>> a[1, 1] = 1 + >>> a + array([[0, 0, 0], + [0, 1, 0], + [0, 0, 0]]) + >>> a = ma.masked_equal(a, 1) + >>> a + masked_array( + data=[[0, 0, 0], + [0, --, 0], + [0, 0, 0]], + mask=[[False, False, False], + [False, True, False], + [False, False, False]], + fill_value=1) + >>> ma.mask_cols(a) + masked_array( + data=[[0, --, 0], + [0, --, 0], + [0, --, 0]], + mask=[[False, True, False], + [False, True, False], + [False, True, False]], + fill_value=1) + + """ + if axis is not np._NoValue: + # remove the axis argument when this deprecation expires + # NumPy 1.18.0, 2019-11-28 + warnings.warn( + "The axis argument has always been ignored, in future passing it " + "will raise TypeError", DeprecationWarning, stacklevel=2) + return mask_rowcols(a, 1) + + +#####-------------------------------------------------------------------------- +#---- --- arraysetops --- +#####-------------------------------------------------------------------------- + +def ediff1d(arr, to_end=None, to_begin=None): + """ + Compute the differences between consecutive elements of an array. + + This function is the equivalent of `numpy.ediff1d` that takes masked + values into account, see `numpy.ediff1d` for details. + + See Also + -------- + numpy.ediff1d : Equivalent function for ndarrays. + + """ + arr = ma.asanyarray(arr).flat + ed = arr[1:] - arr[:-1] + arrays = [ed] + # + if to_begin is not None: + arrays.insert(0, to_begin) + if to_end is not None: + arrays.append(to_end) + # + if len(arrays) != 1: + # We'll save ourselves a copy of a potentially large array in the common + # case where neither to_begin or to_end was given. + ed = hstack(arrays) + # + return ed + + +def unique(ar1, return_index=False, return_inverse=False): + """ + Finds the unique elements of an array. + + Masked values are considered the same element (masked). The output array + is always a masked array. See `numpy.unique` for more details. + + See Also + -------- + numpy.unique : Equivalent function for ndarrays. + + Examples + -------- + >>> import numpy.ma as ma + >>> a = [1, 2, 1000, 2, 3] + >>> mask = [0, 0, 1, 0, 0] + >>> masked_a = ma.masked_array(a, mask) + >>> masked_a + masked_array(data=[1, 2, --, 2, 3], + mask=[False, False, True, False, False], + fill_value=999999) + >>> ma.unique(masked_a) + masked_array(data=[1, 2, 3, --], + mask=[False, False, False, True], + fill_value=999999) + >>> ma.unique(masked_a, return_index=True) + (masked_array(data=[1, 2, 3, --], + mask=[False, False, False, True], + fill_value=999999), array([0, 1, 4, 2])) + >>> ma.unique(masked_a, return_inverse=True) + (masked_array(data=[1, 2, 3, --], + mask=[False, False, False, True], + fill_value=999999), array([0, 1, 3, 1, 2])) + >>> ma.unique(masked_a, return_index=True, return_inverse=True) + (masked_array(data=[1, 2, 3, --], + mask=[False, False, False, True], + fill_value=999999), array([0, 1, 4, 2]), array([0, 1, 3, 1, 2])) + """ + output = np.unique(ar1, + return_index=return_index, + return_inverse=return_inverse) + if isinstance(output, tuple): + output = list(output) + output[0] = output[0].view(MaskedArray) + output = tuple(output) + else: + output = output.view(MaskedArray) + return output + + +def intersect1d(ar1, ar2, assume_unique=False): + """ + Returns the unique elements common to both arrays. + + Masked values are considered equal one to the other. + The output is always a masked array. + + See `numpy.intersect1d` for more details. + + See Also + -------- + numpy.intersect1d : Equivalent function for ndarrays. + + Examples + -------- + >>> x = np.ma.array([1, 3, 3, 3], mask=[0, 0, 0, 1]) + >>> y = np.ma.array([3, 1, 1, 1], mask=[0, 0, 0, 1]) + >>> np.ma.intersect1d(x, y) + masked_array(data=[1, 3, --], + mask=[False, False, True], + fill_value=999999) + + """ + if assume_unique: + aux = ma.concatenate((ar1, ar2)) + else: + # Might be faster than unique( intersect1d( ar1, ar2 ) )? + aux = ma.concatenate((unique(ar1), unique(ar2))) + aux.sort() + return aux[:-1][aux[1:] == aux[:-1]] + + +def setxor1d(ar1, ar2, assume_unique=False): + """ + Set exclusive-or of 1-D arrays with unique elements. + + The output is always a masked array. See `numpy.setxor1d` for more details. + + See Also + -------- + numpy.setxor1d : Equivalent function for ndarrays. + + """ + if not assume_unique: + ar1 = unique(ar1) + ar2 = unique(ar2) + + aux = ma.concatenate((ar1, ar2)) + if aux.size == 0: + return aux + aux.sort() + auxf = aux.filled() +# flag = ediff1d( aux, to_end = 1, to_begin = 1 ) == 0 + flag = ma.concatenate(([True], (auxf[1:] != auxf[:-1]), [True])) +# flag2 = ediff1d( flag ) == 0 + flag2 = (flag[1:] == flag[:-1]) + return aux[flag2] + + +def in1d(ar1, ar2, assume_unique=False, invert=False): + """ + Test whether each element of an array is also present in a second + array. + + The output is always a masked array. See `numpy.in1d` for more details. + + We recommend using :func:`isin` instead of `in1d` for new code. + + See Also + -------- + isin : Version of this function that preserves the shape of ar1. + numpy.in1d : Equivalent function for ndarrays. + + Notes + ----- + .. versionadded:: 1.4.0 + + """ + if not assume_unique: + ar1, rev_idx = unique(ar1, return_inverse=True) + ar2 = unique(ar2) + + ar = ma.concatenate((ar1, ar2)) + # We need this to be a stable sort, so always use 'mergesort' + # here. The values from the first array should always come before + # the values from the second array. + order = ar.argsort(kind='mergesort') + sar = ar[order] + if invert: + bool_ar = (sar[1:] != sar[:-1]) + else: + bool_ar = (sar[1:] == sar[:-1]) + flag = ma.concatenate((bool_ar, [invert])) + indx = order.argsort(kind='mergesort')[:len(ar1)] + + if assume_unique: + return flag[indx] + else: + return flag[indx][rev_idx] + + +def isin(element, test_elements, assume_unique=False, invert=False): + """ + Calculates `element in test_elements`, broadcasting over + `element` only. + + The output is always a masked array of the same shape as `element`. + See `numpy.isin` for more details. + + See Also + -------- + in1d : Flattened version of this function. + numpy.isin : Equivalent function for ndarrays. + + Notes + ----- + .. versionadded:: 1.13.0 + + """ + element = ma.asarray(element) + return in1d(element, test_elements, assume_unique=assume_unique, + invert=invert).reshape(element.shape) + + +def union1d(ar1, ar2): + """ + Union of two arrays. + + The output is always a masked array. See `numpy.union1d` for more details. + + See Also + -------- + numpy.union1d : Equivalent function for ndarrays. + + """ + return unique(ma.concatenate((ar1, ar2), axis=None)) + + +def setdiff1d(ar1, ar2, assume_unique=False): + """ + Set difference of 1D arrays with unique elements. + + The output is always a masked array. See `numpy.setdiff1d` for more + details. + + See Also + -------- + numpy.setdiff1d : Equivalent function for ndarrays. + + Examples + -------- + >>> x = np.ma.array([1, 2, 3, 4], mask=[0, 1, 0, 1]) + >>> np.ma.setdiff1d(x, [1, 2]) + masked_array(data=[3, --], + mask=[False, True], + fill_value=999999) + + """ + if assume_unique: + ar1 = ma.asarray(ar1).ravel() + else: + ar1 = unique(ar1) + ar2 = unique(ar2) + return ar1[in1d(ar1, ar2, assume_unique=True, invert=True)] + + +############################################################################### +# Covariance # +############################################################################### + + +def _covhelper(x, y=None, rowvar=True, allow_masked=True): + """ + Private function for the computation of covariance and correlation + coefficients. + + """ + x = ma.array(x, ndmin=2, copy=True, dtype=float) + xmask = ma.getmaskarray(x) + # Quick exit if we can't process masked data + if not allow_masked and xmask.any(): + raise ValueError("Cannot process masked data.") + # + if x.shape[0] == 1: + rowvar = True + # Make sure that rowvar is either 0 or 1 + rowvar = int(bool(rowvar)) + axis = 1 - rowvar + if rowvar: + tup = (slice(None), None) + else: + tup = (None, slice(None)) + # + if y is None: + xnotmask = np.logical_not(xmask).astype(int) + else: + y = array(y, copy=False, ndmin=2, dtype=float) + ymask = ma.getmaskarray(y) + if not allow_masked and ymask.any(): + raise ValueError("Cannot process masked data.") + if xmask.any() or ymask.any(): + if y.shape == x.shape: + # Define some common mask + common_mask = np.logical_or(xmask, ymask) + if common_mask is not nomask: + xmask = x._mask = y._mask = ymask = common_mask + x._sharedmask = False + y._sharedmask = False + x = ma.concatenate((x, y), axis) + xnotmask = np.logical_not(np.concatenate((xmask, ymask), axis)).astype(int) + x -= x.mean(axis=rowvar)[tup] + return (x, xnotmask, rowvar) + + +def cov(x, y=None, rowvar=True, bias=False, allow_masked=True, ddof=None): + """ + Estimate the covariance matrix. + + Except for the handling of missing data this function does the same as + `numpy.cov`. For more details and examples, see `numpy.cov`. + + By default, masked values are recognized as such. If `x` and `y` have the + same shape, a common mask is allocated: if ``x[i,j]`` is masked, then + ``y[i,j]`` will also be masked. + Setting `allow_masked` to False will raise an exception if values are + missing in either of the input arrays. + + 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 : 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``. This keyword can be overridden by + the keyword ``ddof`` in numpy versions >= 1.5. + allow_masked : bool, optional + If True, masked values are propagated pair-wise: if a value is masked + in `x`, the corresponding value is masked in `y`. + If False, raises a `ValueError` exception when some values are missing. + ddof : {None, int}, optional + If not ``None`` normalization is by ``(N - ddof)``, where ``N`` is + the number of observations; this overrides the value implied by + ``bias``. The default value is ``None``. + + .. versionadded:: 1.5 + + Raises + ------ + ValueError + Raised if some values are missing and `allow_masked` is False. + + See Also + -------- + numpy.cov + + """ + # Check inputs + if ddof is not None and ddof != int(ddof): + raise ValueError("ddof must be an integer") + # Set up ddof + if ddof is None: + if bias: + ddof = 0 + else: + ddof = 1 + + (x, xnotmask, rowvar) = _covhelper(x, y, rowvar, allow_masked) + if not rowvar: + fact = np.dot(xnotmask.T, xnotmask) * 1. - ddof + result = (dot(x.T, x.conj(), strict=False) / fact).squeeze() + else: + fact = np.dot(xnotmask, xnotmask.T) * 1. - ddof + result = (dot(x, x.T.conj(), strict=False) / fact).squeeze() + return result + + +def corrcoef(x, y=None, rowvar=True, bias=np._NoValue, allow_masked=True, + ddof=np._NoValue): + """ + Return Pearson product-moment correlation coefficients. + + Except for the handling of missing data this function does the same as + `numpy.corrcoef`. For more details and examples, see `numpy.corrcoef`. + + 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 + allow_masked : bool, optional + If True, masked values are propagated pair-wise: if a value is masked + in `x`, the corresponding value is masked in `y`. + If False, raises an exception. Because `bias` is deprecated, this + argument needs to be treated as keyword only to avoid a warning. + ddof : _NoValue, optional + Has no effect, do not use. + + .. deprecated:: 1.10.0 + + See Also + -------- + numpy.corrcoef : Equivalent function in top-level NumPy module. + cov : Estimate the covariance matrix. + + Notes + ----- + 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. + """ + msg = 'bias and ddof have no effect and are deprecated' + if bias is not np._NoValue or ddof is not np._NoValue: + # 2015-03-15, 1.10 + warnings.warn(msg, DeprecationWarning, stacklevel=2) + # Get the data + (x, xnotmask, rowvar) = _covhelper(x, y, rowvar, allow_masked) + # Compute the covariance matrix + if not rowvar: + fact = np.dot(xnotmask.T, xnotmask) * 1. + c = (dot(x.T, x.conj(), strict=False) / fact).squeeze() + else: + fact = np.dot(xnotmask, xnotmask.T) * 1. + c = (dot(x, x.T.conj(), strict=False) / fact).squeeze() + # Check whether we have a scalar + try: + diag = ma.diagonal(c) + except ValueError: + return 1 + # + if xnotmask.all(): + _denom = ma.sqrt(ma.multiply.outer(diag, diag)) + else: + _denom = diagflat(diag) + _denom._sharedmask = False # We know return is always a copy + n = x.shape[1 - rowvar] + if rowvar: + for i in range(n - 1): + for j in range(i + 1, n): + _x = mask_cols(vstack((x[i], x[j]))).var(axis=1) + _denom[i, j] = _denom[j, i] = ma.sqrt(ma.multiply.reduce(_x)) + else: + for i in range(n - 1): + for j in range(i + 1, n): + _x = mask_cols( + vstack((x[:, i], x[:, j]))).var(axis=1) + _denom[i, j] = _denom[j, i] = ma.sqrt(ma.multiply.reduce(_x)) + return c / _denom + +#####-------------------------------------------------------------------------- +#---- --- Concatenation helpers --- +#####-------------------------------------------------------------------------- + +class MAxisConcatenator(AxisConcatenator): + """ + Translate slice objects to concatenation along an axis. + + For documentation on usage, see `mr_class`. + + See Also + -------- + mr_class + + """ + concatenate = staticmethod(concatenate) + + @classmethod + def makemat(cls, arr): + # There used to be a view as np.matrix here, but we may eventually + # deprecate that class. In preparation, we use the unmasked version + # to construct the matrix (with copy=False for backwards compatibility + # with the .view) + data = super().makemat(arr.data, copy=False) + return array(data, mask=arr.mask) + + def __getitem__(self, key): + # matrix builder syntax, like 'a, b; c, d' + if isinstance(key, str): + raise MAError("Unavailable for masked array.") + + return super().__getitem__(key) + + +class mr_class(MAxisConcatenator): + """ + Translate slice objects to concatenation along the first axis. + + This is the masked array version of `lib.index_tricks.RClass`. + + See Also + -------- + lib.index_tricks.RClass + + Examples + -------- + >>> np.ma.mr_[np.ma.array([1,2,3]), 0, 0, np.ma.array([4,5,6])] + masked_array(data=[1, 2, 3, ..., 4, 5, 6], + mask=False, + fill_value=999999) + + """ + def __init__(self): + MAxisConcatenator.__init__(self, 0) + +mr_ = mr_class() + + +#####-------------------------------------------------------------------------- +#---- Find unmasked data --- +#####-------------------------------------------------------------------------- + +def ndenumerate(a, compressed=True): + """ + Multidimensional index iterator. + + Return an iterator yielding pairs of array coordinates and values, + skipping elements that are masked. With `compressed=False`, + `ma.masked` is yielded as the value of masked elements. This + behavior differs from that of `numpy.ndenumerate`, which yields the + value of the underlying data array. + + Notes + ----- + .. versionadded:: 1.23.0 + + Parameters + ---------- + a : array_like + An array with (possibly) masked elements. + compressed : bool, optional + If True (default), masked elements are skipped. + + See Also + -------- + numpy.ndenumerate : Equivalent function ignoring any mask. + + Examples + -------- + >>> a = np.ma.arange(9).reshape((3, 3)) + >>> a[1, 0] = np.ma.masked + >>> a[1, 2] = np.ma.masked + >>> a[2, 1] = np.ma.masked + >>> a + masked_array( + data=[[0, 1, 2], + [--, 4, --], + [6, --, 8]], + mask=[[False, False, False], + [ True, False, True], + [False, True, False]], + fill_value=999999) + >>> for index, x in np.ma.ndenumerate(a): + ... print(index, x) + (0, 0) 0 + (0, 1) 1 + (0, 2) 2 + (1, 1) 4 + (2, 0) 6 + (2, 2) 8 + + >>> for index, x in np.ma.ndenumerate(a, compressed=False): + ... print(index, x) + (0, 0) 0 + (0, 1) 1 + (0, 2) 2 + (1, 0) -- + (1, 1) 4 + (1, 2) -- + (2, 0) 6 + (2, 1) -- + (2, 2) 8 + """ + for it, mask in zip(np.ndenumerate(a), getmaskarray(a).flat): + if not mask: + yield it + elif not compressed: + yield it[0], masked + + +def flatnotmasked_edges(a): + """ + Find the indices of the first and last unmasked values. + + Expects a 1-D `MaskedArray`, returns None if all values are masked. + + Parameters + ---------- + a : array_like + Input 1-D `MaskedArray` + + Returns + ------- + edges : ndarray or None + The indices of first and last non-masked value in the array. + Returns None if all values are masked. + + See Also + -------- + flatnotmasked_contiguous, notmasked_contiguous, notmasked_edges + clump_masked, clump_unmasked + + Notes + ----- + Only accepts 1-D arrays. + + Examples + -------- + >>> a = np.ma.arange(10) + >>> np.ma.flatnotmasked_edges(a) + array([0, 9]) + + >>> mask = (a < 3) | (a > 8) | (a == 5) + >>> a[mask] = np.ma.masked + >>> np.array(a[~a.mask]) + array([3, 4, 6, 7, 8]) + + >>> np.ma.flatnotmasked_edges(a) + array([3, 8]) + + >>> a[:] = np.ma.masked + >>> print(np.ma.flatnotmasked_edges(a)) + None + + """ + m = getmask(a) + if m is nomask or not np.any(m): + return np.array([0, a.size - 1]) + unmasked = np.flatnonzero(~m) + if len(unmasked) > 0: + return unmasked[[0, -1]] + else: + return None + + +def notmasked_edges(a, axis=None): + """ + Find the indices of the first and last unmasked values along an axis. + + If all values are masked, return None. Otherwise, return a list + of two tuples, corresponding to the indices of the first and last + unmasked values respectively. + + Parameters + ---------- + a : array_like + The input array. + axis : int, optional + Axis along which to perform the operation. + If None (default), applies to a flattened version of the array. + + Returns + ------- + edges : ndarray or list + An array of start and end indexes if there are any masked data in + the array. If there are no masked data in the array, `edges` is a + list of the first and last index. + + See Also + -------- + flatnotmasked_contiguous, flatnotmasked_edges, notmasked_contiguous + clump_masked, clump_unmasked + + Examples + -------- + >>> a = np.arange(9).reshape((3, 3)) + >>> m = np.zeros_like(a) + >>> m[1:, 1:] = 1 + + >>> am = np.ma.array(a, mask=m) + >>> np.array(am[~am.mask]) + array([0, 1, 2, 3, 6]) + + >>> np.ma.notmasked_edges(am) + array([0, 6]) + + """ + a = asarray(a) + if axis is None or a.ndim == 1: + return flatnotmasked_edges(a) + m = getmaskarray(a) + idx = array(np.indices(a.shape), mask=np.asarray([m] * a.ndim)) + return [tuple([idx[i].min(axis).compressed() for i in range(a.ndim)]), + tuple([idx[i].max(axis).compressed() for i in range(a.ndim)]), ] + + +def flatnotmasked_contiguous(a): + """ + Find contiguous unmasked data in a masked array. + + Parameters + ---------- + a : array_like + The input array. + + Returns + ------- + slice_list : list + A sorted sequence of `slice` objects (start index, end index). + + .. versionchanged:: 1.15.0 + Now returns an empty list instead of None for a fully masked array + + See Also + -------- + flatnotmasked_edges, notmasked_contiguous, notmasked_edges + clump_masked, clump_unmasked + + Notes + ----- + Only accepts 2-D arrays at most. + + Examples + -------- + >>> a = np.ma.arange(10) + >>> np.ma.flatnotmasked_contiguous(a) + [slice(0, 10, None)] + + >>> mask = (a < 3) | (a > 8) | (a == 5) + >>> a[mask] = np.ma.masked + >>> np.array(a[~a.mask]) + array([3, 4, 6, 7, 8]) + + >>> np.ma.flatnotmasked_contiguous(a) + [slice(3, 5, None), slice(6, 9, None)] + >>> a[:] = np.ma.masked + >>> np.ma.flatnotmasked_contiguous(a) + [] + + """ + m = getmask(a) + if m is nomask: + return [slice(0, a.size)] + i = 0 + result = [] + for (k, g) in itertools.groupby(m.ravel()): + n = len(list(g)) + if not k: + result.append(slice(i, i + n)) + i += n + return result + + +def notmasked_contiguous(a, axis=None): + """ + Find contiguous unmasked data in a masked array along the given axis. + + Parameters + ---------- + a : array_like + The input array. + axis : int, optional + Axis along which to perform the operation. + If None (default), applies to a flattened version of the array, and this + is the same as `flatnotmasked_contiguous`. + + Returns + ------- + endpoints : list + A list of slices (start and end indexes) of unmasked indexes + in the array. + + If the input is 2d and axis is specified, the result is a list of lists. + + See Also + -------- + flatnotmasked_edges, flatnotmasked_contiguous, notmasked_edges + clump_masked, clump_unmasked + + Notes + ----- + Only accepts 2-D arrays at most. + + Examples + -------- + >>> a = np.arange(12).reshape((3, 4)) + >>> mask = np.zeros_like(a) + >>> mask[1:, :-1] = 1; mask[0, 1] = 1; mask[-1, 0] = 0 + >>> ma = np.ma.array(a, mask=mask) + >>> ma + masked_array( + data=[[0, --, 2, 3], + [--, --, --, 7], + [8, --, --, 11]], + mask=[[False, True, False, False], + [ True, True, True, False], + [False, True, True, False]], + fill_value=999999) + >>> np.array(ma[~ma.mask]) + array([ 0, 2, 3, 7, 8, 11]) + + >>> np.ma.notmasked_contiguous(ma) + [slice(0, 1, None), slice(2, 4, None), slice(7, 9, None), slice(11, 12, None)] + + >>> np.ma.notmasked_contiguous(ma, axis=0) + [[slice(0, 1, None), slice(2, 3, None)], [], [slice(0, 1, None)], [slice(0, 3, None)]] + + >>> np.ma.notmasked_contiguous(ma, axis=1) + [[slice(0, 1, None), slice(2, 4, None)], [slice(3, 4, None)], [slice(0, 1, None), slice(3, 4, None)]] + + """ + a = asarray(a) + nd = a.ndim + if nd > 2: + raise NotImplementedError("Currently limited to at most 2D array.") + if axis is None or nd == 1: + return flatnotmasked_contiguous(a) + # + result = [] + # + other = (axis + 1) % 2 + idx = [0, 0] + idx[axis] = slice(None, None) + # + for i in range(a.shape[other]): + idx[other] = i + result.append(flatnotmasked_contiguous(a[tuple(idx)])) + return result + + +def _ezclump(mask): + """ + Finds the clumps (groups of data with the same values) for a 1D bool array. + + Returns a series of slices. + """ + if mask.ndim > 1: + mask = mask.ravel() + idx = (mask[1:] ^ mask[:-1]).nonzero() + idx = idx[0] + 1 + + if mask[0]: + if len(idx) == 0: + return [slice(0, mask.size)] + + r = [slice(0, idx[0])] + r.extend((slice(left, right) + for left, right in zip(idx[1:-1:2], idx[2::2]))) + else: + if len(idx) == 0: + return [] + + r = [slice(left, right) for left, right in zip(idx[:-1:2], idx[1::2])] + + if mask[-1]: + r.append(slice(idx[-1], mask.size)) + return r + + +def clump_unmasked(a): + """ + Return list of slices corresponding to the unmasked clumps of a 1-D array. + (A "clump" is defined as a contiguous region of the array). + + Parameters + ---------- + a : ndarray + A one-dimensional masked array. + + Returns + ------- + slices : list of slice + The list of slices, one for each continuous region of unmasked + elements in `a`. + + Notes + ----- + .. versionadded:: 1.4.0 + + See Also + -------- + flatnotmasked_edges, flatnotmasked_contiguous, notmasked_edges + notmasked_contiguous, clump_masked + + Examples + -------- + >>> a = np.ma.masked_array(np.arange(10)) + >>> a[[0, 1, 2, 6, 8, 9]] = np.ma.masked + >>> np.ma.clump_unmasked(a) + [slice(3, 6, None), slice(7, 8, None)] + + """ + mask = getattr(a, '_mask', nomask) + if mask is nomask: + return [slice(0, a.size)] + return _ezclump(~mask) + + +def clump_masked(a): + """ + Returns a list of slices corresponding to the masked clumps of a 1-D array. + (A "clump" is defined as a contiguous region of the array). + + Parameters + ---------- + a : ndarray + A one-dimensional masked array. + + Returns + ------- + slices : list of slice + The list of slices, one for each continuous region of masked elements + in `a`. + + Notes + ----- + .. versionadded:: 1.4.0 + + See Also + -------- + flatnotmasked_edges, flatnotmasked_contiguous, notmasked_edges + notmasked_contiguous, clump_unmasked + + Examples + -------- + >>> a = np.ma.masked_array(np.arange(10)) + >>> a[[0, 1, 2, 6, 8, 9]] = np.ma.masked + >>> np.ma.clump_masked(a) + [slice(0, 3, None), slice(6, 7, None), slice(8, 10, None)] + + """ + mask = ma.getmask(a) + if mask is nomask: + return [] + return _ezclump(mask) + + +############################################################################### +# Polynomial fit # +############################################################################### + + +def vander(x, n=None): + """ + Masked values in the input array result in rows of zeros. + + """ + _vander = np.vander(x, n) + m = getmask(x) + if m is not nomask: + _vander[m] = 0 + return _vander + +vander.__doc__ = ma.doc_note(np.vander.__doc__, vander.__doc__) + + +def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): + """ + Any masked values in x is propagated in y, and vice-versa. + + """ + x = asarray(x) + y = asarray(y) + + m = getmask(x) + if y.ndim == 1: + m = mask_or(m, getmask(y)) + elif y.ndim == 2: + my = getmask(mask_rows(y)) + if my is not nomask: + m = mask_or(m, my[:, 0]) + else: + raise TypeError("Expected a 1D or 2D array for y!") + + if w is not None: + w = asarray(w) + if w.ndim != 1: + raise TypeError("expected a 1-d array for weights") + if w.shape[0] != y.shape[0]: + raise TypeError("expected w and y to have the same length") + m = mask_or(m, getmask(w)) + + if m is not nomask: + not_m = ~m + if w is not None: + w = w[not_m] + return np.polyfit(x[not_m], y[not_m], deg, rcond, full, w, cov) + else: + return np.polyfit(x, y, deg, rcond, full, w, cov) + +polyfit.__doc__ = ma.doc_note(np.polyfit.__doc__, polyfit.__doc__) |