2134 lines
63 KiB
Python
2134 lines
63 KiB
Python
"""
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Masked arrays add-ons.
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A collection of utilities for `numpy.ma`.
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:author: Pierre Gerard-Marchant
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:contact: pierregm_at_uga_dot_edu
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:version: $Id: extras.py 3473 2007-10-29 15:18:13Z jarrod.millman $
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"""
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__all__ = [
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'apply_along_axis', 'apply_over_axes', 'atleast_1d', 'atleast_2d',
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'atleast_3d', 'average', 'clump_masked', 'clump_unmasked', 'column_stack',
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'compress_cols', 'compress_nd', 'compress_rowcols', 'compress_rows',
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'count_masked', 'corrcoef', 'cov', 'diagflat', 'dot', 'dstack', 'ediff1d',
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'flatnotmasked_contiguous', 'flatnotmasked_edges', 'hsplit', 'hstack',
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'isin', 'in1d', 'intersect1d', 'mask_cols', 'mask_rowcols', 'mask_rows',
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'masked_all', 'masked_all_like', 'median', 'mr_', 'ndenumerate',
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'notmasked_contiguous', 'notmasked_edges', 'polyfit', 'row_stack',
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'setdiff1d', 'setxor1d', 'stack', 'unique', 'union1d', 'vander', 'vstack',
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]
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import itertools
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import warnings
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from . import core as ma
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from .core import (
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MaskedArray, MAError, add, array, asarray, concatenate, filled, count,
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getmask, getmaskarray, make_mask_descr, masked, masked_array, mask_or,
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nomask, ones, sort, zeros, getdata, get_masked_subclass, dot
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)
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import numpy as np
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from numpy import ndarray, array as nxarray
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from numpy.core.multiarray import normalize_axis_index
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from numpy.core.numeric import normalize_axis_tuple
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from numpy.lib.function_base import _ureduce
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from numpy.lib.index_tricks import AxisConcatenator
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def issequence(seq):
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"""
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Is seq a sequence (ndarray, list or tuple)?
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"""
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return isinstance(seq, (ndarray, tuple, list))
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def count_masked(arr, axis=None):
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"""
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Count the number of masked elements along the given axis.
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Parameters
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----------
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arr : array_like
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An array with (possibly) masked elements.
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axis : int, optional
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Axis along which to count. If None (default), a flattened
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version of the array is used.
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Returns
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-------
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count : int, ndarray
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The total number of masked elements (axis=None) or the number
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of masked elements along each slice of the given axis.
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See Also
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--------
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MaskedArray.count : Count non-masked elements.
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Examples
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--------
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>>> import numpy.ma as ma
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>>> a = np.arange(9).reshape((3,3))
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>>> a = ma.array(a)
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>>> a[1, 0] = ma.masked
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>>> a[1, 2] = ma.masked
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>>> a[2, 1] = ma.masked
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>>> a
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masked_array(
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data=[[0, 1, 2],
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[--, 4, --],
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[6, --, 8]],
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mask=[[False, False, False],
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[ True, False, True],
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[False, True, False]],
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fill_value=999999)
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>>> ma.count_masked(a)
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3
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When the `axis` keyword is used an array is returned.
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>>> ma.count_masked(a, axis=0)
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array([1, 1, 1])
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>>> ma.count_masked(a, axis=1)
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array([0, 2, 1])
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"""
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m = getmaskarray(arr)
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return m.sum(axis)
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def masked_all(shape, dtype=float):
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"""
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Empty masked array with all elements masked.
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Return an empty masked array of the given shape and dtype, where all the
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data are masked.
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Parameters
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----------
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shape : int or tuple of ints
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Shape of the required MaskedArray, e.g., ``(2, 3)`` or ``2``.
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dtype : dtype, optional
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Data type of the output.
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Returns
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-------
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a : MaskedArray
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A masked array with all data masked.
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See Also
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--------
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masked_all_like : Empty masked array modelled on an existing array.
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Examples
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--------
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>>> import numpy.ma as ma
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>>> ma.masked_all((3, 3))
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masked_array(
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data=[[--, --, --],
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[--, --, --],
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[--, --, --]],
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mask=[[ True, True, True],
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[ True, True, True],
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[ True, True, True]],
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fill_value=1e+20,
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dtype=float64)
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The `dtype` parameter defines the underlying data type.
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>>> a = ma.masked_all((3, 3))
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>>> a.dtype
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dtype('float64')
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>>> a = ma.masked_all((3, 3), dtype=np.int32)
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>>> a.dtype
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dtype('int32')
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"""
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a = masked_array(np.empty(shape, dtype),
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mask=np.ones(shape, make_mask_descr(dtype)))
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return a
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def masked_all_like(arr):
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"""
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Empty masked array with the properties of an existing array.
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Return an empty masked array of the same shape and dtype as
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the array `arr`, where all the data are masked.
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Parameters
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----------
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arr : ndarray
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An array describing the shape and dtype of the required MaskedArray.
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Returns
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-------
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a : MaskedArray
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A masked array with all data masked.
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Raises
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------
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AttributeError
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If `arr` doesn't have a shape attribute (i.e. not an ndarray)
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See Also
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--------
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masked_all : Empty masked array with all elements masked.
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Examples
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--------
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>>> import numpy.ma as ma
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>>> arr = np.zeros((2, 3), dtype=np.float32)
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>>> arr
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array([[0., 0., 0.],
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[0., 0., 0.]], dtype=float32)
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>>> ma.masked_all_like(arr)
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masked_array(
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data=[[--, --, --],
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[--, --, --]],
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mask=[[ True, True, True],
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[ True, True, True]],
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fill_value=1e+20,
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dtype=float32)
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The dtype of the masked array matches the dtype of `arr`.
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>>> arr.dtype
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dtype('float32')
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>>> ma.masked_all_like(arr).dtype
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dtype('float32')
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"""
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a = np.empty_like(arr).view(MaskedArray)
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a._mask = np.ones(a.shape, dtype=make_mask_descr(a.dtype))
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return a
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#####--------------------------------------------------------------------------
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#---- --- Standard functions ---
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#####--------------------------------------------------------------------------
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class _fromnxfunction:
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"""
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Defines a wrapper to adapt NumPy functions to masked arrays.
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An instance of `_fromnxfunction` can be called with the same parameters
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as the wrapped NumPy function. The docstring of `newfunc` is adapted from
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the wrapped function as well, see `getdoc`.
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This class should not be used directly. Instead, one of its extensions that
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provides support for a specific type of input should be used.
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Parameters
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----------
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funcname : str
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The name of the function to be adapted. The function should be
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in the NumPy namespace (i.e. ``np.funcname``).
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"""
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def __init__(self, funcname):
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self.__name__ = funcname
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self.__doc__ = self.getdoc()
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def getdoc(self):
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"""
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Retrieve the docstring and signature from the function.
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The ``__doc__`` attribute of the function is used as the docstring for
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the new masked array version of the function. A note on application
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of the function to the mask is appended.
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Parameters
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----------
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None
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"""
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npfunc = getattr(np, self.__name__, None)
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doc = getattr(npfunc, '__doc__', None)
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if doc:
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sig = self.__name__ + ma.get_object_signature(npfunc)
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doc = ma.doc_note(doc, "The function is applied to both the _data "
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"and the _mask, if any.")
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return '\n\n'.join((sig, doc))
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return
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def __call__(self, *args, **params):
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pass
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class _fromnxfunction_single(_fromnxfunction):
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"""
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A version of `_fromnxfunction` that is called with a single array
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argument followed by auxiliary args that are passed verbatim for
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both the data and mask calls.
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"""
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def __call__(self, x, *args, **params):
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func = getattr(np, self.__name__)
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if isinstance(x, ndarray):
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_d = func(x.__array__(), *args, **params)
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_m = func(getmaskarray(x), *args, **params)
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return masked_array(_d, mask=_m)
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else:
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_d = func(np.asarray(x), *args, **params)
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_m = func(getmaskarray(x), *args, **params)
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return masked_array(_d, mask=_m)
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class _fromnxfunction_seq(_fromnxfunction):
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"""
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A version of `_fromnxfunction` that is called with a single sequence
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of arrays followed by auxiliary args that are passed verbatim for
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both the data and mask calls.
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"""
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def __call__(self, x, *args, **params):
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func = getattr(np, self.__name__)
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_d = func(tuple([np.asarray(a) for a in x]), *args, **params)
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_m = func(tuple([getmaskarray(a) for a in x]), *args, **params)
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return masked_array(_d, mask=_m)
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class _fromnxfunction_args(_fromnxfunction):
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"""
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A version of `_fromnxfunction` that is called with multiple array
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arguments. The first non-array-like input marks the beginning of the
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arguments that are passed verbatim for both the data and mask calls.
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Array arguments are processed independently and the results are
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returned in a list. If only one array is found, the return value is
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just the processed array instead of a list.
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"""
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def __call__(self, *args, **params):
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func = getattr(np, self.__name__)
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arrays = []
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args = list(args)
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while len(args) > 0 and issequence(args[0]):
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arrays.append(args.pop(0))
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res = []
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for x in arrays:
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_d = func(np.asarray(x), *args, **params)
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_m = func(getmaskarray(x), *args, **params)
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res.append(masked_array(_d, mask=_m))
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if len(arrays) == 1:
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return res[0]
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return res
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class _fromnxfunction_allargs(_fromnxfunction):
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"""
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A version of `_fromnxfunction` that is called with multiple array
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arguments. Similar to `_fromnxfunction_args` except that all args
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are converted to arrays even if they are not so already. This makes
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it possible to process scalars as 1-D arrays. Only keyword arguments
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are passed through verbatim for the data and mask calls. Arrays
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arguments are processed independently and the results are returned
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in a list. If only one arg is present, the return value is just the
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processed array instead of a list.
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"""
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def __call__(self, *args, **params):
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func = getattr(np, self.__name__)
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res = []
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for x in args:
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_d = func(np.asarray(x), **params)
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_m = func(getmaskarray(x), **params)
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res.append(masked_array(_d, mask=_m))
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if len(args) == 1:
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return res[0]
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return res
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atleast_1d = _fromnxfunction_allargs('atleast_1d')
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atleast_2d = _fromnxfunction_allargs('atleast_2d')
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atleast_3d = _fromnxfunction_allargs('atleast_3d')
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vstack = row_stack = _fromnxfunction_seq('vstack')
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hstack = _fromnxfunction_seq('hstack')
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column_stack = _fromnxfunction_seq('column_stack')
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dstack = _fromnxfunction_seq('dstack')
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stack = _fromnxfunction_seq('stack')
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hsplit = _fromnxfunction_single('hsplit')
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diagflat = _fromnxfunction_single('diagflat')
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#####--------------------------------------------------------------------------
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#----
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#####--------------------------------------------------------------------------
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def flatten_inplace(seq):
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"""Flatten a sequence in place."""
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k = 0
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while (k != len(seq)):
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while hasattr(seq[k], '__iter__'):
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seq[k:(k + 1)] = seq[k]
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k += 1
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return seq
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def apply_along_axis(func1d, axis, arr, *args, **kwargs):
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"""
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(This docstring should be overwritten)
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"""
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arr = array(arr, copy=False, subok=True)
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nd = arr.ndim
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axis = normalize_axis_index(axis, nd)
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ind = [0] * (nd - 1)
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i = np.zeros(nd, 'O')
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indlist = list(range(nd))
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indlist.remove(axis)
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i[axis] = slice(None, None)
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outshape = np.asarray(arr.shape).take(indlist)
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i.put(indlist, ind)
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res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
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# if res is a number, then we have a smaller output array
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asscalar = np.isscalar(res)
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if not asscalar:
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try:
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len(res)
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except TypeError:
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asscalar = True
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# Note: we shouldn't set the dtype of the output from the first result
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# so we force the type to object, and build a list of dtypes. We'll
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# just take the largest, to avoid some downcasting
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dtypes = []
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if asscalar:
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dtypes.append(np.asarray(res).dtype)
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outarr = zeros(outshape, object)
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outarr[tuple(ind)] = res
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Ntot = np.prod(outshape)
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k = 1
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while k < Ntot:
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# increment the index
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ind[-1] += 1
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n = -1
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while (ind[n] >= outshape[n]) and (n > (1 - nd)):
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ind[n - 1] += 1
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ind[n] = 0
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n -= 1
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i.put(indlist, ind)
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res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
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outarr[tuple(ind)] = res
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dtypes.append(asarray(res).dtype)
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k += 1
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else:
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res = array(res, copy=False, subok=True)
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j = i.copy()
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j[axis] = ([slice(None, None)] * res.ndim)
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j.put(indlist, ind)
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Ntot = np.prod(outshape)
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holdshape = outshape
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outshape = list(arr.shape)
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outshape[axis] = res.shape
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dtypes.append(asarray(res).dtype)
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outshape = flatten_inplace(outshape)
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outarr = zeros(outshape, object)
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outarr[tuple(flatten_inplace(j.tolist()))] = res
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k = 1
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while k < Ntot:
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# increment the index
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ind[-1] += 1
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n = -1
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while (ind[n] >= holdshape[n]) and (n > (1 - nd)):
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ind[n - 1] += 1
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ind[n] = 0
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n -= 1
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i.put(indlist, ind)
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j.put(indlist, ind)
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res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
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outarr[tuple(flatten_inplace(j.tolist()))] = res
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dtypes.append(asarray(res).dtype)
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k += 1
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max_dtypes = np.dtype(np.asarray(dtypes).max())
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if not hasattr(arr, '_mask'):
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result = np.asarray(outarr, dtype=max_dtypes)
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else:
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result = asarray(outarr, dtype=max_dtypes)
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result.fill_value = ma.default_fill_value(result)
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return result
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apply_along_axis.__doc__ = np.apply_along_axis.__doc__
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|
|
|
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def apply_over_axes(func, a, axes):
|
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"""
|
|
(This docstring will be overwritten)
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"""
|
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val = asarray(a)
|
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N = a.ndim
|
|
if array(axes).ndim == 0:
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axes = (axes,)
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for axis in axes:
|
|
if axis < 0:
|
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axis = N + axis
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args = (val, axis)
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res = func(*args)
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if res.ndim == val.ndim:
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val = res
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else:
|
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res = ma.expand_dims(res, axis)
|
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if res.ndim == val.ndim:
|
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val = res
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else:
|
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raise ValueError("function is not returning "
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"an array of the correct shape")
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return val
|
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|
|
|
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if apply_over_axes.__doc__ is not None:
|
|
apply_over_axes.__doc__ = np.apply_over_axes.__doc__[
|
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:np.apply_over_axes.__doc__.find('Notes')].rstrip() + \
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|
"""
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.ma.arange(24).reshape(2,3,4)
|
|
>>> a[:,0,1] = np.ma.masked
|
|
>>> a[:,1,:] = np.ma.masked
|
|
>>> a
|
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masked_array(
|
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data=[[[0, --, 2, 3],
|
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[--, --, --, --],
|
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[8, 9, 10, 11]],
|
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[[12, --, 14, 15],
|
|
[--, --, --, --],
|
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[20, 21, 22, 23]]],
|
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mask=[[[False, True, False, False],
|
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[ True, True, True, True],
|
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[False, False, False, False]],
|
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[[False, True, False, False],
|
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[ True, True, True, True],
|
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[False, False, False, False]]],
|
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fill_value=999999)
|
|
>>> np.ma.apply_over_axes(np.ma.sum, a, [0,2])
|
|
masked_array(
|
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data=[[[46],
|
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[--],
|
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[124]]],
|
|
mask=[[[False],
|
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[ True],
|
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[False]]],
|
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fill_value=999999)
|
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|
|
Tuple axis arguments to ufuncs are equivalent:
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|
|
>>> np.ma.sum(a, axis=(0,2)).reshape((1,-1,1))
|
|
masked_array(
|
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data=[[[46],
|
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[--],
|
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[124]]],
|
|
mask=[[[False],
|
|
[ True],
|
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[False]]],
|
|
fill_value=999999)
|
|
"""
|
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|
|
|
|
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_rowcols(a, axis=None):
|
|
"""
|
|
Mask rows and/or columns of a 2D array that contain masked values.
|
|
|
|
Mask whole rows and/or columns of a 2D array that contain
|
|
masked values. The masking behavior is selected using the
|
|
`axis` parameter.
|
|
|
|
- If `axis` is None, rows *and* columns are masked.
|
|
- If `axis` is 0, only rows are masked.
|
|
- If `axis` is 1 or -1, only columns are masked.
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like, MaskedArray
|
|
The array to mask. If not a MaskedArray instance (or if no array
|
|
elements are masked), the result is a MaskedArray with `mask` set
|
|
to `nomask` (False). Must be a 2D array.
|
|
axis : int, optional
|
|
Axis along which to perform the operation. If None, applies to a
|
|
flattened version of the array.
|
|
|
|
Returns
|
|
-------
|
|
a : MaskedArray
|
|
A modified version of the input array, masked depending on the value
|
|
of the `axis` parameter.
|
|
|
|
Raises
|
|
------
|
|
NotImplementedError
|
|
If input array `a` is not 2D.
|
|
|
|
See Also
|
|
--------
|
|
mask_rows : Mask rows of a 2D array that contain masked values.
|
|
mask_cols : Mask cols of a 2D array that contain masked values.
|
|
masked_where : Mask where a condition is met.
|
|
|
|
Notes
|
|
-----
|
|
The input array's mask is modified by this function.
|
|
|
|
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_rowcols(a)
|
|
masked_array(
|
|
data=[[0, --, 0],
|
|
[--, --, --],
|
|
[0, --, 0]],
|
|
mask=[[False, True, False],
|
|
[ True, True, True],
|
|
[False, True, False]],
|
|
fill_value=1)
|
|
|
|
"""
|
|
a = array(a, subok=False)
|
|
if a.ndim != 2:
|
|
raise NotImplementedError("mask_rowcols works for 2D arrays only.")
|
|
m = getmask(a)
|
|
# Nothing is masked: return a
|
|
if m is nomask or not m.any():
|
|
return a
|
|
maskedval = m.nonzero()
|
|
a._mask = a._mask.copy()
|
|
if not axis:
|
|
a[np.unique(maskedval[0])] = masked
|
|
if axis in [None, 1, -1]:
|
|
a[:, np.unique(maskedval[1])] = masked
|
|
return a
|
|
|
|
|
|
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__)
|