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"""
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
)
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.prod(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.prod(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_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__)