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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 $
"""
from __future__ import division, absolute_import, print_function
__author__ = "Pierre GF Gerard-Marchant ($Author: jarrod.millman $)"
__version__ = '1.0'
__revision__ = "$Revision: 3473 $"
__date__ = '$Date: 2007-10-29 17:18:13 +0200 (Mon, 29 Oct 2007) $'
__all__ = ['apply_along_axis', 'apply_over_axes', 'atleast_1d', 'atleast_2d',
'atleast_3d', 'average',
'clump_masked', 'clump_unmasked', 'column_stack', 'compress_cols',
'compress_rowcols', 'compress_rows', 'count_masked', 'corrcoef',
'cov',
'diagflat', 'dot', 'dstack',
'ediff1d',
'flatnotmasked_contiguous', 'flatnotmasked_edges',
'hsplit', 'hstack',
'in1d', 'intersect1d',
'mask_cols', 'mask_rowcols', 'mask_rows', 'masked_all',
'masked_all_like', 'median', 'mr_',
'notmasked_contiguous', 'notmasked_edges',
'polyfit',
'row_stack',
'setdiff1d', 'setxor1d',
'unique', 'union1d',
'vander', 'vstack',
]
import itertools
import warnings
from . import core as ma
from .core import MaskedArray, MAError, add, array, asarray, concatenate, count, \
filled, getmask, getmaskarray, make_mask_descr, masked, masked_array, \
mask_or, nomask, ones, sort, zeros
#from core import *
import numpy as np
from numpy import ndarray, array as nxarray
import numpy.core.umath as umath
from numpy.lib.index_tricks import AxisConcatenator
from numpy.linalg import lstsq
#...............................................................................
def issequence(seq):
"""Is seq a sequence (ndarray, list or tuple)?"""
if isinstance(seq, (ndarray, tuple, list)):
return True
return False
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 : tuple
Shape of the required MaskedArray.
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)
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)
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`.
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.
.. warning::
If the function docstring already contained a Notes section, the
new docstring will have two Notes sections instead of appending a note
to the existing section.
Parameters
----------
None
"""
npfunc = getattr(np, self.__name__, None)
doc = getattr(npfunc, '__doc__', None)
if doc:
sig = self.__name__ + ma.get_object_signature(npfunc)
locdoc = "Notes\n-----\nThe function is applied to both the _data"\
" and the _mask, if any."
return '\n'.join((sig, doc, locdoc))
return
def __call__(self, *args, **params):
func = getattr(np, self.__name__)
if len(args) == 1:
x = args[0]
if isinstance(x, ndarray):
_d = func(x.__array__(), **params)
_m = func(getmaskarray(x), **params)
return masked_array(_d, mask=_m)
elif isinstance(x, tuple) or isinstance(x, list):
_d = func(tuple([np.asarray(a) for a in x]), **params)
_m = func(tuple([getmaskarray(a) for a in x]), **params)
return masked_array(_d, mask=_m)
else:
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))
return res
atleast_1d = _fromnxfunction('atleast_1d')
atleast_2d = _fromnxfunction('atleast_2d')
atleast_3d = _fromnxfunction('atleast_3d')
#atleast_1d = np.atleast_1d
#atleast_2d = np.atleast_2d
#atleast_3d = np.atleast_3d
vstack = row_stack = _fromnxfunction('vstack')
hstack = _fromnxfunction('hstack')
column_stack = _fromnxfunction('column_stack')
dstack = _fromnxfunction('dstack')
hsplit = _fromnxfunction('hsplit')
diagflat = _fromnxfunction('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
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
% (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)
j = i.copy()
res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
# if res is a number, then we have a smaller output array
asscalar = np.isscalar(res)
if not asscalar:
try:
len(res)
except TypeError:
asscalar = True
# Note: we shouldn't set the dtype of the output from the first result...
#...so we force the type to object, and build a list of dtypes
#...we'll just take the largest, to avoid some downcasting
dtypes = []
if asscalar:
dtypes.append(np.asarray(res).dtype)
outarr = zeros(outshape, object)
outarr[tuple(ind)] = res
Ntot = np.product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
outarr[tuple(ind)] = res
dtypes.append(asarray(res).dtype)
k += 1
else:
res = array(res, copy=False, subok=True)
j = i.copy()
j[axis] = ([slice(None, None)] * res.ndim)
j.put(indlist, ind)
Ntot = np.product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = res.shape
dtypes.append(asarray(res).dtype)
outshape = flatten_inplace(outshape)
outarr = zeros(outshape, object)
outarr[tuple(flatten_inplace(j.tolist()))] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
j.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
outarr[tuple(flatten_inplace(j.tolist()))] = res
dtypes.append(asarray(res).dtype)
k += 1
max_dtypes = np.dtype(np.asarray(dtypes).max())
if not hasattr(arr, '_mask'):
result = np.asarray(outarr, dtype=max_dtypes)
else:
result = asarray(outarr, dtype=max_dtypes)
result.fill_value = ma.default_fill_value(result)
return result
apply_along_axis.__doc__ = np.apply_along_axis.__doc__
def apply_over_axes(func, a, axes):
"""
(This docstring will be overwritten)
"""
val = np.asarray(a)
msk = getmaskarray(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 = ma.array(func(*(val, axis)), mask=func(*(msk, axis)))
if res.ndim == val.ndim:
(val, msk) = (res._data, res._mask)
else:
res = ma.expand_dims(res, axis)
if res.ndim == val.ndim:
(val, msk) = (res._data, res._mask)
else:
raise ValueError("Function is not returning"\
" an array of correct shape")
return val
apply_over_axes.__doc__ = np.apply_over_axes.__doc__
def average(a, axis=None, weights=None, returned=False):
"""
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 the variance is computed. The default is to compute
the variance of 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. If `weights` is complex, the imaginary parts
are ignored.
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.
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, otherwise it is of the same type as `a`.
If returned, `sum_of_weights` is of the same type as `average`.
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)
>>> print x
[[ 0. 1.]
[ 2. 3.]
[ 4. 5.]]
>>> avg, sumweights = np.ma.average(x, axis=0, weights=[1, 2, 3],
... returned=True)
>>> print avg
[2.66666666667 3.66666666667]
"""
a = asarray(a)
mask = a.mask
ash = a.shape
if ash == ():
ash = (1,)
if axis is None:
if mask is nomask:
if weights is None:
n = a.sum(axis=None)
d = float(a.size)
else:
w = filled(weights, 0.0).ravel()
n = umath.add.reduce(a._data.ravel() * w)
d = umath.add.reduce(w)
del w
else:
if weights is None:
n = a.filled(0).sum(axis=None)
d = float(umath.add.reduce((~mask).ravel()))
else:
w = array(filled(weights, 0.0), float, mask=mask).ravel()
n = add.reduce(a.ravel() * w)
d = add.reduce(w)
del w
else:
if mask is nomask:
if weights is None:
d = ash[axis] * 1.0
n = add.reduce(a._data, axis)
else:
w = filled(weights, 0.0)
wsh = w.shape
if wsh == ():
wsh = (1,)
if wsh == ash:
w = np.array(w, float, copy=0)
n = add.reduce(a * w, axis)
d = add.reduce(w, axis)
del w
elif wsh == (ash[axis],):
ni = ash[axis]
r = [None] * len(ash)
r[axis] = slice(None, None, 1)
w = eval ("w[" + repr(tuple(r)) + "] * ones(ash, float)")
n = add.reduce(a * w, axis)
d = add.reduce(w, axis, dtype=float)
del w, r
else:
raise ValueError('average: weights wrong shape.')
else:
if weights is None:
n = add.reduce(a, axis)
d = umath.add.reduce((-mask), axis=axis, dtype=float)
else:
w = filled(weights, 0.0)
wsh = w.shape
if wsh == ():
wsh = (1,)
if wsh == ash:
w = array(w, dtype=float, mask=mask, copy=0)
n = add.reduce(a * w, axis)
d = add.reduce(w, axis, dtype=float)
elif wsh == (ash[axis],):
ni = ash[axis]
r = [None] * len(ash)
r[axis] = slice(None, None, 1)
w = eval ("w[" + repr(tuple(r)) + \
"] * masked_array(ones(ash, float), mask)")
n = add.reduce(a * w, axis)
d = add.reduce(w, axis, dtype=float)
else:
raise ValueError('average: weights wrong shape.')
del w
if n is masked or d is masked:
return masked
result = n / d
del n
if isinstance(result, MaskedArray):
if ((axis is None) or (axis == 0 and a.ndim == 1)) and \
(result.mask is nomask):
result = result._data
if returned:
if not isinstance(d, MaskedArray):
d = masked_array(d)
if isinstance(d, ndarray) and (not d.shape == result.shape):
d = ones(result.shape, dtype=float) * d
if returned:
return result, d
else:
return result
def median(a, axis=None, out=None, overwrite_input=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.
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.extras.median(x)
1.5
>>> x = np.ma.array(np.arange(10).reshape(2, 5), mask=[0]*6 + [1]*4)
>>> np.ma.extras.median(x)
2.5
>>> np.ma.extras.median(x, axis=-1, overwrite_input=True)
masked_array(data = [ 2. 5.],
mask = False,
fill_value = 1e+20)
"""
def _median1D(data):
counts = filled(count(data), 0)
(idx, rmd) = divmod(counts, 2)
if rmd:
choice = slice(idx, idx + 1)
else:
choice = slice(idx - 1, idx + 1)
return data[choice].mean(0)
#
if overwrite_input:
if axis is None:
asorted = a.ravel()
asorted.sort()
else:
a.sort(axis=axis)
asorted = a
else:
asorted = sort(a, axis=axis)
if axis is None:
result = _median1D(asorted)
else:
result = apply_along_axis(_median1D, axis, asorted)
if out is not None:
out = result
return result
#..............................................................................
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
----------
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.extras.compress_rowcols(x)
array([[7, 8]])
>>> np.ma.extras.compress_rowcols(x, 0)
array([[6, 7, 8]])
>>> np.ma.extras.compress_rowcols(x, 1)
array([[1, 2],
[4, 5],
[7, 8]])
"""
x = asarray(x)
if x.ndim != 2:
raise NotImplementedError("compress2d works for 2D arrays only.")
m = getmask(x)
# 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([])
# Builds a list of rows/columns indices
(idxr, idxc) = (list(range(len(x))), list(range(x.shape[1])))
masked = m.nonzero()
if not axis:
for i in np.unique(masked[0]):
idxr.remove(i)
if axis in [None, 1, -1]:
for j in np.unique(masked[1]):
idxc.remove(j)
return x._data[idxr][:, idxc]
def compress_rows(a):
"""
Suppress whole rows of a 2-D array that contain masked values.
This is equivalent to ``np.ma.extras.compress_rowcols(a, 0)``, see
`extras.compress_rowcols` for details.
See Also
--------
extras.compress_rowcols
"""
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.extras.compress_rowcols(a, 1)``, see
`extras.compress_rowcols` for details.
See Also
--------
extras.compress_rowcols
"""
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=np.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=999999)
>>> ma.mask_rowcols(a)
masked_array(data =
[[0 -- 0]
[-- -- --]
[0 -- 0]],
mask =
[[False True False]
[ True True True]
[False True False]],
fill_value=999999)
"""
a = asarray(a)
if a.ndim != 2:
raise NotImplementedError("compress2d 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=None):
"""
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=np.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=999999)
>>> 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=999999)
"""
return mask_rowcols(a, 0)
def mask_cols(a, axis=None):
"""
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=np.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=999999)
>>> 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=999999)
"""
return mask_rowcols(a, 1)
def dot(a, b, strict=False):
"""
Return the dot product of two arrays.
.. note::
Works only with 2-D arrays at the moment.
This function is the equivalent of `numpy.dot` that takes masked values
into account, see `numpy.dot` for details.
Parameters
----------
a, b : ndarray
Inputs arrays.
strict : bool, optional
Whether masked data are propagated (True) or set to 0 (False) for the
computation. Default is False.
Propagating the mask means that if a masked value appears in a row or
column, the whole row or column is considered masked.
See Also
--------
numpy.dot : Equivalent function for ndarrays.
Examples
--------
>>> a = ma.array([[1, 2, 3], [4, 5, 6]], mask=[[1, 0, 0], [0, 0, 0]])
>>> b = ma.array([[1, 2], [3, 4], [5, 6]], mask=[[1, 0], [0, 0], [0, 0]])
>>> np.ma.dot(a, b)
masked_array(data =
[[21 26]
[45 64]],
mask =
[[False False]
[False False]],
fill_value = 999999)
>>> np.ma.dot(a, b, strict=True)
masked_array(data =
[[-- --]
[-- 64]],
mask =
[[ True True]
[ True False]],
fill_value = 999999)
"""
#!!!: Works only with 2D arrays. There should be a way to get it to run with higher dimension
if strict and (a.ndim == 2) and (b.ndim == 2):
a = mask_rows(a)
b = mask_cols(b)
#
d = np.dot(filled(a, 0), filled(b, 0))
#
am = (~getmaskarray(a))
bm = (~getmaskarray(b))
m = ~np.dot(am, bm)
return masked_array(d, mask=m)
#####--------------------------------------------------------------------------
#---- --- 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.
"""
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 = array([1, 3, 3, 3], mask=[0, 0, 0, 1])
>>> y = array([3, 1, 1, 1], mask=[0, 0, 0, 1])
>>> 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.
See Also
--------
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 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)))
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.extras.setdiff1d(x, [1, 2])
masked_array(data = [3 --],
mask = [False True],
fill_value = 999999)
"""
if not assume_unique:
ar1 = unique(ar1)
ar2 = unique(ar2)
aux = in1d(ar1, ar2, assume_unique=True)
if aux.size == 0:
return aux
else:
return ma.asarray(ar1)[aux == 0]
#####--------------------------------------------------------------------------
#---- --- 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:
x.unshare_mask()
y.unshare_mask()
xmask = x._mask = y._mask = ymask = common_mask
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
form 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
.. versionadded:: 1.5
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``.
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=False, allow_masked=True, ddof=None):
"""
Return correlation coefficients of the input array.
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 : bool, optional
Default normalization (False) is by ``(N-1)``, where ``N`` is the
number of observations given (unbiased estimate). If `bias` is 1,
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 an exception.
ddof : {None, int}, optional
.. versionadded:: 1.5
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``.
See Also
--------
numpy.corrcoef : Equivalent function in top-level NumPy module.
cov : Estimate the covariance matrix.
"""
# 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
# 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. - ddof
c = (dot(x.T, x.conj(), strict=False) / fact).squeeze()
else:
fact = np.dot(xnotmask, xnotmask.T) * 1. - ddof
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)
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, ddof=ddof)
_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, ddof=ddof)
_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
"""
def __init__(self, axis=0):
AxisConcatenator.__init__(self, axis, matrix=False)
def __getitem__(self, key):
if isinstance(key, str):
raise MAError("Unavailable for masked array.")
if not isinstance(key, tuple):
key = (key,)
objs = []
scalars = []
final_dtypedescr = None
for k in range(len(key)):
scalar = False
if isinstance(key[k], slice):
step = key[k].step
start = key[k].start
stop = key[k].stop
if start is None:
start = 0
if step is None:
step = 1
if isinstance(step, complex):
size = int(abs(step))
newobj = np.linspace(start, stop, num=size)
else:
newobj = np.arange(start, stop, step)
elif isinstance(key[k], str):
if (key[k] in 'rc'):
self.matrix = True
self.col = (key[k] == 'c')
continue
try:
self.axis = int(key[k])
continue
except (ValueError, TypeError):
raise ValueError("Unknown special directive")
elif type(key[k]) in np.ScalarType:
newobj = asarray([key[k]])
scalars.append(k)
scalar = True
else:
newobj = key[k]
objs.append(newobj)
if isinstance(newobj, ndarray) and not scalar:
if final_dtypedescr is None:
final_dtypedescr = newobj.dtype
elif newobj.dtype > final_dtypedescr:
final_dtypedescr = newobj.dtype
if final_dtypedescr is not None:
for k in scalars:
objs[k] = objs[k].astype(final_dtypedescr)
res = concatenate(tuple(objs), axis=self.axis)
return self._retval(res)
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])]
array([1, 2, 3, 0, 0, 4, 5, 6])
"""
def __init__(self):
MAxisConcatenator.__init__(self, 0)
mr_ = mr_class()
#####--------------------------------------------------------------------------
#---- Find unmasked data ---
#####--------------------------------------------------------------------------
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
----------
arr : 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)
>>> flatnotmasked_edges(a)
[0,-1]
>>> mask = (a < 3) | (a > 8) | (a == 5)
>>> a[mask] = np.ma.masked
>>> np.array(a[~a.mask])
array([3, 4, 6, 7, 8])
>>> flatnotmasked_edges(a)
array([3, 8])
>>> a[:] = np.ma.masked
>>> print flatnotmasked_edges(ma)
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.extras.notmasked_edges(ma)
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 along the given axis.
Parameters
----------
a : narray
The input array.
Returns
-------
slice_list : list
A sorted sequence of slices (start index, end index).
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.extras.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.extras.flatnotmasked_contiguous(a)
[slice(3, 5, None), slice(6, 9, None)]
>>> a[:] = np.ma.masked
>>> print np.ma.extras.flatnotmasked_edges(a)
None
"""
m = getmask(a)
if m is nomask:
return slice(0, a.size, None)
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 or None
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.
Returns
-------
endpoints : list
A list of slices (start and end indexes) of unmasked indexes
in the array.
See Also
--------
flatnotmasked_edges, flatnotmasked_contiguous, notmasked_edges,
clump_masked, clump_unmasked
Notes
-----
Only accepts 2-D arrays at most.
Examples
--------
>>> a = np.arange(9).reshape((3, 3))
>>> mask = np.zeros_like(a)
>>> mask[1:, 1:] = 1
>>> ma = np.ma.array(a, mask=mask)
>>> np.array(ma[~ma.mask])
array([0, 1, 2, 3, 6])
>>> np.ma.extras.notmasked_contiguous(ma)
[slice(0, 4, None), slice(6, 7, None)]
"""
a = asarray(a)
nd = a.ndim
if nd > 2:
raise NotImplementedError("Currently limited to atmost 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[idx]) or None)
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.
"""
#def clump_masked(a):
if mask.ndim > 1:
mask = mask.ravel()
idx = (mask[1:] - mask[:-1]).nonzero()
idx = idx[0] + 1
slices = [slice(left, right)
for (left, right) in zip(itertools.chain([0], idx),
itertools.chain(idx, [len(mask)]),)]
return slices
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.extras.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)]
slices = _ezclump(mask)
if a[0] is masked:
result = slices[1::2]
else:
result = slices[::2]
return result
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.extras.clump_masked(a)
[slice(0, 3, None), slice(6, 7, None), slice(8, 10, None)]
"""
mask = ma.getmask(a)
if mask is nomask:
return []
slices = _ezclump(mask)
if len(slices):
if a[0] is masked:
slices = slices[::2]
else:
slices = slices[1::2]
return slices
#####--------------------------------------------------------------------------
#---- 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:
if w is not None:
w = ~m*w
else:
w = ~m
return np.polyfit(x, y, deg, rcond, full, w, cov)
polyfit.__doc__ = ma.doc_note(np.polyfit.__doc__, polyfit.__doc__)
################################################################################
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