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__all__ = ['column_stack','row_stack', 'dstack','array_split','split','hsplit',
'vsplit','dsplit','apply_over_axes','expand_dims',
'apply_along_axis', 'kron', 'tile', 'get_array_wrap']
import numpy.core.numeric as _nx
from numpy.core.numeric import asarray, zeros, newaxis, outer, \
concatenate, isscalar, array, asanyarray
from numpy.core.fromnumeric import product, reshape
from numpy.core import hstack, vstack, atleast_3d
def apply_along_axis(func1d,axis,arr,*args):
"""
Apply a function to 1-D slices along the given axis.
Execute `func1d(a, *args)` where `func1d` operates on 1-D arrays and `a`
is a 1-D slice of `arr` along `axis`.
Parameters
----------
func1d : function
This function should accept 1-D arrays. It is applied to 1-D
slices of `arr` along the specified axis.
axis : integer
Axis along which `arr` is sliced.
arr : ndarray
Input array.
args : any
Additional arguments to `func1d`.
Returns
-------
outarr : ndarray
The output array. The shape of `outarr` is identical to the shape of
`arr`, except along the `axis` dimension, where the length of `outarr`
is equal to the size of the return value of `func1d`. If `func1d`
returns a scalar `outarr` will have one fewer dimensions than `arr`.
See Also
--------
apply_over_axes : Apply a function repeatedly over multiple axes.
Examples
--------
>>> def my_func(a):
... \"\"\"Average first and last element of a 1-D array\"\"\"
... return (a[0] + a[-1]) * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(my_func, 0, b)
array([4., 5., 6.])
>>> np.apply_along_axis(my_func, 1, b)
array([2., 5., 8.])
For a function that doesn't return a scalar, the number of dimensions in
`outarr` is the same as `arr`.
>>> def new_func(a):
... \"\"\"Divide elements of a by 2.\"\"\"
... return a * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(new_func, 0, b)
array([[ 0.5, 1. , 1.5],
[ 2. , 2.5, 3. ],
[ 3.5, 4. , 4.5]])
"""
arr = asarray(arr)
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 = zeros(nd,'O')
indlist = range(nd)
indlist.remove(axis)
i[axis] = slice(None,None)
outshape = asarray(arr.shape).take(indlist)
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())],*args)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape,asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = 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)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape,asarray(res).dtype)
outarr[tuple(i.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)
res = func1d(arr[tuple(i.tolist())],*args)
outarr[tuple(i.tolist())] = res
k += 1
return outarr
def apply_over_axes(func, a, axes):
"""
Apply a function repeatedly over multiple axes.
`func` is called as `res = func(a, axis)`, where `axis` is the first
element of `axes`. The result `res` of the function call must have
either the same dimensions as `a` or one less dimension. If `res` has one
less dimension than `a`, a dimension is inserted before `axis`.
The call to `func` is then repeated for each axis in `axes`,
with `res` as the first argument.
Parameters
----------
func : function
This function must take two arguments, `func(a, axis)`.
a : ndarray
Input array.
axes : array_like
Axes over which `func` is applied, the elements must be
integers.
Returns
-------
val : ndarray
The output array. The number of dimensions is the same as `a`, but
the shape can be different. This depends on whether `func` changes
the shape of its output with respect to its input.
See Also
--------
apply_along_axis :
Apply a function to 1-D slices of an array along the given axis.
Examples
--------
>>> a = np.arange(24).reshape(2,3,4)
>>> a
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
Sum over axes 0 and 2. The result has same number of dimensions
as the original array:
>>> np.apply_over_axes(np.sum, a, [0,2])
array([[[ 60],
[ 92],
[124]]])
"""
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 = expand_dims(res,axis)
if res.ndim == val.ndim:
val = res
else:
raise ValueError, "function is not returning"\
" an array of correct shape"
return val
def expand_dims(a, axis):
"""
Expand the shape of an array.
Insert a new axis, corresponding to a given position in the array shape.
Parameters
----------
a : array_like
Input array.
axis : int
Position (amongst axes) where new axis is to be inserted.
Returns
-------
res : ndarray
Output array. The number of dimensions is one greater than that of
the input array.
See Also
--------
doc.indexing, atleast_1d, atleast_2d, atleast_3d
Examples
--------
>>> x = np.array([1,2])
>>> x.shape
(2,)
The following is equivalent to ``x[np.newaxis,:]`` or ``x[np.newaxis]``:
>>> y = np.expand_dims(x, axis=0)
>>> y
array([[1, 2]])
>>> y.shape
(1, 2)
>>> y = np.expand_dims(x, axis=1) # Equivalent to x[:,newaxis]
>>> y
array([[1],
[2]])
>>> y.shape
(2, 1)
Note that some examples may use ``None`` instead of ``np.newaxis``. These
are the same objects:
>>> np.newaxis is None
True
"""
a = asarray(a)
shape = a.shape
if axis < 0:
axis = axis + len(shape) + 1
return a.reshape(shape[:axis] + (1,) + shape[axis:])
row_stack = vstack
def column_stack(tup):
"""
Stack 1-D arrays as columns into a 2-D array.
Take a sequence of 1-D arrays and stack them as columns
to make a single 2-D array. 2-D arrays are stacked as-is,
just like with `hstack`. 1-D arrays are turned into 2-D columns
first.
Parameters
----------
tup : sequence of 1-D or 2-D arrays.
Arrays to stack. All of them must have the same first dimension.
Returns
-------
stacked : 2-D array
The array formed by stacking the given arrays.
See Also
--------
hstack, vstack, concatenate
Notes
-----
This function is equivalent to ``np.vstack(tup).T``.
Examples
--------
>>> a = np.array((1,2,3))
>>> b = np.array((2,3,4))
>>> np.column_stack((a,b))
array([[1, 2],
[2, 3],
[3, 4]])
"""
arrays = []
for v in tup:
arr = array(v,copy=False,subok=True)
if arr.ndim < 2:
arr = array(arr,copy=False,subok=True,ndmin=2).T
arrays.append(arr)
return _nx.concatenate(arrays,1)
def dstack(tup):
"""
Stack arrays in sequence depth wise (along third axis).
Takes a sequence of arrays and stack them along the third axis
to make a single array. Rebuilds arrays divided by ``dsplit``.
This is a simple way to stack 2D arrays (images) into a single
3D array for processing.
Parameters
----------
tup : sequence of arrays
Arrays to stack. All of them must have the same shape along all
but the third axis.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
See Also
--------
vstack : Stack along first axis.
hstack : Stack along second axis.
concatenate : Join arrays.
dsplit : Split array along third axis.
Notes
-----
Equivalent to ``np.concatenate(tup, axis=2)``
Examples
--------
>>> a = np.array((1,2,3))
>>> b = np.array((2,3,4))
>>> np.dstack((a,b))
array([[[1, 2],
[2, 3],
[3, 4]]])
>>> a = np.array([[1],[2],[3]])
>>> b = np.array([[2],[3],[4]])
>>> np.dstack((a,b))
array([[[1, 2]],
[[2, 3]],
[[3, 4]]])
"""
return _nx.concatenate(map(atleast_3d,tup),2)
def _replace_zero_by_x_arrays(sub_arys):
for i in range(len(sub_arys)):
if len(_nx.shape(sub_arys[i])) == 0:
sub_arys[i] = _nx.array([])
elif _nx.sometrue(_nx.equal(_nx.shape(sub_arys[i]),0)):
sub_arys[i] = _nx.array([])
return sub_arys
def array_split(ary,indices_or_sections,axis = 0):
"""
Split an array into multiple sub-arrays of equal or near-equal size.
Please refer to the ``split`` documentation. The only difference
between these functions is that ``array_split`` allows
`indices_or_sections` to be an integer that does *not* equally
divide the axis.
See Also
--------
split : Split array into multiple sub-arrays of equal size.
Examples
--------
>>> x = np.arange(8.0)
>>> np.array_split(x, 3)
[array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7.])]
"""
try:
Ntotal = ary.shape[axis]
except AttributeError:
Ntotal = len(ary)
try: # handle scalar case.
Nsections = len(indices_or_sections) + 1
div_points = [0] + list(indices_or_sections) + [Ntotal]
except TypeError: #indices_or_sections is a scalar, not an array.
Nsections = int(indices_or_sections)
if Nsections <= 0:
raise ValueError, 'number sections must be larger than 0.'
Neach_section,extras = divmod(Ntotal,Nsections)
section_sizes = [0] + \
extras * [Neach_section+1] + \
(Nsections-extras) * [Neach_section]
div_points = _nx.array(section_sizes).cumsum()
sub_arys = []
sary = _nx.swapaxes(ary,axis,0)
for i in range(Nsections):
st = div_points[i]; end = div_points[i+1]
sub_arys.append(_nx.swapaxes(sary[st:end],axis,0))
# there is a wierd issue with array slicing that allows
# 0x10 arrays and other such things. The following cluge is needed
# to get around this issue.
sub_arys = _replace_zero_by_x_arrays(sub_arys)
# end cluge.
return sub_arys
def split(ary,indices_or_sections,axis=0):
"""
Split an array into multiple sub-arrays of equal size.
Parameters
----------
ary : ndarray
Array to be divided into sub-arrays.
indices_or_sections : int or 1-D array
If `indices_or_sections` is an integer, N, the array will be divided
into N equal arrays along `axis`. If such a split is not possible,
an error is raised.
If `indices_or_sections` is a 1-D array of sorted integers, the entries
indicate where along `axis` the array is split. For example,
``[2, 3]`` would, for ``axis = 0``, result in
- ary[:2]
- ary[2:3]
- ary[3:]
If an index exceeds the dimension of the array along `axis`,
an empty sub-array is returned correspondingly.
axis : int, optional
The axis along which to split, default is 0.
Returns
-------
sub-arrays : list of ndarrays
A list of sub-arrays.
Raises
------
ValueError
If `indices_or_sections` is given as an integer, but
a split does not result in equal division.
See Also
--------
array_split : Split an array into multiple sub-arrays of equal or
near-equal size. Does not raise an exception if
an equal division cannot be made.
hsplit : Split array into multiple sub-arrays horizontally (column-wise).
vsplit : Split array into multiple sub-arrays vertically (row wise).
dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
concatenate : Join arrays together.
hstack : Stack arrays in sequence horizontally (column wise).
vstack : Stack arrays in sequence vertically (row wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
Examples
--------
>>> x = np.arange(9.0)
>>> np.split(x, 3)
[array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7., 8.])]
>>> x = np.arange(8.0)
>>> np.split(x, [3, 5, 6, 10])
[array([ 0., 1., 2.]),
array([ 3., 4.]),
array([ 5.]),
array([ 6., 7.]),
array([], dtype=float64)]
"""
try: len(indices_or_sections)
except TypeError:
sections = indices_or_sections
N = ary.shape[axis]
if N % sections:
raise ValueError, 'array split does not result in an equal division'
res = array_split(ary,indices_or_sections,axis)
return res
def hsplit(ary,indices_or_sections):
"""
Split an array into multiple sub-arrays horizontally (column-wise).
Please refer to the ``split`` documentation. ``hsplit`` is equivalent
to ``split`` with `axis=1`, the array is always split along the second
axis regardless of the array dimension.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
>>> x = np.arange(16.0).reshape(4, 4)
>>> x
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])
>>> np.hsplit(x, 2)
[array([[ 0., 1.],
[ 4., 5.],
[ 8., 9.],
[ 12., 13.]]),
array([[ 2., 3.],
[ 6., 7.],
[ 10., 11.],
[ 14., 15.]])]
>>> np.hsplit(x, np.array([3, 6]))
[array([[ 0., 1., 2.],
[ 4., 5., 6.],
[ 8., 9., 10.],
[ 12., 13., 14.]]),
array([[ 3.],
[ 7.],
[ 11.],
[ 15.]]),
array([], dtype=float64)]
With a higher dimensional array the split is still along the second axis.
>>> x = np.arange(8.0).reshape(2, 2, 2)
>>> x
array([[[ 0., 1.],
[ 2., 3.]],
[[ 4., 5.],
[ 6., 7.]]])
>>> np.hsplit(x, 2)
[array([[[ 0., 1.]],
[[ 4., 5.]]]),
array([[[ 2., 3.]],
[[ 6., 7.]]])]
"""
if len(_nx.shape(ary)) == 0:
raise ValueError, 'hsplit only works on arrays of 1 or more dimensions'
if len(ary.shape) > 1:
return split(ary,indices_or_sections,1)
else:
return split(ary,indices_or_sections,0)
def vsplit(ary,indices_or_sections):
"""
Split an array into multiple sub-arrays vertically (row-wise).
Please refer to the ``split`` documentation. ``vsplit`` is equivalent
to ``split`` with `axis=0` (default), the array is always split along the
first axis regardless of the array dimension.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
>>> x = np.arange(16.0).reshape(4, 4)
>>> x
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])
>>> np.vsplit(x, 2)
[array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.]]),
array([[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])]
>>> np.vsplit(x, np.array([3, 6]))
[array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.]]),
array([[ 12., 13., 14., 15.]]),
array([], dtype=float64)]
With a higher dimensional array the split is still along the first axis.
>>> x = np.arange(8.0).reshape(2, 2, 2)
>>> x
array([[[ 0., 1.],
[ 2., 3.]],
[[ 4., 5.],
[ 6., 7.]]])
>>> np.vsplit(x, 2)
[array([[[ 0., 1.],
[ 2., 3.]]]),
array([[[ 4., 5.],
[ 6., 7.]]])]
"""
if len(_nx.shape(ary)) < 2:
raise ValueError, 'vsplit only works on arrays of 2 or more dimensions'
return split(ary,indices_or_sections,0)
def dsplit(ary,indices_or_sections):
"""
Split array into multiple sub-arrays along the 3rd axis (depth).
Please refer to the ``split`` documentation. ``dsplit`` is equivalent
to ``split`` with `axis=2`, the array is always split along the third
axis provided the array dimension is greater than or equal to 3.
See Also
--------
split : Split an array into multiple sub-arrays of equal size.
Examples
--------
>>> x = np.arange(16.0).reshape(2, 2, 4)
>>> x
array([[[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.]],
[[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]]])
>>> np.dsplit(x, 2)
[array([[[ 0., 1.],
[ 4., 5.]],
[[ 8., 9.],
[ 12., 13.]]]),
array([[[ 2., 3.],
[ 6., 7.]],
[[ 10., 11.],
[ 14., 15.]]])]
>>> np.dsplit(x, np.array([3, 6]))
[array([[[ 0., 1., 2.],
[ 4., 5., 6.]],
[[ 8., 9., 10.],
[ 12., 13., 14.]]]),
array([[[ 3.],
[ 7.]],
[[ 11.],
[ 15.]]]),
array([], dtype=float64)]
"""
if len(_nx.shape(ary)) < 3:
raise ValueError, 'vsplit only works on arrays of 3 or more dimensions'
return split(ary,indices_or_sections,2)
def get_array_prepare(*args):
"""Find the wrapper for the array with the highest priority.
In case of ties, leftmost wins. If no wrapper is found, return None
"""
wrappers = [(getattr(x, '__array_priority__', 0), -i,
x.__array_prepare__) for i, x in enumerate(args)
if hasattr(x, '__array_prepare__')]
wrappers.sort()
if wrappers:
return wrappers[-1][-1]
return None
def get_array_wrap(*args):
"""Find the wrapper for the array with the highest priority.
In case of ties, leftmost wins. If no wrapper is found, return None
"""
wrappers = [(getattr(x, '__array_priority__', 0), -i,
x.__array_wrap__) for i, x in enumerate(args)
if hasattr(x, '__array_wrap__')]
wrappers.sort()
if wrappers:
return wrappers[-1][-1]
return None
def kron(a,b):
"""
Kronecker product of two arrays.
Computes the Kronecker product, a composite array made of blocks of the
second array scaled by the first.
Parameters
----------
a, b : array_like
Returns
-------
out : ndarray
See Also
--------
outer : The outer product
Notes
-----
The function assumes that the number of dimenensions of `a` and `b`
are the same, if necessary prepending the smallest with ones.
If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`,
the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`.
The elements are products of elements from `a` and `b`, organized
explicitly by::
kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
where::
kt = it * st + jt, t = 0,...,N
In the common 2-D case (N=1), the block structure can be visualized::
[[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ],
[ ... ... ],
[ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]]
Examples
--------
>>> np.kron([1,10,100], [5,6,7])
array([ 5, 6, 7, 50, 60, 70, 500, 600, 700])
>>> np.kron([5,6,7], [1,10,100])
array([ 5, 50, 500, 6, 60, 600, 7, 70, 700])
>>> np.kron(np.eye(2), np.ones((2,2)))
array([[ 1., 1., 0., 0.],
[ 1., 1., 0., 0.],
[ 0., 0., 1., 1.],
[ 0., 0., 1., 1.]])
>>> a = np.arange(100).reshape((2,5,2,5))
>>> b = np.arange(24).reshape((2,3,4))
>>> c = np.kron(a,b)
>>> c.shape
(2, 10, 6, 20)
>>> I = (1,3,0,2)
>>> J = (0,2,1)
>>> J1 = (0,) + J # extend to ndim=4
>>> S1 = (1,) + b.shape
>>> K = tuple(np.array(I) * np.array(S1) + np.array(J1))
>>> C[K] == A[I]*B[J]
True
"""
b = asanyarray(b)
a = array(a,copy=False,subok=True,ndmin=b.ndim)
ndb, nda = b.ndim, a.ndim
if (nda == 0 or ndb == 0):
return _nx.multiply(a,b)
as_ = a.shape
bs = b.shape
if not a.flags.contiguous:
a = reshape(a, as_)
if not b.flags.contiguous:
b = reshape(b, bs)
nd = ndb
if (ndb != nda):
if (ndb > nda):
as_ = (1,)*(ndb-nda) + as_
else:
bs = (1,)*(nda-ndb) + bs
nd = nda
result = outer(a,b).reshape(as_+bs)
axis = nd-1
for _ in xrange(nd):
result = concatenate(result, axis=axis)
wrapper = get_array_prepare(a, b)
if wrapper is not None:
result = wrapper(result)
wrapper = get_array_wrap(a, b)
if wrapper is not None:
result = wrapper(result)
return result
def tile(A, reps):
"""
Construct an array by repeating A the number of times given by reps.
If `reps` has length ``d``, the result will have dimension of
``max(d, A.ndim)``.
If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new
axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,
or shape (1, 1, 3) for 3-D replication. If this is not the desired
behavior, promote `A` to d-dimensions manually before calling this
function.
If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it.
Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as
(1, 1, 2, 2).
Parameters
----------
A : array_like
The input array.
reps : array_like
The number of repetitions of `A` along each axis.
Returns
-------
c : ndarray
The tiled output array.
See Also
--------
repeat : Repeat elements of an array.
Examples
--------
>>> a = np.array([0, 1, 2])
>>> np.tile(a, 2)
array([0, 1, 2, 0, 1, 2])
>>> np.tile(a, (2, 2))
array([[0, 1, 2, 0, 1, 2],
[0, 1, 2, 0, 1, 2]])
>>> np.tile(a, (2, 1, 2))
array([[[0, 1, 2, 0, 1, 2]],
[[0, 1, 2, 0, 1, 2]]])
>>> b = np.array([[1, 2], [3, 4]])
>>> np.tile(b, 2)
array([[1, 2, 1, 2],
[3, 4, 3, 4]])
>>> np.tile(b, (2, 1))
array([[1, 2],
[3, 4],
[1, 2],
[3, 4]])
"""
try:
tup = tuple(reps)
except TypeError:
tup = (reps,)
d = len(tup)
c = _nx.array(A,copy=False,subok=True,ndmin=d)
shape = list(c.shape)
n = max(c.size,1)
if (d < c.ndim):
tup = (1,)*(c.ndim-d) + tup
for i, nrep in enumerate(tup):
if nrep!=1:
c = c.reshape(-1,n).repeat(nrep,0)
dim_in = shape[i]
dim_out = dim_in*nrep
shape[i] = dim_out
n /= max(dim_in,1)
return c.reshape(shape)
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