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Copy pathnumeric.py
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2706 lines (2200 loc) · 78.6 KB
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import builtins
import functools
import itertools
import math
import numbers
import operator
import sys
import warnings
import numpy as np
from numpy.exceptions import AxisError
from . import multiarray, numerictypes, numerictypes as nt, overrides, shape_base, umath
from ._ufunc_config import errstate
from .multiarray import ( # noqa: F401
ALLOW_THREADS,
BUFSIZE,
CLIP,
MAXDIMS,
MAY_SHARE_BOUNDS,
MAY_SHARE_EXACT,
RAISE,
WRAP,
arange,
array,
asanyarray,
asarray,
ascontiguousarray,
asfortranarray,
broadcast,
can_cast,
concatenate,
copyto,
dot,
dtype,
empty,
empty_like,
flatiter,
from_dlpack,
frombuffer,
fromfile,
fromiter,
fromstring,
inner,
lexsort,
matmul,
may_share_memory,
min_scalar_type,
ndarray,
nditer,
nested_iters,
normalize_axis_index,
promote_types,
putmask,
result_type,
shares_memory,
vdot,
vecdot,
where,
zeros,
)
from .overrides import finalize_array_function_like, set_module
from .umath import NAN, PINF, invert, multiply, sin
bitwise_not = invert
ufunc = type(sin)
newaxis = None
array_function_dispatch = functools.partial(
overrides.array_function_dispatch, module='numpy')
__all__ = [
'newaxis', 'ndarray', 'flatiter', 'nditer', 'nested_iters', 'ufunc',
'arange', 'array', 'asarray', 'asanyarray', 'ascontiguousarray',
'asfortranarray', 'zeros', 'count_nonzero', 'empty', 'broadcast', 'dtype',
'fromstring', 'fromfile', 'frombuffer', 'from_dlpack', 'where',
'argwhere', 'copyto', 'concatenate', 'lexsort', 'astype',
'can_cast', 'promote_types', 'min_scalar_type',
'result_type', 'isfortran', 'empty_like', 'zeros_like', 'ones_like',
'correlate', 'convolve', 'inner', 'dot', 'outer', 'vdot', 'roll',
'rollaxis', 'moveaxis', 'cross', 'tensordot', 'little_endian',
'fromiter', 'array_equal', 'array_equiv', 'indices', 'fromfunction',
'isclose', 'isscalar', 'binary_repr', 'base_repr', 'ones',
'identity', 'allclose', 'putmask',
'flatnonzero', 'inf', 'nan', 'False_', 'True_', 'bitwise_not',
'full', 'full_like', 'matmul', 'vecdot', 'shares_memory',
'may_share_memory']
def _zeros_like_dispatcher(
a, dtype=None, order=None, subok=None, shape=None, *, device=None
):
return (a,)
@array_function_dispatch(_zeros_like_dispatcher)
def zeros_like(
a, dtype=None, order='K', subok=True, shape=None, *, device=None
):
"""
Return an array of zeros with the same shape and type as a given array.
Parameters
----------
a : array_like
The shape and data-type of `a` define these same attributes of
the returned array.
dtype : data-type, optional
Overrides the data type of the result.
order : {'C', 'F', 'A', or 'K'}, optional
Overrides the memory layout of the result. 'C' means C-order,
'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
'C' otherwise. 'K' means match the layout of `a` as closely
as possible.
subok : bool, optional.
If True, then the newly created array will use the sub-class
type of `a`, otherwise it will be a base-class array. Defaults
to True.
shape : int or sequence of ints, optional.
Overrides the shape of the result. If order='K' and the number of
dimensions is unchanged, will try to keep order, otherwise,
order='C' is implied.
device : str, optional
The device on which to place the created array. Default: None.
For Array-API interoperability only, so must be ``"cpu"`` if passed.
.. versionadded:: 2.0.0
Returns
-------
out : ndarray
Array of zeros with the same shape and type as `a`.
See Also
--------
empty_like : Return an empty array with shape and type of input.
ones_like : Return an array of ones with shape and type of input.
full_like : Return a new array with shape of input filled with value.
zeros : Return a new array setting values to zero.
Examples
--------
>>> import numpy as np
>>> x = np.arange(6)
>>> x = x.reshape((2, 3))
>>> x
array([[0, 1, 2],
[3, 4, 5]])
>>> np.zeros_like(x)
array([[0, 0, 0],
[0, 0, 0]])
>>> y = np.arange(3, dtype=np.float64)
>>> y
array([0., 1., 2.])
>>> np.zeros_like(y)
array([0., 0., 0.])
"""
res = empty_like(
a, dtype=dtype, order=order, subok=subok, shape=shape, device=device
)
# needed instead of a 0 to get same result as zeros for string dtypes
z = zeros(1, dtype=res.dtype)
multiarray.copyto(res, z, casting='unsafe')
return res
@finalize_array_function_like
@set_module('numpy')
def ones(shape, dtype=None, order='C', *, device=None, like=None):
"""
Return a new array of given shape and type, filled with ones.
Parameters
----------
shape : int or sequence of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype : data-type, optional
The desired data-type for the array, e.g., `numpy.int8`. Default is
`numpy.float64`.
order : {'C', 'F'}, optional, default: C
Whether to store multi-dimensional data in row-major
(C-style) or column-major (Fortran-style) order in
memory.
device : str, optional
The device on which to place the created array. Default: None.
For Array-API interoperability only, so must be ``"cpu"`` if passed.
.. versionadded:: 2.0.0
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
out : ndarray
Array of ones with the given shape, dtype, and order.
See Also
--------
ones_like : Return an array of ones with shape and type of input.
empty : Return a new uninitialized array.
zeros : Return a new array setting values to zero.
full : Return a new array of given shape filled with value.
Examples
--------
>>> import numpy as np
>>> np.ones(5)
array([1., 1., 1., 1., 1.])
>>> np.ones((5,), dtype=np.int_)
array([1, 1, 1, 1, 1])
>>> np.ones((2, 1))
array([[1.],
[1.]])
>>> s = (2,2)
>>> np.ones(s)
array([[1., 1.],
[1., 1.]])
"""
if like is not None:
return _ones_with_like(
like, shape, dtype=dtype, order=order, device=device
)
a = empty(shape, dtype, order, device=device)
multiarray.copyto(a, 1, casting='unsafe')
return a
_ones_with_like = array_function_dispatch()(ones)
def _ones_like_dispatcher(
a, dtype=None, order=None, subok=None, shape=None, *, device=None
):
return (a,)
@array_function_dispatch(_ones_like_dispatcher)
def ones_like(
a, dtype=None, order='K', subok=True, shape=None, *, device=None
):
"""
Return an array of ones with the same shape and type as a given array.
Parameters
----------
a : array_like
The shape and data-type of `a` define these same attributes of
the returned array.
dtype : data-type, optional
Overrides the data type of the result.
order : {'C', 'F', 'A', or 'K'}, optional
Overrides the memory layout of the result. 'C' means C-order,
'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
'C' otherwise. 'K' means match the layout of `a` as closely
as possible.
subok : bool, optional.
If True, then the newly created array will use the sub-class
type of `a`, otherwise it will be a base-class array. Defaults
to True.
shape : int or sequence of ints, optional.
Overrides the shape of the result. If order='K' and the number of
dimensions is unchanged, will try to keep order, otherwise,
order='C' is implied.
device : str, optional
The device on which to place the created array. Default: None.
For Array-API interoperability only, so must be ``"cpu"`` if passed.
.. versionadded:: 2.0.0
Returns
-------
out : ndarray
Array of ones with the same shape and type as `a`.
See Also
--------
empty_like : Return an empty array with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
full_like : Return a new array with shape of input filled with value.
ones : Return a new array setting values to one.
Examples
--------
>>> import numpy as np
>>> x = np.arange(6)
>>> x = x.reshape((2, 3))
>>> x
array([[0, 1, 2],
[3, 4, 5]])
>>> np.ones_like(x)
array([[1, 1, 1],
[1, 1, 1]])
>>> y = np.arange(3, dtype=np.float64)
>>> y
array([0., 1., 2.])
>>> np.ones_like(y)
array([1., 1., 1.])
"""
res = empty_like(
a, dtype=dtype, order=order, subok=subok, shape=shape, device=device
)
multiarray.copyto(res, 1, casting='unsafe')
return res
def _full_dispatcher(
shape, fill_value, dtype=None, order=None, *, device=None, like=None
):
return (like,)
@finalize_array_function_like
@set_module('numpy')
def full(shape, fill_value, dtype=None, order='C', *, device=None, like=None):
"""
Return a new array of given shape and type, filled with `fill_value`.
Parameters
----------
shape : int or sequence of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
fill_value : scalar or array_like
Fill value.
dtype : data-type, optional
The desired data-type for the array The default, None, means
``np.array(fill_value).dtype``.
order : {'C', 'F'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory.
device : str, optional
The device on which to place the created array. Default: None.
For Array-API interoperability only, so must be ``"cpu"`` if passed.
.. versionadded:: 2.0.0
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
out : ndarray
Array of `fill_value` with the given shape, dtype, and order.
See Also
--------
full_like : Return a new array with shape of input filled with value.
empty : Return a new uninitialized array.
ones : Return a new array setting values to one.
zeros : Return a new array setting values to zero.
Examples
--------
>>> import numpy as np
>>> np.full((2, 2), np.inf)
array([[inf, inf],
[inf, inf]])
>>> np.full((2, 2), 10)
array([[10, 10],
[10, 10]])
>>> np.full((2, 2), [1, 2])
array([[1, 2],
[1, 2]])
"""
if like is not None:
return _full_with_like(
like, shape, fill_value, dtype=dtype, order=order, device=device
)
if dtype is None:
fill_value = asarray(fill_value)
dtype = fill_value.dtype
a = empty(shape, dtype, order, device=device)
multiarray.copyto(a, fill_value, casting='unsafe')
return a
_full_with_like = array_function_dispatch()(full)
def _full_like_dispatcher(
a, fill_value, dtype=None, order=None, subok=None, shape=None,
*, device=None
):
return (a,)
@array_function_dispatch(_full_like_dispatcher)
def full_like(
a, fill_value, dtype=None, order='K', subok=True, shape=None,
*, device=None
):
"""
Return a full array with the same shape and type as a given array.
Parameters
----------
a : array_like
The shape and data-type of `a` define these same attributes of
the returned array.
fill_value : array_like
Fill value.
dtype : data-type, optional
Overrides the data type of the result.
order : {'C', 'F', 'A', or 'K'}, optional
Overrides the memory layout of the result. 'C' means C-order,
'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
'C' otherwise. 'K' means match the layout of `a` as closely
as possible.
subok : bool, optional.
If True, then the newly created array will use the sub-class
type of `a`, otherwise it will be a base-class array. Defaults
to True.
shape : int or sequence of ints, optional.
Overrides the shape of the result. If order='K' and the number of
dimensions is unchanged, will try to keep order, otherwise,
order='C' is implied.
device : str, optional
The device on which to place the created array. Default: None.
For Array-API interoperability only, so must be ``"cpu"`` if passed.
.. versionadded:: 2.0.0
Returns
-------
out : ndarray
Array of `fill_value` with the same shape and type as `a`.
See Also
--------
empty_like : Return an empty array with shape and type of input.
ones_like : Return an array of ones with shape and type of input.
zeros_like : Return an array of zeros with shape and type of input.
full : Return a new array of given shape filled with value.
Examples
--------
>>> import numpy as np
>>> x = np.arange(6, dtype=np.int_)
>>> np.full_like(x, 1)
array([1, 1, 1, 1, 1, 1])
>>> np.full_like(x, 0.1)
array([0, 0, 0, 0, 0, 0])
>>> np.full_like(x, 0.1, dtype=np.float64)
array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
>>> np.full_like(x, np.nan, dtype=np.float64)
array([nan, nan, nan, nan, nan, nan])
>>> y = np.arange(6, dtype=np.float64)
>>> np.full_like(y, 0.1)
array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
>>> y = np.zeros([2, 2, 3], dtype=np.int_)
>>> np.full_like(y, [0, 0, 255])
array([[[ 0, 0, 255],
[ 0, 0, 255]],
[[ 0, 0, 255],
[ 0, 0, 255]]])
"""
res = empty_like(
a, dtype=dtype, order=order, subok=subok, shape=shape, device=device
)
multiarray.copyto(res, fill_value, casting='unsafe')
return res
def _count_nonzero_dispatcher(a, axis=None, *, keepdims=None):
return (a,)
@array_function_dispatch(_count_nonzero_dispatcher)
def count_nonzero(a, axis=None, *, keepdims=False):
"""
Counts the number of non-zero values in the array ``a``.
A non-zero value is one that evaluates to truthful in a boolean
context, including any non-zero number and any string that
is not empty. This function recursively counts how many elements
in ``a`` (and its sub-arrays) are non-zero values.
Parameters
----------
a : array_like
The array for which to count non-zeros.
axis : int or tuple, optional
Axis or tuple of axes along which to count non-zeros.
Default is None, meaning that non-zeros will be counted
along a flattened version of ``a``.
keepdims : bool, optional
If this is set to True, the axes that are counted are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the input array.
Returns
-------
count : int or array of int
Number of non-zero values in the array along a given axis.
Otherwise, the total number of non-zero values in the array
is returned.
See Also
--------
nonzero : Return the coordinates of all the non-zero values.
Examples
--------
>>> import numpy as np
>>> np.count_nonzero(np.eye(4))
np.int64(4)
>>> a = np.array([[0, 1, 7, 0],
... [3, 0, 2, 19]])
>>> np.count_nonzero(a)
np.int64(5)
>>> np.count_nonzero(a, axis=0)
array([1, 1, 2, 1])
>>> np.count_nonzero(a, axis=1)
array([2, 3])
>>> np.count_nonzero(a, axis=1, keepdims=True)
array([[2],
[3]])
"""
if axis is None and not keepdims:
return multiarray.count_nonzero(a)
a = asanyarray(a)
# TODO: this works around .astype(bool) not working properly (gh-9847)
if np.issubdtype(a.dtype, np.character):
a_bool = a != a.dtype.type()
else:
a_bool = a.astype(np.bool, copy=False)
return a_bool.sum(axis=axis, dtype=np.intp, keepdims=keepdims)
@set_module('numpy')
def isfortran(a):
"""
Check if the array is Fortran contiguous but *not* C contiguous.
This function is obsolete. If you only want to check if an array is Fortran
contiguous use ``a.flags.f_contiguous`` instead.
Parameters
----------
a : ndarray
Input array.
Returns
-------
isfortran : bool
Returns True if the array is Fortran contiguous but *not* C contiguous.
Examples
--------
np.array allows to specify whether the array is written in C-contiguous
order (last index varies the fastest), or FORTRAN-contiguous order in
memory (first index varies the fastest).
>>> import numpy as np
>>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
>>> a
array([[1, 2, 3],
[4, 5, 6]])
>>> np.isfortran(a)
False
>>> b = np.array([[1, 2, 3], [4, 5, 6]], order='F')
>>> b
array([[1, 2, 3],
[4, 5, 6]])
>>> np.isfortran(b)
True
The transpose of a C-ordered array is a FORTRAN-ordered array.
>>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
>>> a
array([[1, 2, 3],
[4, 5, 6]])
>>> np.isfortran(a)
False
>>> b = a.T
>>> b
array([[1, 4],
[2, 5],
[3, 6]])
>>> np.isfortran(b)
True
C-ordered arrays evaluate as False even if they are also FORTRAN-ordered.
>>> np.isfortran(np.array([1, 2], order='F'))
False
"""
return a.flags.fnc
def _argwhere_dispatcher(a):
return (a,)
@array_function_dispatch(_argwhere_dispatcher)
def argwhere(a):
"""
Find the indices of array elements that are non-zero, grouped by element.
Parameters
----------
a : array_like
Input data.
Returns
-------
index_array : (N, a.ndim) ndarray
Indices of elements that are non-zero. Indices are grouped by element.
This array will have shape ``(N, a.ndim)`` where ``N`` is the number of
non-zero items.
See Also
--------
where, nonzero
Notes
-----
``np.argwhere(a)`` is almost the same as ``np.transpose(np.nonzero(a))``,
but produces a result of the correct shape for a 0D array.
The output of ``argwhere`` is not suitable for indexing arrays.
For this purpose use ``nonzero(a)`` instead.
Examples
--------
>>> import numpy as np
>>> x = np.arange(6).reshape(2,3)
>>> x
array([[0, 1, 2],
[3, 4, 5]])
>>> np.argwhere(x>1)
array([[0, 2],
[1, 0],
[1, 1],
[1, 2]])
"""
# nonzero does not behave well on 0d, so promote to 1d
if np.ndim(a) == 0:
a = shape_base.atleast_1d(a)
# then remove the added dimension
return argwhere(a)[:, :0]
return transpose(nonzero(a))
def _flatnonzero_dispatcher(a):
return (a,)
@array_function_dispatch(_flatnonzero_dispatcher)
def flatnonzero(a):
"""
Return indices that are non-zero in the flattened version of a.
This is equivalent to ``np.nonzero(np.ravel(a))[0]``.
Parameters
----------
a : array_like
Input data.
Returns
-------
res : ndarray
Output array, containing the indices of the elements of ``a.ravel()``
that are non-zero.
See Also
--------
nonzero : Return the indices of the non-zero elements of the input array.
ravel : Return a 1-D array containing the elements of the input array.
Examples
--------
>>> import numpy as np
>>> x = np.arange(-2, 3)
>>> x
array([-2, -1, 0, 1, 2])
>>> np.flatnonzero(x)
array([0, 1, 3, 4])
Use the indices of the non-zero elements as an index array to extract
these elements:
>>> x.ravel()[np.flatnonzero(x)]
array([-2, -1, 1, 2])
"""
return np.nonzero(np.ravel(a))[0]
def _correlate_dispatcher(a, v, mode=None):
return (a, v)
@array_function_dispatch(_correlate_dispatcher)
def correlate(a, v, mode='valid'):
r"""
Cross-correlation of two 1-dimensional sequences.
This function computes the correlation as generally defined in signal
processing texts [1]_:
.. math:: c_k = \sum_n a_{n+k} \cdot \overline{v}_n
with a and v sequences being zero-padded where necessary and
:math:`\overline v` denoting complex conjugation.
Parameters
----------
a, v : array_like
Input sequences.
mode : {'valid', 'same', 'full'}, optional
Refer to the `convolve` docstring. Note that the default
is 'valid', unlike `convolve`, which uses 'full'.
Returns
-------
out : ndarray
Discrete cross-correlation of `a` and `v`.
See Also
--------
convolve : Discrete, linear convolution of two one-dimensional sequences.
scipy.signal.correlate : uses FFT which has superior performance
on large arrays.
Notes
-----
The definition of correlation above is not unique and sometimes
correlation may be defined differently. Another common definition is [1]_:
.. math:: c'_k = \sum_n a_{n} \cdot \overline{v_{n+k}}
which is related to :math:`c_k` by :math:`c'_k = c_{-k}`.
`numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5)
because it does not use the FFT to compute the convolution; in that case,
`scipy.signal.correlate` might be preferable.
References
----------
.. [1] Wikipedia, "Cross-correlation",
https://en.wikipedia.org/wiki/Cross-correlation
Examples
--------
>>> import numpy as np
>>> np.correlate([1, 2, 3], [0, 1, 0.5])
array([3.5])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "same")
array([2. , 3.5, 3. ])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "full")
array([0.5, 2. , 3.5, 3. , 0. ])
Using complex sequences:
>>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')
array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ])
Note that you get the time reversed, complex conjugated result
(:math:`\overline{c_{-k}}`) when the two input sequences a and v change
places:
>>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j])
"""
return multiarray.correlate2(a, v, mode)
def _convolve_dispatcher(a, v, mode=None):
return (a, v)
@array_function_dispatch(_convolve_dispatcher)
def convolve(a, v, mode='full'):
"""
Returns the discrete, linear convolution of two one-dimensional sequences.
The convolution operator is often seen in signal processing, where it
models the effect of a linear time-invariant system on a signal [1]_. In
probability theory, the sum of two independent random variables is
distributed according to the convolution of their individual
distributions.
If `v` is longer than `a`, the arrays are swapped before computation.
Parameters
----------
a : (N,) array_like
First one-dimensional input array.
v : (M,) array_like
Second one-dimensional input array.
mode : {'full', 'valid', 'same'}, optional
'full':
By default, mode is 'full'. This returns the convolution
at each point of overlap, with an output shape of (N+M-1,). At
the end-points of the convolution, the signals do not overlap
completely, and boundary effects may be seen.
'same':
Mode 'same' returns output of length ``max(M, N)``. Boundary
effects are still visible.
'valid':
Mode 'valid' returns output of length
``max(M, N) - min(M, N) + 1``. The convolution product is only given
for points where the signals overlap completely. Values outside
the signal boundary have no effect.
Returns
-------
out : ndarray
Discrete, linear convolution of `a` and `v`.
See Also
--------
scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier
Transform.
scipy.linalg.toeplitz : Used to construct the convolution operator.
polymul : Polynomial multiplication. Same output as convolve, but also
accepts poly1d objects as input.
Notes
-----
The discrete convolution operation is defined as
.. math:: (a * v)_n = \\sum_{m = -\\infty}^{\\infty} a_m v_{n - m}
It can be shown that a convolution :math:`x(t) * y(t)` in time/space
is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier
domain, after appropriate padding (padding is necessary to prevent
circular convolution). Since multiplication is more efficient (faster)
than convolution, the function `scipy.signal.fftconvolve` exploits the
FFT to calculate the convolution of large data-sets.
References
----------
.. [1] Wikipedia, "Convolution",
https://en.wikipedia.org/wiki/Convolution
Examples
--------
Note how the convolution operator flips the second array
before "sliding" the two across one another:
>>> import numpy as np
>>> np.convolve([1, 2, 3], [0, 1, 0.5])
array([0. , 1. , 2.5, 4. , 1.5])
Only return the middle values of the convolution.
Contains boundary effects, where zeros are taken
into account:
>>> np.convolve([1,2,3],[0,1,0.5], 'same')
array([1. , 2.5, 4. ])
The two arrays are of the same length, so there
is only one position where they completely overlap:
>>> np.convolve([1,2,3],[0,1,0.5], 'valid')
array([2.5])
"""
a, v = array(a, copy=None, ndmin=1), array(v, copy=None, ndmin=1)
if len(a) == 0:
raise ValueError('a cannot be empty')
if len(v) == 0:
raise ValueError('v cannot be empty')
if len(v) > len(a):
a, v = v, a
return multiarray.correlate(a, v[::-1], mode)
def _outer_dispatcher(a, b, out=None):
return (a, b, out)
@array_function_dispatch(_outer_dispatcher)
def outer(a, b, out=None):
"""
Compute the outer product of two vectors.
Given two vectors `a` and `b` of length ``M`` and ``N``, respectively,
the outer product [1]_ is::
[[a_0*b_0 a_0*b_1 ... a_0*b_{N-1} ]
[a_1*b_0 .
[ ... .
[a_{M-1}*b_0 a_{M-1}*b_{N-1} ]]
Parameters
----------
a : (M,) array_like
First input vector. Input is flattened if
not already 1-dimensional.
b : (N,) array_like
Second input vector. Input is flattened if
not already 1-dimensional.
out : (M, N) ndarray, optional
A location where the result is stored
Returns
-------
out : (M, N) ndarray
``out[i, j] = a[i] * b[j]``
See also
--------
inner
einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.
ufunc.outer : A generalization to dimensions other than 1D and other
operations. ``np.multiply.outer(a.ravel(), b.ravel())``
is the equivalent.
linalg.outer : An Array API compatible variation of ``np.outer``,
which accepts 1-dimensional inputs only.
tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))``
is the equivalent.
References
----------
.. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd
ed., Baltimore, MD, Johns Hopkins University Press, 1996,
pg. 8.
Examples
--------
Make a (*very* coarse) grid for computing a Mandelbrot set:
>>> import numpy as np
>>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
>>> rl
array([[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.],
[-2., -1., 0., 1., 2.]])
>>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
>>> im
array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
[0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
[0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
[0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
>>> grid = rl + im
>>> grid
array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j],
[-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j],
[-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j],
[-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j],
[-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]])
An example using a "vector" of letters:
>>> x = np.array(['a', 'b', 'c'], dtype=np.object_)
>>> np.outer(x, [1, 2, 3])
array([['a', 'aa', 'aaa'],
['b', 'bb', 'bbb'],
['c', 'cc', 'ccc']], dtype=object)
"""
a = asarray(a)
b = asarray(b)
return multiply(a.ravel()[:, newaxis], b.ravel()[newaxis, :], out)
def _tensordot_dispatcher(a, b, axes=None):
return (a, b)
@array_function_dispatch(_tensordot_dispatcher)
def tensordot(a, b, axes=2):
"""
Compute tensor dot product along specified axes.