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from ..utils import normalize_axis_tuple
[docs]
def vector_norm(x, *, axis=None, keepdims=False, ord=2):
"""
Computes the vector norm of a vector (or batch of vectors) ``x``.
This function is Array API compatible.
Parameters
----------
x : array_like
Input array.
axis : {None, int, 2-tuple of ints}, optional
If an integer, ``axis`` specifies the axis (dimension) along which
to compute vector norms. If an n-tuple, ``axis`` specifies the axes
(dimensions) along which to compute batched vector norms. If ``None``,
the vector norm must be computed over all array values (i.e.,
equivalent to computing the vector norm of a flattened array).
Default: ``None``.
keepdims : bool, optional
If this is set to True, the axes which are normed over are left in
the result as dimensions with size one. Default: False.
ord : {int, float, inf, -inf}, optional
The order of the norm. For details see the table under ``Notes``
in `numpy.linalg.norm`.
See Also
--------
numpy.linalg.norm : Generic norm function
Examples
--------
>>> from numpy import linalg as LA
>>> a = np.arange(9) + 1
>>> a
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> b = a.reshape((3, 3))
>>> b
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
>>> LA.vector_norm(b)
16.881943016134134
>>> LA.vector_norm(b, ord=np.inf)
9.0
>>> LA.vector_norm(b, ord=-np.inf)
1.0
>>> LA.vector_norm(b, ord=0)
9.0
>>> LA.vector_norm(b, ord=1)
45.0
>>> LA.vector_norm(b, ord=-1)
0.3534857623790153
>>> LA.vector_norm(b, ord=2)
16.881943016134134
>>> LA.vector_norm(b, ord=-2)
0.8058837395885292
"""
from ..datasource.array import asarray
from ..misc import transpose
from ..reduction import prod
from .norm import norm
x = asarray(x)
shape = list(x.shape)
if axis is None:
# Note: np.linalg.norm() doesn't handle 0-D arrays
x = x.ravel()
_axis = 0
elif isinstance(axis, tuple):
# Note: The axis argument supports any number of axes, whereas
# np.linalg.norm() only supports a single axis for vector norm.
normalized_axis = normalize_axis_tuple(axis, x.ndim)
rest = tuple(i for i in range(x.ndim) if i not in normalized_axis)
newshape = axis + rest
x = transpose(x, newshape).reshape(
(prod([x.shape[i] for i in axis], dtype=int), *[x.shape[i] for i in rest])
)
_axis = 0
else:
_axis = axis
res = norm(x, axis=_axis, ord=ord)
if keepdims:
# We can't reuse np.linalg.norm(keepdims) because of the reshape hacks
# above to avoid matrix norm logic.
_axis = normalize_axis_tuple(
range(len(shape)) if axis is None else axis, len(shape)
)
for i in _axis:
shape[i] = 1
res = res.reshape(tuple(shape))
return res