haojin2 commented on a change in pull request #15753: Numpy add numpy linalg
norm and numpy min
URL: https://github.com/apache/incubator-mxnet/pull/15753#discussion_r314588331
##
File path: python/mxnet/ndarray/numpy/linalg.py
##
@@ -19,50 +19,184 @@
from __future__ import absolute_import
from . import _op as _mx_nd_np
+from . import _internal as _npi
+
__all__ = ['norm']
+# pylint: disable=line-too-long, too-many-return-statements,
too-many-branches, no-member, consider-using-in, no-else-return
def norm(x, ord=None, axis=None, keepdims=False):
-r"""Matrix or vector norm.
-
-This function can only support Frobenius norm for now.
-The Frobenius norm is given by [1]_:
-
-:math:`||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}`
+r"""Matrix or vector norm..
+This function is able to return one of eight different matrix norms,
+or one of an infinite number of vector norms (described below), depending
+on the value of the ``ord`` parameter.
Parameters
--
x : ndarray
-Input array.
-ord : {'fro'}, optional
-Order of the norm.
+Input array. If `axis` is None, `x` must be 1-D or 2-D.
+ord : {non-zero int, inf, -inf, 'fro', 'nuc'}, optional
+Order of the norm (see table under ``Notes``). inf means numpy's
+`inf` object.
axis : {int, 2-tuple of ints, None}, optional
If `axis` is an integer, it specifies the axis of `x` along which to
compute the vector norms. If `axis` is a 2-tuple, it specifies the
axes that hold 2-D matrices, and the matrix norms of these matrices
-are computed. If `axis` is None, the norm of the whole ndarray is
-returned.
-
+are computed. If `axis` is None then either a vector norm (when `x`
+is 1-D) or a matrix norm (when `x` is 2-D) is returned.
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. With this option the result will
broadcast correctly against the original `x`.
Returns
---
-n : float or ndarray
+n : ndarray
Norm of the matrix or vector(s).
+Notes
+-
+For values of ``ord <= 0``, the result is, strictly speaking, not a
+mathematical 'norm', but it may still be useful for various numerical
+purposes.
+
+The following norms can be calculated:
+
+= ==
+ordnorm for matrices norm for vectors
+= ==
+None Frobenius norm2-norm
+'fro' Frobenius norm--
+'nuc' ----
+infmax(sum(abs(x), axis=1)) max(abs(x))
+-inf min(sum(abs(x), axis=1)) min(abs(x))
+0 --sum(x != 0)
+1 max(sum(abs(x), axis=0)) as below
+-1 min(sum(abs(x), axis=0)) as below
+2 --as below
+-2 --as below
+other --sum(abs(x)**ord)**(1./ord)
+= ==
+
+The Frobenius norm is given by [1]_:
+
+:math:`||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}`
+
+The nuclear norm is the sum of the singular values.
+
+When you want to operate norm for matrices,if you ord is (-1, 1, inf,
-inf),
+you must give you axis, it is not support default axis.
+
References
--
.. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*,
Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15
+
+Examples
+
+>>> from mxnet import np
+>>> a = np.arange(9) - 4
+>>> a
+array([-4., -3., -2., -1., 0., 1., 2., 3., 4.])
+>>> b = a.reshape((3, 3))
+>>> b
+array([[-4., -3., -2.],
+ [-1., 0., 1.],
+ [ 2., 3., 4.]])
+
+>>> np.linalg.norm(a)
+array(7.745967)
+>>> np.linalg.norm(b)
+array(7.745967)
+>>> np.linalg.norm(b, 'fro')
+array(7.745967)
+>>> np.linalg.norm(a, 'inf')
+array(4.)
+>>> np.linalg.norm(b, 'inf', axis=(0, 1))
+array(9.)
+>>> np.linalg.norm(a, '-inf')
+array(0.)
+>>> np.linalg.norm(b, '-inf', axis=(0, 1))
+array(2.)
+
+>>> np.linalg.norm(a, 1)
+array(20.)
+>>> np.linalg.norm(b, 1, axis=(0, 1))
+array(7.)
+>>> np.linalg.norm(a, -1)
+array(0.)
+>>> np.linalg.norm(b, -1, axis=(0, 1))
+array(6.)
+>>> np.linalg.norm(a, 2)
+array(7.745967)
+
+>>> np.linalg.norm(a, -2)
+array(0.)
+>>> np.linalg.norm(a, 3)
+array(5.8480353)
+>>> np.linalg.norm(a, -3)
+array(0.)
+
+Using the `axis` argument to compute vector norms:
+
+>>> c = np.array([[ 1, 2, 3],
+...
