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Posted to commits@mxnet.apache.org by GitBox <gi...@apache.org> on 2019/10/17 03:14:18 UTC
[GitHub] [incubator-mxnet] gyshi commented on a change in pull request
#16129: [Numpy] . add op linalg norm
gyshi commented on a change in pull request #16129: [Numpy] . add op linalg norm
URL: https://github.com/apache/incubator-mxnet/pull/16129#discussion_r335793559
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File path: python/mxnet/ndarray/numpy/linalg.py
##########
@@ -18,5 +18,185 @@
"""Namespace for operators used in Gluon dispatched by F=ndarray."""
from __future__ import absolute_import
+from . import _op as _mx_nd_np
+from . import _internal as _npi
-__all__ = []
+
+__all__ = ['norm']
+
+
+# pylint: disable=too-many-return-statements
+def norm(x, ord=None, axis=None, keepdims=False):
+ 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. 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 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 : 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:
+
+ ===== ============================ ==========================
+ ord norm for matrices norm for vectors
+ ===== ============================ ==========================
+ None Frobenius norm 2-norm
+ 'fro' Frobenius norm --
+ 'nuc' -- --
+ inf max(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],
+ ... [-1, 1, 4]])
+ >>> np.linalg.norm(c, axis=0)
+ array([1.4142135, 2.236068 , 5. ])
+ >>> np.linalg.norm(c, axis=1)
+ array([3.7416573, 4.2426405])
+ >>> np.linalg.norm(c, ord=1, axis=1)
+ array([6., 6.])
+
+ Using the `axis` argument to compute matrix norms:
+
+ >>> m = np.arange(8).reshape(2,2,2)
+ >>> np.linalg.norm(m, axis=(1,2))
+ array([ 3.7416573, 11.224973 ])
+ >>> np.linalg.norm(m[0, :, :]), np.linalg.norm(m[1, :, :])
+ (array(3.7416573), array(11.224973))
+
+ """
+ if ord == 'nuc':
+ raise NotImplementedError("Norm does not support nuclear norm.")
+ if axis is None or isinstance(axis, (int, tuple)): # pylint: disable=too-many-nested-blocks
+ if axis is not None:
+ if isinstance(axis, int):
+ axis = (axis, )
+ if len(axis) == 2:
+ if ord in ['inf', '-inf']:
+ row_axis, col_axis = axis
+ if not keepdims:
+ if row_axis > col_axis:
+ row_axis -= 1
+ if ord == 'inf':
+ return _mx_nd_np.sum(_mx_nd_np.abs(x), axis=col_axis, keepdims=keepdims).max(axis=row_axis, keepdims=keepdims) # pylint: disable=line-too-long
+ else:
+ return _mx_nd_np.sum(_mx_nd_np.abs(x), axis=col_axis, keepdims=keepdims).min(axis=row_axis, keepdims=keepdims) # pylint: disable=line-too-long
+ if ord in [1, -1]:
+ row_axis, col_axis = axis
+ if not keepdims:
+ if row_axis < col_axis:
+ col_axis -= 1
+ if ord == 1:
+ return _mx_nd_np.sum(_mx_nd_np.abs(x), axis=row_axis, keepdims=keepdims).max(axis=col_axis, keepdims=keepdims) # pylint: disable=line-too-long
+ elif ord == -1:
+ return _mx_nd_np.sum(_mx_nd_np.abs(x), axis=row_axis, keepdims=keepdims).min(axis=col_axis, keepdims=keepdims) # pylint: disable=line-too-long
+ if ord == 'inf':
+ return _npi.norm(x, ord=2, axis=axis, keepdims=keepdims, flag=3)
+ elif ord == '-inf':
+ return _npi.norm(x, ord=2, axis=axis, keepdims=keepdims, flag=4)
+ elif ord is None:
+ return _npi.norm(x, ord=2, axis=axis, keepdims=keepdims, flag=0)
+ elif ord == 2:
+ return _npi.norm(x, ord=2, axis=axis, keepdims=keepdims, flag=-1)
+ elif ord == 'nuc':
Review comment:
yes, it's necessary, bacaue if i want to add nuclear norm, i will use it, you can think it is repeating。
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