# SOME DESCRIPTIVE TITLE.
# Copyright (C) 1999-2020, The Alibaba Group Holding Ltd.
# This file is distributed under the same license as the mars package.
# FIRST AUTHOR <EMAIL@ADDRESS>, 2020.
#
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"Project-Id-Version: mars 0.5.0a2\n"
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#: ../../source/reference/tensor/generated/mars.tensor.linalg.norm.rst:2
msgid "mars.tensor.linalg.norm"
msgstr ""

#: mars.tensor.linalg.norm:1 of
msgid "Matrix or vector norm."
msgstr ""

#: mars.tensor.linalg.norm:3 of
msgid ""
"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."
msgstr ""

#: mars.tensor.linalg.norm of
msgid "Parameters"
msgstr ""

#: mars.tensor.linalg.norm:7 of
msgid "Input tensor.  If `axis` is None, `x` must be 1-D or 2-D."
msgstr ""

#: mars.tensor.linalg.norm:9 of
msgid ""
"Order of the norm (see table under ``Notes``). inf means mars tensor's "
"`inf` object."
msgstr ""

#: mars.tensor.linalg.norm:12 of
msgid ""
"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."
msgstr ""

#: mars.tensor.linalg.norm:18 of
msgid ""
"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`."
msgstr ""

#: mars.tensor.linalg.norm of
msgid "Returns"
msgstr ""

#: mars.tensor.linalg.norm:23 of
msgid "**n** -- Norm of the matrix or vector(s)."
msgstr ""

#: mars.tensor.linalg.norm of
msgid "Return type"
msgstr ""

#: mars.tensor.linalg.norm:27 of
msgid "Notes"
msgstr ""

#: mars.tensor.linalg.norm:28 of
msgid ""
"For values of ``ord <= 0``, the result is, strictly speaking, not a "
"mathematical 'norm', but it may still be useful for various numerical "
"purposes."
msgstr ""

#: mars.tensor.linalg.norm:32 of
msgid "The following norms can be calculated:"
msgstr ""

#: mars.tensor.linalg.norm:35 of
msgid "ord"
msgstr ""

#: mars.tensor.linalg.norm:35 of
msgid "norm for matrices"
msgstr ""

#: mars.tensor.linalg.norm:35 of
msgid "norm for vectors"
msgstr ""

#: mars.tensor.linalg.norm:37 of
msgid "None"
msgstr ""

#: mars.tensor.linalg.norm:37 mars.tensor.linalg.norm:38 of
msgid "Frobenius norm"
msgstr ""

#: mars.tensor.linalg.norm:37 of
msgid "2-norm"
msgstr ""

#: mars.tensor.linalg.norm:38 of
msgid "'fro'"
msgstr ""

#: mars.tensor.linalg.norm:38 mars.tensor.linalg.norm:39
#: mars.tensor.linalg.norm:42 mars.tensor.linalg.norm:47 of
msgid "--"
msgstr ""

#: mars.tensor.linalg.norm:39 of
msgid "'nuc'"
msgstr ""

#: mars.tensor.linalg.norm:39 of
msgid "nuclear norm"
msgstr ""

#: mars.tensor.linalg.norm:40 of
msgid "inf"
msgstr ""

#: mars.tensor.linalg.norm:40 of
msgid "max(sum(abs(x), axis=1))"
msgstr ""

#: mars.tensor.linalg.norm:40 of
msgid "max(abs(x))"
msgstr ""

#: mars.tensor.linalg.norm:41 of
msgid "-inf"
msgstr ""

#: mars.tensor.linalg.norm:41 of
msgid "min(sum(abs(x), axis=1))"
msgstr ""

#: mars.tensor.linalg.norm:41 of
msgid "min(abs(x))"
msgstr ""

#: mars.tensor.linalg.norm:42 of
msgid "0"
msgstr ""

#: mars.tensor.linalg.norm:42 of
msgid "sum(x != 0)"
msgstr ""

#: mars.tensor.linalg.norm:43 of
msgid "1"
msgstr ""

#: mars.tensor.linalg.norm:43 of
msgid "max(sum(abs(x), axis=0))"
msgstr ""

#: mars.tensor.linalg.norm:43 mars.tensor.linalg.norm:44
#: mars.tensor.linalg.norm:45 mars.tensor.linalg.norm:46 of
msgid "as below"
msgstr ""

#: mars.tensor.linalg.norm:44 of
msgid "-1"
msgstr ""

#: mars.tensor.linalg.norm:44 of
msgid "min(sum(abs(x), axis=0))"
msgstr ""

#: mars.tensor.linalg.norm:45 of
msgid "2"
msgstr ""

#: mars.tensor.linalg.norm:45 of
msgid "2-norm (largest sing. value)"
msgstr ""

#: mars.tensor.linalg.norm:46 of
msgid "-2"
msgstr ""

#: mars.tensor.linalg.norm:46 of
msgid "smallest singular value"
msgstr ""

#: mars.tensor.linalg.norm:47 of
msgid "other"
msgstr ""

#: mars.tensor.linalg.norm:47 of
msgid "sum(abs(x)**ord)**(1./ord)"
msgstr ""

#: mars.tensor.linalg.norm:50 of
msgid "The Frobenius norm is given by [1]_:"
msgstr ""

#: mars.tensor.linalg.norm:52 of
msgid ":math:`||A||_F = [\\\\sum_{i,j} abs(a_{i,j})^2]^{1/2}`"
msgstr ""

#: mars.tensor.linalg.norm:54 of
msgid "The nuclear norm is the sum of the singular values."
msgstr ""

#: mars.tensor.linalg.norm:57 of
msgid "References"
msgstr ""

#: mars.tensor.linalg.norm:58 of
msgid ""
"G. H. Golub and C. F. Van Loan, *Matrix Computations*, Baltimore, MD, "
"Johns Hopkins University Press, 1985, pg. 15"
msgstr ""

#: mars.tensor.linalg.norm:62 of
msgid "Examples"
msgstr ""

#: mars.tensor.linalg.norm:111 of
msgid "Using the `axis` argument to compute vector norms:"
msgstr ""

#: mars.tensor.linalg.norm:122 of
msgid "Using the `axis` argument to compute matrix norms:"
msgstr ""

