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# 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.cholesky.rst:2
msgid "mars.tensor.linalg.cholesky"
msgstr ""

#: mars.tensor.linalg.cholesky:1 of
msgid "Cholesky decomposition."
msgstr ""

#: mars.tensor.linalg.cholesky:3 of
msgid ""
"Return the Cholesky decomposition, `L * L.H`, of the square matrix `a`, "
"where `L` is lower-triangular and .H is the conjugate transpose operator "
"(which is the ordinary transpose if `a` is real-valued).  `a` must be "
"Hermitian (symmetric if real-valued) and positive-definite.  Only `L` is "
"actually returned."
msgstr ""

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

#: mars.tensor.linalg.cholesky:9 of
msgid ""
"Hermitian (symmetric if all elements are real), positive-definite input "
"matrix."
msgstr ""

#: mars.tensor.linalg.cholesky:12 of
msgid ""
"Whether to compute the upper or lower triangular Cholesky factorization."
"  Default is upper-triangular."
msgstr ""

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

#: mars.tensor.linalg.cholesky:16 of
msgid "**L** -- Upper or lower-triangular Cholesky factor of `a`."
msgstr ""

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

#: mars.tensor.linalg.cholesky of
msgid "Raises"
msgstr ""

#: mars.tensor.linalg.cholesky:19 of
msgid ""
"If the decomposition fails, for example, if `a` is not     positive-"
"definite."
msgstr ""

#: mars.tensor.linalg.cholesky:22 of
msgid "Notes"
msgstr ""

#: mars.tensor.linalg.cholesky:23 of
msgid "Broadcasting rules apply, see the `mt.linalg` documentation for details."
msgstr ""

#: mars.tensor.linalg.cholesky:26 of
msgid "The Cholesky decomposition is often used as a fast way of solving"
msgstr ""

#: mars.tensor.linalg.cholesky:28 of
msgid "A \\mathbf{x} = \\mathbf{b}"
msgstr ""

#: mars.tensor.linalg.cholesky:30 of
msgid "(when `A` is both Hermitian/symmetric and positive-definite)."
msgstr ""

#: mars.tensor.linalg.cholesky:32 of
msgid "First, we solve for :math:`\\mathbf{y}` in"
msgstr ""

#: mars.tensor.linalg.cholesky:34 of
msgid "L \\mathbf{y} = \\mathbf{b},"
msgstr ""

#: mars.tensor.linalg.cholesky:36 of
msgid "and then for :math:`\\mathbf{x}` in"
msgstr ""

#: mars.tensor.linalg.cholesky:38 of
msgid "L.H \\mathbf{x} = \\mathbf{y}."
msgstr ""

#: mars.tensor.linalg.cholesky:41 of
msgid "Examples"
msgstr ""

