# 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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"POT-Creation-Date: 2020-06-16 16:57+0800\n"
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#: ../../source/reference/tensor/generated/mars.tensor.cov.rst:2
msgid "mars.tensor.cov"
msgstr ""

#: mars.tensor.cov:1 of
msgid "Estimate a covariance matrix, given data and weights."
msgstr ""

#: mars.tensor.cov:3 of
msgid ""
"Covariance indicates the level to which two variables vary together. If "
"we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`, then"
" the covariance matrix element :math:`C_{ij}` is the covariance of "
":math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance "
"of :math:`x_i`."
msgstr ""

#: mars.tensor.cov:9 of
msgid "See the notes for an outline of the algorithm."
msgstr ""

#: mars.tensor.cov of
msgid "Parameters"
msgstr ""

#: mars.tensor.cov:11 of
msgid ""
"A 1-D or 2-D array containing multiple variables and observations. Each "
"row of `m` represents a variable, and each column a single observation of"
" all those variables. Also see `rowvar` below."
msgstr ""

#: mars.tensor.cov:15 of
msgid ""
"An additional set of variables and observations. `y` has the same form as"
" that of `m`."
msgstr ""

#: mars.tensor.cov:18 of
msgid ""
"If `rowvar` is True (default), then each row represents a variable, with "
"observations in the columns. Otherwise, the relationship is transposed: "
"each column represents a variable, while the rows contain observations."
msgstr ""

#: mars.tensor.cov:23 of
msgid ""
"Default normalization (False) is by ``(N - 1)``, where ``N`` is the "
"number of observations given (unbiased estimate). If `bias` is True, then"
" normalization is by ``N``. These values can be overridden by using the "
"keyword ``ddof`` in numpy versions >= 1.5."
msgstr ""

#: mars.tensor.cov:28 of
msgid ""
"If not ``None`` the default value implied by `bias` is overridden. Note "
"that ``ddof=1`` will return the unbiased estimate, even if both "
"`fweights` and `aweights` are specified, and ``ddof=0`` will return the "
"simple average. See the notes for the details. The default value is "
"``None``."
msgstr ""

#: mars.tensor.cov:34 of
msgid ""
"1-D tensor of integer freguency weights; the number of times each "
"observation vector should be repeated."
msgstr ""

#: mars.tensor.cov:37 of
msgid ""
"1-D tensor of observation vector weights. These relative weights are "
"typically large for observations considered \"important\" and smaller for"
" observations considered less \"important\". If ``ddof=0`` the array of "
"weights can be used to assign probabilities to observation vectors."
msgstr ""

#: mars.tensor.cov of
msgid "Returns"
msgstr ""

#: mars.tensor.cov:43 of
msgid "**out** -- The covariance matrix of the variables."
msgstr ""

#: mars.tensor.cov of
msgid "Return type"
msgstr ""

#: mars.tensor.cov:48 of
msgid ":func:`corrcoef`"
msgstr ""

#: mars.tensor.cov:49 of
msgid "Normalized covariance matrix"
msgstr ""

#: mars.tensor.cov:52 of
msgid "Notes"
msgstr ""

#: mars.tensor.cov:53 of
msgid ""
"Assume that the observations are in the columns of the observation array "
"`m` and let ``f = fweights`` and ``a = aweights`` for brevity. The steps "
"to compute the weighted covariance are as follows::"
msgstr ""

#: mars.tensor.cov:63 of
msgid ""
"Note that when ``a == 1``, the normalization factor ``v1 / (v1**2 - ddof "
"* v2)`` goes over to ``1 / (np.sum(f) - ddof)`` as it should."
msgstr ""

#: mars.tensor.cov:68 of
msgid "Examples"
msgstr ""

#: mars.tensor.cov:69 of
msgid ""
"Consider two variables, :math:`x_0` and :math:`x_1`, which correlate "
"perfectly, but in opposite directions:"
msgstr ""

#: mars.tensor.cov:79 of
msgid ""
"Note how :math:`x_0` increases while :math:`x_1` decreases. The "
"covariance matrix shows this clearly:"
msgstr ""

#: mars.tensor.cov:86 of
msgid ""
"Note that element :math:`C_{0,1}`, which shows the correlation between "
":math:`x_0` and :math:`x_1`, is negative."
msgstr ""

#: mars.tensor.cov:89 of
msgid "Further, note how `x` and `y` are combined:"
msgstr ""

