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#: ../../source/reference/tensor/generated/mars.tensor.random.multivariate_normal.rst:2
msgid "mars.tensor.random.multivariate\\_normal"
msgstr ""

#: mars.tensor.random.multivariate_normal:1 of
msgid "Draw random samples from a multivariate normal distribution."
msgstr ""

#: mars.tensor.random.multivariate_normal:3 of
msgid ""
"The multivariate normal, multinormal or Gaussian distribution is a "
"generalization of the one-dimensional normal distribution to higher "
"dimensions.  Such a distribution is specified by its mean and covariance "
"matrix.  These parameters are analogous to the mean (average or "
"\"center\") and variance (standard deviation, or \"width,\" squared) of "
"the one-dimensional normal distribution."
msgstr ""

#: mars.tensor.random.multivariate_normal of
msgid "Parameters"
msgstr ""

#: mars.tensor.random.multivariate_normal:10 of
msgid "Mean of the N-dimensional distribution."
msgstr ""

#: mars.tensor.random.multivariate_normal:12 of
msgid ""
"Covariance matrix of the distribution. It must be symmetric and positive-"
"semidefinite for proper sampling."
msgstr ""

#: mars.tensor.random.multivariate_normal:15 of
msgid ""
"Given a shape of, for example, ``(m,n,k)``, ``m*n*k`` samples are "
"generated, and packed in an `m`-by-`n`-by-`k` arrangement.  Because each "
"sample is `N`-dimensional, the output shape is ``(m,n,k,N)``. If no shape"
" is specified, a single (`N`-D) sample is returned."
msgstr ""

#: mars.tensor.random.multivariate_normal:20 of
msgid "Behavior when the covariance matrix is not positive semidefinite."
msgstr ""

#: mars.tensor.random.multivariate_normal:22 of
msgid "Tolerance when checking the singular values in covariance matrix."
msgstr ""

#: mars.tensor.random.multivariate_normal:24 of
msgid "Desired chunk size on each dimension"
msgstr ""

#: mars.tensor.random.multivariate_normal:26 of
msgid "Allocate the tensor on GPU if True, False as default"
msgstr ""

#: mars.tensor.random.multivariate_normal:28 of
msgid "Data-type of the returned tensor."
msgstr ""

#: mars.tensor.random.multivariate_normal of
msgid "Returns"
msgstr ""

#: mars.tensor.random.multivariate_normal:31 of
msgid ""
"**out** -- The drawn samples, of shape *size*, if that was provided.  If "
"not, the shape is ``(N,)``.  In other words, each entry "
"``out[i,j,...,:]`` is an N-dimensional value drawn from the distribution."
msgstr ""

#: mars.tensor.random.multivariate_normal:31 of
msgid ""
"**out** -- The drawn samples, of shape *size*, if that was provided.  If "
"not, the shape is ``(N,)``."
msgstr ""

#: mars.tensor.random.multivariate_normal:34 of
msgid ""
"In other words, each entry ``out[i,j,...,:]`` is an N-dimensional value "
"drawn from the distribution."
msgstr ""

#: mars.tensor.random.multivariate_normal of
msgid "Return type"
msgstr ""

#: mars.tensor.random.multivariate_normal:39 of
msgid "Notes"
msgstr ""

#: mars.tensor.random.multivariate_normal:40 of
msgid ""
"The mean is a coordinate in N-dimensional space, which represents the "
"location where samples are most likely to be generated.  This is "
"analogous to the peak of the bell curve for the one-dimensional or "
"univariate normal distribution."
msgstr ""

#: mars.tensor.random.multivariate_normal:45 of
msgid ""
"Covariance indicates the level to which two variables vary together. From"
" the multivariate normal distribution, we draw N-dimensional samples, "
":math:`X = [x_1, x_2, ... x_N]`.  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` (i.e. its "
"\"spread\")."
msgstr ""

#: mars.tensor.random.multivariate_normal:52 of
msgid ""
"Instead of specifying the full covariance matrix, popular approximations "
"include:"
msgstr ""

#: mars.tensor.random.multivariate_normal:55 of
msgid "Spherical covariance (`cov` is a multiple of the identity matrix)"
msgstr ""

#: mars.tensor.random.multivariate_normal:56 of
msgid ""
"Diagonal covariance (`cov` has non-negative elements, and only on the "
"diagonal)"
msgstr ""

#: mars.tensor.random.multivariate_normal:59 of
msgid ""
"This geometrical property can be seen in two dimensions by plotting "
"generated data-points:"
msgstr ""

#: mars.tensor.random.multivariate_normal:65 of
msgid "Diagonal covariance means that points are oriented along x or y-axis:"
msgstr ""

#: mars.tensor.random.multivariate_normal:74 of
msgid ""
"Note that the covariance matrix must be positive semidefinite (a.k.a. "
"nonnegative-definite). Otherwise, the behavior of this method is "
"undefined and backwards compatibility is not guaranteed."
msgstr ""

#: mars.tensor.random.multivariate_normal:79 of
msgid "References"
msgstr ""

#: mars.tensor.random.multivariate_normal:80 of
msgid ""
"Papoulis, A., \"Probability, Random Variables, and Stochastic "
"Processes,\" 3rd ed., New York: McGraw-Hill, 1991."
msgstr ""

#: mars.tensor.random.multivariate_normal:82 of
msgid ""
"Duda, R. O., Hart, P. E., and Stork, D. G., \"Pattern Classification,\" "
"2nd ed., New York: Wiley, 2001."
msgstr ""

#: mars.tensor.random.multivariate_normal:86 of
msgid "Examples"
msgstr ""

#: mars.tensor.random.multivariate_normal:93 of
msgid ""
"The following is probably true, given that 0.6 is roughly twice the "
"standard deviation:"
msgstr ""

