Lines Matching full:covariance
1865 Covariance Estimation
1872 non-linear least squares solve is to analyze the covariance of the
1881 covariance. Then the maximum likelihood estimate of :math:`x` given
1887 And the covariance of :math:`x^*` is given by
1894 If :math:`J(x^*)` is rank deficient, then the covariance matrix :math:`C(x^*)`
1899 Note that in the above, we assumed that the covariance matrix for
1906 covariance of :math:`y`, then the maximum likelihood problem to be
1911 and the corresponding covariance estimate of :math:`x^*` is given by
1916 covariance matrix not equal to identity, then it is the user's
1920 where :math:`S^{-1/2}` is the inverse square root of the covariance
1934 :class:`Covariance`
1937 :class:`Covariance` allows the user to evaluate the covariance for a
1940 residuals such that their covariance is identity.
1942 Since the computation of the covariance matrix requires computing the
1945 user is only interested in a small part of the covariance
1946 matrix. Quite often just the block diagonal. :class:`Covariance`
1947 allows the user to specify the parts of the covariance matrix that she
1949 store those parts of the covariance matrix.
1977 deficiency to the :class:`Covariance` object so that it can
1987 :class:`Covariance::Options`
1989 .. class:: Covariance::Options
1991 .. member:: int Covariance::Options::num_threads
1996 estimation of covariance.
1998 .. member:: CovarianceAlgorithmType Covariance::Options::algorithm_type
2002 Ceres supports three different algorithms for covariance
2040 efficient method for solving for rows of the covariance
2059 the covariance if the Jacobian is rank deficient.
2061 .. member:: int Covariance::Options::min_reciprocal_condition_number
2086 :func:`Covariance::Compute` will return ``false`` if a rank
2109 :func:`Covariance::Compute` may return false even if it is
2110 possible to estimate the covariance reliably. In such cases, the
2122 .. member:: int Covariance::Options::null_space_rank
2125 with singular and near singular covariance matrices.
2127 As mentioned above, when the covariance matrix is near singular,
2149 then the `Covariance::Compute()` will fail and return `false`.
2158 .. member:: bool Covariance::Options::apply_loss_function
2165 function and in turn its effect on the covariance.
2167 .. class:: Covariance
2169 :class:`Covariance::Options` as the name implies is used to control
2170 the covariance estimation algorithm. Covariance estimation is a
2172 entire documentation for :class:`Covariance::Options` before using
2173 :class:`Covariance`.
2175 .. function:: bool Covariance::Compute(const vector<pair<const double*, const double*> >& covariance_blocks, Problem* problem)
2177 Compute a part of the covariance matrix.
2179 The vector ``covariance_blocks``, indexes into the covariance
2181 covariance estimation algorithm to only compute and store these
2184 Since the covariance matrix is symmetric, if the user passes
2192 determine what parts of the covariance matrix are computed. The
2196 The return value indicates the success or failure of the covariance
2198 :class:`Covariance::Options` for more on the conditions under which
2203 Return the block of the covariance matrix corresponding to
2214 returned covariance will be a row-major matrix.
2230 Covariance::Options options;
2231 Covariance covariance(options);
2238 CHECK(covariance.Compute(covariance_blocks, &problem));
2243 covariance.GetCovarianceBlock(x, x, covariance_xx)
2244 covariance.GetCovarianceBlock(y, y, covariance_yy)
2245 covariance.GetCovarianceBlock(x, y, covariance_xy)
