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55 // This class allows the user to evaluate the covariance for a
62 // non-linear least squares solve is to analyze the covariance of the
70 // independent variable x with mean f(x) and identity covariance. Then
76 // And the covariance of x* is given by
83 // If J(x*) is rank deficient, then the covariance matrix C(x*) is
88 // Note that in the above, we assumed that the covariance
94 // Where S is a positive semi-definite matrix denoting the covariance
99 // and the corresponding covariance estimate of x* is given by
104 // covariance matrix not equal to identity, then it is the user's
108 // is the inverse square root of the covariance matrix S.
110 // This class allows the user to evaluate the covariance for a
113 // residuals such that their covariance is identity.
115 // Since the computation of the covariance matrix requires computing
119 // covariance matrix. Quite often just the block diagonal. This class
120 // allows the user to specify the parts of the covariance matrix that
122 // and store those parts of the covariance matrix.
148 // the rank deficiency to the Covariance object so that it can
182 // Covariance::Options options;
183 // Covariance covariance(options);
190 // CHECK(covariance.Compute(covariance_blocks, &problem));
195 // covariance.GetCovarianceBlock(x, x, covariance_xx)
196 // covariance.GetCovarianceBlock(y, y, covariance_yy)
197 // covariance.GetCovarianceBlock(x, y, covariance_xy)
199 class Covariance {
214 // Ceres supports three different algorithms for covariance
252 // more efficient method for solving for rows of the covariance
270 // the covariance if the Jacobian is rank deficient.
286 // Covariance::Compute will return false if a rank deficient
308 // Covariance::Compute may return false even if it is possible
309 // to estimate the covariance reliably. In such cases, the user
324 // singular and near singular covariance matrices.
326 // As mentioned above, when the covariance matrix is near
347 // min_reciprocal_condition_number, then the Covariance::Compute()
363 // function and in turn its effect on the covariance.
369 explicit Covariance(const Options& options);
370 ~Covariance();
372 // Compute a part of the covariance matrix.
374 // The vector covariance_blocks, indexes into the covariance matrix
376 // covariance estimation algorithm to only compute and store these
379 // Since the covariance matrix is symmetric, if the user passes
387 // what parts of the covariance matrix are computed. The full
392 // covariance computation. Please see the documentation for
393 // Covariance::Options for more on the conditions under which this
399 // Return the block of the covariance matrix corresponding to
411 // returned covariance