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56 // This class allows the user to evaluate the covariance for a
63 // non-linear least squares solve is to analyze the covariance of the
71 // independent variable x with mean f(x) and identity covariance. Then
77 // And the covariance of x* is given by
84 // If J(x*) is rank deficient, then the covariance matrix C(x*) is
89 // Note that in the above, we assumed that the covariance
95 // Where S is a positive semi-definite matrix denoting the covariance
100 // and the corresponding covariance estimate of x* is given by
105 // covariance matrix not equal to identity, then it is the user's
109 // is the inverse square root of the covariance matrix S.
111 // This class allows the user to evaluate the covariance for a
114 // residuals such that their covariance is identity.
116 // Since the computation of the covariance matrix requires computing
120 // covariance matrix. Quite often just the block diagonal. This class
121 // allows the user to specify the parts of the covariance matrix that
123 // and store those parts of the covariance matrix.
149 // the rank deficiency to the Covariance object so that it can
183 // Covariance::Options options;
184 // Covariance covariance(options);
191 // CHECK(covariance.Compute(covariance_blocks, &problem));
196 // covariance.GetCovarianceBlock(x, x, covariance_xx)
197 // covariance.GetCovarianceBlock(y, y, covariance_yy)
198 // covariance.GetCovarianceBlock(x, y, covariance_xy)
200 class CERES_EXPORT Covariance {
215 // Ceres supports three different algorithms for covariance
247 // computing the covariance if the Jacobian is rank deficient.
262 // Covariance::Compute will return false if a rank deficient
284 // singular and near singular covariance matrices.
286 // As mentioned above, when the covariance matrix is near
307 // min_reciprocal_condition_number, then the Covariance::Compute()
323 // function and in turn its effect on the covariance.
329 explicit Covariance(const Options& options);
330 ~Covariance();
332 // Compute a part of the covariance matrix.
334 // The vector covariance_blocks, indexes into the covariance matrix
336 // covariance estimation algorithm to only compute and store these
339 // Since the covariance matrix is symmetric, if the user passes
347 // what parts of the covariance matrix are computed. The full
352 // covariance computation. Please see the documentation for
353 // Covariance::Options for more on the conditions under which this
359 // Return the block of the covariance matrix corresponding to
371 // returned covariance will be a row-major matrix.