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Update documentation
Update the linear solver documentation thoroughly as it had bit rotted and was flat out wrong in some places and incomplete in others. https://github.com/ceres-solver/ceres-solver/issues/865 https://github.com/ceres-solver/ceres-solver/issues/862 Change-Id: Ic395efabd0589a401e2b971c45869bd881b68a34
This commit is contained in:
Sameer Agarwal
@@ -45,6 +45,9 @@ References
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.. [Conn] A.R. Conn, N.I.M. Gould, and P.L. Toint, **Trust region
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methods**, *Society for Industrial Mathematics*, 2000.
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.. [Davis] Timothy A. Davis, **Direct methods for Sparse Linear
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Systems**, *SIAM*, 2006.
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.. [Dellaert] F. Dellaert, J. Carlson, V. Ila, K. Ni and C. E. Thorpe,
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**Subgraph-preconditioned conjugate gradients for large scale SLAM**,
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*International Conference on Intelligent Robots and Systems*, 2010.
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@@ -58,7 +61,7 @@ References
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Preconditioners for Sparse Linear Least-Squares Problems**,
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*ACM Trans. Math. Softw.*, 43(4), 2017.
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.. [HartleyZisserman] R.I. Hartley & A. Zisserman, **Multiview
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.. [HartleyZisserman] R.I. Hartley and A. Zisserman, **Multiview
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Geometry in Computer Vision**, Cambridge University Press, 2004.
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.. [Hertzberg] C. Hertzberg, R. Wagner, U. Frese and L. Schroder,
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@@ -93,6 +96,11 @@ References
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preconditioner for large sparse least squares problems**, *SIAM
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Journal on Matrix Analysis and Applications*, 28(2):524-550, 2007.
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.. [LourakisArgyros] M. L. A. Lourakis, A. A. Argyros, **Is
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Levenberg-Marquardt the most efficient algorithm for implementing
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bundle adjustment?**, *International Conference on Computer
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Vision*, 2005.
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.. [Madsen] K. Madsen, H.B. Nielsen, and O. Tingleff, **Methods for
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nonlinear least squares problems**, 2004.
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@@ -114,7 +122,7 @@ References
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.. [Nocedal] J. Nocedal, **Updating Quasi-Newton Matrices with Limited
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Storage**, *Mathematics of Computation*, 35(151): 773--782, 1980.
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.. [NocedalWright] J. Nocedal & S. Wright, **Numerical Optimization**,
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.. [NocedalWright] J. Nocedal and S. Wright, **Numerical Optimization**,
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Springer, 2004.
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.. [Oren] S. S. Oren, **Self-scaling Variable Metric (SSVM) Algorithms
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@@ -122,7 +130,7 @@ References
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20(5), 863-874, 1974.
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.. [Press] W. H. Press, S. A. Teukolsky, W. T. Vetterling
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& B. P. Flannery, **Numerical Recipes**, Cambridge University
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and B. P. Flannery, **Numerical Recipes**, Cambridge University
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Press, 2007.
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.. [Ridders] C. J. F. Ridders, **Accurate computation of F'(x) and
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@@ -136,27 +144,37 @@ References
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systems**, SIAM, 2003.
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.. [Simon] I. Simon, N. Snavely and S. M. Seitz, **Scene Summarization
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for Online Image Collections**, *International Conference on Computer Vision*, 2007.
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for Online Image Collections**, *International Conference on
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Computer Vision*, 2007.
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.. [Stigler] S. M. Stigler, **Gauss and the invention of least
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squares**, *The Annals of Statistics*, 9(3):465-474, 1981.
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.. [TenenbaumDirector] J. Tenenbaum & B. Director, **How Gauss
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.. [TenenbaumDirector] J. Tenenbaum and B. Director, **How Gauss
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Determined the Orbit of Ceres**.
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.. [TrefethenBau] L.N. Trefethen and D. Bau, **Numerical Linear
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Algebra**, SIAM, 1997.
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.. [Triggs] B. Triggs, P. F. Mclauchlan, R. I. Hartley &
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.. [Triggs] B. Triggs, P. F. Mclauchlan, R. I. Hartley and
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A. W. Fitzgibbon, **Bundle Adjustment: A Modern Synthesis**,
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Proceedings of the International Workshop on Vision Algorithms:
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Theory and Practice, pp. 298-372, 1999.
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.. [Weber] S. Weber, N. Demmel, TC Chan, D. Cremers, **Power Bundle
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Adjustment for Large-Scale 3D Reconstruction**, *IEEE Conference on
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Computer Vision and Pattern Recognition*, 2023.
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.. [Wiberg] T. Wiberg, **Computation of principal components when data
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are missing**, In Proc. *Second Symp. Computational Statistics*,
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pages 229-236, 1976.
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.. [WrightHolt] S. J. Wright and J. N. Holt, **An Inexact
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Levenberg Marquardt Method for Large Sparse Nonlinear Least
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Squares**, *Journal of the Australian Mathematical Society Series
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B*, 26(4):387-403, 1985.
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.. [WrightHolt] S. J. Wright and J. N. Holt, **An Inexact Levenberg
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Marquardt Method for Large Sparse Nonlinear Least Squares**,
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*Journal of the Australian Mathematical Society Series B*,
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26(4):387-403, 1985.
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.. [Zheng] Q. Zheng, Y. Xi and Y. Saad, **A power Schur Complement
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low-rank correction preconditioner for general sparse linear
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systems**, *SIAM Journal on Matrix Analysis and
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Applications*, 2021.
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+613
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-61
@@ -64,8 +64,6 @@ class CERES_EXPORT Solver {
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// with a message describing the problem.
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bool IsValid(std::string* error) const;
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// Minimizer options ----------------------------------------
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// Ceres supports the two major families of optimization strategies -
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// Trust Region and Line Search.
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//
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@@ -571,13 +569,6 @@ class CERES_EXPORT Solver {
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// This settings only affects the SPARSE_NORMAL_CHOLESKY solver.
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bool dynamic_sparsity = false;
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// TODO(sameeragarwal): Further expand the documentation for the
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// following two options.
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// TODO(joydeepbiswas): Update the documentation for the mixed precision
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// option with CUDA.
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// NOTE1: EXPERIMENTAL FEATURE, UNDER DEVELOPMENT, USE AT YOUR OWN RISK.
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//
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// If use_mixed_precision_solves is true, the Gauss-Newton matrix
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// is computed in double precision, but its factorization is
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// computed in single precision. This can result in significant
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@@ -588,16 +579,57 @@ class CERES_EXPORT Solver {
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// If use_mixed_precision_solves is true, we recommend setting
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// max_num_refinement_iterations to 2-3.
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//
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// NOTE2: The following two options are currently only applicable
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// if sparse_linear_algebra_library_type is EIGEN_SPARSE or
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// ACCELERATE_SPARSE, and linear_solver_type is SPARSE_NORMAL_CHOLESKY
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// or SPARSE_SCHUR.
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// This options is available when linear solver uses sparse or dense
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// cholesky factorization, except when sparse_linear_algebra_library_type =
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// SUITE_SPARSE.
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bool use_mixed_precision_solves = false;
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// Number steps of the iterative refinement process to run when
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// computing the Gauss-Newton step.
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int max_num_refinement_iterations = 0;
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// Minimum number of iterations for which the linear solver should
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// run, even if the convergence criterion is satisfied.
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int min_linear_solver_iterations = 0;
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// Maximum number of iterations for which the linear solver should
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// run. If the solver does not converge in less than
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// max_linear_solver_iterations, then it returns MAX_ITERATIONS,
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// as its termination type.
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int max_linear_solver_iterations = 500;
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// Maximum number of iterations performed by SCHUR_POWER_SERIES_EXPANSION.
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// Each iteration corresponds to one more term in the power series expansion
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// od the inverse of the Schur complement. This value controls the maximum
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// number of iterations whether it is used as a preconditioner or just to
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// initialize the solution for ITERATIVE_SCHUR.
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int max_num_spse_iterations = 5;
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// Use SCHUR_POWER_SERIES_EXPANSION to initialize the solution for
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// ITERATIVE_SCHUR. This option can be set true regardless of what
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// preconditioner is being used.
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bool use_spse_initialization = false;
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// When use_spse_initialization is true, this parameter along with
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// max_num_spse_iterations controls the number of
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// SCHUR_POWER_SERIES_EXPANSION iterations performed for initialization. It
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// is not used to control the preconditioner.
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double spse_tolerance = 0.1;
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// Forcing sequence parameter. The truncated Newton solver uses
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// this number to control the relative accuracy with which the
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// Newton step is computed.
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//
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// This constant is passed to ConjugateGradientsSolver which uses
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// it to terminate the iterations when
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//
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// (Q_i - Q_{i-1})/Q_i < eta/i
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double eta = 1e-1;
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// Normalize the jacobian using Jacobi scaling before calling
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// the linear least squares solver.
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bool jacobi_scaling = true;
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// Some non-linear least squares problems have additional
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// structure in the way the parameter blocks interact that it is
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// beneficial to modify the way the trust region step is computed.
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@@ -681,49 +713,6 @@ class CERES_EXPORT Solver {
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// iterations is disabled.
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double inner_iteration_tolerance = 1e-3;
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// Minimum number of iterations for which the linear solver should
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// run, even if the convergence criterion is satisfied.
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int min_linear_solver_iterations = 0;
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// Maximum number of iterations for which the linear solver should
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// run. If the solver does not converge in less than
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// max_linear_solver_iterations, then it returns MAX_ITERATIONS,
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// as its termination type.
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int max_linear_solver_iterations = 500;
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// Maximum number of iterations performed by SCHUR_POWER_SERIES_EXPANSION.
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// This value controls the maximum number of iterations whether it is used
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// as a preconditioner or just to initialize the solution for
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// ITERATIVE_SCHUR.
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int max_num_spse_iterations = 5;
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// Use SCHUR_POWER_SERIES_EXPANSION to initialize the solution for
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// ITERATIVE_SCHUR. This option can be set true regardless of what
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// preconditioner is being used.
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bool use_spse_initialization = false;
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// When use_spse_initialization is true, this parameter along with
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// max_num_spse_iterations controls the number of
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// SCHUR_POWER_SERIES_EXPANSION iterations performed for initialization. It
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// is not used to control the preconditioner.
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double spse_tolerance = 0.1;
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// Forcing sequence parameter. The truncated Newton solver uses
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// this number to control the relative accuracy with which the
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// Newton step is computed.
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//
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// This constant is passed to ConjugateGradientsSolver which uses
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// it to terminate the iterations when
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//
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// (Q_i - Q_{i-1})/Q_i < eta/i
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double eta = 1e-1;
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// Normalize the jacobian using Jacobi scaling before calling
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// the linear least squares solver.
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bool jacobi_scaling = true;
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// Logging options ---------------------------------------------------------
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LoggingType logging_type = PER_MINIMIZER_ITERATION;
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// By default the Minimizer progress is logged to VLOG(1), which
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@@ -860,10 +849,9 @@ class CERES_EXPORT Solver {
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// IterationSummary for each minimizer iteration in order.
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std::vector<IterationSummary> iterations;
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// Number of minimizer iterations in which the step was
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// accepted. Unless use_non_monotonic_steps is true this is also
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// the number of steps in which the objective function value/cost
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// went down.
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// Number of minimizer iterations in which the step was accepted. Unless
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// use_nonmonotonic_steps is true this is also the number of steps in which
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// the objective function value/cost went down.
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int num_successful_steps = -1;
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// Number of minimizer iterations in which the step was rejected
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@@ -1077,7 +1065,7 @@ class CERES_EXPORT Solver {
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PreconditionerType preconditioner_type_used = IDENTITY;
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// Type of clustering algorithm used for visibility based
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// preconditioning. Only meaningful when the preconditioner_type
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// preconditioning. Only meaningful when the preconditioner_type_used
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// is CLUSTER_JACOBI or CLUSTER_TRIDIAGONAL.
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VisibilityClusteringType visibility_clustering_type = CANONICAL_VIEWS;
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