When using sparse cholesky factorization to solve the linear
least squares problem:
Ax = b
There are two sources of computational complexity.
1. Computing H = A'A
2. Computing the sparse Cholesky factorization of H.
Doing 1. using CX_SPARSE is particularly expensive, as it uses
a generic cs_multiply function which computes the structure of
the matrix H everytime, reallocates memory and does not take
advantage of the fact that the matrix being computed is a symmetric
outer product.
This change adds a custom symmetric outer product algorithm for
CompressedRowSparseMatrix.
It has a symbolic phase, where it computes the sparsity structure
of the output matrix and a "program" which allows the actual
multiplication routine to determine exactly which entry in the
values array each term in the product contributes to.
With these two bits of information, the outer product H = A'A
can be computed extremely fast without any reasoning about
the structure of H.
Further gains in efficiency are made by exploiting the block
structure of A.
With this change, SPARSE_NORMAL_CHOLESKY with CX_SPARSE as the
backend results in > 300% speedup for some problems.
The symbolic analysis phase of the solver is a bit more expensive
now but the increased cost is made up in 3-4 iterations.
Change-Id: I5e4a72b4d03ba41b378a2634330bc22b299c0f12
1. When protocol buffers support is enabled CompressedRowSparseMatrix
has a missing virtual method.
2. When SuiteSparse is missing, covariance_test tries to run the
large scale covariance computation test.
Thanks to Alex Stewart for reporting #1.
Change-Id: I4238c966036362175e31749595ea8bb6f12a696c
Drop support for protocol buffers.
Add CompressedRowSparseMatrix::CreateBlockDiagonalMatrix.
Add CompressedRowSparseMatrix::SolveLowerTriangularInPlace.
Add CompressedRowSparseMatrix::SolveLowerTriangularTranposeInPlace.
Add CompressedRowSparseMatrix::Transpose.
Change-Id: I2328afca9fac632685eac72ebb00998bd3510187
1. Added CRSMatrix object which will store the initial
and final jacobians if requested by the user.
2. Conversion routine and test for converting a
CompressedRowSparseMatrix to CRSMatrix.
3. New Evaluator::Evaluate function to do the actual evaluation.
4. Changes to Program::StateVectorToParmeterBlocks and
Program::SetParameterBlockStatePtrstoUserStatePtrs so that
they do not try to set the state of constant parameter blocks.
5. Tests for Evaluator::Evaluate.
6. Minor cleanups in SolverImpl.
7. Minor cpplint cleanups triggered by this CL.
Change-Id: I3ac446484692f943c28f2723b719676f8c83ca3d
By virtue of the modeling layer in Ceres being block oriented,
all the matrices used by Ceres are also block oriented.
When doing sparse direct factorization of these matrices, the
fill-reducing ordering algorithms can either be run on the
block or the scalar form of these matrices. Running it on the
block form exposes more of the super-nodal structure of the
matrix to the Cholesky factorization routines. This leads to
substantial gains in factorization performance.
This changelist adds support for approximate minimium degree
orderings to be computed on the block structure of the
Schur complement matrix. This affects, SchurComplementSolver
and VisibilityBasedPreconditioner and SparseNormalCholesky
when using SuiteSparse.
A bool, use_block_amd has been added to Solver::Options and
bundle_adjuster.cc has been updated to allow testing with it.
When combined with a multithreaded Schur elimination, speed ups
can be seen quite uniformly across the board. For some problems
this can be dramatic, reducing the factorization time from 70
seconds down to 17 seconds.
Change-Id: I15ebb0afcbc85ada032ec8d179ee3a2f7c8d3e46
1. Make the mechanism for writing problems to disk, generic and
controllable using an enum DumpType visible in the API.
2. Instead of single file containing protocol buffers, now matrices can
be written in a matlab/octave friendly format. This is now the default.
3. The support for writing problems to disk is moved into
linear_least_squares_problem.cc/h
4. SparseMatrix now has a ToTextFile virtual method which is
implemented by each of its subclasses to write a (i,j,s) triplets.
5. Minor changes to simple_bundle_adjuster to enable logging at startup.
Sameer Agarwal