The standard sparse normal Cholesky solver assumes a fixed
sparsity pattern which is useful for a large number of problems
presented to Ceres. However, some problems are symbolically dense
but numerically sparse i.e. each residual is a function of a
large number of parameters but at any given state the residual
only depends on a sparse subset of them. For these class of
problems it is faster to re-analyse the sparsity pattern of the
jacobian at each iteration of the non-linear optimisation instead
of including all of the zero entries in the step computation.
The proposed solution adds the dynamic_sparsity option which can
be used with SPARSE_NORMAL_CHOLESKY. A
DynamicCompressedRowSparseMatrix type (which extends
CompressedRowSparseMatrix) has been introduced which allows
dynamic addition and removal of elements. A Finalize method is
provided which then consolidates the matrix so that it can be
used in place of a regular CompressedRowSparseMatrix. An
associated jacobian writer has also been provided.
Changes that were required to make this extension were adding the
SetMaxNumNonZeros method to CompressedRowSparseMatrix and adding
a JacobianFinalizer template parameter to the ProgramEvaluator.
Change-Id: Ia5a8a9523fdae8d5b027bc35e70b4611ec2a8d01
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
CompressedRowSparseMatrix can store the row and column block structure
but the AppendRows and DeleteRows methods did not pay attention to them.
This meant that it was possible to get to a CompressedRowSparseMatrix
whose block structure did not match the contents of the matrix.
This change fixes this problem.
Change-Id: I1b3c807fc03d8c049ee20511e2bc62806d211b81
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
unnecessarily complexity in the structure of linear solvers and preconditioners.
This is the first step towards cleaning up the Preconditioner interface.
2. Minor tweaks and cleanups to the various linear solvers.
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.
Richard Stebbing