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
Richard Bowen