Reference book for math principles in BlockCholeskyLinearSystemSolver.cpp

[wushichatong]

I want to multithreading BlockCholeskyLinearSystemSolver to accelarate and could you provide some math reference for BlockCholeskyLinearSystemSolver

[goldbattle]

I am not sure of any reference, but likely searching block cholesky is a good starting point. I believe also the sparse matrix library is based on the g2o paper, which discusses about the "special structure" when we have SLAM with landmarks.
http://ais.informatik.uni-freiburg.de/publications/papers/kuemmerle11icra.pdf

I believe the current code uses this function by default:

kalibr/aslam_optimizer/sparse_block_matrix/include/sparse_block_matrix/linear_solver_cholmod.h

Lines 70 to 112 in 1f60227

	bool solve(const SparseBlockMatrix<MatrixType>& A, double* x, double* b)
	{
	//cerr << __PRETTY_FUNCTION__ << " using cholmod" << endl;
	fillCholmodExt(A, _cholmodFactor); // _cholmodFactor used as bool, if not existing will copy the whole structure, otherwise only the values
	if (! _cholmodFactor) {
	computeSymbolicDecomposition(A);
	assert(_cholmodFactor && "Symbolic cholesky failed");
	}
	//double t=get_time();
	// setting up b for calling cholmod
	cholmod_dense bcholmod;
	bcholmod.nrow = bcholmod.d = _cholmodSparse->nrow;
	bcholmod.ncol = 1;
	bcholmod.x = b;
	bcholmod.xtype = CHOLMOD_REAL;
	bcholmod.dtype = CHOLMOD_DOUBLE;
	cholmod_factorize(_cholmodSparse, _cholmodFactor, &_cholmodCommon);
	if (_cholmodCommon.status == CHOLMOD_NOT_POSDEF) {
	if (_cholmodFactor) {
	cholmod_free_factor(&_cholmodFactor, &_cholmodCommon);
	_cholmodFactor = 0;
	}
	//std::cerr << "Cholesky failure\n";//, writing debug.txt (Hessian loadable by Octave)" << std::endl;
	//writeCCSMatrix("debug.txt", _cholmodSparse->nrow, _cholmodSparse->ncol, (int*)_cholmodSparse->p, (int*)_cholmodSparse->i, (double*)_cholmodSparse->x, true);
	return false;
	}
	cholmod_dense* xcholmod = cholmod_solve(CHOLMOD_A, _cholmodFactor, &bcholmod, &_cholmodCommon);
	memcpy(x, xcholmod->x, sizeof(double) * bcholmod.nrow); // copy back to our array
	cholmod_free_dense(&xcholmod, &_cholmodCommon);
	//if (globalStats){
	// globalStats->timeNumericDecomposition = get_time() - t;
	// globalStats->choleskyNNZ = _cholmodCommon.method[0].lnz;
	//}
	return true;
	}