Getting Started with LBL

LBL is a part of the NASOQ repository and can be installed similarly. Here we explain how LBL C++ API can be used to solve your sparse indefinite linear systems.

Installation

LBL installation is the same as NASOQ installation instructions

C++ API examples

C++ API examples for how to use LBL and SoMod in-tree and out-of-tree are provided in thenasoq/examples directory. For details, please see NASOQ C++ API.

Here we show a snapshot of the LBL linear solver example (nasoq/examples/lbl_main.cpp):

#include <nasoq/QP/linear_solver_wrapper.h>

/*
 * Solving Hx = q
 * H is a sparse matrix stored in CSC format
 * q is a dense array
 */

int main(int argc, char *argv[]){

 /// Declaring input matrices
 // allocate
    ...
 q[0] = -4; q[1] = -4;

 Hp[0]=0;Hp[1]=1;Hp[2]=2;
 Hi[0]=0;Hi[1]=1;
 Hx[0]=2;Hx[1]=2;

 auto *H = new nasoq::CSC; H->nzmax = nnzH; H->ncol= H->nrow =sizeH;
 H->p = Hp; H->i = Hi; H->x = Hx; H->stype=-1;

/// Solving the linear system
 auto *lbl = new nasoq::SolverSettings(H,q);
 lbl->ldl_variant = 4;
 lbl->req_ref_iter = 2;
 lbl->solver_mode = 0;
 lbl->reg_diag = pow(10,-9);
 lbl->symbolic_analysis();
 lbl->numerical_factorization();
 double *x = lbl->solve_only();


 /// Printing results
 // expected x={-2,-2};
 std::cout<<"Solution: ";
 for (int i = 0; i < sizeH; ++i) {
  std::cout<<x[i]<<",";
 }
 /// Free memory
 ...

}

For details about inputs, outputs, and settings of LBL, please see the LBL document page.

SoMoD: Sparsity Oriented Row Modification

SoMoD is designed to update the factors of LDL factorization after one or multiple rows of the input matrix is modified. SoMoD is an expert routine that is only used inside NASOQ. SoMoD works when the sparsity pattern of changes is known as a priory. There is an example, lbl_somod_main.cpp on how to use SoMoD in nasoq/examples.