Dense (cuSOLVER Based)

This section demonstrates how to solve dense systems of linear equations on GPU using standard factorization methods.

LU Decomposition (General Matrices)

Performs LU factorization with partial pivoting for general matrices on GPU.

Source Code

Console Output

#include <iostream> #include <cla3p/dense.hpp> #include <cla3p/algebra.hpp> #include <culite/dense.hpp> #include <culite/linsol.hpp> int main() { /* * Create a random dense objects on host */ const cla3p::dns::RdMatrix HostA = cla3p::dns::RdMatrix::random(5,5); const cla3p::dns::RdVector HostBv = cla3p::dns::RdVector::random(5); const cla3p::dns::RdMatrix HostBm = cla3p::dns::RdMatrix::random(5,3); /* * Transfer to device */ culite::dns::RdMatrix A ; culite::dns::RdVector b; culite::dns::RdMatrix B; HostA >> A; HostBv >> b; HostBm >> B; /* * Instantiate LU solver */ culite::LapackLU<culite::dns::RdMatrix> luSolver; /* * Decompose A into LU product */ luSolver.decompose(A); { /* * Single column (vector) rhs * Overwrite x with the solution (A^{-1} * Bv) */ culite::dns::RdVector x = b; luSolver.solve(x); // Check error norm on host cla3p::dns::RdVector HostX; x >> HostX; std::cout << "Dense Vector rhs::Absolute Error: " << (HostBv - HostA * HostX).evaluate().normOne() << std::endl; } { /* * Multiple column (matrix) rhs * Overwrite X with the solution (A^{-1} * B) */ culite::dns::RdMatrix X = B; luSolver.solve(X); // Check error norm on host cla3p::dns::RdMatrix HostX; X >> HostX; std::cout << "Dense Matrix rhs::Absolute Error: " << (HostBm - HostA * HostX).evaluate().normOne() << std::endl; } return 0; }

Dense Vector rhs::Absolute Error: 1.7656e-16 Dense Matrix rhs::Absolute Error: 6.66134e-16