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pgesvx

The pgesvx solver supports the following input types.

  • data type: DSZC
  • index type: std::int32_t, std::int64_t

The pgesvx solves a square matrix using LU decomposition with partial pivoting. The matrix of size \(N\) is stored in a memory block of size \(N^2\). The solver can apply equilibration and iterative refinement. This is an expert solver.

Constructor

There are four template arguments.

  1. data type, e.g., double, float, std::complex<double>, std::complex<float>.
  2. index type, e.g., std::int32_t, std::int64_t.
  3. equilibration flag, F, N, E.
  4. proccess grid order, R or C.

This solver uses a 2D process grid, so one can choose from Row major or Column major ordering.

With np_row and np_col denoting the numbers of rows and columns of the process grid, a solver can be constructed using the following.

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auto solver = pgesvx<double, int, 'E', 'R'>(np_row, np_col);

It is possible to let the library automatically determine the numbers of rows and columns, then the solver can be constructed as

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auto solver = pgesvx<double, int, 'E', 'R'>();

Solving

Prepare matrices \(A\) and \(B\) on the root process in whatever form of choice. Those two matrices need to be wrapped into template<data_t DT, index_t IT> struct full_mat objects, which require

  1. the number of rows of the matrix, n_rows,
  2. the number of columns of the matrix, n_cols,
  3. a pointer pointing to the data, data.

Then one can call the solver via

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constexpr auto N = 6, NRHS = 2;
// storage for the matrices A and B
std::vector<double> A, B;
// ...
// ... storage is populated by some utility on the root process
// ...
const auto info = solver.solve({N, N, A.data()}, {N, NRHS, B.data()});

The factorization cannnot be reused. Thus, every call to solve(full_mat<DT, IT>&& A, full_mat<DT, IT>&& B) will invalidate the previous factorization and perform the factorization again even if the matrix \(A\) does not change. This is a costly solver, if pgesv suffices, pgesvx shall only be used in advanced cases.

On return, B will be replaced by the solution. In the above example, std::vector<double> B will contain the solution.