Detailed Description

Solver for general band matrices.

Note: Although the pdbsv solver supports KL=0 and/or KU=0, a zero (half) bandwidth would lead to unwanted warning message from ScaLAPACK.; See: https://github.com/Reference-ScaLAPACK/scalapack/issues/116

It solves the system of linear equations A*X=B with a general band matrix A. The band matrix A has KL sub-diagonals and KU super-diagonals. It shall be stored in the following format. The band storage scheme is illustrated by the following example, when M=N=6, KL=2, KU=1.

 .   a12  a23  a34  a45  a56
a11  a22  a33  a44  a55  a66
a21  a32  a43  a54  a65   .
a31  a42  a53  a64   .    .

The lead dimension should be (KL+KU+1).

With zero based indexing, for a general band matrix A, the element at row i and column j is stored at A[IDX(i, j)].

const auto IDX = [&](const int i, const int j) {
    if(i - j > KL || j - i > KU) return -1;
    return KU + i - j + j * (KL + KU + 1);
};

Author: tlc

Date: 07/03/2025

Version: 1.0.0

The documentation for this class was generated from the following file:

ezp/pdbsv.hpp