pgbsv Class Reference

Solver for general band matrices. More...

#include <pgbsv.hpp>

Detailed Description

Solver for general band matrices.

Note

Although the pgbsv 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 2*(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 2 * KU + KL + i + 2 * j * (KL + KU);
};

Author

tlc

Date

07/03/2025

Version

1.0.0

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

• ezp/pgbsv.hpp