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qrupdate-ng: A Library for Fast Updating of QR and Cholesky Decompositions

• License: GPL-3.0-or-later (opensource.org/licenses/GPL-3.0)
• Version: 1.1.5 (2022-02-04)
• Authors: M. Koehler (0000-0003-2338-9904), C. Himpe (0000-0003-2194-6754)
• Original Author: Jaroslav Hajek (VZLU Prague)
• Summary: A FORTRAN library for rank-1 matrix decomposition updates

Supported Matrix Decompositions

QR Decomposition

• QR rank-1 update (qr1up)

  Updates the QR factorization after an additive rank-1 update to the original matrix (A = A + u*v'). Works for full & economized factorization.

• QR column insert (qrinc)

  Updates the QR factorization after an inserting a column to the original matrix. Works for full & economized factorization.

• QR column delete (qrdec)

  Updates the QR factorization after an deleting a column from the original matrix. Works for full & economized factorization.

• QR column shift (qrshc)

  Updates the QR factorization after a circular shift of columns in the original matrix. Works for full & economized factorization.

• QR row insert (qrinr)

  Updates the QR factorization after an inserting a row to the original matrix. Works for full factorization only.

• QR row delete (qrder)

  Updates the QR factorization after an deleting a row from the original matrix. Works for full factorization only.

Cholesky Decomposition

• Cholesky rank-1 update (ch1up)

  Updates the Cholesky factorization after positive rank-1 update A = A + u*u'.

• Cholesky rank-1 downdate (ch1dn)

  Updates the Cholesky factorization after positive rank-1 downdate A = A - u*u'.

• Cholesky symmetric insert (chinx)

  Updates the Cholesky factorization after a symmetric column/row insertion.

• Cholesky symmetric insert (chdex)

  Updates the Cholesky factorization after a symmetric column/row deletion.

• Cholesky symmetric shift (chshx)

  Updates the Cholesky factorization after a symmetric column/row left/right circular shift.

LU Decomposition

• LU rank-1 update (lu1up)

  Updates the LU factorization after a rank-1 update (A = A + u*v.'). No pivoting available. Faster than lup1up, but less stable.

• LU pivoted rank-1 update (lup1up)

  Updates a row-pivoted LUP factorization after a rank-1 update (A = A + u*v.'). Also updates the row permutation matrix. Slower than lu1up, but more stable.

Based on

qrupdate-ng is a modernized and maintained fork of:

qrupdate (Version 1.1.2)

For a list of original authors see CHANGELOG file.

License

See the LICENSE file.

Installation

See the INSTALL file for installation details. Consult individual routines for documentation.