band_qr, a Fortran90 code which includes LAPACK-style routines to compute the QR factorization of a banded matrix, by Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti.

The distinguishing features of these routines include the fact that

The routines, as originally developed, did not include a routine to solve linear systems A*x=b once the QR factors had been computed. A routine DGBBQRS() has been written to carry out this computation in cases where the QR factors were computed using DGBBQR2(), that is, the unblocked code.


This software library includes routines which are distributed under a separate license. Each such routine is individually marked with the following information:

        Copyright (c) 2007, Universidad Jaume I de Castellon
        All rights reserved.

        Redistribution and use in source and binary forms, with or without
        modification, are permitted provided that the following conditions
        are met:
          * Redistributions of source code must retain the above copyright
            notice, this list of conditions and the following disclaimer.
          * Redistributions in binary form must reproduce the above copyright
            notice, this list of conditions and the following disclaimer in the
            documentation and/or other materials provided with the distribution.
          * Neither the name of the  nor the
            names of its contributors may be used to endorse or promote
            products derived from this software without specific prior written

        This software is provided by  ''as is'' and any
        express or implied warranties, including, but not limited to, the
        implied warranties of merchantability and fitness for a particular
        purpose are disclaimed.  In no event shall  be liable
        for any direct, indirect, incidental, special, exemplary, or
        consequential damages (including, but not limited to, procurement of
        substitute goods or services; loss of use, data, or profits; or
        business interruption) however caused and on any theory of liability,
        whether in contract, strict liability, or tort (including negligence
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        if advised of the possibility of such damage.

Code not covered under the above license is made available under the GNU LGPL license.


band_qr is available in a FORTRAN90 version.

Related Data and Programs:


lapack, a FORTRAN90 library which contains modern linear algebra routines.

LINPLUS, a FORTRAN90 library which carries out some linear algebra operations on matrices in a variety of formats.


Certain routines in this library represent the work of:
Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti,
Dept. de Ingenieria y Ciencia de Computadores, Universidad Jaume I,
12.080 Castellon, Spain,


  1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
    LAPACK User's Guide,
    Third Edition,
    SIAM, 1999,
    ISBN: 0898714478,
    LC: QA76.73.F25L36
  2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
    LINPACK User's Guide,
    SIAM, 1979,
    ISBN13: 978-0-898711-72-1,
    LC: QA214.L56.
  3. Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti,
    LAPACK-Style Codes for the QR Factorization of Banded Matrices,
    To Appear.

Source Code:

Last revised on 09 September 2023.