BAND_QR
LAPACK-Style QR Factorization of Banded Matrices

BAND_QR is a FORTRAN77 library 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

• they accept the banded matrix in the compact "GB" ("General Banded") format
• the QR factors are also stored compactly, by overwriting the input matrix storage.
• large problems are handled efficiently by taking advantage of the blocked version of the algorithm.

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.

Licensing:

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
            permission.

        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,
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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.

Languages:

BAND_QR is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

GEQP3, a FORTRAN77 library which contains the portion of the LAPACK library that carries out the QR factorization of a rectangular matrix. The famous "backslash" operator in MATLAB is based on the same algorithm embodied in GEQP3.

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

LINPLUS, a FORTRAN77 library which carries out some linear algebra operations on matrices in a variety of formats.

QR_SOLVE, a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

Author:

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,
{gquintan,remon,quintana}@icc.uji.es

Reference:

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:

• band_qr.f, the source code.
• band_qr.sh, commands to compile the source code.

Examples and Tests:

• band_qr_prb.f, a sample calling program.
• band_qr_prb.sh, commands to compile and run the sample program.
• band_qr_prb_output.txt, the output file.

List of Routines:

• DGBBQR2 QR factors an M by N band matrix in GB format, without blocking.
• DGBBQRF QR factors an M by N band matrix in GB format, using blocking.
• DGBBQRS solves A*X = B when A has been factored by DGBBQR2.
• DGEBQR2 QR factors an M by N band matrix in GE format, with no blocking.
• DGEBQRF QR factors an M by N band matrix stored in GE format, with blocking.
• DGEQRS solves a linear system factored by DGEQRF.
• DGEQRS_TWO solves A*X = B when A has been factored by DGEQRF or DGEBQR2.
• R8GB_PRINT prints an R8GB matrix.
• R8GB_PRINT_SOME prints some of an R8GB matrix.
• R8GE_PRINT prints an R8 GE matrix
• R8GE_PRINT_SOME prints some of an R8 GE matrix.
• R8VEC_PRINT prints an R8VEC.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.