| [9] | 1 | NOTE: Files in this subdirectory are NOT part of the GLPK package, but |
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| 2 | are used with GLPK. |
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| 3 | |
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| 4 | The original code was modified according to GLPK requirements by |
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| 5 | Andrew Makhorin <mao@gnu.org>. |
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| 6 | ************************************************************************ |
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| 7 | COLAMD/SYMAMD Version 2.7, Copyright (C) 1998-2007, Timothy A. Davis, |
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| 8 | All Rights Reserved. |
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| 9 | |
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| 10 | Description: |
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| 11 | |
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| 12 | colamd: an approximate minimum degree column ordering algorithm, |
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| 13 | for LU factorization of symmetric or unsymmetric matrices, |
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| 14 | QR factorization, least squares, interior point methods for |
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| 15 | linear programming problems, and other related problems. |
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| 16 | |
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| 17 | symamd: an approximate minimum degree ordering algorithm for |
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| 18 | Cholesky factorization of symmetric matrices. |
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| 19 | |
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| 20 | Purpose: |
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| 21 | |
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| 22 | Colamd computes a permutation Q such that the Cholesky factorization |
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| 23 | of (AQ)'(AQ) has less fill-in and requires fewer floating point |
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| 24 | operations than A'A. This also provides a good ordering for sparse |
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| 25 | partial pivoting methods, P(AQ) = LU, where Q is computed prior to |
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| 26 | numerical factorization, and P is computed during numerical |
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| 27 | factorization via conventional partial pivoting with row |
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| 28 | interchanges. Colamd is the column ordering method used in SuperLU, |
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| 29 | part of the ScaLAPACK library. It is also available as built-in |
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| 30 | function in MATLAB Version 6, available from MathWorks, Inc. |
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| 31 | (http://www.mathworks.com). This routine can be used in place of |
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| 32 | colmmd in MATLAB. |
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| 33 | |
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| 34 | Symamd computes a permutation P of a symmetric matrix A such that |
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| 35 | the Cholesky factorization of PAP' has less fill-in and requires |
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| 36 | fewer floating point operations than A. Symamd constructs a matrix |
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| 37 | M such that M'M has the same nonzero pattern of A, and then orders |
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| 38 | the columns of M using colmmd. The column ordering of M is then |
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| 39 | returned as the row and column ordering P of A. |
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| 40 | |
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| 41 | Authors: |
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| 42 | |
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| 43 | The authors of the code itself are Stefan I. Larimore and Timothy A. |
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| 44 | Davis (davis at cise.ufl.edu), University of Florida. The algorithm |
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| 45 | was developed in collaboration with John Gilbert, Xerox PARC, and |
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| 46 | Esmond Ng, Oak Ridge National Laboratory. |
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| 47 | |
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| 48 | Acknowledgements: |
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| 49 | |
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| 50 | This work was supported by the National Science Foundation, under |
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| 51 | grants DMS-9504974 and DMS-9803599. |
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| 52 | |
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| 53 | License: |
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| 54 | |
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| 55 | This library is free software; you can redistribute it and/or |
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| 56 | modify it under the terms of the GNU Lesser General Public License |
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| 57 | as published by the Free Software Foundation; either version 2.1 of |
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| 58 | the License, or (at your option) any later version. |
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| 59 | |
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| 60 | This library is distributed in the hope that it will be useful, |
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| 61 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 62 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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| 63 | Lesser General Public License for more details. |
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| 64 | |
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| 65 | You should have received a copy of the GNU Lesser General Public |
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| 66 | License along with this library; if not, write to the Free Software |
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| 67 | Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 |
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| 68 | USA. |
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| 69 | |
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| 70 | Permission is hereby granted to use or copy this program under the |
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| 71 | terms of the GNU LGPL, provided that the Copyright, this License, |
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| 72 | and the Availability of the original version is retained on all |
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| 73 | copies. User documentation of any code that uses this code or any |
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| 74 | modified version of this code must cite the Copyright, this License, |
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| 75 | the Availability note, and "Used by permission." Permission to |
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| 76 | modify the code and to distribute modified code is granted, provided |
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| 77 | the Copyright, this License, and the Availability note are retained, |
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| 78 | and a notice that the code was modified is included. |
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| 79 | |
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| 80 | COLAMD is also available under alternate licenses, contact T. Davis |
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| 81 | for details. |
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| 82 | |
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| 83 | Availability: |
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| 84 | |
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| 85 | The colamd/symamd library is available at: |
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| 86 | |
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| 87 | http://www.cise.ufl.edu/research/sparse/colamd/ |
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| 88 | |
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| 89 | References: |
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| 90 | |
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| 91 | T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate |
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| 92 | column minimum degree ordering algorithm, ACM Transactions on |
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| 93 | Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004. |
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| 94 | |
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| 95 | T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: |
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| 96 | COLAMD, an approximate column minimum degree ordering algorithm, ACM |
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| 97 | Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380, |
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| 98 | 2004. |
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