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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