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1 # Copyright (C) 1993, 1998, 1999 A. Scottedward Hodel |
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2 # |
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3 # This file is part of Octave. |
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4 # |
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5 # Octave is free software; you can redistribute it and/or modify it |
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6 # under the terms of the GNU General Public License as published by the |
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7 # Free Software Foundation; either version 2, or (at your option) any |
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8 # later version. |
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9 # |
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10 # Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 # for more details. |
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14 # |
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15 # You should have received a copy of the GNU General Public License |
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16 # along with Octave; see the file COPYING. If not, write to the Free |
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17 # Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
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18 |
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19 function [Uret,Ucols] = krylovb(A,V,k,eps1,pflg); |
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20 # function [U,Ucols] = krylovb(A,V,k{,eps1,pflg}); |
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21 # construct orthogonal basis U of block Krylov subspace; |
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22 # [V AV A^2*V ... A^(k+1)*V]; |
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23 # method used: householder reflections to guard against loss of |
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24 # orthogonality |
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25 # eps1: threshhold for 0 (default: 1e-12) |
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26 # pflg: permutation flag |
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27 # outputs: |
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28 # returned basis U is orthogonal matrix; due to "zeroed" |
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29 # columns of product, may not satisfy A U = U H identity |
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30 # Ucols: dimension of span of krylov subspace (based on eps1) |
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31 # if k > m-1, krylov returns the Hessenberg decompostion of A. |
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32 # |
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33 # Note: krylovb directly calls and is superseded by krylov. |
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34 |
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35 switch(nargin) |
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36 case(3), |
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37 [Uret,H,Ucols] = krylov(A,V,k); |
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38 case(4), |
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39 [Uret,H,Ucols] = krylov(A,V,k,eps1); |
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40 case(5), |
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41 [Uret,H,Ucols] = krylov(A,V,k,eps1,pflg); |
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42 otherwise, |
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43 usage("[Uret,Ucols] = krylovb(A,V,k{,eps1,pflg}); %d arguments passed", ... |
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44 nargin); |
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45 endswitch |
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46 |
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47 endfunction |
