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1 ## Copyright (C) 1996, 1997 John W. Eaton |
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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 |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## Undocumented internal function. |
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20 |
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21 ## Author: jwe |
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22 |
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23 function retval = __norm__ (x, p) |
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24 |
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25 if (nargin < 1 || nargin > 2) |
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26 print_usage (); |
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27 endif |
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28 |
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29 if (isempty (x)) |
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30 retval = []; |
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31 return; |
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32 endif |
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33 |
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34 if (ndims (x) > 2) |
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35 error ("norm: only valid on 2-D objects") |
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36 endif |
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37 |
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38 if (nargin == 1) |
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39 p = 2; |
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40 endif |
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41 |
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42 ## Do we have a vector or matrix as the first argument? |
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43 |
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44 if (ndims(x) == 2 && (rows (x) == 1 || columns (x) == 1)) |
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45 if (ischar (p)) |
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46 if (strcmp (p, "fro")) |
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47 retval = sqrt (sum (abs (x) .^ 2)); |
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48 elseif (strcmp (p, "inf")) |
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49 retval = max (abs (x)); |
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50 else |
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51 error ("norm: unrecognized norm"); |
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52 endif |
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53 else |
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54 if (p == Inf) |
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55 retval = max (abs (x)); |
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56 elseif (p == -Inf) |
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57 retval = min (abs (x)); |
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58 elseif (p == 1) |
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59 retval = sum (abs (x)); |
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60 elseif (p == 2) |
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61 if (iscomplex (x)) |
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62 x = abs (x); |
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63 endif |
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64 retval = sqrt (sumsq (x)); |
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65 else |
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66 retval = sum (abs (x) .^ p) ^ (1/p); |
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67 endif |
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68 endif |
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69 else |
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70 if (ischar (p)) |
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71 if (strcmp (p, "fro")) |
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72 retval = sqrt (sum (sum (abs (x) .^ 2))); |
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73 elseif (strcmp (p, "inf")) |
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74 retval = max (sum (abs (x'))); |
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75 else |
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76 error ("norm: unrecognized vector norm"); |
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77 endif |
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78 else |
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79 if (p == 1) |
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80 retval = max (sum (abs (x))); |
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81 elseif (p == 2) |
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82 s = svd (x); |
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83 retval = s (1); |
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84 elseif (p == Inf) |
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85 retval = max (sum (abs (x'))); |
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86 else |
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87 error ("norm: unrecognized matrix norm"); |
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88 endif |
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89 endif |
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90 endif |
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91 |
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92 endfunction |
