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1 # Copyright (C) 1993, 1994, 1995 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 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 retval = norm (x, p) |
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20 |
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21 # usage: norm (x, p) |
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22 # |
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23 # Compute the p-norm of x. |
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24 # |
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25 # If x is a matrix: |
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26 # |
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27 # value of p norm returns |
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28 # ---------- ------------ |
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29 # 1 1-norm, the largest column sum of x |
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30 # 2 largest singular value of x |
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31 # Inf infinity norm, the largest row sum of x |
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32 # "fro" Frobenius norm of x, sqrt (sum (diag (x' * x))) |
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33 # |
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34 # If x is a vector or a scalar: |
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35 # |
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36 # value of p norm returns |
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37 # ---------- ------------ |
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38 # Inf max (abs (x)) |
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39 # -Inf min (abs (x)) |
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40 # other p-norm of x, sum (abs (x) .^ p) ^ (1/p) |
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41 # |
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42 # If the second argument is missing, p = 2 is assumed. |
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43 # |
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44 # See also: cond, svd |
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45 |
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46 if (nargin < 1 || nargin > 2) |
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47 error ("usage: norm (x [, p])") |
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48 endif |
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49 |
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50 if (isempty (x)) |
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51 retval = []; |
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52 return; |
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53 endif |
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54 |
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55 # Do we have a vector or matrix as the first argument? |
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56 |
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57 if (rows (x) == 1 || columns (x) == 1) |
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58 |
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59 if (nargin == 2) |
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60 if (isstr (p)) |
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61 if (strcmp (p, "fro")) |
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62 retval = sqrt (sum (diag (x' * x))); |
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63 else |
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64 error ("norm: unrecognized norm"); |
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65 endif |
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66 else |
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67 if (p == Inf) |
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68 retval = max (abs (x)); |
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69 elseif (p == -Inf) |
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70 retval = min (abs (x)); |
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71 else |
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72 retval = sum (abs (x) .^ p) ^ (1/p); |
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73 endif |
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74 endif |
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75 elseif (nargin == 1) |
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76 retval = sum (abs (x) .^ 2) ^ 0.5; |
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77 endif |
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78 |
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79 else |
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80 |
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81 if (nargin == 2) |
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82 if (isstr (p)) |
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83 if (strcmp (p, "fro")) |
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84 retval = sqrt (sum (diag (x' * x))); |
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85 else |
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86 error ("norm: unrecognized norm"); |
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87 endif |
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88 else |
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89 if (p == 1) |
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90 retval = max (sum (abs (real (x)) + abs (imag (x)))); |
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91 elseif (p == 2) |
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92 s = svd (x); |
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93 retval = s (1); |
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94 elseif (p == Inf) |
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95 xp = x'; |
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96 retval = max (sum (abs (real (xp)) + abs (imag (xp)))); |
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97 endif |
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98 endif |
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99 elseif (nargin == 1) |
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100 s = svd (x); |
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101 retval = s (1); |
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102 endif |
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103 |
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104 endif |
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105 |
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106 endfunction |
