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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, 59 Temple Place - Suite 330, Boston, MA 02111-1307, 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 # "inf" same as Inf |
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33 # "fro" Frobenius norm of x, sqrt (sum (diag (x' * x))) |
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34 # |
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35 # If x is a vector or a scalar: |
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36 # |
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37 # value of p norm returns |
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38 # ---------- ------------ |
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39 # Inf max (abs (x)) |
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40 # -Inf min (abs (x)) |
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41 # other p-norm of x, sum (abs (x) .^ p) ^ (1/p) |
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42 # |
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43 # If the second argument is missing, p = 2 is assumed. |
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44 # |
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45 # See also: cond, svd |
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46 |
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47 if (nargin < 1 || nargin > 2) |
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48 error ("usage: norm (x [, p])") |
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49 endif |
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50 |
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51 if (isempty (x)) |
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52 retval = []; |
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53 return; |
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54 endif |
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55 |
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56 # Do we have a vector or matrix as the first argument? |
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57 |
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58 if (rows (x) == 1 || columns (x) == 1) |
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59 |
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60 if (nargin == 2) |
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61 if (isstr (p)) |
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62 if (strcmp (p, "fro")) |
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63 retval = sqrt (sum (diag (x' * x))); |
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64 elseif (strcmp (p, "inf")) |
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65 retval = max (abs (x)); |
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66 else |
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67 error ("norm: unrecognized norm"); |
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68 endif |
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69 else |
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70 if (p == Inf) |
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71 retval = max (abs (x)); |
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72 elseif (p == -Inf) |
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73 retval = min (abs (x)); |
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74 else |
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75 retval = sum (abs (x) .^ p) ^ (1/p); |
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76 endif |
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77 endif |
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78 elseif (nargin == 1) |
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79 retval = sum (abs (x) .^ 2) ^ 0.5; |
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80 endif |
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81 |
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82 else |
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83 |
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84 if (nargin == 2) |
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85 if (isstr (p)) |
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86 if (strcmp (p, "fro")) |
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87 retval = sqrt (sum (diag (x' * x))); |
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88 elseif (strcmp (p, "inf")) |
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89 xp = x'; |
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90 retval = max (sum (abs (real (xp)) + abs (imag (xp)))); |
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91 else |
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92 error ("norm: unrecognized norm"); |
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93 endif |
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94 else |
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95 if (p == 1) |
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96 retval = max (sum (abs (real (x)) + abs (imag (x)))); |
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97 elseif (p == 2) |
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98 s = svd (x); |
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99 retval = s (1); |
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100 elseif (p == Inf) |
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101 xp = x'; |
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102 retval = max (sum (abs (real (xp)) + abs (imag (xp)))); |
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103 endif |
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104 endif |
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105 elseif (nargin == 1) |
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106 s = svd (x); |
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107 retval = s (1); |
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108 endif |
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109 |
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110 endif |
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111 |
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112 endfunction |
