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1 ### Copyright (C) 1996 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 2, or (at your option) |
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8 ### 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, write to the Free |
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17 ### Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ### 02111-1307, USA. |
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19 |
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20 ## usage: norm (x, p) |
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21 ## |
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22 ## Compute the p-norm of x. |
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23 ## |
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24 ## If x is a matrix: |
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25 ## |
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26 ## value of p norm returns |
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27 ## ---------- ------------ |
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28 ## 1 1-norm, the largest column sum of x |
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29 ## 2 largest singular value of x |
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30 ## Inf infinity norm, the largest row sum of x |
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31 ## "inf" same as Inf |
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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 function retval = norm (x, p) |
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47 |
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48 if (nargin < 1 || nargin > 2) |
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49 error ("usage: norm (x [, p])"); |
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50 endif |
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51 |
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52 if (isempty (x)) |
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53 retval = []; |
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54 return; |
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55 endif |
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56 |
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57 ## Do we have a vector or matrix as the first argument? |
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58 |
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59 if (rows (x) == 1 || columns (x) == 1) |
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60 |
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61 if (nargin == 2) |
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62 if (isstr (p)) |
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63 if (strcmp (p, "fro")) |
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64 retval = sqrt (sum (diag (x' * x))); |
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65 elseif (strcmp (p, "inf")) |
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66 retval = max (abs (x)); |
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67 else |
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68 error ("norm: unrecognized norm"); |
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69 endif |
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70 else |
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71 if (p == Inf) |
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72 retval = max (abs (x)); |
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73 elseif (p == -Inf) |
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74 retval = min (abs (x)); |
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75 else |
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76 retval = sum (abs (x) .^ p) ^ (1/p); |
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77 endif |
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78 endif |
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79 elseif (nargin == 1) |
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80 retval = sum (abs (x) .^ 2) ^ 0.5; |
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81 endif |
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82 |
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83 else |
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84 |
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85 if (nargin == 2) |
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86 if (isstr (p)) |
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87 if (strcmp (p, "fro")) |
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88 retval = sqrt (sum (diag (x' * x))); |
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1479
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89 elseif (strcmp (p, "inf")) |
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90 xp = x'; |
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91 retval = max (sum (abs (real (xp)) + abs (imag (xp)))); |
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92 else |
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93 error ("norm: unrecognized norm"); |
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94 endif |
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95 else |
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96 if (p == 1) |
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97 retval = max (sum (abs (real (x)) + abs (imag (x)))); |
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98 elseif (p == 2) |
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99 s = svd (x); |
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100 retval = s (1); |
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101 elseif (p == Inf) |
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102 xp = x'; |
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103 retval = max (sum (abs (real (xp)) + abs (imag (xp)))); |
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104 endif |
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105 endif |
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106 elseif (nargin == 1) |
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107 s = svd (x); |
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108 retval = s (1); |
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109 endif |
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110 |
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111 endif |
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112 |
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113 endfunction |
