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comparison scripts/linear-algebra/norm.m @ 3426:f8dde1807dee

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[project @ 2000-01-13 08:40:00 by jwe]
author jwe
date Thu, 13 Jan 2000 08:40:53 +0000
parents ae7adbb591e8
children 434790acb067
comparison
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3425:8625164a0a39 3426:f8dde1807dee
19 19
20 ## -*- texinfo -*- 20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {} norm (@var{a}, @var{p}) 21 ## @deftypefn {Function File} {} norm (@var{a}, @var{p})
22 ## Compute the p-norm of the matrix @var{a}. If the second argument is 22 ## Compute the p-norm of the matrix @var{a}. If the second argument is
23 ## missing, @code{p = 2} is assumed. 23 ## missing, @code{p = 2} is assumed.
24 ## 24 ##
25 ## If @var{a} is a matrix: 25 ## If @var{a} is a matrix:
26 ## 26 ##
27 ## @table @asis 27 ## @table @asis
28 ## @item @var{p} = @code{1} 28 ## @item @var{p} = @code{1}
29 ## 1-norm, the largest column sum of @var{a}. 29 ## 1-norm, the largest column sum of @var{a}.
30 ## 30 ##
31 ## @item @var{p} = @code{2} 31 ## @item @var{p} = @code{2}
32 ## Largest singular value of @var{a}. 32 ## Largest singular value of @var{a}.
33 ## 33 ##
34 ## @item @var{p} = @code{Inf} 34 ## @item @var{p} = @code{Inf}
35 ## @cindex infinity norm 35 ## @cindex infinity norm
36 ## Infinity norm, the largest row sum of @var{a}. 36 ## Infinity norm, the largest row sum of @var{a}.
37 ## 37 ##
38 ## @item @var{p} = @code{"fro"} 38 ## @item @var{p} = @code{"fro"}
39 ## @cindex Frobenius norm 39 ## @cindex Frobenius norm
40 ## Frobenius norm of @var{a}, @code{sqrt (sum (diag (@var{a}' * @var{a})))}. 40 ## Frobenius norm of @var{a}, @code{sqrt (sum (diag (@var{a}' * @var{a})))}.
41 ## @end table 41 ## @end table
42 ## 42 ##
43 ## If @var{a} is a vector or a scalar: 43 ## If @var{a} is a vector or a scalar:
44 ## 44 ##
45 ## @table @asis 45 ## @table @asis
46 ## @item @var{p} = @code{Inf} 46 ## @item @var{p} = @code{Inf}
47 ## @code{max (abs (@var{a}))}. 47 ## @code{max (abs (@var{a}))}.
48 ## 48 ##
49 ## @item @var{p} = @code{-Inf} 49 ## @item @var{p} = @code{-Inf}
50 ## @code{min (abs (@var{a}))}. 50 ## @code{min (abs (@var{a}))}.
51 ## 51 ##
52 ## @item other 52 ## @item other
53 ## p-norm of @var{a}, @code{(sum (abs (@var{a}) .^ @var{p})) ^ (1/@var{p})}. 53 ## p-norm of @var{a}, @code{(sum (abs (@var{a}) .^ @var{p})) ^ (1/@var{p})}.
54 ## @end table 54 ## @end table
55 ## @end deftypefn 55 ## @end deftypefn
56 ## @seealso{cond and svd} 56 ## @seealso{cond and svd}
80 retval = max (abs (x)); 80 retval = max (abs (x));
81 else 81 else
82 error ("norm: unrecognized norm"); 82 error ("norm: unrecognized norm");
83 endif 83 endif
84 else 84 else
85 if (p == Inf) 85 if (p == Inf)
86 retval = max (abs (x)); 86 retval = max (abs (x));
87 elseif (p == -Inf) 87 elseif (p == -Inf)
88 retval = min (abs (x)); 88 retval = min (abs (x));
89 else 89 else
90 retval = sum (abs (x) .^ p) ^ (1/p); 90 retval = sum (abs (x) .^ p) ^ (1/p);
91 endif 91 endif
92 endif 92 endif
93 elseif (nargin == 1) 93 elseif (nargin == 1)
94 retval = sum (abs (x) .^ 2) ^ 0.5; 94 retval = sum (abs (x) .^ 2) ^ 0.5;
95 endif 95 endif
96 96