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comparison scripts/sparse/svds.m @ 9051:1bf0ce0930be

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Grammar check TexInfo in all .m files Cleanup documentation sources to follow a few consistent rules. Spellcheck was NOT done. (but will be in another changeset)
author Rik <rdrider0-list@yahoo.com>
date Fri, 27 Mar 2009 22:31:03 -0700
parents eb63fbe60fab
children be150a172010
comparison
equal deleted inserted replaced
9044:656ad518f385 9051:1bf0ce0930be
18 ## @deftypefnx {Function File} {@var{s} =} svds (@var{a}, @var{k}) 18 ## @deftypefnx {Function File} {@var{s} =} svds (@var{a}, @var{k})
19 ## @deftypefnx {Function File} {@var{s} =} svds (@var{a}, @var{k}, @var{sigma}) 19 ## @deftypefnx {Function File} {@var{s} =} svds (@var{a}, @var{k}, @var{sigma})
20 ## @deftypefnx {Function File} {@var{s} =} svds (@var{a}, @var{k}, @var{sigma}, @var{opts}) 20 ## @deftypefnx {Function File} {@var{s} =} svds (@var{a}, @var{k}, @var{sigma}, @var{opts})
21 ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}, @var{flag}] =} svds (@dots{}) 21 ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}, @var{flag}] =} svds (@dots{})
22 ## 22 ##
23 ## Find a few singular values of the matrix @var{a}. The singular values 23 ## Find a few singular values of the matrix @var{a}. The singular values
24 ## are calculated using 24 ## are calculated using
25 ## 25 ##
26 ## @example 26 ## @example
27 ## @group 27 ## @group
28 ## [@var{m}, @var{n}] = size(@var{a}) 28 ## [@var{m}, @var{n}] = size(@var{a})
30 ## @var{a}', sparse(@var{n}, @var{n})]) 30 ## @var{a}', sparse(@var{n}, @var{n})])
31 ## @end group 31 ## @end group
32 ## @end example 32 ## @end example
33 ## 33 ##
34 ## The eigenvalues returned by @code{eigs} correspond to the singular 34 ## The eigenvalues returned by @code{eigs} correspond to the singular
35 ## values of @var{a}. The number of singular values to calculate is given 35 ## values of @var{a}. The number of singular values to calculate is given
36 ## by @var{k}, whose default value is 6. 36 ## by @var{k}, whose default value is 6.
37 ## 37 ##
38 ## The argument @var{sigma} can be used to specify which singular values 38 ## The argument @var{sigma} can be used to specify which singular values
39 ## to find. @var{sigma} can be either the string 'L', the default, in 39 ## to find. @var{sigma} can be either the string 'L', the default, in
40 ## which case the largest singular values of @var{a} are found. Otherwise 40 ## which case the largest singular values of @var{a} are found. Otherwise
41 ## @var{sigma} should be a real scalar, in which case the singular values 41 ## @var{sigma} should be a real scalar, in which case the singular values
42 ## closest to @var{sigma} are found. Note that for relatively small values 42 ## closest to @var{sigma} are found. Note that for relatively small values
43 ## of @var{sigma}, there is the chance that the requested number of singular 43 ## of @var{sigma}, there is the chance that the requested number of singular
44 ## values are not returned. In that case @var{sigma} should be increased. 44 ## values are not returned. In that case @var{sigma} should be increased.
45 ## 45 ##
46 ## If @var{opts} is given, then it is a structure that defines options 46 ## If @var{opts} is given, then it is a structure that defines options
47 ## that @code{svds} will pass to @var{eigs}. The possible fields of this 47 ## that @code{svds} will pass to @var{eigs}. The possible fields of this
48 ## structure are therefore determined by @code{eigs}. By default three 48 ## structure are therefore determined by @code{eigs}. By default three
49 ## fields of this structure are set by @code{svds}. 49 ## fields of this structure are set by @code{svds}.
50 ## 50 ##
51 ## @table @code 51 ## @table @code
52 ## @item tol 52 ## @item tol
53 ## The required convergence tolerance for the singular values. @code{eigs} 53 ## The required convergence tolerance for the singular values. @code{eigs}
54 ## is passed @var{tol} divided by @code{sqrt(2)}. The default value is 54 ## is passed @var{tol} divided by @code{sqrt(2)}. The default value is
55 ## 1e-10. 55 ## 1e-10.
56 ## 56 ##
57 ## @item maxit 57 ## @item maxit
58 ## The maximum number of iterations. The defaut is 300. 58 ## The maximum number of iterations. The defaut is 300.
59 ## 59 ##
60 ## @item disp 60 ## @item disp
61 ## The level of diagnostic printout. If @code{disp} is 0 then there is no 61 ## The level of diagnostic printout. If @code{disp} is 0 then there is no
62 ## printout. The default value is 0. 62 ## printout. The default value is 0.
63 ## @end table 63 ## @end table
64 ## 64 ##
65 ## If more than one output argument is given, then @code{svds} also 65 ## If more than one output argument is given, then @code{svds} also
66 ## calculates the left and right singular vectors of @var{a}. @var{flag} 66 ## calculates the left and right singular vectors of @var{a}. @var{flag}
67 ## is used to signal the convergence of @code{svds}. If @code{svds} 67 ## is used to signal the convergence of @code{svds}. If @code{svds}
68 ## converges to the desired tolerance, then @var{flag} given by 68 ## converges to the desired tolerance, then @var{flag} given by
69 ## 69 ##
70 ## @example 70 ## @example
71 ## @group 71 ## @group
72 ## norm (@var{a} * @var{v} - @var{u} * @var{s}, 1) <= @dots{} 72 ## norm (@var{a} * @var{v} - @var{u} * @var{s}, 1) <= @dots{}