Mercurial > hg > octave-max

comparison scripts/sparse/pcr.m @ 14335:ce2b59a6d0e5

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
maint: periodic merge of stable to default.
author Rik <octave@nomad.inbox5.com>
date Sun, 05 Feb 2012 15:32:24 -0800
parents 11949c9795a0 4d917a6a858b
children f3d52523cde1
comparison
equal deleted inserted replaced
14333:6dd710b73150 14335:ce2b59a6d0e5
99 ## Let us consider a trivial problem with a diagonal matrix (we exploit the 99 ## Let us consider a trivial problem with a diagonal matrix (we exploit the
100 ## sparsity of A) 100 ## sparsity of A)
101 ## 101 ##
102 ## @example 102 ## @example
103 ## @group 103 ## @group
104 ## n = 10; 104 ## n = 10;
105 ## A = sparse (diag (1:n)); 105 ## A = sparse (diag (1:n));
106 ## b = rand (N, 1); 106 ## b = rand (N, 1);
107 ## @end group 107 ## @end group
108 ## @end example 108 ## @end example
109 ## 109 ##
110 ## @sc{Example 1:} Simplest use of @code{pcr} 110 ## @sc{Example 1:} Simplest use of @code{pcr}
111 ## 111 ##
112 ## @example 112 ## @example
113 ## x = pcr (A, b) 113 ## x = pcr (A, b)
114 ## @end example 114 ## @end example
115 ## 115 ##
116 ## @sc{Example 2:} @code{pcr} with a function which computes 116 ## @sc{Example 2:} @code{pcr} with a function which computes
117 ## @code{@var{A} * @var{x}}. 117 ## @code{@var{A} * @var{x}}.
118 ## 118 ##
119 ## @example 119 ## @example
120 ## @group 120 ## @group
121 ## function y = apply_a (x) 121 ## function y = apply_a (x)
122 ## y = [1:10]'.*x; 122 ## y = [1:10]' .* x;
123 ## endfunction 123 ## endfunction
124 ## 124 ##
125 ## x = pcr ("apply_a", b) 125 ## x = pcr ("apply_a", b)
126 ## @end group 126 ## @end group
127 ## @end example 127 ## @end example
128 ## 128 ##
129 ## @sc{Example 3:} Preconditioned iteration, with full diagnostics. The 129 ## @sc{Example 3:} Preconditioned iteration, with full diagnostics. The
130 ## preconditioner (quite strange, because even the original matrix 130 ## preconditioner (quite strange, because even the original matrix
131 ## @var{A} is trivial) is defined as a function 131 ## @var{A} is trivial) is defined as a function
132 ## 132 ##
133 ## @example 133 ## @example
134 ## @group 134 ## @group
135 ## function y = apply_m (x) 135 ## function y = apply_m (x)
136 ## k = floor (length(x)-2); 136 ## k = floor (length (x) - 2);
137 ## y = x; 137 ## y = x;
138 ## y(1:k) = x(1:k)./[1:k]'; 138 ## y(1:k) = x(1:k) ./ [1:k]';
139 ## endfunction 139 ## endfunction
140 ## 140 ##
141 ## [x, flag, relres, iter, resvec] = ... 141 ## [x, flag, relres, iter, resvec] = ...
142 ## pcr (A, b, [], [], "apply_m") 142 ## pcr (A, b, [], [], "apply_m")
143 ## semilogy([1:iter+1], resvec); 143 ## semilogy ([1:iter+1], resvec);
144 ## @end group 144 ## @end group
145 ## @end example 145 ## @end example
146 ## 146 ##
147 ## @sc{Example 4:} Finally, a preconditioner which depends on a 147 ## @sc{Example 4:} Finally, a preconditioner which depends on a
148 ## parameter @var{k}. 148 ## parameter @var{k}.
149 ## 149 ##
150 ## @example 150 ## @example
151 ## @group 151 ## @group
152 ## function y = apply_m (x, varargin) 152 ## function y = apply_m (x, varargin)
153 ## k = varargin@{1@}; 153 ## k = varargin@{1@};
154 ## y = x; y(1:k) = x(1:k)./[1:k]'; 154 ## y = x;
155 ## endfunction 155 ## y(1:k) = x(1:k) ./ [1:k]';
156 ## 156 ## endfunction
157 ## [x, flag, relres, iter, resvec] = ... 157 ##
158 ## pcr (A, b, [], [], "apply_m"', [], 3) 158 ## [x, flag, relres, iter, resvec] = ...
159 ## pcr (A, b, [], [], "apply_m"', [], 3)
159 ## @end group 160 ## @end group
160 ## @end example 161 ## @end example
161 ## 162 ##
162 ## References: 163 ## References:
163 ## 164 ##