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Fix help string in general/quadv.m
author Carlo de Falco <kingcrimson@tiscali.it>
date Tue, 05 Oct 2010 03:29:43 -0400
parents be55736a0783
children fd0a3ac60b0e
comparison
equal deleted inserted replaced
11077:5dd5df43d392 11078:2aec7e3b8553
21 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}) 21 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol})
22 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}) 22 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace})
23 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}, @var{p1}, @var{p2}, @dots{}) 23 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}, @var{p1}, @var{p2}, @dots{})
24 ## @deftypefnx {Function File} {[@var{q}, @var{fcnt}] =} quadv (@dots{}) 24 ## @deftypefnx {Function File} {[@var{q}, @var{fcnt}] =} quadv (@dots{})
25 ## 25 ##
26 ## Numerically evaluate integral using adaptive Simpson's rule. 26 ## Numerically evaluate the integral of @var{f} from @var{a} to @var{b}
27 ## @code{quadv (@var{f}, @var{a}, @var{b})} approximates the integral of 27 ## using adaptive Simpson's rule.
28 ## @code{@var{f}(@var{x})} to the default absolute tolerance of @code{1e-6}.
29 ## @var{f} is either a function handle, inline function or string 28 ## @var{f} is either a function handle, inline function or string
30 ## containing the name of the function to evaluate. The function @var{f} 29 ## containing the name of the function to evaluate.
31 ## must accept a string, and can return a vector representing the 30 ## The function defined by @var{f} may be a scalar, vector or array-valued.
32 ## approximation to @var{n} different sub-functions.
33 ## 31 ##
34 ## If defined, @var{tol} defines the absolute tolerance to which to 32 ## If a value for @var{tol} is given, it defines the tolerance used to stop
35 ## which to integrate each sub-interval of @code{@var{f}(@var{x})}. 33 ## the adaptation procedure, otherwise the default value of 1e-6 is used.
36 ## While if @var{trace} is defined, displays the left end point of the 34 ##
37 ## current interval, the interval length, and the partial integral. 35 ## The algorithm used by @code{quadv}, involves recursively subdividing the
36 ## integration interval and applying Simpson's rule on each sub-interval.
37 ## If @var{trace} is @var{true}, after computing each of these partial integrals,
38 ## display the total number of function evaluations, the left end of the sub-interval,
39 ## the length of the sub-interval and the approximation of the integral over the sub-interval.
38 ## 40 ##
39 ## Additional arguments @var{p1}, etc., are passed directly to @var{f}. 41 ## Additional arguments @var{p1}, etc., are passed directly to @var{f}.
40 ## To use default values for @var{tol} and @var{trace}, one may pass 42 ## To use default values for @var{tol} and @var{trace}, one may pass
41 ## empty matrices. 43 ## empty matrices.
44 ##
42 ## @seealso{triplequad, dblquad, quad, quadl, quadgk, trapz} 45 ## @seealso{triplequad, dblquad, quad, quadl, quadgk, trapz}
43 ## @end deftypefn 46 ## @end deftypefn
44 47
45 function [q, fcnt] = quadv (f, a, b, tol, trace, varargin) 48 function [q, fcnt] = quadv (f, a, b, tol, trace, varargin)
46 if (nargin < 3) 49 if (nargin < 3)
78 endif 81 endif
79 if (isinf (fb)) 82 if (isinf (fb))
80 fb = feval (f, b - myeps * (b-a), varargin{:}); 83 fb = feval (f, b - myeps * (b-a), varargin{:});
81 endif 84 endif
82 85
83 h = (b - a) / 2; 86 h = (b - a);
84 q = (b - a) / 6 * (fa + 4 * fc + fb); 87 q = (b - a) / 6 * (fa + 4 * fc + fb);
85 88
86 [q, fcnt, hmin] = simpsonstp (f, a, b, c, fa, fb, fc, q, fcnt, abs (b - a), 89 [q, fcnt, hmin] = simpsonstp (f, a, b, c, fa, fb, fc, q, fcnt, abs (h),
87 tol, trace, varargin{:}); 90 tol, trace, varargin{:});
88 91
89 if (fcnt > 10000) 92 if (fcnt > 10000)
90 warning ("maximum iteration count reached"); 93 warning ("maximum iteration count reached");
91 elseif (isnan (q) || isinf (q)) 94 elseif (isnan (q) || isinf (q))
132 %!assert (quadv (@sin, 0, pi), 2, 1e-5) 135 %!assert (quadv (@sin, 0, pi), 2, 1e-5)
133 136
134 %% Handles weak singularities at the edge 137 %% Handles weak singularities at the edge
135 %!assert (quadv (@(x) 1 ./ sqrt(x), 0, 1), 2, 1e-5) 138 %!assert (quadv (@(x) 1 ./ sqrt(x), 0, 1), 2, 1e-5)
136 139
140 %% Handles vector-valued functions
141 %!assert (quadv (@(x) [(sin (x)), (sin (2 * x))], 0, pi), [2, 0], 1e-5)
142