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doubleintegral 1.0

  Date Added: May 13, 2013  |  Visits: 233


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The intention is to make a more flexible and more general function than the Matlab function dblquad. Especially the domain may be given in a more general way, it may be a circle, a rectangle, or any convex polygon. Also different methods may be used. Q = DOUBLEINTEGRAL(FUN, DOMAIN, PARAM) FUN is (normally) a function handle. When method is 'dblquad' the function Z=FUN(X,Y) should accept a vector X and a scalar Y and return a vector Z of values as Matlab's 'dblquad'. For other methods the function just need to handle single element arguments. The function may accept matrix, and vector, arguments of the same size and return a matrix also with this size, such that Z(i) = FUN(X(i),Y(i)). The function will be used this way if parameter 'matrixarg' is also included in the PARAM struct and set to true. Default is false, and used if 'matrixarg' is not a field in PARAM. If FUN == 1, then area of domain is returned. DOMAIN is a struct where the field 'type' gives how the domain is given. Examples: domain = struct('type','circle','xc',0,'yc',0,'radius',1); domain = struct('type','sector','th1',-pi,'th2',pi,'r1',0,'r2',1,'xc',0,'yc',0); domain = struct('type','box','x1',-1,'x2',1,'y1',-1,'y2',1); domain = struct('type','area','x1',-1,'x2',1,'y1',@(x) sqrt(x),'y2',@(x) x.^2); domain = struct('type','polygon','x',[0,2,2,1,0],'y',[0,0,1,2,1]); PARAM is a struct where the field 'method' always must be included. It gives the method used, often in both x and y direction. Examples for Matlab quad, i.e. dblquad, fuction with argument tol, Gauss Quadrature method and Clenshaw-Curtis method: param = struct('method','dblquad','tol',1e-6); param = struct('method','gauss','points',6); param = struct('method','cc','points',10); param.matrixarg = true; % use vector-arguments in fun Q = DOUBLEINTEGRAL(FUN, DOMAIN, PARAM, verbose, makefigure) verbose = 0 (display only errors), 1 (+ if arguments are overruled), 2 (+ results), 3 (+ some status information), 4 (+ some debugging info) makefigure = 0 (default) for no figure, 1 for domain, 5 for contour of function in domain. Examples: fun = @(x,y) y*sin(x)+x*cos(y); domain = struct('type','box','x1',pi,'x2',2*pi,'y1',0,'y2',pi); param = struct('method','dblquad','tol',1e-6); Q = doubleintegral(fun, domain, param); % -pi^2 fun = @(x,y) y.*sin(x)+x.*cos(y); % allows vectors in both x and y domain = struct('type','box','x1',pi,'x2',2*pi,'y1',0,'y2',pi); param = struct('method','gauss','points',6,'matrixarg',true); Q = doubleintegral(fun, domain, param, 3, 5); % -pi^2 fun = 1; % Area is one dimensional integral of f(x) = abs(y2(x)-y1(x)) domain = struct('type','area','x1',0,'x2',1,'y1',@(x) x.^2,'y2',@(x) sqrt(x)); param = struct('method','cc','points',12); Q = doubleintegral(fun, domain, param); % 1/3 fun = @(x,y) sqrt(max(zeros(size(x)), 1-x.^2-y.^2)); % unit sphere domain = struct('type','circle','xc',0,'yc',0,'radius',1); param = struct('method','gauss','points',25,'matrixarg',true); Q = doubleintegral(fun, domain, param); % 2*pi/3 % an alternative is to use dblquad, domain may be a circle or a box. domain = struct('type','box','x1',-1,'x2',1,'y1',-1,'y2',1); param = struct('method','dblquad','tol',1e-6); % or polygon to find just a sector domain = struct('type','polygon','x',[0,1,1],'y',[0,0,1]); Q = doubleintegral(fun, domain, param); % pi/12 % or grid of points in sector. Note still fun = @(x,y) domain = struct('type','sector','th1',0,'th2',pi/4,'r1',0,'r2',1,'xc',0,'yc',0); param = struct('method','dblquad','tol',1e-6); Q = doubleintegral(fun, domain, param); % pi/12

Requirements: No special requirements
Platforms: Matlab
Keyword: Clenshawcurtis Display Errors Makefigure Overruled Param Parammatrixarg Results Vectorarguments Verbose
Users rating: 0/10

License: Shareware Size: 10 KB
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