complex integral problem

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Yalcin
Yalcin 2012-4-16
Hi all,
I have to solve following complex integral with 4 variables (s1x,s1y,s2x,s2y) numerically in Matlab GUI. But i i have error and couldn’t find the error till now. And codes are as follows too.
Could anyone show me the error?
Thanks in advance.
??? Error using ==> quadgk at 140
Parameters must be a character.
Error in ==> TransCalc>ApproveBut_Callback at 784
TransCoeff{m}=quadgk(y{m},handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,handles.S2xMaxVal,handles.S2yMinVal,handles.S2yMaxVal)
Error in ==> gui_mainfcn at 96
feval(varargin{:});
Error in ==> TransCalc at 42
gui_mainfcn(gui_State, varargin{:});
Error in ==> @(hObject,eventdata)TransCalc('ApproveBut_Callback',hObject,eventdata,guidata(hObject))
??? Error while evaluating uicontrol Callback
for d=floor(10000/handles.WaveUp):1:ceil(10000/handles.WaveLow)
a(m)=d;
k(m)=2*pi/((10000*(1e-6)/d));
lamda(m)=10000*(1e-6)/d;
n_alfa(m)=0.5*gamma(handles.AlfaPowLaw)*((2*pi)^(-11/6+(handles.AlfaPowLaw)/2)).*((lamda(m).*(handles.DistLow))^(11/6-(handles.AlfaPowLaw)/2));
d_alfa=gamma(1-handles.AlfaPowLaw/2)*((gamma(handles.AlfaPowLaw/2))^2)*gamma(handles.AlfaPowLaw-1)*cos(pi*handles.AlfaPowLaw/2)*sin(pi*handles.AlfaPowLaw/4);
cn2tilda(m)=(n_alfa(m)/d_alfa)*handles.StrConst;
set(handles.StrucConstNonKolmNum,'String',num2str(d_alfa));
ro_0(m)=(((-2)^(1-handles.AlfaPowLaw))*gamma((2-handles.AlfaPowLaw)/2)*gamma(handles.AlfaPowLaw-1)*cos(0.5*pi*handles.AlfaPowLaw)*((k(m))^2)*handles.DistLow*((cn2tilda(m))^2)/gamma(handles.AlfaPowLaw/2))^(-1/(handles.AlfaPowLaw-2));
f1=exp((-1/((handles.BeamRad)^2))*(((s1x)^2)+((s1y)^2)+((s2x)^2)+((s2y)^2)));
f2{m}=exp((1i*(k(m)/(2*handles.DistLow)))*((((s1x)^2)-(2*s1x*handles.PxAxisValue))+(((s1y)^2)-(2*s1y*handles.PyAxisValue))+((2*s2x*handles.PxAxisValue)-((s2x)^2))+((2*s2y*handles.PyAxisValue)-((s2y)^2))))
f3{m}=exp((-1/((ro_0(m))^(handles.AlfaPowLaw-2)))*((((s1x-s2x)^2)+((s1y-s2y)^2))^((handles.AlfaPowLaw-2)/2)));
f4(m)=((handles.DistLow*handles.DistLow+k(m)*k(m)*((handles.BeamRad)^4)))/((4*pi*pi*handles.DistLow*handles.DistLow*((handles.BeamRad)^4))*((handles.PxAxisValue*handles.PxAxisValue+handles.PyAxisValue*handles.PyAxisValue)*((-k(m)*k(m)*(handles.BeamRad)*(handles.BeamRad))/(handles.DistLow*handles.DistLow+k(m)*k(m)*((handles.BeamRad)^4)))));
y{m} = @(s1x,s1y,s2x,s2y) (f1.*f2{m}.*f3{m})
TransCoeff{m}=quadgk(y{m},handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,handles.S2xMaxVal,handles.S2yMinVal,handles.S2yMaxVal)
m=m+1;
end

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采纳的回答

Walter Roberson
Walter Roberson 2012-4-16
You cannot pass variables to quadgk that way. See instead http://www.mathworks.com/help/techdoc/math/bsgprpq-5.html
  1 个评论
Walter Roberson
Walter Roberson 2012-4-16
quadgk is *not* a routine for integrating over 4 variables: the "quad" refers to adaptive quadrature.
There are techniques for doing multiple integrals, starting from the lower-dimensional routines such as triplequad . I do not recall the method at the moment. If I recall correctly, Mike Hosa has shown a general method, but I do not find it right now.

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更多回答（1 个）

Yalcin
Yalcin 2012-4-17
Thanks for your answer. I changed 4-d integration as follow. But now i have following error. what should i do?
for d=floor(10000/handles.WaveUp):1:ceil(10000/handles.WaveLow) a(m)=d; k(m)=2*pi/((10000*(1e-6)/d)); lamda(m)=10000*(1e-6)/d; n_alfa(m)=0.5*gamma(handles.AlfaPowLaw)*((2*pi)^(-11/6+(handles.AlfaPowLaw)/2)).*((lamda(m).*(handles.DistLow))^(11/6-(handles.AlfaPowLaw)/2)); d_alfa=gamma(1-handles.AlfaPowLaw/2)*((gamma(handles.AlfaPowLaw/2))^2)*gamma(handles.AlfaPowLaw-1)*cos(pi*handles.AlfaPowLaw/2)*sin(pi*handles.AlfaPowLaw/4); cn2tilda(m)=(n_alfa(m)/d_alfa)*handles.StrConst;
ro_0(m)=(((-2)^(1-handles.AlfaPowLaw))*gamma((2-handles.AlfaPowLaw)/2)*gamma(handles.AlfaPowLaw-1)*cos(0.5*pi*handles.AlfaPowLaw)*((k(m))^2)*handles.DistLow*((cn2tilda(m))^2)/gamma(handles.AlfaPowLaw/2))^(-1/(handles.AlfaPowLaw-2));
f1=@(s1x,s1y,s2x,s2y)exp((-1/((handles.BeamRad)^2))*(((s1x)^2)+((s1y)^2)+((s2x)^2)+((s2y)^2)));
f2(m)=@(s1x,s1y,s2x,s2y)exp((1i*(k(m)/(2*handles.DistLow)))*((((s1x)^2)-(2*s1x*handles.PxAxisValue))+(((s1y)^2)-(2*s1y*handles.PyAxisValue))+((2*s2x*handles.PxAxisValue)-((s2x)^2))+((2*s2y*handles.PyAxisValue)-((s2y)^2))));
f3(m)=@(s1x,s1y,s2x,s2y)exp((-1/((ro_0(m))^(handles.AlfaPowLaw-2)))*((((s1x-s2x)^2)+((s1y-s2y)^2))^((handles.AlfaPowLaw-2)/2)));
f4(m)=((handles.DistLow*handles.DistLow+k(m)*k(m)*((handles.BeamRad)^4)))/((4*pi*pi*handles.DistLow*handles.DistLow*((handles.BeamRad)^4))*((handles.PxAxisValue*handles.PxAxisValue+handles.PyAxisValue*handles.PyAxisValue)*((-k(m)*k(m)*(handles.BeamRad)*(handles.BeamRad))/(handles.DistLow*handles.DistLow+k(m)*k(m)*((handles.BeamRad)^4)))));
y(m) = @(s1x,s1y,s2x,s2y)(f4(m)*f1*f2(m)*f3(m));
tol=1e4;
%f5(m) = @(s1x,s1y,s2x) quadv(@(s2y) y(m),handles.S2yMinVal,handles.S2yMaxVal,tol);
%TransCoeff = triplequad(f5(m), handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,handles.S2xMaxVal, tol);
TransCoeff = triplequad((@(s1x,s1y,s2x) quadv(@(s2y) y(m),handles.S2yMinVal,handles.S2yMaxVal,tol)), handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,handles.S2xMaxVal,tol);
m=m+1;
end
??? Undefined function or method 'mtimes' for input arguments of type 'function_handle'.
Error in ==> TransCalc>@(s1x,s1y,s2x,s2y)(f4(m)*f1*f2(m)*f3(m)) at 804 y(m) = @(s1x,s1y,s2x,s2y)(f4(m)*f1*f2(m)*f3(m));
Error in ==> TransCalc>@(s2y)y(m) at 811 TransCoeff = triplequad((@(s1x,s1y,s2x) quadv(@(s2y) y(m),handles.S2yMinVal,handles.S2yMaxVal,tol)), handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,hand Error in ==> quadv at 57 y{j} = feval(f, x(j), varargin{:}); %#ok<AGROW>
Error in ==> TransCalc>@(s1x,s1y,s2x)quadv(@(s2y)y(m),handles.S2yMinVal,handles.S2yMaxVal,tol) at 811 TransCoeff = triplequad((@(s1x,s1y,s2x) quadv(@(s2y) y(m),handles.S2yMinVal,handles.S2yMaxVal,tol)), handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,hand Error in ==> triplequad>innerintegral at 59 fcl = intfcn(xmin, y(1), z(1), varargin{:});
Error in ==> dblquad>innerintegral at 74 fcl = intfcn(xmin, y(1), varargin{:}); %evaluate only to get the class below
Error in ==> quad at 77 y = f(x, varargin{:});
Error in ==> dblquad at 54 Q = quadf(@innerintegral, ymin, ymax, tol, trace, intfcn, ...
Error in ==> triplequad at 47 Q = dblquad(@innerintegral, ymin, ymax, zmin, zmax, tol, quadf, intfcn, ...
Error in ==> TransCalc>ApproveBut_Callback at 811 TransCoeff = triplequad((@(s1x,s1y,s2x) quadv(@(s2y) y(m),handles.S2yMinVal,handles.S2yMaxVal,tol)), handles.S1xMinVal,handles.S1xMaxVal,handles.S1yMinVal,handles.S1yMaxVal,handles.S2xMinVal,hand Error in ==> gui_mainfcn at 96 feval(varargin{:});
Error in ==> TransCalc at 42 gui_mainfcn(gui_State, varargin{:});
Error in ==> @(hObject,eventdata)TransCalc('ApproveBut_Callback',hObject,eventdata,guidata(hObject))
??? Error while evaluating uicontrol Callback

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