# Defining a mathematical function as the summation of multiple functions

조회 수: 1 (최근 30일)
Memo Remo 2022년 3월 31일
댓글: Memo Remo 2022년 4월 7일
Hi,
I want to define the function below in MATLAB and then minimized it using fminsearch.
What I did was to define a loop along with syms function to generate this function and then used matlabFunction() command to convert it to a function.
--------------------------------------------------------------------------------------------------------------------
syms x0 y0 z0 b
S=0;
NumberOfNeighbors=100;
for i = 1:NumberOfNeighbors
Xd=xdata(i,1);
Yd=ydata(i,1);
Zd=zdata(i,1);
Sum=abs(((Xd-x0)^2)+((Yd--y0)^2)+((Zd--z0)^2)-b^2);
S=S+Sum;
end
ht = matlabFunction(S)
Init=[0,0,0,0];
Fmin = fminsearch(ht,Init)
--------------------------------------------------------------------------------------------------------------------
My code worked perfectly, but when I use the generated function as an input in fminsearch, I get the following error message:
"Not enough input arguments."
The reason is that the generated function by the matlabFunction() command is a function of (x0 y0 z0 b), while it should be a function of u(1),u(2),u(3) and u(4).
We are not allowed to define variables of the form u(1),u(2),u(3) and u(4) using syms.
I would appreciate any help that you can provide. Thanks.

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### 채택된 답변

Star Strider 2022년 3월 31일
To get all the arguments as elements of a single vector. use the 'Vars' name-value pair and enclose the arguments in square brackets []:
ht = matlabFunction(S, 'Vars',{[x0,y0,z0,b]})
To see how that works in practice —
xdata = randn(100,1);
ydata = randn(100,1);
zdata = randn(100,1);
syms x0 y0 z0 b
S=0;
NumberOfNeighbors=100;
for i = 1:NumberOfNeighbors
Xd=xdata(i,1);
Yd=ydata(i,1);
Zd=zdata(i,1);
Sum=abs(((Xd-x0)^2)+((Yd--y0)^2)+((Zd--z0)^2)-b^2);
S=S+Sum;
end
ht = matlabFunction(S, 'Vars',{[x0,y0,z0,b]})
ht = function_handle with value:
@(in1)abs((in1(:,1)+6.031542382955758e-1).^2-in1(:,4).^2+(in1(:,3)-4.514357154410683e-1).^2+(in1(:,2)-1.113945828129602).^2)+abs((in1(:,3)-1.45783769930615e-1).^2+(in1(:,1)+1.087893584703542).^2+(in1(:,2)-1.573349894165783).^2-in1(:,4).^2)+abs((in1(:,1)+3.73489278607807e-2).^2+(in1(:,2)+8.421479945678007e-2).^2-in1(:,4).^2+(in1(:,3)-9.53913989327878e-1).^2)+abs((in1(:,2)+1.739400576709651).^2+(in1(:,1)-1.254083115563258).^2-in1(:,4).^2+(in1(:,3)+3.640522000383975e-1).^2)+abs((in1(:,1)+1.420768366051117).^2+(in1(:,2)-2.369807124107065e-1).^2+(in1(:,3)-4.059170202704624e-1).^2-in1(:,4).^2)+abs((in1(:,2)-4.418970545030066e-1).^2-in1(:,4).^2+(in1(:,1)-9.294218879765488e-1).^2+(in1(:,3)-3.909414337345544e-1).^2)+abs((in1(:,2)+5.893359922897708e-1).^2-in1(:,4).^2+(in1(:,1)+4.017260527656553e-1).^2+(in1(:,3)+5.383304350975927e-1).^2)+abs((in1(:,1)-1.005831521757571).^2+(in1(:,3)-2.48584028231891e-1).^2+(in1(:,2)+2.22135632952146).^2-in1(:,4).^2)+abs((in1(:,1)-2.614894839493323).^2+(in1(:,3)+1.68014627666172).^2+(in1(:,2)-8.753995052294088e-1).^2-in1(:,4).^2)+abs((in1(:,2)+4.250057231383061e-1).^2-in1(:,4).^2+(in1(:,3)+5.958307109475643e-1).^2+(in1(:,1)-1.963442762847612).^2)+abs((in1(:,1)+1.361188709078525).^2+(in1(:,2)+1.788579253947234).^2+(in1(:,3)+1.55732668135481).^2-in1(:,4).^2)+abs((in1(:,3)+1.682161641512796).^2-in1(:,4).^2+(in1(:,1)+1.50312354803044).^2+(in1(:,2)-6.137691803445755e-2).^2)+abs((in1(:,2)+1.777935747636345).^2+(in1(:,1)+2.659359288794637e-1).^2-in1(:,4).^2+(in1(:,3)+1.825161793758771e-1).^2)+abs((in1(:,3)+1.383952830502305).^2+(in1(:,1)-1.26483344600822).^2-in1(:,4).^2+(in1(:,2)+6.273348896641698e-1).^2)+abs((in1(:,2)+1.095837479066349).^2+(in1(:,3)+6.077104329760737e-1).^2+(in1(:,1)+9.064717472692025e-1).^2-in1(:,4).^2)+abs((in1(:,2)+1.31879035499212).^2+(in1(:,1)+1.929669660101218e-1).^2+(in1(:,3)+3.732958753983768e-1).^2-in1(:,4).^2)+abs((in1(:,1)-1.200864405758769).^2+(in1(:,2)+6.27206382466213e-2).^2+(in1(:,3)+5.198673963147101e-1).^2-in1(:,4).^2)+abs((in1(:,1)-1.581547044506651).^2-in1(:,4).^2+(in1(:,2)+3.620925494209677e-1).^2+(in1(:,3)-7.044194738397551e-2).^2)+abs((in1(:,3)-6.548227714747618e-1).^2+(in1(:,1)+2.825735466530732e-1).^2+(in1(:,2)+3.259493628823217e-1).^2-in1(:,4).^2)+abs((in1(:,2)+8.921898061332503e-2).^2+(in1(:,1)+3.082275937268097e-1).^2+(in1(:,3)-3.819268521923411e-1).^2-in1(:,4).^2)+abs((in1(:,2)-2.278773605485153e-1).^2+(in1(:,1)-6.792084827277662e-1).^2+(in1(:,3)+1.021268242380771).^2-in1(:,4).^2)+abs((in1(:,3)-3.79371832206307e-1).^2+(in1(:,1)+9.546033119797254e-1).^2-in1(:,4).^2+(in1(:,2)-1.044470930741223).^2)+abs((in1(:,2)-3.278595881747381e-1).^2+(in1(:,1)+1.461312049815205e-1).^2+(in1(:,3)-1.638932662570746).^2-in1(:,4).^2)+abs((in1(:,3)-1.766735366563113).^2-in1(:,4).^2+(in1(:,1)+4.787799542333162e-1).^2+(in1(:,2)-6.395823993438856e-1).^2)+abs((in1(:,3)-1.845733333167634).^2+(in1(:,2)+3.411769508739287e-2).^2+(in1(:,1)-4.783777414294033e-1).^2-in1(:,4).^2)+abs((in1(:,3)+1.457043078662576).^2-in1(:,4).^2+(in1(:,2)+6.483781581359259e-1).^2+(in1(:,1)-1.425926882549134).^2)+abs((in1(:,2)-1.440733474340873e-1).^2+(in1(:,3)-3.207188382667299e-1).^2+(in1(:,1)+8.426540081158101e-1).^2-in1(:,4).^2)+abs((in1(:,3)+3.610479448645704e-1).^2+(in1(:,2)-6.227386698512922e-1).^2+(in1(:,1)+7.528681220823847e-1).^2-in1(:,4).^2)+abs((in1(:,3)+5.479812064743947e-1).^2+(in1(:,1)+1.0483287710631).^2+(in1(:,2)+5.359958852619184e-4).^2-in1(:,4).^2)+abs((in1(:,3)-4.39298391951065e-1).^2+(in1(:,1)+3.629444385673342e-1).^2+(in1(:,2)-4.219839195636151e-1).^2-in1(:,4).^2)+abs((in1(:,1)+1.850306756465896e-1).^2+(in1(:,2)+9.064343571726161e-1).^2-in1(:,4).^2+(in1(:,3)-7.959049051103456e-1).^2)+abs((in1(:,3)+1.19869242299813).^2+(in1(:,2)-8.429389697296127e-1).^2-in1(:,4).^2+(in1(:,1)+2.898944054138064).^2)+abs((in1(:,3)-1.036116495883203).^2+(in1(:,2)+1.26954868098272).^2-in1(:,4).^2+(in1(:,1)-7.880260812273465e-1).^2)+abs((in1(:,2)+1.749780575106909).^2+(in1(:,3)+5.15561660582576e-1).^2-in1(:,4).^2+(in1(:,1)+1.108622159833217e-1).^2)+abs((in1(:,1)+1.279103201379184).^2+(in1(:,2)-3.127398926250695e-1).^2-in1(:,4).^2+(in1(:,3)-7.745531578740871e-1).^2)+abs((in1(:,2)-1.555708032993002).^2+(in1(:,1)-5.693922664792982e-1).^2-in1(:,4).^2+(in1(:,3)+4.871536081882957e-1).^2)+abs((in1(:,2)+2.584045753466138e-1).^2+(in1(:,3)-9.35470686819427e-1).^2-in1(:,4).^2+(in1(:,1)-2.415589178446184e-1).^2)+abs((in1(:,3)-8.007172628545135e-1).^2+(in1(:,1)+3.811013483931354e-1).^2+(in1(:,2)-3.185379809688022e-1).^2-in1(:,4).^2)+abs((in1(:,3)-3.357927323835146e-1).^2+(in1(:,2)+1.130949547274701).^2+(in1(:,1)+6.8617747680658e-1).^2-in1(:,4).^2)+abs((in1(:,3)-7.856936284014074e-1).^2+(in1(:,1)+2.260270318231605e-1).^2-in1(:,4).^2+(in1(:,2)+8.79969513358513e-1).^2)+abs((in1(:,2)-1.309495598598901).^2+(in1(:,1)-7.486826232772817e-1).^2-in1(:,4).^2+(in1(:,3)-3.387412490796151e-1).^2)+abs((in1(:,1)+1.021339881713544).^2-in1(:,4).^2+(in1(:,2)-1.128049502818774).^2+(in1(:,3)-6.388404335532554e-1).^2)+abs((in1(:,3)-7.99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1812131464e-1).^2+(in1(:,2)-1.193650199361929).^2+(in1(:,1)+9.326013358897691e-1).^2-in1(:,4).^2)+abs((in1(:,3)-1.25376913901259).^2+(in1(:,2)+1.17012674076671).^2-in1(:,4).^2+(in1(:,1)-5.313065504354205e-1).^2)+abs((in1(:,3)+5.254125343078276e-1).^2+(in1(:,1)-5.55158126541898e-1).^2+(in1(:,2)-2.930711078161298e-1).^2-in1(:,4).^2)+abs((in1(:,2)+1.461252251647627).^2+(in1(:,3)+1.108496623161207).^2-in1(:,4).^2+(in1(:,1)+5.003231999415112e-1).^2)+abs((in1(:,3)-2.399970223748402e-1).^2+(in1(:,1)-3.096003525615665e-1).^2-in1(:,4).^2+(in1(:,2)-7.185311441992477e-1).^2)+abs((in1(:,3)+1.314318464910931).^2+(in1(:,1)+1.09737803133872e-1).^2-in1(:,4).^2+(in1(:,2)+4.069016614242763e-1).^2)+abs((in1(:,1)-1.438189873280947e-1).^2+(in1(:,2)-6.59181765090162e-1).^2-in1(:,4).^2+(in1(:,3)+6.679061104676695e-1).^2)+abs((in1(:,3)-3.320129715836648e-1).^2+(in1(:,2)+1.932888431680579e-1).^2-in1(:,4).^2+(in1(:,1)+1.545766956818623).^2)+abs((in1(:,3)+9.858908931056823e-2).^2+(in1(:,1)-1.421038070431656).^2-in1(:,4).^2+(in1(:,2)+4.213054258491518e-1).^2)+abs((in1(:,3)+6.599205674831305e-1).^2+(in1(:,2)+1.043073578687401).^2-in1(:,4).^2+(in1(:,1)-1.593215088321644).^2)+abs((in1(:,3)-5.262473663775586e-1).^2+(in1(:,2)+1.192173494244443).^2-in1(:,4).^2+(in1(:,1)+1.065805107277744).^2)+abs((in1(:,2)-2.741391264684298e-1).^2+(in1(:,1)-6.016302194456916e-1).^2+(in1(:,3)-4.31249978778074e-1).^2-in1(:,4).^2)+abs((in1(:,3)-6.840798421194227e-1).^2+(in1(:,1)+1.097939879451589e-1).^2+(in1(:,2)-4.652125895096236e-1).^2-in1(:,4).^2)+abs((in1(:,3)-1.385055397715085).^2+(in1(:,1)-6.716385958416079e-1).^2+(in1(:,2)+6.33179342396904e-1).^2-in1(:,4).^2)+abs((in1(:,2)-9.457196966330426e-1).^2+(in1(:,3)-2.361969182680211).^2+(in1(:,1)+8.859427712877517e-1).^2-in1(:,4).^2)+abs((in1(:,1)-1.363868744265735).^2-in1(:,4).^2+(in1(:,2)-7.275679857997771e-1).^2+(in1(:,3)-9.901317438821206e-1).^2)
Init=[0,0,0,0];
Fmin = fminsearch(ht,Init)
Fmin = 1×4
-0.0582 0.0601 -0.1977 -1.5811
Here, the row vector of the input arguments is called ‘in1’ not ‘u’. There does not appear to be a way to change the name.
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##### 댓글 수: 2없음 표시없음 숨기기
Memo Remo 2022년 3월 31일
Your help is GREATLY appreciated! Thank you very much.
Star Strider 2022년 3월 31일
As always, my pleasure!

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### 추가 답변 (1개)

Jan 2022년 3월 31일
편집: Jan 2022년 4월 4일
Why do you want to create the function symbolically? It is easy to define it directly:
ht = @(u1, u2, u3, u4) sum((xdata(:, 1) - u1) .^ 2 + ...
(xdata(:, 2) - u2) .^ 2 + ...
(xdata(:, 3) - u3) .^ 2 - u4 ^ 2);
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Jan 2022년 4월 4일
Maybe you have to change the function to:
ht = @(u) sum((xdata(:, 1) - u(1)) .^ 2 + ...
(xdata(:, 2) - u(2)) .^ 2 + ...
(xdata(:, 3) - u(3)) .^ 2 - u(4) ^ 2);
with a vector u instead of 4 inputs u1,u2,u3,u4.
Memo Remo 2022년 4월 7일
Yes. It works now! Thanks for letting me know about this efficient way of defining such function. This is very helpful to speed up the calculations. I appreciate your help.

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