Unexpected complex coefficients in a matrix

Question

Enterprixe 2017-3-30

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https://ww2.mathworks.cn/matlabcentral/answers/332841-unexpected-complex-coefficients-in-a-matrix

回答： David Goodmanson 2017-3-30

Hello, im trying to create a panel method for the study of an airfoil. Inside this problem, i have to obtain a matrix by combination of points created which define the panel distributions and their middle points. So the code is:

    for n=1:201
    x(n)= 1/2-1/2*cos((n-1)*pi/200);
     end
     for n=1:200
    Pc(n)=(x(n)+x(n+1))/2;
  end
for i=1:200
    for j=1:200
B(i,j)=(-((Pc(i)-x(j+1))/(x(j+1)-x(j)))*log((Pc(i)-x(j+1))/(Pc(i)-x(j)))-1);
    end 
end

So, in theory, the matrix B should be not complex at all, with its main diagonal full of just '-1' in each tearm, and that main diagonal should be dominant compared to the rest of coefficients of the matrix.

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Answer 1

David Goodmanson 2017-3-30

1
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https://ww2.mathworks.cn/matlabcentral/answers/332841-unexpected-complex-coefficients-in-a-matrix#answer_261100

Hello Javier, The only opportunity here to get a complex number is if the argument of the log term is negative. For all the nondiagonal terms of B you are all right, but for i=j the code produces log(-1) and you get an extra i pi/2 on the diagonal.