如何在Matlab中使用Quadgk函數作為函數句柄？

Question

我正在嘗試求解一個雙重積分，其中我要通過Quadgk函數求解內部和外部積分。

% The integrand is of course a function of both x and y
integrand = @(x,y) (phi(j,y,X) - phi(j,x,X))*(phi(i,y,X) - phi(i,x,X))/abs(y-x)^(2*s+1)

% The inner integral is a function of x, and integrates over y
inner = @(x) quadgk(@(y)integrand(x,y), x-lambda, x+lambda)

% The inner integral is integrated over x to yield the value of the double integral 
dblIntegral = quadgk(inner, -(1+lambda), 1+lambda)

我收到以下錯誤：

integrand = @(x,y)(phi(j,y,X)-phi(j,x,X))*(phi(i,y,X)-phi(i,x,X))/abs(y-x)^(2*s+1)
inner = @(x)quadgk(@(y)integrand(x,y),x-lambda,x+lambda)

??? Error using ==> quadgk at 108
A and B must be scalar floats.

Error in ==> @(x)quadgk(@(y)integrand(x,y),x-lambda,x+lambda)
Error in ==> quadgk>evalFun at 344
        fx = FUN(x);

Error in ==> quadgk>f1 at 362
    [y,too_close] = evalFun(tt);

Error in ==> quadgk>vadapt at 258
        [fx,too_close] = f(x);

Error in ==> quadgk at 197
[q,errbnd] = vadapt(@f1,interval);

Error in ==> frational_laplacian at 29
dblIntegral = quadgk(inner, -(1+lambda), 1+lambda)

Answer 1

之所以會遇到這個問題，是因為在內部quadgk使用值向量評估傳遞的函數。 這意味着

dblIntegral = quadgk(inner, -(1+lambda), 1+lambda)

函數inner以x為向量被調用。 quadgk要求a和b（在本例中為x±lambda）為標量，因此您會看到錯誤。 如果要確保inner始終獲得標量作為輸入，則可以使用

dblIntegral = quadgk(@(x)arrayfun(inner,x), -(1+lambda), 1+lambda)