在MATLAB中绘制复杂函数的水平曲线

Question

我正在尝试为给定的函数绘制等高线图

syms r x y k z
[ph,r] = meshgrid((0:5:360)*pi/180,0:.5:10);
[X,Y] = pol2cart(ph,r);
Z = X+i*Y;
J = besselj(k,l.*r);
J2 = besselj(k,m.*r);
Y = bessely(k,l.*r);
Y2 = bessely(k,m.*r);
H = besselh(k,r);
F1 = symsum((J).*exp(1i*k*ph),k,-5,5);
F2 = symsum((J2+Y2).*exp(1i.*k.*ph),k,-5,5);
F3 = symsum(H.*exp(1i.*k.*ph),k,-5,5);
pwu = nan(size(F1), 'like', F1);
mask = 0 <= r & r < 0.5;
pwu(mask) = F1(mask);
mask = 0.5 <= r & r < 1;
pwu(mask) = F2(mask);
mask = r >= 1;
pwu(mask) = F3(mask);
U = subs(pwu, {l, m}, {1.5, 3});hold on
contour(X,Y,imag(double(U)),30)
axis equal
xlabel('r','FontSize',14);
ylabel('phi','FontSize',14);

但我在最后一行第4行的形式上一直有失误。显然U不能转换为双精度。还有别的办法吗？

感谢

Answer 1

此代码有效：

syms r x y k z
[ph,r] = meshgrid((0:5:360)*pi/180,0:.5:10);
[x,y] = pol2cart(ph,r);
Z = x+1i*y;
J = besselj(k,l.*r);
J2 = besselj(k,m.*r);
Y = bessely(k,l.*r);
Y2 = bessely(k,m.*r);
H = besselh(k,r);
F1 = symsum((J).*exp(1i*k*ph),k,-5,5);
F2 = symsum((J2+Y2).*exp(1i.*k.*ph),k,-5,5);
F3 = symsum(H.*exp(1i.*k.*ph),k,-5,5);
pwu = nan(size(F1), 'like', F1);
mask = 0 <= r & r < 0.5;
pwu(mask) = F1(mask);
mask = 0.5 <= r & r < 1;
pwu(mask) = F2(mask);
mask = r >= 1;
pwu(mask) = F3(mask);
U = subs(pwu, {l, m}, {1.5, 3});hold on
J0 = besselj(k,r);
u0 = symsum(1i.^(-k).*J0.*exp(1i*k*ph),k,-5,5);
W = U+u0;
contour(x, y, angle(double(W)), 30);
axis equal
xlabel('r','FontSize',14);
ylabel('phi','FontSize',14);

感谢您的评论！