www.gusucode.com > matlab 案例源码 matlab代码程序 > matlab/LaplacianOfNaturalLogarithmFunctionExample.m
%% Laplacian of Natural Logarithm Function % Calculate the discrete Laplacian of a natural logarithm function. %% % Define the x and y domain of the function on a grid of real numbers. % Copyright 2015 The MathWorks, Inc. [x,y] = meshgrid(-5:5,-5:0.5:5); %% % Define the function $U(x,y) = \frac{1}{2} \log\left(x^2y\right)$ over % this domain. U = 0.5*log(x.^2.*y); %% % The logarithm is complex-valued when the argument |y| is negative. %% % Use |del2| to calculate the discrete Laplacian of this function. Specify % the spacing between grid points in each direction. hx = 1; hy = 0.5; L = 4*del2(U,hx,hy); %% % Analytically, the Laplacian is equal to $\Delta U(x,y) = - \left( % 1/x^2+1/2y^2 \right)$. This function is not defined on % the lines $x = 0$ or $y = 0$. %% % Plot the real parts of |U| and |L| on the same graph. figure surf(x,y,real(L)) hold on surf(x,y,real(U)) grid on title('Plot of U(x,y) and $\Delta$ U(x,y)','Interpreter','latex') xlabel('x') ylabel('y') zlabel('z') view(41,58) %% % The top surface is |U| and the bottom surface is |L|.