gusucode.com > demos工具箱matlab源码程序 > demos/cplxdemo.m
%% Functions of Complex Variables % This example shows how to perform some very interesting manipulations on % complex variables. % Copyright 1984-2015 The MathWorks, Inc. %% % Let f(z) be a function of a complex variable. Consider the domain formed by % the unit disc (displayed below in polar coordinates). The height of the % surface is the real part, REAL(f(z)). The color of the surface is the % imaginary part, IMAG(f(z)). The color map varies the hue in the HSV color % model. % % CPLXMAP plots a function of a complex variable. It has the syntax % CPLXMAP(z,f(z),bound), where z is the domain, and f(z) is the mapping that % generates the range. % % CPLXGRID generates a polar coordinate complex grid. Z = CPLXGRID(m) is an % (m+1)-by-(2*m+1) complex polar grid. colormap(hsv(64)) z = cplxgrid(30); cplxmap(z,z) title('z') %% % f(z) = z^3. Three maxima at the cube roots of 1. cplxmap(z,z.^3) title('z^3') %% % f(z) = (z^4-1)^(1/4). Four zeros at the fourth roots of 1. cplxmap(z,(z.^4-1).^(1/4)); title('(z^4-1)^{(1/4)}') %% % f(z) = 1/z. A simple pole at the origin. cplxmap(z,1./(z+eps*(abs(z)==0)),5*pi); title('1/z') %% % f(z) = atan(2*z). Branch cut singularities at +-i/2. cplxmap(z,atan(2*z),1.9) title('atan(2*z)') %% % f(z) = z^1/2. Viewed from the negative imaginary axis. cplxroot(2) view(0,0) title('sqrt(z)') %% % Another view for f(z) = z^1/2. The Riemann surface for the square root. cplxroot(2) title('sqrt(z)') %% % f(z) = z^1/3. The Riemann surface for the cube root. cplxroot(3) title('z^{(1/3)}')