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Zlab: Explore the complex plane in Matlab



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Zlab Explore the complex plane in Matlab Robert L Parker A series of matlab scripts allows the user to generate informative views of an analytic function of a complex variable in the complex plane The user provides the matlab formula for the function which can be displayed in various ways magnitude phase contour diagram with singularities and branch cuts indicated perspective views of the function magnitude or its real and imaginary parts Help scripts are provided enabling the user to move around the plane or to zoom in on interesting features and to rotate any of the perspective plots In addition a program is provided for performing a contour integral numerically on a path specified by mouse over the plane Zlab comprises a series of scripts and runs essentially as command line language with occasionally mouse input The master routine is zlab which generates the function values and updates the contour map All the other routines work on the values that zmap creates some invoke zmap to move the center of the graph window or investigate the z plane on a new scale Here is an example of a run made with zlab If you type in these instructions using the top function in the script fun m provided various features of the complex plane will be illuminated The top function is a hankel function zmap solid turn zooom zooom pan pullback pullback pullback clear Plots a magnitude phase contour plot of the Hankel function The log branch cut and a simple zero appear A perspective fish net plot is drawn of the same area The perspective figure is rotated Move in getting a closer view of the branch point Move in further Using the mouse chose another center for the plot say the saddle point at 0 0575 0 0838i Reverse the last zooom We can see a larger area including more zeros Restore all default settings Prolog At first blush it may seem trivial to get matlab to contour up analytic function of a complex variable why would anyone need a whole collection of special scripts To do the job



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