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# Dynamic Plots Using an Equation Function

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This blog post continues to explore the Dynamic Visualizations available using  the Equation argument on the PLOT  function. In this example, we explore the use of a function name rather than an equation string. See Dynamic  Plots Using an Equation String for the first article in this series.

Using an equation string has some limitations:

• You can only have a single statement
• You cannot easily change the equation unless youset a new string
• You cannot pass parameters into your equation

As a different approach, create an IDL function containing your equation and then pass the function name to the Equation argument. This method allows you a bit more flexibility in your input equations.

For example, in the first line of the code above, we could have simply written:

p1= PLOT('LambertW', '2', DIMENSIONS=[400,400],\$

NAME='Upperbranch', \$

TITLE='LambertW Function', XRANGE=[-0.4, 2])

Notice that we no longer have an X variable in our equation, we just have the name of the function. We can also create our own routine which accepts our X vector and some optional user data.

First, create a new IDL routine called ex_plot_function andsave it in a file ex_plot_function.pro on IDL's path:

FUNCTIONex_plot_function, x, k

COMPILE_OPTIDL2

RETURN,LAMBERTW(DCOMPLEX(x), k)

END

Next, we create our plot visualization, passing in the nameof our equation along with our user data containing the "branch"parameter k:

p1= PLOT('ex_plot_function', '2', DIMENSIONS=[400,400],\$

NAME='k= 0', EQN_USERDATA=0, \$

TITLE='\$\Re\${LambertW}',XRANGE=[-1, 2])

p2r= PLOT('ex_plot_function', '2r', /OVERPLOT, \$

NAME='k= -1', EQN_USERDATA=-1)

p3r= PLOT('ex_plot_function', '2g', /OVERPLOT, \$

NAME='k= 1', EQN_USERDATA=1)

p4r= PLOT('ex_plot_function', '2b', /OVERPLOT, \$

NAME='k= 2', EQN_USERDATA=2)

lg= LEGEND(/DATA, POSITION=[1.9, -4], LINESTYLE=6, SHADOW=0)

Our plot should now look like the following: Again, we can pan and zoom around the plot, and IDL willautomatically update the equations.