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Re: ContourPlot
*To*: mathgroup at yoda.ncsa.uiuc.edu
*Subject*: Re: ContourPlot
*From*: uunet!itk.unit.no!lie
*Date*: Thu, 16 Nov 89 17:35:19 GMT
[Here are more details on the question regarding contour plots
previously sent to the mailing list. -s christensen]
More details.
Assume that you want to pick the pair (x,y) that minimize the function
f[x_,y_]={x-3,y-5}.{{5,2},{2,5}}.{x-3,y-5}
By simplifying this expression, you get:
f[x_,y_]=230 - 50x + 5x^2 - 62y + 4x y + 5y^2
The minimum is obviously the pair (x=3,y=5). Now, suppose that the solution is
constrained to lie on the curve:
y[x_]=6 - 0.5x
What is then the pair (x,y) that minimize f[x,y]? This can be solved
graphically by plotting the contours of f[x,y] into the x-y plane for different
values of f. Then plot the constraint (y[x]) in the x-y plane of the same
display. This will produce a visualization of the solution.
I tried to:
1. ContourPlot[f[x,y],{x,-1,5},{y,0,8}]
2. Plot[z[x],{x,-1,5}] (I denoted y[x] by z[x])
3. Show[%(no. of ContourPlot output), %(no. of Plot output)]
The result:
a. Warning:
Show::nocombine: Graphics of type ContourGraphics cannot be combined.
b. Out[nn]=Show[-ContourGraphics-,-Graphics-]
Question: How can I solve my problem, i.e., how can I plot a ContourPlot
in the same display as an ordinary plot??
Thanks!
Bernt Lie,
e-mail: lie at itk.unit.no
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