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Re: Basic plotting of an evaluated function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg86906] Re: Basic plotting of an evaluated function
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Wed, 26 Mar 2008 04:48:36 -0500 (EST)
*Organization*: The Open University, Milton Keynes, UK
*References*: <fsa5cd$ab2$1@smc.vnet.net>
lederer at ssb.rochester.edu wrote:
> I have some function in two varaibles
>
> f[x_,y_]= some arbitrary polynomial
>
> Now I want to minimize the function with respect to y over some
> compact interval with fixed x
>
> NMinimize[{f[x,y],y=995,y=989},y]
There are two syntax errors in the above line:
First, the expression y = 995 _assigns_ the integer value 995 to the
symbol y. What you had in mind was the comparison operator for equality,
which is written as a double equal sign == in Mathematica. (See Set, =,
and Equal, ==, and also SameQ, ===, in the online documentation.)
Second, NMinimize accepts constraints expressed in the form of
inequalities and domain specification. Therefore, your expression should
read,
Minimize[{f[x, y], 989 <= y <= 995}, y]
> I want to plot the y's versus the x's.
>
> I have tried many things like defining
>
> s[x_]=Part[NMinimize[{f[x,y],y=995,y=989},y],2]
Using SetDelayed, :=, and the replacement operator /. should work here.
s[x_] := y /. Last@NMinimize[{f[x, y], 989 <= y <= 995}, y]
> Plot[s[x],{x,-14, 46}]
<snip>
The following expressions are a working example of what you are looking for.
f[x_, y_] := x^2 - 3 y^2 + x y + 10
s[x_] := y /. Last@NMinimize[{f[x, y], 989 <= y <= 995}, y]
Plot[s[x], {x, -14, 46}]
Hope this helps,
--
Jean-Marc
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