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How to rewrite 2D Gaussian eqn in terms of x?

  • Thread starter ireland01
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  • #1
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http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png" [Broken]

How to rewrite this 2D Gaussian eqn in terms of x?
i need to calculate the x and y values.
let x0=0 and y0=0.

is it complex?
 
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Answers and Replies

  • #2
HallsofIvy
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What do you mean by "write in terms of x"? It is already written in terms of x and y and cannot be written in terms of x only.

Do you mean "solve for x"? Again, because it is a function of both x and y, you cannot solve it for x alone. You can assume a specific value for y and then solve for x.

But to "solve for x" you would also have to have a specific value of f(x,y).

I simply don't understand what you mean by "calculate the x and y values". In general, x and y can have any real values. What conditions are you placing on f(x,y) to give specific x and y values that you could calculate?
 
  • #3
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yes sorry i mean solve for x

let f(x,y) = y = 2. say
 
  • #4
Mentallic
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I've never seen [itex]\sigma[/itex] so assuming it's to be treated as a constant, yes you certainly can solve for x given y and f(x,y). It's relatively simple too.

[tex]-ln\left(\frac{f(x,y)}{A}\right)=\frac{(x-x_0)^2}{2\sigma_x^2}+\frac{(y-y_0)^2}{2\sigma_y^2}[/tex]

It should be obvious from here how to solve for x.
 

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