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Re: Polar coordinates - ReplaceAll issue
Posted:
Feb 14, 2010 8:17 AM
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\[Rule] and \[RightArrow] appear identically on screen. Replace the the
\[RightArrow] with \[Rule] (shortcut is ESC -> ESC, but better always is ->
only )
after this change it would work.
yehuda
On Sun, Feb 14, 2010 at 12:58 PM, Andrej <andrej.kastrin@gmail.com> wrote:
> Hi,
>
> this is my first post to this group. Yes, I'm a newbie in Mathematica.
> I'm trying to compute the probability of circular disc (in R^2).
> Suppose that vertical and horizontal deviations from the center of the
> disc follows bivariate normal distribution. I hope that the code below
> is self explained. The main issue is the transformation from Cartesian
> to polar coordinates as follows:
>
> # First I set up the appropriate bivariate normal distribution:
> Needs["MultivariateStatistics`"]
> X = {x1, x2};
> mu = {0, 0};
> Sigma = sigma^2 ({{1,rho}, {rho,1}});
> dist = MultinormalDistribution[mu, Sigma];
> cond = {sigma > 0, -1 < rho < 1, r > 0, 0 < theta < 2 \[Pi]};
> f = Simplify[PDF[dist, X], cond]
> domain[f] = {{x1, -\[Infinity], \[Infinity]}, {x2, -\[Infinity], \
> [Infinity]}} && cond;
>
> # Transformation to polar coordinates:
> Omega = {x1 \[RightArrow] r Cos[theta], x2 \[RightArrow] r
> Sin[theta]};
> g = Simplify[(f /. Omega) Jacob[X /. Omega, {r, theta}], cond]
>
> And the message I get:
>
> ReplaceAll::reps: {x1\[RightArrow]r Cos[theta],x2\[RightArrow]r
> Sin[theta]} is neither a list of replacement rules nor a valid
> dispatch table, and so cannot be used for replacing. >>
>
> Thanks in advance for any suggestions or pointers.
>
> Best, Andrej
>
>
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