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Re: Polar coordinates  ReplaceAll issue
Posted:
Feb 14, 2010 8:17 AM


\[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 > >



