Polar coordinates - ReplaceAll issue
- To: mathgroup at smc.vnet.net
- Subject: [mg107479] Polar coordinates - ReplaceAll issue
- From: Andrej <andrej.kastrin at gmail.com>
- Date: Sun, 14 Feb 2010 05:58:09 -0500 (EST)
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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