Found the following significant warnings:

  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in 1 + rho^2 - 2 * rho * cos(x - mu) : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in (1 - rho^2) * (1 + rho^2 - 2 * rho * cos(x - mu)) : Recycling array of length 1 in array-vector arithmetic is deprecated.
Deprecated functions may be defunct as soon as of the next release of
R.
See ?Deprecated.