Found the following significant warnings:

  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], by[, j]) * by[, j] : Recycling array of length 1 in array-vector arithmetic is deprecated.
  Warning in crossprod(x[, j], x[, i]) * x[, i] : 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.