Test case checks the numerical stability of MultivariateGaussian.pdf when sigma is near singluar

MultivariateGaussianCheck.scala

import breeze.linalg.{det, DenseMatrix}
import org.apache.spark.mllib.linalg.{Matrices, Vectors}
import org.apache.spark.mllib.stat.distribution.MultivariateGaussian

object GaussianTest extends App {
  val x = Vectors.dense(2.1, 3.1, 3.9)

  val mu = Vectors.dense(2, 3, 4)
  val sigma =
    Matrices.dense(3, 3, Array(1.0, 0.0, 3.0, 0.0, 0.0, 0.0, 3.0, 0.0, 11.0).map(_ + 0.0001))

  val determinant = det(new DenseMatrix(sigma.numRows, sigma.numCols, sigma.toArray))
  val gaussian = new MultivariateGaussian(mu, sigma)
  
  // Generate R code for cross check
  println(s"""
       |x = c${x.toArray.mkString("(", ", ", ")")}
       |mu = c${mu.toArray.mkString("(", ", ", ")")}
       |sigma = matrix(
       | c${sigma.toArray.mkString("(", ", ", ")")},
       | nrow = ${sigma.numRows},
       | ncol = ${sigma.numCols}
       |)
       |dmvnorm(x, mu, sigma, log=FALSE)
     """.stripMargin)
  
  println("determinant = " + determinant)
  println("pdf = " + gaussian.pdf(x))
}