Moved MultivariateGaussian utility class

Author: tgaloppo

mllib/src/main/scala/org/apache/spark/mllib/stat/impl/MultivariateGaussian.scala

@@ -0,0 +1,39 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.mllib.stat.impl
+
+import breeze.linalg.{DenseVector => BreezeVector, DenseMatrix => BreezeMatrix}
+import breeze.linalg.{Transpose, det, inv}
+
+/** 
+   * Utility class to implement the density function for multivariate Gaussian distribution.
+   * Breeze provides this functionality, but it requires the Apache Commons Math library,
+   * so this class is here so-as to not introduce a new dependency in Spark.
+   */
+private[mllib] class MultivariateGaussian(
+    val mu: BreezeVector[Double], 
+    val sigma: BreezeMatrix[Double]) extends Serializable {
+  private val sigmaInv2 = inv(sigma) * -0.5
+  private val U = math.pow(2.0 * math.Pi, -mu.length / 2.0) * math.pow(det(sigma), -0.5)
+    
+  def pdf(x: BreezeVector[Double]): Double = {
+    val delta = x - mu
+    val deltaTranspose = new Transpose(delta)
+    U * math.exp(deltaTranspose * sigmaInv2 * delta)
+  }
+}