Github user yanboliang commented on a diff in the pull request:

    https://github.com/apache/spark/pull/15394#discussion_r83021809
  
    --- Diff: 
mllib/src/main/scala/org/apache/spark/ml/optim/NormalEquationSolver.scala ---
    @@ -0,0 +1,165 @@
    +/*
    + * 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.ml.optim
    +
    +import breeze.linalg.{DenseVector => BDV}
    +import breeze.optimize.{CachedDiffFunction, DiffFunction, LBFGS => 
BreezeLBFGS, OWLQN => BreezeOWLQN}
    +import scala.collection.mutable
    +
    +import org.apache.spark.ml.linalg.{BLAS, DenseVector, Vectors}
    +import org.apache.spark.mllib.linalg.CholeskyDecomposition
    +
    +private[ml] class NormalEquationSolution(
    +    val fitIntercept: Boolean,
    +    private val _coefficients: Array[Double],
    +    val aaInv: Option[DenseVector],
    +    val objectiveHistory: Option[Array[Double]]) {
    +
    +  def coefficients: DenseVector = {
    +    if (fitIntercept) {
    +      new DenseVector(_coefficients.slice(0, _coefficients.length - 1))
    +    } else {
    +      new DenseVector(_coefficients)
    +    }
    +  }
    +
    +  def intercept: Double = if (fitIntercept) _coefficients.last else 0.0
    +}
    +
    +/**
    + * Interface for classes that solve the normal equations locally.
    + */
    +private[ml] sealed trait NormalEquationSolver {
    +
    +  /** Solve the normal equations from summary statistics. */
    +  def solve(
    +      bBar: Double,
    +      bbBar: Double,
    +      abBar: DenseVector,
    +      aaBar: DenseVector,
    +      aBar: DenseVector): NormalEquationSolution
    +}
    +
    +/**
    + * A class that solves the normal equations directly, using Cholesky 
decomposition.
    + */
    +private[ml] class CholeskySolver(val fitIntercept: Boolean) extends 
NormalEquationSolver {
    +
    +  def solve(
    +      bBar: Double,
    +      bbBar: Double,
    +      abBar: DenseVector,
    +      aaBar: DenseVector,
    +      aBar: DenseVector): NormalEquationSolution = {
    +    val k = abBar.size
    +    val x = CholeskyDecomposition.solve(aaBar.values, abBar.values)
    +    val aaInv = CholeskyDecomposition.inverse(aaBar.values, k)
    +
    +    new NormalEquationSolution(fitIntercept, x, Some(new 
DenseVector(aaInv)), None)
    +  }
    +}
    +
    +/**
    + * A class for solving the normal equations using Quasi-Newton 
optimization methods.
    + */
    +private[ml] class QuasiNewtonSolver(
    --- End diff --
    
    That's OK. We can change it later if necessary, it's private.


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