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

    https://github.com/apache/spark/pull/15018#discussion_r93266668
  
    --- Diff: 
mllib/src/main/scala/org/apache/spark/mllib/regression/IsotonicRegression.scala 
---
    @@ -328,74 +336,69 @@ class IsotonicRegression private (private var 
isotonic: Boolean) extends Seriali
           return Array.empty
         }
     
    -    // Pools sub array within given bounds assigning weighted average 
value to all elements.
    -    def pool(input: Array[(Double, Double, Double)], start: Int, end: 
Int): Unit = {
    -      val poolSubArray = input.slice(start, end + 1)
     
    -      val weightedSum = poolSubArray.map(lp => lp._1 * lp._3).sum
    -      val weight = poolSubArray.map(_._3).sum
    +    // Keeps track of the start and end indices of the blocks. 
blockBounds(start) gives the
    +    // index of the end of the block and blockBounds(end) gives the index 
of the start of the
    +    // block. Entries that are not the start or end of the block are 
meaningless. The idea is that
    --- End diff --
    
    It relies on knowing ahead of time wether `x` is the start or end 
index<sup>1</sup>. If it's a start index, `blockBounds(x)` gives the ending 
index of that block. If it's an end index, `blockBounds(x)` gives the starting 
index of the block. So yes, the implementations of `blockStart` and `blockEnd` 
are identical. I just have two different functions because it makes the code 
more readable.
    
    Maybe the comment from scikit-learn (where I borrowed this idea from) 
explains it better? (their `target` = my `blockBounds`)
    
    > target describes a list of blocks.  At any time, if [i..j] (inclusive) is
    > an active block, then blockBounds[i] := j and target[j] := i.
    
    The trick is just in maintaining the array so that the above property is 
always true. At initialization, it's trivially true because all blocks have 
only one element, and `blockBounds(x)` = `x`. After initialization, 
`blockBounds` is only modified by the merge function, which is set up to modify 
`blockBounds` so that this property is preserved, then return the starting 
index of the newly-merged block.
    
    This is admittedly a bit tricky, but it's a lot faster than the 
implementation I did where created a doubly-linked list of `Block` case 
classes. I'm open to suggestions on how to explain it better.
    
    <sup>1</sup> You could actually figure out whether you have a start or an 
end index by comparing `blockBounds(x)` to `x`. The lesser value will be the 
start index.


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