implicit Impl method for collections in scala breeze

Question

I have a type alias on a SortedMap[Int, Double] and I'd like to have an implicit that allows me to pass my SortedMap to some of the built-in functions in breeze, specifically the breeze.stats._ functions variance and stddev.

Here's a working example without implicits:

package com.soquestion

import breeze.linalg._
import breeze.stats._
import scala.collection.SortedMap
import scala.language.implicitConversions

object proof {
  type Series = SortedMap[Int, Double]

  def example: Double = {
    val s: Series = SortedMap(1 -> 9.0, 2 -> 2.0, 3 -> 5.0, 4 -> 4.0, 5 -> 12.0, 6 -> 7.0, 7 -> 8.0, 8 -> 11.0, 9 -> 9.0, 10 -> 3.0, 11 -> 7.0, 12 -> 4.0, 13 -> 12.0, 14 -> 5.0, 15 -> 4.0, 16 -> 10.0, 17 -> 9.0, 18 -> 6.0, 19 -> 9.0, 20 -> 4.0)

    stddev(s.values)
  }
}

run in sbt console

scala> com.soquestion.proof.example
res0: Double = 3.0607876523260447

What I'd like is to not have to specify the .values and just call stddev(s) and variance(s).

Here's what I tried

package com.soquestion

import breeze.linalg._
import breeze.stats._
import scala.collection.SortedMap
import scala.language.implicitConversions

object proof {
    // Implicitly convert the SortedMap, or any map, to a DenseVector[Double]
  implicit def series2DenseVector(s: Traversable[(Int, Double)]): DenseVector[Double] = {
    DenseVector(s.map(_._2).toArray)
  }
  type Series = SortedMap[Int, Double]

  def example: Double = {
    val s: Series = SortedMap(1 -> 9.0, 2 -> 2.0, 3 -> 5.0, 4 -> 4.0, 5 -> 12.0, 6 -> 7.0, 7 -> 8.0, 8 -> 11.0, 9 -> 9.0, 10 -> 3.0, 11 -> 7.0, 12 -> 4.0, 13 -> 12.0, 14 -> 5.0, 15 -> 4.0, 16 -> 10.0, 17 -> 9.0, 18 -> 6.0, 19 -> 9.0, 20 -> 4.0)

    stddev(s) // <--- compiler error here
  }
}

but I get a compiler error of

could not find implicit value for parameter impl: breeze.stats.stddev.Impl[com.soquestion.proof.Series,VR]

going through the breeze documentation I wasn't able to find a good example of what implicit I need to provide. Ideally I'd like to make one implicit that would allow me to call both stdev and variance without multiple implicits.

I did see the question Scala Breeze DenseVector Implicit failure, but I don't see how it would apply to this scenario.

Full formatted answer based on @dlwh's answer below in case anyone needs it in the future

package com.soquestion

import breeze.linalg.support._
import breeze.linalg.support.CanTraverseValues._
import breeze.stats._
import scala.annotation.tailrec
import scala.collection.SortedMap
import scala.language.implicitConversions

object proof {
  type Series = SortedMap[Int, Double]

  def example: Double = {
    // ideally this implicit would go in a scope higher up so it could be
    // brought in wherever it's needed, but this works for a sample
    implicit object SeriesIter extends CanTraverseValues[Series, Double] {
      def isTraversableAgain(from: Series) = true
      def traverse(from: Series, fn: ValuesVisitor[Double]): Unit = {
        @tailrec def traverser(idx: Int, t: Array[Double]): Unit = {
          if (idx == 1) fn.visit(t.head)
          else {
            fn.visit(t.head)
            traverser(idx - 1, t.tail)
          }
        }
        val v: Array[Double] = from.values.toArray
        fn.zeros(0, 0d)
        traverser(v.size, v)
      }
    }

    val s: Series = SortedMap(1 -> 9.0, 2 -> 2.0, 3 -> 5.0, 4 -> 4.0, 5 -> 12.0, 6 -> 7.0, 7 -> 8.0, 8 -> 11.0, 9 -> 9.0, 10 -> 3.0, 11 -> 7.0, 12 -> 4.0, 13 -> 12.0, 14 -> 5.0, 15 -> 4.0, 16 -> 10.0, 17 -> 9.0, 18 -> 6.0, 19 -> 9.0, 20 -> 4.0)
    stddev(s)
  }
}

Answer 1

The docs could be much better for this, and I do wish I could make the error messages more helpful.

If you look at stddev's source you'll see that it requires an implementation of variance.Impl, which requires a meanAndVariance.Impl, which can be provided for any type that has a CanTraverseValues[T, Double] implicit. By default, there's a CanTraverseValues implicit for collections, but only on the contained type, not the values of a scala's Map types. Implementing CanTraverseValues and CanMapValues will enable most breeze UFuncs.

Scala generally won't "chain" implicits, which is why your proof example didn't work.