Breeze Linear Algebra with custom data type

Question

I'm trying to implement Humming coding using Breeze Linear Algebra package (https://github.com/scalanlp/breeze) and my own data type that represents GF2 field. So far I was successfully able to implement my GF2:

package humming

trait GF2 {
  def + (that: GF2): GF2
  def * (that: GF2): GF2

  def / (that: GF2) = that match {
    case Zero => throw new IllegalArgumentException("Div by 0")
    case _ => this
  }
}

object Zero extends GF2 {
  override def toString = "Zero"
  def + (that: GF2) = that
  def * (that: GF2) = this
}

object One extends GF2 {
  override def toString = "One"
  def + (that: GF2) = that match { case One => Zero ; case _ => this }
  def * (that: GF2) = that match { case One => this ; case _ => that }
}

and needed type classes to create a matrix of GF2 values:

import breeze.linalg._
import breeze.numerics._
import breeze.storage._
import scala.reflect._
import breeze.math._
import humming._

implicit object GF2DefaultArrayValue extends DefaultArrayValue[GF2] {
  override def value = Zero
}

implicit object GF2Semiring extends Semiring[GF2] {
  def defaultArrayValue = GF2DefaultArrayValue
  def manifest = classTag[GF2]
  def zero = Zero
  def one = One

  def ==(a: GF2, b: GF2) = a == b
  def !=(a: GF2, b: GF2) = a != b
  def +(a: GF2, b: GF2) = a + b
  def *(a: GF2, b: GF2) = a * b
}

val a = DenseMatrix.eye[GF2](5)

But when I try to add matrix to itself I get the following error:

a + a  
// could not find implicit value for parameter op:  
// breeze.linalg.operators.BinaryOp[breeze.linalg.DenseMatrix[humming.GF2],  
// breeze.linalg.DenseMatrix[humming.GF2],breeze.linalg.operators.OpAdd,That]

At this point I'm stuck because I don't quite understand what type class I should implement now. Looking at breeze.linalg.operators did not help much. So the question is what should I do to marry my GF2 with Breeze in a way that all matrix/vector operations could be supported?

==============
The problem above is solved in version 0.6
However, I still can't multiply matrix by vector or by value:

val a = DenseMatrix.eye[GF2](5)
val b = DenseVector.ones[GF2](5)
a + a // OK

a * b  
// Could not find an implicit implementation for this UFunc with arguments  
// breeze.linalg.DenseMatrix[humming.GF2], breeze.linalg.DenseVector[humming.GF2]

a + One  
// Could not find an implicit implementation for this UFunc with arguments  
// breeze.linalg.DenseMatrix[humming.GF2], humming.One.type

I suppose I have to provide a UFunc implementation. What should it look like?

Answer 1

This works in the latest snapshot of Breeze. I'll be releasing 0.6 this weekend.

scala> val a = DenseMatrix.eye[GF2](5)
a: breeze.linalg.DenseMatrix[X.GF2] =
One   Zero  Zero  Zero  Zero
Zero  One   Zero  Zero  Zero
Zero  Zero  One   Zero  Zero
Zero  Zero  Zero  One   Zero
Zero  Zero  Zero  Zero  One

scala> a + a
res0: breeze.linalg.DenseMatrix[X.GF2] =
Zero  Zero  Zero  Zero  Zero
Zero  Zero  Zero  Zero  Zero
Zero  Zero  Zero  Zero  Zero
Zero  Zero  Zero  Zero  Zero
Zero  Zero  Zero  Zero  Zero