Scala 具有自定义数据类型的Breeze线性代数

我正在尝试使用Breeze线性代数包（）和我自己表示GF2字段的数据类型来实现Humming编码。到目前为止，我成功地实现了我的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 }
}

以及创建GF2值矩阵所需的类型类：

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)

但当我尝试将矩阵添加到自身时，我得到以下错误：

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]

在这一点上，我被卡住了，因为我不太明白我现在应该实现什么类型的类。查看

breeze.linalg.operators

并没有多大帮助。所以问题是，我应该怎么做才能将我的GF2与Breeze结合起来，以支持所有矩阵/向量运算

===================
上述问题在0.6版中得到解决
但是，我仍然不能将矩阵乘以向量或值：

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

---

我想我必须提供一个

UFunc

实现。它应该是什么样子？

这在微风的最新快照中起作用。这个周末我将发布0.6

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

---

这在Breeze的最新快照中起作用。这个周末我将发布0.6

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

---

谢谢也许你也可以帮我解决后续问题（矩阵向量乘法）？谢谢！也许你也可以帮我解决后续问题（矩阵向量乘法）？