Question

I’d like to implement a “matrix dot product” in Scala in the following way:

type Real = Double
type Row = Array[Real]
type Matrix = Array[Row]

def dot[T](f: (T,T) => Real)(as: Iterable[T], bs: Iterable[T]): Real =
  (for ((a, b) <- as zip bs) yield f(a, b)) sum

def rowDot(r1: Row, r2: Row) = dot(_*_)(r1, r2)
def matDot(m1: Matrix, m2: Matrix) = dot(rowDot)(m1, m2)

However, the definition of rowDot doesn’t work. Scala needs explicit type annotations for the anonymous function (_*_), so instead I must write

def rowDot(r1: Row, r2: Row) = dot((x:Real, y: Real) => x*y)(r1, r2)

or

def rowDot = dot((x:Real, y: Real) => x*y) _

Is there some way to change the definition of dot so that the shorthand (_*_) can be used?

Edit: Another confusion: matDot also gives type errors in certain circumstances. It fails with Arrays of Arrays, but not with Lists of Arrays

scala> matDot(Array(Array(1.0,2.0)), Array(Array(1.0,2.0,3.0)))
<console>:27: error: type mismatch;
 found   : Array[Array[Double]]
 required: Iterable[Iterable[Real]]
              matDot(Array(Array(1.0,2.0)), Array(Array(1.0,2.0,3.0)))
                          ^

scala> matDot(List(Array(1.0,2.0)), List(Array(1.0,2.0,3.0)))
res135: Real = 5.0

What’s the difference?

Answer 1

specifying dot[Real] explicitly should work too.

def rowDot(r1: Row, r2: Row) = dot[Real](_*_)(r1, r2)

EDIT

replying to your edit: I think the issue is that the implicit conversion from Array to WrappedArray is not applied recursively when you have a Array[Array].

Array[Int] is not an Iterable[Int]; normally, when you assign it to a Iterable, an Array[Int] is implicitly converted to a WrappedArray[Int] (where WrappedArray is a Iterable[Int]). This is what happens when you use List[Array[Int]] (you get a List[WrappedArray[Int]] implicitly).

However, as I said, the implicit conversion is not applied recursively, so an Array[Array[Int]] is not implicitly converted to WrappedArray[WrappedArray[Int]].

Here’s a REPL session that demonstrates the problem:

A List[Array[Int]] can be assigned to Iterable[Iterable[Int]] (note that Array is converted to WrappedArray)

scala> val i : Iterable[Iterable[Int]] = List(Array(1,2), Array(1,2,3))
i: Iterable[Iterable[Int]] = List(WrappedArray(1, 2), WrappedArray(1, 2, 3))

An Array[Array[Int]] does not work automatically (as you discovered)

scala> val j : Iterable[Iterable[Int]] = Array(Array(1,2), Array(1,2,3))
<console>:9: error: type mismatch;
 found   : Array[Array[Int]]
 required: Iterable[Iterable[Int]]
       val j : Iterable[Iterable[Int]] = Array(Array(1,2), Array(1,2,3))
                                              ^

However, with some hand-holding (converting manually the inner Arrays to WrappedArrays) everything works again:

    scala> import scala.collection.mutable.WrappedArray
    import scala.collection.mutable.WrappedArray

    scala> val k : Iterable[Iterable[Int]] = Array(WrappedArray.make(Array(1,2)),
 WrappedArray.make(Array(1,2,3)))
    k: Iterable[Iterable[Int]] = WrappedArray(WrappedArray(1, 2), WrappedArray(1, 2,
     3))