single precision support added for LeastSquares calculation

[dineshdharme]

Hello David Hall,

This PR adds support for doing Least Squares calculation for Float datatype.
Please review this.

  def NaiveMultiplicationFloat(n: Int, flag: Boolean): Unit = {


    val N_Dim = 4
    val rows = N_Dim + 5
    val columns = N_Dim
    val randomDoubleArray = Array.fill(rows * columns) {math.random}.map(ele => ele.toFloat)
    val sm: DenseMatrix[Float] = DenseMatrix.create(rows, columns, randomDoubleArray)

    val features2DMatrix = sm(::, 1 to -1)
    val targetPPNRVector = sm(::, 0)
   println("sm" +  sm)
    val result = leastSquares(features2DMatrix, targetPPNRVector)
    println("Breeze Linear Equation Solver results")


    println(s"intercept = ${result.coefficients.toArray.slice(1 , 5).mkString("[", ",", "]")}")
   println(s"r^2 = ${result.rSquared}")


  }

This code should allow you to test the Float datatype.

[dlwh]

Hi @dineshdharme thanks for submitting this!

So, typically in Breeze we aim for compile time errors rather than runtime errors. Here, we would get a runtime error if we tried to use it for Complex or something. so rather than the match, it would be better if there were two implementations of each of matrixVector, matrixVectorSpecifiedWork and matrixVectorSpecifiedWork

[dineshdharme]

Thank you, I will update the PR tomorrow and let you know.

[dineshdharme]

Hi David,

I made changes as you requested. Please take a look and let me know.

[dlwh]

almost there, thank you

[dlwh]

let's make this method something like

def apply(x: DenseVector[T])(implicit can_dot: OpMulInner.Impl2[DenseVector[T], DenseVector[T], T]) = {
}

and then you can remove all of the switches and exception stuff.

[dlwh]

similarly

let's make this method something like

def apply(x: DenseVector[T])(implicit can_dot: OpMulMatrix.Impl2[DenseMatrix[T], DenseVector[T], T]) = {
}

and then you can remove all of the switches and exception stuff.

[dineshdharme]

I made the changes you requested. The only difference is for first apply I had to move the implicit can_dot to case class
as scala didn't recognize it to be Function1's apply method.

Please review. thanks!

[dlwh]

thanks!