let SumSquares (theta:Vector<float>) (y:Vector<float>) (trainingData:Matrix<float>) =
    let m = trainingData.RowCount
    let theta' = theta.ToRowMatrix()
    trainingData
    |> Matrix.mapRows(fun a r -> (theta' * r) - y.[a] )

let tData = matrix [[1.0; 2.0]
                    [1.0; 3.0]
                    [1.0; 3.0]
                    [1.0; 4.0]]
let yVals = vector [5.0; 6.0; 7.0; 11.0]
let theta = vector [1.0; 0.2]

let theta' = theta.ToRowMatrix()
(theta.ToRowMatrix() * tData.[0, 0 .. 1]) - yVals.[0]

tData |> SumSquares theta yVals

let SumSquares (theta:Vector<float>) (y:Vector<float>) (trainingData:Matrix<float>) =
    let m = trainingData.RowCount
    let theta' = theta.ToRowMatrix()
    [0..m-1] |> List.map (fun i -> (((theta' * trainingData.[i,0..1]) |> Seq.exactlyOne) - yVals.[i] ))

tData
    |> Matrix.toRowSeqi
    |> Seq.map (fun (i,x) -> (theta' * x) - yVals.[i])
    |> DenseMatrix.ofRowSeq

let square (x:Vector<float>) = x * x
let subtract (x:Vector<float>) (y:Vector<float>) = y - x
let divideBy (x:float) (y:float) = y / x

let SumSquares (theta:Vector<float>) (y:Vector<float>) (trainingData:Matrix<float>) =
    let m = trainingData.RowCount |> float
    (trainingData * theta)
    |> subtract y
    |> square
    |> divideBy m