matrix vector multiply

[Debasish Das]

Hi,

When I am doing the following:

res := ata * x

ata is a DenseMatrix[Double]

x is DenseVector[Double]

res is DenseVector[Double]

basically I wanted to do blas.dgemv(ata, x, res) with no memory allocation. 

Are they equivalent ?

Thanks.

Deb

[Debasish Das]

Or do I have to use OpMulMatrix.Impl2[M, T, T] and run res := mult(ata, x) to get blas.gemv ?

[Debasish Das]

Seems default DenseMatrix * DenseVector will allocate memory for result but for almost all iterative optimizers the workspace memory that comes bundled in the State can be re-used. Today we are running DenseMatrices but then for CSCMatrics also this will show up...

Is it possible to have a in-place alternative for the result ?

Even if I use OpMulMatrix.Impl2[M, T, T] and do res := mult(ata, x), the output of gemv will be allocated but I already have the memory of res allocated in the state and I want something like mult(ata, x, res)

I see something like this is done in axpy through InPlaceImpl3 but that's defined for vector operations y = ax + b only...

def axpy[A, X, Y](a: A, x: X, y: Y)(implicit axpy: scaleAdd.InPlaceImpl3[Y, A, X]): Unit = { axpy(y, a, x) }

We need to define these in-place operators for matrices...

Should I list these down and open up an issue ? I need these 5 in-place for now I think

1. dgemv : for dense matrix vector multiply

2. dgetrf: LU triangular factorization cache

3. dpotrf: cholesky triangular factorization cache

4. dgetrs: for triangular back solves related to LU

5. dpotrs: for triangular back solves related to Cholesky

[David Hall]

I need to come up with a general solution for operations that specify a sink. I've known about it for a while, but haven't decided what to do about it. Ultimately something expression tree or macro based is going to be the answer, but that's a ton of work.

In the short term, if you'd make a new trait parallel to UFunc.InPlaceImpl called UFunc.WithSinkImpl or something and make that the implicit capability trait, I'd appreciate it. That is,

def dgemv[Sink, M, V](m: M, v: V, sink: Sink)(implicit op: OpMulMatrix.WithSinkImpl[Sink, M, V]) = op(sink, m, v)

if you want to add scale parameters you can.

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