How to perform Vector-Matrix Multiplication with BLAS ?
BLAS defines the GEMV (Matrix-Vector Multiplication) level-2 operation. How to use a BLAS Library to perform Vector-Matrix Multiplication ?
It's probably obvious, but I don't see how to use BLAS operation for this multiplication. I would have expected a GEVM operation.
Answer
The Matrix-Vector multiplication of a (M x N) Matrix with a (N x 1) Vector will result an (M x 1) Vector. In short a*A(MxN)*X(Nx1) + b*Y(Mx1) -> Y(Mx1). Of course you can use INCX and INCY when your vector is included in a matrix.
In order to define a Vector-Matrix multiplication The Vector should be transposed. i.e. a*X(1xM)*A(MxN) + b*Y(1xN) -> Y(1xN). Basically you do not have a vector but a single row matrix.
Starting from this point there are two possibilities.
Either use level-3 "GEMM"
?gemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
using
?gemm('N', 'N', 1, N, M, a, X, 1, A, M, b, Y, 1)
Or do some more math. Considering that (X*A)^T = A^T * X^T the row matrix X is converted to vector X^T(MX1). Also Y transpose is vector Y^T(Nx1). Of course memory-wise both X and X^T are store with the same way, sequentially. This means you can use again GEMV using transpose matrix A
?gemv('T', M, N, a, A, M, X, 1, b, Y, 1)