Using the Scipy cython_blas interface from Cython not working on vectors Mx1 1xN

Question

This has to deal with a similar problem here: Calling BLAS / LAPACK directly using the SciPy interface and Cython but is different because I\'m using the actual code in the

Answer 1

If I see it right, you try to use fortran-routines for arrays with c-memory-layout.

Even if it is obviously known to you, I would like first to elaborate on the row-major-order (c-memory-layout) and the column-major-order (fortran-memory-layout), in order to deduce my answer.

So if we have a 2x3 matrix (i.e. 2 rows and 3 columns) A, and store it in some continuous memory we get:

row-major-order(A) = A11, A12, A13, A21, A22, A23
col-major-order(A) = A11, A21, A12, A22, A13, A33

That means if we get a continuous memory, which represents a matrix in the row-major-order, and interpret it as a matrix in column-major-order we will get quite a different matrix!

However, we we take a look at the transposed matrix A^t we can easily see:

row-major-order(A) = col-major-order(A^t)
col-major-order(A) = row-major-order(A^t)

That means, if we would like to get the matrix C in row-major-order as result, the blas-routine should write the transposed matrix C in column-major-order (after all this we cannot change) into this very memory. However, C^t=(AB)^t=B^t*A^t and B^t an A^t are the original matrices reinterpreted in column-major-order.

Now, let A be a n x k-matrix and B a k x m-matrix, the call of dgemm routine should be as follows:

dgemm(transa, transb, &m, &n, &k, &alpha, b0, &m, a0, &k, &beta, c0, &m)

As you can see, you switched some n and m in your code.