Block Sparse Matrix with the support of BufferView

[alanray-tech]

Block Sparse Matrix

Sparse Matrix View is built on the facility of BufferView(#467) , with the ability to take a submatrix[row/col offset/count] + a subview[triplet offset/count], which represent a linear subsystem to prevent subsystem-level out of bound access.

Say:

triplet = Triplet.Matrix()
# take 10 triplets of (i,j,mat3x3), logically we write to triplet[4+k]=(i,j,mat3x3)
subview = triplet.subview(4, 10) 
# take a logical area of matrix, 
# so that the i,j in triplet (i, j, mat3x3) must be in the range of row/col extent (5<=i,j<5+10)
submatrix = triplet.submatrix(row_offset=5, col_offset=5, row_count=10, col_count=10) 

N = 4
count = 4
triplet = Triplet.Matrix()
triplet.reshape(N, N)      
triplet.resize_triplets(count)

@qd.kernel
def assemble_diagonal(view: Triplet.MatrixView):
    for I in range(view.row_indices.count):
        block = mat3d(0.0)
        for k in range(3):
            block[k, k] = 2.0
        Triplet.write(view, I, Triplet.Entry(row=I, col=I, block=block))

TODO: API discussion.
TODO: Whether we want to put this in quadrants as a feature?