Consider the partitioning
The blockings of matrices A and L are identical. Blocks and are scalars, and are row vectors, and and are column vectors. Sub-matrices , , , and are square matrices.
The assumption is that bold-face parts of the lower triangular matrix have already been computed, and have overwritten the corresponding parts of A . The rest of the matrix has not been updated at all, and the object of the next step is to compute the next parts of the lower triangular matrix, and , overwriting the corresponding parts of A . From the above equation, we derive
Thus if and are to be updated by and , the following step will suffice:
The algorithm of left looking version of Cholesky factorization can be given as follows using the above equations
The PLAPACK implementation using global level-2 BLAS is given in Figure 8.3. In this code, at the top of the loop, a_1 references the matrix
and a_cur the matrix