Paul Wang’s scientific contributions

... The pseudocode for the optimized algorithm for a lower triangular non-transposed matrix is given in Algorithm 4. It traverses the matrix "bottom-up". For the last columns, calculations are performed using the baseline algorithm (lines [4][5][6][7][8][9][10][11][12][13][14], and for the remaining columns, they are performed by an optimized algorithm that traverses along diagonals (lines 15-31). AXPY(length + 1, alpha * X[i], a + lda * i, Y + i); 7: end for 8: for (i = 0; i < iend; i += BLOCK_SIZE) do 9: y_copy =LOAD(y + i); 10: for (INT j = 0; j < k; j++) do 11: x_copy = LOAD(x + i + 1 + j); 12: diag_a = LOAD_WITH_STRIDE(a + 1 + j, STRIDE); 13: mul = MUL_VV(x_copy, diag_a); 14: y_copy = FMA_VF(y_copy, alpha, mul); 15: end for 16: SAVE(y + i, y_copy); 17: a += BLOCK_SIZE * lda; 18: end for 19: for (; i < n -k; i++) do 20: length = MIN(n -i -1, k); 21: Y[i] += alpha * DOT(length, a + 1, X + i + 1); 22: a += lda; 23: end for 24: for (; i < n; i++) do 25: length = MIN(n -i -1, k); 26: AXPY(length + 1, alpha * X[i], a + k -length, 27: Y + i -length); 28: Y[i] += alpha * DOT(length, a + 1, X + i + 1); 29: a += lda; 30: end for 31: } Depending on stored triangle of the matrix and whether the matrix is transposed or not, this operation is performed using the DOT or AXPY. ...

Reference:

Performance optimization of BLAS algorithms with band matrices for RISC-V processors