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Thinking about Systolic Arrays Peter Cappello This presentation assumes that you have read the Chapter by C. Leiserson and H.-T. Kung
2 Matrix-Vector Product b = Ax, illustrated with a 3X3 matrix, A. _______________________________ b1 = a11*x1 + a12*x2 + a13*x3 b2 = a21*x1 + a22*x2 + a23*x3 b3 = a31*x1 + a32*x2 + a33*x3
3 a31a32a33 a21a22a23 a11a12a13 x1x2x3 x1 x2 x3 y1 y2 y3 x1x2x3
4 a31a32a33 a21a22a23 a11a12a13 x1x2x3 x1 x2 x3 TIME SPACESPACE
5 a31 a32 a33 a2 1 a2 2 a2 3 a1 1 a1 2 a1 3 x1x1 x2x2 x3x3 x1x1 x1x1 x2x2 x2x2 x3x3 x3x3 SPACESPACE TIME
6 a31a32a33 a21a22a23 a11a12a13 x1x2x3 x1 x2 x3 SPACESPACE TIME
7 Matrix Product C = AB, illustrated with a 2X2 matrices. c11 = a11*b11 + a12*b21 c12 = a11*b12 + a12*b22 c21 = a21*b11 + a22*b21 c12 = a21*b12 + a22*b22
8 a21a22 a11a12 b11 b21 T S a21a22 a11a12b12 b21 b12 b22 S
9 a21a22 a11a12 b11 b21 T S a21a22 a11a12b12 b21 b12 b22 S
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