Assume a $3$ GHz processor that can execute $40$ flops$/$cycle$,$ and the peak memory bandwidth

is $20$ Gbytes$/$s$,$ and the cache size is unlimited.

$(1)$ Draw the roofline model $($use log$-$log scale$)$

$(2)$ Consider these three operations: $($A$)$ vector$-$vector multiplication, $($B$)$ matrix$-$vector

multiplication, and $($C$)$ matrix$-$matrix multiplication. For each operation,

$($a$)$ If N$=16,$ calculate their arithmetic intensity and label them in the roofline model.

$($b$)$ If N$=48,$ calculate their arithmetic intensity and label them in the roofline model.