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zhanqiuzhang avatar zhanqiuzhang commented on July 20, 2024

||h||_2^2=h_0^2+h_1^2
||r||_2^2 =r_0^2+r_1^2
||h||_2^2 * ||r||_2^2 =h_0^2r_0^2+h_0^2r_1^2+h_1^2r_0^2+h_1^2r_1^2

||h \overline{R}||_2^2
=(h_0r_0 - h_1r_1)^2+(h_0r_1 + h_1r_0)^2
=(h_0r_0)^2+(h_1r_1)^2-2h_0r_0h_1r_1+(h_0r_1 )^2+(h_1r_0)^2+2h_0r_1h_1r_0
=(h_0r_0)^2+(h_1r_1)^2+(h_0r_1 )^2+(h_1r_0)^2

Obviously, the above two items are equal.

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Wentao-Xu avatar Wentao-Xu commented on July 20, 2024

OK, thanks for your reply, and it addresses my concern.
The calculation of ||h||_2^2 * ||r||_2^2 is indeed more effcient than ||h \overline{R}||_2^2.

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