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docs:utils:l2ip [2010/02/02 07:55] |
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+ | ====== L2IP ====== | ||
+ | compute the L2 inner product between two fields | ||
+ | |||
+ | options | ||
+ | <code> | ||
+ | -d --digits <int> default == 7 number of digits | ||
+ | -n --normalize normalize by norms of each field | ||
+ | <flowfield> (trailing arg 2) input field #1 | ||
+ | <flowfield> (trailing arg 1) input field #2 | ||
+ | </code> | ||
+ | |||
+ | usage | ||
+ | <code> | ||
+ | L2IP u.ff v.ff | ||
+ | </code> | ||
+ | |||
+ | returns | ||
+ | |||
+ | <latex> | ||
+ | \text{L2IP(u,v)} = ({\bf u}, {\bf v}) = \frac{1}{L_x L_y L_z} \int_{\Omega} {\bf u} \cdot {\bf v} \,\, d{\bf x} | ||
+ | </latex> | ||
+ | |||
+ | or, if -n option is specified, %%L2IP(u,v) / (L2Norm(u) L2Norm(v))%% |