[petsc-dev] various dot products messed up for complex numbers?

[Jed Brown]

On Sun, Apr 15, 2012 at 13:32, Barry Smith <bsmith at mcs.anl.gov> wrote:

> (ax,y)  = a(x,y)


This is an arbitrary convention that isn't universal. You occasionally see
a(x,y) = (x,Ay). You certainly see <x|H|y> which is equal to <x|H y>. I
like to write things like

v^H J(u) w \sim J[u](v,w) = (v,J[u] w) = \int_\Omega v^* \cdot J(u) w

where the left side of the \sim is discrete with v,u,w vectors and J(u) the
Jacobian; and versions to the right are all continuous (with J[u] an
operator and J(u) the tensor-valued field).

If I had to use that screwy inner product notation, this would become

v^H J(u) w \sim J[u](w,v) = (J[u] w,v) = \int_\Omega v^* \cdot J(u) w

which is needlessly error-prone.
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