dotc and dotu in glas

  Hello,


Where could a vectorspace concept be used?

Iterative methods, time integration.

When I look at my own implementations for those, I think the
following 
list is pretty complete for linear system solvers with a
single 
right-hand side. (Although, for efficient implementation of
gmres and 
bicgstab(ell), we also need matrices for storing basis
vectors and 
matrix vector operations)

Operations:
Let v, and w be vectors, s a scalar.
v += w
v -= w
v += s*w
v -= s*w
v *= s
v /= s
s * v returning a vector expression
v / s returning a vector expression
v = vector expression

The following operations can be written as a combination of
the previous 
ones.
v - w returning a vector expression
v + w returning a vector expression
-v returning a vector expression

Creation of new containers (vectors in the vector space) for
auxiliary 
results.

inner_product(x,y) (can be implemented via dotc() or dotu()
or dot() or 
x^HERM * y or whathever syntax we decide to use when a
Euclidean 
vectorspace is used), where x and y belong to the same
vectorspace.

bilinear_form(x,y) for x and y in a different vectorspace.

norm(x) (can be implemented using norm_2(x) when a Euclidean
vectorspace 
is used)

Can vectors x and y of different types below to the same
vectorspace? 
What about subspaces, etc.?


Karl

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