On 12/27/2017 10:15 PM, Phani Motamarri wrote:
I have a STL array of parallel distributed vectors
*std::vector<VectorType> X;*
This unrelated to your problem, but storing (linear algebra) vectors in
std::vector is awkward because it may require copying vectors around when you
resize the std::vector. A useful design pattern is to use
std::vector<std::unique_ptr<VectorType>>
instead. If you resize the vector, then you only need to copy the pointer, not
the entire vector.
In the above VectorType denotes parallel::distributed::Vector<double>. The
size of X (numVectorsX) can be close to 5,000 to 10,000 for very large
problems. All these vectors in X form a subspace and I would like to
evaluate the overlap matrix associated with these vectors i.e I would like to
evaluate the matrix A = Q^T*Q where Q is the matrix whose column vectors are
the vectors in X and the matrix A is a square matrix
with dimension equal to numVectorsX.
I was wondering if anyone can suggest a computationally efficient way of
evaluating this overlap matrix A using deal ii functionality.
I don't see a different way than to do the N^2/2 dot products that make up the
matrix A:
for (unsigned int i=0; i<N; ++i)
for (unsigned int j=i; j<N; ++j)
A(i,j) = A(j,i) = X[i] * X[j];
This could be made more efficient if you didn't store a vector of vectors, but
instead a dense matrix that is distributed across processors. PETSc has a
matrix type for this (see
http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreateDense.html#MatCreateDense)
but we don't currently have wrappers for the parallel version
(PETScWrappers::FullMatrix is apparently only sequential). It would not be
terribly difficult to extend these wrappers to the parallel case, if you
wanted to go this route -- and we'd be happy to guide you in this direction.
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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