It seems common practice to store only the upper or lower triangular part of a sparse symmetric matrix to save memory. Now I am wondering how, e.g. the SpMV kernel in CSR format is designed and how the matrix elements are accessed which are not stored explicitly when only the upper triangular part is given (typical matrix market cases).
The basic CSR SpMV kernel is defined as:
for each row i for k=ptr[i] to ptr[i+1] do y[i] = y[i] + val[k]*x[ind[k]]
ptr defines the row pointer,
ind defines the column index,
val defines the value and
y defines the vector.