template<int dim, int n_rows, int n_columns, typename Number, typename Number2>
struct internal::EvaluatorTensorProduct< evaluate_evenodd, dim, n_rows, n_columns, Number, Number2 >
Internal evaluator for 1d3d shape function using the tensor product form of the basis functions.
This class implements a different approach to the symmetric case for values, gradients, and Hessians also treated with the above functions: It is possible to reduce the cost per dimension from N^2 to N^2/2, where N is the number of 1D dofs (there are only N^2/2 different entries in the shape matrix, so this is plausible). The approach is based on the idea of applying the operator on the even and odd part of the input vectors separately, given that the shape functions evaluated on quadrature points are symmetric. This method is presented e.g. in the book "Implementing
Spectral Methods for Partial Differential Equations" by David A. Kopriva, Springer, 2009, section 3.5.3 (EvenOddDecomposition). Even though the experiments in the book say that the method is not efficient for N<20, it is more efficient in the context where the loop bounds are compiletime constants (templates).
 Template Parameters

dim  Space dimension in which this class is applied 
n_rows  Number of rows in the transformation matrix, which corresponds to the number of 1d shape functions in the usual tensor contraction setting 
n_columns  Number of columns in the transformation matrix, which corresponds to the number of 1d shape functions in the usual tensor contraction setting 
Number  Abstract number type for input and output arrays 
Number2  Abstract number type for coefficient arrays (defaults to same type as the input/output arrays); must implement operator* with Number and produce Number as an output to be a valid type 
Definition at line 1455 of file tensor_product_kernels.h.
template<int dim, int n_rows, int n_columns, typename Number , typename Number2 >
template<int direction, bool contract_over_rows, bool add, int type, bool one_line>
This function applies the tensor product kernel, corresponding to a multiplication of 1D stripes, along the given direction
of the tensor data in the input array. This function allows the in
and out
arrays to alias for the case n_rows == n_columns, i.e., it is safe to perform the contraction in place where in
and out
point to the same address. For the case n_rows != n_columns, the output is only correct if one_line
is set to true.
 Template Parameters

direction  Direction that is evaluated 
contract_over_rows  If true, the tensor contraction sums over the rows in the given shape_data array, otherwise it sums over the columns 
add  If true, the result is added to the output vector, else the computed values overwrite the content in the output 
type  Determines whether to use the symmetries appearing in shape values (type=0), shape gradients (type=1) or second derivatives (type=2, similar to type 0 but without two additional zero entries) 
one_line  If true, the kernel is only applied along a single 1D stripe within a dimdimensional tensor, not the full n_rows^dim points as in the false case. 
 Parameters

shape_data  Transformation matrix with n_rows rows and n_columns columns, stored in rowmajor format 
in  Pointer to the start of the input data vector 
out  Pointer to the start of the output data vector 
Definition at line 1628 of file tensor_product_kernels.h.