Tensor Operations

In 4.6 several tensor operations have been described. The numerical tensor calculus requires the practical realisation of these operations. In this chapter we describe the performance and arithmetical cost of the operations for the different formats. The discussed operations are the addition in Section 13.1, evaluation of tensor entries in Section 13.2, the scalar product and partial scalar product in Section 13.3, the change of bases in Section 13.4, general binary operations in Section 13.5, Hadamard product in Section 13.6, convolution of tensors in Section 13.7, matrixmatrix multiplication in Section 13.8, and matrix-vector multiplication in Section 13.9. Section 13.10 is devoted to special functions applied to tensors. In the last Section 13.11 we comment on the operations required for the treatment of Hartree– Fock and Kohn-Sham applications in quantum chemistry. In connection with the tensorisation discussed in Chapter 14, further operations and their cost will be discussed.