Outer product algorithm

Figure 8. Pictorial representation of the outer product matrix multiplication algorithm. ...

A general way of exploiting this sparseness in both the gradient and the Hessian construction involves the use of outer product algorithms to perform the matrix element assembly. In the case of the matrix multiplications required in the F matrix construction, this simply means that the innermost DO loop is over X in Eq. (260). (If t were the innermost DO loop, the result would be a series of dot products or an inner product algorithm.) When an outer product algorithm is used, the magnitude of the density matrix elements may be tested and the innermost DO loop is only performed for non-zero elements. (In the case of Hessian matrix construction, the test may occur outside of the two... 

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