Method on @infsup: dot (X, Y)

Method on @infsup: dot (X, Y, DIM)

Compute the dot product of two interval vectors.

If X and Y are arrays, calculate the dot products along the first non-singleton dimension. If the optional argument DIM is given, calculate the dot products along this dimension.

Conceptually this is equivalent to sum (X .* Y) but it is computed in such a way that no intermediate round-off errors are introduced.

Broadcasting is performed along all dimensions except if X and Y are both vectors and DIM is not specified, in which case they are aligned along dimension 1.

Accuracy: The result is a tight enclosure.

dot ([infsup(1), 2, 3], [infsup(2), 3, 4])
  ⇒ ans = [20]

dot (infsup ([realmax; realmin; realmax]), [1; -1; -1], 1)
  ⇒ ans ⊂ [-2.2251e-308, -2.225e-308]

See also: @infsup/plus, @infsup/sum, @infsup/times, @infsup/sumabs, @infsup/sumsq.

Package: interval