By Kardi Teknomo, PhD.
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MatrixSet
To derive the formulation in the
paper, we use a combination of both matrix and set operations. In contrast to
ordinary matrices in linear algebra whose elements are numbers or scalar values
(which we call matrixcount), it is necessary to create our own mathematical
concept of a matrixset which is a matrix whose elements are sets. We
use tilde on the top of a matrix to indicate matrixset, such as Flowset
matrix and ODset matrix. Operations on matrixset are similar to both
operations in matrix and set theory where the members in each matrix element
must be unique and the order of the elements in a set is not important. We also
extend the Hadamard multiplication to involve a matrixset and a binary matrix.
The Hadamard product between a matrix set and a binary matrix is computed by
multiplication of corresponding elements, resulting either in the original
element of the matrix set (if multiplied with 1) or an empty set (if multiplied
by 0). We have developed special numerical library of matrixset to serve the
purpose of this research.
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These tutorial is copyrighted.
Preferable reference for this tutorial is
Teknomo, Kardi. (2013) Relationship between Generalized Origin Destination and Flow Matrix – A Tutorial
http://people.revoledu.com/kardi/research/trajectory/od/
