The scaling produced by equilibrate is known as Hungarian scaling, and its computation involves solving a linear assignment problem. See, for example, the recent paper Max-Balanced Hungarian Scalings by Hook, Pestana, Tisseur, and Hogg. This matrix equilibration can improve conditioning and can be a useful preprocessing step both in computing incomplete LU preconditioners and in iterative solvers. The equilibrate function take as input a matrix A (dense or sparse) and returns a permutation matrix P and nonsingular diagonal matrices R and C such that R*P*A*C has diagonal entries of magnitude 1 and off-diagonal entries of magnitude at most 1. The problem arises in sparse matrix computations. What I want to do is to be able to mark a datapoint in the plot and then be able to toggle along the plotted curve (datapoints of) by using the arrows on the keyboard, as it have been possible in previous MATLAB versions. This problem can also be described as finding a minimum-weight matching in a weighted bipartite graph. I just downloaded the MATLAB 2019a version and I realized that the figure widow has a somewhat new interface. The matchpairs function solves the linear assignment problem, which requires each row of a matrix to be assigned to a column in such a way that the total cost of the assignments (given by the “sum of assigned elements” of the matrix) is minimized (or maximized).
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