The DO Loop
Statistical programming in SAS with an emphasis on SAS/IML programs
Given a set of N points in k-dimensional space, can you find the location that minimizes the sum of the distances to the points? The location that minimizes the distances is called the geometric median of the points. For univariate data, the "points" are merely a set of numbers $$\{p_1,
While writing an article about labeling a polygon by using the centroid, I almost made a false claim about the centroid. I almost claimed that that the centroid is the point in a polygon that minimizes the sum of the distances to the vertices. It is not. The point that
A colleague asked how to compute the barycentric coordinates of a point inside a triangle. Given a triangle in the plane with vertices p1, p2, and p3, every point in the triangle can be represented as a convex combination of the vertices: c1*p1 + c2*p2 + c3*p3, where c1,c2,c3 ≥
Part of the power of the SAS ODS system is the ability to visualize data by using ODS templates. An ODS template describes how to render data as a table or as a graph. A lot of papers and documentation have been written about how to define a custom template
While writing an article about Toeplitz matrices, I saw an interesting fact about the eigenvalues of tridiagonal Toeplitz matrices on Nick Higham's blog. Recall that a Toeplitz matrix is a banded matrix that is constant along each diagonal. A tridiagonal Toeplitz matrix is zero except for the main diagonal, the
A Toeplitz matrix is a banded matrix. You can construct it by specifying the parameters that are constant along each diagonal, including sub- and super-diagonals. For a square N x N matrix, there is one main diagonal, N-1 sub-diagonals, and N-1 super-diagonals, for a total of 2N-1 parameters. In statistics and applied