Uniform Sampling of Some Quadrics
I recently encountered a problem in which I needed to uniformly sample vectors with positive values in \(\mathbb{R}^n \) that had unit \(L_1 \) norm, where the \(L_1 \) norm is\[ \lVert (x_1, x_2, \ldots, x_n)^T \rVert = |x_1| + |x_2| + \ldots + |x_n| \] The solution was actually quite straightforward: The isosurfaces of the \(L_1\) norm in \(\mathbb{R}^n\) look something like this, which each color corresponding to a particular isosurface:...