L1TestPack has just been updated to version 1.1. With the help of Andreas Tillmann I enhanced this small gadget for issues related to ${\ell^1}$ minimization. New functions are

• Routines to directly calculate a source element for a given matrix ${A}$ and a vector ${x^\dagger}$, that is, calculate a vector ${y}$ such that

$\displaystyle A^* y \in\partial\|x^\dagger\|_1.$

The existence of such a vector ${y}$ ensures that the minimization problem (the Basis Pursuit problem)

$\displaystyle \min_x \|x\|_1\ \text{ s.t. }\ Ax = Ax^\dagger$

has the unique solution ${x^\dagger}$ (is other words: ${x^\dagger}$ is recovered exactly). This is particularly helpful is you are interested in unique solutions for Basis pursuit without posing strong conditions which even imply ${\ell^0}$${\ell^1}$-equivalence.

• Routines related to RIP constants, the ERC coefficient of Joel Tropp and the mutual coherence.
• An implementation of the heuristic support evaluation HSE (also described in my previous post). (By the way: We were tempted to call this device “support evaluation routine” with acronym SuppER but abandoned this idea.)