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.)