SPG_BP Solve the basis pursuit (BP) problem
[x, r, g, info] = spg_bp(A, b, options)
(IN) is an m-by-n matrix, explicit or an operator.
(IN) is an m-vector.
(IN) is a structure of options from spgSetParms
(OUT) is a solution of the problem
(OUT) is the residual, r = b - Ax
(OUT) is the gradient, g = -A'r
(OUT) is a structure with output information
SPG_BP is designed to solve the basis pursuit problem
(BP) minimize ||X||_1 subject to AX = B,
where A is an M-by-N matrix, B is an M-vector, and SIGMA is a nonnegative scalar. In all cases below, A can be an explicit M-by-N matrix or matrix-like object for which the operations A*x and A'*y are defined (i.e., matrix-vector multiplication with A and its adjoint.)
Also, A can be a function handle that points to a function with the signature
v = A(w,mode) which returns v = A *w if mode == 1; v = A'*w if mode == 2.
X = SPG_BP(A,B) solves the BP problem.
X = SPG_BP(A,B,OPTIONS) specifies options that are set using SPGSETPARMS.
[X,R,G,INFO] = SPG_BP(A,B,OPTIONS) additionally returns the residual R = B - A*X (which should be small), the objective gradient G = A'*R, and an INFO structure. (See SPGL1 for a description of this last output argument.)