%SPGL1　Solve basis pursuit, basis pursuit denoise, and LASSO
%
% [x, r, g, info] = spgl1(A, b, tau, sigma, x0, options)
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% Solve the basis pursuit denoise (BPDN) problem
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% (BPDN)　 minimize　||x||_1　subj to　||Ax-b||_2 <= sigma,
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% or the l1-regularized least-squares problem
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% (LASSO)　minimize　||Ax-b||_2　subj to　||x||_1 <= tau.
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% INPUTS
% ======
% A　　　　is an m-by-n matrix, explicit or an operator.
%　　　　　If A is a function, then it must have the signature
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%　　　　　y = A(x,mode)　 if mode == 1 then y = A x　(y is m-by-1);
%　　　　　　　　　　　　　if mode == 2 then y = A'x　(y is n-by-1).
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% b　　　　is an m-vector.
% tau　　　is a nonnegative scalar; see (LASSO).
% sigma　　if sigma != inf or != [], then spgl1 will launch into a
%　　　　　root-finding mode to find the tau above that solves (BPDN).
%　　　　　In this case, it's STRONGLY recommended that tau = 0.
% x0　　　 is an n-vector estimate of the solution (possibly all
%　　　　　zeros). If x0 = [], then SPGL1 determines the length n via
%　　　　　n = length( A'b ) and sets　x0 = zeros(n,1).
% options　is a structure of options from spgSetParms. Any unset options
%　　　　　are set to their default value; set options=[] to use all
%　　　　　default values.