sparse.relaxation.basis_pursuit.basis_pursuit_admm¶
- sparse.relaxation.basis_pursuit.basis_pursuit_admm(A, b, lambd, tol=0.0001, max_iters=100, cholesky=False)[source]¶
Basis Pursuit solver for the \(Q_1^\epsilon\) problem
\[\min_x \frac{1}{2} \left|\left| \boldsymbol{A}\vec{x} - \vec{b} \right|\right|_2^2 + \lambda \|x\|_1\]via the alternating direction method of multipliers (ADMM).
- Parameters
- A(N, M) np.ndarray
The input weight matrix \(\boldsymbol{A}\).
- b(N,) np.ndarray
The right side of the equation \(\boldsymbol{A}\vec{x} = \vec{b}\).
- lambdfloat
The soft-shrinkage threshold \(\lambda\), controls the sparsity of \(\vec{x}\).
- tolfloat
The accuracy tolerance of ADMM.
- max_itersint
Run for at most max_iters iterations.
- choleskybool
Whether to use the Cholesky factorization (slow, but stable) or the inverse (fast, but might be unstable) of a matrix.
- Returns
- v(M,) np.ndarray
The solution vector \(\vec{x}\).