- pylops.optimization.sparsity.spgl1(Op, y, x0=None, SOp=None, tau=0.0, sigma=0.0, show=False, **kwargs_spgl1)¶
Spectral Projected-Gradient for L1 norm.
Solve a constrained system of equations given the operator
Opand a sparsyfing transform
SOpaiming to retrive a model that is sparse in the sparsyfing domain.
Operator to invert
Non-negative LASSO scalar. If different from
0, SPGL1 will solve LASSO problem
BPDN scalar. If different from
0, SPGL1 will solve BPDN problem
Display iterations log
Arbitrary keyword arguments for
Inverted model in original domain.
Inverted model in sparse domain.
Dictionary with the following information:
tau, final value of tau (see sigma above)
rnorm, two-norm of the optimal residual
rgap, relative duality gap (an optimality measure)
gnorm, Lagrange multiplier of (LASSO)
stat, final status of solver
1: found a BPDN solution,
2: found a BP solution; exit based on small gradient,
3: found a BP solution; exit based on small residual,
4: found a LASSO solution,
5: error, too many iterations,
6: error, linesearch failed,
7: error, found suboptimal BP solution,
8: error, too many matrix-vector products.
niters, number of iterations
nProdA, number of multiplications with A
nProdAt, number of multiplications with A’
n_newton, number of Newton steps
time_project, projection time (seconds)
time_matprod, matrix-vector multiplications time (seconds)
time_total, total solution time (seconds)
niters_lsqr, number of lsqr iterations (if
xnorm1, L1-norm model solution history through iterations
rnorm2, L2-norm residual history through iterations
lambdaa, Lagrange multiplier history through iterations
spgl1library is not installed