Actual source code: brgn.h

      1: /*
      2: Context for Bounded Regularized Gauss-Newton algorithm.
      3: Extended with L1-regularizer with a linear transformation matrix D:
      4: 0.5*||Ax-b||^2 + lambda*||D*x||_1
      5: When D is an identity matrix, we have the classic lasso, aka basis pursuit denoising in compressive sensing problem.
      6: */

      8: #pragma once

     10: #include <../src/tao/bound/impls/bnk/bnk.h>
     11: #include <petsc/private/taoimpl.h>

     13: #define BRGN_REGULARIZATION_USER   0
     14: #define BRGN_REGULARIZATION_L2PROX 1
     15: #define BRGN_REGULARIZATION_L2PURE 2
     16: #define BRGN_REGULARIZATION_L1DICT 3
     17: #define BRGN_REGULARIZATION_LM     4
     18: #define BRGN_REGULARIZATION_TYPES  5

     20: typedef struct {
     21:   PetscErrorCode (*regularizerobjandgrad)(Tao, Vec, PetscReal *, Vec, void *);
     22:   PetscErrorCode (*regularizerhessian)(Tao, Vec, Mat, void *);
     23:   void                     *reg_obj_ctx;
     24:   void                     *reg_hess_ctx;
     25:   Mat                       H, Hreg, D;                             /* Hessian, Hessian for regulization part, and Dictionary matrix have size N*N, and K*N respectively. (Jacobian M*N not used here) */
     26:   Vec                       x_old, x_work, r_work, diag, y, y_work; /* x, r=J*x, and y=D*x have size N, M, and K respectively. */
     27:   Vec                       damping;                                /* Optional diagonal damping matrix. */
     28:   Tao                       subsolver, parent;
     29:   PetscReal                 lambda, epsilon, fc_old;                      /* lambda is regularizer weight for both L2-norm Gaussian-Newton and L1-norm, ||x||_1 is approximated with sum(sqrt(x.^2+epsilon^2)-epsilon)*/
     30:   PetscReal                 downhill_lambda_change, uphill_lambda_change; /* With the lm regularizer lambda diag(J^T J),
     31:                                                                  lambda = downhill_lambda_change * lambda on steps that decrease the objective.
     32:                                                                  lambda = uphill_lambda_change * lambda on steps that increase the objective. */
     33:   TaoBRGNRegularizationType reg_type;
     34:   PetscBool                 mat_explicit;
     35: } TAO_BRGN;