apply_jacobian_design apply_jacobian_design apply_jacobian_design apply_jacobian_design_transpose apply_jacobian_design_transpose apply_jacobian_design_transpose apply_linearization apply_linearization_transpose assemble_jacobian_state assemble_residual assemble_residual DesignVec DesignVecGhosted get_da init IP_SSATaucForwardProblem linearize_at m_du_global m_du_local m_dzeta_local m_element m_element_index m_fixed_tauc_locations m_J_state m_ksp m_reason m_rebuild_J_state m_tauc_copy m_tauc_param m_velocity_shared m_zeta set_design set_tauc_fixed_locations solution StateVec StateVec1 tauc_param ~IP_SSATaucForwardProblem

apply_linearization_transpose() void pism::inverse::IP_SSATaucForwardProblem::apply_linearization_transpose ( array::Vector &  du, array::Scalar &  dzeta  ) virtual Applies the transpose of the linearization of the forward map (i.e. the transpose of the reduced gradient \(DF\) described in the class-level documentation.) As described previously, \[ Df = J_{\rm State}^{-1} J_{\rm Design}. \] so \[ Df^t = J_{\rm Design}^t \; (J_{\rm State}^t)^{-1} . \] Applying the transpose of the linearization then involves the solution of a linear equation. The matrices \(J_{\rm State}\) and \(J_{\rm Design}\) both depend on the value of the design variable \(\zeta\) and the value of the corresponding state variable \(u=F(\zeta)\). These are established by first calling linearize_at. Parameters [in] du Perturbation of the state variable [out] dzeta Computed corresponding perturbation of the design variable; ghosts (if present) are updated. Definition at line 580 of file IP_SSATaucForwardProblem.cc. References apply_jacobian_design_transpose(), pism::array::Array2D< T >::array(), assemble_jacobian_state(), pism::array::Array2D< T >::copy_from(), pism::fem::DirichletData_Vector::fix_residual_homogeneous(), pism::RuntimeError::formatted(), pism::stressbalance::SSAFEM::m_bc_mask, pism::stressbalance::SSAFEM::m_bc_values, pism::stressbalance::SSAFEM::m_dirichletScale, m_du_global, m_J_state, m_ksp, pism::Component::m_log, m_rebuild_J_state, pism::stressbalance::ShallowStressBalance::m_velocity, PISM_CHK, PISM_ERROR_LOCATION, pism::array::Array::scale(), pism::array::Array::stencil_width(), pism::array::Array::update_ghosts(), and pism::array::Array::vec(). Referenced by pism::inverse::IP_SSATaucTikhonovGNSolver::apply_GN(), pism::inverse::IP_SSATaucTikhonovGNSolver::assemble_GN_rhs(), and pism::inverse::IP_SSATaucTikhonovGNSolver::evaluate_objective_and_gradient().