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 design_param DesignVec DesignVecGhosted get_da init IP_SSAHardavForwardProblem linearize_at m_design_param m_du_global m_du_local m_dzeta_local m_element m_element_index m_fixed_design_locations m_hardav m_J_state m_ksp m_reason m_rebuild_J_state m_stencil_width m_velocity_shared m_zeta set_design set_design_fixed_locations solution StateVec StateVec1 ~IP_SSAHardavForwardProblem

apply_linearization_transpose() void pism::inverse::IP_SSAHardavForwardProblem::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 631 of file IP_SSAHardavForwardProblem.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().