gradientAt IPFunctional IPFunctional m_element m_element_index m_grid operator= valueAt ~IPFunctional

gradientAt() template<class IMVecType > virtual void pism::inverse::IPFunctional< IMVecType >::gradientAt ( IMVecType &  x, IMVecType &  gradient  ) pure virtual Computes the gradient of the functional at the vector x. On an \(m\times n\) Grid, an array::Array \(x\) with \(d\) degrees of freedom will be \(d m n\)-dimensional with components \(x_i\). The gradient computed here is the vector of directional derivatives \(\nabla J\) of the functional \(J\) with respect to \(x\). Concretely, the \(i^{\rm th}\) component of \(\nabla J\) is \[ \nabla J_i = \frac{\partial}{\partial x_i} J(x). \] This vector is returned as gradient. Implemented in pism::inverse::IPMeanSquareFunctional2V, pism::inverse::IPLogRelativeFunctional, pism::inverse::IPLogRatioFunctional, pism::inverse::IP_L2NormFunctional2V, pism::inverse::IPTotalVariationFunctional2S, pism::inverse::IPMeanSquareFunctional2S, pism::inverse::IPGroundedIceH1NormFunctional2S, pism::inverse::IP_L2NormFunctional2S, and pism::inverse::IP_H1NormFunctional2S. Referenced by pism::inverse::IP_SSATaucTaoTikhonovProblemLCL::evaluateObjectiveAndGradient(), and pism::inverse::IPInnerProductFunctional< IMVecType >::interior_product().