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80 lines
3.1 KiB
80 lines
3.1 KiB
2 years ago
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#ifndef MEDUSA_BITS_APPROXIMATIONS_WLSAPPROXIMANT_FWD_HPP_
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#define MEDUSA_BITS_APPROXIMATIONS_WLSAPPROXIMANT_FWD_HPP_
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/**
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* @file
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* Declaration of the function, obtained by WLS approximation.
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*
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* @example test/approximations/WLSApproximant_test.cpp
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*/
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#include <medusa/Config.hpp>
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#include <Eigen/Core>
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namespace mm {
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/**
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* Class representing the function that is a WLS approximant using some
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* basis function over some points. These must satisfy the @ref basis-concept.
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* @note This class does not compute the approximant, that is done by WLS::getApproximant.
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* @sa WLS
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* @tparam basis_t Basis function type.
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*
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* Usage example:
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* @snippet test/approximations/WLSApproximant_test.cpp WLSApproximant usage example
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*/
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template <typename basis_t>
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class WLSApproximant {
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public:
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typedef typename basis_t::scalar_t scalar_t; ///< Scalar type.
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typedef typename basis_t::vector_t vector_t; ///< Vector type.
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private:
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basis_t basis_; ///< Basis.
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vector_t point_; ///< Center point.
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std::vector<vector_t> support_; ///< Local scaled stencil points.
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scalar_t scale_; ///< Scale.
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Eigen::Matrix<scalar_t, Eigen::Dynamic, 1> coefficients_; ///< Coefficients (for scaled fn.)
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scalar_t residual_; ///< Store residual of the approximation.
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public:
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/**
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* Construct a WLS approximant with known coefficients. The approximant is of the form
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* @f[ u(p) = \sum_{i=1}^m \alpha_i b_i\left(\frac{p - p_c}{s}\right), @f]
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* where @f$b_i@f$ may depend on the stencil nodes (e.g. RBF-s).
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* @param basis Basis functions @f$b_i@f$ to be used, must satisfy the @ref basis-concept.
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* @param point Center point @f$p_c@f$ of the WLS approximation.
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* @param support Nonscaled stencil of the WLS approximation.
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* @param scale Scale @f$s@f$ used in WLS computation, see @ref scale-concept.
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* @param coefficients Coefficients @f$\alpha_i@f$ of the approximation.
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* @param residual The resudial of the weighted least squares approximation. If 0, this
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* function is an interpolant.
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*/
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WLSApproximant(const basis_t& basis, const vector_t& point,
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const std::vector<vector_t>& support, scalar_t scale,
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const Eigen::Matrix<scalar_t, Eigen::Dynamic, 1>& coefficients,
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scalar_t residual = NaN);
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/// Evaluate the approximant at given `point`.
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scalar_t operator()(const vector_t& point) const;
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/// Evaluate an operator applied to approximant at given `point`.
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template <typename operator_t>
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scalar_t operator()(const vector_t& point, const operator_t& op) const;
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/// Get the basis functions.
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const basis_t& basis() const { return basis_; }
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/// Get the center point.
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const vector_t& point() const { return point_; }
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/// Get the scale.
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scalar_t scale() const { return scale_; }
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/// Get the coefficient vector.
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const Eigen::Matrix<scalar_t, Eigen::Dynamic, 1>& coefficients() const { return coefficients_; }
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/// Get the residual.
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scalar_t residual() const { return residual_; }
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};
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} // namespace mm
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#endif // MEDUSA_BITS_APPROXIMATIONS_WLSAPPROXIMANT_FWD_HPP_
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