NumA/interpolation/Chebyshev.h

0001 /**
0002  * @file Chebyshev.h
0003  * @author Nabil Chouika (Irfu/SPhN - CEA Saclay)
0004  * @date 22 mars 2016
0005  * @version 1.0
0006  */
0007
0008 #ifndef CHEBYSHEV_H_
0009 #define CHEBYSHEV_H_
0010
0011 #include "../linear_algebra/matrix/MatrixD.h"
0012 #include "../linear_algebra/vector/VectorD.h"
0013
0014 namespace NumA {
0015
0016 /**
0017  * @class Chebyshev
0018  * @brief Chebyshev expansion class.
0019  *
0020  * Interpolation \f$ f(x) = \sum_{i=0}^{N-1} c_i T_i \left( x \right) \f$ for \f$ x \in \left[ -1, 1 \right] \f$ ,
0021  * where \f$ N \f$ is the order of the expansion.
0022  *
0023  * TODO: \f$ x \in \f$ any interval.
0024  */
0025
0026 class Chebyshev {
0027 public:
0028     /**
0029      * Default Constructor with the order N of the expansion.
0030      * @param N Order of the expansion.
0031      */
0032     Chebyshev(unsigned int N = 50);
0033     /**
0034      * Default destructor.
0035      */
0036     virtual ~Chebyshev();
0037
0038     /**
0039      * Get the order N of the expansion.
0040      * @return N unsigned int
0041      */
0042     unsigned int getN() const;
0043     /**
0044      * Set the order N of the expansion/
0045      * @param n unsigned int
0046      */
0047     void setN(unsigned int n);
0048
0049     const NumA::VectorD& getRoots() const;
0050
0051     /**
0052      * Interpolation matrix.
0053      * @return Matrix which gives a vector of the coefficients for the expansion when applied to a vector of values on Chebyshev nodes.
0054      */
0055     const NumA::MatrixD& getValuesToCoeffsMatrix() const;
0056     /**
0057      *
0058      * @return Matrix which gives a vector of the values on Chebyshev nodes when applied to a vector of coefficients for the expansion.
0059      */
0060     const NumA::MatrixD& getCoeffsToValuesMatrix() const;
0061
0062     /**
0063      *
0064      * @param points Points where to evaluate the expansion.
0065      * @return Matrix which gives a vector of the values on given points when applied to a vector of coefficients for the expansion.
0066      */
0067     NumA::MatrixD getCoeffsToValuesMatrix(const NumA::VectorD& points) const;
0068     /**
0069      *
0070      * @param x Point where the expansion is evaluated.
0071      * @return Vector which gives the Chebyshev expansion on x when a scalar product is taken with a vector of coefficients for the expansion.
0072      */
0073     NumA::VectorD getCoeffsToValueVector(double x) const;
0074
0075     /**
0076      * Interpolation matrix.
0077      * @param points Points where to evaluate the expansion.
0078      * @return Matrix which gives a vector of values on given points when applied to a vector of values on Chebyshev nodes.
0079      */
0080     NumA::MatrixD getValuesToValuesMatrix(const NumA::VectorD& points) const;
0081     /**
0082      *
0083      * @param x Point where the expansion is evaluated.
0084      * @return Vector which gives the Chebyshev expansion on x when a scalar product is taken with a vector of values on Chebyshev nodes.
0085      */
0086     NumA::VectorD getValuesToValueVector(double x) const;
0087
0088     /**
0089      * Evaluate the Chebyshev expansion.
0090      * @param coeffs Coefficients \f$ c_i \f$ of the expansion.
0091      * @param x Point where the expansion is evaluated.
0092      * @return Chebyshev expansion: \sum_{i=0}^{N-1} c_i T_i \left( x \right) \f$.
0093      */
0094     double evaluateExpansion(const NumA::VectorD& coeffs, double x) const;
0095
0096     static double T(unsigned int i, double x); ///< \f$ T_i \left( x \right) = \cos \left( i \arccos \left( x \right) \right) \f$.
0097
0098 private:
0099     unsigned int m_N; ///< Order of the expansion.
0100     NumA::VectorD m_roots; ///< Roots of T_N, i.e. the nodes of the expansion.
0101     NumA::MatrixD m_valuesToCoeffsMatrix; ///< Transformation matrix from the values on nodes to the coefficients of the expansion.
0102     NumA::MatrixD m_coeffsToValuesMatrix; ///< Transformation matrix from the coefficients of the expansion to the values on nodes.
0103
0104     void initRoots(); ///< Initialize the roots.
0105     void initValuesToCoeffsMatrix(); ///< Initialize the interpolation matrix.
0106 };
0107
0108 } /* namespace NumA */
0109
0110 #endif /* CHEBYSHEV_H_ */