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CubicSplineInterpolator.h 5.8KB

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  1. /* This file is part of Lemma, a geophysical modelling and inversion API.
  2. * More information is available at http://lemmasoftware.org
  3. */
  4. /* This Source Code Form is subject to the terms of the Mozilla Public
  5. * License, v. 2.0. If a copy of the MPL was not distributed with this
  6. * file, You can obtain one at http://mozilla.org/MPL/2.0/.
  7. */
  8. /**
  9. * @file
  10. * @date 09/25/2013 08:20:14 AM
  11. * @version $Id$
  12. * @author Trevor Irons (ti)
  13. * @email Trevor.Irons@lemmasoftware.org
  14. * @copyright Copyright (c) 2013,2018 Trevor Irons
  15. */
  16. #ifndef CUBICSPLINEINTERPOLATOR_INC
  17. #define CUBICSPLINEINTERPOLATOR_INC
  18. #include "LemmaObject.h"
  19. namespace Lemma {
  20. /**
  21. * \brief Simple struct to hold spline terms
  22. * \details This struct holds the actual knot and spline interpolation terms.
  23. */
  24. struct SplineSet{
  25. VectorXr a;
  26. VectorXr b;
  27. VectorXr c;
  28. VectorXr d;
  29. VectorXr x;
  30. SplineSet( ) {
  31. }
  32. SplineSet(const Index& n) {
  33. a = VectorXr::Zero(n+1);
  34. b = VectorXr::Zero(n);
  35. c = VectorXr::Zero(n+1);
  36. d = VectorXr::Zero(n);
  37. x = VectorXr::Zero(n+1);
  38. }
  39. };
  40. /**
  41. * \ingroup LemmaCore
  42. * \brief Real 1D Natural cubic spline interpolator.
  43. * \details Splines are fit between knots \f$j\f$ according to the forulae
  44. * \f[ S_j(x) = a_j + b_j(x - x_j) + c_j(x-x_j)^2 + d_j(x-x_y)^3 \f]
  45. * The spline must satisfy the following conditions
  46. * \f{eqnarray} {
  47. * S_i(x_i) & = & y_i = S_{i-1}(x_i), i = 1,..., n-1 \\
  48. * S'_i(x_i) & = & S'_{i-1}(x_i), i = 1,..., n-1 \\
  49. * S''_i(x_i) & = & S''_{i-1}(x_i), i = 1,..., n-1 \\
  50. * S''_0(x_0) & = & S''_{n-1}(x_n) = 0
  51. * \f}
  52. */
  53. class CubicSplineInterpolator : public LemmaObject {
  54. friend std::ostream &operator<<(std::ostream &stream,
  55. const CubicSplineInterpolator& ob);
  56. //struct ctor_key {};
  57. public:
  58. // ==================== LIFECYCLE =======================
  59. /** Default constructor */
  60. explicit CubicSplineInterpolator ( const ctor_key& );
  61. /** DeSerializing constructor, locked use factory DeSerialize method*/
  62. CubicSplineInterpolator ( const YAML::Node& node, const ctor_key& );
  63. /** Destructor use smart pointers to auto delete */
  64. virtual ~CubicSplineInterpolator ();
  65. /**
  66. * Factory method for generating concrete class.
  67. * @return a std::shared_ptr of type CubicSplineInterpolator
  68. */
  69. static std::shared_ptr<CubicSplineInterpolator> NewSP();
  70. /**
  71. * Uses YAML to serialize this object.
  72. * @return a YAML::Node
  73. */
  74. virtual YAML::Node Serialize() const;
  75. /**
  76. * Constructs an object from a YAML::Node.
  77. */
  78. static std::shared_ptr< CubicSplineInterpolator > DeSerialize(const YAML::Node& node);
  79. // ==================== OPERATORS =======================
  80. // ==================== OPERATIONS =======================
  81. /** Sets the knots to use for interpolation.
  82. @param[in] x are the absissa values
  83. @param[in] y are the ordinate values
  84. */
  85. void SetKnots(const VectorXr& x, const VectorXr& y);
  86. /** Resets the knots to use for interpolation, when abscissa values haven't changed.
  87. @param[in] y are the ordinate values
  88. */
  89. void ResetKnotOrdinate( const VectorXr& y );
  90. /** Interpolate a monotonically increasing ordered set.
  91. @param[in] x are the interpolation abscissa points
  92. @return the ordinate values at x
  93. */
  94. VectorXr InterpolateOrderedSet(const VectorXr& x);
  95. /** integrates the spline from x0 to x1. Uses composite Simpson's rule and n is the number of segments
  96. * @param[in] x0 is left argument
  97. * @param[in] x1 is right argument
  98. * @param[in] n is the number of points, must be even
  99. */
  100. Real Integrate(const Real& x0, const Real& x1, const int& n);
  101. /** integrates using cubic spline values. Taken from AMRIRA P223F project code Leroi, which in turn was based on
  102. This is a modification of the FUNCTION PPVALU in the book
  103. "A PRACTICAL GUIDE TO SPLINES" by C. DE BOOR
  104. */
  105. Real Integrate(const Real& x0, const Real& x1);
  106. /** @returns the know abscissa values
  107. */
  108. VectorXr GetKnotAbscissa();
  109. /** @returns the know abscissa values
  110. */
  111. VectorXr GetKnotOrdinate();
  112. /** Interpolation at a single point.
  113. @param[in] x is the interpolation abscissa point
  114. @param[in] i is an optional index to start searching at. Defaults to zero
  115. @return the ordinate value at x
  116. */
  117. Real Interpolate(const Real& x, int& i);
  118. /** Interpolation at a single point.
  119. @param[in] x is the interpolation abscissa point
  120. @return the ordinate value at x
  121. */
  122. Real Interpolate(const Real& x);
  123. // ==================== ACCESS =======================
  124. // ==================== INQUIRY =======================
  125. /** Returns the name of the underlying class, similiar to Python's type */
  126. virtual inline std::string GetName() const {
  127. return CName;
  128. }
  129. protected:
  130. // ==================== OPERATIONS =======================
  131. /** Finds the interval of knots in spline to use for integration.
  132. */
  133. Index Interval(const Real& x);
  134. private:
  135. /** Copy */
  136. CubicSplineInterpolator( const CubicSplineInterpolator& ) = delete;
  137. /** ASCII string representation of the class name */
  138. static constexpr auto CName = "CubicSplineInterpolator";
  139. SplineSet Spline;
  140. Index ilo;
  141. int mflag;
  142. // ==================== DATA MEMBERS =========================
  143. }; // ----- end of class CubicSplineInterpolator -----
  144. } // ----- end of Lemma name -----
  145. #endif // ----- #ifndef CUBICSPLINEINTERPOLATOR_INC -----
  146. /* vim: set tabstop=4 expandtab: */
  147. /* vim: set filetype=cpp syntax=cpp.doxygen: */