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CubicSplineInterpolator.h 5.7KB

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