Lemma is an Electromagnetics API
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CubicSplineInterpolator.h 5.1KB

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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. \brief Real 1D Natural cubic spline interpolator.
  40. \details Splines are fit between knots \f$j\f$ according to the forulae
  41. \f[ S_j(x) = a_j + b_j(x - x_j) + c_j(x-x_j)^2 + d_j(x-x_y)^3 \f]
  42. The spline must satisfy the following conditions
  43. \f{eqnarray} {
  44. S_i(x_i) & = & y_i = S_{i-1}(x_i), i = 1,..., n-1 \\
  45. S'_i(x_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''_0(x_0) & = & S''_{n-1}(x_n) = 0
  48. \f}
  49. */
  50. class CubicSplineInterpolator : public LemmaObject {
  51. friend std::ostream &operator<<(std::ostream &stream,
  52. const CubicSplineInterpolator &ob);
  53. public:
  54. // ==================== LIFECYCLE =======================
  55. /**
  56. * @copybrief LemmaObject::New()
  57. * @copydetails LemmaObject::New()
  58. */
  59. static CubicSplineInterpolator* New();
  60. /**
  61. * @copybrief LemmaObject::Delete()
  62. * @copydetails LemmaObject::Delete()
  63. */
  64. void Delete();
  65. // ==================== OPERATORS =======================
  66. // ==================== OPERATIONS =======================
  67. /** Sets the knots to use for interpolation.
  68. @param[in] x are the absissa values
  69. @param[in] y are the ordinate values
  70. */
  71. void SetKnots(const VectorXr& x, const VectorXr& y);
  72. /** Resets the knots to use for interpolation, when abscissa values haven't changed.
  73. @param[in] y are the ordinate values
  74. */
  75. void ResetKnotOrdinate( const VectorXr& y );
  76. /** Interpolate a monotonically increasing ordered set.
  77. @param[in] x are the interpolation abscissa points
  78. @return the ordinate values at x
  79. */
  80. VectorXr InterpolateOrderedSet(const VectorXr& x);
  81. /** integrates the spline from x0 to x1. Uses composite Simpson's rule and n is the number of segments
  82. * @param[in] x0 is left argument
  83. * @param[in] x1 is right argument
  84. * @param[in] n is the number of points, must be even
  85. */
  86. Real Integrate(const Real& x0, const Real& x1, const int& n);
  87. /** integrates using cubic spline values. Taken from AMRIRA P223F project code Leroi, which in turn was based on
  88. This is a modification of the FUNCTION PPVALU in the book
  89. "A PRACTICAL GUIDE TO SPLINES" by C. DE BOOR
  90. */
  91. Real Integrate(const Real& x0, const Real& x1);
  92. /** @returns the know abscissa values
  93. */
  94. VectorXr GetKnotAbscissa();
  95. /** @returns the know abscissa values
  96. */
  97. VectorXr GetKnotOrdinate();
  98. /** Interpolation at a single point.
  99. @param[in] x is the interpolation abscissa point
  100. @param[in] i is an optional index to start searching at. Defaults to zero
  101. @return the ordinate value at x
  102. */
  103. Real Interpolate(const Real& x, int& i);
  104. /** Interpolation at a single point.
  105. @param[in] x is the interpolation abscissa point
  106. @return the ordinate value at x
  107. */
  108. Real Interpolate(const Real& x);
  109. // ==================== ACCESS =======================
  110. // ==================== INQUIRY =======================
  111. protected:
  112. // ==================== LIFECYCLE =======================
  113. /** Default protected constructor, use New */
  114. CubicSplineInterpolator (const std::string& name);
  115. /** Default protected destructor, use Delete */
  116. ~CubicSplineInterpolator ();
  117. /**
  118. * @copybrief LemmaObject::Release()
  119. * @copydetails LemmaObject::Release()
  120. */
  121. void Release();
  122. // ==================== OPERATIONS =======================
  123. /**
  124. Performs spline fitting.
  125. */
  126. //void Spline() {
  127. // }
  128. /** Finds the interval of knots in spline to use for integration.
  129. */
  130. int Interval(const Real& x);
  131. private:
  132. SplineSet Spline;
  133. int ilo;
  134. int mflag;
  135. // ==================== DATA MEMBERS =========================
  136. }; // ----- end of class CubicSplineInterpolator -----
  137. } // ----- end of Lemma name -----
  138. #endif // ----- #ifndef CUBICSPLINEINTERPOLATOR_INC -----