ADD: new track message, Entity class and Position class

libs/geographiclib/include/GeographicLib/DST.hpp

@@ -0,0 +1,177 @@
+/**
+ * \file DST.hpp
+ * \brief Header for GeographicLib::DST class
+ *
+ * Copyright (c) Charles Karney (2022) <charles@karney.com> and licensed under
+ * the MIT/X11 License.  For more information, see
+ * https://geographiclib.sourceforge.io/
+ **********************************************************************/
+
+#if !defined(GEOGRAPHICLIB_DST_HPP)
+#define GEOGRAPHICLIB_DST_HPP 1
+
+#include <GeographicLib/Constants.hpp>
+
+#include <functional>
+#include <memory>
+
+/// \cond SKIP
+template<typename scalar_t>
+class kissfft;
+/// \endcond
+
+namespace GeographicLib {
+
+  /**
+   * \brief Discrete sine transforms
+   *
+   * This decomposes periodic functions \f$ f(\sigma) \f$ (period \f$ 2\pi \f$)
+   * which are odd about \f$ \sigma = 0 \f$ and even about \f$ \sigma = \frac12
+   * \pi \f$ into a Fourier series
+   * \f[
+   *   f(\sigma) = \sum_{l=0}^\infty F_l \sin\bigl((2l+1)\sigma\bigr).
+   * \f]
+   *
+   * The first \f$ N \f$ components of \f$ F_l \f$, for \f$0 \le l < N\f$ may
+   * be approximated by
+   * \f[
+   *   F_l = \frac2N \sum_{j=1}^{N}
+   *   p_j f(\sigma_j)  \sin\bigl((2l+1)\sigma_j\bigr),
+   * \f]
+   * where \f$ \sigma_j = j\pi/(2N) \f$ and \f$ p_j = \frac12 \f$ for \f$ j = N
+   * \f$ and \f$ 1 \f$ otherwise.  \f$ F_l \f$ is a discrete sine transform of
+   * type DST-III and may be conveniently computed using the fast Fourier
+   * transform, FFT; this is implemented with the DST::transform method.
+   *
+   * Having computed \f$ F_l \f$ based on \f$ N \f$ evaluations of \f$
+   * f(\sigma) \f$ at \f$ \sigma_j = j\pi/(2N) \f$, it is possible to
+   * refine these transform values and add another \f$ N \f$ coefficients by
+   * evaluating \f$ f(\sigma) \f$ at \f$ (j-\frac12)\pi/(2N) \f$; this is
+   * implemented with the DST::refine method.
+   *
+   * Here we compute FFTs using the kissfft package
+   * https://github.com/mborgerding/kissfft by Mark Borgerding.
+   *
+   * Example of use:
+   * \include example-DST.cpp
+   *
+   * \note The FFTW package https://www.fftw.org/ can also be used.  However
+   * this is a more complicated dependency, its CMake support is broken, and it
+   * doesn't work with mpreals (GEOGRAPHICLIB_PRECISION = 5).
+   **********************************************************************/
+
+  class DST {
+  private:
+    typedef Math::real real;
+    int _N;
+    typedef kissfft<real> fft_t;
+    std::shared_ptr<fft_t> _fft;
+    // Implement DST-III (centerp = false) or DST-IV (centerp = true)
+    void fft_transform(real data[], real F[], bool centerp) const;
+    // Add another N terms to F
+    void fft_transform2(real data[], real F[]) const;
+  public:
+    /**
+     * Constructor specifying the number of points to use.
+     *
+     * @param[in] N the number of points to use.
+     **********************************************************************/
+    GEOGRAPHICLIB_EXPORT DST(int N = 0);
+
+    /**
+     * Reset the given number of points.
+     *
+     * @param[in] N the number of points to use.
+     **********************************************************************/
+    void GEOGRAPHICLIB_EXPORT reset(int N);
+
+    /**
+     * Return the number of points.
+     *
+     * @return the number of points to use.
+     **********************************************************************/
+    int N() const { return _N; }
+
+    /**
+     * Determine first \e N terms in the Fourier series
+     *
+     * @param[in] f the function used for evaluation.
+     * @param[out] F  the first \e N coefficients of the Fourier series.
+     *
+     * The evaluates \f$ f(\sigma) \f$ at \f$ \sigma = (j + 1) \pi / (2 N) \f$
+     * for integer \f$ j \in [0, N) \f$.  \e F should be an array of length at
+     * least \e N.
+     **********************************************************************/
+    void GEOGRAPHICLIB_EXPORT transform(std::function<real(real)> f, real F[])
+      const;
+
+    /**
+     * Refine the Fourier series by doubling the number of points sampled
+     *
+     * @param[in] f the function used for evaluation.
+     * @param[inout] F on input the first \e N coefficents of the Fourier
+     *   series; on output the refined transform based on 2\e N points, i.e.,
+     *   the first 2\e N coefficents.
+     *
+     * The evaluates \f$ f(\sigma) \f$ at additional points \f$ \sigma = (j +
+     * \frac12) \pi / (2 N) \f$ for integer \f$ j \in [0, N) \f$, computes the
+     * DST-IV transform of these, and combines this with the input \e F to
+     * compute the 2\e N term DST-III discrete sine transform.  This is
+     * equivalent to calling transform with twice the value of \e N but is more
+     * efficient, given that the \e N term coefficients are already known.  See
+     * the example code above.
+     **********************************************************************/
+    void GEOGRAPHICLIB_EXPORT refine(std::function<real(real)> f, real F[])
+      const;
+
+    /**
+     * Evaluate the Fourier sum given the sine and cosine of the angle
+     *
+     * @param[in] sinx sin&sigma;.
+     * @param[in] cosx cos&sigma;.
+     * @param[in] F the array of Fourier coefficients.
+     * @param[in] N the number of Fourier coefficients.
+     * @return the value of the Fourier sum.
+     **********************************************************************/
+    static real GEOGRAPHICLIB_EXPORT eval(real sinx, real cosx,
+                                          const real F[], int N);
+
+    /**
+     * Evaluate the integral of Fourier sum given the sine and cosine of the
+     * angle
+     *
+     * @param[in] sinx sin&sigma;.
+     * @param[in] cosx cos&sigma;.
+     * @param[in] F the array of Fourier coefficients.
+     * @param[in] N the number of Fourier coefficients.
+     * @return the value of the integral.
+     *
+     * The constant of integration is chosen so that the integral is zero at
+     * \f$ \sigma = \frac12\pi \f$.
+     **********************************************************************/
+    static real GEOGRAPHICLIB_EXPORT integral(real sinx, real cosx,
+                                              const real F[], int N);
+
+    /**
+     * Evaluate the definite integral of Fourier sum given the sines and
+     * cosines of the angles at the endpoints.
+     *
+     * @param[in] sinx sin&sigma;<sub>1</sub>.
+     * @param[in] cosx cos&sigma;<sub>1</sub>.
+     * @param[in] siny sin&sigma;<sub>2</sub>.
+     * @param[in] cosy cos&sigma;<sub>2</sub>.
+     * @param[in] F the array of Fourier coefficients.
+     * @param[in] N the number of Fourier coefficients.
+     * @return the value of the integral.
+     *
+     * The integral is evaluated between limits &sigma;<sub>1</sub> and
+     * &sigma;<sub>2</sub>.
+     **********************************************************************/
+    static real GEOGRAPHICLIB_EXPORT integral(real sinx, real cosx,
+                                              real siny, real cosy,
+                                              const real F[], int N);
+  };
+
+} // namespace GeographicLib
+
+#endif  // GEOGRAPHICLIB_DST_HPP