This file is indexed.

/usr/include/GeographicLib/SphericalHarmonic1.hpp is in libgeographic-dev 1.49-2.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
/**
 * \file SphericalHarmonic1.hpp
 * \brief Header for GeographicLib::SphericalHarmonic1 class
 *
 * Copyright (c) Charles Karney (2011) <charles@karney.com> and licensed under
 * the MIT/X11 License.  For more information, see
 * https://geographiclib.sourceforge.io/
 **********************************************************************/

#if !defined(GEOGRAPHICLIB_SPHERICALHARMONIC1_HPP)
#define GEOGRAPHICLIB_SPHERICALHARMONIC1_HPP 1

#include <vector>
#include <GeographicLib/Constants.hpp>
#include <GeographicLib/SphericalEngine.hpp>
#include <GeographicLib/CircularEngine.hpp>

namespace GeographicLib {

  /**
   * \brief Spherical harmonic series with a correction to the coefficients
   *
   * This classes is similar to SphericalHarmonic, except that the coefficients
   * <i>C</i><sub><i>nm</i></sub> are replaced by
   * <i>C</i><sub><i>nm</i></sub> + \e tau <i>C'</i><sub><i>nm</i></sub> (and
   * similarly for <i>S</i><sub><i>nm</i></sub>).
   *
   * Example of use:
   * \include example-SphericalHarmonic1.cpp
   **********************************************************************/

  class GEOGRAPHICLIB_EXPORT SphericalHarmonic1 {
  public:
    /**
     * Supported normalizations for associate Legendre polynomials.
     **********************************************************************/
    enum normalization {
      /**
       * Fully normalized associated Legendre polynomials.  See
       * SphericalHarmonic::FULL for documentation.
       *
       * @hideinitializer
       **********************************************************************/
      FULL = SphericalEngine::FULL,
      /**
       * Schmidt semi-normalized associated Legendre polynomials.  See
       * SphericalHarmonic::SCHMIDT for documentation.
       *
       * @hideinitializer
       **********************************************************************/
      SCHMIDT = SphericalEngine::SCHMIDT,
    };

  private:
    typedef Math::real real;
    SphericalEngine::coeff _c[2];
    real _a;
    unsigned _norm;

  public:
    /**
     * Constructor with a full set of coefficients specified.
     *
     * @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
     * @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
     * @param[in] N the maximum degree and order of the sum
     * @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
     * @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
     * @param[in] N1 the maximum degree and order of the correction
     *   coefficients <i>C'</i><sub><i>nm</i></sub> and
     *   <i>S'</i><sub><i>nm</i></sub>.
     * @param[in] a the reference radius appearing in the definition of the
     *   sum.
     * @param[in] norm the normalization for the associated Legendre
     *   polynomials, either SphericalHarmonic1::FULL (the default) or
     *   SphericalHarmonic1::SCHMIDT.
     * @exception GeographicErr if \e N and \e N1 do not satisfy \e N &ge;
     *   \e N1 &ge; &minus;1.
     * @exception GeographicErr if any of the vectors of coefficients is not
     *   large enough.
     *
     * See SphericalHarmonic for the way the coefficients should be stored.
     *
     * The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
     * C', and \e S'.  These arrays should not be altered or destroyed during
     * the lifetime of a SphericalHarmonic object.
     **********************************************************************/
    SphericalHarmonic1(const std::vector<real>& C,
                       const std::vector<real>& S,
                       int N,
                       const std::vector<real>& C1,
                       const std::vector<real>& S1,
                       int N1,
                       real a, unsigned norm = FULL)
      : _a(a)
      , _norm(norm) {
      if (!(N1 <= N))
        throw GeographicErr("N1 cannot be larger that N");
      _c[0] = SphericalEngine::coeff(C, S, N);
      _c[1] = SphericalEngine::coeff(C1, S1, N1);
    }

    /**
     * Constructor with a subset of coefficients specified.
     *
     * @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
     * @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
     * @param[in] N the degree used to determine the layout of \e C and \e S.
     * @param[in] nmx the maximum degree used in the sum.  The sum over \e n is
     *   from 0 thru \e nmx.
     * @param[in] mmx the maximum order used in the sum.  The sum over \e m is
     *   from 0 thru min(\e n, \e mmx).
     * @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
     * @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
     * @param[in] N1 the degree used to determine the layout of \e C' and \e
     *   S'.
     * @param[in] nmx1 the maximum degree used for \e C' and \e S'.
     * @param[in] mmx1 the maximum order used for \e C' and \e S'.
     * @param[in] a the reference radius appearing in the definition of the
     *   sum.
     * @param[in] norm the normalization for the associated Legendre
     *   polynomials, either SphericalHarmonic1::FULL (the default) or
     *   SphericalHarmonic1::SCHMIDT.
     * @exception GeographicErr if the parameters do not satisfy \e N &ge; \e
     *   nmx &ge; \e mmx &ge; &minus;1; \e N1 &ge; \e nmx1 &ge; \e mmx1 &ge;
     *   &minus;1; \e N &ge; \e N1; \e nmx &ge; \e nmx1; \e mmx &ge; \e mmx1.
     * @exception GeographicErr if any of the vectors of coefficients is not
     *   large enough.
     *
     * The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
     * C', and \e S'.  These arrays should not be altered or destroyed during
     * the lifetime of a SphericalHarmonic object.
     **********************************************************************/
    SphericalHarmonic1(const std::vector<real>& C,
                       const std::vector<real>& S,
                       int N, int nmx, int mmx,
                       const std::vector<real>& C1,
                       const std::vector<real>& S1,
                       int N1, int nmx1, int mmx1,
                       real a, unsigned norm = FULL)
      : _a(a)
      , _norm(norm) {
      if (!(nmx1 <= nmx))
        throw GeographicErr("nmx1 cannot be larger that nmx");
      if (!(mmx1 <= mmx))
        throw GeographicErr("mmx1 cannot be larger that mmx");
      _c[0] = SphericalEngine::coeff(C, S, N, nmx, mmx);
      _c[1] = SphericalEngine::coeff(C1, S1, N1, nmx1, mmx1);
    }

    /**
     * A default constructor so that the object can be created when the
     * constructor for another object is initialized.  This default object can
     * then be reset with the default copy assignment operator.
     **********************************************************************/
    SphericalHarmonic1() {}

    /**
     * Compute a spherical harmonic sum with a correction term.
     *
     * @param[in] tau multiplier for correction coefficients \e C' and \e S'.
     * @param[in] x cartesian coordinate.
     * @param[in] y cartesian coordinate.
     * @param[in] z cartesian coordinate.
     * @return \e V the spherical harmonic sum.
     *
     * This routine requires constant memory and thus never throws
     * an exception.
     **********************************************************************/
    Math::real operator()(real tau, real x, real y, real z) const {
      real f[] = {1, tau};
      real v = 0;
      real dummy;
      switch (_norm) {
      case FULL:
        v = SphericalEngine::Value<false, SphericalEngine::FULL, 2>
          (_c, f, x, y, z, _a, dummy, dummy, dummy);
        break;
      case SCHMIDT:
        v = SphericalEngine::Value<false, SphericalEngine::SCHMIDT, 2>
          (_c, f, x, y, z, _a, dummy, dummy, dummy);
        break;
      }
      return v;
    }

    /**
     * Compute a spherical harmonic sum with a correction term and its
     * gradient.
     *
     * @param[in] tau multiplier for correction coefficients \e C' and \e S'.
     * @param[in] x cartesian coordinate.
     * @param[in] y cartesian coordinate.
     * @param[in] z cartesian coordinate.
     * @param[out] gradx \e x component of the gradient
     * @param[out] grady \e y component of the gradient
     * @param[out] gradz \e z component of the gradient
     * @return \e V the spherical harmonic sum.
     *
     * This is the same as the previous function, except that the components of
     * the gradients of the sum in the \e x, \e y, and \e z directions are
     * computed.  This routine requires constant memory and thus never throws
     * an exception.
     **********************************************************************/
    Math::real operator()(real tau, real x, real y, real z,
                          real& gradx, real& grady, real& gradz) const {
      real f[] = {1, tau};
      real v = 0;
      switch (_norm) {
      case FULL:
        v = SphericalEngine::Value<true, SphericalEngine::FULL, 2>
          (_c, f, x, y, z, _a, gradx, grady, gradz);
        break;
      case SCHMIDT:
        v = SphericalEngine::Value<true, SphericalEngine::SCHMIDT, 2>
          (_c, f, x, y, z, _a, gradx, grady, gradz);
        break;
      }
      return v;
    }

    /**
     * Create a CircularEngine to allow the efficient evaluation of several
     * points on a circle of latitude at a fixed value of \e tau.
     *
     * @param[in] tau the multiplier for the correction coefficients.
     * @param[in] p the radius of the circle.
     * @param[in] z the height of the circle above the equatorial plane.
     * @param[in] gradp if true the returned object will be able to compute the
     *   gradient of the sum.
     * @exception std::bad_alloc if the memory for the CircularEngine can't be
     *   allocated.
     * @return the CircularEngine object.
     *
     * SphericalHarmonic1::operator()() exchanges the order of the sums in the
     * definition, i.e., &sum;<sub><i>n</i> = 0..<i>N</i></sub>
     * &sum;<sub><i>m</i> = 0..<i>n</i></sub> becomes &sum;<sub><i>m</i> =
     * 0..<i>N</i></sub> &sum;<sub><i>n</i> = <i>m</i>..<i>N</i></sub>.
     * SphericalHarmonic1::Circle performs the inner sum over degree \e n
     * (which entails about <i>N</i><sup>2</sup> operations).  Calling
     * CircularEngine::operator()() on the returned object performs the outer
     * sum over the order \e m (about \e N operations).
     *
     * See SphericalHarmonic::Circle for an example of its use.
     **********************************************************************/
    CircularEngine Circle(real tau, real p, real z, bool gradp) const {
      real f[] = {1, tau};
      switch (_norm) {
      case FULL:
        return gradp ?
          SphericalEngine::Circle<true, SphericalEngine::FULL, 2>
          (_c, f, p, z, _a) :
          SphericalEngine::Circle<false, SphericalEngine::FULL, 2>
          (_c, f, p, z, _a);
        break;
      case SCHMIDT:
      default:                  // To avoid compiler warnings
        return gradp ?
          SphericalEngine::Circle<true, SphericalEngine::SCHMIDT, 2>
          (_c, f, p, z, _a) :
          SphericalEngine::Circle<false, SphericalEngine::SCHMIDT, 2>
          (_c, f, p, z, _a);
        break;
      }
    }

    /**
     * @return the zeroth SphericalEngine::coeff object.
     **********************************************************************/
    const SphericalEngine::coeff& Coefficients() const
    { return _c[0]; }
    /**
     * @return the first SphericalEngine::coeff object.
     **********************************************************************/
    const SphericalEngine::coeff& Coefficients1() const
    { return _c[1]; }
  };

} // namespace GeographicLib

#endif  // GEOGRAPHICLIB_SPHERICALHARMONIC1_HPP