cubic.h

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#ifndef CUBIC_H
#define CUBIC_H
 
#include <complex>
 
/*
Copyright (c) 2005 Igor B. Smirnov
 
The file can be used, copied, modified, and distributed
according to the terms of GNU Lesser General Public License version 2.1
as published by the Free Software Foundation,
and provided that the above copyright notice, this permission notice,
and notices about any modifications of the original text
appear in all copies and in supporting documentation.
The file is provided "as is" without express or implied warranty.
*/
 
namespace Heed {
 
/// Find solution to cubic equation.
 
class Cubic {
 public:
  typedef std::complex<double> double_complex;
  double a() const { return da; }
  double b() const { return db; }
  double c() const { return dc; }
  double d() const { return dd; }
  double s_xzero() const { return s_dxzero; }  // for debug
  void put_a(double fa) {
    da = fa;
    s_dxzero = 0;
  }
  void put_b(double fb) {
    db = fb;
    s_dxzero = 0;
  }
  void put_c(double fc) {
    dc = fc;
    s_dxzero = 0;
  }
  void put_d(double fd) {
    dd = fd;
    s_dxzero = 0;
  }
 
  Cubic() : da(0.0), db(0.0), dc(0.0), dd(0.0), s_dxzero(0) {}
  Cubic(double fa, double fb, double fc, double fd)
      : da(fa), db(fb), dc(fc), dd(fd), s_dxzero(0) {}
 
  double y(double x) const {
    return da * x * x * x + db * x * x + dc * x + dd;
  }
 
  void find_zero(double_complex& z1, double_complex& z2,
                 double_complex& z3) const;
  // They are not ordered and analysed
  int find_real_zero(double z[3]) const;
  // returns number of solutions
  // Analysed and ordered real solutions
 
  // returns number of solutions
  // first is the least.
  int find_maxmin(double xmm[2], double ymm[2],
                  int s_mm[2]) const;  // 1 - maximum, -1 - minimum, 0 - non
 private:
  static const double_complex iu;
  double da, db, dc, dd;
  mutable int s_dxzero;
  mutable double_complex dz1;
  mutable double_complex dz2;
  mutable double_complex dz3;
};
 
std::ostream& operator<<(std::ostream& file, const Cubic& f);
}
 
#endif