Heed::Cubic Class Reference

Find solution to cubic equation. More...

#include <cubic.h>

Public Types
typedef std::complex< double >	double_complex

Public Member Functions
double	a () const
double	b () const
double	c () const
double	d () const
double	s_xzero () const
void	put_a (double fa)
void	put_b (double fb)
void	put_c (double fc)
void	put_d (double fd)
	Cubic ()
	Cubic (double fa, double fb, double fc, double fd)
double	y (double x) const
void	find_zero (double_complex &z1, double_complex &z2, double_complex &z3) const
int	find_real_zero (double z[3]) const
int	find_maxmin (double xmm[2], double ymm[2], int s_mm[2]) const

Detailed Description

Find solution to cubic equation.

Definition at line 22 of file cubic.h.

Member Typedef Documentation

double_complex

typedef std::complex<double> Heed::Cubic::double_complex

Definition at line 24 of file cubic.h.

Constructor & Destructor Documentation

Cubic() [1/2]

Heed::Cubic::Cubic ( )

inline

Definition at line 47 of file cubic.h.

: da(0.0), db(0.0), dc(0.0), dd(0.0), s_dxzero(0) {}

Cubic() [2/2]

Heed::Cubic::Cubic ( double  fa, double  fb, double  fc, double  fd  )

inline

Definition at line 48 of file cubic.h.

      : da(fa), db(fb), dc(fc), dd(fd), s_dxzero(0) {}

Member Function Documentation

a()

double Heed::Cubic::a ( ) const

inline

Definition at line 25 of file cubic.h.

{ return da; }

Referenced by find_maxmin(), and Heed::operator<<().

b()

double Heed::Cubic::b ( ) const

inline

Definition at line 26 of file cubic.h.

{ return db; }

Referenced by Heed::operator<<().

c()

double Heed::Cubic::c ( ) const

inline

Definition at line 27 of file cubic.h.

{ return dc; }

Referenced by Heed::operator<<().

d()

double Heed::Cubic::d ( ) const

inline

Definition at line 28 of file cubic.h.

{ return dd; }

Referenced by Heed::operator<<().

find_maxmin()

int Heed::Cubic::find_maxmin	(	double	xmm[2],
		double	ymm[2],
		int	s_mm[2]
	)		const

Definition at line 121 of file cubic.cpp.

                                                                      {
  mfunname(
      "int Cubic::find_maxmin(double xmm[2], double ymm[2], int s_mm[2]) "
      "const");
  double ap = 3 * da;
  double bp = 2 * db;
  double cp = dc;
  Parabola par(ap, bp, cp);
  s_mm[0] = 0;
  s_mm[1] = 0;
  int qz = par.find_zero(xmm);
  if (qz == 1) {
    s_mm[0] = 0;
  }
  if (qz == 2) {
    if (a() > 0) {
      s_mm[0] = 1;
      s_mm[1] = -1;
    } else {
      s_mm[0] = -1;
      s_mm[1] = 1;
    }
  }
  for (int n = 0; n < qz; ++n) {
    ymm[n] = y(xmm[n]);
  }
  return qz;
}

Referenced by Heed::operator<<().

find_real_zero()

int Heed::Cubic::find_real_zero

(

double

z[3]

)

const

Definition at line 74 of file cubic.cpp.

                                           {
  mfunname("int Cubic::find_real_zero(double z[3]) const");
  double_complex zc1;
  double_complex zc2;
  double_complex zc3;
  find_zero(zc1, zc2, zc3);
  double thresh = 10.0 * DBL_MIN;
  int q = 0;
  if (fabs(zc1.imag()) < thresh ||
      (zc1.real() != 0.0 && fabs(zc1.imag() / zc1.real()) < thresh)) {
    z[q] = zc1.real();
    q++;
  }
  if (fabs(zc2.imag()) < thresh ||
      (zc2.real() != 0.0 && fabs(zc2.imag() / zc2.real()) < thresh)) {
    z[q] = zc2.real();
    q++;
  }
  if (fabs(zc3.imag()) < thresh ||
      (zc3.real() != 0.0 && fabs(zc3.imag() / zc3.real()) < thresh)) {
    z[q] = zc3.real();
    q++;
  }
  int n2 = 0;
  for (int n1 = 0; n1 < q - 1; n1++) {
    for (n2 = n1; n2 < q; n2++) {
      if (z[n1] > z[n2]) {
        double t = z[n1];
        z[n1] = z[n2];
        z[n2] = t;
      }
    }
  }
  for (int n1 = 0; n1 < q - 1; n1++) {
    // TODO: debug.
    if ((fabs(z[n1]) < thresh && fabs(z[n2]) < thresh) ||
        fabs((z[n1] - z[n1 + 1]) / (z[n1] + z[n1 + 1])) < thresh) {
      for (n2 = n1 + 1; n2 < q - 1; n2++) {
        z[n2] = z[n2 + 1];
      }
      q--;
      n1--;
    }
  }
  return q;
}

Referenced by Heed::operator<<(), and Heed::VanDerWaals::volume_of_mole().

find_zero()

void Heed::Cubic::find_zero	(	double_complex &	z1,
		double_complex &	z2,
		double_complex &	z3
	)		const

Definition at line 23 of file cubic.cpp.

                                                {
  mfunname("void Cubic::find_zero(...) const");
  const Cubic& t = (*this);
  if (s_dxzero != 0) {
    z1 = dz1;
    z2 = dz2;
    z3 = dz3;
    return;
  }
 
  check_econd11a(da, == 0.0, "this is not cubic polynomial!", mcerr);
  double a2 = db / da;
  double a1 = dc / da;
  double a0 = dd / da;
  double Q = (3.0 * a1 - a2 * a2) / 9.0;
  double R = (9.0 * a2 * a1 - 27.0 * a0 - 2.0 * a2 * a2 * a2) / 54.0;
  double D = Q * Q * Q + R * R;
  double sD = sqrt(fabs(D));
  double_complex S;
  double_complex T;
  if (D >= 0.0) {
    double tt = R + sD;
    if (tt > 0.0) {
      S = pow(tt, 1 / 3.0);
    } else if (tt < 0.0) {
      S = -pow(-tt, 1 / 3.0);
    } else {
      S = 0.0;
    }
    tt = R - sD;
    if (tt > 0.0) {
      T = pow(tt, 1 / 3.0);
    } else if (tt < 0.0) {
      T = -pow(-tt, 1 / 3.0);
    } else {
      T = 0.0;
    }
  } else {
    S = pow(R + iu * sD, 1 / 3.0);
    T = pow(R - iu * sD, 1 / 3.0);
  }
  z1 = -a2 / 3.0 + (S + T);
  z2 = -a2 / 3.0 - (S + T) / 2.0 + 0.5 * iu * std::sqrt(3.0) * (S - T);
  z3 = -a2 / 3.0 - (S + T) / 2.0 - 0.5 * iu * std::sqrt(3.0) * (S - T);
  t.dz1 = z1;
  t.dz2 = z2;
  t.dz3 = z3;
  t.s_dxzero = 3;
}

Referenced by find_real_zero(), and Heed::operator<<().

put_a()

void Heed::Cubic::put_a ( double  fa )

inline

Definition at line 30 of file cubic.h.

                        {
    da = fa;
    s_dxzero = 0;
  }

put_b()

void Heed::Cubic::put_b ( double  fb )

inline

Definition at line 34 of file cubic.h.

                        {
    db = fb;
    s_dxzero = 0;
  }

put_c()

void Heed::Cubic::put_c ( double  fc )

inline

Definition at line 38 of file cubic.h.

                        {
    dc = fc;
    s_dxzero = 0;
  }

put_d()

void Heed::Cubic::put_d ( double  fd )

inline

Definition at line 42 of file cubic.h.

                        {
    dd = fd;
    s_dxzero = 0;
  }

s_xzero()

double Heed::Cubic::s_xzero ( ) const

inline

Definition at line 29 of file cubic.h.

{ return s_dxzero; }  // for debug

Referenced by Heed::operator<<().

y()

double Heed::Cubic::y ( double  x ) const

inline

Definition at line 51 of file cubic.h.

                           {
    return da * x * x * x + db * x * x + dc * x + dd;
  }

Referenced by find_maxmin().

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The documentation for this class was generated from the following files:

• cubic.h
• cubic.cpp