abs_inverse.h File Reference

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Macros
#define	ALWAYS_USE_TEMPLATE_PAR_AS_FUN_PAR

Functions
template<class M , class X >
X	abstract_determinant (M &mi, long q, X)

Macro Definition Documentation

ALWAYS_USE_TEMPLATE_PAR_AS_FUN_PAR

#define ALWAYS_USE_TEMPLATE_PAR_AS_FUN_PAR

Definition at line 95 of file abs_inverse.h.

Function Documentation

abstract_determinant()

template<class M , class X >

X abstract_determinant	(	M &	mi,
		long	q,
		X
	)

Definition at line 104 of file abs_inverse.h.

    {
  if (q == 1) {
    return mi.ac(0, 0);
  } else if (q == 2) {
    return mi.ac(0, 0) * mi.ac(1, 1) - mi.ac(0, 1) * mi.ac(1, 0);
  } else if (q == 3) {
    return mi.ac(0, 0) * mi.ac(1, 1) * mi.ac(2, 2) +
           mi.ac(0, 2) * mi.ac(1, 0) * mi.ac(2, 1) +
           mi.ac(0, 1) * mi.ac(1, 2) * mi.ac(2, 0) -
           mi.ac(0, 2) * mi.ac(1, 1) * mi.ac(2, 0) -
           mi.ac(0, 0) * mi.ac(1, 2) * mi.ac(2, 1) -
           mi.ac(0, 1) * mi.ac(1, 0) * mi.ac(2, 2);
  } else {
    long nr, nr1, nc;
    X koef = 1;
    for (nr = 0; nr < q; nr++) {
      long nmax = 0;
      double d = 0;
      for (nr1 = nr; nr1 < q; nr1++) {
        if (fabs(mi.ac(nr1, nr)) > d) {
          d = fabs(mi.ac(nr1, nr));
          nmax = nr1;
        }
      }
      //mcout<<"d="<<d<<'\n';
      //mcout<<"nmax="<<nmax<<'\n';
      if (d == 0) {
        //serr = 1;
        return koef * mi.ac(nmax, nr);
      }
      if (nmax > nr) {
        for (nc = nr; nc < q; nc++) {
          X t(mi.ac(nr, nc));
          mi.ac(nr, nc) = mi.ac(nmax, nc);
          mi.ac(nmax, nc) = t;
        }
        koef *= -1;  // trancposition of rows: determinant changes sign
      }
      X t = mi.ac(nr, nr);
      for (nr1 = nr + 1; nr1 < q; nr1++) {
        X k(mi.ac(nr1, nr) / t);
        //mcout<<"nr1="<<nr1<<" nr="<<nr<<'\n';
        //mcout<<"k="<<k<<'\n';
        for (nc = nr; nc < q; nc++) {
          mi.ac(nr1, nc) -= k * mi.ac(nr, nc);
        }  // add elements of another row: the main value of
           // determinant is not affected (proven in linear algebra)
           // But the resolution gets worser.
      }
      for (nc = nr; nc < q; nc++) {
        mi.ac(nr, nc) /= t;
      }
      koef *= t;
    }
    return koef;
  }
}

Referenced by determinant_DynArr().