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[Functions] source/numericalTools/Roots/Roots_x3Polynomial





  call Roots_x3Polynomial (real,              intent (in)  :: c2,
                           real,              intent (in)  :: c1,
                           real,              intent (in)  :: c0,
                           integer,           intent (out) :: nReal,
                           real,              intent (out) :: root (1:3,1:2),
                           logical, optional, intent (in)  :: printInfo,
                           integer, optional, intent (in)  :: printUnit)


  Calculates all real + complex roots of the cubic polynomial:

                 x^3 + c2 * x^2 + c1 * x + c0

  The first real root (which always exists) is obtained using an optimized
  Newton-Raphson scheme. The other remaining roots are obtained through
  composite deflation to a quadratic.

  The cubic root solver can handle any size of cubic coefficients and there is
  no danger of overflow due to proper rescaling of the cubic polynomial.

  The order of the roots is as follows:

        1) For real roots, the order is according to their algebraic value
           on the number scale (largest positive first, largest negative last).

        2) Since there can be only one complex conjugate pair root, no order
           is necessary.

        3) All real roots preceede the complex ones.


  c2         : coefficient of x^2 term
  c1         : coefficient of x term
  c0         : independent coefficient
  nReal      : number of different real roots found
  root (n,1) : real part of n-th root
  root (n,2) : imaginary part of n-th root
  printInfo  : if given and true, detailed info will be printed about intermediate stages
  printUnit  : the unit ID, where the info will be printed


  Only passing both printInfo AND printUnit will result in printing out the info.
  Giving only one of them results in no printing action.