root_pol

Functions

int main(int argc, char *argv[])

root_pol [ option ] [ infile ]

• -m int

  • order of polynomial \((1 \le M)\)

• -i int

  • maximum number of iterations

• -d double

  • convergence threshold

• -q int

  • input format

    • 0 forward order

    • 1 reverse order

• -o int

  • output format

    • 0 rectangular form

    • 1 polar form

• infile str

  • double-type coefficients of polynomial

• stdout

  • double-type roots of polynomial

If -o is 0, real and imaginary parts of roots are written.

echo 3 4 5 | root_pol -m 2 -o 0 | x2x +da -c 2
# -0.666667 1.10554
# -0.666667 -1.10554

If -o is 1, radius and angle of roots are written.

echo 3 4 5 | root_pol -m 2 -o 1 | x2x +da -c 2
# 1.29099 2.11344
# 1.29099 -2.11344

See also

gpolezero

class DurandKernerMethod

Find roots of a polynomial.

The input is the \(M\)-th order polynomial coefficients:

\[ \begin{array}{cccc} a(1), & a(2), & \ldots, & a(M), \end{array} \]

where the polynomial is represented as

\[ x^M + a(1) x^{M-1} + \cdots + a(M-1) x + a(M). \]

The output is the complex-valued roots of the polynomial:

\[ \begin{array}{cccc} z(0), & z(1), & \ldots, & z(M-1). \end{array} \]

They are found by the Durand-Kerner method.

Public Functions

DurandKernerMethod(int num_order, int num_iteration, double convergence_threshold)

Parameters:

• num_order – [in] Order of coefficients, \(M\).

• num_iteration – [in] Number of iterations.

• convergence_threshold – [in] Convergence threshold.

inline int GetNumOrder() const

Returns:

Order of coefficients.

inline int GetNumIteration() const

Returns:

Number of iterations.

inline double GetConvergenceThreshold() const

Returns:

Convergence threshold.

inline bool IsValid() const

Returns:

True if this object is valid.

bool Run(const std::vector<double> &coefficients, std::vector<std::complex<double>> *roots, bool *is_converged) const

Parameters:

• coefficients – [in] Coefficients of polynomial.

• roots – [out] Root of the polynomial.

• is_converged – [out] True if convergence is reached.

Returns:

True on success, false on failure.