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 sptk::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.