mathutils.py 文件源码

def realpolyroots(*cs):
    """returns the roots of a polynom with given coefficients

    polynomial with coefficients given in cs:
      0 = \sum_i  cs[i] * x^(len(cs)-i-1)
    """
    if not cs:
        return [0]
    try:
        f = 1.0/cs[0]
        cs = [f*c for c in cs[1:]]
    except ArithmeticError:
        return realpolyroots(*cs[1:])
    else:
        n = len(cs)
        if n == 0:
            return []
        elif n == 1:
            return [-cs[0]]
        elif n == 2:
            return _realroots_quadratic(*cs)
        elif n == 3:
            return _realroots_cubic(*cs)
        elif n == 4:
            return _realroots_quartic(*cs)
        else:
            raise RuntimeError("realpolyroots solver currently limited to polynoms up to the power of 4")


# def realpolyroots_eigenvalue(*cs):
#     # as realpolyroots but using an equivalent eigenvalue problem
#     # (this code is currently used for functional tests only)
#     if not _has_numeric:
#         raise RuntimeError("realpolyroots_eigenvalue depends on Numeric")
#     if not cs:
#         return [0]
#     try:
#         f = 1.0/cs[0]
#         cs = [f*c for c in cs[1:]]
#     except ArithmeticError:
#         return realpolyroots_eigenvalue(*cs[1:])
#     else:
#         if not cs:
#             return []
#         n = len(cs)
#         a = Numeric.zeros((n, n), Numeric.Float)
#         for i in range(n-1):
#             a[i+1][i] = 1
#         for i in range(n):
#             a[0][i] = -cs[i]
#         rs = []
#         for r in LinearAlgebra.eigenvalues(a):
#             if type(r) == types.ComplexType:
#                 if not r.imag:
#                     rs.append(r.real)
#             else:
#                 rs.append(r)
#         return rs
#