dfzero hybrd1 rpzero2

rpzero2() def rpzero2 ( n  , a  , rr  , ri  , s  , iflag  = 0, maxiter  = 100  ) Roots of a polynomial (real coefficients) (Netwon method) (complex type is not used) Purpose rpzero2 computes all roots of a polynomial p(z) with real coefficients by Netwon method. p(z) = a0*z^n + a1*z^(n-1) + ... + an The obtained zeros are output to the separate real type variables for real and imaginary parts. Returns (iter, info) iter (int): Number of iterations required to converge. info (int): = 0: Successful exit = -1: The argument n had an illegal value (n < 1) = -2: The argument a is invalid (e.g. a[0] = 0) = -3: The argument rr is invalid. = -4: The argument ri is invalid. = -5: The argument s is invalid. = -7: The argument maxiter had an illegal value (maxiter <= 0) = 1: Failed to converge after maxiter iterations. Best current estimates of the zeros are in rr and ri. Error bounds in s are not calculated. Parameters [in] n Degree of polynomial. (n >= 1) [in] a Numpy ndarray (1-dimensional, float, length n + 1) Real coefficient vector of p(z) (a0 to an). [in,out] rr Numpy ndarray (1-dimensional, float, length n) [in] Real parts of initial estimates for zeros. If these are unknown, set iflag = 0 and it is not necessary to set estimates in rr.   Note - Initial estimates must be separated, that is, distinct or not repeated. [out] Real part of the obtained zeros. [in,out] ri Numpy ndarray (1-dimensional, float, length n) [in] Imaginary parts of initial estimates for zeros. If these are unknown, set iflag = 0 and it is not necessary to set estimates in ri.   Note - Initial estimates must be separated, that is, distinct or not repeated. [out] Imaginary part of the obtained zeros. [out] s Numpy ndarray (1-dimensional, float, length n) Error bound for the obtained zeros. [in] iflag (Optional) Flag to indicate if initial estimates of zeros are input. (default = 0) = 0: No estimates are input. != 0: rr and ri contain estimates of zeros. [in] maxiter (Optional) Maximum number of iterations. (maxitr >= 1) (default = 100) Reference SLATEC Example Program Solve the following algebraic equation. x^5 + 2*x^3 + 2*x^2 - 15*x + 10 = 0 The exact solutions are 1(double root), -2 and ±√5i. def TestRpzero2(): n = 5; a = np.array([1.0, 0.0, 2.0, 2.0, -15.0, 10.0]) rr = np.empty(n) ri = np.empty(n) s = np.empty(n) iter, info = rpzero2(n, a, rr, ri, s) for i in range(n): print(rr[i], ri[i], s[i]) print(iter, info) Example Results >>> TestRpzero2() 1.0000000135981033 2.146253582923928e-08 1.265979321229113e-07 1.4829843740329862e-18 2.23606797749979 8.99528943854828e-15 -2.0 1.1504163109909317e-19 7.53855142372064e-15 7.942413118753155e-17 -2.23606797749979 9.067230800947384e-15 0.9999999870464613 -2.247841617388521e-08 1.2657854084498727e-07 30 0 Note - Only half precision for double roots.