Find the roots of a function.
Description:
Return the roots of the (non-linear) equations defined by func(x)=0 given a starting estimate.
Inputs:
- func – A Python function or method which takes at least one
- (possibly vector) argument.
x0 – The starting estimate for the roots of func(x)=0. args – Any extra arguments to func are placed in this tuple. fprime – A function or method to compute the Jacobian of func with
derivatives across the rows. If this is None, the Jacobian will be estimated.full_output – non-zero to return the optional outputs. col_deriv – non-zero to specify that the Jacobian function
computes derivatives down the columns (faster, because there is no transpose operation).
- warning – True to print a warning message when the call is
- unsuccessful; False to suppress the warning message.
Outputs: (x, {infodict, ier, mesg})
- x – the solution (or the result of the last iteration for an
- unsuccessful call.
- infodict – a dictionary of optional outputs with the keys:
‘nfev’ : the number of function calls ‘njev’ : the number of jacobian calls ‘fvec’ : the function evaluated at the output ‘fjac’ : the orthogonal matrix, q, produced by the
QR factorization of the final approximate Jacobian matrix, stored column wise.
- ‘r’ : upper triangular matrix produced by QR
- factorization of same matrix.
‘qtf’ : the vector (transpose(q) * fvec).
- ier – an integer flag. If it is equal to 1 the solution was
- found. If it is not equal to 1, the solution was not found and the following message gives more information.
- mesg – a string message giving information about the cause of
- failure.
Extended Inputs:
- xtol – The calculation will terminate if the relative error
- between two consecutive iterates is at most xtol.
- maxfev – The maximum number of calls to the function. If zero,
- then 100*(N+1) is the maximum where N is the number of elements in x0.
- band – If set to a two-sequence containing the number of sub-
- and superdiagonals within the band of the Jacobi matrix, the Jacobi matrix is considered banded (only for fprime=None).
- epsfcn – A suitable step length for the forward-difference
- approximation of the Jacobian (for fprime=None). If epsfcn is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision.
- factor – A parameter determining the initial step bound
- (factor * || diag * x||). Should be in interval (0.1,100).
- diag – A sequency of N positive entries that serve as a
- scale factors for the variables.
Remarks:
“fsolve” is a wrapper around MINPACK’s hybrd and hybrj algorithms.
See also:
scikits.openopt, which offers a unified syntax to call this and other solvers
- fmin, fmin_powell, fmin_cg,
- fmin_bfgs, fmin_ncg – multivariate local optimizers
leastsq – nonlinear least squares minimizer
- fmin_l_bfgs_b, fmin_tnc,
- fmin_cobyla – constrained multivariate optimizers
anneal, brute – global optimizers
fminbound, brent, golden, bracket – local scalar minimizers
brentq, brenth, ridder, bisect, newton – one-dimensional root-finding
fixed_point – scalar and vector fixed-point finder