scipy.optimize.fsolve¶
- scipy.optimize.fsolve(func, x0, args=(), fprime=None, full_output=0, col_deriv=0, xtol=1.49012e-08, maxfev=0, band=None, epsfcn=None, factor=100, diag=None)[source]¶
Find the roots of a function.
Return the roots of the (non-linear) equations defined by func(x) = 0 given a starting estimate.
Parameters : func : callable f(x, *args)
A function that takes at least one (possibly vector) argument.
x0 : ndarray
The starting estimate for the roots of func(x) = 0.
args : tuple, optional
Any extra arguments to func.
fprime : callable(x), optional
A function to compute the Jacobian of func with derivatives across the rows. By default, the Jacobian will be estimated.
full_output : bool, optional
If True, return optional outputs.
col_deriv : bool, optional
Specify whether the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation).
xtol : float
The calculation will terminate if the relative error between two consecutive iterates is at most xtol.
maxfev : int, optional
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 : tuple, optional
If set to a two-sequence containing the number of sub- and super-diagonals within the band of the Jacobi matrix, the Jacobi matrix is considered banded (only for fprime=None).
epsfcn : float, optional
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 : float, optional
A parameter determining the initial step bound (factor * || diag * x||). Should be in the interval (0.1, 100).
diag : sequence, optional
N positive entries that serve as a scale factors for the variables.
Returns : x : ndarray
The solution (or the result of the last iteration for an unsuccessful call).
infodict : dict
A dictionary of optional outputs with the keys:
- nfev
number of function calls
- njev
number of Jacobian calls
- fvec
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 the same matrix
- qtf
the vector (transpose(q) * fvec)
ier : int
An integer flag. Set to 1 if a solution was found, otherwise refer to mesg for more information.
mesg : str
If no solution is found, mesg details the cause of failure.
Notes
fsolve is a wrapper around MINPACK’s hybrd and hybrj algorithms.