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:

Parameters:	func : callable `f(x, args)` A function that takes at least one (possibly vector) argument, and returns a value of the same length. x0 : ndarray The starting estimate for the roots of `func(x) = 0`. args* : tuple, optional Any extra arguments to func. fprime : callable `f(x, args)`, 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, optional 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.

func : callable f(x, *args): A function that takes at least one (possibly vector) argument, and returns a value of the same length.
x0 : ndarray: The starting estimate for the roots of func(x) = 0.
args : tuple, optional: Any extra arguments to func.
fprime : callable f(x, *args), 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, optional: 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.

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