scipy.optimize.fsolve(func, x0, args=(), fprime=None, full_output=0, col_deriv=0, xtol=1.49012e-08, maxfev=0, band=None, epsfcn=0.0, factor=100, diag=None, warning=True)

Find the roots of a function.


Return the roots of the (non-linear) equations defined by func(x)=0 given a starting estimate.


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

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.


“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

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