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=0.0, factor=100, diag=None, warning=True)

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