naginterfaces.library.roots.sys_​func_​easy

naginterfaces.library.roots.sys_func_easy(fcn, x, xtol=1.0536712127723509e-08, data=None)[source]

sys_func_easy is an easy-to-use function that finds a solution of a system of nonlinear equations by a modification of the Powell hybrid method.

For full information please refer to the NAG Library document for c05qb

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/c05/c05qbf.html

Parameters
fcncallable fvec = fcn(x, data=None)

must return the values of the functions at a point .

Parameters
xfloat, ndarray, shape

The components of the point at which the functions must be evaluated.

dataarbitrary, optional, modifiable in place

User-communication data for callback functions.

Returns
fvecfloat, array-like, shape

The function values .

xfloat, array-like, shape

An initial guess at the solution vector.

xtolfloat, optional

The accuracy in to which the solution is required.

dataarbitrary, optional

User-communication data for callback functions.

Returns
xfloat, ndarray, shape

The final estimate of the solution vector.

fvecfloat, ndarray, shape

The function values at the final point returned in .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

There have been at least calls to . Consider restarting the calculation from the point held in .

(errno )

No further improvement in the solution is possible. is too small: .

(errno )

The iteration is not making good progress. This failure exit may indicate that the system does not have a zero, or that the solution is very close to the origin (see Accuracy). Otherwise, rerunning sys_func_easy from a different starting point may avoid the region of difficulty.

NagCallbackTerminateWarning
(errno )

Termination requested in .

Notes

The system of equations is defined as:

sys_func_easy is based on the MINPACK routine HYBRD1 (see Moré et al. (1980)). It chooses the correction at each step as a convex combination of the Newton and scaled gradient directions. The Jacobian is updated by the rank-1 method of Broyden. At the starting point, the Jacobian is approximated by forward differences, but these are not used again until the rank-1 method fails to produce satisfactory progress. For more details see Powell (1970).

References

Moré, J J, Garbow, B S and Hillstrom, K E, 1980, User guide for MINPACK-1, Technical Report ANL-80-74, Argonne National Laboratory

Powell, M J D, 1970, A hybrid method for nonlinear algebraic equations, Numerical Methods for Nonlinear Algebraic Equations, (ed P Rabinowitz), Gordon and Breach