root_find_system

root_find_system(f, jacobian, first_guess, tolerance=None, max_iterations=None)

Solve a system of nonlinear equations.

Solves F(x) = 0 for a vector-valued F with the ported Numerics multivariate Newton-Raphson method, iterating x_(n+1) = x_n - J(x_n)^-1 F(x_n).

Parameters

Name	Type	Description	Default
f	callable	The system of equations: a function taking a sequence of numbers and returning a sequence of numbers of the same length.	required
jacobian	callable	The Jacobian of f: a function taking the same sequence and returning the square matrix of partial derivatives (a sequence of rows, or a 2-D array), one ROW per equation.	required
first_guess	array_like	The starting vector; its length fixes the dimension of the system.	required
tolerance	float	The convergence tolerance, applied to both the step size and the residual. Left unset, the ported solver’s own default (1e-8) applies.	None
max_iterations	int	The iteration cap; the search raises if it is reached. Left unset, the ported solver’s own default (1000) applies.	None

Returns

Name	Type	Description
	numpy.ndarray	The root, the length of first_guess.

Examples

>>> import corehydropy as ch
>>> f = lambda v: [3 * v[0] + v[1] - 9, v[0] + 2 * v[1] - 8]
>>> j = lambda v: [[3, 1], [1, 2]]
>>> ch.root_find_system(f, j, first_guess=[0, 0]).round(6)
array([2., 3.])