plot_root.plot_root

plot_root.plot_root(
    f,
    dfdx,
    xmin,
    xmax,
    tol1,
    tol2,
    max_iter1=500,
    max_iter2=500,
    npts=1000,
    n=50,
)

Plot a scalar function and visualize its roots using a hybrid bisection-Newton root-finding algorithm.

This function computes the roots of a scalar function f within a given interval using the hybrid method and returns a Matplotlib figure containing the function plot and the detected roots.

Parameters

Name	Type	Description	Default
f	callable	Scalar function to be plotted. Must accept a single scalar argument.	required
dfdx	callable	Derivative of f. Must accept a single scalar argument.	required
xmin	float	Lower bound of the plotting and root-search interval.	required
xmax	float	Upper bound of the plotting and root-search interval.	required
tol1	float	Convergence tolerance passed to the bisection-based root search stage of the hybrid method. Must be strictly positive.	required
tol2	float	Relative convergence tolerance passed to the Newton-Raphson refinement stage of the hybrid method. Must be strictly positive.	required
max_iter1	int	Maximum number of iterations allowed for the bisection-based root search. Default is 500.	500
max_iter2	int	Maximum number of iterations allowed for Newton’s method. Default is 500.	500
npts	int	Number of points used to discretize the interval [xmin, xmax] for plotting the function. Default is 1000.	1000
n	int	Number of subintervals used by the bisection-based root search. Passed to the hybrid solver. Default is 50.	50

Returns

Name	Type	Description
fig	matplotlib.figure.Figure	The Matplotlib figure object.
ax	matplotlib.axes.Axes	The Matplotlib axes containing the plot.

Examples

>>> f = lambda x: x**2 - 4
>>> df = lambda x: 2*x
>>> fig, ax = plot_root(f, df, -3, 3, 1e-6, 1e-12)
>>> fig.savefig("roots.png")