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+"""Numerical approximation methods"""
+
+def bisect(fun, a, b, *, xtol=2.4e-7, maxiter=100) -> float:
+ """
+ :param callable f: The function to bisect
+ :param float a: The left side of the interval
+ :param float b: The right side of the interval
+ :param float xtol: The tolerance value
+ :param float maxiter: The maximum number of iterations to perform
+
+ Find a solution (zero) of the function ``f(x)`` on the interval
+ (``a``..``b``) using the bisection method. The result is accurate to within
+ ``xtol`` unless more than ``maxiter`` steps are required."""
+ ...
+
+def newton(fun, x0, *, xtol=2.4e-7, rtol=0.0, maxiter=50) -> float:
+ """
+ :param callable f: The function to bisect
+ :param float x0: The initial x value
+ :param float xtol: The absolute tolerance value
+ :param float rtol: The relative tolerance value
+ :param float maxiter: The maximum number of iterations to perform
+
+ Find a solution (zero) of the function ``f(x)`` using Newton's Method.
+ The result is accurate to within ``xtol * rtol * |f(x)|`` unless more than
+ ``maxiter`` steps are requried."""
+ ...
+
+def fmin(fun, x0, *, xatol=2.4e-7, fatol=2.4e-7, maxiter=200) -> float:
+ """
+ :param callable f: The function to bisect
+ :param float x0: The initial x value
+ :param float xatol: The absolute tolerance value
+ :param float fatol: The relative tolerance value
+
+ Find a minimum of the function ``f(x)`` using the downhill simplex method.
+ The located ``x`` is within ``fxtol`` of the actual minimum, and ``f(x)``
+ is within ``fatol`` of the actual minimum unless more than ``maxiter``
+ steps are requried."""
+ ...
+
+def interp(x: ulab.array, xp:ulab.array, fp:ulab.array, *, left=None, right=None) -> ulab.array:
+ """
+ :param ulab.array x: The x-coordinates at which to evaluate the interpolated values.
+ :param ulab.array xp: The x-coordinates of the data points, must be increasing
+ :param ulab.array fp: The y-coordinates of the data points, same length as xp
+ :param left: Value to return for ``x < xp[0]``, default is ``fp[0]``.
+ :param right: Value to return for ``x > xp[-1]``, default is ``fp[-1]``.
+
+ Returns the one-dimensional piecewise linear interpolant to a function with given discrete data points (xp, fp), evaluated at x."""
+ ...
+