:mod:`ulab.approx`
==================

.. py:module:: ulab.approx

.. autoapi-nested-parse::

   Numerical approximation methods





.. function:: bisect(fun, a, b, \*, xtol=2.4e-07, 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.


.. function:: fmin(fun, x0, \*, xatol=2.4e-07, fatol=2.4e-07, 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.


.. function:: 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.


.. function:: newton(fun, x0, \*, xtol=2.4e-07, 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.


.. function:: trapz(y: ulab.array, x=None, dx=1.0) -> float

   :param 1D ulab.array y: the values of the dependent variable
   :param 1D ulab.array x: optional, the coordinates of the independent variable. Defaults to uniformly spaced values.
   :param float dx: the spacing between sample points, if x=None

   Returns the integral of y(x) using the trapezoidal rule.