quadtools

This module specialises class Submodel for quadrature problems.

Module quadtools provides Python interfaces only. See the Cython extension module quadutils for the actual implementations of the mathematical algorithms.

Module quadtools implements the following members:

• Quad Numerical solver for quadrature problems based on the Gauss-Lobatto quadrature.

---

class hydpy.auxs.quadtools.Quad(model: Model)

Bases: Submodel

Numerical solver for quadrature problems based on the Gauss-Lobatto quadrature.

CYTHONBASECLASS

alias of QuadBase

PYTHONCLASS

alias of QuadPython

integrate(x0: float, x1: float, nmin: int, nmax: int, tol: float) → float

Repeatedly integrate the target function within the interval \(x0 \leq x \leq x1\) until the estimated accuracy is smaller than tol using at least xmin and at most xmax number of nodes.

The algorithm underlying Quad works acceptable, but should be improvable both regarding accuracy and efficiency. We postpone this and provide example calculations afterwards. Please see the documentation on method Calc_DVEq_V1 to see Quad in action until then.

apply_method0(value: float) → float

Apply the model method to be integrated.

For example, submodel QuadDVEq_V1 integrates method Return_DVH_V1:

>>> from hydpy.models.wland import *
>>> parameterstep()
>>> thetas(0.4)
>>> psiae(300.0)
>>> b(5.0)
>>> sh(0.0)
>>> derived.rh1.update()
>>> from hydpy import round_
>>> round_(model.return_dvh_v1(600.0))
0.05178
>>> round_(model.quaddveq_v1.apply_method0(600.0))
0.05178

name = 'quad'