Other functions#

On this page we describe formally unrelated functions and modules of wulfric that were not mentioned in the previous pages. We do not describe all of them. To see full list of wulfric capabilities see API reference.

In the examples of this page we assume that wulfric is imported as

>>> import wulfric

Comparing of numbers#

Due to the limitations of the float point arithmetics or expected inaccuracy of the input data two numbers might be considered equal even if they are not exactly equal. For example 1.0000000001 and 1.0000000002 are equal with the accuracy 1e-9, but different with the accuracy of 1e-11. Same logic can be applied to other comparison operators. We enjoyed the formal definition from [1] and implemented it as a standalone function in wulfric

>>> wulfric.compare_with_tolerance(1.0000000001, "==", 1.0000000002, eps=1e-9)
True
>>> wulfric.compare_with_tolerance(1.0000000001, "==", 1.0000000002, eps=1e-11)
False
>>> wulfric.compare_with_tolerance(1.02, "<", 1.03, eps=0.001)
True
>>> wulfric.compare_with_tolerance(1.02, "<", 1.03, eps=0.1)
False
>>> wulfric.compare_with_tolerance(1.02, "<=", 1.03, eps=0.1)
True

This function return boolean value and support python's comparison operators. See wulfric.compare_with_tolerance() for details.

Parallelepiped#

Not every set of six numbers might be used to form a parallelepiped. Wulfric implements a function to check if the set of parameters is correct

>>> a = 1
>>> b = 1
>>> c = 1
>>> alpha = 90
>>> beta = 90
>>> gamma = 90
>>> wulfric.geometry.parallelepiped_check(a, b, c, alpha, beta, gamma)
True
>>> wulfric.geometry.parallelepiped_check(a, b, c, alpha, beta, 181)
False

Volume and angle#

It is often required to compute angle between two vectors or a volume of the cell. Wulfric implements two functions just for that.

To compute an angle between two vectors use

>>> a = [1, 0, 0]
>>> b = [0, 1, 0]
>>> # In degrees by default
>>> wulfric.geometry.get_angle(a, b)
90.0
>>> # In radians
>>> round(wulfric.geometry.get_angle(a, b, radians=True), 4)
1.5708
>>> # For the zero vector the angle is not defined
>>> wulfric.geometry.get_angle(a, [0, 0, 0])
Traceback (most recent call last):
...
ValueError: Angle is ill defined (zero vector).

For the volume wulfric accepts three types of inputs:

  • Cell

    \(3\times3\) array, rows are the cell vectors, columns are the \(xyz\) coordinates.

    >>> cell = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
>>> wulfric.geometry.get_volume(cell)
1.0

  • Three vectors

    >>> a = [1, 0, 0]
>>> b = [0, 1, 0]
>>> c = [0, 0, 1]
>>> wulfric.geometry.get_volume(a, b, c)
1.0

  • Six cell parameters

    >>> a = 1
>>> b = 1
>>> c = 1
>>> alpha = 90
>>> beta = 90
>>> gamma = 90
>>> wulfric.geometry.get_volume(a, b, c, alpha, beta, gamma)
1.0

Spherical coordinates#

>>> import wulfric
>>> wulfric.geometry.get_spherical([1, 0, 0])
(1.0, 90.0, 0.0)
>>> wulfric.geometry.get_spherical([-1, 0, 0])
(1.0, 90.0, 180.0)
>>> wulfric.geometry.get_spherical([0, 1, 0])
(1.0, 90.0, 90.0)
>>> wulfric.geometry.get_spherical([0, -1, 0])
(1.0, 90.0, 270.0)
>>> wulfric.geometry.get_spherical([0, 0, 1])
(1.0, 0.0, 0.0)
>>> wulfric.geometry.get_spherical([0, 0, -1])
(1.0, 180.0, 180.0)
>>> wulfric.geometry.get_spherical([1, 0, 0], polar_axis = [1, 0, 0])
(1.0, 0.0, 0.0)

References#