# -*- coding: utf-8 -*-
# pylint: disable=too-many-lines
r"""Klassen für dreidimensionale Vektoren und 3*3-Matrizen.
.. moduleauthor:: Michael Rippstein <info@comlab.ch>
Idea and parts of the source from [Montenbruck2004a]_.
For the classes `Vec3D` and `Mat3D` the following operation are definde.
=========== ========= ========= ======== =================== ============================
Funktion Arg_1 (a) Arg_2 (b) Wert (c) Notation Bedeutung
=========== ========= ========= ======== =================== ============================
`-` `Vec3D` `Vec3D` .. math:: c = -a Unäres Minus
\ `Mat3D` `Mat3D` .. math:: C = -A
`-` `Vec3D` `Vec3D` `Vec3D` .. math:: c = a - b Vektor-Subtraktion
\ `Mat3D` `Mat3D` `Mat3D` .. math:: C = A - B Matrix-Subtraktion
`+` `Vec3D` `Vec3D` `Vec3D` .. math:: c = a + b Vektor-Addition
\ `Mat3D` `Mat3D` `Mat3D` .. math:: C = A + B Matrix-Addition
`*` `int` `Vec3D` `Vec3D` .. math:: c = ab Skalar-Multiplikation
\ `float` `Vec3D` `Vec3D` .. math:: c = ab
\ `Vec3D` `int` `Vec3D` .. math:: c = ab
\ `Vec3D` `float` `Vec3D` .. math:: c = ab
\ `int` `Mat3D` `Mat3D` .. math:: C = aB
\ `float` `Mat3D` `Mat3D` .. math:: C = aB
\ `Mat3D` `int` `Mat3D` .. math:: C = Ab
\ `Mat3D` `float` `Mat3D` .. math:: C = Ab
`*` `Mat3D` `Vec3D` `Vec3D` .. math:: c = Ab Matrix/Vektor-Multiplikation
`/` `Vec3D` `int` `Vec3D` .. math:: c = a/b Skalar-Division
\ `Vec3D` `float` `Vec3D` .. math:: c = a/b
\ `Mat3D` `int` `Mat3D` .. math:: C = A/b
\ `Mat3D` `float` `Mat3D` .. math:: C = A/b
`abs` `Vec3D` `float` .. math:: c = |a|
`dot` `Vec3D` `Vec3D` `float` .. math:: c = ab Skalarprodukt
`cross` `@` `Vec3D` `Vec3D` `Vec3D` .. math:: c = a × b Vektorprodukt, Kreuzprodukt
`tranp` `Mat3D` `Mat3D` .. math:: C = A^T Transponierte
`einmat` `Mat3D` Einheitsmatrix
`rotmatx` `float` `Mat3D` Elementare Drehmatrix
`rotmaty` `float` `Mat3D`
`rotmatz` `float` `Mat3D`
`==` `Vec3D` `Vec3D` `bool`
=========== ========= ========= ======== =================== ============================
Bedeutung der Winkel bei den Kugelkoordinaten
---------------------------------------------
.. todo:: Korekte winkel bezeichungen im den bilder!
.. image:: _static/sphere.png
:scale: 50 %
References
----------
.. [Montenbruck2004a] Montenbruck, Oliver; Pfleger, Thomas:
"Astronomie mit dem Personal
Computer"; 4. Auflage; Springer-Verlag; Berlin,
Heidelberg 2004
"""
import math
from typing import List, Optional, Tuple, Union
import numpy as np
__all__ = ['Vec3D', 'Mat3D', 'cross', 'dot', 'transp', 'einmat', 'rotmatx', 'rotmaty', 'rotmatz', 'polar2kart']
_TYPEERRORTEXT = "unsupported operand type(s) for '{}': '{}' and '{}'"
[docs]class Vec3D:
r"""Dreidimensionaler Vector.
Der Aufruf ohne die angabe von Parameter initialisiert einen Null-Vector.
.. code-block:: python
null_vector = Vec3D()
Parameters
----------
\**kwargs
siehe unten
arg
siehe unten
.. code-block:: python
Vec3D([x, y, z])
Vec3D((x, y, z))
Keyword Arguments
-----------------
phi, theta, r
Polarkoordinaten
.. code-block:: python
Vec3D(theta=, phi=, r=)
az, elev
Polarkoordinaten
.. code-block:: python
Vec3D(az=, elev=)
az, elev, r : float
Polarkoordinaten
.. code-block:: python
Vec3D(az=, elev=, r=)
Raises
------
TypeError
Examples
--------
.. testsetup:: vec
import math
from mrmath.vecmat3d import Vec3D
.. doctest:: vec
>>> nullvector = Vec3D()
>>> print(nullvector)
Vec3D([0, 0, 0])
>>> print(nullvector.xyz)
[0, 0, 0]
>>> repr(nullvector.array)
'array([[0],\n [0],\n [0]])'
>>> print("x: {}, y: {}, z: {}".format(nullvector.x, nullvector.y, nullvector.z))
x: 0, y: 0, z: 0
>>> print("phi: {}, theta: {}, r: {}".format(nullvector.phi,
... nullvector.theta,
... nullvector.r))
phi: 0, theta: 0, r: 0
>>> print(Vec3D([1, 2, 3]))
Vec3D([1, 2, 3])
>>> print(Vec3D([1.0, 2.0, 3.0]))
Vec3D([1.0, 2.0, 3.0])
>>> vector = Vec3D()
>>> vector.x = 9.9
>>> vector.y = 5
>>> vector.z = 1.1
>>> print(vector)
Vec3D([9.9, 5, 1.1])
>>> polar = Vec3D(theta=math.pi/2, phi=math.pi/2, r=1)
>>> '{:.3f}, {:.3f}, {:.3f}'.format(polar.x, polar.y, polar.z)
'0.000, 0.000, 1.000'
>>> vector.x = 'text'
Traceback (most recent call last):
...
TypeError: unsupported type for setter: '<class 'str'>'
"""
# pylint: disable=too-many-instance-attributes
def __init__( # pylint: disable=too-many-branches
self, arg: Union[None, Tuple, List] = None, **kwargs: Optional[float]
) -> None:
self.__x = 0.0
self.__y = 0.0
self.__z = 0.0 #: Komponenten des Vektors
self.__phi: float #: Polarwinkel (Azimut)
self.__theta: float #: Polarwinkel (Elevation)
self.__r: float #: Betrag des Vektors
self.__polarvalid = False #: zeigt, ob Polarkomponenten gueltig sind
if (arg is None) and not kwargs:
# initialisierung: null vector
self.__x = 0
self.__y = 0
self.__z = 0 #: Komponenten des Vektors
self.__phi = 0 #: Polarwinkel (Azimut)
self.__theta = 0 #: Polarwinkel (Elevation)
self.__r = 0 #: Betrag des Vektors
self.__polarvalid = True #: zeigt, ob Polarkomponenten gueltig sind
elif isinstance(arg, (list, tuple)) and len(arg) == 3:
self.x = arg[0]
self.y = arg[1]
self.z = arg[2]
elif (arg is None) and 'phi' in kwargs and 'theta' in kwargs and 'r' in kwargs:
if (
isinstance(kwargs['phi'], (int, float))
and isinstance(kwargs['theta'], (int, float))
and isinstance(kwargs['r'], (int, float))
):
self.__phi = kwargs['phi']
self.__theta = kwargs['theta']
self.__r = kwargs['r']
self.__polarvalid = True
self.x = self.__r * math.cos(self.__phi) * math.cos(self.__theta)
self.y = self.__r * math.sin(self.__phi) * math.cos(self.__theta)
self.z = self.__r * math.sin(self.__theta)
else:
raise TypeError
elif (arg is None) and 'az' in kwargs and 'elev' in kwargs:
if isinstance(kwargs['az'], (int, float)) and isinstance(kwargs['elev'], (int, float)):
self.__phi = kwargs['az']
self.__theta = kwargs['elev']
if 'r' in kwargs:
if isinstance(kwargs['r'], (int, float)):
self.__r = kwargs['r']
else:
raise TypeError
else:
self.__r = 1.0
self.__polarvalid = True
self.x = self.__r * math.cos(self.__phi) * math.cos(self.__theta)
self.y = self.__r * math.sin(self.__phi) * math.cos(self.__theta)
self.z = self.__r * math.sin(self.__theta)
else:
raise TypeError
else:
raise TypeError
@property
def xyz(self) -> List[float]:
"""Gibt die kartesischen Koordinaten zurück.
Returns
-------
List[float]
Kartesischekoordinaten ``[x, y, z]``
"""
return [self.__x, self.__y, self.__z]
@property
def polar(self) -> List[float]:
"""Gibt die polar Koordinaten zurück.
Returns
-------
List[float]
Polarkoordinaten: ``[phi, theta, r]``
"""
return [self.phi, self.theta, self.r]
@property
def array(self) -> np.ndarray:
"""Gibt die kartesischen Koordinaten als Spaltenvector in einem `numpy.array` zurück.
Returns
-------
numpy.ndarray
Spaltenvektor ``[[x][y][z]]``
"""
return np.array([[self.__x], [self.__y], [self.__z]])
@property
def x(self) -> float:
"""x-axis in the cartesian coordinate system.
Returns
-------
float
x-axis
"""
return self.__x
@x.setter
def x(self, value: float) -> None:
if isinstance(value, (int, float)):
self.__x = value
self.__polarvalid = False
else:
raise TypeError("unsupported type for setter: '{}'".format(type(value)))
@property
def y(self) -> float:
"""y-axis in the cartesian coordinate system."""
return self.__y
@y.setter
def y(self, value: float) -> None:
if isinstance(value, (int, float)):
self.__y = value
self.__polarvalid = False
else:
raise TypeError("unsupported type for setter: '{}'".format(type(value)))
@property
def z(self) -> float:
"""z-axis in the cartesian coordinate system."""
return self.__z
@z.setter
def z(self, value: float) -> None:
if isinstance(value, (int, float)):
self.__z = value
self.__polarvalid = False
else:
raise TypeError("unsupported type for setter: '{}'".format(type(value)))
@property
def phi(self) -> float:
"""Azimut in den Polarkoordinaten."""
if not self.__polarvalid:
self._calcpolar()
return self.__phi
@property
def theta(self) -> float:
"""Elevation in den Polarkoordinaten."""
if not self.__polarvalid:
self._calcpolar()
return self.__theta
@property
def r(self) -> float:
"""Radius in den Polarkoordinaten."""
if not self.__polarvalid:
self._calcpolar()
return self.__r
[docs] def __abs__(self) -> float:
"""Betrag (Radius).
Returns
-------
float
Betrag des Vektors
Examples
--------
.. testsetup:: vecabs
from mrmath.vecmat3d import Vec3D
.. doctest:: vecabs
>>> vector = Vec3D([1, 0, 0])
>>> print('{:.4f}'.format(abs(vector)))
1.0000
>>> vector = Vec3D([1, 1, 0])
>>> print('{:.4f}'.format(abs(vector)))
1.4142
>>> vector = Vec3D([1, 0, 1])
>>> print('{:.4f}'.format(abs(vector)))
1.4142
"""
return self.r
[docs] def __getitem__(self, key: int) -> float:
"""Implement the ``self[key]`` call.
Returns
-------
float
for key = 0: x
for key = 1: y
for key = 2: z
Raises
------
IndexError
When key outside of 0…2
Examples
--------
.. testsetup:: vecitem
from mrmath.vecmat3d import Vec3D
.. doctest:: vecitem
>>> vector = Vec3D([3, 7, 13])
>>> print(vector[0])
3
>>> print(vector[1])
7
>>> print(vector[2])
13
>>> print(vector[3])
Traceback (most recent call last):
...
IndexError: list index out of range
>>> for m in vector:
... print(m)
3
7
13
"""
if key == 0:
return self.x
if key == 1:
return self.y
if key == 2:
return self.z
raise IndexError('list index out of range')
[docs] def __setitem__(self, key: int, value: float) -> None:
"""Implement the assignment to ``self[key]``.
Parameters
----------
key
Schlüssel
value
Wert
Raises
------
IndexError:
When key outside of 0…2
Examples
--------
.. testsetup:: vecitem
from mrmath.vecmat3d import Vec3D
.. doctest:: vecitem
>>> vector = Vec3D()
>>> vector[0] = 3
>>> vector[1] = 7
>>> vector[2] = 13
>>> print(vector)
Vec3D([3, 7, 13])
>>> vector[3] = 17
Traceback (most recent call last):
...
IndexError: list index out of range
>>> for m in vector:
... print(m)
3
7
13
"""
if key == 0:
self.x = value
elif key == 1:
self.y = value
elif key == 2:
self.z = value
else:
raise IndexError('list index out of range')
[docs] def _calcpolar(self) -> None:
"""Berechne polare Komponenten.
Berechnet die polaren Komponenten des Vektors mit den
aktuellen kartesischen Daten. Setzt `__polarvalid` auf
`True`.
Examples
--------
.. testsetup:: veccalpol
from mrmath.vecmat3d import Vec3D
.. doctest:: veccalpol
>>> vector1 = Vec3D([1, 0, 0])
>>> print("phi: {}, theta: {}, r: {}".format(vector1.phi,
... vector1.theta,
... vector1.r))
phi: 0.0, theta: 0.0, r: 1.0
>>> vector2 = Vec3D([0, 1, 0])
>>> print("phi: {:.4f}, theta: {}, r: {}".format(vector2.phi,
... vector2.theta,
... vector2.r))
phi: 1.5708, theta: 0.0, r: 1.0
>>> vector3 = Vec3D([0, 0, 1])
>>> print("phi: {}, theta: {:.4f}, r: {}".format(vector3.phi,
... vector3.theta,
... vector3.r))
phi: 0.0, theta: 1.5708, r: 1.0
>>> vector4 = Vec3D([-1, -1, -1])
>>> print("phi: {:.4f}, theta: {:.4f}, r: {:.4f}".format(vector4.phi,
... vector4.theta,
... vector4.r))
phi: 3.9270, theta: -0.6155, r: 1.7321
"""
# Laenge der Projektion des Vektors in die x-y-Ebene
rho_sqr = self.__x ** 2 + self.__y ** 2
# Betrag des Vektors
self.__r = math.sqrt(rho_sqr + self.__z ** 2)
# Azimut des Vektors
if (self.__x == 0.0) and (self.__y == 0.0):
self.__phi = 0.0
else:
self.__phi = math.atan2(self.__y, self.__x)
if self.__phi < 0.0:
self.__phi += math.tau
# Elevation des Vektors
rho = math.sqrt(rho_sqr)
if (self.__z == 0.0) and (rho == 0.0):
self.__theta = 0.0
else:
self.__theta = math.atan2(self.__z, rho)
self.__polarvalid = True
[docs] def __repr__(self) -> str:
"""Reprentation des Vectors.
Returns
-------
str
Reprepresantation
"""
return 'Vec3D([{}, {}, {}])'.format(self.x, self.y, self.z)
[docs] def __neg__(self) -> 'Vec3D':
"""Negation: `-self`.
Returns
-------
Vec3D
inverted vector
Examples
--------
.. testsetup:: vecneg
from mrmath.vecmat3d import Vec3D
.. doctest:: vecneg
>>> vector = Vec3D([1, 2, 3])
>>> print(-vector)
Vec3D([-1, -2, -3])
>>> vector = Vec3D([-1, -2, -3])
>>> print(-vector)
Vec3D([1, 2, 3])
"""
return Vec3D([-self.__x, -self.__y, -self.__z])
[docs] def __add__(self, other: Union['Vec3D', float]) -> 'Vec3D':
"""Addition: ``self + other``.
Parameters
----------
other
Summand
Returns
-------
Vec3D
Summe
Examples
--------
.. testsetup:: vecadd
from mrmath.vecmat3d import Vec3D
.. doctest:: vecadd
>>> summand = Vec3D([2, 6, 20])
>>> summe = summand + -9
>>> print(summe)
Vec3D([-7, -3, 11])
>>> summand1 = Vec3D([2, 6, 20])
>>> summand2 = Vec3D([-9.0, -9.0, -9.0])
>>> summe = summand1 + summand2
>>> print(summe)
Vec3D([-7.0, -3.0, 11.0])
"""
if isinstance(other, self.__class__):
tempx = self.__x + other.x
tempy = self.__y + other.y
tempz = self.__z + other.z
elif isinstance(other, (int, float)):
tempx = self.__x + other
tempy = self.__y + other
tempz = self.__z + other
else:
return NotImplemented
return Vec3D([tempx, tempy, tempz])
[docs] def __radd__(self, other: Union['Vec3D', float]) -> 'Vec3D':
"""Addition: ``other + self``.
Parameters
----------
other
Summand
Returns
-------
Vec3D
Summe
Examples
--------
.. testsetup:: vecadd
from mrmath.vecmat3d import Vec3D
.. doctest:: vecadd
>>> summand = Vec3D([2, 6, 20])
>>> summe = -9 + summand
>>> print(summe)
Vec3D([-7, -3, 11])
"""
# if isinstance(other, self.__class__):
# tempx = other.x + self.__x
# tempy = other.y + self.__y
# tempz = other.z + self.__z
if isinstance(other, (int, float)):
tempx = other + self.__x
tempy = other + self.__y
tempz = other + self.__z
else:
return NotImplemented
return Vec3D([tempx, tempy, tempz])
[docs] def __iadd__(self, other: Union['Vec3D', float]) -> 'Vec3D':
"""Addition: ``self += other``.
Parameters
----------
other
Summand
Returns
-------
Vec3D
Summe
Examples
--------
.. testsetup:: vecadd
from mrmath.vecmat3d import Vec3D
.. doctest:: vecadd
>>> summe = Vec3D([2, 6, 20])
>>> summe += -9
>>> print(summe)
Vec3D([-7, -3, 11])
>>> summe = Vec3D([2, 6, 20])
>>> summand = Vec3D([-9.0, -9.0, -9.0])
>>> summe += summand
>>> print(summe)
Vec3D([-7.0, -3.0, 11.0])
"""
if isinstance(other, self.__class__):
self.__x += other.x
self.__y += other.y
self.__z += other.z
self.__polarvalid = False
elif isinstance(other, (int, float)):
self.__x += other
self.__y += other
self.__z += other
self.__polarvalid = False
else:
return NotImplemented
return self
[docs] def __sub__(self, other: Union['Vec3D', float]) -> 'Vec3D':
"""Subtraktion: `self - other`.
Parameters
----------
other
Subtrahend
Returns
-------
Vec3D
Differenz
Examples
--------
.. testsetup:: vecsub
from mrmath.vecmat3d import Vec3D
.. doctest:: vecsub
>>> minuend = Vec3D([4, 8, 16])
>>> subtrahend = Vec3D([3, 9, 27])
>>> differenz = minuend - 2
>>> print(differenz)
Vec3D([2, 6, 14])
>>> differenz = minuend - subtrahend
>>> print(differenz)
Vec3D([1, -1, -11])
"""
if isinstance(other, self.__class__):
tempx = self.__x - other.x
tempy = self.__y - other.y
tempz = self.__z - other.z
elif isinstance(other, (int, float)):
tempx = self.__x - other
tempy = self.__y - other
tempz = self.__z - other
else:
return NotImplemented
return Vec3D([tempx, tempy, tempz])
[docs] def __rsub__(self, other: Union['Vec3D', float]) -> 'Vec3D':
"""Subraktion: `other - self`.
Parameters
----------
other
Minuend
Returns
-------
Vec3D
Differenz
Examples
--------
.. testsetup:: vecsub
from mrmath.vecmat3d import Vec3D
.. doctest:: vecsub
>>> minuend = Vec3D([4, 8, 16])
>>> subtrahend = Vec3D([3, 9, 27])
>>> differenz = 2 - subtrahend
>>> print(differenz)
Vec3D([-1, -7, -25])
>>> differenz = minuend - subtrahend
>>> print(differenz)
Vec3D([1, -1, -11])
"""
if isinstance(other, self.__class__):
tempx = other.x - self.__x
tempy = other.y - self.__y
tempz = other.z - self.__z
elif isinstance(other, (int, float)):
tempx = other - self.__x
tempy = other - self.__y
tempz = other - self.__z
else:
return NotImplemented
return Vec3D([tempx, tempy, tempz])
[docs] def __isub__(self, other: Union['Vec3D', float]) -> 'Vec3D':
"""Subtraktion: `self -= other`.
Parameters
----------
other
Subtrahend
Returns
-------
Vec3D
Differenz
Examples
--------
.. testsetup:: vecsub
from mrmath.vecmat3d import Vec3D
.. doctest:: vecsub
>>> differenz = Vec3D([4, 8, 16])
>>> differenz -= 2
>>> print(differenz)
Vec3D([2, 6, 14])
"""
if isinstance(other, self.__class__):
self.__x -= other.x
self.__y -= other.y
self.__z -= other.z
self.__polarvalid = False
elif isinstance(other, (int, float)):
self.__x -= other
self.__y -= other
self.__z -= other
self.__polarvalid = False
else:
return NotImplemented
return self
[docs] def __mul__(self, other: Union['Mat3D', float]) -> 'Vec3D':
"""Multiplikation `self * other`.
Parameters
----------
other
Multiplikatand
Returns
-------
Vec3D
Produkt
Examples
--------
.. testsetup:: vecmul
from mrmath.vecmat3d import Vec3D
.. doctest:: vecmul
>>> faktor1 = Vec3D((2,4,6))
>>> produkt = faktor1 * 3.75
>>> print(produkt)
Vec3D([7.5, 15.0, 22.5])
>>> produkt = faktor1 * 'text'
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for '*': '<class '__main__.Vec3D'>' and '<class 'str'>'
"""
if isinstance(other, (int, float)):
tempx = self.__x * other
tempy = self.__y * other
tempz = self.__z * other
result = [tempx, tempy, tempz]
elif isinstance(other, Mat3D):
result = [0, 0, 0]
for j in range(3):
scalp = 0.0
for i in range(3):
scalp += self[i] * other._mat[i][j]
result[j] = scalp
else:
return NotImplemented
return Vec3D(result)
[docs] def __rmul__(self, other: Union['Mat3D', float]) -> 'Vec3D':
"""Multiplikation `other * self`.
Parameters
----------
other
Multiplikator
Returns
-------
Vec3D
Produkt
Examples
--------
.. testsetup:: vecmul
from mrmath.vecmat3d import Vec3D
.. doctest:: vecmul
>>> faktor2 = Vec3D((2,4,6))
>>> produkt = 3.75 * faktor2
>>> print(produkt)
Vec3D([7.5, 15.0, 22.5])
>>> produkt = faktor2 * 'text'
Traceback (most recent call last):
...
TypeError: ...
"""
if isinstance(other, (int, float)):
tempx = other * self.__x
tempy = other * self.__y
tempz = other * self.__z
result = [tempx, tempy, tempz]
elif isinstance(other, Mat3D):
result = [0, 0, 0]
for i in range(3):
scalp = 0.0
for j in range(3):
scalp += other._mat[i][j] * self[j]
result[i] = scalp
else:
return NotImplemented
return Vec3D(result)
[docs] def __imul__(self, other: Union['Mat3D', float]) -> 'Vec3D':
"""Multiplikation: `self = self * other`.
Parameters
----------
other
Multiplikand
Returns
-------
Vex3D
Produkt
Examples
--------
.. testsetup:: vecmul
import math
from mrmath.vecmat3d import Vec3D, rotmatx
.. doctest:: vecmul
>>> faktor1 = Vec3D((2, 4, 6))
>>> produkt = faktor1 * 3.75
>>> print(produkt)
Vec3D([7.5, 15.0, 22.5])
>>> faktor1 = Vec3D((2, 4, 6))
>>> faktor2 = rotmatx(0.5 * math.pi)
>>> produkt = faktor1 * faktor2
>>> print(produkt)
Vec3D([2, -4, 6])
>>> produkt = faktor1 * 'text'
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for '*': '<class '__main__.Vec3D'>' and '<class 'str'>'
"""
if isinstance(other, (int, float)):
self.__x *= other
self.__y *= other
self.__z *= other
self.__polarvalid = False
elif isinstance(other, Mat3D):
result = [0.0, 0.0, 0.0]
for j in range(3):
scalp = 0.0
for i in range(3):
scalp += other._mat[i][j] * self[i]
result[j] = scalp
self.__x *= result[0]
self.__y *= result[1]
self.__z *= result[2]
self.__polarvalid = False
else:
return NotImplemented
return self
[docs] def __truediv__(self, other: float) -> 'Vec3D':
"""Division `self / other`.
Parameters
----------
other
Divisor
Returns
-------
Vec3D
Quotient
Examples
--------
.. testsetup:: vecdiv
from mrmath.vecmat3d import Vec3D
.. doctest:: vecdiv
>>> dividend = Vec3D([1, 2, 3])
>>> quotient = dividend / 2
>>> print(quotient)
Vec3D([0.5, 1.0, 1.5])
"""
if isinstance(other, (int, float)):
tempx = self.__x / other
tempy = self.__y / other
tempz = self.__z / other
else:
return NotImplemented
return Vec3D([tempx, tempy, tempz])
[docs] def __itruediv__(self, other: Union[int, float]) -> 'Vec3D':
"""Division `self /= other`.
Parameters
----------
other
Divisor
Returns
-------
Vec3D
Quotient
Examples
--------
.. testsetup:: vecdiv
from mrmath.vecmat3d import Vec3D
.. doctest:: vecdiv
>>> quotient = Vec3D([1, 2, 3])
>>> quotient /= 2
>>> print(quotient)
Vec3D([0.5, 1.0, 1.5])
>>> quotient /= 'string'
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for '/=': '<class '__main__.Vec3D'>' and '<class 'str'>'
"""
if isinstance(other, (int, float)):
self.__x /= other
self.__y /= other
self.__z /= other
self.__polarvalid = False
else:
return NotImplemented
return self
[docs] def __eq__(self, other: object) -> bool:
"""Comparisons ``self == other``."""
if not isinstance(other, Vec3D):
return NotImplemented
return self.__x == other.x and self.__y == other.y and self.__z == other.z
[docs]class Mat3D:
"""3x3 Matrix."""
def __init__(self, args: List) -> None: # noqa: D107
self._mat = args # [[None, None, None], [None, None, None], [None, None, None]]
[docs] def __getitem__(self, key: int) -> float:
"""FIXME! briefly describe function."""
return self._mat[key]
# def __setitem__(self, key: int, value: Union[int, float]) -> None:
# """FIXME! briefly describe function.
#
# :param key:
# :type: int or (int, int)
# :param value:
# :type: int or float
#
# """
# pass
[docs] def __repr__(self) -> str:
"""FIXME! briefly describe function."""
return 'Mat3D([[{},{},{}],[{},{},{}],[{},{},{}]])'.format( # noqa: F524
self._mat[0][0],
self._mat[1][0],
self._mat[2][0],
self._mat[0][1],
self._mat[1][1],
self._mat[2][1],
self._mat[0][2],
self._mat[1][2],
self._mat[2][2],
)
[docs] def __mul__(self, other: Union['Mat3D', int, float]) -> 'Mat3D':
"""Multiplikation: 'self * other'.
Parameters
----------
other
Multiplikator
Returns
-------
Mat3D
Produkt
"""
if isinstance(other, Mat3D):
res = Mat3D([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
for i in range(3):
for j in range(3):
for k in range(3):
res._mat[i][k] += self._mat[i][j] * other._mat[j][k]
return res
if isinstance(other, (int, float)):
# res = Mat3D(self._mat * other)
return NotImplemented
return NotImplemented
# def __rmul__(self, other):
# """Multiplikation: 'other * self'.
#
# :param other: Multiplikator
# :type other: int, float or Mat3D
# :returns: Produkt
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(other._mat * self._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(other * self._mat)
# else:
# return NotImplemented
# return res
#
# def __imul__(self, other):
# """Multiplikation: 'self *= other'.
#
# :param other: Multiplikator
# :type other: int, float or Mat3D
# :returns: Produkt
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# self.__mat = self.__mat * other._mat
# elif isinstance(other, (int, float)):
# self.__mat = self.__mat * other
# else:
# return NotImplemented
# return self
#
# def __truediv__(self, other):
# """Division: 'self / other'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(self._mat / other._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(self._mat / other)
# else:
# return NotImplemented
# return res
#
# def __rtruediv__(self, other):
# """Division: 'other / self'.
#
# :param other: Dividend
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(other._mat / self._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(other / self._mat)
# else:
# return NotImplemented
# return res
#
# def __itruediv__(self, other):
# """Division: 'self /= other'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# self.__mat = self.__mat / other._mat
# elif isinstance(other, (int, float)):
# self.__mat = self._mat / other
# else:
# return NotImplemented
# return self
#
# def __floordiv__(self, other):
# """Ganzzahlige Division: 'self // other'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(self._mat // other._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(self._mat // other)
# else:
# return NotImplemented
# return res
#
# def __rfloordiv__(self, other):
# """Ganzzahlige Division: 'other // self'.
#
# :param other: Dividend
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(other._mat // self._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(other // self._mat)
# else:
# return NotImplemented
# return res
#
# def __ifloordiv__(self, other):
# """Ganzzahlige Division: 'self //= other'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# self.__mat = self.__mat // other._mat
# elif isinstance(other, (int, float)):
# self.__mat = self._mat // other
# else:
# return NotImplemented
# return self
#
# def __mod__(self, other):
# """Division mit Rest: 'self % other'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(self._mat % other._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(self._mat % other)
# else:
# return NotImplemented
# return res
#
# def __rmod__(self, other):
# """Division mit Rest: 'other % self'.
#
# :param other: Dividend
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = Mat3D(other._mat % self._mat)
# elif isinstance(other, (int, float)):
# res = Mat3D(other % self._mat)
# else:
# return NotImplemented
# return res
#
# def __imod__(self, other):
# """Division mit Rest: 'self %= other'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# self.__mat = self.__mat % other._mat
# elif isinstance(other, (int, float)):
# self.__mat = self._mat % other
# else:
# return NotImplemented
# return self
#
# def __divmod__(self, other):
# """Ganzzahlige Division mit Rest: 'divmod(self, other)'.
#
# :param other: Divisor
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = divmod(self._mat % other._mat)
# elif isinstance(other, (int, float)):
# res = divmod(self._mat % other)
# else:
# return NotImplemented
# return res
#
# def __rdivmod__(self, other):
# """Ganzzahlige Division mit Rest: 'divmod(other, self)'.
#
# :param other: Dividend
# :type other: int, float or Mat3D
# :returns: Quotient
# :rtype: Mat3D
# """
# if isinstance(other, Mat3D):
# res = divmod(other._mat % self._mat)
# elif isinstance(other, (int, float)):
# res = divmod(other % self._mat)
# else:
# return NotImplemented
# return res
# -- funktionen
[docs]def cross(left: Vec3D, right: Vec3D) -> Vec3D:
"""Vektorprodukt (Kreuzprodukt).
Parameters
----------
left
Linker Vektor
right
Rechter Vektor
Returns
-------
Vec3D
Kreuzprodukt
Raises
------
TypeError
If `left` or `right` is not from type :class:`Vec3D`
"""
if isinstance(left, Vec3D) and isinstance(right, Vec3D):
cross_x = left.y * right.z - left.z * right.y
cross_y = left.z * right.x - left.x * right.z
cross_z = left.x * right.y - left.y * right.x
return Vec3D((cross_x, cross_y, cross_z))
raise TypeError(_TYPEERRORTEXT.format('cross', type(left), type(right)))
[docs]def dot(left: Vec3D, right: Vec3D) -> float:
"""Skalarprodukt zweier Vektoren.
Parameters
----------
left
Linker Vektor
right
Rechter Vektor
Returns
-------
float
Skalarprodukt
Raises
------
TypeError
If `left` or `right` is not from type :class:`Vec3D`
"""
if isinstance(left, Vec3D) and isinstance(right, Vec3D):
return left.x * right.x + left.y * right.y + left.z * left.z
raise TypeError(_TYPEERRORTEXT.format('dot', type(left), type(right)))
[docs]def transp(matrix: Mat3D) -> Mat3D:
"""Transponierte einer Matrix.
Parameters
----------
matrix
Originalmatrix
Returns
-------
Mat3D
Transponierte Matrix
"""
return Mat3D(
[
[ # pylint: disable=protected-access # noqa: E501
matrix._mat[0][0],
matrix._mat[1][0],
matrix._mat[2][0],
],
[ # pylint: disable=protected-access # noqa: E501
matrix._mat[0][1],
matrix._mat[1][1],
matrix._mat[2][1],
],
[ # pylint: disable=protected-access # noqa: E501
matrix._mat[0][2],
matrix._mat[1][2],
matrix._mat[2][2],
],
]
)
[docs]def einmat() -> Mat3D:
"""Einheitsmatrix.
Returns
-------
Mat3D
Einheitsmatrix
"""
return Mat3D([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
[docs]def rotmatx(alpha: float) -> Mat3D:
"""Matrix für die rotation um die x-achse.
.. image:: _static/rotmatx.png
:scale: 20 %
Parameters
----------
alpha
Drehwinkel
Returns
-------
Mat3D
Rotationsmatrix
Examples
--------
.. testsetup:: rotmatx
import math
from mrmath.vecmat3d import rotmatx, Vec3D
.. doctest:: rotmatx
>>> a = rotmatx(0.25 * math.pi)
>>> a._mat
[[1, 0, 0], [0, 0.7071067811865476, 0.7071067811865475], [0, -0.7071067811865475, 0.7071067811865476]]
>>> a = rotmatx(0.5 * math.pi)
>>> b = Vec3D((0.0, 1.0, 0.0))
>>> a * b
Vec3D([0.0, 6.123233995736766e-17, -1.0])
"""
return Mat3D([[1, 0, 0], [0, math.cos(alpha), math.sin(alpha)], [0, -math.sin(alpha), math.cos(alpha)]])
[docs]def rotmaty(alpha: float) -> Mat3D:
"""Matrix für die rotation um die y-achse.
.. image:: _static/rotmaty.png
:scale: 20 %
Parameters
----------
alpha
Drehwinkel
Returns
-------
Mat3D
Rotationsmatrix
"""
return Mat3D([[math.cos(alpha), 0, -math.sin(alpha)], [0, 1, 0], [math.sin(alpha), 0, math.cos(alpha)]])
[docs]def rotmatz(alpha: float) -> Mat3D:
"""Matrix für die Rotation um die Z-Achse.
.. image:: _static/rotmatz.png
:scale: 20 %
Parameters
----------
alpha
Drehwinkel
Returns
-------
Mat3D
Rotationsmatrix
"""
return Mat3D([[math.cos(alpha), math.sin(alpha), 0], [-math.sin(alpha), math.cos(alpha), 0], [0, 0, 1]])
[docs]def polar2kart(phi: float, theta: float, r: float) -> Tuple[float, float, float]:
"""Polarkoordinaten zu Kartesischenkoordinaten.
.. image:: _static/sphere.png
:scale: 50 %
Parameters
----------
phi
winkel zwischen z-achse und vektor
theta
winkel zwischen x-achse und vektor
r
länge des vector
Returns
-------
(x, y, z) kart.-koord.
"""
x = r * math.cos(phi) * math.cos(theta)
y = r * math.sin(phi) * math.cos(theta)
z = r * math.sin(theta)
return x, y, z
