# Source code for pyrr.objects.matrix33

```# -*- coding: utf-8 -*-
"""Represents a 3x3 Matrix.

The Matrix33 class provides a number of convenient functions and
conversions.
::

import numpy as np
from pyrr import Quaternion, Matrix33, Matrix44, Vector3

m = Matrix33()
m = Matrix33([[1.,0.,0.],[0.,1.,0.],[0.,0.,1.]])

# copy constructor
m = Matrix44(Matrix44())

# explicit creation
m = Matrix33.identity()
m = Matrix33.from_matrix44(Matrix44())

# inferred conversions
m = Matrix33(Quaternion())
m = Matrix33(Matrix44())

# multiply matricies together
m = Matrix33() * Matrix33()
m = Matrix33() * Matrix44()

# extract a quaternion from a matrix
q = m.quaternion

# convert from quaternion back to matrix
m = q.matrix33
m = Matrix33(q)

# rotate a matrix by a quaternion
m = Matrix33.identity() * Quaternion()

# rotate a vector 3 by a matrix
v = Matrix33.from_x_rotation(np.pi) * Vector3([1.,2.,3.])

# undo a rotation
m = Matrix33.from_x_rotation(np.pi)
v = m * Vector3([1.,1.,1.])
# ~m is the same as m.inverse
v = ~m * v

# access specific parts of the matrix
# first row
m1 = m.m1
# first element, first row
m11 = m.m11
# third element, third row
m33 = m.m33
# first row, same as m1
r1 = m.r1
# first column
c1 = m.c1
"""
from __future__ import absolute_import
from numbers import Number
import numpy as np
from multipledispatch import dispatch
from .base import BaseObject, BaseMatrix, BaseMatrix33, BaseQuaternion, BaseVector, NpProxy
from .. import matrix33

[docs]class Matrix33(BaseMatrix33):
_module = matrix33
_shape = (3,3,)

# m<c> style access
#: The first row of this Matrix as a numpy.ndarray.
m1 = NpProxy(0)
#: The second row of this Matrix as a numpy.ndarray.
m2 = NpProxy(1)
#: The third row of this Matrix as a numpy.ndarray.
m3 = NpProxy(2)

# m<r><c> access
#: The [0,0] value of this Matrix.
m11 = NpProxy((0,0))
#: The [0,1] value of this Matrix.
m12 = NpProxy((0,1))
#: The [0,2] value of this Matrix.
m13 = NpProxy((0,2))
#: The [1,0] value of this Matrix.
m21 = NpProxy((1,0))
#: The [1,1] value of this Matrix.
m22 = NpProxy((1,1))
#: The [1,2] value of this Matrix.
m23 = NpProxy((1,2))
#: The [2,0] value of this Matrix.
m31 = NpProxy((2,0))
#: The [2,1] value of this Matrix.
m32 = NpProxy((2,1))
#: The [2,2] value of this Matrix.
m33 = NpProxy((2,2))

# rows
#: The first row of this Matrix as a numpy.ndarray. This is the same as m1.
r1 = NpProxy(0)
#: The second row of this Matrix as a numpy.ndarray. This is the same as m2.
r2 = NpProxy(1)
#: The third row of this Matrix as a numpy.ndarray. This is the same as m3.
r3 = NpProxy(2)

# columns
#: The first column of this Matrix as a numpy.ndarray.
c1 = NpProxy((slice(0,3),0))
#: The second column of this Matrix as a numpy.ndarray.
c2 = NpProxy((slice(0,3),1))
#: The third column of this Matrix as a numpy.ndarray.
c3 = NpProxy((slice(0,3),2))

########################
# Creation
[docs]    @classmethod
def from_matrix44(cls, matrix, dtype=None):
"""Creates a Matrix33 from a Matrix44.

The Matrix44 translation will be lost.
"""
return cls(matrix33.create_from_matrix44(matrix, dtype))

def __new__(cls, value=None, dtype=None):
if value is not None:
obj = value
if not isinstance(value, np.ndarray):
obj = np.array(value, dtype=dtype)

# matrix44
if obj.shape == (4,4) or isinstance(obj, Matrix44):
obj = matrix33.create_from_matrix44(obj, dtype=dtype)
# quaternion
elif obj.shape == (4,) or isinstance(obj, Quaternion):
obj = matrix33.create_from_quaternion(obj, dtype=dtype)
else:
obj = np.zeros(cls._shape, dtype=dtype)
obj = obj.view(cls)
return super(Matrix33, cls).__new__(cls, obj)

########################
# Basic Operators

@dispatch(BaseObject)

@dispatch(BaseObject)
def __sub__(self, other):
self._unsupported_type('subtract', other)

@dispatch(BaseObject)
def __mul__(self, other):
self._unsupported_type('multiply', other)

@dispatch(BaseObject)
def __truediv__(self, other):
self._unsupported_type('divide', other)

@dispatch(BaseObject)
def __div__(self, other):
self._unsupported_type('divide', other)

def __invert__(self):
return self.inverse

########################
# Matrices
@dispatch((BaseMatrix, np.ndarray, list))

@dispatch((BaseMatrix, np.ndarray, list))
def __sub__(self, other):
return Matrix33(super(Matrix33, self).__sub__(Matrix33(other)))

@dispatch((BaseMatrix, np.ndarray, list))
def __mul__(self, other):
return Matrix33(matrix33.multiply(Matrix33(other), self))

@dispatch((BaseMatrix, np.ndarray, list))
def __ne__(self, other):
return bool(np.any(super(Matrix33, self).__ne__(other)))

@dispatch((BaseMatrix, np.ndarray, list))
def __eq__(self, other):
return bool(np.all(super(Matrix33, self).__eq__(other)))

########################
# Quaternions
@dispatch(BaseQuaternion)
def __mul__(self, other):
m = other.matrix33
return self * m

########################
# Vectors
@dispatch(BaseVector)
def __mul__(self, other):
return type(other)(matrix33.apply_to_vector(self, other))

########################
# Number
@dispatch((Number, np.number))

@dispatch((Number, np.number))
def __sub__(self, other):
return Matrix33(super(Matrix33, self).__sub__(other))

@dispatch((Number, np.number))
def __mul__(self, other):
return Matrix33(super(Matrix33, self).__mul__(other))

@dispatch((Number, np.number))
def __truediv__(self, other):
return Matrix33(super(Matrix33, self).__truediv__(other))

@dispatch((Number, np.number))
def __div__(self, other):
return Matrix33(super(Matrix33, self).__div__(other))

########################
# Methods and Properties
@property
def matrix33(self):
"""Returns the Matrix33.

This can be handy if you're not sure what type of Matrix class you have
but require a Matrix33.
"""
return self

@property
def matrix44(self):
"""Returns a Matrix44 representing this matrix.
"""
return Matrix44(self)

@property
def quaternion(self):
"""Returns a Quaternion representing this matrix.
"""
return Quaternion(self)

from .matrix44 import Matrix44
from .quaternion import Quaternion
```