# Source code for pyrr.objects.matrix44

```# -*- coding: utf-8 -*-
"""Represents a 4x4 Matrix.

The Matrix44 class provides a number of convenient functions and
conversions.
::

import numpy as np
from pyrr import Quaternion, Matrix33, Matrix44, Vector4

m = Matrix44()
m = Matrix44([[1.,0.,0.,0.],[0.,1.,0.,0.],[0.,0.,1.,0.],[0.,0.,0.,1.]])

# copy constructor
m = Matrix44(Matrix44())

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

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

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

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

# convert from quaternion back to matrix
m = q.matrix44
m = Matrix44(q)

# rotate a matrix by a quaternion
m = Matrix44.identity() * Quaternion()

# rotate a vector 4 by a matrix
v = Matrix44.from_x_rotation(np.pi) * Vector4([1.,2.,3.,1.])

# undo a rotation
m = Matrix44.from_x_rotation(np.pi)
v = m * Vector4([1.,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
# fourth element, fourth row
m44 = m.m44
# 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, BaseMatrix44, BaseQuaternion, BaseVector, NpProxy
from .. import matrix44

[docs]class Matrix44(BaseMatrix44):
_module = matrix44
_shape = (4,4,)

# 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)
#: The fourth row of this Matrix as a numpy.ndarray.
m4 = NpProxy(3)

# 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 [0,3] value of this Matrix.
m14 = NpProxy((0,3))
#: 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 [1,3] value of this Matrix.
m24 = NpProxy((1,3))
#: 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))
#: The [2,3] value of this Matrix.
m34 = NpProxy((2,3))
#: The [3,0] value of this Matrix.
m41 = NpProxy((3,0))
#: The [3,1] value of this Matrix.
m42 = NpProxy((3,1))
#: The [3,2] value of this Matrix.
m43 = NpProxy((3,2))
#: The [3,3] value of this Matrix.
m44 = NpProxy((3,3))

# 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)
#: The fourth row of this Matrix as a numpy.ndarray. This is the same as m4.
r4 = NpProxy(3)

# columns
#: The first column of this Matrix as a numpy.ndarray.
c1 = NpProxy((slice(0,4),0))
#: The second column of this Matrix as a numpy.ndarray.
c2 = NpProxy((slice(0,4),1))
#: The third column of this Matrix as a numpy.ndarray.
c3 = NpProxy((slice(0,4),2))
#: The fourth column of this Matrix as a numpy.ndarray.
c4 = NpProxy((slice(0,4),3))

########################
# Creation
[docs]    @classmethod
def from_matrix33(cls, matrix, dtype=None):
"""Creates a Matrix44 from a Matrix33.
"""
return cls(matrix44.create_from_matrix33(matrix, dtype))

[docs]    @classmethod
def perspective_projection(cls, fovy, aspect, near, far, dtype=None):
"""Creates a Matrix44 for use as a perspective projection matrix.
"""
return cls(matrix44.create_perspective_projection(fovy, aspect, near, far, dtype))

[docs]    @classmethod
def perspective_projection_bounds(cls, left, right, top, bottom, near, far, dtype=None):
"""Creates a Matrix44 for use as a perspective projection matrix.
"""
return cls(matrix44.create_perspective_projection_from_bounds(left, right, top, bottom, near, far, dtype))

[docs]    @classmethod
def orthogonal_projection(cls, left, right, top, bottom, near, far, dtype=None):
"""Creates a Matrix44 for use as an orthogonal projection matrix.
"""
return cls(matrix44.create_orthogonal_projection(left, right, top, bottom, near, far, dtype))

[docs]    @classmethod
def look_at(cls, eye, target, up, dtype=None):
"""Creates a Matrix44 for use as a lookAt matrix.
"""
return cls(matrix44.create_look_at(eye, target, up, dtype))

[docs]    @classmethod
def from_translation(cls, translation, dtype=None):
"""Creates a Matrix44 from the specified translation.
"""
return cls(matrix44.create_from_translation(translation, dtype=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)

# matrix33
if obj.shape == (3,3) or isinstance(obj, Matrix33):
obj = matrix44.create_from_matrix33(obj, dtype=dtype)
# quaternion
elif obj.shape == (4,) or isinstance(obj, Quaternion):
obj = matrix44.create_from_quaternion(obj, dtype=dtype)
else:
obj = np.zeros(cls._shape, dtype=dtype)
obj = obj.view(cls)
return super(Matrix44, 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 Matrix44(super(Matrix44, self).__sub__(Matrix44(other)))

@dispatch((BaseMatrix, np.ndarray, list))
def __mul__(self, other):
return Matrix44(matrix44.multiply(Matrix44(other), self))

@dispatch((BaseMatrix, np.ndarray, list))
def __ne__(self, other):
return bool(np.any(super(Matrix44, self).__ne__(other)))

@dispatch((BaseMatrix, np.ndarray, list))
def __eq__(self, other):
return bool(np.all(super(Matrix44, self).__eq__(other)))

########################
# Quaternions
@dispatch(BaseQuaternion)
def __mul__(self, other):
m = other.matrix44
return self * m

########################
# Vectors
@dispatch(BaseVector)
def __mul__(self, other):
return type(other)(matrix44.apply_to_vector(self, other))

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

@dispatch((Number, np.number))
def __sub__(self, other):
return Matrix44(super(Matrix44, self).__sub__(other))

@dispatch((Number, np.number))
def __mul__(self, other):
return Matrix44(super(Matrix44, self).__mul__(other))

@dispatch((Number, np.number))
def __truediv__(self, other):
return Matrix44(super(Matrix44, self).__truediv__(other))

@dispatch((Number, np.number))
def __div__(self, other):
return Matrix44(super(Matrix44, self).__div__(other))

########################
# Methods and Properties
@property
def matrix33(self):
"""Returns a Matrix33 representing this matrix.
"""
return Matrix33(self)

@property
def matrix44(self):
"""Returns the Matrix44.

This can be handy if you're not sure what type of Matrix class you have
but require a Matrix44.
"""
return self

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

[docs]    def decompose(self):
"""Decomposes an affine transformation matrix into its scale, rotation and
translation components.

:param numpy.array m: A matrix.
:return: tuple (scale, rotation, translation)
Vector3 scale
Quaternion rotation
Vector3 translation
"""
scale, rotate, translate = matrix44.decompose(self)
return Vector3(scale), Quaternion(rotate), Vector3(translate)

from .matrix33 import Matrix33
from .quaternion import Quaternion
from .vector3 import Vector3
```