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Matrix.py
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import math
class Matrix:
@staticmethod
def Add(matA, matB):
"""
Description
----------
Adds the two input matrices.
Parameters
----------
matA : list
The first input matrix.
matB : list
The second input matrix.
Returns
-------
list
The matrix resulting from the addition of the two input matrices.
"""
matC = []
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
for i in range(len(matA)):
tempRow = []
for j in range(len(matB)):
tempRow.append(matA[i][j] + matB[i][j])
matC.append(tempRow)
return matC
@staticmethod
def ByRotation(rx=0, ry=0, rz=0, order="xyz"):
"""
Description
----------
Creates a 4x4 rotation matrix.
Parameters
----------
rx : float , optional
The desired rotation around the X axis. The default is 0.
ry : float , optional
The desired rotation around the Y axis. The default is 0.
rz : float , optional
The desired rotation around the Z axis. The default is 0.
order : string , optional
The order by which the roatations will be applied. The possible values are any permutation of "xyz". This input is case insensitive. The default is "xyz".
Returns
-------
list
The created 4X4 rotation matrix.
"""
def rotateXMatrix(radians):
""" Return matrix for rotating about the x-axis by 'radians' radians """
c = math.cos(radians)
s = math.sin(radians)
return [[1, 0, 0, 0],
[0, c,-s, 0],
[0, s, c, 0],
[0, 0, 0, 1]]
def rotateYMatrix(radians):
""" Return matrix for rotating about the y-axis by 'radians' radians """
c = math.cos(radians)
s = math.sin(radians)
return [[ c, 0, s, 0],
[ 0, 1, 0, 0],
[-s, 0, c, 0],
[ 0, 0, 0, 1]]
def rotateZMatrix(radians):
""" Return matrix for rotating about the z-axis by 'radians' radians """
c = math.cos(radians)
s = math.sin(radians)
return [[c,-s, 0, 0],
[s, c, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]
xMat = rotateXMatrix(math.radians(rx))
yMat = rotateYMatrix(math.radians(ry))
zMat = rotateZMatrix(math.radians(rz))
if order.lower() == "xyz":
return Matrix.Multiply(Matrix.Multiply(zMat,yMat),xMat)
if order.lower() == "xzy":
return Matrix.Multiply(Matrix.Multiply(yMat,zMat),xMat)
if order.lower() == "yxz":
return Matrix.Multiply(Matrix.Multiply(zMat,xMat),yMat)
if order.lower == "yzx":
return Matrix.Multiply(Matrix.Multiply(xMat,zMat),yMat)
if order.lower() == "zxy":
return Matrix.Multiply(Matrix.Multiply(yMat,xMat),zMat)
if order.lower() == "zyx":
return Matrix.Multiply(Matrix.Multiply(xMat,yMat),zMat)
@staticmethod
def ByScaling(sx=1.0, sy=1.0, sz=1.0):
"""
Description
----------
Creates a 4x4 scaling matrix.
Parameters
----------
sx : float , optional
The desired scaling factor along the X axis. The default is 1.
sy : float , optional
The desired scaling factor along the X axis. The default is 1.
sz : float , optional
The desired scaling factor along the X axis. The default is 1.
Returns
-------
list
The created 4X4 scaling matrix.
"""
return Matrix.Transpose([[sx,0,0,0],
[0,sy,0,0],
[0,0,sz,0],
[0,0,0,1]])
@staticmethod
def ByTranslation(tx=0, ty=0, tz=0):
"""
Description
----------
Creates a 4x4 translation matrix.
Parameters
----------
tx : float , optional
The desired translation distance along the X axis. The default is 0.
ty : float , optional
The desired translation distance along the X axis. The default is 0.
tz : float , optional
The desired translation distance along the X axis. The default is 0.
Returns
-------
list
The created 4X4 translation matrix.
"""
return Matrix.Transpose([[1,0,0,tx],
[0,1,0,ty],
[0,0,1,tz],
[0,0,0,1]])
@staticmethod
def Multiply(matA, matB):
"""
Description
----------
Multiplies the two input matrices.
Parameters
----------
matA : list
The first input matrix.
matB : list
The second input matrix.
Returns
-------
list
The matrix resulting from the multiplication of the two input matrices.
"""
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
nr = len(matA)
nc = len(matA[0])
matC = []
for i in range(nr):
tempRow = []
for j in range(nc):
tempRow.append(0)
matC.append(tempRow)
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
# iterate through rows of X
for i in range(len(matA)):
# iterate through columns of Y
tempRow = []
for j in range(len(matB[0])):
# iterate through rows of Y
for k in range(len(matB)):
matC[i][j] += matA[i][k] * matB[k][j]
return matC
@staticmethod
def Subtract(matA, matB):
"""
Description
----------
Subtracts the two input matrices.
Parameters
----------
matA : list
The first input matrix.
matB : list
The second input matrix.
Returns
-------
list
The matrix resulting from the subtraction of the second input matrix from the first input matrix.
"""
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
matC = []
for i in range(len(matA)):
tempRow = []
for j in range(len(matB)):
tempRow.append(matA[i][j] - matB[i][j])
matC.append(tempRow)
return matC
@staticmethod
def Transpose(matrix):
"""
Description
----------
Transposes the input matrix.
Parameters
----------
matrix : list
The input matrix.
Returns
-------
list
The transposed matrix.
"""
return [list(x) for x in zip(*matrix)]