Matrices in Python without Numpy: Part 3
Today's functions will focus on exact calculations for determinants and inverses for certain sizes: 2 x 2 and 3 x3.
In the following examples:
mat2 = [ [ 11, 2 ] , [ -8, 4 ] ]
mat3 = [ [ 11, 2, 3 ], [ 4, 51, 6 ], [ 17, 8, 19 ] ]
Screenshots are made using an emulator on my.numworks.com.
Determinants
det2(matrix): determinant of a 2 x 2 matrix
det3(matrix): determinant of a 3 x 3 matrix
def det2(M):
if len(M)==2 and len(M[0])==2:
return M[0][0]*M[1][1]-M[0][1]*M[1][0]
else:
return "not a 2 x 2 matrix"
def det3(M):
if len(M)==3 and len(M[0])==3:
m10=M[1][0]
m20=M[2][0]
m11=M[1][1]
m21=M[2][1]
m12=M[1][2]
m22=M[2][2]
t=M[0][0]*det2([[m11,m12],[m21,m22]])
t-=M[0][1]*det2([[m10,m12],[m20,m22]])
t+=M[0][2]*det2([[m10,m11],[m20,m21]])
return t
else:
return "not a 3 x 3 matrix"
Inverses
inv2(matrix): inverse of a 2 x 2 matrix
inv3(matrix): inverse of a 3 x 3 matrix
def inv2(M):
if len(M)==2 and len(M[0])==2:
MT=newmatrix(2,2)
t=det2(MT)
MT[0][0]=M[0][0]*1/t
MT[0][1]=-M[1][0]*1/t
MT[1][0]=-M[0][1]*1/t
MT[1][1]=M[1][1]*1/t
return MT
else:
"not a 2 x 2 matrix"
def inv3(M):
if len(M)==3 and len(M[0])==3:
t=det3(M)
A=newmatrix(3,3)
A[0][0]=det2([[M[1][1],M[1][2]],[M[2][1],M[2][2]]])/t
A[0][1]=det2([[M[0][2],M[0][1]],[M[2][2],M[2][1]]])/t
A[0][2]=det2([[M[0][1],M[0][2]],[M[1][1],M[1][2]]])/t
A[1][0]=det2([[M[1][2],M[1][0]],[M[2][2],M[2][0]]])/t
A[1][1]=det2([[M[0][0],M[0][2]],[M[2][0],M[2][2]]])/t
A[1][2]=det2([[M[0][2],M[0][0]],[M[1][2],M[1][0]]])/t
A[2][0]=det2([[M[1][0],M[1][1]],[M[2][0],M[2][1]]])/t
A[2][1]=det2([[M[0][1],M[0][0]],[M[2][1],M[2][0]]])/t
A[2][2]=det2([[M[0][0],M[0][1]],[M[1][0],M[1][1]]])/t
return A
else:
"not a 3 x 3 matrix"
The functions inv2, inv3, and det3 require det2. I am using mprint to print matrices as they are supposed to appear. Please see the blog post on October 3 for the code for mprint.
Coming up in Part 4, row operations, upper triangular matrices, and determinants of matrices of any size.
Happy computing,
Eddie
Source:
Ives, Thom. "BASIC Linear Algebra Tools in Pure Python without Numpy or Scipy" Integrated Machine Learning & AI December 11, 2018. https://integratedmlai.com/basic-linear-algebra-tools-in-pure-python-without-numpy-or-scipy/
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
