Homework, Material, and Software Manual for Math 4610
Routine Name: cholSolv
Author: Tanner Wheeler
Language: Python. This code can be run on a python 3 compiler. The file can be imported and then the method will run.
Description/Purpose: This method will use Cholesky factorization to split a matrix A into a lower triangular part and an upper triangular part that are transposes of each other. It will then perform forward substitution and back substitution to solve the equation Ax = b. This method uses the methodschol(a), forwardSub(a,b), and backSub(a,b).
Input: This method takes two inputs. The first is a two dimensional array of dimensions mxn. The second input should be an array of length n.
Output: This method will return the answer to the equation Ax = b. This will be an array of length n.
Usage/Example:
First we need to define c and d
c = [[0.0] * 5 for k in range(0,5)]
c[0][0] = 7.0
c[0][1] = 3.0
c[0][2] = 1.0
c[1][0] = 3.0
c[1][1] = 10.0
c[1][2] = 2.0
c[2][0] = 1.0
c[2][1] = 2.0
c[2][2] = 15.0
c[3][3] = 10.0
c[4][4] = 12.0
d = [0.0 for i in range(0, 5)]
d[0] = 11.0
d[1] = 15.0
d[2] = 18.0
d[3] = 10.0
d[4] = 12.0
Now we have
c = [[7.0, 3.0, 1.0, 0.0, 0.0],
[3.0, 10.0, 2.0, 0.0, 0.0],
[1.0, 2.0, 15.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 10.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 12.0]]
d = [11.0, 15.0, 18.0, 10.0, 12.0]
Let’s perform our method using c and d and print the output to the console.
print(cholSolv(c, d))
This will print
[0.9999999999999997, 1.0000000000000002, 1.0000000000000002, 0.9999999999999999, 1.0000000000000002]
Implementation/Code: The following is the code for cholSolv(a,b)
def cholSolv(a, b):
chol(a)
return backSub(a, forwardSub(a,b))
Last Modified: December 2018