Homework, Material, and Software Manual for Math 4610
Routine Name: gaussSolv
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 will solve the equation Ax = b where A is of dimensions mxn and b is a vector of length n. The method uses the methods gaussElim(a,b) and backSub(a,b).
Input: The first input will need to be a two dimensional array of dimensions mxn. The second input will need to be an array of length n. The dimensions of the inputs need to be checked before calling the method.
Output: This method will return the solution x to the equation Ax = b. This will be an array of length n.
Usage/Example:
First define c and d
c = [[0.0] * 3 for k in range(0, 3)]
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
d = [0.0 for i in range(0, 3)]
d[0] = 11.0
d[1] = 15.0
d[2] = 18.0
Now we have
c = [[7.0, 3.0, 1.0],
[3.0, 10.0, 2.0],
[1.0, 2.0, 15.0]]
d = [11.0, 15.0, 18.0]
Now let’s print to the console the solution to our method
print(gaussSolv(c, d))
This prints
[1.0000000000000002, 0.9999999999999998, 0.9999999999999999]
Implementation/Code: The following is the code for gaussSolv(a, b)
def gaussSolv(a,b):
gaussElim(a,b)
return backSub(a,b)
Last Modified: December 2018