Homework, Material, and Software Manual for Math 4610
Routine Name: fowardSub
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 perform forward substitution given a matrix and a vector. It solves the equation Ax = b where A is a lower triangular matrix of dimensions mxn and b is a vector of length n.
Input: The first input needs to be a two dimensional array of dimensions mxn. The second input needs to be an array of length n. The dimensions need to be checked before calling the method.
Output: This method will return the solution x to the equation Ax = b. This will be returned as an array of length n.
Usage/Example:
First let’s define c and d
c = [[0.0] * 3 for k in range(0, 3)]
c[0][0] = 7.0
c[1][0] = 3.0
c[1][1] = 10.0
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] = 2
d[1] = 3
d[2] = 2
Now we have
c = [[7.0, 0.0, 0.0],
[3.0, 10.0, 0.0],
[1.0, 2.0, 15.0]]
d = [2, 3, 2]
Now let’s print to the console the solution to our method
print(forwardSub(c, d))
This prints
[0.2857142857142857, 0.21428571428571427, 0.08571428571428572]
Implementation/Code: The following is the code for forwardSub(a, b)
def forwardSub(a,b):
n = len(b)
x = [0.0 for i in range(0,n)]
x[0] = b[0]/a[0][0]
for i in range(1,n):
sumVal = 0.0
for j in range(0, i):
sumVal = sumVal + a[i][j]*x[j]
x[i] = (b[i] - sumVal)/a[i][i]
return x
Last Modified: December 2018