Q1)$Implementing$Gaussian$Elimination$Method$
i) Find$the$approximate$time$your$computer$takes$for$a$single$addition$by$adding$
first$106"positive$integers$using$a$for$loop$and$dividing$the$time$taken$by$106.$
Similarly$find$the$approximate$time$taken$for$a$single$multiplication$and$division.$
Report$the$result$obtained$in$the$form$of$a$table.$(
Deliverable(s):-A-tabular-column-indicating-the-time-taken-for-each-of-the-
operations--
Answer:$
Time taken for Addition(in
Sec)
Time taken for Multiplication(in
Sec)
Time taken for Division(in
Sec)
9.656799999999998e-08
PS: Total is
0.09656799999999999
0.00037666722
PS: Total is 376.66722
0.0003767326
PS: Total is 376.7326
ii) Deliverable(s):-The-code-for-the-Gaussian-elimination-with-and-with--out-partial-
pivoting-with-the-rounding-part-!
Answer:$
Code: GIT Link :
https://github.com/deysandip81/BITS_MTECH_Projects/blob/main/GaussElimination
.py
import numpy as np
# defining a function for
# round s.
def round_s(n, decimals=0):
if decimals == 0:
n_5s = n + 5 * pow(10, -(decimals+1))
else:
n_5s = n + 5 * pow(10, -(decimals))
if '.' in str(n_5s) and '-' in str(n_5s):
return(float(str(n_5s)[0:decimals+2]))
elif '.' in str(n_5s) or '-' in str(n_5s):
return (float(str(n_5s)[0:decimals + 1]))
else:
return (float(str(n_5s)[0:decimals]))
def Cal_LU(D,g,ds):
A=np.array((D),dtype=float)
f=np.array((g),dtype=float)
num_add = 0
num_sub = 0
num_div = 0
num_mult = 0
n = f.size
for i in range(0,n-1): # Loop through the columns of the matrix
for j in range(i+1,n): # Loop through rows below diagonal for each
column