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Problem 1:

You are running Python v3.7.1 with NumPy v1.15.4 and SciPy v1.1.0

Running test for problem 2 and 3:

First implementation

In [3]: import MATH7015_HW2_Test

In [4]: MATH7015_HW2_Test.HW2_Test("MATH7015_HW2_Template")
Testing for N = 2
Memory Usage:  0.003 MB
Gaussian Elimination Time:  0.004 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 5
Memory Usage:  0.008 MB
Gaussian Elimination Time:  0.002 seconds
LU Factorization Time:  0.007 seconds
Testing for N = 10
Memory Usage:  0.016 MB
Gaussian Elimination Time:  0.004 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 100
Memory Usage:  0.229 MB
Gaussian Elimination Time:  0.014 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 1000
Memory Usage:  9.155 MB
Gaussian Elimination Time:  1.940 seconds
LU Factorization Time:  0.072 seconds
Testing for N = 2000
Memory Usage: 33.569 MB
Gaussian Elimination Time: 11.972 seconds
LU Factorization Time:  0.357 seconds
Testing for N = 4000
Memory Usage: 128.174 MB
Gaussian Elimination Time: 83.655 seconds
LU Factorization Time:  1.654 seconds
Problem #2 and #3 Tests Finished.
Tests passed!
Out[4]: True

Second implementation

In [5]: MATH7015_HW2_Test.HW2_Test("MATH7015_HW2_Template")
Testing for N = 2
Memory Usage:  0.003 MB
Gaussian Elimination Time:  0.002 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 5
Memory Usage:  0.008 MB
Gaussian Elimination Time:  0.002 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 10
Memory Usage:  0.016 MB
Gaussian Elimination Time:  0.002 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 100
Memory Usage:  0.229 MB
Gaussian Elimination Time:  0.013 seconds
LU Factorization Time:  0.005 seconds
Testing for N = 1000
Memory Usage:  9.155 MB
Gaussian Elimination Time:  1.989 seconds
LU Factorization Time:  0.073 seconds
Testing for N = 2000
Memory Usage: 33.569 MB
Gaussian Elimination Time: 11.723 seconds
LU Factorization Time:  0.355 seconds
Testing for N = 4000
Memory Usage: 128.174 MB
Gaussian Elimination Time: 83.709 seconds
LU Factorization Time:  2.012 seconds
Problem #2 and #3 Tests Finished.
Tests passed!
Out[5]: True