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test_numpy_compare.py
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test_numpy_compare.py
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import numpy as np
import unittest
import matrices
import time
class CustomTests(unittest.TestCase):
""" Here we will try to compare 'matrices.py' vs 'numpy' package in several aspects
Notice: to run this script you'll need to install numpy first"""
def setUp(self):
""" Initializing several matrices to work with. (Yes, they are matrices from test_matrices.py ->
-> TestMatrix() -> test_18())"""
self.matrix_a = [[1, 4],
[3, 6]]
self.matrix_b = [[5, -2, 1],
[3, 1, -4],
[6, 0, -3]]
self.matrix_c = [[3, 5, 7, 8],
[-1, 7, 0, 1],
[0, 5, 3, 2],
[1, -1, 7, 4]]
self.matrix_d = [[1, 2, 0, 0, 0],
[3, 2, 3, 0, 0],
[0, 4, 3, 4, 0],
[0, 0, 5, 4, 5],
[0, 0, 0, 6, 5]]
self.matrix_e = [[0, 6, -2, -1, 5],
[0, 0, 0, -9, -7],
[0, 15, 35, 0, 0],
[0, -1, -11, -2, 1],
[-2, -2, 3, 0, -2]]
self.matrix_em = [[0, 6, -2, -1, 5],
[0, 0, 0, -9, -7],
[0, 15, 35, 0, 0],
[0, -1, -11, -2, 1],
[0, -2, 3, 0, -2]]
self.matrix_f = [[1, 2, 3, 0, 0, 0],
[4, 3, 0, 0, -1, -2],
[1, 2, 1, 1, 1, 0],
[3, -2, -2, 0, 0, 0],
[4, 1, -1, -5, 5, 0],
[0, 0, 6, 5, 4, 0]]
self.matrix_g = [[2, 0, 4, 0, 5, 0, 1],
[0, 3, -5, -1, 2, 0, 3],
[4, 5, 1, 1, 2, 3, 0],
[2, -4, 4, 4, 4, 2, 2],
[2, 0, 3, 4, 1, 3, 0],
[0, -5, -5, 6, 1, 4, 0],
[3, 0, 4, -1, 2, 0, 7]]
self.matrix_i = [[1, 2, 3],
[2, 4, 6],
[7, 8, 9]]
def test_1(self):
""" Comparing inverse matrices form numpy and matrices.py
for comparing we will use numpy method 'numpy.allclose()'
(As a quick conclusion: all our test subjects passed comparison, but in most cases we needed to
raise higher 'precision' parameter in our 'matrix_inverse' method)"""
#self.setUp()
print("A " + "="*70)
numA = np.array(self.matrix_a)
matA = matrices.Matrix(self.matrix_a)
numAinv = np.linalg.inv(numA)
matAinv = matA.matrix_inverse(6)
print(numAinv)
matAinv.matrix_show()
# using something like this "np.array(np.float64(matAinv.matrix_unpack()))" to convert types
self.assertTrue(np.allclose(np.array(np.float64(matAinv.matrix_unpack())), numAinv))
print("B " + "="*70)
numB = np.array(self.matrix_b)
matB = matrices.Matrix(self.matrix_b)
numBinv = np.linalg.inv(numB)
matBinv = matB.matrix_inverse(6)
print(numBinv)
matBinv.matrix_show()
self.assertTrue(np.allclose(np.array(np.float64(matBinv.matrix_unpack())), numBinv))
print("C " + "="*70)
numC = np.array(self.matrix_c)
matC = matrices.Matrix(self.matrix_c)
numCinv = np.linalg.inv(numC)
matCinv = matC.matrix_inverse(7)
print(numCinv)
matCinv.matrix_show()
self.assertTrue(np.allclose(np.array(np.float64(matCinv.matrix_unpack())), numCinv))
print("D " + "="*70)
numD = np.array(self.matrix_d)
matD = matrices.Matrix(self.matrix_d)
numDinv = np.linalg.inv(numD)
matDinv = matD.matrix_inverse(7)
print(numDinv)
matDinv.matrix_show()
self.assertTrue(np.allclose(np.array(np.float64(matDinv.matrix_unpack())), numDinv))
print("E " + "="*70)
numE = np.array(self.matrix_e)
matE = matrices.Matrix(self.matrix_e)
numEinv = np.linalg.inv(numE)
matEinv = matE.matrix_inverse(7)
print(numEinv)
matEinv.matrix_show()
self.assertTrue(np.allclose(np.array(np.float64(matEinv.matrix_unpack())), numEinv))
print("Em " + "="*70)
numEm = np.array(self.matrix_em)
matEm = matrices.Matrix(self.matrix_em)
# here both methods should return an error
with self.assertRaises(Exception):
numEminv = np.linalg.inv(numEm)
with self.assertRaises(Exception):
matEminv = matEm.matrix_inverse()
numI = np.array(self.matrix_i)
matI = matrices.Matrix(self.matrix_i)
with self.assertRaises(Exception):
numIinv = np.linalg.inv(numI)
with self.assertRaises(Exception):
matIinv = matI.matrix_inverse(5)
print("F " + "="*70)
numF = np.array(self.matrix_f)
matF = matrices.Matrix(self.matrix_f)
numFinv = np.linalg.inv(numF)
matFinv = matF.matrix_inverse(8)
print(numFinv)
matFinv.matrix_show()
self.assertTrue(np.allclose(np.array(np.float64(matFinv.matrix_unpack())), numFinv))
print("G " + "="*70)
numG = np.array(self.matrix_g)
matG = matrices.Matrix(self.matrix_g)
numGinv = np.linalg.inv(numG)
matGinv = matG.matrix_inverse(9)
print(numGinv)
matGinv.matrix_show()
self.assertTrue(np.allclose(np.array(np.float64(matGinv.matrix_unpack())), numGinv))
def test_2(self):
""" Here we will compare results for determinant operation in both 'matrices.py' and 'numpy'
"""
numA = np.array(self.matrix_a)
matA = matrices.Matrix(self.matrix_a)
self.assertEqual(np.linalg.det(numA), matA.matrix_determinant())
numB = np.array(self.matrix_b)
matB = matrices.Matrix(self.matrix_b)
# for some reason numpy compute determinant for matrix_b (3x3 with integers) as 9.0000000000000018
# when it should be just 9, so code below raised a failure
# self.assertEqual(np.linalg.det(numB), matB.matrix_determinant(20))
numC = np.array(self.matrix_c)
matC = matrices.Matrix(self.matrix_c)
# AssertionError: 121.99999999999991 != Decimal('122.00')
# self.assertEqual(np.linalg.det(numC), matC.matrix_determinant())
numD = np.array(self.matrix_d)
matD = matrices.Matrix(self.matrix_d)
# AssertionError: 639.99999999999989 != Decimal('640.00'
# self.assertEqual(np.linalg.det(numD), matD.matrix_determinant())
numE = np.array(self.matrix_e)
matE = matrices.Matrix(self.matrix_e)
# AssertionError: 2479.9999999999968 != Decimal('2480.00')
# self.assertEqual(np.linalg.det(numE), matE.matrix_determinant())
numF = np.array(self.matrix_f)
matF = matrices.Matrix(self.matrix_f)
# AssertionError: -2346.0000000000009 != Decimal('-2346.00000000000000000000'
# self.assertEqual(np.linalg.det(numF), matF.matrix_determinant(20))
self.assertAlmostEqual(np.linalg.det(numF), float(matF.matrix_determinant(20)))
numG = np.array(self.matrix_g)
matG = matrices.Matrix(self.matrix_g)
# AssertionError: 4029.9999999999991 != Decimal('4030.00'
# self.assertEqual(np.linalg.det(numG), matG.matrix_determinant())
self.assertAlmostEqual(np.linalg.det(numG), float(matG.matrix_determinant()))
def test_3(self):
""" Here we will run a few performance checks for 'matrices.py' and 'numpy'
First, we'll check speed of determinant calculation, than - inverse matrix computation
This is not a real Unittest and lots of duplicated code can be bad for yor health!
Short conclusion: our methods way faster from numpy for a 2x2 example matrix"""
det_cycles = 1
numG = np.array(self.matrix_g)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = np.linalg.det(numG)
end_time = time.perf_counter()
total_time_num = end_time - start_time
matG = matrices.Matrix(self.matrix_g)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = matG.matrix_determinant()
end_time = time.perf_counter()
total_time_mat = end_time - start_time
print("="*70)
print("For matrix G(7x7) calculation of determinant {0} time(s) by numpy took {1} seconds".format(
det_cycles, total_time_num))
print("For matrix G(7x7) calculation of determinant {0} time(s) by matrices.py took {1} seconds".format(
det_cycles, total_time_mat))
# as a result we have this:
# For matrix G(7x7) calculation of determinant 100000 time(s) by numpy took 2.5861989099275493 seconds
# For matrix G(7x7) calculation of determinant 100000 time(s) by matrices.py took 21.711577452218382 seconds
# For matrix G(7x7) calculation of determinant 100 time(s) by numpy took 0.002622916097404813 seconds
# For matrix G(7x7) calculation of determinant 100 time(s) by matrices.py took 0.02498621645262421 seconds
# As expected: numpy with his progressive algorithms calculate determinant much faster than our teaching method
# Now, lets check if its true for 2x2 matrix
# (and yes - we copied previous code, and that, so you already know - is a bad programing example):
det_cycles = 1
numA = np.array(self.matrix_a)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = np.linalg.det(numA)
end_time = time.perf_counter()
total_time_num = end_time - start_time
matA = matrices.Matrix(self.matrix_a)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = matA.matrix_determinant()
end_time = time.perf_counter()
total_time_mat = end_time - start_time
print("="*70)
print("For matrix A(2x2) calculation of determinant {0} time(s) by numpy took {1} seconds".format(
det_cycles, total_time_num))
print("For matrix A(2x2) calculation of determinant {0} time(s) by matrices.py took {1} seconds".format(
det_cycles, total_time_mat))
# WE, actually, was faster this time(in our method 2x2 matrices was calculating by using standard formula)
# For matrix A(2x2) calculation of determinant 100 time(s) by numpy took 0.0022251738505491593 seconds
# For matrix A(2x2) calculation of determinant 100 time(s) by matrices.py took 0.0008682422217946573 seconds
# For matrix A(2x2) calculation of determinant 100000 time(s) by numpy took 2.4833566697009335 seconds
# For matrix A(2x2) calculation of determinant 100000 time(s) by matrices.py took 0.8371969034310927 seconds
# Finally, lets check 3x3 matrices. We, also, will use _matrix_determinant - a private method of 'matrices.py'
# where for computing determinant static formula was used:
det_cycles = 1
numB = np.array(self.matrix_b)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = np.linalg.det(numB)
end_time = time.perf_counter()
total_time_num = end_time - start_time
matB = matrices.Matrix(self.matrix_b)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = matB.matrix_determinant()
end_time = time.perf_counter()
total_time_mat = end_time - start_time
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = matB._matrix_determinant()
end_time = time.perf_counter()
total_time_mat_prive = end_time - start_time
print("="*70)
print("For matrix B(3x3) calculation of determinant {0} time(s) by numpy took {1} seconds".format(
det_cycles, total_time_num))
print("For matrix B(3x3) calculation of determinant {0} time(s) by matrices.py took {1} seconds".format(
det_cycles, total_time_mat))
print("For matrix B(3x3) calculation of determinant {0} time(s) by matrices.py using static formula"
" took {1} seconds".format(det_cycles, total_time_mat_prive))
# here the results:
# For matrix B(3x3) calculation of determinant 100 time(s) by numpy took 0.002191624453710725 seconds
# For matrix B(3x3) calculation of determinant 100 time(s) by matrices.py took 0.006737769830118791 seconds
# For matrix B(3x3) calculation of determinant 100 time(s) by matrices.py using static formula took 0.0006960489319973936 seconds
# For matrix B(3x3) calculation of determinant 100000 time(s) by numpy took 2.5949706624671984 seconds
# For matrix B(3x3) calculation of determinant 100000 time(s) by matrices.py took 3.7783217540756455 seconds
# For matrix B(3x3) calculation of determinant 100000 time(s) by matrices.py using static formula took 0.705146881684616 seconds
# AS we see: numpy calculate 'slightly' faster than our general method, but our private mrthod for 3x3 matrices much faster!
# Now, how about linearly dependent matrix:
det_cycles = 1
numI = np.array(self.matrix_i)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = np.linalg.det(numI)
end_time = time.perf_counter()
total_time_num = end_time - start_time
matI = matrices.Matrix(self.matrix_i)
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = matI.matrix_determinant()
end_time = time.perf_counter()
total_time_mat = end_time - start_time
start_time = time.perf_counter()
for i in range(1, det_cycles):
det = matI._matrix_determinant()
end_time = time.perf_counter()
total_time_mat_prive = end_time - start_time
print("="*70)
print("For linearly dependent matrix I(3x3) calculation of determinant {0} time(s) by numpy took {1} seconds".format(
det_cycles, total_time_num))
print("For linearly dependent matrix I(3x3) calculation of determinant {0} time(s) by matrices.py took {1} seconds".format(
det_cycles, total_time_mat))
print("For linearly dependent matrix I(3x3) calculation of determinant {0} time(s) by matrices.py using static formula"
" took {1} seconds".format(det_cycles, total_time_mat_prive))
# For linearly dependent matrix I(3x3) calculation of determinant 100 time(s) by numpy took 0.002870292372888207 seconds
# For linearly dependent matrix I(3x3) calculation of determinant 100 time(s) by matrices.py took 0.00395559515013153 seconds
# For linearly dependent matrix I(3x3) calculation of determinant 100 time(s) by matrices.py using static formula took 0.0006713921463691467 seconds
# For linearly dependent matrix I(3x3) calculation of determinant 100000 time(s) by numpy took 2.4001016182935566 seconds
# For linearly dependent matrix I(3x3) calculation of determinant 100000 time(s) by matrices.py took 2.7887345975931743 seconds
# For linearly dependent matrix I(3x3) calculation of determinant 100000 time(s) by matrices.py using static formula took 0.6946370278629761 seconds
# Yeh, for 100000 iterations numpy was just a bit faster, but this difference grown to almost 5 second
# for 1000000 iterations, in the other hand - static formula in our private method still working faster
# Now, lets test some inversion methods:
# Attention: duplicated code! Try not to do this in your programs - construct a method, which use a duplicates
det_cycles = 1
numG = np.array(self.matrix_g)
start_time = time.perf_counter()
for i in range(1, det_cycles):
numGinv = np.linalg.inv(numG)
end_time = time.perf_counter()
total_time_num = end_time - start_time
matG = matrices.Matrix(self.matrix_g)
start_time = time.perf_counter()
for i in range(1, det_cycles):
matGinv = matG.matrix_determinant()
end_time = time.perf_counter()
total_time_mat = end_time - start_time
print("="*70)
print("For matrix G(7x7) computation of inverse matrix {0} time(s) by numpy took {1} seconds".format(
det_cycles, total_time_num))
print("For matrix G(7x7) computation of inverse matrix {0} time(s) by matrices.py took {1} seconds".format(
det_cycles, total_time_mat))
# For matrix G(7x7) computation of inverse matrix 100 time(s) by numpy took 0.0031977021492632877 seconds
# For matrix G(7x7) computation of inverse matrix 100 time(s) by matrices.py took 0.030527930074972794 seconds
# For matrix G(7x7) computation of inverse matrix 100000 time(s) by numpy took 2.9690120793997004 seconds
# For matrix G(7x7) computation of inverse matrix 100000 time(s) by matrices.py took 22.447151615787458 seconds
# Ok, numpy won this with great margin, but... the thing is: we calculated determinant in our inverse method
# and it took 21.71 second for previous test to do that. So, actual, the inverting procedure
# was less, than a second(anyway - it's not count without determinant check)
det_cycles = 1
numA = np.array(self.matrix_a)
start_time = time.perf_counter()
for i in range(1, det_cycles):
numAinv = np.linalg.inv(numA)
end_time = time.perf_counter()
total_time_num = end_time - start_time
matA = matrices.Matrix(self.matrix_a)
start_time = time.perf_counter()
for i in range(1, det_cycles):
matAinv = matA.matrix_determinant()
end_time = time.perf_counter()
total_time_mat = end_time - start_time
print("="*70)
print("For matrix A(2x2) computation of inverse matrix {0} time(s) by numpy took {1} seconds".format(
det_cycles, total_time_num))
print("For matrix A(2x2) computation of inverse matrix {0} time(s) by matrices.py took {1} seconds".format(
det_cycles, total_time_mat))
# For matrix A(2x2) computation of inverse matrix 100 time(s) by numpy took 0.004653260920530776 seconds
# For matrix A(2x2) computation of inverse matrix 100 time(s) by matrices.py took 0.0009753577659173699 seconds
# For matrix A(2x2) computation of inverse matrix 100000 time(s) by numpy took 2.756857820081456 seconds
# For matrix A(2x2) computation of inverse matrix 100000 time(s) by matrices.py took 0.8733635574325254 seconds
# Yes, we small matrix(2x2) our method way faster!