def two_variable_function(x, y):
return (x - 1)**2 + (y - 1)**3
def three_variable_function(x, y, z):
return (x - 1)**2 + (y - 1)**3 + (z - 1)**4
def six_variable_function(x1, x2, x3, x4, x5, x6):
return (x1 - 1)**2 + (x2 - 1)**3 + (x3 - 1)**4 + x4 + 2 * x5 + 3 * x6
minimizer = GradientDescent(f=single_variable_function, initial_point=[0])
assert minimizer.point == [0], minimizer.point
assert minimizer.compute_gradient(delta=0.01) == [
-2.000
], minimizer.compute_gradient(delta=0.01)
# rounded to 5 decimal places
minimizer.descend(alpha=0.001, delta=0.01, num_steps=1)
assert minimizer.point == [0.002], minimizer.point
minimizer = GradientDescent(f=two_variable_function, initial_point=[0, 0])
assert (minimizer.point) == [0, 0], (minimizer.point)
assert (minimizer.compute_gradient(delta=0.01)) == [
-2.000, 3.000
], (minimizer.compute_gradient(delta=0.01))
minimizer.descend(alpha=0.001, delta=0.01, num_steps=1)
assert (minimizer.point) == [0.002, -0.003], (minimizer.point)
def two_variable_function(x, y):
return (x - 1)**2 + (y - 1)**3
def three_variable_function(x, y, z):
return (x - 1)**2 + (y - 1)**3 + (z - 1)**4
def six_variable_function(x1, x2, x3, x4, x5, x6):
return (x1 - 1)**2 + (x2 - 1)**3 + (x3 - 1)**4 + x4 + 2 * x5 + 3 * x6
print('Does GradientDescent work for a single variable function?')
minimizer = GradientDescent(f=single_variable_function, initial_point=[0])
assert minimizer.point == [0], 'The inital point was off'
ans = minimizer.compute_gradient(delta=0.01)
ans_rounded = [round(num, 3) for num in ans]
assert ans_rounded == [
-2.000
], 'The rounded gradient wasnt quite right' #rounded to 5 decimal places
minimizer.descend(alpha=0.001, delta=0.01, num_steps=1)
point_rounded = [round(num, 3) for num in minimizer.point]
assert point_rounded == [0.002], 'The rounded final answer wasnt quite right'
print('Yes, it does!', "\n")
print('Does GradientDescent work for a two variable function?')
minimizer = GradientDescent(f=two_variable_function, initial_point=[0, 0])
assert minimizer.point == [0, 0], 'The inital point was off'
ans = minimizer.compute_gradient(delta=0.01)
ans_rounded = [round(num, 3) for num in ans]
assert ans_rounded == [-2.000, 3.000], 'The rounded gradient wasnt quite right'
return (x - 1)**2 + (y - 1)**3
def three_variable_function(x, y, z):
return (x - 1)**2 + (y - 1)**3 + (z - 1)**4
def six_variable_function(x1, x2, x3, x4, x5, x6):
return (x1 - 1)**2 + (x2 - 1)**3 + (x3 - 1)**4 + x4 + 2 * x5 + 3 * x6
minimizer = GradientDescent(f=single_variable_function, initial_point=[0])
assert minimizer.point == [0]
print('Testing gradient on single_variable_function...')
assert [round(i, 3)
for i in minimizer.compute_gradient(delta=0.01)] == [-2.000]
print('PASSED')
minimizer.descend(alpha=0.001, delta=0.01, num_steps=1)
print('Testing descend on single_variable_function...')
assert [round(i, 3) for i in minimizer.point] == [0.002]
print('PASSED')
minimizer = GradientDescent(f=two_variable_function, initial_point=[0, 0])
assert minimizer.point == [0, 0]
print('Testing gradient on two_variable_function...')
assert [round(i, 3)
for i in minimizer.compute_gradient(delta=0.01)] == [-2.000, 3.000]
print('PASSED')
minimizer.descend(alpha=0.001, delta=0.01, num_steps=1)
print('Testing descend on two_variable_function...')
assert [round(i, 3) for i in minimizer.point] == [0.002, -0.003]
