def test_sigma_condition(self):
f = lambda x: x**2 - 1
df = lambda x: 2 * x
x0 = 1
with self.assertRaises(ValueError):
gradient_descent(f, df, x0, sigma=-100)
gradient_descent(f, df, x0, sigma=100)
def test_gradient_maxima(self,sigma=0.5):
f = lambda x: -x**2
df = lambda x: -2*x
x0 = 0
with self.assertRaises(ValueError):
gradient_descent(f,df,x0,sigma=0.5)
gradient_descent(f,df,x0,sigma=0.2)
def test_sigma_condition(self):
f = lambda x: x**2 - 1
df = lambda x: 2*x
x0 = 1
with self.assertRaises(ValueError):
gradient_descent(f, df, x0, sigma=-100)
gradient_descent(f, df, x0, sigma=100)
def test_gradiet_descent_error(self):
f = lambda x: x**2 - 1
df = lambda x: 2*x
x0 = 1
with self.assertRaises(ValueError):
gradient_descent(f,df,x0,sigma=1.1)
gradient_descent(f,df,x0,sigma=-0.1)
def test_gradient_error(self):
# it demonstrates how to test if a
# function raises an error
f = lambda x: x**2 - 1
df = lambda x: 2 * x
x0 = -2
with self.assertRaises(ValueError):
gradient_descent(f, df, x0, sigma=1, epsilon=1e-8)
gradient_descent(f, df, x0, sigma=0, epsilon=1e-8)
def test_gradient_doubleWell(self,sigma=0.5):
f = lambda x: 0.25*x**4 -0.5*x**2
df = lambda x: x**3-x
x0 = 0
xmin_actual = -1
xmin = gradient_descent(f,df,x0,sigma=0.5)
self.assertAlmostEqual(xmin, xmin_actual)
x0 = 0.1
xmin_actual = 1
xmin = gradient_descent(f,df,x0,sigma=0.5)
self.assertAlmostEqual(xmin, xmin_actual)
def test_double_well(self): # in this function there is a maximum in between 2 minima f = lambda x: 0.25*x**4 - 0.5*x**2 df = lambda x: x**3 - x x0 = 0 #local maxima in between 2 minima x1 = gradient_descent(f, df, x0, sigma = 0.5) x1_actual = -1 self.assertAlmostEqual(x1, x1_actual, places = 2) x0 = 0.1 x1_actual = 1 x1 = gradient_descent(f, df, x0, sigma = 0.5) self.assertAlmostEqual(x1, x1_actual, places = 2)
def test_gradient_descent_robust(self):
f = lambda x: 0.1*x**4-x**3+3.5*x**2-5*x+2.4
df = lambda x: -5+7*x-3*x**2+0.4*x**3
xf = gradient_descent(f,df,2.5,0.3,1e-10)
xf_actual1 = 3.618034
xf_actual2 = 1.381966
self.assertTrue(round(xf-xf_actual1,7)==0 or round(xf-xf_actual2,7)==0)
def test_gradient_parabola(self):
f = lambda x: x**2 - 1
df = lambda x: 2*x
x0 = 1
xmin_actual = 0.0
xmin = gradient_descent(f,df,x0,sigma=0.5)
self.assertAlmostEqual(xmin, xmin_actual)
def test_gradient_quartic(self):
f = lambda x: x**4
df = lambda x: 4*x**3
x0 = 0.5
xmin_actual = 0.0
xmin = gradient_descent(f,df,x0,sigma=0.6)
self.assertAlmostEqual(xmin, xmin_actual,places=2)
def test_convexfunctions(self):
# this test verfies whether gradient_step works correctly for a variety of examples
# verify the test on different function examples
f = lambda x: x**2
df = lambda x: 2*x
x0 = 1
x1 = gradient_descent(f, df, x0)
x1_actual = 0
self.assertAlmostEqual(x1, x1_actual)
f = lambda x: x**4
df = lambda x: 4*x**3
x0 = 0.5
x1 = gradient_descent(f, df, x0, sigma = 0.6)
x1_actual = 0
self.assertAlmostEqual(x1, x1_actual, places=2)
def test_gradient_descent_robust(self):
f = lambda x: 0.1 * x**4 - x**3 + 3.5 * x**2 - 5 * x + 2.4
df = lambda x: -5 + 7 * x - 3 * x**2 + 0.4 * x**3
xf = gradient_descent(f, df, 2.5, 0.3, 1e-10)
xf_actual1 = 3.618034
xf_actual2 = 1.381966
self.assertTrue(
round(xf - xf_actual1, 7) == 0 or round(xf - xf_actual2, 7) == 0)
def test_gradient_descent_trig(self): # tests whether a trig function correctly outputs a local minima f = lambda x : sin(x) df = lambda x : cos(x) x0 = 0.1 x1 = gradient_descent(f, df, x0, sigma = 0.8) x1_actual = -(1.0*numpy.pi)/2 self.assertAlmostEqual(x1, x1_actual, places=2)
def test_gradient_descent3(self):
# scaling factor sigma is chosen to be small
f = lambda x: x**3 - x
df = lambda x: 3 * x**2 - 1
x0 = 1
x1 = gradient_descent(f, df, x0, sigma=0.1, epsilon=1e-8)
x1_actual = 0.57735026
self.assertAlmostEqual(x1, x1_actual)
def test_gradient_descent2(self):
# the global minimum of functions that have a single, global minimum
f = lambda x: x**2 - 1
df = lambda x: 2 * x
x0 = -2
x1 = gradient_descent(f, df, x0, sigma=0.5, epsilon=1e-8)
x1_actual = 0.0
self.assertAlmostEqual(x1, x1_actual)
def test_gradient_descent1(self):
#a example:f(x) = x**3 - 6*x**2 + 9*x +15
f = lambda x: x**3 - 6 * x**2 + 9 * x + 15
df = lambda x: 3 * x**2 - 12 * x + 9
#correctly d when f'(x) = 0 but it's local maximun=m
x0 = 1.6
x1 = gradient_descent(f, df, x0, sigma=0.5, epsilon=1e-8)
x1_actual = 99
self.assertAlmostEqual(x1, x1_actual)
def test_sigmaAndEpsilon(self):
# this test determines whether gradient_step and gradient descent raises
# value errors on sigma and epsilon
f = lambda x: x**2 - 1
df = lambda x: 2*x
x = 1
with self.assertRaises(ValueError):
gradient_step(x, df, sigma=1.5)
gradient_step(x, df, sigma=-1)
gradient_descent(f, df, x, sigma=0.5, epsilon=-1)
gradient_descent(f, df, x, sigma=0.5, epsilon=2)
gradient_descent(f, df, x, sigma=2, epsilon=0.1)
def test_gradient_descent_nearmin_smallsig(self):
f = lambda x: 0.1*x**4-x**3+3.5*x**2-5*x+2.4
df = lambda x: -5+7*x-3*x**2+0.4*x**3
xf = gradient_descent(f,df,1.3,0.05,1e-10)
xf_actual = 1.381966 # 1.3819660093917199
self.assertAlmostEqual(xf, xf_actual)
def test_gradient_descent(self):
f = lambda x: x**2 - 1
df = lambda x: 2*x
xf = gradient_descent(f,df,1,0.5,1e-10)
xf_actual = 0.0
self.assertAlmostEqual(xf, xf_actual)
def test_gradient_descent(self):
f = lambda x: x**2 - 1
df = lambda x: 2 * x
xf = gradient_descent(f, df, 1, 0.5, 1e-10)
xf_actual = 0.0
self.assertAlmostEqual(xf, xf_actual)
def test_gradient_descent_nearmin_smallsig(self):
f = lambda x: 0.1 * x**4 - x**3 + 3.5 * x**2 - 5 * x + 2.4
df = lambda x: -5 + 7 * x - 3 * x**2 + 0.4 * x**3
xf = gradient_descent(f, df, 1.3, 0.05, 1e-10)
xf_actual = 1.381966 # 1.3819660093917199
self.assertAlmostEqual(xf, xf_actual)
