def test_sub_vector_results():
x = AutoDiff([3, 1], [2, 1], 2, 1)
y = AutoDiff([2, -3], [3, 2], 2, 2)
f = x - y
assert np.all(f.val == np.array([[1], [4]]))
assert np.all(f.der == np.array([[2, -3], [1, -2]]))
assert np.all(f.jacobian == np.array([[1, -1], [1, -1]]))
def test_tan_ad_results(): # Defined value and derivative when cos(val)!=0 # Positive reals x = AutoDiff(0.5, 2.0) f = ef.tan(x) assert f.val == np.array([[np.tan(0.5)]]) assert f.der == np.array([[2.0 / (np.cos(0.5)**2)]]) assert f.jacobian == np.array([[1.0 / (np.cos(0.5)**2)]]) # Negative reals y = AutoDiff(-0.5, 2.0) f = ef.tan(y) assert f.val == np.array([[np.tan(-0.5)]]) assert f.der == np.array([[2.0 / (np.cos(-0.5)**2)]]) assert f.jacobian == np.array([[1.0 / (np.cos(-0.5)**2)]]) # Zero z = AutoDiff(0.0, 2.0) f = ef.tan(z) assert f.val == np.array([[np.tan(0)]]) assert f.der == np.array([[2.0]]) assert f.jacobian == np.array([[1.0]]) # Undefined value and derivative when cos(val)==0 with pytest.warns(RuntimeWarning): h = AutoDiff(np.pi/2, 1.0) f = ef.tan(h) assert np.isnan(f.val) assert np.isnan(f.der) assert np.isnan(f.jacobian)
def test_arctanh_ad_results(): # value defined at real numbers (-1, 1) x = AutoDiff(0.5, 2) f = ef.arctanh(x) assert f.val == np.arctanh(0.5) assert f.der == np.array([[((2)/(1-(0.5)**2))]]) assert f.jacobian == np.array([[((1)/(1-(0.5)**2))]]) y = AutoDiff(-0.99999, 2) f = ef.arctanh(y) assert f.val == np.arctanh(-0.99999) assert f.der == np.array([[((2)/(1-(-0.99999)**2))]]) assert f.jacobian == np.array([[((1)/(1-(-0.99999)**2))]]) # test for real numbers not in (-1, 1) with pytest.warns(RuntimeWarning): z = AutoDiff(-1, 2) f = ef.arctanh(z) assert np.isinf(f.val) assert np.isinf(f.der) assert np.isinf(f.jacobian) with pytest.warns(RuntimeWarning): z = AutoDiff(10, 2) f = ef.arctanh(z) assert np.isnan(f.val) assert f.der == np.array([[((2)/(1-(10)**2))]]) assert f.jacobian == np.array([[((1)/(1-(10)**2))]])
def test_arccos_ad_results(): # positive real numbers x = AutoDiff(0.5, 2) f = ef.arccos(x) assert f.val == np.array([[np.arccos(0.5)]]) assert f.der == np.array([[-2/np.sqrt(1-0.5**2)]]) assert f.jacobian == np.array([[-1/np.sqrt(1-0.5**2)]]) # out of bounds - negative sqrt with pytest.warns(RuntimeWarning): y = AutoDiff(-2, 2) f = ef.arccos(y) assert np.isnan(f.val[0][0]) assert np.isnan(f.der[0][0]) assert np.isnan(f.jacobian[0][0]) # out of bounds - divide by 0 with pytest.warns(RuntimeWarning): y = AutoDiff(1, 2) f = ef.arccos(y) assert f.val == np.array([[np.arccos(1)]]) assert np.isneginf(f.der[0][0]) assert np.isneginf(f.jacobian[0][0]) # zero z = AutoDiff(0, 2) f = ef.arccos(z) assert f.val == np.array([[np.arccos(0)]]) assert f.der == np.array([[-2/np.sqrt(1-0**2)]]) assert f.jacobian == np.array([[-1/np.sqrt(1-0**2)]])
def test_arcsin_ad_results(): # positive real numbers x = AutoDiff(0.5, 2) f = ef.arcsin(x) assert f.val == np.array([[np.arcsin(0.5)]]) assert f.der == np.array([[2/np.sqrt(1-0.5**2)]]) assert f.jacobian == np.array([[1/np.sqrt(1-0.5**2)]]) # out of bounds - undefined sqrt with pytest.warns(RuntimeWarning): y = AutoDiff(-2, 2) f = ef.arcsin(y) assert np.isnan(f.val[0][0]) assert np.isnan(f.der[0][0]) assert np.isnan(f.jacobian[0][0]) # out of bounds - div by zero with pytest.warns(RuntimeWarning): y = AutoDiff(1, 2) f = ef.arcsin(y) assert f.val == np.array([[np.arcsin(1)]]) assert np.isinf(f.der[0][0]) assert np.isinf(f.jacobian[0][0]) # zero z = AutoDiff(0, 2) f = ef.arcsin(z) assert f.val == np.array([[0.0]]) assert f.der == np.array([[2.0]]) assert f.jacobian == np.array([[1.0]])
def test_mul_ad_results():
# single input case
# positive numbers
x = AutoDiff(5, 2)
f = x * x
assert f.val == 25
assert f.der == 20
assert f.jacobian == 10
# negative numbers
x = AutoDiff(-5, 2)
f = x * x
assert f.val == 25
assert f.der == -20
assert f.jacobian == -10
def test_sub_ad_results():
# single input cases
# positive numbers
x = AutoDiff(5, 2)
f = x - x
assert f.val == 0
assert f.der == 0
assert f.jacobian == 0
# negative numbers
y = AutoDiff(-5, 2)
f = y - y
assert f.val == 0
assert f.der == 0
assert f.jacobian == 0
def logistic(x): ''' Compute logistic function for AutoDiff or Dual object. INPUTS ====== x: an AutoDiff object or Dual object RETURNS ======= A new AutoDiff or Dual object with calculated value and derivative. ''' try: f_l = (1/(1+np.exp(-x.val))) new_val = f_l new_der = (1 - f_l)*f_l*x.der new_jacobian = (1 - f_l)*f_l*x.jacobian return AutoDiff(new_val, new_der, x.n, 0, new_jacobian) except AttributeError: try: f_l = (1/(1 + np.exp(-x.Real))) return Dual(f_l, (1 - f_l)*f_l*x.Dual) except AttributeError: try: return Dual(logistic(x.Real), (1 - logistic(x.Real))*logistic(x.Real)*x.Dual) except AttributeError: # Constant return_val = (1/(1+np.exp(-x))) return return_val
def tanh(X): ''' Compute the tanh of an AutoDiff object and its derivative. INPUTS ====== X: an AutoDiff object RETURNS ======= A new AutoDiff object with calculated value and derivative. EXAMPLES ======== >>> X = AutoDiff(0.5, 2, 1) >>> tanhAutoDiff = tanh(X) >>> tanhAutoDiff.val 0.46211715726000974 >>> tanhAutoDiff.der 1.572895465931855 >>>tanhAutoDiff.jacobian 0.7864477329659275 ''' try: val = np.tanh(X.val) der = 1/(np.cosh(X.val)**2)*X.der jacobian = 1/(np.cosh(X.val)**2)*X.jacobian return AutoDiff(val, der, X.n, 0, jacobian) except AttributeError: try: return Dual(np.tanh(X.Real), X.Dual/(np.cosh(X.Real)**2)) except AttributeError: try: X.Real return sinh(X)/cosh(X) except AttributeError: # Constant return_val = np.tanh(X) return return_val
def cosh(X): ''' Compute the cosh of an AutoDiff object and its derivative. INPUTS ====== X: an AutoDiff object RETURNS ======= A new AutoDiff object with calculated value and derivative. EXAMPLES ======== >>> X = AutoDiff(0.5, 2, 1) >>> coshAutoDiff = cosh(X) >>> coshAutoDiff.val 1.1276259652063807 >>> coshAutoDiff.der 1.0421906109874948 >>> coshAutoDiff.jacobian 0.5210953054937474 ''' try: val = np.cosh(X.val) der = np.sinh(X.val)*X.der jacobian = np.sinh(X.val)*X.jacobian return AutoDiff(val, der, X.n, 0, jacobian) except AttributeError: try: return Dual(np.cosh(X.Real), X.Dual*np.sinh(X.Real)) except AttributeError: try: return Dual(cosh(X.Real), X.Dual*sinh(X.Real)) except AttributeError: # Constant return_val = np.cosh(X) return return_val
def sinh(X): ''' Compute the sinh of an AutoDiff object and its derivative. INPUTS ====== X: an AutoDiff object RETURNS ======= A new AutoDiff object with calculated value and derivative. EXAMPLES ======== >>> X = AutoDiff(0.5, 2, 1) >>> sinhAutoDiff = sinh(X) >>> sinhAutoDiff.val 0.5210953054937474 >>> sinhAutoDiff.der 2.2552519304127614 >>> sinhAutoDiff.jacobian 1.1276259652063807 ''' try: val = np.sinh(X.val) der = np.cosh(X.val)*X.der jacobian = np.cosh(X.val)*X.jacobian return AutoDiff(val, der, X.n, 0, jacobian) except AttributeError: try: return Dual(np.sinh(X.Real), X.Dual*np.cosh(X.Real)) except AttributeError: try: return Dual(sinh(X.Real), X.Dual*cosh(X.Real)) except AttributeError: # Constant return_val = np.sinh(X) return return_val