def sqrt(obj):
"""
Returns the square root of the input object
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object or a scalar
"""
if isinstance(obj, Variable):
new_Variable = Variable(obj.val, obj.der)
return new_Variable.__pow__(0.5)
else:
return np.sqrt(obj)
def test_sqrt():
x1 = Variable(1)
x2 = fun.sqrt(x1)
x3 = 1
assert x2.val == 1
assert x2.der == {'x': 0.5}
assert x3 == 1
def arccos(obj):
"""
Returns the inverse cosine of the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
if pre_val >= 1 or pre_val <= -1:
raise ValueError("arccos does not exist beyond (-1,1)")
der = {
x: (-(1 - (pre_val)**2)**(-0.5)) * pre_der.get(x, 0)
for x in set(pre_der)
}
val = np.arccos(pre_val)
return Variable(val, der=der)
except AttributeError:
if obj >= 1 or obj <= -1:
raise ValueError("arccos does not exist beyond (-1,1)")
return np.arccos(obj)
def arccos(obj):
"""
Returns the inverse cosine of the input object
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object
"""
if isinstance(obj, Variable):
values = map(lambda x: -1 <= x <= 1, obj.val)
if not all(values):
raise ValueError("Domain of arccos is [-1, 1].")
val = np.arccos(obj.val)
if obj.val == 1:
der = np.nan
elif obj.val == -1:
der = np.nan
else:
der = -1 / np.sqrt(1 - (obj.val**2))
if len(obj.der.shape) > len(der.shape):
der = np.expand_dims(der, 1)
der = np.multiply(der, obj.der)
return Variable(val, der)
else:
if obj >= 1 or obj <= -1:
raise ValueError("Domain of arccos is [-1, 1].")
return np.arccos(obj)
def logistic(obj):
"""
Return the logistic function evaluation (sigmoid): f(x) = 1 / (1 + e^{-x})
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object or a scalar
"""
# Case for constant scalar or vector with no derivative
if isinstance(obj, Variable):
val = 1 / (1 + np.exp(-obj.val))
der = np.exp(obj.val) / ((1 + np.exp(obj.val))**2)
if len(obj.der.shape) > 1:
new_der = np.reshape(der, [-1, 1])
else:
new_der = der
final_der = new_der * obj.der
return Variable(val, final_der)
else:
val = 1 / (1 + np.exp(-obj))
return val
def test_exp():
x1 = fun.exp(Variable(1))
# x2 = Variable(1)
# x3 = AutoDiff.exp(x1 + x2)
x4 = fun.exp(1)
assert x1.val == np.exp(1)
assert x1.der == {'x': np.exp(1)}
# assert x3.der == {'x1': np.exp(1+1), 'x2': np.exp(1+1)}
assert x4 == np.exp(1)
def test_inverse_trigonometric():
x1 = fun.arcsin(Variable(0.1))
x2 = fun.arccos(Variable(0.2))
x3 = fun.arctan(Variable(0.3))
# x4 = AutoDiff.arcsin(x1) + AutoDiff.arccos(x2) + AutoDiff.arctan(x3)
x5 = 0.1
x6 = 0.2
x7 = 0.3
x8 = fun.arcsin(x5) + fun.arccos(x6) + fun.arctan(x7)
assert x1.val == np.arcsin(0.1)
assert x2.val == np.arccos(0.2)
assert x3.val == np.arctan(0.3)
assert x1.der == {'x': 1.005037815259212}
assert x2.der == {'x': -1.0206207261596576}
assert x3.der == {'x': 0.9174311926605504}
# assert x4.val == 1.7610626216439926
# assert x4.der == {'x1': 1.005037815259212,
# 'x2': -1.0206207261596576,
# 'x3': 0.9174311926605504}
assert x8 == 1.7610626216439926
def test_hyberbolic():
x1 = fun.sinh(Variable(1))
x2 = fun.cosh(Variable(1))
x3 = fun.tanh(Variable(1))
# x4 = AutoDiff.sinh(x1) + AutoDiff.cosh(x2) + AutoDiff.tanh(x3)
x5 = 1
x6 = 1
x7 = 1
x8 = fun.sinh(x5) + fun.cosh(x6) + fun.tanh(x7)
assert x1.val == np.sinh(1)
assert x2.val == np.cosh(1)
assert x3.val == np.tanh(1)
assert x1.der == {'x': np.cosh(1)}
assert x2.der == {'x': np.sinh(1)}
assert x3.der == {'x': 1 - np.tanh(1)**2}
# assert x4.val == np.sinh(1)+np.cosh(1)+np.tanh(1)
# assert x4.der == {'x1': np.cosh(1),
# 'x2': np.sinh(1),
# 'x3': 1-np.tanh(1)**2}
assert x8 == np.sinh(1) + np.cosh(1) + np.tanh(1)
def test_log():
x1 = fun.log(Variable(1))
# x2 = Variable(1, name='x2')
# x3 = AutoDiff.log(x1 + x2)
x4 = fun.log(1)
x5 = fun.log2(Variable(1))
x6 = fun.log2(1)
x7 = fun.log10(Variable(1))
x8 = fun.log10(1)
assert x1.val == np.log(1)
assert x1.der == {'x': 1}
assert x5.val == np.log2(1)
assert x5.der == {'x': 1}
assert x7.val == np.log10(1)
assert x7.der == {'x': 1}
# assert x3.val == np.log(1+1)
# assert x3.der == {'x1': 1/2, 'x2': 1/2}
assert x4 == np.log(1)
assert x6 == np.log2(1)
assert x8 == np.log10(1)
def test_trigonometric():
x1 = fun.sin(Variable(np.pi / 4))
x2 = fun.cos(Variable(np.pi / 4))
x3 = fun.tan(Variable(np.pi / 4))
# x4 = AutoDiff.sin(x1) + AutoDiff.cos(x2) + AutoDiff.tan(x3)
x5 = np.pi / 4
x6 = np.pi / 4
x7 = np.pi / 4
x8 = fun.sin(x5) + fun.cos(x6) + fun.tan(x7)
assert x1.val == np.sin(np.pi / 4)
assert x2.val == np.cos(np.pi / 4)
assert x3.val == np.tan(np.pi / 4)
assert x1.der == {'x': np.cos(np.pi / 4)}
assert x2.der == {'x': -np.sin(np.pi / 4)}
assert abs(x3.der['x'] - 1 / np.cos(np.pi / 4)**2 < 1e-8)
# assert x4.val == 2**0.5 + 1
# assert x4.der == {'x1': np.cos(np.pi/4),
# 'x2': -np.sin(np.pi/4),
# 'x3': 1/np.cos(np.pi/4)**2}
assert x8 == 2**0.5 + 1
def test_error():
try:
fun.arcsin(Variable(2))
assert False
except ValueError:
assert True
try:
fun.arcsin(Variable(-2))
assert False
except ValueError:
assert True
try:
fun.arccos(Variable(2))
assert False
except ValueError:
assert True
try:
fun.arccos(Variable(-2))
assert False
except ValueError:
assert True
try:
fun.arcsin(2)
assert False
except ValueError:
assert True
try:
fun.arcsin(-2)
assert False
except ValueError:
assert True
try:
fun.arccos(2)
assert False
except ValueError:
assert True
try:
fun.arccos(-2)
assert False
except ValueError:
assert True
def exp(obj):
"""
Returns e raised to the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
der = {x: np.exp(pre_val) * pre_der.get(x, 0) for x in set(pre_der)}
val = np.exp(pre_val)
return Variable(val, der=der)
except:
return np.exp(obj)
def cosh(obj):
"""
Returns the hyperbolic cosine of the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
der = {x: np.sinh(pre_val) * pre_der.get(x, 0) for x in set(pre_der)}
val = np.cosh(pre_val)
return Variable(val, der=der)
except:
return np.cosh(obj)
def cosh(obj):
"""
Returns the hyperbolic cosine of the input object
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object
"""
if isinstance(obj, Variable):
val = np.cosh(obj.val)
der = np.sinh(obj.val)
if len(obj.der.shape) > len(der.shape):
der = np.expand_dims(der, 1)
der = np.multiply(der, obj.der)
return Variable(val, der)
else:
return np.cosh(obj)
def log10(obj):
"""
Returns the natrual log of the input object
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object
"""
if isinstance(obj, Variable):
val = np.log10(obj.val)
der = np.divide(1, obj.val)
if len(obj.der.shape) > len(der.shape):
der = np.expand_dims(der, 1)
der = np.multiply(der, obj.der)
return Variable(val, der)
else:
return np.log10(obj)
def arctan(obj):
"""
Returns the inverse tangent of the input object
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object
"""
if isinstance(obj, Variable):
val = np.arctan(obj.val)
der = 1 / (1 + (obj.val)**2)
if len(obj.der.shape) > len(der.shape):
der = np.expand_dims(der, 1)
der = np.multiply(der, obj.der)
return Variable(val, der)
else:
return np.arctan(obj)
def exp(obj):
"""
Returns e raised to the input object
Inputs:
obj: Autodiff.Variableiable object or a number
Output:
Autodiff.Variableiable object or scalar
"""
if isinstance(obj, Variable):
val = np.exp(obj.val)
der = np.exp(obj.val)
if len(obj.der.shape) > len(der.shape):
der = np.expand_dims(der, 1)
der = np.multiply(der, obj.der)
return Variable(val, der)
else:
return np.exp(obj)
def log10(obj):
"""
Returns the natrual log of the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
der = {
x: np.divide(1, pre_val) * pre_der.get(x, 0)
for x in set(pre_der)
}
val = np.log10(pre_val)
return Variable(val, der=der)
except:
return np.log10(obj)
def sqrt(obj):
"""
Returns the square root of the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
der = {
x: (0.5 * pre_val**(-0.5)) * pre_der.get(x, 0)
for x in set(pre_der)
}
val = np.sqrt(pre_val)
return Variable(val, der=der)
except:
return np.sqrt(obj)
def arctan(obj):
"""
Returns the inverse tangent of the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
der = {
x: np.divide(1, 1 + (pre_val)**2) * pre_der.get(x, 0)
for x in set(pre_der)
}
val = np.arctan(pre_val)
return Variable(val, der=der)
except:
return np.arctan(obj)
def tanh(obj):
"""
Returns hyperbolic tangent of the input object
Inputs:
obj: Autodiff.Variable object or a number
Output:
Autodiff.Variable object or a scalar
"""
try:
pre_der = obj.der
pre_val = obj.val
der = {
x: (1 - np.tanh(pre_val)**2) * pre_der.get(x, 0)
for x in set(pre_der)
}
val = np.tanh(pre_val)
return Variable(val, der=der)
except:
return np.tanh(obj)
