def exp_(a, x):
'''
Returns the exponential of a given constant or scalar or Element object with base a
INPUTS
=======
x: Numeric constant or Scalar object or Element object
a: Numeric constant
RETURNS
=======
exponential of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant sin(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
try:
return Element(a**x._val, x._jacob * np.log(a) * (a**x._val))
except AttributeError:
try: # If scalar variable
return Scalar(a**x._val, x._der * np.log(a) * (a**x._val))
except AttributeError: # If contant
return a**x
def sin(x):
'''
Returns the sine of a given constant, Scalar, or Element object
INPUTS
=======
x: Numeric constant, Scalar object or Element object
RETURNS
=======
sine of numeric constant, Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant sin(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
try:
return Element(np.sin(x._val), np.cos(x._val) * x._jacob)
except AttributeError: # If contant
try: # If scalar variable
return Scalar(np.sin(x._val), x._der * np.cos(x._val))
except AttributeError: # If contant
return np.sin(x)
def logistic(x):
'''
Returns the logistic of a given constant or scalar or Element object
INPUTS
=======
x: Numeric constant or Scalar object or Element object
RETURNS
=======
logistic of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant logistic(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
try:
return Element(1 / (1 + np.exp(-x._val)),
x._jacob * (x._val**2 * np.exp(-x._val)))
except AttributeError:
try:
return Scalar(1 / (1 + np.exp(-x._val)),
x._der * (x._val**2 * np.exp(-x._val)))
except AttributeError: #if constant
return 1 / (1 + np.exp(-x))
def element(val, jacob):
'''
Creates an Element object with the value given and jacobian matrix
INPUTS
=======
val: The numeric value of the function
jacob: The jacobian matrix value of the function at which to evaluate
RETURNS
=======
Element objects
'''
return Element(val, jacob)
def log(*args):
'''
Returns the log of a given constant or scalar or Element object
INPUTS
=======
if the lenth of input is 2:
a: Numeric constant
x: Numeric constant or Scalar object or Element object
if the lenth of input is 1:
x: Numeric constant or Scalar object or Element object
RETURNS
=======
log of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant sin(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
if len(args) == 2:
return Operator.log_(args[0], args[1])
else:
x = args[0]
try:
j = x._jacob
if x._val <= 0:
raise ValueError('out of domain')
else:
return Element(np.log(x._val), x._jacob / x._val)
except AttributeError:
try: # If scalar variable
if x._val <= 0:
raise ValueError('out of domain')
else:
return Scalar(np.log(x._val), x._der / x._val)
except AttributeError: # If contant
if x <= 0:
raise ValueError('out of domain')
else:
return np.log(x)
def log_(a, x):
'''
Returns the log of a given constant or scalar or Element object with base a
INPUTS
=======
x: Numeric constant or Scalar object or Element object
a: Numeric constant
RETURNS
=======
log of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant sin(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
try:
j = x._jacob
if x._val <= 0:
raise ValueError('out of domain')
else:
return Element(math.log(x._val, a),
x._jacob / (x._val * np.log(a)))
except AttributeError:
try: # If scalar variable
if x._val <= 0:
raise ValueError('out of domain')
else:
return Scalar(math.log(x._val, a),
x._der / (x._val * np.log(a)))
except AttributeError: # If contant
if x <= 0:
raise ValueError('out of domain')
else:
return math.log(x, a)
def arccosh(x):
'''
Returns the arccosh of a given constant or scalar or Element object
INPUTS
=======
x: Numeric constant or Scalar object or Element object
RETURNS
=======
arccosh of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant sin(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
try:
j = x._jacob
if x._val < 1:
raise ValueError('out of domain')
else:
return Element(
np.arccosh(x._val),
x._jacob * (-np.arccosh(x._val) * np.tanh(x._val)))
except AttributeError:
try: # if scalar variable
if x._val < 1:
raise ValueError('out of domain')
else:
return Scalar(
np.arccosh(x._val),
x._der * (-np.arccosh(x._val) * np.tanh(x._val)))
except AttributeError: #if constant
if x < 1:
raise ValueError('out of domain')
else:
return np.arccosh(x)
def square_root(x):
'''
Returns the square root of a given constant or scalar or Element object
INPUTS
=======
x: Numeric constant or Scalar object or Element object
RETURNS
=======
square root of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant square root(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
try:
j = x._jacob
if x._val <= 0:
raise ValueError('out of domain')
else:
return Element(x._val**0.5, x._jacob * (x._val**(-1 / 2) / 2))
except AttributeError:
try:
if x._val <= 0:
raise ValueError('out of domain')
else:
return Scalar(x._val**0.5, x._der * (x._val**(-1 / 2) / 2))
except AttributeError: #if constant
if x <= 0:
raise ValueError('out of domain')
else:
return x**0.5
def exp(*args):
'''
Returns the exponential of a given constant or scalar or Element object
INPUTS
=======
if the lenth of input is 2:
The first is a and the second is x.
a: Numeric constant
x: Numeric constant or Scalar object or Element object
if the lenth of input is 1:
x: Numeric constant or Scalar object or Element object
RETURNS
=======
exponential of numeric constant or Scalar object or Element object
NOTES
=======
If x is a constant, this method returns the constant sin(x). If
x is a Scalar object, this method returns a new Scalar with the
appropriate functions performed on the Scalar's value and
derivative. If x is a Element object, this method returns a new
Element with the appropriate functions performed on the Element's
value and Jacobian matrix.
'''
if len(args) == 2:
return Operator.exp_(args[0], args[1])
else:
x = args[0]
try:
return Element(np.exp(x._val), x._jacob * (np.exp(x._val)))
except AttributeError:
try: # If scalar variable
return Scalar(np.exp(x._val), x._der * np.exp(x._val))
except AttributeError: # If contant
return np.exp(x)
