def arccosh(x):
"""
Returns a constant, Scalar, or Vector object that is the arccosh of the user specified value.
INPUTS
=======
val: real valued numeric type
RETURNS
=======
Scalar or Vector class instance
NOTES
======
If the input value is a constant, each operator method returns a constant with the operation
applied. If the input value is a Scalar object, the operator method applies the operator to the value
and propagates the derivative through the chain rule, wrapping the results in a new Scalar object. If the
input value is a vector, the operator method updates the value of the element, and the jacobian of the vector,
returning a new vector object with these properties.
"""
try:
j = x._jacobian
except AttributeError:
return np.arccosh(x) # If x is a constant
else:
try:
k = j.keys() # To tell whether x is a scalar or vector
except AttributeError:
new = Vector(np.arccosh(x._val),
x._jacobian) # If x is a vector variable
try:
dict_self = x._dict.copy(
) # If x is a complex vector variable, it will update the original dictionary
for key in dict_self.keys():
dict_self[key] = dict_self[key] * -np.arccosh(
x._val) * np.tanh(x._val)
new._dict = dict_self
return new
except AttributeError:
derivative = Counter()
derivative[x] = x._jacobian * -np.arccosh(
x._val) * np.tanh(x._val)
new._dict = derivative # If x is not a complex vector variable, it will add an attribute to the new variable
return new
else:
jacobian = {
k: x.partial(k) * -np.arccosh(x._val) * np.tanh(x._val)
for k in x._jacobian.keys()
}
return Scalar(np.arccosh(x._val), jacobian)
def create_vector(vals):
'''
Return a list of vector variables with values as defined in vals
INPUTS
======
vals: list of lists of floats, compulsory
Value of the list of Vector variables
RETURNS
========
A list of Vector variables
'''
vectors = [None] * len(vals)
for i in range(len(vals)):
vectors[i] = Vector(vals[i])
return vectors
import numpy as np from Dotua.nodes.vector import Vector ''' Test for vector variable basic functions and the jacobian of vector function to vector ''' # Define vector objects x = Vector([1, 2]) y = Vector([0, 1]) z = Vector([2, 1]) a = Vector([0, 0]) b = Vector([1, 1]) c = Vector([1, 0]) f_1 = x[0] + x[1] f_2 = x[0] - 3 - x[1] - x[1] f_3 = 1 + x[1] - x[0] * x[1] - x[0] - 3 f_4 = 3 / x[0] + (x[0] * x[1]) / 2 - 4 * x[1] f_5 = x[0]**3 + x[1] / x[0] f_6 = 2**x[1] f_7 = 3 + x + y - 2 f_8 = -1 - x - y - 3 f_9 = 3 * x + y * 2 + x * y f_10 = y / 3 + 2 / x + y / x f_11 = z + x f_12 = z + a f_13 = f_11 + f_12 f_14 = b - 1 f_15 = f_11 - f_12 f_16 = c - f_11 f_17 = f_11 - x