tswedish

Keybase proof

I hereby claim:

• I am tswedish on github.
• I am tswedish (https://keybase.io/tswedish) on keybase.
• I have a public key ASBmF9szOq6XhfbyhBf4NY1dTFdefEIf91vI5vstfqE7Ugo

To claim this, I am signing this object:

tswedish

def super_complicated_function(x):
	return x * sin(x+6.)**2. / 2. - 2. / 2.**x

tswedish

class Dual:
    def __init__(self, value=0., derivative=0.):
        self.value = value
        self.derivative = derivative

    def __add__(self, other):
        return Dual(self.value + other.value, self.derivative + other.derivative)

    def __mul__(self, other):
        return Dual(self.value * other.value, self.value*other.derivative + self.derivative * other.value)

tswedish

def __add__(self, other):
         if isinstance(other, self.__class__):
            return Dual(self.value + other.value, self.derivative + other.derivative)
        else:
            return self + Dual(other)

tswedish

import math

def sin(dual):
    return Dual(math.sin(dual.value), dual.derivative * math.cos(dual.value))

tswedish

def super_complicated_function(x):
    return x * sin(x+6.)**2. / 2. - 2. / 2.**x

# symbolic derivative by running the above in mathematica (wolfram alpha)
def d_super_complicated_function(x):
    return 2**(1 - x) * math.log(2) + 0.5 * sin(x + 6)**2 + x * math.sin(x + 6) * math.cos(x + 6)

for x in [-1., 0.5, 3., 2.]:
    print('Function Input: {}'.format(x))
    print('Function Value: {}'.format(super_complicated_function(x)))

tswedish

def create_diff_fn(fn):
        def diff_fn(*argv):
            jacobian = []
            Dual_arguments = [Dual(x, 0.) for x in argv]
            for input_arg in Dual_arguments:
                input_arg.derivative = 1.
                result = fn(*Dual_arguments)
                jacobian.append(result.derivative)
                input_arg.derivative = 0.

tswedish

# compose a graph of nodes

x = Variable(10.01)
y = Variable(0.05)

z = x * y
m = 1.3
q = m+y

L = (q - (z**(m/2.) + z**2. - 1./z))**2

tswedish

class Variable:
    def __init__(self, operation, input_variables=[]):
        # note the setter for @property value below
        self.value = operation
        self.input_variables = input_variables
        self.gradient = 0.

tswedish

    def calc_input_values(self):
        # calculate the real-valued input to operation
        return [v.value for v in self.input_variables]

    def forward(self):  
        # calculate the real-valued output of operation              
        return self.forward_op(*self.calc_input_values())

    @property
    def value(self):