Here is the python library tested on MNIST dataset written by e for testing algorithms such as forward backward propagation, and Adam, RMSprop. momentum optimizers:
https://github.com/mathraim/deepmath

University of California, Berkeley

```python
import numpy as np

class Adam():
  
    self.beta1 = 0.9
    self.beta2 = 0.99

    # Here is the M amd V matrices for the parameters and biases
    self.m_weights = np.zeros((input_dims, nodes))
    self.v_weights = np.zeros((input_dims, nodes))
    self.m_biases = np.zeros(nodes)
    self.v_biases = np.zeros(nodes)

    # need to track thecurrent time stamp
    self.curr_iter = 0

    def get_steps(self, grad_weights, grad_biases, learning_rate):

        eps = 1e-8

        # Just follows the formula and returns the update that have to be 
        # subtracted from the parametes and biases
      
        self.m_weights = self.beta1 * self.m_weights + (1 - self.beta1) * grad_weights
        self.v_weights = self.beta2 * self.v_weights + (1 - self.beta2) * np.power(grad_weights, 2)
        self.m_biases = self.beta1 * self.m_biases + (1 - self.beta1) * grad_biases
        self.v_biases = self.beta2 * self.v_biases + (1 - self.beta2) * np.power(grad_biases, 2)

        self.curr_iter += 1
        self.m_weights = self.m_weights / (1 - np.power(self.beta1, self.curr_iter))
        self.v_weights = self.v_weights / (1 - np.power(self.beta2, self.curr_iter))
        self.m_biases = self.m_biases / (1 - np.power(self.beta1, self.curr_iter))
        self.v_biases = self.v_biases / (1 - np.power(self.beta2, self.curr_iter))

        weights_step = np.multiply((learning_rate / (np.sqrt(self.v_weights) + eps)), self.m_weights)
        biases_step = np.multiply((learning_rate / (np.sqrt(self.v_biases) + eps)), self.m_biases)

        return weights_step, biases_step
```

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