Class Affine

numpy_ml/neural_nets/activations/activations.py:342–392

class Affine(ActivationBase):
    def __init__(self, slope=1, intercept=0):
        """
        An affine activation function.

        Parameters
        ----------
        slope: float
            Activation slope. Default is 1.
        intercept: float
            Intercept/offset term. Default is 0.
        """
        self.slope = slope
        self.intercept = intercept
        super().__init__()

    def __str__(self):
        """Return a string representation of the activation function"""
        return "Affine(slope={}, intercept={})".format(self.slope, self.intercept)

    def fn(self, z):
        r"""
        Evaluate the Affine activation on the elements of input `z`.

        .. math::

            \text{Affine}(z_i)  =  \text{slope} \times z_i + \text{intercept}
        """
        return self.slope * z + self.intercept

    def grad(self, x):
        r"""
        Evaluate the first derivative of the Affine activation on the elements
        of input `x`.

        .. math::

            \frac{\partial \text{Affine}}{\partial x_i}  =  \text{slope}
        """
        return self.slope * np.ones_like(x)

    def grad2(self, x):
        r"""
        Evaluate the second derivative of the Affine activation on the elements
        of input `x`.

        .. math::

            \frac{\partial^2 \text{Affine}}{\partial x_i^2}  =  0
        """
        return np.zeros_like(x)


class Identity(Affine):