class

AtanBackward

AtanBackward

source edit

Python wrappers

pylucid.ops.atanfunction

Autograd node for element-wise arctangent $y = \arctan(x)$ .

Saves the input x so the backward pass can compute the denominator $1 + x^2$ . Defined on all of $\mathbb{R}$ with range $(-\tfrac{\pi}{2}, \tfrac{\pi}{2})$ and a smooth, bounded gradient.

Math

\frac{\partial y}{\partial x} = \frac{1}{1 + x^2}, \qquad \frac{\partial \mathcal{L}}{\partial x} = \frac{1}{1 + x^2}\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "arctan" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvatanf/vvatan (CPU) / MLX arctan (GPU).

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & s, Dtype dt)

source edit

Forward — calls IBackend::atan to compute $y = \arctan x$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = 1/(1 + x^2)$ , scaled by grad_out.

class

AtanBackward

AtanBackward

source edit

Python wrappers

pylucid.ops.atanfunction

Autograd node for element-wise arctangent $y = \arctan(x)$ .

Saves the input x so the backward pass can compute the denominator $1 + x^2$ . Defined on all of $\mathbb{R}$ with range $(-\tfrac{\pi}{2}, \tfrac{\pi}{2})$ and a smooth, bounded gradient.

Math

\frac{\partial y}{\partial x} = \frac{1}{1 + x^2}, \qquad \frac{\partial \mathcal{L}}{\partial x} = \frac{1}{1 + x^2}\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "arctan" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvatanf/vvatan (CPU) / MLX arctan (GPU).

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & s, Dtype dt)

source edit

Forward — calls IBackend::atan to compute $y = \arctan x$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = 1/(1 + x^2)$ , scaled by grad_out.