class

AsinBackward

AsinBackward

source edit

Python wrappers

pylucid.ops.asinfunction

Autograd node for element-wise arcsine $y = \arcsin(x)$ .

Saves the input x so the backward pass can form the radicand $1 - x^2$ . Defined on the closed input domain $[-1, 1]$ with range $[-\tfrac{\pi}{2}, \tfrac{\pi}{2}]$ ; the gradient is unbounded at the endpoints $x = \pm 1$ .

Math

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

Attributes

schema_v1OpSchema

Registered as "arcsin" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvasinf/vvasin (CPU) / MLX arcsin (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::asin to compute $y = \arcsin x$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = 1/\sqrt{1 - x^2}$ , scaled by grad_out.

class

AsinBackward

AsinBackward

source edit

Python wrappers

pylucid.ops.asinfunction

Autograd node for element-wise arcsine $y = \arcsin(x)$ .

Math

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

Attributes

schema_v1OpSchema

Registered as "arcsin" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvasinf/vvasin (CPU) / MLX arcsin (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::asin to compute $y = \arcsin x$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = 1/\sqrt{1 - x^2}$ , scaled by grad_out.