class

AcosBackward

AcosBackward

source edit

Python wrappers

pylucid.ops.acosfunction

Autograd node for element-wise arccosine $y = \arccos(x)$ .

Shares the radicand $1 - x^2$ with AsinBackward but with a negated sign in the derivative. Defined on $[-1, 1]$ with range $[0, \pi]$ ; the gradient is unbounded at $x = \pm 1$ .

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 "arccos" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvacosf/vvacos (CPU) / MLX arccos (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::acos to compute $y = \arccos x$ .

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

AcosBackward

AcosBackward

source edit

Python wrappers

pylucid.ops.acosfunction

Autograd node for element-wise arccosine $y = \arccos(x)$ .

Shares the radicand $1 - x^2$ with AsinBackward but with a negated sign in the derivative. Defined on $[-1, 1]$ with range $[0, \pi]$ ; the gradient is unbounded at $x = \pm 1$ .

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 "arccos" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvacosf/vvacos (CPU) / MLX arccos (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::acos to compute $y = \arccos x$ .

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.