class

AffineGridBackward

AffineGridBackward

source edit

Python wrappers

pylucid.nn.functional.affine_gridfunction

Autograd node for affine grid generation.

Builds an (N, H, W, 2) sampling grid by applying the per-sample affine matrix $\theta_n \in \mathbb{R}^{2 \times 3}$ to a regular $H \times W$ output lattice:

\begin{pmatrix} x_s \\ y_s \end{pmatrix} = \theta_n \begin{pmatrix} x_t \\ y_t \\ 1 \end{pmatrix}

where $(x_t, y_t)$ are the normalised output coordinates in $[-1, 1]$ and $(x_s, y_s)$ are the corresponding source coordinates that will be passed to grid_sample. The backward propagates grad_out (shape (N, H, W, 2)) back into theta by summing the outer products with the homogeneous lattice coordinates.

Math

Lattice generation depends on align_corners_:

x_t = \begin{cases} -1 + 2 j / (W - 1) & \text{align\_corners} \\ -1 + (2 j + 1) / W & \text{otherwise} \end{cases}, \quad y_t = \begin{cases} -1 + 2 i / (H - 1) & \text{align\_corners} \\ -1 + (2 i + 1) / H & \text{otherwise} \end{cases}

Attributes

schema_v1OpSchema

"affine_grid", AmpPolicy::Promote.

align_corners_bool

When true, the four corners of the output lattice map exactly to [-1, +1] on each axis; when false, the lattice is placed on pixel centres.

N_, H_, W_int

Batch size and output spatial dimensions.

orig_theta_shape_Shape

Original (N, 2, 3) shape used to materialise the gradient.

Static methods

static

forward

→TensorImplPtr

int forward(const int & theta, int N, int H, int W, bool align_corners)

source edit

Generate the sampling grid with autograd wiring.

Parameters

thetaTensorImplPtr

Affine matrices of shape (N, 2, 3).

Nint

Batch size (must equal theta.shape()[0]).

Hint

Output grid height.

Wint

Output grid width.

align_cornersbool

Lattice placement mode.

Returns

TensorImplPtr

Sampling grid of shape (N, H, W, 2) with last-axis ordering (x, y) (i.e. [..., 0] is the x-coordinate).

Methods

apply

int apply(int grad_out)

source edit

Backward pass: gradient w.r.t. the affine matrices theta.

class

AffineGridBackward

AffineGridBackward

source edit

Python wrappers

pylucid.nn.functional.affine_gridfunction

Autograd node for affine grid generation.

Builds an (N, H, W, 2) sampling grid by applying the per-sample affine matrix $\theta_n \in \mathbb{R}^{2 \times 3}$ to a regular $H \times W$ output lattice:

\begin{pmatrix} x_s \\ y_s \end{pmatrix} = \theta_n \begin{pmatrix} x_t \\ y_t \\ 1 \end{pmatrix}

Math

Lattice generation depends on align_corners_:

x_t = \begin{cases} -1 + 2 j / (W - 1) & \text{align\_corners} \\ -1 + (2 j + 1) / W & \text{otherwise} \end{cases}, \quad y_t = \begin{cases} -1 + 2 i / (H - 1) & \text{align\_corners} \\ -1 + (2 i + 1) / H & \text{otherwise} \end{cases}

Attributes

schema_v1OpSchema

"affine_grid", AmpPolicy::Promote.

align_corners_bool

When true, the four corners of the output lattice map exactly to [-1, +1] on each axis; when false, the lattice is placed on pixel centres.

N_, H_, W_int

Batch size and output spatial dimensions.

orig_theta_shape_Shape

Original (N, 2, 3) shape used to materialise the gradient.

Static methods

static

forward

→TensorImplPtr

int forward(const int & theta, int N, int H, int W, bool align_corners)

source edit

Generate the sampling grid with autograd wiring.

Parameters

thetaTensorImplPtr

Affine matrices of shape (N, 2, 3).

Nint

Batch size (must equal theta.shape()[0]).

Hint

Output grid height.

Wint

Output grid width.

align_cornersbool

Lattice placement mode.

Returns

TensorImplPtr

Sampling grid of shape (N, H, W, 2) with last-axis ordering (x, y) (i.e. [..., 0] is the x-coordinate).

Methods

apply

int apply(int grad_out)

source edit

Backward pass: gradient w.r.t. the affine matrices theta.