# AffineGrid¶

## AffineGrid - 20¶

### Version¶

• name: AffineGrid (GitHub)

• domain: main

• since_version: 20

• function: True

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 20.

### Summary¶

Generates a 2D or 3D flow field (sampling grid), given a batch of affine matrices theta (https://pytorch.org/docs/stable/generated/torch.nn.functional.affine_grid.html). An affine matrix theta is applied to a position tensor represented in its homogeneous expression. Here is an example in 3D:

[r00, r01, r02, t0]   [x]   [x']
[r10, r11, r12, t1] * [y] = [y']
[r20, r21, r22, t2]   [z]   [z']
[0,   0,   0,   1 ]   [1]   [1 ]


where (x, y, z) is the position in the original space, (x', y', z') is the position in the output space. The last row is always [0, 0, 0, 1] and is not stored in the affine matrix. Therefore we have theta of shape (N, 2, 3) for 2D or (N, 3, 4) for 3D.

Input size is used to define grid of positions evenly spaced in the original 2D or 3D space, with dimensions ranging from -1 to 1. The output grid contains positions in the output space.

When align_corners=1, consider -1 and 1 to refer to the centers of the corner pixels (mark v in illustration).

v            v            v            v
|-------------------|------------------|
-1                  0                  1


When align_corners=0, consider -1 and 1 to refer to the outer edge of the corner pixels.

    v        v         v         v
|------------------|-------------------|
-1                 0                   1


#### Function Body¶

The function definition for this operator.

<
domain: "",
opset_import: ["" : 20]
>
AffineGrid <align_corners>(theta, size) => (grid)
{
one = Constant <value_int: int = 1> ()
two = Constant <value_int: int = 2> ()
zero = Constant <value_int: int = 0> ()
four = Constant <value_int: int = 4> ()
one_1d = Constant <value_ints: ints = [1]> ()
zero_1d = Constant <value_ints: ints = [0]> ()
minus_one = Constant <value_int: int = -1> ()
minus_one_f = CastLike (minus_one, theta)
zero_f = CastLike (zero, theta)
one_f = CastLike (one, theta)
two_f = CastLike (two, theta)
constant_align_corners = Constant <value_int: int = @align_corners> ()
constant_align_corners_equal_zero = Equal (constant_align_corners, zero)
size_ndim = Size (size)
condition_is_2d = Equal (size_ndim, four)
N, C, D, H, W = If (condition_is_2d) <then_branch: graph = g1 () => ( N_then,  C_then,  D_then,  H_then,  W_then) {
N_then, C_then, H_then, W_then = Split <num_outputs: int = 4> (size)
D_then = Identity (one_1d)
}, else_branch: graph = g2 () => ( N_else,  C_else,  D_else,  H_else,  W_else) {
N_else, C_else, D_else, H_else, W_else = Split <num_outputs: int = 5> (size)
}>
size_NCDHW = Concat <axis: int = 0> (N, C, D, H, W)
theta_3d = If (condition_is_2d) <then_branch: graph = g3 () => ( theta_then) {
gather_idx_6 = Constant <value_ints: ints = [0, 1, 2, 0, 1, 2]> ()
shape_23 = Constant <value_ints: ints = [2, 3]> ()
gather_idx_23 = Reshape (gather_idx_6, shape_23)
shape_N23 = Concat <axis: int = 0> (N, shape_23)
gather_idx_N23 = Expand (gather_idx_23, shape_N23)
thetaN23 = GatherElements <axis: int = 2> (theta, gather_idx_N23)
r1, r2 = Split <axis: int = 1, num_outputs: int = 2> (thetaN23)
r1_ = Squeeze (r1)
r2_ = Squeeze (r2)
r11, r12, t1 = Split <axis: int = 1, num_outputs: int = 3> (r1_)
r21, r22, t2 = Split <axis: int = 1, num_outputs: int = 3> (r2_)
r11_shape = Shape (r21)
float_zero_1d_ = ConstantOfShape (r11_shape)
float_zero_1d = CastLike (float_zero_1d_, theta)
R1 = Concat <axis: int = 1> (r11, r12, float_zero_1d, t1)
R2 = Concat <axis: int = 1> (r21, r22, float_zero_1d, t2)
R3 = Concat <axis: int = 1> (float_zero_1d, float_zero_1d, float_one_1d, float_zero_1d)
R1_ = Unsqueeze (R1, one_1d)
R2_ = Unsqueeze (R2, one_1d)
R3_ = Unsqueeze (R3, one_1d)
theta_then = Concat <axis: int = 1> (R1_, R2_, R3_)
}, else_branch: graph = g4 () => ( theta_else) {
theta_else = Identity (theta)
}>
two_1d = Constant <value_ints: ints = [2]> ()
three_1d = Constant <value_ints: ints = [3]> ()
five_1d = Constant <value_ints: ints = [5]> ()
constant_D_H_W_shape = Slice (size_NCDHW, two_1d, five_1d)
zeros_D_H_W_ = ConstantOfShape (constant_D_H_W_shape)
zeros_D_H_W = CastLike (zeros_D_H_W_, theta)
D_float = CastLike (D, zero_f)
H_float = CastLike (H, zero_f)
W_float = CastLike (W, zero_f)
start_d, step_d, start_h, step_h, start_w, step_w = If (constant_align_corners_equal_zero) <then_branch: graph = h1 () => ( start_d_then,  step_d_then,  start_h_then,  step_h_then,  start_w_then,  step_w_then) {
step_d_then = Div (two_f, D_float)
step_h_then = Div (two_f, H_float)
step_w_then = Div (two_f, W_float)
step_d_half = Div (step_d_then, two_f)
step_h_half = Div (step_h_then, two_f)
step_w_half = Div (step_w_then, two_f)
}, else_branch: graph = h2 () => ( start_d_else,  step_d_else,  start_h_else,  step_h_else,  start_w_else,  step_w_else) {
D_float_nimus_one = Sub (D_float, one_f)
H_float_nimus_one = Sub (H_float, one_f)
W_float_nimus_one = Sub (W_float, one_f)
D_equals_one = Equal (D, one)
step_d_else = If (D_equals_one) <then_branch: graph = g5 () => ( step_d_else_then) {
step_d_else_then = Identity (zero_f)
}, else_branch: graph = g6 () => ( step_d_else_else) {
step_d_else_else = Div (two_f, D_float_nimus_one)
}>
step_h_else = Div (two_f, H_float_nimus_one)
step_w_else = Div (two_f, W_float_nimus_one)
start_d_else = Identity (minus_one_f)
start_h_else = Identity (minus_one_f)
start_w_else = Identity (minus_one_f)
}>
grid_w_steps_int = Range (zero, W, one)
grid_w_steps_float = CastLike (grid_w_steps_int, step_w)
grid_w_steps = Mul (grid_w_steps_float, step_w)
grid_h_steps_int = Range (zero, H, one)
grid_h_steps_float = CastLike (grid_h_steps_int, step_h)
grid_h_steps = Mul (grid_h_steps_float, step_h)
grid_d_steps_int = Range (zero, D, one)
grid_d_steps_float = CastLike (grid_d_steps_int, step_d)
grid_d_steps = Mul (grid_d_steps_float, step_d)
zeros_H_W_D = Transpose <perm: ints = [1, 2, 0]> (zeros_D_H_W)
grid_d = Transpose <perm: ints = [2, 0, 1]> (grid_d_1)
zeros_D_W_H = Transpose <perm: ints = [0, 2, 1]> (zeros_D_H_W)
grid_h = Transpose <perm: ints = [0, 2, 1]> (grid_h_1)
grid_w_usqzed = Unsqueeze (grid_w, minus_one)
grid_h_usqzed = Unsqueeze (grid_h, minus_one)
grid_d_usqzed = Unsqueeze (grid_d, minus_one)
ones_D_H_W_usqzed = Unsqueeze (ones_D_H_W, minus_one)
original_grid = Concat <axis: int = -1> (grid_w_usqzed, grid_h_usqzed, grid_d_usqzed, ones_D_H_W_usqzed)
constant_shape_DHW_4 = Constant <value_ints: ints = [-1, 4]> ()
original_grid_DHW_4 = Reshape (original_grid, constant_shape_DHW_4)
original_grid_4_DHW_ = Transpose (original_grid_DHW_4)
original_grid_4_DHW = CastLike (original_grid_4_DHW_, theta_3d)
grid_N_3_DHW = MatMul (theta_3d, original_grid_4_DHW)
grid_N_DHW_3 = Transpose <perm: ints = [0, 2, 1]> (grid_N_3_DHW)
N_D_H_W_3 = Concat <axis: int = -1> (N, D, H, W, three_1d)
grid_3d_else_ = Reshape (grid_N_DHW_3, N_D_H_W_3)
grid_3d = CastLike (grid_3d_else_, theta_3d)
grid = If (condition_is_2d) <then_branch: graph = g1 () => ( grid_then) {
grid_squeezed = Squeeze (grid_3d, one_1d)
grid_then = Slice (grid_squeezed, zero_1d, two_1d, three_1d)
}, else_branch: graph = g2 () => ( grid_else) {
grid_else = Identity (grid_3d)
}>
}


### Attributes¶

• align_corners - INT (default is '0'):

if align_corners=1, consider -1 and 1 to refer to the centers of the corner pixels. if align_corners=0, consider -1 and 1 to refer to the outer edge the corner pixels.

### Inputs¶

• theta (heterogeneous) - T1:

input batch of affine matrices with shape (N, 2, 3) for 2D or (N, 3, 4) for 3D

• size (heterogeneous) - T2:

the target output image size (N, C, H, W) for 2D or (N, C, D, H, W) for 3D

### Outputs¶

• grid (heterogeneous) - T1:

output tensor of shape (N, H, W, 2) of 2D sample coordinates or (N, D, H, W, 3) of 3D sample coordinates.

### Type Constraints¶

• T1 in ( tensor(bfloat16), tensor(double), tensor(float), tensor(float16) ):

Constrain grid types to float tensors.

• T2 in ( tensor(int64) ):

Constrain size’s type to int64 tensors.