import numpy as np
from pathlib import Path
from typing import List, Optional, Tuple, Union
from autoconf import conf
from autoconf import cached_property
from autoarray.mask.mask_2d import Mask2D
from autoarray.structures.abstract_structure import Structure
from autoarray.structures.arrays.uniform_2d import Array2D
from autoarray.structures.arrays.irregular import ArrayIrregular
from autoarray.structures.grids.irregular_2d import Grid2DIrregular
from autoarray.structures.arrays import array_2d_util
from autoarray.structures.grids import grid_2d_util
from autoarray.geometry import geometry_util
from autoarray import type as ty
[docs]class Grid2D(Structure):
def __init__(
self,
values: Union[np.ndarray, List],
mask: Mask2D,
store_native: bool = False,
*args,
**kwargs
):
"""
A grid of 2D (y,x) coordinates, which are paired to a uniform 2D mask of pixels and sub-pixels. Each entry
on the grid corresponds to the (y,x) coordinates at the centre of a sub-pixel of an unmasked pixel.
A `Grid2D` is ordered such that pixels begin from the top-row (e.g. index [0, 0]) of the corresponding mask
and go right and down. The positive y-axis is upwards and positive x-axis to the right.
The grid can be stored in two formats:
- slimmed: all masked entries are removed so the ndarray is shape [total_unmasked_coordinates*sub_size**2, 2]
- native: it retains the original shape of the grid so the ndarray is
shape [total_y_coordinates*sub_size, total_x_coordinates*sub_size, 2].
**Case 1 (sub-size=1, slim)**
The Grid2D is an ndarray of shape [total_unmasked_coordinates, 2], therefore when `slim` the shape of
the grid is 2, not 1.
The first element of the ndarray corresponds to the pixel index and second element the y or x coordinate value.
For example:
- grid[3,0] = the 4th unmasked pixel's y-coordinate.
- grid[6,1] = the 7th unmasked pixel's x-coordinate.
Below is a visual illustration of a grid, where a total of 10 pixels are unmasked and are included in \
the grid.
.. code-block:: bash
x x x x x x x x x x
x x x x x x x x x x This is an example mask.Mask2D, where:
x x x x x x x x x x
x x x x O O x x x x x = `True` (Pixel is masked and excluded from the grid)
x x x O O O O x x x O = `False` (Pixel is not masked and included in the grid)
x x x O O O O x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
The mask pixel index's will come out like this (and the direction of scaled coordinates is highlighted
around the mask.
.. code-block:: bash
pixel_scales = 1.0"
<--- -ve x +ve -->
y x
x x x x x x x x x x ^ grid[0] = [ 1.5, -0.5]
x x x x x x x x x x I grid[1] = [ 1.5, 0.5]
x x x x x x x x x x I grid[2] = [ 0.5, -1.5]
x x x x 0 1 x x x x +ve grid[3] = [ 0.5, -0.5]
x x x 2 3 4 5 x x x y grid[4] = [ 0.5, 0.5]
x x x 6 7 8 9 x x x -ve grid[5] = [ 0.5, 1.5]
x x x x x x x x x x I grid[6] = [-0.5, -1.5]
x x x x x x x x x x I grid[7] = [-0.5, -0.5]
x x x x x x x x x x \/ grid[8] = [-0.5, 0.5]
x x x x x x x x x x grid[9] = [-0.5, 1.5]
**Case 2 (sub-size>1, slim)**
If the mask's `sub_size` is > 1, the grid is defined as a sub-grid where each entry corresponds to the (y,x)
coordinates at the centre of each sub-pixel of an unmasked pixel. The Grid2D is therefore stored as an ndarray
of shape [total_unmasked_coordinates*sub_size**2, 2]
The sub-grid indexes are ordered such that pixels begin from the first (top-left) sub-pixel in the first
unmasked pixel. Indexes then go over the sub-pixels in each unmasked pixel, for every unmasked pixel.
Therefore, the sub-grid is an ndarray of shape [total_unmasked_coordinates*(sub_grid_shape)**2, 2].
For example:
- grid[9, 1] - using a 2x2 sub-grid, gives the 3rd unmasked pixel's 2nd sub-pixel x-coordinate.
- grid[9, 1] - using a 3x3 sub-grid, gives the 2nd unmasked pixel's 1st sub-pixel x-coordinate.
- grid[27, 0] - using a 3x3 sub-grid, gives the 4th unmasked pixel's 1st sub-pixel y-coordinate.
Below is a visual illustration of a sub grid. Indexing of each sub-pixel goes from the top-left corner. In
contrast to the grid above, our illustration below restricts the mask to just 2 pixels, to keep the
illustration brief.
.. code-block:: bash
x x x x x x x x x x
x x x x x x x x x x This is an example mask.Mask2D, where:
x x x x x x x x x x
x x x x x x x x x x x = `True` (Pixel is masked and excluded from lens)
x x x x O O x x x x O = `False` (Pixel is not masked and included in lens)
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
Our grid with a sub-size looks like it did before:
.. code-block:: bash
pixel_scales = 1.0"
<--- -ve x +ve -->
x x x x x x x x x x ^
x x x x x x x x x x I
x x x x x x x x x x I y x
x x x x x x x x x x +ve grid[0] = [0.5, -1.5]
x x x x 0 1 x x x x y grid[1] = [0.5, -0.5]
x x x x x x x x x x -ve
x x x x x x x x x x I
x x x x x x x x x x I
x x x x x x x x x x \/
x x x x x x x x x x
However, if the sub-size is 2, we go to each unmasked pixel and allocate sub-pixel coordinates for it. For
example, for pixel 0, if *sub_size=2*, we use a 2x2 sub-grid:
.. code-block:: bash
Pixel 0 - (2x2):
y x
grid[0] = [0.66, -1.66]
I0I1I grid[1] = [0.66, -1.33]
I2I3I grid[2] = [0.33, -1.66]
grid[3] = [0.33, -1.33]
If we used a sub_size of 3, for the pixel we we would create a 3x3 sub-grid:
.. code-block:: bash
y x
grid[0] = [0.75, -0.75]
grid[1] = [0.75, -0.5]
grid[2] = [0.75, -0.25]
I0I1I2I grid[3] = [0.5, -0.75]
I3I4I5I grid[4] = [0.5, -0.5]
I6I7I8I grid[5] = [0.5, -0.25]
grid[6] = [0.25, -0.75]
grid[7] = [0.25, -0.5]
grid[8] = [0.25, -0.25]
**Case 3 (sub_size=1, native)**
The Grid2D has the same properties as Case 1, but is stored as an an ndarray of shape
[total_y_coordinates, total_x_coordinates, 2]. Therefore when `native` the shape of the
grid is 3, not 2.
All masked entries on the grid has (y,x) values of (0.0, 0.0).
For the following example mask:
.. code-block:: bash
x x x x x x x x x x
x x x x x x x x x x This is an example mask.Mask2D, where:
x x x x x x x x x x
x x x x O O x x x x x = `True` (Pixel is masked and excluded from the grid)
x x x O O O O x x x O = `False` (Pixel is not masked and included in the grid)
x x x O O O O x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
In the above grid:
- grid[0,0,0] = 0.0 (it is masked, thus zero)
- grid[0,0,1] = 0.0 (it is masked, thus zero)
- grid[3,3,0] = 0.0 (it is masked, thus zero)
- grid[3,3,1] = 0.0 (it is masked, thus zero)
- grid[3,4,0] = 1.5
- grid[3,4,1] = -0.5
**Case 4 (sub_size>1 native)**
The properties of this grid can be derived by combining Case's 2 and 3 above, whereby the grid is stored as
an ndarray of shape [total_y_coordinates*sub_size, total_x_coordinates*sub_size, 2].
All sub-pixels in masked pixels have values (0.0, 0.0).
**Grid2D Mapping:**
Every set of (y,x) coordinates in a pixel of the sub-grid maps to an unmasked pixel in the mask. For a uniform
grid, every (y,x) coordinate directly corresponds to the location of its paired unmasked pixel.
It is not a requirement that grid is uniform and that their coordinates align with the mask. The input grid
could be an irregular set of (y,x) coordinates where the indexing signifies that the (y,x) coordinate
*originates* or *is paired with* the mask's pixels but has had its value change by some aspect of the
calculation.
This is important for the child project *PyAutoLens*, where grids in the image-plane are ray-traced and
deflected to perform lensing calculations. The grid indexing is used to map pixels between the image-plane and
source-plane.
Parameters
----------
values
The (y,x) coordinates of the grid.
mask
The 2D mask associated with the grid, defining the pixels each grid coordinate is paired with and
originates from.
store_native
If True, the ndarray is stored in its native format [total_y_pixels, total_x_pixels, 2]. This avoids
mapping large data arrays to and from the slim / native formats, which can be a computational bottleneck.
"""
values = grid_2d_util.convert_grid_2d(
grid_2d=values,
mask_2d=mask,
store_native=store_native,
)
super().__init__(values)
self.mask = mask
grid_2d_util.check_grid_2d(grid_2d=values)
[docs] @classmethod
def no_mask(
cls,
values: Union[np.ndarray, List],
pixel_scales: ty.PixelScales,
shape_native: Tuple[int, int] = None,
sub_size: int = 1,
origin: Tuple[float, float] = (0.0, 0.0),
) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) by inputting the grid coordinates in 1D or 2D, automatically
determining whether to use the 'manual_slim' or 'manual_native' methods.
From 1D input the method cannot determine the 2D shape of the grid and its mask, thus the shape_native must be
input into this method. The mask is setup as a unmasked `Mask2D` of shape_native.
The 2D shape of the grid and its mask are determined from the input grid and the mask is setup as an
unmasked `Mask2D` of shape_native.
Parameters
----------
values
The (y,x) coordinates of the grid input as an ndarray of shape [total_unmasked_pixells*(sub_size**2), 2]
or a list of lists.
shape_native
The 2D shape of the mask the grid is paired with.
pixel_scales
The (y,x) arcsecond-to-pixel units conversion factor of every pixel. If this is input as a `float`,
it is converted to a (float, float).
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-grid.
origin
The origin of the grid's mask.
"""
pixel_scales = geometry_util.convert_pixel_scales_2d(pixel_scales=pixel_scales)
values = grid_2d_util.convert_grid(grid=values)
if len(values.shape) == 2:
grid_2d_util.check_grid_slim(grid=values, shape_native=shape_native)
else:
shape_native = (
int(values.shape[0] / sub_size),
int(values.shape[1] / sub_size),
)
mask = Mask2D.all_false(
shape_native=shape_native,
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
return Grid2D(values=values, mask=mask)
[docs] @classmethod
def from_yx_1d(
cls,
y: Union[np.ndarray, List],
x: np.ndarray,
shape_native: Tuple[int, int],
pixel_scales: ty.PixelScales,
sub_size: int = 1,
origin: Tuple[float, float] = (0.0, 0.0),
) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) by inputting the grid coordinates as 1D y and x values.
From 1D input the method cannot determine the 2D shape of the grid and its mask, thus the shape_native must be
input into this method. The mask is setup as a unmasked `Mask2D` of shape_native.
Parameters
----------
y or list
The y coordinates of the grid input as an ndarray of shape [total_coordinates] or list.
x or list
The x coordinates of the grid input as an ndarray of shape [total_coordinates] or list.
shape_native
The 2D shape of the mask the grid is paired with.
pixel_scales
The (y,x) arcsecond-to-pixel units conversion factor of every pixel. If this is input as a `float`,
it is converted to a (float, float).
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-grid.
origin
The origin of the grid's mask.
Examples
--------
.. code-block:: python
import autoarray as aa
# Make Grid2D from input np.ndarray.
grid_2d = aa.Grid2D.from_yx_1d(
y=np.array([1.0, 3.0, 5.0, 7.0]),
x=np.array([2.0, 4.0, 6.0, 8.0]),
shape_native=(2, 2),
pixel_scales=1.0,
)
# Make Grid2D from input list.
grid_2d = aa.Grid2D.from_yx_1d(
y=[1.0, 3.0, 5.0, 7.0],
x=[2.0, 4.0, 6.0, 8.0],
shape_native=(2, 2),
pixel_scales=1.0,
)
# Print grid's slim (masked 1D data representation) and
# native (masked 2D data representation)
print(grid_2d.slim)
print(grid_2d.native)
"""
if type(y) is list:
y = np.asarray(y)
if type(x) is list:
x = np.asarray(x)
return cls.no_mask(
values=np.stack((y, x), axis=-1),
shape_native=shape_native,
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
[docs] @classmethod
def from_yx_2d(
cls,
y: Union[np.ndarray, List],
x: Union[np.ndarray, List],
pixel_scales: ty.PixelScales,
sub_size: int = 1,
origin: Tuple[float, float] = (0.0, 0.0),
) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) by inputting the grid coordinates as 2D y and x values.
The 2D shape of the grid and its mask are determined from the input grid and the mask is setup as an
unmasked `Mask2D` of shape_native.
Parameters
----------
y or list
The y coordinates of the grid input as an ndarray of shape [total_coordinates] or list.
x or list
The x coordinates of the grid input as an ndarray of shape [total_coordinates] or list.
pixel_scales
The (y,x) arcsecond-to-pixel units conversion factor of every pixel. If this is input as a `float`,
it is converted to a (float, float).
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-grid.
origin
The origin of the grid's mask.
Examples
--------
.. code-block:: python
import autoarray as aa
# Make Grid2D from input list(s).
grid_2d = aa.Grid2D.from_yx_2d(
y=[[1.0], [3.0]],
x=[[2.0], [4.0]],
pixel_scales=1.0
)
"""
if type(y) is list:
y = np.asarray(y)
if type(x) is list:
x = np.asarray(x)
return cls.no_mask(
values=np.stack((y, x), axis=-1),
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
[docs] @classmethod
def from_extent(
cls,
extent: Tuple[float, float, float, float],
shape_native: Tuple[int, int],
sub_size: int = 1,
) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) by inputting the extent of the (y,x) grid coordinates as an input
(x0, x1, y0, y1) tuple.
The (y,x) `shape_native` in pixels is also input which determines the resolution of the `Grid2D`.
(The **PyAutoArray** API typically uses a (y,x) notation, however extent variables begin with x currently.
This will be updated in a future release):
extent = (x0, x1, y0, y1) = (2.0, 4.0, -2.0, 6.0)
shape_native = (y,x) = (10, 20)
Parameters
----------
extent
The (x0, x1, y0, y1) extent of the grid in scaled coordinates over which the grid is created.
shape_native
The 2D shape of the grid that is created within this extent.
pixel_scales
The (y,x) arcsecond-to-pixel units conversion factor of every pixel. If this is input as a `float`,
it is converted to a (float, float).
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-grid.
origin
The origin of the grid's mask.
"""
x0, x1, y0, y1 = extent
ys = np.linspace(y1, y0, shape_native[0] * sub_size)
xs = np.linspace(x0, x1, shape_native[1] * sub_size)
xs_grid, ys_grid = np.meshgrid(xs, ys)
xs_grid_1d = xs_grid.ravel()
ys_grid_1d = ys_grid.ravel()
grid_2d = np.vstack((ys_grid_1d, xs_grid_1d)).T
grid_2d = grid_2d.reshape(
(shape_native[0] * sub_size, shape_native[1] * sub_size, 2)
)
pixel_scales = (
abs(grid_2d[0, 0, 0] - grid_2d[1, 0, 0]),
abs(grid_2d[0, 0, 1] - grid_2d[0, 1, 1]),
)
return Grid2D.no_mask(values=grid_2d, pixel_scales=pixel_scales)
[docs] @classmethod
def bounding_box(
cls,
bounding_box: np.ndarray,
shape_native: Tuple[int, int],
sub_size: int = 1,
buffer_around_corners: bool = False,
) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) from an input bounding box with coordinates [y_min, y_max, x_min, x_max],
where the shape_native is used to compute the (y,x) grid values within this bounding box.
If buffer_around_corners=True, the grid's (y,x) values fully align with the input bounding box values. This
means the mask's edge pixels extend beyond the bounding box by pixel_scale/2.0. If buffer_around_corners=False,
the grid (y,x) coordinates are defined within the bounding box such that the mask's edge pixels align with
the bouning box.
Parameters
----------
shape_native
The 2D shape of the uniform grid and the mask that it is paired with.
pixel_scales
The (y,x) arcsecond-to-pixel units conversion factor of every pixel. If this is input as a `float`,
it is converted to a (float, float).
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-grid.
origin
The origin of the grid's mask.
buffer_around_corners
Whether the grid is buffered such that the (y,x) values in the centre of its masks' edge pixels align
with the input bounding box values.
"""
y_min, y_max, x_min, x_max = bounding_box
if not buffer_around_corners:
pixel_scales = (
(y_max - y_min) / (shape_native[0]),
(x_max - x_min) / (shape_native[1]),
)
else:
pixel_scales = (
(y_max - y_min) / (shape_native[0] - 1),
(x_max - x_min) / (shape_native[1] - 1),
)
origin = ((y_max + y_min) / 2.0, (x_max + x_min) / 2.0)
return cls.uniform(
shape_native=shape_native,
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
[docs] @classmethod
def from_mask(cls, mask: Mask2D) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) from a mask, where only unmasked pixels are included in the grid (if the
grid is represented in its native 2D masked values are (0.0, 0.0)).
The mask's pixel_scales, sub_size and origin properties are used to compute the grid (y,x) coordinates.
Parameters
----------
mask
The mask whose masked pixels are used to setup the sub-pixel grid.
"""
sub_grid_1d = grid_2d_util.grid_2d_slim_via_mask_from(
mask_2d=np.array(mask),
pixel_scales=mask.pixel_scales,
sub_size=mask.sub_size,
origin=mask.origin,
)
return Grid2D(values=sub_grid_1d, mask=mask)
[docs] @classmethod
def from_fits(
cls,
file_path: Union[Path, str],
pixel_scales: ty.PixelScales,
sub_size: int = 1,
origin: Tuple[float, float] = (0.0, 0.0),
) -> "Grid2D":
"""
Create a Grid2D (see *Grid2D.__new__*) from a mask, where only unmasked pixels are included in the grid (if the
grid is represented in its native 2D masked values are (0.0, 0.0)).
The mask's pixel_scales, sub_size and origin properties are used to compute the grid (y,x) coordinates.
Parameters
----------
mask
The mask whose masked pixels are used to setup the sub-pixel grid.
"""
sub_grid_2d = array_2d_util.numpy_array_2d_via_fits_from(
file_path=file_path, hdu=0
)
return Grid2D.no_mask(
values=sub_grid_2d,
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
[docs] @classmethod
def blurring_grid_from(
cls, mask: Mask2D, kernel_shape_native: Tuple[int, int]
) -> "Grid2D":
"""
Setup a blurring-grid from a mask, where a blurring grid consists of all pixels that are masked (and
therefore have their values set to (0.0, 0.0)), but are close enough to the unmasked pixels that their values
will be convolved into the unmasked those pixels. This when computing images from
light profile objects.
The mask's pixel_scales, sub_size and origin properties are used to compute the blurring grid's (y,x)
coordinates.
For example, if our mask is as follows:
.. code-block:: bash
x x x x x x x x x xI
x x x x x x x x x xI This is an imaging.Mask2D, where
x x x x x x x x x xI
x x x x x x x x x xI x = `True` (Pixel is masked and excluded from lens)
x x x O O O x x x xI O = `False` (Pixel is not masked and included in lens)
x x x O O O x x x xI
x x x O O O x x x xI
x x x x x x x x x xI
x x x x x x x x x xI
x x x x x x x x x xI
For a PSF of shape (3,3), the following blurring mask is computed (noting that only pixels that are direct
neighbors of the unmasked pixels above will blur light into an unmasked pixel)
.. code-block:: bash
x x x x x x x x xI This is an example grid.Mask2D, where
x x x x x x x x xI
x x O O O O O x xI x = `True` (Pixel is masked and excluded from lens)
x x O x x x O x xI O = `False` (Pixel is not masked and included in lens)
x x O x x x O x xI
x x O x x x O x xI
x x O O O O O x xI
x x x x x x x x xI
x x x x x x x x xI
Thus, the blurring grid coordinates and indexes will be as follows
.. code-block:: bash
pixel_scales = 1.0"
positive negative
y x y x
x x x x x x x x xI I blurring_grid[0] = [2.0, -2.0] blurring_grid[9] = [-1.0, -2.0]
x x x x x x x x xI I blurring_grid[1] = [2.0, -1.0] blurring_grid[10] = [-1.0, 2.0]
x xI0 I1 I2 I3 I4 x xI pos blurring_grid[2] = [2.0, 0.0] blurring_grid[11] = [-2.0, -2.0]
x xI5 x x x I6 x xI y blurring_grid[3] = [2.0, 1.0] blurring_grid[12] = [-2.0, -1.0]
x xI7 x x x I8 x xI I blurring_grid[4] = [2.0, 2.0] blurring_grid[13] = [-2.0, 0.0]
x xI9 x x x I10 x xI neg blurring_grid[5] = [1.0, -2.0] blurring_grid[14] = [-2.0, 1.0]
x xI11I12I13I14I15 x xI I blurring_grid[6] = [1.0, 2.0] blurring_grid[15] = [-2.0, 2.0]
x x x x x x x x xI I blurring_grid[7] = [0.0, -2.0]
x x x x x x x x xI I blurring_grid[8] = [0.0, 2.0]
For a PSF of shape (5,5), the following blurring mask is computed (noting that pixels are 2 pixels from a
direct unmasked pixels now blur light into an unmasked pixel)
.. code-block:: bash
x x x x x x x x xI This is an example grid.Mask2D, where
xIoIoIoIoIoIoIo xI
xIoIoIoIoIoIoIo xI x = `True` (Pixel is masked and excluded from lens)
xIoIo x x xIoIo xI O = `False` (Pixel is not masked and included in lens)
xIoIo x x xIoIo xI
xIoIo x x xIoIo xI
xIoIoIoIoIoIoIo xI
xIoIoIoIoIoIoIo xI
x x x x x x x x xI
Parameters
----------
mask
The mask whose masked pixels are used to setup the blurring grid.
kernel_shape_native
The 2D shape of the kernel which convolves signal from masked pixels to unmasked pixels.
"""
blurring_mask = mask.derive_mask.blurring_from(
kernel_shape_native=kernel_shape_native
)
return cls.from_mask(mask=blurring_mask)
@property
def slim(self) -> "Grid2D":
"""
Return a `Grid2D` where the data is stored its `slim` representation, which is an ndarray of shape
[total_unmasked_pixels * sub_size**2, 2].
If it is already stored in its `slim` representation it is returned as it is. If not, it is mapped from
`native` to `slim` and returned as a new `Grid2D`.
"""
return Grid2D(values=self, mask=self.mask)
@property
def native(self) -> "Grid2D":
"""
Return a `Grid2D` where the data is stored in its `native` representation, which has shape
[sub_size*total_y_pixels, sub_size*total_x_pixels, 2].
If it is already stored in its `native` representation it is return as it is. If not, it is mapped from
`slim` to `native` and returned as a new `Grid2D`.
This method is used in the child `Grid2D` classes to create their `native` properties.
"""
return Grid2D(values=self, mask=self.mask, store_native=True)
@property
def binned(self) -> "Grid2D":
"""
Return a `Grid2D` of the binned-up grid in its 1D representation, which is stored with
shape [total_unmasked_pixels, 2].
The binning up process converts a grid from (y,x) values where each value is a coordinate on the sub-grid to
(y,x) values where each coordinate is at the centre of its mask (e.g. a grid with a sub_size of 1). This is
performed by taking the mean of all (y,x) values in each sub pixel.
If the grid is stored in 1D it is return as is. If it is stored in 2D, it must first be mapped from 2D to 1D.
"""
grid_2d_slim = self.slim
grid_2d_slim_binned_y = np.multiply(
self.mask.sub_fraction,
grid_2d_slim[:, 0].reshape(-1, self.mask.sub_length).sum(axis=1),
)
grid_2d_slim_binned_x = np.multiply(
self.mask.sub_fraction,
grid_2d_slim[:, 1].reshape(-1, self.mask.sub_length).sum(axis=1),
)
grid_2d_binned = np.stack(
(grid_2d_slim_binned_y, grid_2d_slim_binned_x), axis=-1
)
return Grid2D(values=grid_2d_binned, mask=self.mask.derive_mask.sub_1)
@property
def flipped(self) -> "Grid2D":
"""
Return the grid as an ndarray of shape [total_unmasked_pixels, 2] with flipped values such that coordinates
are given as (x,y) values.
This is used to interface with Python libraries that require the grid in (x,y) format.
"""
return self.with_new_array(np.fliplr(self.array))
@property
def in_radians(self) -> "Grid2D":
"""
Return the grid as an ndarray where all (y,x) values are converted to Radians.
This grid is used by the interferometer module.
"""
return (self * np.pi) / 648000.0
[docs] def grid_2d_via_deflection_grid_from(self, deflection_grid: "Grid2D") -> "Grid2D":
"""
Returns a new Grid2D from this grid, where the (y,x) coordinates of this grid have a grid of (y,x) values,
termed the deflection grid, subtracted from them to determine the new grid of (y,x) values.
This is used by PyAutoLens to perform grid ray-tracing.
Parameters
----------
deflection_grid
The grid of (y,x) coordinates which is subtracted from this grid.
"""
return Grid2D(values=self - deflection_grid, mask=self.mask)
[docs] def blurring_grid_via_kernel_shape_from(
self, kernel_shape_native: Tuple[int, int]
) -> "Grid2D":
"""
Returns the blurring grid from a grid, via an input 2D kernel shape.
For a full description of blurring grids, checkout *blurring_grid_from*.
Parameters
----------
kernel_shape_native
The 2D shape of the kernel which convolves signal from masked pixels to unmasked pixels.
"""
return Grid2D.blurring_grid_from(
mask=self.mask, kernel_shape_native=kernel_shape_native
)
[docs] def grid_with_coordinates_within_distance_removed_from(
self, coordinates: Union[np.ndarray, List], distance: float
) -> "Grid2D":
"""Remove all coordinates from this Grid2D which are within a certain distance of an input list of coordinates.
For example, if the grid has the coordinate (0.0, 0.0) and coordinates=[(0.0, 0.0)], distance=0.1 is input into
this function, a new Grid2D will be created which removes the coordinate (0.0, 0.0).
Parameters
----------
coordinates : [(float, float)]
The list of coordinates which are removed from the grid if they are within the distance threshold.
distance
The distance threshold that coordinates are removed if they are within that of the input coordinates.
"""
if not isinstance(coordinates, list):
coordinates = [coordinates]
distance_mask = np.full(fill_value=False, shape=self.shape_native)
for coordinate in coordinates:
distances = self.distances_to_coordinate_from(coordinate=coordinate)
distance_mask += distances.native < distance
mask = Mask2D(
mask=distance_mask,
pixel_scales=self.pixel_scales,
sub_size=self.sub_size,
origin=self.origin,
)
return Grid2D.from_mask(mask=mask)
[docs] def structure_2d_from(self, result: np.ndarray) -> Union[Array2D, "Grid2D"]:
"""
Convert a result from an ndarray to an aa.Array2D or aa.Grid2D structure, where the conversion depends on
type(result) as follows:
- 1D np.ndarray -> aa.Array2D
- 2D np.ndarray -> aa.Grid2D
This function is used by the grid_2d_to_structure decorator to convert the output result of a function
to an autoarray structure when a `Grid2D` instance is passed to the decorated function.
Parameters
----------
result or [np.ndarray]
The input result (e.g. of a decorated function) that is converted to a PyAutoArray structure.
"""
from autoarray.structures.grids.transformed_2d import Grid2DTransformed
from autoarray.structures.grids.transformed_2d import Grid2DTransformedNumpy
if len(result.shape) == 1:
return Array2D(values=result, mask=self.mask)
else:
if isinstance(result, Grid2DTransformedNumpy):
return Grid2DTransformed(values=result, mask=self.mask)
return Grid2D(values=result, mask=self.mask)
[docs] def structure_2d_list_from(
self, result_list: List
) -> List[Union[Array2D, "Grid2D"]]:
"""
Convert a result from a list of ndarrays to a list of aa.Array2D or aa.Grid2D structure, where the conversion
depends on type(result) as follows:
- [1D np.ndarray] -> [aa.Array2D]
- [2D np.ndarray] -> [aa.Grid2D]
This function is used by the grid_like_list_to_structure-list decorator to convert the output result of a
function to a list of autoarray structure when a `Grid2D` instance is passed to the decorated function.
Parameters
----------
result_list or [np.ndarray]
The input result (e.g. of a decorated function) that is converted to a PyAutoArray structure.
"""
return [self.structure_2d_from(result=result) for result in result_list]
[docs] def values_from(self, array_slim: np.ndarray) -> ArrayIrregular:
"""
Create a *ArrayIrregular* object from a 1D NumPy array of values of shape [total_coordinates]. The
*ArrayIrregular* are structured following this `Grid2DIrregular` instance.
"""
return ArrayIrregular(values=array_slim)
[docs] def squared_distances_to_coordinate_from(
self, coordinate: Tuple[float, float] = (0.0, 0.0)
) -> Array2D:
"""
Returns the squared distance of every coordinate on the grid from an input coordinate.
Parameters
----------
coordinate
The (y,x) coordinate from which the squared distance of every grid (y,x) coordinate is computed.
"""
squared_distances = np.square(self[:, 0] - coordinate[0]) + np.square(
self[:, 1] - coordinate[1]
)
return Array2D(values=squared_distances, mask=self.mask)
[docs] def distances_to_coordinate_from(
self, coordinate: Tuple[float, float] = (0.0, 0.0)
) -> Array2D:
"""
Returns the distance of every coordinate on the grid from an input (y,x) coordinate.
Parameters
----------
coordinate
The (y,x) coordinate from which the distance of every grid (y,x) coordinate is computed.
"""
distances = np.sqrt(
self.squared_distances_to_coordinate_from(coordinate=coordinate)
)
return Array2D(values=distances, mask=self.mask)
[docs] def grid_2d_radial_projected_shape_slim_from(
self, centre: Tuple[float, float] = (0.0, 0.0)
) -> int:
"""
The function `grid_scaled_2d_slim_radial_projected_from()` determines a projected radial grid of points from a
2D region of coordinates defined by an extent [xmin, xmax, ymin, ymax] and with a (y,x) centre.
To do this, the function first performs these 3 steps:
1) Given the region defined by the extent [xmin, xmax, ymin, ymax], the algorithm finds the longest 1D distance
of the 4 paths from the (y,x) centre to the edge of the region (e.g. following the positive / negative y and
x axes).
2) Use the pixel-scale corresponding to the direction chosen (e.g. if the positive x-axis was the longest, the
pixel_scale in the x dimension is used).
3) Determine the number of pixels between the centre and the edge of the region using the longest path between
the two chosen above.
A schematic is shown below:
.. code-block:: bash
-------------------
| |
|<- - - - ->x | x = centre
| | <-> = longest radial path from centre to extent edge
| |
-------------------
Using the centre x above, this function finds the longest radial path to the edge of the extent window.
This function returns the integer number of pixels given by this radial grid, which is then used to create
the radial grid.
Parameters
----------
extent
The extent of the grid the radii grid is computed using, with format [xmin, xmax, ymin, ymax]
centre : (float, flloat)
The (y,x) central coordinate which the radial grid is traced outwards from.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the 2D mask array.
sub_size
The size of the sub-grid that each pixel of the 2D mask array is divided into.
Returns
-------
int
The 1D integer shape of a radial set of points sampling the longest distance from the centre to the edge of the
extent in along the positive x-axis.
"""
return grid_2d_util._radial_projected_shape_slim_from(
extent=self.geometry.extent,
centre=centre,
pixel_scales=self.mask.pixel_scales,
sub_size=self.mask.sub_size,
)
[docs] def grid_2d_radial_projected_from(
self,
centre: Tuple[float, float] = (0.0, 0.0),
angle: float = 0.0,
shape_slim: Optional[int] = 0,
) -> Grid2DIrregular:
"""
Determine a projected radial grid of points from a 2D region of coordinates defined by an
extent [xmin, xmax, ymin, ymax] and with a (y,x) centre.
This functions operates as follows:
1) Given the region defined by the extent [xmin, xmax, ymin, ymax], the algorithm finds the longest 1D distance
of the 4 paths from the (y,x) centre to the edge of the region e.g. following the positive / negative y and
x axes.
2) Use the pixel-scale corresponding to the direction chosen e.g. if the positive x-axis was the longest, the
pixel_scale in the x dimension is used.
3) Determine the number of pixels between the centre and the edge of the region using the longest path between
the two chosen above.
4) Create a (y,x) grid of radial points where all points are at the centre's y value = 0.0 and the x values
iterate from the centre in increasing steps of the pixel-scale.
5) Rotate these radial coordinates by the input `angle` clockwise.
A schematic is shown below:
.. code-block:: bash
-------------------
| |
|<- - - - ->x | x = centre
| | <-> = longest radial path from centre to extent edge
| |
-------------------
Parameters
----------
centre
The (y,x) central coordinate which the radial grid is traced outwards from.
angle
The angle with which the radial coordinates are rotated clockwise.
Returns
-------
Grid2DIrregular
A radial set of points sampling the longest distance from the centre to the edge of the extent in along the
positive x-axis.
"""
grid_radial_projected_2d = (
grid_2d_util.grid_scaled_2d_slim_radial_projected_from(
extent=self.geometry.extent,
centre=centre,
pixel_scales=self.mask.pixel_scales,
sub_size=self.mask.sub_size,
shape_slim=shape_slim,
)
)
grid_radial_projected_2d = geometry_util.transform_grid_2d_to_reference_frame(
grid_2d=grid_radial_projected_2d, centre=centre, angle=angle
)
grid_radial_projected_2d = geometry_util.transform_grid_2d_from_reference_frame(
grid_2d=grid_radial_projected_2d, centre=centre, angle=0.0
)
if conf.instance["general"]["grid"]["remove_projected_centre"]:
grid_radial_projected_2d = grid_radial_projected_2d[1:, :]
return Grid2DIrregular(values=grid_radial_projected_2d)
@property
def shape_native_scaled_interior(self) -> Tuple[float, float]:
"""
The (y,x) interior 2D shape of the grid in scaled units, computed from the minimum and maximum y and x
values of the grid.
This differs from the `shape_native_scaled` because the edges of the shape are at the maxima and minima
of the grid's (y,x) values, whereas the `shape_native_scaled` uses the uniform geometry of the grid and its
``pixel_scales``, which means it has a buffer at each edge of half a ``pixel_scale``.
"""
return (
np.amax(self[:, 0]) - np.amin(self[:, 0]),
np.amax(self[:, 1]) - np.amin(self[:, 1]),
)
@property
def scaled_minima(self) -> Tuple:
"""
The (y,x) minimum values of the grid in scaled units, buffed such that their extent is further than the grid's
extent.
"""
return (
np.amin(self[:, 0]).astype("float"),
np.amin(self[:, 1]).astype("float"),
)
@property
def scaled_maxima(self) -> Tuple:
"""
The (y,x) maximum values of the grid in scaled units, buffed such that their extent is further than the grid's
extent.
"""
return (
np.amax(self[:, 0]).astype("float"),
np.amax(self[:, 1]).astype("float"),
)
[docs] def extent_with_buffer_from(self, buffer: float = 1.0e-8) -> List[float]:
"""
The extent of the grid in scaled units returned as a list [x_min, x_max, y_min, y_max], where all values are
buffed such that their extent is further than the grid's extent..
This follows the format of the extent input parameter in the matplotlib method imshow (and other methods) and
is used for visualization in the plot module.
"""
return [
self.scaled_minima[1] - buffer,
self.scaled_maxima[1] + buffer,
self.scaled_minima[0] - buffer,
self.scaled_maxima[0] + buffer,
]
@cached_property
def sub_border_grid(self) -> np.ndarray:
"""
The (y,x) grid of all sub-pixels which are at the border of the mask.
This is NOT all sub-pixels which are in mask pixels at the mask's border, but specifically the sub-pixels
within these border pixels which are at the extreme edge of the border.
"""
return self[self.mask.derive_indexes.sub_border_slim]
[docs] def padded_grid_from(self, kernel_shape_native: Tuple[int, int]) -> "Grid2D":
"""
When the edge pixels of a mask are unmasked and a convolution is to occur, the signal of edge pixels will
be 'missing' if the grid is used to evaluate the signal via an analytic function.
To ensure this signal is included the padded grid is used, which is 'buffed' such that it includes all pixels
whose signal will be convolved into the unmasked pixels given the 2D kernel shape.
Parameters
----------
kernel_shape_native
The 2D shape of the kernel which convolves signal from masked pixels to unmasked pixels.
"""
shape = self.mask.shape
padded_shape = (
shape[0] + kernel_shape_native[0] - 1,
shape[1] + kernel_shape_native[1] - 1,
)
padded_mask = Mask2D.all_false(
shape_native=padded_shape,
pixel_scales=self.mask.pixel_scales,
sub_size=self.mask.sub_size,
)
return Grid2D.from_mask(mask=padded_mask)
[docs] def relocated_grid_from(self, grid: "Grid2D") -> "Grid2D":
"""
Relocate the coordinates of a grid to the border of this grid if they are outside the border, where the
border is defined as all pixels at the edge of the grid's mask (see *mask._border_1d_indexes*).
This is performed as follows:
1: Use the mean value of the grid's y and x coordinates to determine the origin of the grid.
2: Compute the radial distance of every grid coordinate from the origin.
3: For every coordinate, find its nearest pixel in the border.
4: Determine if it is outside the border, by comparing its radial distance from the origin to its paired
border pixel's radial distance.
5: If its radial distance is larger, use the ratio of radial distances to move the coordinate to the
border (if its inside the border, do nothing).
The method can be used on uniform or irregular grids, however for irregular grids the border of the
'image-plane' mask is used to define border pixels.
Parameters
----------
grid : Grid2D
The grid (uniform or irregular) whose pixels are to be relocated to the border edge if outside it.
"""
if len(self.sub_border_grid) == 0:
return grid
return Grid2D(
values=grid_2d_util.relocated_grid_via_jit_from(
grid=np.array(grid),
border_grid=np.array(self.sub_border_grid),
),
mask=grid.mask,
sub_size=grid.mask.sub_size,
)
[docs] def relocated_mesh_grid_from(self, mesh_grid: Grid2DIrregular) -> Grid2DIrregular:
"""
Relocate the coordinates of a pixelization grid to the border of this grid. See the
method ``relocated_grid_from()`` for a full description of how this grid relocation works.
Parameters
----------
grid
The pixelization grid whose pixels are relocated to the border edge if outside it.
"""
if len(self.sub_border_grid) == 0:
return mesh_grid
return Grid2DIrregular(
values=grid_2d_util.relocated_grid_via_jit_from(
grid=np.array(mesh_grid),
border_grid=np.array(self.sub_border_grid),
),
)