autolens.Grid1D#

class Grid1D[source]#

Bases: Structure

A grid of 1D (x) coordinates, which are paired to a uniform 1D mask of pixels and sub-pixels. Each entry on the grid corresponds to the (x) coordinates at the centre of a sub-pixel of an unmasked pixel.

A Grid1D is ordered such that pixels begin from the left (e.g. index [0]) of the corresponding mask and go right. The positive x-axis is 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]

  • 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 Grid1D is an ndarray of shape [total_unmasked_coordinates].

The first element of the ndarray corresponds to the pixel index. For example:

  • grid[3] = the 4th unmasked pixel’s x-coordinate.

  • grid[6] = the 7th unmasked pixel’s x-coordinate.

Below is a visual illustration of a grid, where a total of 3 pixels are unmasked and are included in the grid.

<--- -ve  x  +ve -->

x x x O o x O x x x

This is an example mask.Mask1D, where:

x = `True` (Pixel is masked and excluded from the grid)
O = `False` (Pixel is not masked and included in the grid)

The mask pixel index’s will come out like this (and the direction of scaled coordinates is highlighted around the mask.

pixel_scales = 1.0"

<--- -ve  x  +ve -->

x x x 0 1 x 2 x x x

grid[0] = [-1.5]
grid[1] = [-0.5]
grid[2] = [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 (x) coordinates at the centre of each sub-pixel of an unmasked pixel. The Grid1D is therefore stored as an ndarray of shape [total_unmasked_coordinates*sub_size].

The sub-grid indexes are ordered such that pixels begin from the first (leftmost) 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]. For example:

  • grid[5] - using sub_size=2, gives the 3rd unmasked pixel’s 2nd sub-pixel x-coordinate.

  • grid[3] - using sub_size=3, gives the 2nd unmasked pixel’s 1st sub-pixel x-coordinate.

  • grid[10] - using sub_size=3, 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.

x x x O x O x x x

This is an example mask.Mask1D, where:

x = `True` (Pixel is masked and excluded from the grid)
O = `False` (Pixel is not masked and included in the grid)

Our grid with a sub-size=1 looks like it did before:

pixel_scales = 1.0"

<--- -ve  x  +ve -->

 x x x 0 x 1 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:

grid[0] = [-0.75]
grid[1] = [-0.25]

If we used a sub_size of 3, for the pixel we we would create a 3x3 sub-grid:

grid[0] = [-0.833]
grid[1] = [-0.5]
grid[2] = [-0.166]

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_x_coordinates].

All masked entries on the grid has (y,x) values of (0.0, 0.0).

For the following example mask:

x x x O O x O x x x

- grid[0] = 0.0 (it is masked, thus zero)
- grid[1] = 0.0 (it is masked, thus zero)
- grid[2] = 0.0 (it is masked, thus zero)
- grid[3] = -1.5
- grid[4] = -0.5
- grid[5] = 0.0 (it is masked, thus zero)
- grid[6] = 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_x_coordinates*sub_size,].

All sub-pixels in masked pixels have value 0.0.

Grid1D Mapping

Every set of (x) coordinates in a pixel of the sub-grid maps to an unmasked pixel in the mask. For a uniform grid, every 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 x coordinates where the indexing signifies that the 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 (Union[ndarray, List]) – The (y,x) coordinates of the grid.

  • mask (Mask1D) – The 2D mask associated with the grid, defining the pixels each grid coordinate is paired with and originates from.

Methods

all

astype

rtype:

AbstractNDArray

copy

flip_hdu_for_ds9

from_mask

Create a Grid1D (see Grid1D.__new__) from a mask, where only unmasked pixels are included in the grid (if the grid is represented in its native 1D masked values are 0.0).

grid_2d_radial_projected_from

Project the 1D grid of (y,x) coordinates to an irregular 2d grid of (y,x) coordinates.

instance_flatten

Flatten an instance of an autoarray class into a tuple of its attributes (i.e.

instance_unflatten

Unflatten a tuple of attributes (i.e.

invert

max

min

no_mask

Create a Grid1D (see Grid1D.__new__) by inputting the grid coordinates in 1D.

output_to_fits

Output the grid to a .fits file.

reshape

rtype:

AbstractNDArray

sqrt

rtype:

AbstractNDArray

structure_2d_from

Convert a result from an ndarray to an aa.Array2D or aa.Grid2D structure, where the conversion depends on type(result) as follows:

structure_2d_list_from

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:

sum

trimmed_after_convolution_from

rtype:

Structure

uniform

Create a Grid1D (see Grid`D.__new__) as a uniform grid of (x) values given an input shape_native and pixel_scales of the grid.

uniform_from_zero

Create a Grid1D (see Grid`D.__new__) as a uniform grid of (x) values given an input shape_native and pixel_scales of the grid, where the first (x) coordinate of the grid is 0.0 and all other values ascend positively.

with_new_array

Copy this object but give it a new array.

Attributes

array

binned

Convenience method to access the binned-up grid in its 1D representation, which is a Grid2D stored as an ndarray of shape [total_unmasked_pixels, 2].

derive_grid

rtype:

DeriveGrid2D

derive_indexes

rtype:

DeriveIndexes2D

derive_mask

rtype:

DeriveMask2D

dtype

geometry

hdu_for_output

imag

rtype:

AbstractNDArray

native

Return a Grid1D where the data is stored in its native representation, which is an ndarray of shape [sub_size*total_x_pixels, 2].

ndim

origin

rtype:

Tuple[int, ...]

pixel_area

pixel_scale

rtype:

float

pixel_scale_header

rtype:

Dict

pixel_scales

rtype:

Tuple[float, ...]

real

rtype:

AbstractNDArray

shape

shape_native

rtype:

Tuple[int, ...]

shape_slim

rtype:

int

size

slim

Return a Grid1D where the data is stored its slim representation, which is an ndarray of shape [total_unmasked_pixels * sub_size, 2].

sub_shape_native

rtype:

Tuple[int, ...]

sub_shape_slim

rtype:

int

sub_size

rtype:

int

total_area

total_pixels

rtype:

int

unmasked_grid

rtype:

Union[Grid1D, Grid2D]

classmethod no_mask(values, pixel_scales, sub_size=1, origin=(0.0,))[source]#

Create a Grid1D (see Grid1D.__new__) by inputting the grid coordinates in 1D.

Parameters:
  • values (Union[ndarray, List]) – 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.

  • pixel_scales (Union[Tuple[float], Tuple[float, float], float]) – 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 (int) – The size (sub_size x sub_size) of each unmasked pixels sub-grid.

  • origin (Tuple[float]) – The origin of the grid’s mask.

Examples

import autogrid as aa

# Make Grid1D from input np.ndgrid.

grid_1d = aa.Grid1D.no_mask(grid=np.grid([1.0, 2.0, 3.0, 4.0]), pixel_scales=1.0)

# Make Grid2D from input list.

grid_1d = aa.Grid1D.no_mask(grid=[1.0, 2.0, 3.0, 4.0], pixel_scales=1.0)

# Print grid's slim (masked 1D data representation) and
# native (masked 1D data representation)

print(grid_1d.slim)
print(grid_1d.native)
Return type:

Grid1D

classmethod from_mask(mask)[source]#

Create a Grid1D (see Grid1D.__new__) from a mask, where only unmasked pixels are included in the grid (if the grid is represented in its native 1D masked values are 0.0).

The mask’s pixel_scales, sub_size and origin properties are used to compute the grid (x) coordinates.

Parameters:

mask (Mask1D) – The mask whose masked pixels are used to setup the sub-pixel grid.

Return type:

Grid1D

classmethod uniform(shape_native, pixel_scales, sub_size=1, origin=(0.0, 0.0))[source]#

Create a Grid1D (see Grid`D.__new__) as a uniform grid of (x) values given an input shape_native and pixel_scales of the grid.

Parameters:
  • shape_native (Tuple[int]) – The 1D shape of the uniform grid and the mask that it is paired with.

  • pixel_scales (Union[Tuple[float], Tuple[float, float], float]) – The (x) scaled units to pixel units conversion factor of every pixel. If this is input as a float, it is converted to a (float,) tuple.

  • sub_size (int) – The size (sub_size) of each unmasked pixels sub-grid.

  • origin (Tuple[float]) – The origin of the grid’s mask and coordinate system.

Return type:

Grid1D

classmethod uniform_from_zero(shape_native, pixel_scales, sub_size=1)[source]#

Create a Grid1D (see Grid`D.__new__) as a uniform grid of (x) values given an input shape_native and pixel_scales of the grid, where the first (x) coordinate of the grid is 0.0 and all other values ascend positively.

Parameters:
  • shape_native (Tuple[int]) – The 1D shape of the uniform grid and the mask that it is paired with.

  • pixel_scales (Union[Tuple[float], Tuple[float, float], float]) – The (x) scaled units to pixel units conversion factor of every pixel. If this is input as a float, it is converted to a (float,) tuple. it is converted to a (float,) tuple.

  • sub_size (int) – The size (sub_size) of each unmasked pixels sub-grid.

Return type:

Grid1D

property slim: Grid1D#

Return a Grid1D where the data is stored its slim representation, which is an ndarray of shape [total_unmasked_pixels * sub_size, 2].

If it is already stored in its slim representation the Grid1D is returned as it is. If not, it is mapped from native to slim and returned as a new Grid1D.

Return type:

Grid1D

property native: Grid1D#

Return a Grid1D where the data is stored in its native representation, which is an ndarray of shape [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 Grid1D.

Return type:

Grid1D

property binned: Grid1D#

Convenience method to access the binned-up grid in its 1D representation, which is a Grid2D stored as an ndarray of 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.

Return type:

Grid1D

grid_2d_radial_projected_from(angle=0.0)[source]#

Project the 1D grid of (y,x) coordinates to an irregular 2d grid of (y,x) coordinates. The projection works as follows:

1) Map the 1D (x) coordinates to 2D along the x-axis, such that the x value of every 2D coordinate is the corresponding (x) value in the 1D grid, and every y value is 0.0.

  1. Rotate this projected 2D grid clockwise by the input angle.

Parameters:

angle (float) – The angle with which the project 2D grid of coordinates is rotated clockwise.

Returns:

The projected and rotated 2D grid of (y,x) coordinates.

Return type:

Grid2DIrregular

structure_2d_from(result)[source]#

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 (ndarray) – The input result (e.g. of a decorated function) that is converted to a PyAutoArray structure.

Return type:

Union[Array1D, Grid2D, Grid2DTransformed, Grid2DTransformedNumpy]

structure_2d_list_from(result_list)[source]#

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 (List) – The input result (e.g. of a decorated function) that is converted to a PyAutoArray structure.

Return type:

List[Union[Array1D, Grid2D, Grid2DTransformed, Grid2DTransformedNumpy]]