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 – 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.

Methods

`all`	Returns True if all elements evaluate to True.
`any`	Returns True if any of the elements of a evaluate to True.
`argmax`	Return indices of the maximum values along the given axis.
`argmin`	Return indices of the minimum values along the given axis.
`argpartition`	Returns the indices that would partition this array.
`argsort`	Returns the indices that would sort this array.
`astype`	Copy of the array, cast to a specified type.
`byteswap`	Swap the bytes of the array elements
`choose`	Use an index array to construct a new array from a set of choices.
`clip`	Return an array whose values are limited to `[min, max]`.
`compress`	Return selected slices of this array along given axis.
`conj`	Complex-conjugate all elements.
`conjugate`	Return the complex conjugate, element-wise.
`copy`	Return a copy of the array.
`cumprod`	Return the cumulative product of the elements along the given axis.
`cumsum`	Return the cumulative sum of the elements along the given axis.
`diagonal`	Return specified diagonals.
`dot`
`dump`	Dump a pickle of the array to the specified file.
`dumps`	Returns the pickle of the array as a string.
`fill`	Fill the array with a scalar value.
`flatten`	Return a copy of the array collapsed into one dimension.
`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).
`getfield`	Returns a field of the given array as a certain type.
`grid_2d_radial_projected_from`	Project the 1D grid of (y,x) coordinates to an irregular 2d grid of (y,x) coordinates.
`item`	Copy an element of an array to a standard Python scalar and return it.
`itemset`	Insert scalar into an array (scalar is cast to array's dtype, if possible)
`max`	Return the maximum along a given axis.
`mean`	Returns the average of the array elements along given axis.
`min`	Return the minimum along a given axis.
`newbyteorder`	Return the array with the same data viewed with a different byte order.
`no_mask`	Create a Grid1D (see Grid1D.__new__) by inputting the grid coordinates in 1D.
`nonzero`	Return the indices of the elements that are non-zero.
`output_to_fits`	Output the grid to a .fits file.
`partition`	Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array.
`prod`	Return the product of the array elements over the given axis
`ptp`	Peak to peak (maximum - minimum) value along a given axis.
`put`	Set `a.flat[n] = values[n]` for all n in indices.
`ravel`	Return a flattened array.
`repeat`	Repeat elements of an array.
`reshape`	Returns an array containing the same data with a new shape.
`resize`	Change shape and size of array in-place.
`round`	Return a with each element rounded to the given number of decimals.
`searchsorted`	Find indices where elements of v should be inserted in a to maintain order.
`setfield`	Put a value into a specified place in a field defined by a data-type.
`setflags`	Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
`sort`	Sort an array in-place.
`squeeze`	Remove axes of length one from a.
`std`	Returns the standard deviation of the array elements along given axis.
`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`	Return the sum of the array elements over the given axis.
`swapaxes`	Return a view of the array with axis1 and axis2 interchanged.
`take`	Return an array formed from the elements of a at the given indices.
`tobytes`	Construct Python bytes containing the raw data bytes in the array.
`tofile`	Write array to a file as text or binary (default).
`tolist`	Return the array as an `a.ndim`-levels deep nested list of Python scalars.
`tostring`	A compatibility alias for tobytes, with exactly the same behavior.
`trace`	Return the sum along diagonals of the array.
`transpose`	Returns a view of the array with axes transposed.
`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.
`var`	Returns the variance of the array elements, along given axis.
`view`	New view of array with the same data.

Attributes

`T`	The transposed array.
`base`	Base object if memory is from some other object.
`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].
`ctypes`	An object to simplify the interaction of the array with the ctypes module.
`data`	Python buffer object pointing to the start of the array's data.
`derive_grid`	rtype `DeriveGrid2D`
`derive_indexes`	rtype `DeriveIndexes2D`
`derive_mask`	rtype `DeriveMask2D`
`dtype`	Data-type of the array's elements.
`flags`	Information about the memory layout of the array.
`flat`	A 1-D iterator over the array.
`geometry`
`hdu_for_output`
`imag`	The imaginary part of the array.
`itemsize`	Length of one array element in bytes.
`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].
`nbytes`	Total bytes consumed by the elements of the array.
`ndim`	Number of array dimensions.
`origin`	rtype `Tuple`[`int`, `...`]
`pixel_area`
`pixel_scale`	rtype `float`
`pixel_scale_header`	rtype `Dict`
`pixel_scales`	rtype `Tuple`[`float`, `...`]
`real`	The real part of the array.
`shape`	Tuple of array dimensions.
`shape_native`	rtype `Tuple`[`int`, `...`]
`shape_slim`	rtype `int`
`size`	Number of elements in the array.
`slim`	Return a Grid1D where the data is stored its slim representation, which is an ndarray of shape [total_unmasked_pixels * sub_size, 2].
`strides`	Tuple of bytes to step in each dimension when traversing an array.
`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.

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]]