Geometry

This module is used as for calculating geometric shapes on coordinate arrays, used to generate apertures. Each shape has two functions. One that generates a hard-edged oversampled one for more accurate aperture shapes, but is not differentiable/jittable. These are the circle, square, etc functions. The other type are differentiable and jittable in order to gain dynamic aperture that can be fit to data. These instead calculate the distance of each pixel from an edge and 'clip' the values between 0-1 for distances above a specified threshold. These functions are denoted with a soft_ prefix, ie soft_circle, soft_square, etc.

There are also some other helper functions for scaling and downsampling.

TODO: Little tutorial on generating apertures.

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circle

Calculates a soft-edged circle via downsampling. This function is not differentiable.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the circle on.	required
radius	float	The radius of the circle.	required
invert	bool = False	Whether to invert the circle.	False

Returns:

Name	Type	Description
circle	Array	The circle.

Source code in src/dLux/utils/geometry.py

def circle(coords: Array, radius: float, invert: bool = False) -> Array:
    """
    Calculates a soft-edged circle via downsampling. This function is not
    differentiable.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the circle on.
    radius : float
        The radius of the circle.
    invert : bool = False
        Whether to invert the circle.

    Returns
    -------
    circle : Array
        The circle.
    """
    if invert:
        return (circ_distance(coords, radius) > 0).astype(float)
    return (circ_distance(coords, radius) < 0).astype(float)

square

Calculates a soft-edged square via downsampling. This function is not differentiable.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the square on.	required
width	float	The width of the square.	required
invert	bool = False	Whether to invert the square.	False

Returns:

Name	Type	Description
square	Array	The square.

Source code in src/dLux/utils/geometry.py

def square(coords: Array, width: float, invert: bool = False) -> Array:
    """
    Calculates a soft-edged square via downsampling. This function is not
    differentiable.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the square on.
    width : float
        The width of the square.
    invert : bool = False
        Whether to invert the square.

    Returns
    -------
    square : Array
        The square.
    """
    if invert:
        return (square_distance(coords, width) > 0).astype(float)
    return (square_distance(coords, width) < 0).astype(float)

rectangle

Calculates a soft-edged rectangle via downsampling. This function is not differentiable.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the rectangle on.	required
width	float	The width of the rectangle.	required
height	float	The height of the rectangle.	required

Returns:

Name	Type	Description
rectangle	Array	The rectangle.

Source code in src/dLux/utils/geometry.py

def rectangle(
    coords: Array, width: float, height: float, invert: bool = False
) -> Array:
    """
    Calculates a soft-edged rectangle via downsampling. This function is not
    differentiable.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the rectangle on.
    width : float
        The width of the rectangle.
    height : float
        The height of the rectangle.

    Returns
    -------
    rectangle : Array
        The rectangle.
    """
    if invert:
        return (rectangle_distance(coords, width, height) > 0).astype(float)
    return (rectangle_distance(coords, width, height) < 0).astype(float)

reg_polygon

Calculates a soft-edged regular polygon via downsampling. This function is not differentiable.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the polygon on.	required
rmax	float	The radius of the polygon.	required
nsides	int	The number of sides of the polygon.	required
invert	bool = False	Whether to invert the polygon.	False

Returns:

Name	Type	Description
polygon	Array	The polygon.

Source code in src/dLux/utils/geometry.py

def reg_polygon(
    coords: Array, rmax: float, nsides: int, invert: bool = False
) -> Array:
    """
    Calculates a soft-edged regular polygon via downsampling. This function is not
    differentiable.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the polygon on.
    rmax : float
        The radius of the polygon.
    nsides : int
        The number of sides of the polygon.
    invert : bool = False
        Whether to invert the polygon.

    Returns
    -------
    polygon : Array
        The polygon.
    """
    if invert:
        return (reg_polygon_distance(coords, nsides, rmax) > 0).astype(float)
    return (reg_polygon_distance(coords, nsides, rmax) < 0).astype(float)

spider

Calculates a soft-edged spider via downsampling. This function is not differentiable.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the spider on.	required
width	float	The width of the spider.	required
angles	Array	The angles of the spider.	required

Returns:

Name	Type	Description
spider	Array	The spider.

Source code in src/dLux/utils/geometry.py

def spider(coords: Array, width: float, angles: Array) -> Array:
    """
    Calculates a soft-edged spider via downsampling. This function is not
    differentiable.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the spider on.
    width : float
        The width of the spider.
    angles : Array
        The angles of the spider.

    Returns
    -------
    spider : Array
        The spider.
    """
    angles = np.array(angles) if not isinstance(angles, np.ndarray) else angles
    calc_fn = vmap(lambda angle: spider_distance(coords, width, angle) < 0)
    return (
        ~lax.reduce(calc_fn(angles), np.array(False), lax.bitwise_or, (0,))
    ).astype(float)

combine

Combines multiple arrays by multiplying them together, and downsampling the output.

Parameters:

Name	Type	Description	Default
arrays	Array	The arrays to be combined. Should have shape (n_arrays, npix, npix).	required
oversample	int = 1	The amount to downsample the output by.	1
sum	bool = False	Whether to sum the arrays instead of multiplying them.	False

Source code in src/dLux/utils/geometry.py

def combine(arrays: Array, oversample: int = 1, sum: bool = False) -> Array:
    """
    Combines multiple arrays by multiplying them together, and downsampling the output.

    Parameters
    ----------
    arrays : Array
        The arrays to be combined. Should have shape (n_arrays, npix, npix).
    oversample : int = 1
        The amount to downsample the output by.
    sum : bool = False
        Whether to sum the arrays instead of multiplying them.
    """
    method = np.sum if sum else np.prod
    array = np.array(arrays)
    if oversample == 1:
        return method(array, 0)
    return dlu.downsample(method(array, 0), oversample)

soft_circle

Calculates a soft-edged circle differentiably. The 'clip_dist' parameter defines the distance from the edge to 'soften' up to. A large clip_dist will result in a circle with a very soft edge, while a small clip_dist will result in a circle with a very hard edge.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the circle on.	required
radius	float	The radius of the circle.	required
clip_dist	float = 0.1	The distance from the edge to 'soften' up to. circle.	0.1
invert	bool = False	Whether to invert the circle.	False

Returns:

Name	Type	Description
circle	Array	The softened circle.

Source code in src/dLux/utils/geometry.py

def soft_circle(
    coords: Array, radius: float, clip_dist: float = 0.1, invert: bool = False
) -> Array:
    """
    Calculates a soft-edged circle differentiably. The 'clip_dist' parameter defines
    the distance from the edge to 'soften' up to. A large clip_dist will result in a
    circle with a very soft edge, while a small clip_dist will result in a circle with
    a very hard edge.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the circle on.
    radius : float
        The radius of the circle.
    clip_dist : float = 0.1
        The distance from the edge to 'soften' up to.
        circle.
    invert : bool = False
        Whether to invert the circle.

    Returns
    -------
    circle : Array
        The softened circle.
    """
    distances = -circ_distance(coords, radius)
    return soften(distances, clip_dist, invert)

soft_square

Calculates a soft-edged square differentiably. The 'clip_dist' parameter defines the distance from the edge to 'soften' up to. A large clip_dist will result in a square with a very soft edge, while a small clip_dist will result in a square with a very hard edge.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the square on.	required
width	float	The width of the square.	required
clip_dist	float = 0.1	The distance from the edge to 'soften' up to. square.	0.1
invert	bool = False	Whether to invert the square.	False

Returns:

Name	Type	Description
square	Array	The softened square.

Source code in src/dLux/utils/geometry.py

def soft_square(
    coords: Array, width: float, clip_dist: float = 0.1, invert: bool = False
) -> Array:
    """
    Calculates a soft-edged square differentiably. The 'clip_dist' parameter defines
    the distance from the edge to 'soften' up to. A large clip_dist will result in a
    square with a very soft edge, while a small clip_dist will result in a square with
    a very hard edge.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the square on.
    width : float
        The width of the square.
    clip_dist : float = 0.1
        The distance from the edge to 'soften' up to.
        square.
    invert : bool = False
        Whether to invert the square.

    Returns
    -------
    square : Array
        The softened square.
    """
    distances = -square_distance(coords, width)
    return soften(distances, clip_dist, invert)

soft_rectangle

Calculates a soft-edged rectangle differentiably. The 'clip_dist' parameter defines the distance from the edge to 'soften' up to. A large clip_dist will result in a rectangle with a very soft edge, while a small clip_dist will result in a rectangle with a very hard edge.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the rectangle on.	required
width	float	The width of the rectangle.	required
height	float	The height of the rectangle.	required
clip_dist	float = 0.1	The distance from the edge to 'soften' up to.	0.1

Returns:

Name	Type	Description
rectangle	Array	The softened rectangle.

Source code in src/dLux/utils/geometry.py

def soft_rectangle(
    coords: Array,
    width: float,
    height: float,
    clip_dist: float = 0.1,
    invert: bool = False,
) -> Array:
    """
    Calculates a soft-edged rectangle differentiably. The 'clip_dist' parameter defines
    the distance from the edge to 'soften' up to. A large clip_dist will result in a
    rectangle with a very soft edge, while a small clip_dist will result in a rectangle
    with a very hard edge.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the rectangle on.
    width : float
        The width of the rectangle.
    height : float
        The height of the rectangle.
    clip_dist : float = 0.1
        The distance from the edge to 'soften' up to.

    Returns
    -------
    rectangle : Array
        The softened rectangle.
    """
    distances = -rectangle_distance(coords, width, height)
    return soften(distances, clip_dist, invert)

soft_reg_polygon

Calculates a soft-edged regular polygon differentiably. The 'clip_dist' parameter defines the distance from the edge to 'soften' up to. A large clip_dist will result in a polygon with a very soft edge, while a small clip_dist will result in a polygon with a very hard edge.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the polygon on.	required
radius	float	The radius of the polygon.	required
nsides	int	The number of sides of the polygon.	required
clip_dist	float = 0.1	The distance from the edge to 'soften' up to.	0.1
invert	bool = False	Whether to invert the polygon.	False

Returns:

Name	Type	Description
polygon	Array	The softened polygon.

Source code in src/dLux/utils/geometry.py

def soft_reg_polygon(
    coords: Array,
    radius: float,
    nsides: int,
    clip_dist: float = 0.1,
    invert: bool = False,
) -> Array:
    """
    Calculates a soft-edged regular polygon differentiably. The 'clip_dist' parameter
    defines the distance from the edge to 'soften' up to. A large clip_dist will result
    in a polygon with a very soft edge, while a small clip_dist will result in a polygon
    with a very hard edge.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the polygon on.
    radius : float
        The radius of the polygon.
    nsides : int
        The number of sides of the polygon.
    clip_dist : float = 0.1
        The distance from the edge to 'soften' up to.
    invert : bool = False
        Whether to invert the polygon.

    Returns
    -------
    polygon : Array
        The softened polygon.
    """
    distances = -reg_polygon_distance(coords, nsides, radius)
    return soften(distances, clip_dist, invert)

soft_spider

Calculates a soft-edged spider differentiably. The 'clip_dist' parameter defines the distance from the edge to 'soften' up to. A large clip_dist will result in a spider with a very soft edge, while a small clip_dist will result in a spider with a very hard edge.

Parameters:

Name	Type	Description	Default
coords	Array	The coordinates to calculate the spider on.	required
width	float	The width of the spider.	required
angles	Array	The angles of the spider.	required
clip_dist	float = 0.1	The distance from the edge to 'soften' up to.	0.1
invert	bool = False	Whether to invert the spider.	False

Returns:

Name	Type	Description
spider	Array	The softened spider.

Source code in src/dLux/utils/geometry.py

def soft_spider(
    coords: Array,
    width: float,
    angles: Array,
    clip_dist: float = 0.1,
    invert: bool = False,
) -> Array:
    """
    Calculates a soft-edged spider differentiably. The 'clip_dist' parameter defines
    the distance from the edge to 'soften' up to. A large clip_dist will result in a
    spider with a very soft edge, while a small clip_dist will result in a spider with
    a very hard edge.

    Parameters
    ----------
    coords : Array
        The coordinates to calculate the spider on.
    width : float
        The width of the spider.
    angles : Array
        The angles of the spider.
    clip_dist : float = 0.1
        The distance from the edge to 'soften' up to.
    invert : bool = False
        Whether to invert the spider.

    Returns
    -------
    spider : Array
        The softened spider.
    """
    angles = np.array(angles) if not isinstance(angles, np.ndarray) else angles
    spider_fn = vmap(lambda angle: spider_distance(coords, width, angle))
    spiders = -spider_fn(angles).min(axis=0)
    return soften(spiders, clip_dist, invert)