transform-1.5.0
Transform extension 1.5.0
Description
A set of tags for serializing data transforms.
Outline
Schema Definitions ¶
This node has no type definition (unrestricted)
Original Schema ¶
id: asdf://asdf-format.org/transform/manifests/transform-1.5.0
extension_uri: asdf://asdf-format.org/transform/extensions/transform-1.5.0
title: Transform extension 1.5.0
description: |-
A set of tags for serializing data transforms.
tags:
- tag_uri: tag:stsci.edu:asdf/transform/add-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/add-1.2.0
title: Perform a list of subtransforms in parallel and then add their results together.
description: |-
Each of the subtransforms must have the same number of inputs and
outputs.
- tag_uri: tag:stsci.edu:asdf/transform/affine-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/affine-1.3.0
title: An affine transform.
description: |-
Invertibility: All ASDF tools are required to be able to compute the
analytic inverse of this transform.
- tag_uri: tag:stsci.edu:asdf/transform/airy-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/airy-1.2.0
title: The Airy projection.
description: |-
Corresponds to the `AIR` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
- tag_uri: tag:stsci.edu:asdf/transform/airy_disk2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/airy_disk2d-1.0.0
title: Two dimensional Airy disk model.
description: |-
Two dimensional Airy disk model.
- tag_uri: tag:stsci.edu:asdf/transform/blackbody-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/blackbody-1.0.0
title: Blackbody model.
description: |-
Blackbody model using the Planck function.
$$B_{\\nu}(T) = A \frac{2 h \nu^{3} / c^{2}}{exp(h \nu / k T) - 1}$$
- tag_uri: tag:stsci.edu:asdf/transform/bonne_equal_area-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/bonne_equal_area-1.3.0
title: Bonne's equal area pseudoconic projection.
description: |-
Corresponds to the `BON` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= \frac{\pi}{180^\circ} A_\phi R_\theta / \cos \theta \\
\theta &= Y_0 - R_\theta$$
where:
$$R_\theta &= \mathrm{sign} \theta_1 \sqrt{x^2 + (Y_0 - y)^2} \\
A_\phi &= \arg\left(\frac{Y_0 - y}{R_\theta}, \frac{x}{R_\theta}\right)$$
And the sky-to-pixel transformation is defined as:
$$x &= R_\theta \sin A_\phi \\
y &= -R_\theta \cos A_\phi + Y_0$$
where:
$$A_\phi &= \frac{180^\circ}{\pi R_\theta} \phi \cos \theta \\
R_\theta &= Y_0 - \theta \\
Y_0 &= \frac{180^\circ}{\pi} \cot \theta_1 + \theta_1$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/box1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/box1d-1.0.0
title: One dimensional box model.
description: |-
One dimensional box.
- tag_uri: tag:stsci.edu:asdf/transform/box2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/box2d-1.0.0
title: Two dimensional box model.
description: |-
Two dimensional box.
- tag_uri: tag:stsci.edu:asdf/transform/broken_power_law1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/broken_power_law1d-1.0.0
title: One dimensional power law model with a break.
description: |-
One dimensional power law model with a break.
- tag_uri: tag:stsci.edu:asdf/transform/cobe_quad_spherical_cube-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/cobe_quad_spherical_cube-1.2.0
title: COBE quadrilateralized spherical cube projection.
description: |-
Corresponds to the `CSC` projection in the FITS WCS standard.
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/compose-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/compose-1.2.0
title: Perform a list of subtransforms in series.
description: |-
The output of each subtransform is fed into the input of the next
subtransform.
The number of output dimensions of each subtransform must be equal
to the number of input dimensions of the next subtransform in list.
To reorder or add/drop axes, insert `remap_axes` transforms in the
subtransform list.
Invertibility: All ASDF tools are required to be able to compute the
analytic inverse of this transform, by reversing the list of
transforms and applying the inverse of each.
- tag_uri: tag:stsci.edu:asdf/transform/concatenate-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/concatenate-1.2.0
title: Send axes to different subtransforms.
description: |-
Transforms a set of separable inputs by splitting the axes apart,
sending them through the given subtransforms in parallel, and
finally concatenating the subtransform output axes back together.
The input axes are assigned to each subtransform in order. If the
number of input axes is unequal to the sum of the number of input
axes of all of the subtransforms, that is considered an error case.
The output axes from each subtransform are appended together to make
up the resulting output axes.
For example, given 5 input axes, and 3 subtransforms with the
following orders:
1. transform A: 2 in -> 2 out
1. transform B: 1 in -> 2 out
1. transform C: 2 in -> 1 out
The transform is performed as follows:
```
: i0 i1 i2 i3 i4
: | | | | |
: +---------+ +---------+ +----------+
: | A | | B | | C |
: +---------+ +---------+ +----------+
: | | | | |
: o0 o1 o2 o3 o4
```
If reordering of the input or output axes is required, use in series
with the `remap_axes` transform.
Invertibility: All ASDF tools are required to be able to compute the
analytic inverse of this transform.
- tag_uri: tag:stsci.edu:asdf/transform/conic_equal_area-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/conic_equal_area-1.3.0
title: Alber's conic equal area projection.
description: |-
Corresponds to the `COE` projection in the FITS WCS standard.
See
[conic](ref:transform/conic-1.3.0)
for the definition of the full transformation.
The transformation is defined as:
$$C &= \gamma / 2 \\
R_\theta &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin \theta} \\
Y_0 &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin((\theta_1 + \theta_2)/2)}$$
where:
$$\gamma = \sin \theta_1 + \sin \theta_2$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/conic_equidistant-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/conic_equidistant-1.3.0
title: Conic equidistant projection.
description: |-
Corresponds to the `COD` projection in the FITS WCS standard.
See
[conic](ref:transform/conic-1.3.0)
for the definition of the full transformation.
The transformation is defined as:
$$C &= \frac{180^\circ}{\pi} \frac{\sin\theta_a\sin\eta}{\eta} \\
R_\theta &= \theta_a - \theta + \eta\cot\eta\cot\theta_a \\
Y_0 = \eta\cot\eta\cot\theta_a$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/conic_orthomorphic-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/conic_orthomorphic-1.3.0
title: Conic orthomorphic projection.
description: |-
Corresponds to the `COO` projection in the FITS WCS standard.
See
[conic](ref:transform/conic-1.3.0)
for the definition of the full transformation.
The transformation is defined as:
$$C &= \frac{\ln \left( \frac{\cos\theta_2}{\cos\theta_1} \right)}
{\ln \left[ \frac{\tan\left(\frac{90^\circ-\theta_2}{2}\right)}
{\tan\left(\frac{90^\circ-\theta_1}{2}\right)} \right] } \\
R_\theta &= \psi \left[ \tan \left( \frac{90^\circ - \theta}{2} \right) \right]^C \\
Y_0 &= \psi \left[ \tan \left( \frac{90^\circ - \theta_a}{2} \right) \right]^C$$
where:
$$\psi = \frac{180^\circ}{\pi} \frac{\cos \theta}
{C\left[\tan\left(\frac{90^\circ-\theta}{2}\right)\right]^C}$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/conic_perspective-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/conic_perspective-1.3.0
title: Colles' conic perspecitve projection.
description: |-
Corresponds to the `COP` projection in the FITS WCS standard.
See
[conic](ref:transform/conic-1.3.0)
for the definition of the full transformation.
The transformation is defined as:
$$C &= \sin \theta_a \\
R_\theta &= \frac{180^\circ}{\pi} \cos \eta [ \cot \theta_a - \tan(\theta - \theta_a)] \\
Y_0 &= \frac{180^\circ}{\pi} \cos \eta \cot \theta_a$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/constant-1.4.0
schema_uri: http://stsci.edu/schemas/asdf/transform/constant-1.4.0
title: A Constant transform.
description: |-
Invertibility: A transform which takes one or two inputs based on
dimensionality and returns a constant value. It has no analytical inverse.
- tag_uri: tag:stsci.edu:asdf/transform/cylindrical_equal_area-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/cylindrical_equal_area-1.3.0
title: The cylindrical equal area projection.
description: |-
Corresponds to the `CEA` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= x \\
\theta &= \sin^{-1}\left(\frac{\pi}{180^{\circ}}\lambda y\right)$$
And the sky-to-pixel transformation is defined as:
$$x &= \phi \\
y &= \frac{180^{\circ}}{\pi}\frac{\sin \theta}{\lambda}$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/cylindrical_perspective-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/cylindrical_perspective-1.3.0
title: The cylindrical perspective projection.
description: |-
Corresponds to the `CYP` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= \frac{x}{\lambda} \\
\theta &= \arg(1, \eta) + \sin{-1}\left(\frac{\eta \mu}{\sqrt{\eta^2 + 1}}\right)$$
And the sky-to-pixel transformation is defined as:
$$x &= \lambda \phi \\
y &= \frac{180^{\circ}}{\pi}\left(\frac{\mu + \lambda}{\mu + \cos \theta}\right)\sin \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/disk2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/disk2d-1.0.0
title: Two dimensional disk model.
description: |-
Two dimensional radially symmetric disk.
- tag_uri: tag:stsci.edu:asdf/transform/divide-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/divide-1.2.0
title: Perform a list of subtransforms in parallel and then divide their results.
description: |-
Each of the subtransforms must have the same number of inputs and
outputs.
Invertibility: This transform is not automatically invertible.
- tag_uri: tag:stsci.edu:asdf/transform/drude1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/drude1d-1.0.0
title: One dimensional Drude model
description: |-
Drude model based one the behavior of electons in materials (esp. metals).
- tag_uri: tag:stsci.edu:asdf/transform/ellipse2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/ellipse2d-1.0.0
title: Two dimensional ellipse model.
description: |-
Two dimensional ellipse.
- tag_uri: tag:stsci.edu:asdf/transform/exponential1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/exponential1d-1.0.0
title: One dimensional exponential model.
description: |-
One dimensional exponential model.
- tag_uri: tag:stsci.edu:asdf/transform/exponential_cutoff_power_law1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/exponential_cutoff_power_law1d-1.0.0
title: One dimensional power law model with an exponential cutoff.
description: |-
One dimensional power law model with an exponential cutoff.
- tag_uri: tag:stsci.edu:asdf/transform/fix_inputs-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/fix_inputs-1.2.0
title: Set to a constant selected input arguments of a model.
description: |-
This operation takes as the right hand side a dict equivalent
that consists of key:value pairs where the key identifies
the input argument to be set, either by position number
(0 based) or name, and the value is the floating point value
that should be assigned to that input. The result is a
compound model with n fewer input arguments where n is
the number of input values to be set (i.e., the number
of keys in the dict).
- tag_uri: tag:stsci.edu:asdf/transform/gaussian1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/gaussian1d-1.0.0
title: A 1D Gaussian model.
description: |-
A 1D gaussian distribution.
- tag_uri: tag:stsci.edu:asdf/transform/gaussian2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/gaussian2d-1.0.0
title: A 2D Gaussian model.
description: |-
A 2D gaussian distribution.
- tag_uri: tag:stsci.edu:asdf/transform/gnomonic-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/gnomonic-1.2.0
title: The gnomonic projection.
description: |-
Corresponds to the `TAN` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
The pixel-to-sky transformation is defined as:
$$\theta = \tan^{-1}\left(\frac{180^{\circ}}{\pi R_\theta}\right)$$
And the sky-to-pixel transformation is defined as:
$$R_\theta = \frac{180^{\circ}}{\pi}\cot \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/hammer_aitoff-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/hammer_aitoff-1.2.0
title: Hammer-Aitoff projection.
description: |-
Corresponds to the `AIT` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= 2 \arg \left(2Z^2 - 1, \frac{\pi}{180^\circ} \frac{Z}{2}x\right) \\
\theta &= \sin^{-1}\left(\frac{\pi}{180^\circ}yZ\right)$$
And the sky-to-pixel transformation is defined as:
$$x &= 2 \gamma \cos \theta \sin \frac{\phi}{2} \\
y &= \gamma \sin \theta$$
where:
$$\gamma = \frac{180^\circ}{\pi} \sqrt{\frac{2}{1 + \cos \theta \cos(\phi / 2)}}$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/healpix-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/healpix-1.2.0
title: HEALPix projection.
description: |-
Corresponds to the `HPX` projection in the FITS WCS standard.
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/healpix_polar-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/healpix_polar-1.2.0
title: HEALPix polar, aka "butterfly", projection.
description: |-
Corresponds to the `XPH` projection in the FITS WCS standard.
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/identity-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/identity-1.2.0
title: The identity transform.
description: |-
Invertibility: The inverse of this transform is also the identity transform.
- tag_uri: tag:stsci.edu:asdf/transform/king_projected_analytic1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/king_projected_analytic1d-1.0.0
title: Projected (surface density) analytic King Model.
description: |-
Projected (surface density) analytic King Model.
- tag_uri: tag:stsci.edu:asdf/transform/linear1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/linear1d-1.0.0
title: A one dimensional line model
description: |-
A one dimensional line model
- tag_uri: tag:stsci.edu:asdf/transform/log_parabola1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/log_parabola1d-1.0.0
title: One dimensional log parabola model (sometimes called curved power law).
description: |-
One dimensional log parabola model (sometimes called curved power law).
- tag_uri: tag:stsci.edu:asdf/transform/logarithmic1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/logarithmic1d-1.0.0
title: One dimensional (natural) logarithmic model.
description: |-
One dimensional (natural) logarithmic model.
- tag_uri: tag:stsci.edu:asdf/transform/lorentz1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/lorentz1d-1.0.0
title: One dimensional Lorentzian model.
description: |-
One dimensional Lorentzian model.
- tag_uri: tag:stsci.edu:asdf/transform/math_functions-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/math_functions-1.0.0
title: Math functions.
description: |-
Commonly used math funcitons.
- tag_uri: tag:stsci.edu:asdf/transform/mercator-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/mercator-1.2.0
title: The Mercator projection.
description: |-
Corresponds to the `MER` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= x \\
\theta &= 2 \tan^{-1}\left(e^{y \pi / 180^{\circ}}\right)-90^{\circ}$$
And the sky-to-pixel transformation is defined as:
$$x &= \phi \\
y &= \frac{180^{\circ}}{\pi}\ln \tan \left(\frac{90^{\circ} + \theta}{2}\right)$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/moffat1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/moffat1d-1.0.0
title: One dimensional Moffat model.
description: |-
One dimensional Moffat distribution.
- tag_uri: tag:stsci.edu:asdf/transform/moffat2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/moffat2d-1.0.0
title: Two dimensional Moffat model.
description: |-
Two dimensional Moffat distribution.
- tag_uri: tag:stsci.edu:asdf/transform/molleweide-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/molleweide-1.2.0
title: Molleweide's projection.
description: |-
Corresponds to the `MOL` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= \frac{\pi x}{2 \sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}} \\
\theta &= \sin^{-1}\left(\frac{1}{90^\circ}\sin^{-1}\left(\frac{\pi}{180^\circ}\frac{y}{\sqrt{2}}\right) + \frac{y}{180^\circ}\sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}\right)$$
And the sky-to-pixel transformation is defined as:
$$x &= \frac{2 \sqrt{2}}{\pi} \phi \cos \gamma \\
y &= \sqrt{2} \frac{180^\circ}{\pi} \sin \gamma$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/multiply-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/multiply-1.2.0
title: Perform a list of subtransforms in parallel and then multiply their results.
description: |-
Each of the subtransforms must have the same number of inputs and
outputs.
Invertibility: This transform is not automatically invertible.
- tag_uri: tag:stsci.edu:asdf/transform/multiplyscale-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/multiplyscale-1.0.0
title: A Multiply model.
description: |-
Multiply the input by a factor.
- tag_uri: tag:stsci.edu:asdf/transform/ortho_polynomial-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/ortho_polynomial-1.0.0
title: Respresents various Orthogonal Polynomial models.
description: |-
A polynomial model represented by its coefficients stored in
an ndarray of shape $(n+1)$ for univariate polynomials or $(n+1, n+1)$
for polynomials with 2 variables, where $n$ is the highest total degree
of the polynomial. The property polynomial_type defines what kind of
polynomial is defined.
$$P = \sum_{i, j=0}^{i+j=n}c_{ij} * x^{i} * y^{j}$$
Invertibility: This transform is not automatically invertible.
- tag_uri: tag:stsci.edu:asdf/transform/parabolic-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/parabolic-1.2.0
title: Parabolic projection.
description: |-
Corresponds to the `PAR` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= \frac{180^\circ}{\pi} \frac{x}{1 - 4(y / 180^\circ)^2} \\
\theta &= 3 \sin^{-1}\left(\frac{y}{180^\circ}\right)$$
And the sky-to-pixel transformation is defined as:
$$x &= \phi \left(2\cos\frac{2\theta}{3} - 1\right) \\
y &= 180^\circ \sin \frac{\theta}{3}$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/planar2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/planar2d-1.0.0
title: Two dimensional plane model.
description: |-
Two dimensional plane model.
- tag_uri: tag:stsci.edu:asdf/transform/plate_carree-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/plate_carree-1.2.0
title: "The plate carr\xE9e projection."
description: |-
Corresponds to the `CAR` projection in the FITS WCS standard.
The main virtue of this transformation is its simplicity.
The pixel-to-sky transformation is defined as:
$$\phi &= x \\
\theta &= y$$
And the sky-to-pixel transformation is defined as:
$$x &= \phi \\
y &= \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/plummer1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/plummer1d-1.0.0
title: Two dimensional Plummer model.
description: |-
One dimensional Plummer density profile model.
- tag_uri: tag:stsci.edu:asdf/transform/polyconic-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/polyconic-1.2.0
title: Polyconic projection.
description: |-
Corresponds to the `PCO` projection in the FITS WCS standard.
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/polynomial-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/polynomial-1.2.0
title: A Polynomial model.
description: |-
A polynomial model represented by its coefficients stored in
an ndarray of shape $(n+1)$ for univariate polynomials or $(n+1, n+1)$
for polynomials with 2 variables, where $n$ is the highest total degree
of the polynomial.
$$P = \sum_{i, j=0}^{i+j=n}c_{ij} * x^{i} * y^{j}$$
Invertibility: This transform is not automatically invertible.
- tag_uri: tag:stsci.edu:asdf/transform/spline1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/spline1d-1.0.0
title: A spline1d model.
description: |-
A spline1d model represented by an array of its knots, an array of its
coefficients, and its degree. In addition the bounding endpoints
of the spline can be represented as well
- tag_uri: tag:stsci.edu:asdf/transform/power-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/power-1.2.0
title: Perform a list of subtransforms in parallel and then raise each result to
the power of the next.
description: |-
Each of the subtransforms must have the same number of inputs and
outputs.
Invertibility: This transform is not automatically invertible.
- tag_uri: tag:stsci.edu:asdf/transform/power_law1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/power_law1d-1.0.0
title: One dimensional power law model.
description: |-
One dimensional power law model.
- tag_uri: tag:stsci.edu:asdf/transform/quad_spherical_cube-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/quad_spherical_cube-1.2.0
title: Quadrilateralized spherical cube projection.
description: |-
Corresponds to the `QSC` projection in the FITS WCS standard.
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/redshift_scale_factor-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/redshift_scale_factor-1.0.0
title: One dimensional redshift scale factor model.
description: |-
One dimensional redshift scale factor model.
- tag_uri: tag:stsci.edu:asdf/transform/remap_axes-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/remap_axes-1.3.0
title: Reorder, add and drop axes.
description: "This transform allows the order of the input axes to be shuffled and\n\
returned as the output axes.\n\nIt is a list made up of integers. Each item\n\
in the list corresponds to an output axis. Each item is the index of\nthe input\
\ axis to send to the output axis.\n\nIf an object with `mapping` and `n_inputs`\
\ properties is provided, the\nnumber of input axes is explicitly set by the `n_inputs`\
\ value.\nIf only a list is provided, the number of input axes is\nautomatically\
\ determined from the maximum index in the list. \n\nInvertibility: This transform\
\ does not have a general analytical inverse.\nIn some well defined cases it is\
\ possible to invert automatically"
- tag_uri: tag:stsci.edu:asdf/transform/ricker_wavelet1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/ricker_wavelet1d-1.0.0
title: One dimensional Ricker Wavelet model.
description: |-
One dimensional Ricker Wavelet model
- tag_uri: tag:stsci.edu:asdf/transform/ricker_wavelet2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/ricker_wavelet2d-1.0.0
title: Two dimensional Ricker Wavelet model.
description: |-
Two dimensional Ricker Wavelet model.
- tag_uri: tag:stsci.edu:asdf/transform/ring2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/ring2d-1.0.0
title: Two dimensional radially symmetric ring model.
description: |-
Two dimensional radially symmetric ring.
- tag_uri: tag:stsci.edu:asdf/transform/rotate2d-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/rotate2d-1.3.0
title: A 2D rotation.
description: |-
A 2D rotation around the origin, in degrees.
Invertibility: All ASDF tools are required to be able to compute the analytic inverse of this transform.
- tag_uri: tag:stsci.edu:asdf/transform/rotate3d-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/rotate3d-1.3.0
title: Rotation in 3D space.
description: |-
Euler angle rotation around 3 axes.
Invertibility: All ASDF tools are required to be able to compute the
analytic inverse of this transform.
- tag_uri: tag:stsci.edu:asdf/transform/rotate_sequence_3d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/rotate_sequence_3d-1.0.0
title: Rotation in 3D space.
description: |-
Rotation in 3D space by arbitrary number of angles about
arbitrary order of "x", "y", "z" axes.
- tag_uri: tag:stsci.edu:asdf/transform/sanson_flamsteed-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/sanson_flamsteed-1.2.0
title: The Sanson-Flamsteed projection.
description: |-
Corresponds to the `SFL` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= \frac{x}{\cos y} \\
\theta &= y$$
And the sky-to-pixel transformation is defined as:
$$x &= \phi \cos \theta \\
y &= \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/scale-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/scale-1.2.0
title: A Scale model.
description: |-
Scale the input by a dimensionless factor.
- tag_uri: tag:stsci.edu:asdf/transform/schechter1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/schechter1d-1.0.0
title: Schechter luminosity function
description: |-
Schechter luminosity function
- tag_uri: tag:stsci.edu:asdf/transform/sersic1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/sersic1d-1.0.0
title: One dimensional Sersic surface brightness profile.
description: |-
One dimensional Sersic surface brightness profile.
- tag_uri: tag:stsci.edu:asdf/transform/sersic2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/sersic2d-1.0.0
title: Two dimensional Sersic surface brightness profile.
description: |-
Two dimensional Sersic surface brightness profile.
- tag_uri: tag:stsci.edu:asdf/transform/shift-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/shift-1.2.0
title: A Shift opeartion.
description: |-
Apply an offset in one direction.
- tag_uri: tag:stsci.edu:asdf/transform/sine1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/sine1d-1.0.0
title: One dimensional sine model.
description: |-
One dimensional sine.
- tag_uri: tag:stsci.edu:asdf/transform/cosine1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/cosine1d-1.0.0
title: One dimensional cosine model.
description: |-
One dimensional cosine.
- tag_uri: tag:stsci.edu:asdf/transform/tangent1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/tangent1d-1.0.0
title: One dimensional tangent model.
description: |-
One dimensional tangent.
- tag_uri: tag:stsci.edu:asdf/transform/arcsine1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/arcsine1d-1.0.0
title: One dimensional arcsine model.
description: |-
One dimensional arcsine.
- tag_uri: tag:stsci.edu:asdf/transform/arccosine1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/arccosine1d-1.0.0
title: One dimensional arccosine model.
description: |-
One dimensional arccosine.
- tag_uri: tag:stsci.edu:asdf/transform/arctangent1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/arctangent1d-1.0.0
title: One dimensional arctangent model.
description: |-
One dimensional arctangent.
- tag_uri: tag:stsci.edu:asdf/transform/slant_orthographic-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/slant_orthographic-1.2.0
title: The slant orthographic projection.
description: |-
Corresponds to the `SIN` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
The pixel-to-sky transformation is defined as:
$$\theta = \cos^{-1}\left(\frac{\pi}{180^{\circ}}R_\theta\right)$$
And the sky-to-pixel transformation is defined as:
$$R_\theta = \frac{180^{\circ}}{\pi}\cos \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/slant_zenithal_perspective-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/slant_zenithal_perspective-1.2.0
title: The slant zenithal perspective projection.
description: |-
Corresponds to the `SZP` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
The pixel-to-sky transformation is defined as:
$$\theta = \tan^{-1}\left(\frac{180^{\circ}}{\pi R_\theta}\right)$$
And the sky-to-pixel transformation is defined as:
$$R_\theta = \frac{180^{\circ}}{\pi}\cot \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/smoothly_broken_power_law1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/smoothly_broken_power_law1d-1.0.0
title: One dimensional smoothly broken power law model.
description: |-
One dimensional smoothly broken power law model.
- tag_uri: tag:stsci.edu:asdf/transform/stereographic-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/stereographic-1.2.0
title: The stereographic projection.
description: |-
Corresponds to the `STG` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
The pixel-to-sky transformation is defined as:
$$\theta = 90^{\circ} - 2 \tan^{-1}\left(\frac{\pi R_\theta}{360^{\circ}}\right)$$
And the sky-to-pixel transformation is defined as:
$$R_\theta = \frac{180^{\circ}}{\pi}\frac{2 \cos \theta}{1 + \sin \theta}$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/subtract-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/subtract-1.2.0
title: Perform a list of subtransforms in parallel and then subtract their results.
description: |-
Each of the subtransforms must have the same number of inputs and
outputs.
Invertibility: This transform is not automatically invertible.
- tag_uri: tag:stsci.edu:asdf/transform/tabular-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/tabular-1.2.0
title: A Tabular model.
description: |-
Tabular represents a lookup table with values corresponding to
some grid points.
It computes the interpolated values corresponding to the given
inputs. Three methods of interpolation are supported -
"linear", "nearest" and "splinef2d". It supports extrapolation.
- tag_uri: tag:stsci.edu:asdf/transform/tangential_spherical_cube-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/tangential_spherical_cube-1.2.0
title: Tangential spherical cube projection.
description: |-
Corresponds to the `TSC` projection in the FITS WCS standard.
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/trapezoid1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/trapezoid1d-1.0.0
title: One dimensional trapezoid model.
description: |-
One dimensional trapezoid.
- tag_uri: tag:stsci.edu:asdf/transform/trapezoid_disk2d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/trapezoid_disk2d-1.0.0
title: Two dimensional circular trapezoid model.
description: |-
Two dimensional circular trapezoid.
- tag_uri: tag:stsci.edu:asdf/transform/voigt1d-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/voigt1d-1.0.0
title: One dimensional model for the Voigt profile.
description: |-
One dimensional model for the Voigt profile.
- tag_uri: tag:stsci.edu:asdf/transform/zenithal_equal_area-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/zenithal_equal_area-1.2.0
title: The zenithal equal area projection.
description: |-
Corresponds to the `ZEA` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
The pixel-to-sky transformation is defined as:
$$\theta = 90^\circ - 2 \sin^{-1} \left(\frac{\pi R_\theta}{360^\circ}\right)$$
And the sky-to-pixel transformation is defined as:
$$R_\theta &= \frac{180^\circ}{\pi} \sqrt{2(1 - \sin\theta)} \\
&= \frac{360^\circ}{\pi} \sin\left(\frac{90^\circ - \theta}{2}\right)$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/zenithal_equidistant-1.2.0
schema_uri: http://stsci.edu/schemas/asdf/transform/zenithal_equidistant-1.2.0
title: The zenithal equidistant projection.
description: |-
Corresponds to the `ARC` projection in the FITS WCS standard.
See
[zenithal](ref:transform/zenithal-1.2.0)
for the definition of the full transformation.
The pixel-to-sky transformation is defined as:
$$\theta = 90^\circ - R_\theta$$
And the sky-to-pixel transformation is defined as:
$$R_\theta = 90^\circ - \theta$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/zenithal_perspective-1.3.0
schema_uri: http://stsci.edu/schemas/asdf/transform/zenithal_perspective-1.3.0
title: The zenithal perspective projection.
description: |-
Corresponds to the `AZP` projection in the FITS WCS standard.
The pixel-to-sky transformation is defined as:
$$\phi &= \arg(-y \cos \gamma, x) \\
\theta &= \left\{\genfrac{}{}{0pt}{}{\psi - \omega}{\psi + \omega + 180^{\circ}}\right.$$
where:
$$\psi &= \arg(\rho, 1) \\
\omega &= \sin^{-1}\left(\frac{\rho \mu}{\sqrt{\rho^2 + 1}}\right) \\
\rho &= \frac{R}{\frac{180^{\circ}}{\pi}(\mu + 1) + y \sin \gamma} \\
R &= \sqrt{x^2 + y^2 \cos^2 \gamma}$$
And the sky-to-pixel transformation is defined as:
$$x &= R \sin \phi \\
y &= -R \sec \gamma \cos \theta$$
where:
$$R = \frac{180^{\circ}}{\pi} \frac{(\mu + 1) \cos \theta}{(\mu + \sin \theta) + \cos \theta \cos \phi \tan \gamma}$$
Invertibility: All ASDF tools are required to provide the inverse of
this transform.
- tag_uri: tag:stsci.edu:asdf/transform/property/bounding_box-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/property/bounding_box-1.0.0
title: Bounding box for a model.
description: |-
This object contains the bounding box for a model, which defines
the domain of valid inputs to the model. The bounds for each input
is are listed as a map under the interval keyword as ordered pairs of
lower/upper bounds with key being the input name. If any model inputs
are to be ignored by the bounding box then they need to be listed under
the ignore keyword. Finally, the tuple representation's input ordering
can be listed under the order keyword, C for C-ordering, F for Fortran
ordering.
- tag_uri: tag:stsci.edu:asdf/transform/property/compound_bounding_box-1.0.0
schema_uri: http://stsci.edu/schemas/asdf/transform/property/compound_bounding_box-1.0.0
title: Compound bounding box for a model.
description: |-
This object contains a compound bounding box for a model, which defines
a set of input-selectable bounding boxes. It consists of a list of selector_args
together with a list of input-key bounding box pairs. The selector
args are an ordered list of model inputs with an indication of whether
or not to ignore the input in the bounding box selected. The key for
each bounding box entry corresponds to the values of the selector args
(in the order listed) which will select the accompanying bounding box.