gaussian2d-1.0.0¶

A 2D Gaussian model.

Description

A 2D gaussian distribution.

Outline

Schema Definitions
Examples
Original Schema

Schema Definitions ¶

This node must validate against all of the following:

This type is an object with the following properties:
- amplitude
  object Required
  Amplitude.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- x_mean
  object Required
  Mean in x.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- y_mean
  object Required
  Mean in y.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- x_stddev
  object Required
  Standard deviation in x.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- y_stddev
  object Required
  Standard deviation in y.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- theta
  object Required
  Rotation angle in radians, increases counterclockwise.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number

Examples ¶

\(f(x, y) = 10.0 e^{-a\left(x - 1.5\right)^{2} -b\left(x - 1.5\right) \left(y - 2.5\right) -c\left(y - 2.5\right)^{2}}\) using the following definitions \(a = \left(\frac{\cos^{2}{\left (0 \right )}}{2*0.25^{2}} +\frac{\sin^{2}{\left (0 \right )}}{2*0.375^{2}}\right)\), \(b = \left(\frac{\sin{\left (2 *0 \right )}}{2 *0.25^{2}} -\frac{\sin{\left (2 *0 \right )}}{2*0.375^{2}}\right)\), \(c = \left(\frac{\sin^{2}{\left (0\right )}}{2*0.25^{2}} +\frac{\cos^{2}{\left (0 \right )}}{2*0.375^{2}}\right)\):

!transform/gaussian2d-1.0.0
  amplitude: 10.0
  bounding_box:
  - [0.4375, 4.5625]
  - [0.125, 2.875]
  theta: 0.0
  x_mean: 1.5
  x_stddev: 0.25
  y_mean: 2.5
  y_stddev: 0.375

Original Schema ¶

%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/gaussian2d-1.0.0"
title: >
  A 2D Gaussian model.

description: >
  A 2D gaussian distribution.

examples:
  -
    - $f(x, y) = 10.0 e^{-a\left(x - 1.5\right)^{2}  -b\left(x - 1.5\right) \left(y - 2.5\right)  -c\left(y - 2.5\right)^{2}}$ using the following definitions $a = \left(\frac{\cos^{2}{\left (0 \right )}}{2*0.25^{2}} +\frac{\sin^{2}{\left (0 \right )}}{2*0.375^{2}}\right)$, $b = \left(\frac{\sin{\left (2 *0 \right )}}{2 *0.25^{2}} -\frac{\sin{\left (2 *0 \right )}}{2*0.375^{2}}\right)$, $c = \left(\frac{\sin^{2}{\left (0\right )}}{2*0.25^{2}} +\frac{\cos^{2}{\left (0 \right )}}{2*0.375^{2}}\right)$
    - |
      !transform/gaussian2d-1.0.0
        amplitude: 10.0
        bounding_box:
        - [0.4375, 4.5625]
        - [0.125, 2.875]
        theta: 0.0
        x_mean: 1.5
        x_stddev: 0.25
        y_mean: 2.5
        y_stddev: 0.375

allOf:
  - $ref: "transform-1.2.0"
  - type: object
    properties:
      amplitude:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Amplitude.
      x_mean:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Mean in x.
      y_mean:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Mean in y.
      x_stddev:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Standard deviation in x.
      y_stddev:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Standard deviation in y.
      theta:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Rotation angle in radians, increases counterclockwise.

    required: ['amplitude', 'x_mean', 'y_mean', 'x_stddev', 'y_stddev', 'theta']
...