smoothly_broken_power_law1d-1.0.0¶

One dimensional smoothly broken power law model.

Description

One dimensional smoothly broken power law model.

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
  Model amplitude at the break point.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- x_break
  object Required
  Break point.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- alpha_1
  object Required
  Power law index for x < x_break.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- alpha_2
  object Required
  Power law index for x > x_break.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number
- delta
  object Required
  Smoothness parameter.
  This node must validate against any of the following:
  
  ../unit/quantity-1.1.0
  
  number

Examples ¶

\[f(x) = 10*(\frac{x}{5.0})^{-2.0}\{\frac{1}{2}[1+(\frac{x}{5.0})^{1/0.5}]\}^{(2.0- 3.0)0.5}\]

!transform/smoothly_broken_power_law1d-1.0.0 {alpha_1: 2.0, alpha_2: 2.0, amplitude: 10.0, delta: 0.5, x_break: 5.0}

Original Schema ¶

%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "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.

examples:
  -
    - $$f(x) = 10*(\frac{x}{5.0})^{-2.0}\{\frac{1}{2}[1+(\frac{x}{5.0})^{1/0.5}]\}^{(2.0- 3.0)0.5}$$
    - |
      !transform/smoothly_broken_power_law1d-1.0.0 {alpha_1: 2.0, alpha_2: 2.0, amplitude: 10.0, delta: 0.5, x_break: 5.0}

allOf:
  - $ref: "transform-1.2.0"
  - type: object
    properties:
      amplitude:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Model amplitude at the break point.
      x_break:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Break point.
      alpha_1:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Power law index for x < x_break.
      alpha_2:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Power law index for x > x_break.
      delta:
        anyOf:
          - $ref: "../unit/quantity-1.1.0"
          - type: number
        description: Smoothness parameter.

    required: ['amplitude', 'x_break', 'alpha_1', 'alpha_2', 'delta']
...