(md_legacy_framework)=

# Original three-dataset framework

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The current multidimensional GP models support an arbitrary number of datasets and heterogeneous cadences. `PyORBIT` also keeps the older Rajpaul-style framework, where the model is built from exactly three synchronous datasets: radial velocities, one chromospheric activity indicator, and BIS.

This model is mainly retained for reproducibility of older analyses. For new analyses, the multidimensional models described in [the quasi-periodic kernel page](md_quasiperiodic.md) are usually more flexible.

## Model definition and requirements

**model name**: `gp_framework_quasiperiodic`
- required common object: `activity`
- expects three datasets with the same times and length
- supported dataset roles: RV, one of `H-alpha`, `S_index`, or `Ca_HK`, and `BIS`

**model name**: `gp_pyaneti_quasiperiodic`
- required common object: `activity`
- multidimensional quasi-periodic model using the `pyaneti` backend
- supports the same dataset coefficient notation as the newer multidimensional models

## Keywords

Model-wide keywords, with the default value in boldface.

**hyperparameters_condition**
* accepted values: `True` | **`False`**
* activates the quasi-periodic hyperparameter condition described in the [quasi-periodic kernel](../gaussian_process/quasiperiodic_kernel).

**rotation_decay_condition**
* accepted values: `True` | **`False`**
* if activated, requires `Pdec > 2 Prot`.

**use_stellar_rotation_period**
* accepted values: `True` | **`False`**
* replaces `Prot` with `rotation_period` from `star_parameters`.

**use_stellar_activity_decay**
* accepted values: `True` | **`False`**
* replaces `Pdec` with `activity_decay` from `star_parameters`.

**derivative**
* accepted values: mapping of dataset names to booleans
* available for `gp_pyaneti_quasiperiodic`. If `False`, the derivative coefficient `rot_amp` is fixed to zero for that dataset.

## Examples

Original fixed framework:

```yaml
inputs:
  RVdata:
    file: datasets/RV_PyORBIT.dat
    kind: RV
    models:
      - gp_framework
  Sdata:
    file: datasets/Sindex_PyORBIT.dat
    kind: S_index
    models:
      - gp_framework
  BISdata:
    file: datasets/BIS_PyORBIT.dat
    kind: BIS
    models:
      - gp_framework
common:
  activity:
    boundaries:
      Prot: [10.0, 20.0]
      Pdec: [20.0, 1000.0]
      Oamp: [0.001, 1.0]
      Vc: [-100.0, 100.0]
      Vr: [-100.0, 100.0]
      Lc: [-10.0, 10.0]
      Bc: [-100.0, 100.0]
      Br: [-100.0, 100.0]
models:
  gp_framework:
    model: gp_framework_quasiperiodic
    common: activity
    hyperparameters_condition: True
```

`pyaneti` multidimensional backend:

```yaml
models:
  gp_pyaneti:
    model: gp_pyaneti_quasiperiodic
    common: activity
    hyperparameters_condition: True
    RVdata:
      boundaries:
        rot_amp: [0.0, 20.0]
        con_amp: [-20.0, 20.0]
      derivative: True
    Sdata:
      boundaries:
        con_amp: [-1.0, 1.0]
      derivative: False
```

## Model parameters

### `gp_framework_quasiperiodic`

| Name | Parameter | Common? | Definition | Notes |
| :--- | :-------- | :------ | :--------- | :---- |
| `Prot` | Rotational period of the star | common | `activity` | |
| `Pdec` | Decay timescale of active regions | common | `activity` | |
| `Oamp` | Coherence scale | common | `activity` | |
| `Vc` | Coefficient of `G(t)` in the RV model | common | `activity` | |
| `Vr` | Coefficient of `G'(t)` in the RV model | common | `activity` | |
| `Lc` | Coefficient of `G(t)` in the chromospheric-index model | common | `activity` | |
| `Bc` | Coefficient of `G(t)` in the BIS model | common | `activity` | |
| `Br` | Coefficient of `G'(t)` in the BIS model | common | `activity` | |

### `gp_pyaneti_quasiperiodic`

| Name | Parameter | Common? | Definition | Notes |
| :--- | :-------- | :------ | :--------- | :---- |
| `Prot` | Rotational period of the star | common | `activity` | |
| `Pdec` | Decay timescale of active regions | common | `activity` | |
| `Oamp` | Coherence scale | common | `activity` | |
| `con_amp` | Coefficient of the latent GP | dataset | `activity` | |
| `rot_amp` | Coefficient of the first derivative of the latent GP | dataset | `activity` | Fixed to zero when `derivative: False` |