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      "name": "python"
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  "cells": [
    {
      "cell_type": "code",
      "source": [
        "try:\n",
        "    import pgmuvi\n",
        "except (ImportError, ModuleNotFoundError):\n",
        "    %pip install -q git+https://github.com/ICSM/pgmuvi.git\n",
        "    import pgmuvi"
      ],
      "metadata": {
        "id": "l_ZXfL9bLq8c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6f66c96b-d589-4124-cd1f-07b823675763"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m291.2/291.2 kB\u001b[0m \u001b[31m8.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m756.0/756.0 kB\u001b[0m \u001b[31m25.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m174.8/174.8 kB\u001b[0m \u001b[31m10.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Building wheel for pgmuvi (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Core imports for the GP-fitting sections\n",
        "\n",
        "import random\n",
        "import numpy as np\n",
        "import torch\n",
        "import gpytorch\n",
        "\n",
        "from pgmuvi.lightcurve import Lightcurve\n",
        "from pgmuvi import synthetic\n",
        "import pgmuvi.gps as gps\n",
        "\n",
        "SEED = 0\n",
        "random.seed(SEED)\n",
        "np.random.seed(SEED)\n",
        "torch.manual_seed(SEED)\n",
        "\n",
        "DTYPE = torch.float64\n",
        "DEVICE = torch.device(\"cpu\")"
      ],
      "metadata": {
        "id": "bD3dVOBnLnhZ"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Gaussian-process fitting in `pgmuvi`\n",
        "\n",
        "The central method for GP fitting in `pgmuvi` is `Lightcurve.fit()`. It accepts a `Lightcurve` object and fits one of several Gaussian-process models to the data.\n",
        "\n",
        "At a high level, the workflow is:\n",
        "\n",
        "1. construct a `Lightcurve`,\n",
        "2. choose a GP model,\n",
        "3. optionally provide period guesses or let the code initialise them from Lomb--Scargle,\n",
        "4. optimise the model hyperparameters,\n",
        "5. inspect the fitted kernel and interpret the implied power spectral density (PSD).\n",
        "\n",
        "The same interface is used for both 1D and 2D light curves, but the available models differ depending on whether the data contain only a time axis or both time and wavelength."
      ],
      "metadata": {
        "id": "VVvUq-JWLR7q"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## GP model families available in `pgmuvi`\n",
        "\n",
        "`pgmuvi` provides several GP model families. They are not interchangeable: each encodes a different assumption about the temporal or multiwavelength structure of the variability.\n",
        "\n",
        "### 1D models\n",
        "\n",
        "These are intended for single-band light curves.\n",
        "\n",
        "- **`'1D'`**: spectral-mixture GP  \n",
        "  Flexible and often the most useful model when multiple periodic or quasi-periodic components may be present.  \n",
        "  This is the main model for interpreting variability through the GP-derived PSD.\n",
        "\n",
        "- **`'1DQuasiPeriodic'`**: quasi-periodic GP  \n",
        "  Appropriate when one dominant repeating timescale is present, but the signal evolves gradually in amplitude or phase.\n",
        "\n",
        "- **`'1DMatern'`**: Matérn GP  \n",
        "  Appropriate for correlated stochastic variability without a strong periodic component.\n",
        "\n",
        "- **`'1DPeriodicStochastic'`**: periodic + stochastic GP  \n",
        "  Useful when a source shows both a repeating component and additional correlated noise or structured residual variability.\n",
        "\n",
        "### 2D models\n",
        "\n",
        "These are intended for light curves with both time and wavelength.\n",
        "\n",
        "- **`'2D'`**: 2D spectral-mixture GP  \n",
        "  A flexible model that can represent complex joint structure in time and wavelength.\n",
        "\n",
        "- **`'2DSeparable'`**: separable time--wavelength GP  \n",
        "  Assumes the covariance can be factorised into a temporal part and a wavelength part.\n",
        "\n",
        "- **`'2DAchromatic'`**: achromatic GP  \n",
        "  Appropriate when the temporal variability is shared across wavelengths.\n",
        "\n",
        "- **`'2DWavelengthDependent'`**: wavelength-dependent GP  \n",
        "  Appropriate when the temporal behaviour is correlated across wavelength but not identical in every band.\n",
        "\n",
        "- **`'2DDustMean'`** and **`'2DPowerLawMean'`**: wavelength-dependent GPs with physically motivated mean functions  \n",
        "  These are useful when the mean spectral behaviour itself carries physical information and should be modeled explicitly.\n",
        "\n",
        "In this notebook, the main emphasis will be on **spectral-mixture models**, because they provide a natural route from the fitted kernel to a PSD and then to dominant periods."
      ],
      "metadata": {
        "id": "1gpMtul9LYQX"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "enfbMXG2LH1h",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fca86983-427f-4a49-ef77-88b343c5aa85"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1D                   -> SpectralMixtureGPModel         | Flexible 1D periodic or multi-periodic variability\n",
            "1DQuasiPeriodic      -> QuasiPeriodicGPModel           | One dominant evolving cycle\n",
            "1DMatern             -> MaternGPModel                  | Correlated stochastic variability\n",
            "1DPeriodicStochastic -> PeriodicPlusStochasticGPModel  | Periodic signal plus correlated stochastic structure\n",
            "2D                   -> TwoDSpectralMixtureGPModel     | Flexible joint time-wavelength structure\n",
            "2DSeparable          -> SeparableGPModel               | Factorised time and wavelength covariance\n",
            "2DAchromatic         -> AchromaticGPModel              | Same temporal behaviour across wavelength\n",
            "2DWavelengthDependent -> WavelengthDependentGPModel     | Smoothly varying temporal behaviour across wavelength\n",
            "2DDustMean           -> DustMeanGPModel                | Wavelength-dependent variability with dust-like mean structure\n",
            "2DPowerLawMean       -> PowerLawMeanGPModel            | Wavelength-dependent variability with power-law mean structure\n"
          ]
        }
      ],
      "source": [
        "# A compact reference table for the models that we will actually use in this notebook\n",
        "\n",
        "MODEL_REFERENCE = {\n",
        "    \"1D\": {\n",
        "        \"class\": gps.SpectralMixtureGPModel,\n",
        "        \"use_case\": \"Flexible 1D periodic or multi-periodic variability\",\n",
        "    },\n",
        "    \"1DQuasiPeriodic\": {\n",
        "        \"class\": gps.QuasiPeriodicGPModel,\n",
        "        \"use_case\": \"One dominant evolving cycle\",\n",
        "    },\n",
        "    \"1DMatern\": {\n",
        "        \"class\": gps.MaternGPModel,\n",
        "        \"use_case\": \"Correlated stochastic variability\",\n",
        "    },\n",
        "    \"1DPeriodicStochastic\": {\n",
        "        \"class\": gps.PeriodicPlusStochasticGPModel,\n",
        "        \"use_case\": \"Periodic signal plus correlated stochastic structure\",\n",
        "    },\n",
        "    \"2D\": {\n",
        "        \"class\": gps.TwoDSpectralMixtureGPModel,\n",
        "        \"use_case\": \"Flexible joint time-wavelength structure\",\n",
        "    },\n",
        "    \"2DSeparable\": {\n",
        "        \"class\": gps.SeparableGPModel,\n",
        "        \"use_case\": \"Factorised time and wavelength covariance\",\n",
        "    },\n",
        "    \"2DAchromatic\": {\n",
        "        \"class\": gps.AchromaticGPModel,\n",
        "        \"use_case\": \"Same temporal behaviour across wavelength\",\n",
        "    },\n",
        "    \"2DWavelengthDependent\": {\n",
        "        \"class\": gps.WavelengthDependentGPModel,\n",
        "        \"use_case\": \"Smoothly varying temporal behaviour across wavelength\",\n",
        "    },\n",
        "    \"2DDustMean\": {\n",
        "        \"class\": gps.DustMeanGPModel,\n",
        "        \"use_case\": \"Wavelength-dependent variability with dust-like mean structure\",\n",
        "    },\n",
        "    \"2DPowerLawMean\": {\n",
        "        \"class\": gps.PowerLawMeanGPModel,\n",
        "        \"use_case\": \"Wavelength-dependent variability with power-law mean structure\",\n",
        "    },\n",
        "}\n",
        "\n",
        "for model_name, info in MODEL_REFERENCE.items():\n",
        "    print(f\"{model_name:20s} -> {info['class'].__name__:30s} | {info['use_case']}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A practical way to choose a GP model\n",
        "\n",
        "There is no universally best kernel. The choice should follow the scientific question.\n",
        "\n",
        "A reasonable starting point is:\n",
        "\n",
        "- use **`'1D'`** for single-band light curves when the goal is to recover one or more characteristic periods from the GP PSD;\n",
        "- use **`'1DQuasiPeriodic'`** when there is one clear cycle and a simpler model is preferred;\n",
        "- use **`'1DMatern'`** when the variability is correlated but not obviously periodic;\n",
        "- use **`'2D'`** when a fully flexible joint model in time and wavelength is desired;\n",
        "- use **`'2DAchromatic'`** when the same temporal pattern is expected in all bands;\n",
        "- use **`'2DWavelengthDependent'`** when nearby wavelengths should behave similarly, but not identically.\n",
        "\n",
        "In the examples below, we will begin with spectral-mixture models because they connect directly to the PSD-based interpretation of the GP fit."
      ],
      "metadata": {
        "id": "GOOb8eGRL904"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Basic GP-fitting workflow in `pgmuvi`\n",
        "\n",
        "The method used throughout this notebook is:\n",
        "\n",
        "```python\n",
        "lc.fit(\n",
        "    model=...,\n",
        "    training_iter=...,\n",
        "    use_mls_init=True,\n",
        "    use_best_band_init=False,\n",
        "    num_mixtures=...,\n",
        ")```\n",
        "\n",
        "Some arguments that will matter later are:\n",
        "\n",
        "`model`: selects the GP model family;\n",
        "`training_iter`: number of optimisation iterations;\n",
        "`num_mixtures`: number of spectral-mixture components when using spectral-mixture kernels;\n",
        "`use_mls_init`: initialise spectral-mixture components from Lomb--Scargle peaks;\n",
        "`use_best_band_init`: for multi-band data, use the best individual band to initialise the period guesses;\n",
        "`periods`: manual period guesses, if desired.\n",
        "\n",
        "For spectral-mixture models, `use_mls_init=True` is often a sensible default because it gives the optimiser a physically motivated starting point."
      ],
      "metadata": {
        "id": "_QiFoQrFMAGi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Minimal synthetic example using the actual keyword pattern from the tutorial notebook\n",
        "\n",
        "lc_template = synthetic.make_chromatic_sinusoid_2d(\n",
        "    period=150,\n",
        "    t_span=150 * 2.3,\n",
        "    n_per_band=(25, 40),\n",
        "    wavelengths=[0.8, 1.2, 2.2],\n",
        "    amplitude_law=\"extinction\",\n",
        "    seed=SEED,\n",
        ")\n",
        "\n",
        "lc_template.plot()\n",
        "print(type(lc_template))\n",
        "print(\"Number of data points:\", lc_template.ydata.numel())"
      ],
      "metadata": {
        "id": "GkA5PkCqL67z",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "d1add25f-cf39-4ed8-f6b2-9a1681dbaa5c"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pgmuvi.lightcurve.Lightcurve'>\n",
            "Number of data points: 106\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The example above is only meant to show the basic `Lightcurve.fit()` workflow on a synthetic light curve generated with the same configuration pattern used in the tutorial notebook.\n",
        "\n",
        "Although this dataset is generated by a 2D synthetic generator, it is sufficient for demonstrating the fitting interface. The dedicated 1D and 2D examples below will use more appropriate datasets for scientific interpretation."
      ],
      "metadata": {
        "id": "yD1IRnH-NCg8"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "CnY8ZLOTMdit"
      },
      "execution_count": 5,
      "outputs": []
    }
  ]
}