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    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "### Preamble"
      ],
      "metadata": {
        "id": "i9AQs7_jTjlo"
      }
    },
    {
      "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": "g4ZTxhIV69P4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c8f686f3-a00d-460b-97a3-617312ca42e9"
      },
      "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[31m3.7 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[31m14.3 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[31m13.2 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": [
        "# Imports and seeds for reproducibility\n",
        "import gpytorch\n",
        "from gpytorch.likelihoods import FixedNoiseGaussianLikelihood\n",
        "\n",
        "seed = 0\n",
        "import torch\n",
        "torch.manual_seed(seed)\n",
        "\n",
        "import numpy as np\n",
        "np.random.seed(seed)\n",
        "\n",
        "import random\n",
        "random.seed(seed)\n",
        "\n",
        "from pgmuvi.lightcurve import Lightcurve\n",
        "from gpytorch.constraints import Interval\n",
        "import pgmuvi.gps as gps\n",
        "from pgmuvi import synthetic\n",
        "from pgmuvi.preprocess import subsample_lightcurve\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "SEED = 0\n",
        "TRAINING_ITER = 1000\n",
        "DTYPE = torch.float64\n",
        "DEVICE = torch.device(\"cpu\")"
      ],
      "metadata": {
        "id": "OgsFewYt62Tu"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Purpose of this notebook\n",
        "\n",
        "This notebook discusses the `fit_LS()` method implemented in the `Lightcurve` class in PGMUVI and demonstrates how to use it for Lomb--Scargle period analysis of astronomical light curves.\n",
        "\n",
        "In PGMUVI, `fit_LS()` is primarily useful as a fast diagnostic and exploratory tool. It can be used to:\n",
        "\n",
        "- identify candidate periodicities in a light curve,\n",
        "- inspect the full Lomb--Scargle periodogram,\n",
        "- compare the strongest peaks in the frequency domain,\n",
        "- provide initial guidance before fitting more flexible Gaussian-process models.\n",
        "\n",
        "This notebook focuses specifically on how `fit_LS()` behaves in the current PGMUVI codebase, rather than on Lomb--Scargle analysis in the abstract. In particular, we will examine:\n",
        "\n",
        "- how the method behaves for 1D and multiband light curves,\n",
        "- what the different return modes mean,\n",
        "- how significance flags are computed,\n",
        "- and what practical caveats arise when interpreting the output.\n",
        "\n",
        "A central theme of this notebook is that Lomb--Scargle in PGMUVI should usually be treated as a useful diagnostic and initialization step, not as the final word on the physically correct period in difficult or irregularly sampled cases."
      ],
      "metadata": {
        "id": "DXa1wyBv3l1G"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Where `fit_LS()` sits in the PGMUVI workflow\n",
        "\n",
        "The `fit_LS()` method is part of the `Lightcurve` class and operates directly on the time-series data stored within it. Depending on how the `Lightcurve` object is constructed, this can represent:\n",
        "\n",
        "- a single-band (1D) light curve, or  \n",
        "- a multiband (2D) light curve with multiple wavelengths or bands.\n",
        "\n",
        "The role of `fit_LS()` within the broader PGMUVI workflow is intentionally limited but important:\n",
        "\n",
        "- It provides a **fast, non-parametric estimate** of periodic structure in the data.\n",
        "- It can be used to **identify candidate frequencies** before fitting more flexible models.\n",
        "- It helps **diagnose sampling limitations**, aliasing, and noise-dominated regimes.\n",
        "- It is often used to **initialize or guide Gaussian-process (GP) models**, especially those with spectral-mixture or periodic structure.\n",
        "\n",
        "### Return modes of `fit_LS()`\n",
        "\n",
        "The behavior of `fit_LS()` depends on the keyword arguments used. There are three practically relevant modes:\n",
        "\n",
        "1. **Full periodogram mode**\n",
        "   \n",
        "   - `freq_only=True`\n",
        "   - Returns:\n",
        "     - frequency grid\n",
        "     - power evaluated at each frequency\n",
        "\n",
        "   This is the mode to use when you want to **inspect or plot the full Lomb--Scargle periodogram**.\n",
        "\n",
        "2. **Peak summary mode (default)**\n",
        "   \n",
        "   - `freq_only=False`, `return_full=False`\n",
        "   - Returns:\n",
        "     - peak frequencies (ordered by decreasing power)\n",
        "     - boolean significance flags for each peak\n",
        "\n",
        "   This is the mode to use when you only care about the **strongest candidate periodicities**.\n",
        "\n",
        "3. **Combined mode**\n",
        "   \n",
        "   - `freq_only=False`, `return_full=True`\n",
        "   - Returns:\n",
        "     - peak frequencies\n",
        "     - significance flags\n",
        "     - full frequency grid\n",
        "     - full power array\n",
        "\n",
        "   This is the most complete mode and is useful when you want **both a summary and the full periodogram** in a single call.\n",
        "\n",
        "### Key points to keep in mind\n",
        "\n",
        "- The method works in **frequency space**, not period space. Any interpretation in terms of periods requires converting frequency → period.\n",
        "- Peaks are returned in **descending order of power**, not by frequency or period.\n",
        "- The meaning of the **significance flags differs between 1D and multiband cases**, and will be discussed later.\n",
        "\n",
        "In the following sections, we will demonstrate these modes in practice, starting with a simple 1D example."
      ],
      "metadata": {
        "id": "hXyiJDoh3v-I"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Basic 1D example\n",
        "\n",
        "We begin with a simple synthetic example for which the true period is known. The synthetic generator in `synthetic.py` produces a multiband light curve, but for this first demonstration we will extract a single band and treat it as a 1D light curve.\n",
        "\n",
        "This lets us study the basic behavior of `fit_LS()` in the simplest possible setting before moving on to multiband use.\n",
        "\n",
        "In this section we will:\n",
        "\n",
        "- extract one band from the synthetic light curve,\n",
        "- compute the full Lomb--Scargle periodogram,\n",
        "- convert frequency to period,\n",
        "- and visualize the resulting power spectrum.\n",
        "\n",
        "For this mono-periodic example, the injected period is 150 d."
      ],
      "metadata": {
        "id": "gIKlcSUm32_E"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"Generate a set of mono-periodic light curves using synthetic.py\"\"\"\n",
        "\n",
        "n_per_band = (25, 40)  # number of data points per light curve limited to this range\n",
        "\n",
        "SINGLE_DATASET_CONFIG = dict(\n",
        "    period=150,\n",
        "    t_span=150 * 2.3,\n",
        "    n_per_band=n_per_band,\n",
        "    wavelengths=[0.8, 1.2, 2.2],  # wavelengths in µm\n",
        "    amplitude_law=\"extinction\",\n",
        "    seed=SEED,\n",
        ")\n",
        "\n",
        "lc2d_synth_1comp = synthetic.make_chromatic_sinusoid_2d(**SINGLE_DATASET_CONFIG)\n",
        "\n",
        "# ------------------------------------------------------------------\n",
        "# Ensure 'band' attribute exists (synthetic generator does not set it)\n",
        "# ------------------------------------------------------------------\n",
        "# wavelengths = lc2d_synth_1comp.xdata[:, 1]\n",
        "wavelengths = np.asarray(lc2d_synth_1comp.xdata[:, 1], dtype=float)\n",
        "\n",
        "unique_waves = np.unique(wavelengths)\n",
        "\n",
        "# Map each wavelength to a string band label\n",
        "wave_to_band = {w: str(i) for i, w in enumerate(unique_waves)}\n",
        "\n",
        "band = np.array([f\"band {wave_to_band[w]}\" for w in wavelengths], dtype=object)\n",
        "lc2d_synth_1comp.band = band"
      ],
      "metadata": {
        "id": "Mu-f2C9k4KQa"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note: PGMUVI does not currently provide a built-in plotting utility for Lomb--Scargle periodograms. The user is expected to retrieve the frequency grid and power using `fit_LS(freq_only=True)` and construct plots manually."
      ],
      "metadata": {
        "id": "hUk0uT6u486N"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Use one band from the synthetic mono-periodic 2D light curve as a 1D example\n",
        "lc2d = lc2d_synth_1comp\n",
        "\n",
        "# Inspect available band labels\n",
        "bands = np.unique(lc2d.band)\n",
        "print(\"Available bands:\", bands)\n",
        "\n",
        "# Extract the first band as a 1D light curve\n",
        "band0 = bands[0]\n",
        "lc1d = lc2d.select_bands([band0])\n",
        "\n",
        "print(f\"Selected band: {band0}\")\n",
        "print(f\"Number of points in 1D light curve: {len(lc1d.xdata)}\")\n",
        "\n",
        "# Compute the full Lomb--Scargle periodogram\n",
        "freq, power = lc1d.fit_LS(freq_only=True)\n",
        "\n",
        "# Convert frequency grid to period\n",
        "period = 1.0 / freq\n",
        "\n",
        "# Sort by period for plotting\n",
        "idx = np.argsort(period)\n",
        "period_sorted = period[idx]\n",
        "power_sorted = power[idx]\n",
        "\n",
        "# Plot Lomb--Scargle power as a function of period\n",
        "plt.figure(figsize=(7, 4.5))\n",
        "plt.plot(period_sorted, power_sorted)\n",
        "plt.axvline(150.0, linestyle=\"--\", label=\"Injected period = 150 d\")\n",
        "plt.xscale(\"log\")\n",
        "plt.xlabel(\"Period [d]\")\n",
        "plt.ylabel(\"Lomb--Scargle power\")\n",
        "plt.title(f\"1D Lomb--Scargle periodogram for {band0}\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 509
        },
        "id": "H8S_TOiP3n9l",
        "outputId": "99619301-795d-4e91-caa9-adfe667bf142"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Available bands: ['band 0' 'band 1' 'band 2']\n",
            "Selected band: band 0\n",
            "Number of points in 1D light curve: 38\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x450 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Extracting the strongest peaks\n",
        "\n",
        "The previous example used `freq_only=True`, which returns the full frequency grid and the corresponding Lomb--Scargle power. That is useful for plotting the periodogram.\n",
        "\n",
        "Often, however, we only want a compact summary of the strongest candidate periodicities. In that case, we use the default summary mode:\n",
        "\n",
        "- `freq_only=False`\n",
        "- `return_full=False`\n",
        "\n",
        "In this mode, `fit_LS()` returns:\n",
        "\n",
        "- the frequencies of the strongest detected peaks, ordered by decreasing power,\n",
        "- and a boolean mask indicating which of those peaks are considered significant.\n",
        "\n",
        "Since `fit_LS()` works in frequency space, we will explicitly convert the returned peak frequencies to periods before interpreting them."
      ],
      "metadata": {
        "id": "ke8fzgNiFotx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Extract the strongest Lomb--Scargle peaks from the same 1D light curve\n",
        "peak_freqs, signif_mask = lc1d.fit_LS(\n",
        "    freq_only=False,\n",
        "    num_peaks=5,\n",
        "    return_full=False,\n",
        ")\n",
        "\n",
        "peak_periods = 1.0 / peak_freqs\n",
        "\n",
        "print(\"Strongest detected peaks:\")\n",
        "for i, (f, p, is_sig) in enumerate(zip(peak_freqs, peak_periods, signif_mask), start=1):\n",
        "    print(\n",
        "        f\"Peak {i}: \"\n",
        "        f\"frequency = {float(f):.6f}, \"\n",
        "        f\"period = {float(p):.3f} d, \"\n",
        "        f\"significant = {bool(is_sig)}\"\n",
        "    )\n",
        "\n",
        "print(\"\\nInjected period = 150.0 d\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pl-uDyY44l_a",
        "outputId": "89202488-7d89-4208-91c7-6ae3de513ec8"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Strongest detected peaks:\n",
            "Peak 1: frequency = 0.006704, period = 149.171 d, significant = True\n",
            "Peak 2: frequency = 0.039931, period = 25.043 d, significant = False\n",
            "Peak 3: frequency = 0.061499, period = 16.260 d, significant = False\n",
            "Peak 4: frequency = 0.248038, period = 4.032 d, significant = False\n",
            "Peak 5: frequency = 0.069660, period = 14.355 d, significant = False\n",
            "\n",
            "Injected period = 150.0 d\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Returning both the peak summary and the full periodogram\n",
        "\n",
        "In some situations, we want both views of the Lomb--Scargle result at once:\n",
        "\n",
        "- a compact summary of the strongest peaks, and\n",
        "- the full frequency grid and periodogram power for plotting or further analysis.\n",
        "\n",
        "For that, `fit_LS()` provides the option:\n",
        "\n",
        "- `freq_only=False`\n",
        "- `return_full=True`\n",
        "\n",
        "In this mode, the method returns four objects:\n",
        "\n",
        "1. the frequencies of the strongest peaks,\n",
        "2. a boolean mask indicating which of those peaks are significant,\n",
        "3. the full frequency grid,\n",
        "4. and the full Lomb--Scargle power evaluated on that grid.\n",
        "\n",
        "This can be convenient because it avoids having to call `fit_LS()` twice when both the peak summary and the full periodogram are needed."
      ],
      "metadata": {
        "id": "JxN_lrpwGOtd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Return both the peak summary and the full periodogram\n",
        "peak_freqs_full, signif_mask_full, freq_full, power_full = lc1d.fit_LS(\n",
        "    freq_only=False,\n",
        "    num_peaks=5,\n",
        "    return_full=True,\n",
        ")\n",
        "\n",
        "peak_periods_full = 1.0 / peak_freqs_full\n",
        "period_full = 1.0 / freq_full\n",
        "\n",
        "print(\"Peak summary from combined return mode:\")\n",
        "for i, (f, p, is_sig) in enumerate(\n",
        "    zip(peak_freqs_full, peak_periods_full, signif_mask_full),\n",
        "    start=1,\n",
        "):\n",
        "    print(\n",
        "        f\"Peak {i}: \"\n",
        "        f\"frequency = {float(f):.6f}, \"\n",
        "        f\"period = {float(p):.3f} d, \"\n",
        "        f\"significant = {bool(is_sig)}\"\n",
        "    )\n",
        "\n",
        "print(f\"\\nLength of full frequency grid: {len(freq_full)}\")\n",
        "print(f\"Length of full power array:    {len(power_full)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i1F2zfs54mhu",
        "outputId": "2313bd1b-a642-4cd1-e58f-24829264f413"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Peak summary from combined return mode:\n",
            "Peak 1: frequency = 0.006704, period = 149.171 d, significant = True\n",
            "Peak 2: frequency = 0.039931, period = 25.043 d, significant = False\n",
            "Peak 3: frequency = 0.061499, period = 16.260 d, significant = False\n",
            "Peak 4: frequency = 0.248038, period = 4.032 d, significant = False\n",
            "Peak 5: frequency = 0.069660, period = 14.355 d, significant = False\n",
            "\n",
            "Length of full frequency grid: 475\n",
            "Length of full power array:    475\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## How to interpret the outputs\n",
        "\n",
        "Before moving on to more complex cases, it is important to be precise about what `fit_LS()` actually returns and how those outputs should be interpreted.\n",
        "\n",
        "### Frequencies vs periods\n",
        "\n",
        "All outputs from `fit_LS()` are in **frequency space**. This means:\n",
        "\n",
        "- the returned peak values are frequencies,\n",
        "- the period must always be computed explicitly as:\n",
        "\n",
        "  period = 1 / frequency\n",
        "\n",
        "Any scientific interpretation (e.g., comparing with expected pulsation timescales) should be done in period space, not frequency space.\n",
        "\n",
        "### Ordering of peaks\n",
        "\n",
        "The returned peaks are:\n",
        "\n",
        "- ordered by **decreasing Lomb--Scargle power**,\n",
        "- not by frequency or period.\n",
        "\n",
        "This is important because:\n",
        "\n",
        "- the first peak is simply the strongest in the periodogram,\n",
        "- it is not guaranteed to correspond to the physically correct period.\n",
        "\n",
        "### Meaning of the significance mask\n",
        "\n",
        "The boolean array returned alongside the peak frequencies indicates whether each peak passes an internal significance criterion.\n",
        "\n",
        "However:\n",
        "\n",
        "- this is **not a direct p-value**,  \n",
        "- it is the result of a thresholding procedure applied to the Lomb--Scargle false-alarm probabilities.\n",
        "\n",
        "In particular:\n",
        "\n",
        "- significance is determined differently for single-band and multiband cases,\n",
        "- and should be treated as a **heuristic filter**, not a definitive statistical decision.\n",
        "\n",
        "### Practical takeaway\n",
        "\n",
        "- Always convert frequencies to periods before interpretation.\n",
        "- Do not assume that the top-ranked peak is physically correct.\n",
        "- Treat the significance mask as a guide, not a guarantee.\n",
        "\n",
        "In the following sections, we will explore how these issues become more pronounced in multiband data and in realistic sampling conditions."
      ],
      "metadata": {
        "id": "T9zZD6G4GXzn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Multiband Lomb--Scargle in PGMUVI\n",
        "\n",
        "So far, we have treated a single band extracted from a multiband light curve. However, `fit_LS()` can operate directly on the full multiband dataset.\n",
        "\n",
        "In this case:\n",
        "\n",
        "- the input light curve contains multiple bands (stored via the `band` attribute),\n",
        "- the method uses a multiband Lomb--Scargle implementation internally,\n",
        "- and all bands are analyzed simultaneously.\n",
        "\n",
        "This is not equivalent to running Lomb--Scargle independently on each band. Instead, the method attempts to infer a shared periodic signal across bands, while allowing for differences in sampling and amplitude.\n",
        "\n",
        "This can be advantageous when:\n",
        "\n",
        "- individual bands are sparsely sampled,\n",
        "- or when the signal is present across multiple wavelengths but is weak in any one band.\n",
        "\n",
        "In this section, we will:\n",
        "\n",
        "- run `fit_LS()` directly on the full multiband light curve,\n",
        "- inspect the resulting periodogram,\n",
        "- and compare it with the single-band result from earlier."
      ],
      "metadata": {
        "id": "vjm0am4jGgiw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Run Lomb–Scargle directly on the full multiband light curve\n",
        "lc2d = lc2d_synth_1comp\n",
        "\n",
        "# Compute full multiband periodogram\n",
        "freq_mb, power_mb = lc2d.fit_LS(freq_only=True)\n",
        "\n",
        "# Convert to period\n",
        "period_mb = 1.0 / freq_mb\n",
        "\n",
        "# Sort for plotting\n",
        "idx = np.argsort(period_mb)\n",
        "period_mb_sorted = period_mb[idx]\n",
        "power_mb_sorted = power_mb[idx]\n",
        "\n",
        "# Plot multiband periodogram\n",
        "plt.figure(figsize=(7, 4.5))\n",
        "plt.plot(period_mb_sorted, power_mb_sorted, label=\"Multiband LS\")\n",
        "plt.axvline(150.0, linestyle=\"--\", label=\"Injected period = 150 d\")\n",
        "plt.xscale(\"log\")\n",
        "plt.xlabel(\"Period [d]\")\n",
        "plt.ylabel(\"Lomb--Scargle power\")\n",
        "plt.title(\"Multiband Lomb--Scargle periodogram\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "r9sDPFQrGRP-",
        "outputId": "372a9d8e-f0c9-4d2d-aa01-ff26a2122914"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x450 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## How multiband Lomb--Scargle differs from single-band analysis\n",
        "\n",
        "At first glance, applying `fit_LS()` to a multiband light curve may seem like a straightforward extension of the single-band case. In practice, there are several important differences that affect both the results and their interpretation.\n",
        "\n",
        "### Joint analysis across bands\n",
        "\n",
        "In the multiband case:\n",
        "\n",
        "- all bands are analyzed simultaneously,\n",
        "- the method attempts to identify a **shared periodic signal**,\n",
        "- rather than treating each band independently.\n",
        "\n",
        "This means that:\n",
        "\n",
        "- information from well-sampled bands can help constrain poorly sampled ones,\n",
        "- but inconsistencies between bands can also broaden or shift the detected peaks.\n",
        "\n",
        "### Sensitivity to heterogeneous sampling\n",
        "\n",
        "A key issue in multiband datasets is that different bands often have:\n",
        "\n",
        "- different numbers of observations,\n",
        "- different time coverage,\n",
        "- and different noise levels.\n",
        "\n",
        "As a result:\n",
        "\n",
        "- the effective sensitivity of the periodogram can be dominated by one or two bands,\n",
        "- and the resulting peak structure may not reflect all bands equally.\n",
        "\n",
        "This is particularly important in PGMUVI, where multiband light curves are often constructed from heterogeneous surveys.\n",
        "\n",
        "### Interpretation of peaks\n",
        "\n",
        "Compared to the 1D case:\n",
        "\n",
        "- peaks in the multiband periodogram may be broader,\n",
        "- multiple nearby peaks may appear due to competing constraints across bands,\n",
        "- and the highest peak is not necessarily the most physically meaningful solution.\n",
        "\n",
        "### Significance in the multiband case\n",
        "\n",
        "The significance flags returned by `fit_LS()`:\n",
        "\n",
        "- are computed differently in the multiband case,\n",
        "- and should be interpreted with additional caution.\n",
        "\n",
        "In particular:\n",
        "\n",
        "- they do not fully capture inter-band inconsistencies,\n",
        "- and should not be treated as definitive evidence for or against a periodic signal.\n",
        "\n",
        "### Practical takeaway\n",
        "\n",
        "When working with multiband data:\n",
        "\n",
        "- always compare multiband results with single-band results,\n",
        "- inspect multiple peaks, not just the top one,\n",
        "- and consider the sampling properties of each band.\n",
        "\n",
        "In the next section, we will examine one specific option that can strongly affect multiband results: `use_best_band_init`."
      ],
      "metadata": {
        "id": "nvRR2YiMGux-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Effect of `use_best_band_init` on the frequency grid\n",
        "\n",
        "One subtle but important option in `fit_LS()` is:\n",
        "\n",
        "    use_best_band_init=True\n",
        "\n",
        "This affects how the frequency grid is constructed in the multiband case.\n",
        "\n",
        "### Why this matters\n",
        "\n",
        "The Lomb--Scargle periodogram is evaluated on a grid of frequencies. In multiband data, this grid must be chosen based on the sampling properties of the data.\n",
        "\n",
        "By default:\n",
        "\n",
        "- the frequency grid is determined using the combined dataset,\n",
        "- which may include sparsely sampled bands.\n",
        "\n",
        "However, if one band is significantly better sampled than the others, this default choice can:\n",
        "\n",
        "- reduce the effective resolution of the grid,\n",
        "- or bias the search toward the characteristics of the combined sampling rather than the best band.\n",
        "\n",
        "### What `use_best_band_init=True` does\n",
        "\n",
        "When this option is enabled:\n",
        "\n",
        "- the frequency grid is derived from the **best-sampled band**,\n",
        "- and then applied to the full multiband dataset.\n",
        "\n",
        "This can improve:\n",
        "\n",
        "- frequency resolution,\n",
        "- peak sharpness,\n",
        "- and recovery of the true underlying period.\n",
        "\n",
        "### When to use it\n",
        "\n",
        "This option is particularly useful when:\n",
        "\n",
        "- one band clearly dominates in terms of sampling quality,\n",
        "- or when multiband results appear smeared or poorly resolved.\n",
        "\n",
        "In the example below, we compare the multiband periodogram with and without this option."
      ],
      "metadata": {
        "id": "cTWPS3fVG4N8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compare multiband LS with and without use_best_band_init\n",
        "\n",
        "lc2d = lc2d_synth_1comp\n",
        "\n",
        "# Default multiband LS\n",
        "freq_default, power_default = lc2d.fit_LS(freq_only=True)\n",
        "\n",
        "# Best-band-initialized multiband LS\n",
        "freq_best, power_best = lc2d.fit_LS(\n",
        "    freq_only=True,\n",
        "    use_best_band_init=True,\n",
        ")\n",
        "\n",
        "# Convert to periods\n",
        "period_default = 1.0 / freq_default\n",
        "period_best = 1.0 / freq_best\n",
        "\n",
        "# Sort for plotting\n",
        "idx_def = np.argsort(period_default)\n",
        "idx_best = np.argsort(period_best)\n",
        "\n",
        "period_default = period_default[idx_def]\n",
        "power_default = power_default[idx_def]\n",
        "\n",
        "period_best = period_best[idx_best]\n",
        "power_best = power_best[idx_best]\n",
        "\n",
        "# Plot comparison\n",
        "plt.figure(figsize=(7, 4.5))\n",
        "plt.plot(period_default, power_default, label=\"Default multiband LS\")\n",
        "plt.plot(period_best, power_best, linestyle=\"--\", label=\"use_best_band_init=True\")\n",
        "\n",
        "plt.axvline(150.0, linestyle=\":\", label=\"Injected period = 150 d\")\n",
        "\n",
        "plt.xscale(\"log\")\n",
        "plt.xlabel(\"Period [d]\")\n",
        "plt.ylabel(\"Lomb--Scargle power\")\n",
        "plt.title(\"Effect of best-band initialization on multiband LS\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "XWGUqyMDGief",
        "outputId": "69a3b5e8-11c1-496e-a5b8-15ab55ba33b1"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x450 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Quantitative comparison of periodogram peaks\n",
        "\n",
        "The visual comparison above suggests that `use_best_band_init=True` produces a sharper and higher peak at the true period.\n",
        "\n",
        "To make this precise, we can compare:\n",
        "\n",
        "- **peak height**: the maximum Lomb--Scargle power.  \n",
        "  This measures how strong the detected signal is relative to the noise background.\n",
        "\n",
        "- **peak prominence**: how distinct the peak is relative to its surroundings.  \n",
        "  A peak with high prominence stands clearly above neighboring structure, while a low-prominence peak may be part of a broader plateau or contaminated by nearby competing frequencies. This is especially important in irregularly sampled data where aliases and side lobes can appear.\n",
        "\n",
        "- **area fraction**: how concentrated the total power is around the peak.  \n",
        "  This measures the fraction of the total periodogram power contained within a window around the peak. A high area fraction indicates a well-localized, coherent signal, whereas a low value suggests that the power is spread over a wide range of frequencies, which can indicate poor constraint, multiple competing solutions, or long-timescale structure.\n",
        "\n",
        "These metrics help quantify whether a detected period is:\n",
        "\n",
        "- sharply localized (high coherence),\n",
        "- or broad and diffuse (low coherence / possible artifacts).\n",
        "\n",
        "In the following cell, we compute these quantities for both configurations."
      ],
      "metadata": {
        "id": "t1_1cDHtILoF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Quantitative comparison of peak properties\n",
        "\n",
        "from scipy.signal import find_peaks, peak_prominences\n",
        "from scipy.integrate import trapezoid as trapz\n",
        "\n",
        "def compute_peak_metrics(period, power):\n",
        "    # Identify peaks\n",
        "    peaks, _ = find_peaks(power)\n",
        "\n",
        "    if len(peaks) == 0:\n",
        "        return None\n",
        "\n",
        "    # Take the highest peak\n",
        "    peak_idx = peaks[np.argmax(power[peaks])]\n",
        "\n",
        "    peak_height = power[peak_idx]\n",
        "\n",
        "    # Prominence\n",
        "    prominences = peak_prominences(power, peaks)[0]\n",
        "    peak_prominence = prominences[np.argmax(power[peaks])]\n",
        "\n",
        "    # Area fraction: integrate power in a window around the peak\n",
        "    # Define a window of ±10% in period space\n",
        "    p0 = period[peak_idx]\n",
        "    mask = (period > 0.9 * p0) & (period < 1.1 * p0)\n",
        "\n",
        "    area_peak = trapz(power[mask], period[mask])\n",
        "    area_total = trapz(power, period)\n",
        "\n",
        "    area_fraction = area_peak / area_total if area_total > 0 else np.nan\n",
        "\n",
        "    return {\n",
        "        \"peak_period\": p0,\n",
        "        \"peak_height\": peak_height,\n",
        "        \"peak_prominence\": peak_prominence,\n",
        "        \"area_fraction\": area_fraction,\n",
        "    }\n",
        "\n",
        "# Compute metrics\n",
        "metrics_default = compute_peak_metrics(period_default, power_default)\n",
        "metrics_best = compute_peak_metrics(period_best, power_best)\n",
        "\n",
        "print(\"Default multiband LS:\")\n",
        "for k, v in metrics_default.items():\n",
        "    print(f\"  {k}: {float(v):.6f}\")\n",
        "\n",
        "print(\"\\nuse_best_band_init=True:\")\n",
        "for k, v in metrics_best.items():\n",
        "    print(f\"  {k}: {float(v):.6f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MscC0H6LG6U5",
        "outputId": "e4294260-6c97-48c7-be61-36bf06379fc9"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Default multiband LS:\n",
            "  peak_period: 149.170715\n",
            "  peak_height: 0.909449\n",
            "  peak_prominence: 0.579050\n",
            "  area_fraction: 0.016485\n",
            "\n",
            "use_best_band_init=True:\n",
            "  peak_period: 149.170715\n",
            "  peak_height: 0.992789\n",
            "  peak_prominence: 0.859738\n",
            "  area_fraction: 0.020845\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Interpreting the quantitative comparison\n",
        "\n",
        "These results support the visual impression from the previous figure.\n",
        "\n",
        "Both configurations recover essentially the same peak period, about 149.17 d, which is close to the injected 150 d period. The main difference is therefore not the location of the peak, but how clearly and how strongly that peak is represented in the periodogram.\n",
        "\n",
        "In this example, `use_best_band_init=True` gives:\n",
        "\n",
        "- a higher **peak height**,\n",
        "- a higher **peak prominence**,\n",
        "- and a higher **area fraction**.\n",
        "\n",
        "Taken together, this indicates that the signal is not merely detected at the correct period, but is also more sharply localized and more distinct from surrounding structure when the frequency grid is initialized from the best-sampled band. In other words, the periodogram is cleaner and less smeared in the neighborhood of the true solution.\n",
        "\n",
        "However, this does **not** mean that `use_best_band_init=True` should always be expected to perform better.\n",
        "\n",
        "The reason is that this option assumes that the best-sampled band provides the most useful frequency-grid initialization for the full multiband problem. That will often be a good assumption, but not always. Situations that can deviate from this expectation include:\n",
        "\n",
        "- cases where the best-sampled band is also the noisiest band,\n",
        "- cases where that band contains systematics or artifacts not present in the other bands,\n",
        "- cases where another band has fewer points but a much cleaner periodic signal,\n",
        "- or cases where all bands are already sampled similarly well, so that using the best band provides little practical advantage.\n",
        "\n",
        "In such situations, `use_best_band_init=True` can produce little improvement, or in some cases even emphasize a suboptimal part of frequency space.\n",
        "\n",
        "The practical lesson is that `use_best_band_init=True` should be treated as a useful option to test, not as a universally superior setting. In well-behaved heterogeneous datasets such as the present synthetic example, it can sharpen the recovery of the true period. But its effect should always be judged from the resulting periodogram and, when possible, from quantitative diagnostics such as those computed above."
      ],
      "metadata": {
        "id": "10Pj0dS_J4fa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Two-component multiband example\n",
        "\n",
        "So far, we have worked with a mono-periodic light curve. In realistic applications, light curves often contain multiple periodic components.\n",
        "\n",
        "In this section, we construct a synthetic multiband light curve with:\n",
        "\n",
        "- two periodic components,\n",
        "- different amplitudes,\n",
        "- and a phase offset between them.\n",
        "\n",
        "We then modify this setup in an important way: after generating the baseline multiband dataset, we add one extra band with substantially denser sampling than the others.\n",
        "\n",
        "This is done deliberately so that `use_best_band_init=True` has a clearly distinct, most-observed band from which to construct the initial frequency grid. In the earlier version of this example, all bands had roughly similar sampling, which made it difficult to isolate the effect of this option.\n",
        "\n",
        "This provides a more informative test of `fit_LS()`, since:\n",
        "\n",
        "- multiple peaks should appear in the periodogram,\n",
        "- the strongest peak may not correspond to the dominant physical component in all bands,\n",
        "- peak structure can become more complex due to interference between components,\n",
        "- and the effect of `use_best_band_init=True` can be tested in a setting with genuinely heterogeneous sampling.\n",
        "\n",
        "We will:\n",
        "\n",
        "- generate the baseline two-component synthetic dataset,\n",
        "- generate one additional high-sampling band,\n",
        "- merge that band into the multiband light curve,\n",
        "- and then inspect how the multiple periods are recovered with and without `use_best_band_init=True`."
      ],
      "metadata": {
        "id": "ZEyifUG1J_Gg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"Generate a set of light curves with two period components and a phase lag\"\"\"\n",
        "\n",
        "n_per_band = (25, 40)  # baseline sampling\n",
        "\n",
        "MULTI_DATASET_CONFIG = dict(\n",
        "    components=[\n",
        "        {\"period\": 150.0, \"amplitude_fraction\": 1.0, \"phase\": 0.0},\n",
        "        {\"period\": 66.0, \"amplitude_fraction\": 0.3, \"phase\": np.pi / 2 * 0.85},\n",
        "    ],\n",
        "    t_span=150 * 2.3,\n",
        "    n_per_band=n_per_band,\n",
        "    wavelengths=[0.8, 1.2, 2.2],\n",
        "    amplitude_law=\"extinction\",\n",
        "    noise_level=0.05,\n",
        "    seed=SEED,\n",
        ")\n",
        "\n",
        "lc2d_synth_2comp = synthetic.make_multi_sinusoid_chromatic_2d(**MULTI_DATASET_CONFIG)\n",
        "\n",
        "# ------------------------------------------------------------------\n",
        "# Ensure 'band' attribute exists\n",
        "# ------------------------------------------------------------------\n",
        "wavelengths = np.asarray(lc2d_synth_2comp.xdata[:, 1], dtype=float)\n",
        "\n",
        "unique_waves = np.unique(wavelengths)\n",
        "wave_to_band = {w: str(i) for i, w in enumerate(unique_waves)}\n",
        "\n",
        "band = np.array([f\"band {wave_to_band[w]}\" for w in wavelengths], dtype=object)\n",
        "\n",
        "lc2d_synth_2comp.band = band"
      ],
      "metadata": {
        "id": "9DpD7VgzIOKG"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"Generate one additional band with significantly denser sampling\"\"\"\n",
        "\n",
        "n_per_band_hs = (100, 250)\n",
        "\n",
        "HS_DATASET_CONFIG = dict(\n",
        "    components=[\n",
        "        {\"period\": 150.0, \"amplitude_fraction\": 1.0, \"phase\": 0.0},\n",
        "        {\"period\": 66.0, \"amplitude_fraction\": 0.3, \"phase\": np.pi / 2 * 0.85},\n",
        "    ],\n",
        "    t_span=150 * 2.3,\n",
        "    n_per_band=n_per_band_hs,\n",
        "    wavelengths=[1.02],\n",
        "    amplitude_law=\"extinction\",\n",
        "    noise_level=0.05,\n",
        "    seed=SEED + 1,\n",
        ")\n",
        "\n",
        "lc_HS = synthetic.make_multi_sinusoid_chromatic_2d(**HS_DATASET_CONFIG)\n",
        "\n",
        "# ------------------------------------------------------------------\n",
        "# Assign band label explicitly\n",
        "# ------------------------------------------------------------------\n",
        "wavelengths = np.asarray(lc_HS.xdata[:, 1], dtype=float)\n",
        "\n",
        "band = np.repeat(\"band 3\", len(wavelengths))\n",
        "\n",
        "lc_HS.band = band"
      ],
      "metadata": {
        "id": "U0G403x0RHLu"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Merge the high-sampling band into the multiband dataset\n",
        "\n",
        "lc2d_synth_2comp_hs = lc2d_synth_2comp.merge(lc_HS)\n",
        "\n",
        "# Sanity check: count points per band\n",
        "bands = np.unique(lc2d_synth_2comp_hs.band)\n",
        "band_counts = {band: int(np.sum(lc2d_synth_2comp_hs.band == band)) for band in bands}\n",
        "\n",
        "print(\"Band counts after merge:\")\n",
        "for k, v in band_counts.items():\n",
        "    print(f\"  {k}: {v}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mepACP-0OyS7",
        "outputId": "24fe9dbb-62af-4f79-9102-388af9e1522a"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Band counts after merge:\n",
            "  band 0: 38\n",
            "  band 1: 35\n",
            "  band 2: 33\n",
            "  band 3: 171\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Run multiband Lomb–Scargle on the two-component dataset\n",
        "# after adding one extra high-sampling band\n",
        "\n",
        "freq_2c, power_2c = lc2d_synth_2comp_hs.fit_LS(freq_only=True)\n",
        "\n",
        "period_2c = 1.0 / freq_2c\n",
        "\n",
        "# Sort for plotting\n",
        "idx = np.argsort(period_2c)\n",
        "period_2c = period_2c[idx]\n",
        "power_2c = power_2c[idx]\n",
        "\n",
        "# Plot\n",
        "plt.figure(figsize=(7, 4.5))\n",
        "plt.plot(period_2c, power_2c)\n",
        "\n",
        "plt.axvline(150.0, linestyle=\"--\", label=\"Component 1: 150 d\")\n",
        "plt.axvline(66.0, linestyle=\"--\", label=\"Component 2: 66 d\")\n",
        "\n",
        "plt.xscale(\"log\")\n",
        "plt.xlabel(\"Period [d]\")\n",
        "plt.ylabel(\"Lomb--Scargle power\")\n",
        "plt.title(\"Multiband Lomb--Scargle (two-component signal + high-sampling band)\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "wzjigr8VKBgd",
        "outputId": "e2bfde8e-8ee9-4d46-9275-731c8d71fe41"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x450 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comparing the two-component case with and without `use_best_band_init`\n",
        "\n",
        "We now compare the multiband Lomb--Scargle periodogram for the merged dataset:\n",
        "\n",
        "- once using the default initialization, and\n",
        "- once using `use_best_band_init=True`.\n",
        "\n",
        "This comparison is now more informative than before, because the dataset has been constructed to include one clearly distinct, high-sampling band.\n",
        "\n",
        "In the current implementation, `use_best_band_init=True` selects the band with the largest number of observations and uses that band to define the initial frequency grid. Since we explicitly added such a band, this example provides a cleaner test of how that choice affects the recovery of the periodic components.\n",
        "\n",
        "For a two-component signal, this comparison is useful because it can affect:\n",
        "\n",
        "- how sharply the dominant component is localized,\n",
        "- how clearly the weaker component is separated from nearby structure,\n",
        "- and how much additional fine-scale structure appears elsewhere in the periodogram.\n",
        "\n",
        "In the next cell, we compare the two periodograms directly."
      ],
      "metadata": {
        "id": "yNeEEcPlKQYP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compare the two-component multiband LS periodogram\n",
        "# with and without use_best_band_init\n",
        "\n",
        "lc2d = lc2d_synth_2comp_hs\n",
        "\n",
        "# Default multiband LS\n",
        "freq_2c_default, power_2c_default = lc2d.fit_LS(freq_only=True)\n",
        "\n",
        "# Best-band-initialized multiband LS\n",
        "freq_2c_best, power_2c_best = lc2d.fit_LS(\n",
        "    freq_only=True,\n",
        "    use_best_band_init=True,\n",
        ")\n",
        "\n",
        "# Convert to periods\n",
        "period_2c_default = 1.0 / freq_2c_default\n",
        "period_2c_best = 1.0 / freq_2c_best\n",
        "\n",
        "# Sort for plotting\n",
        "idx_def = np.argsort(period_2c_default)\n",
        "idx_best = np.argsort(period_2c_best)\n",
        "\n",
        "period_2c_default = period_2c_default[idx_def]\n",
        "power_2c_default = power_2c_default[idx_def]\n",
        "\n",
        "period_2c_best = period_2c_best[idx_best]\n",
        "power_2c_best = power_2c_best[idx_best]\n",
        "\n",
        "# Plot comparison\n",
        "plt.figure(figsize=(7, 4.5))\n",
        "plt.plot(period_2c_default, power_2c_default, label=\"Default multiband LS\")\n",
        "plt.plot(period_2c_best, power_2c_best, linestyle=\"--\", label=\"use_best_band_init=True\")\n",
        "\n",
        "plt.axvline(150.0, linestyle=\":\", label=\"Component 1: 150 d\")\n",
        "plt.axvline(66.0, linestyle=\":\", label=\"Component 2: 66 d\")\n",
        "\n",
        "plt.xscale(\"log\")\n",
        "plt.xlabel(\"Period [d]\")\n",
        "plt.ylabel(\"Lomb--Scargle power\")\n",
        "plt.title(\"Two-component multiband LS with a high-sampling band\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "oekJErU2KQF5",
        "outputId": "4fe3d1cd-9ee4-436f-aeca-f0a565605bb7"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x450 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Interpreting the two-component comparison with a high-sampling band\n",
        "\n",
        "In this modified example, we have explicitly introduced a band with substantially denser sampling than the others. As a result, `use_best_band_init=True` now selects a band that genuinely provides finer temporal resolution than the rest of the dataset.\n",
        "\n",
        "This produces a noticeably different behavior compared to the earlier case with nearly uniform sampling.\n",
        "\n",
        "### Dominant component (~150 d)\n",
        "\n",
        "The dominant peak near 150 d is:\n",
        "\n",
        "- slightly higher,\n",
        "- and more sharply localized\n",
        "\n",
        "when `use_best_band_init=True` is used.\n",
        "\n",
        "This is consistent with the expectation that a better-sampled band can provide a more refined frequency grid, allowing the periodogram to localize the strongest signal more precisely.\n",
        "\n",
        "### Secondary component (~66 d)\n",
        "\n",
        "The behavior of the secondary component is less encouraging.\n",
        "\n",
        "- The peak near 66 d is present in both cases,\n",
        "- but it is not clearly better isolated when `use_best_band_init=True` is used.\n",
        "\n",
        "In particular:\n",
        "\n",
        "- the dip on the lower-period side is not substantially improved,\n",
        "- and on the higher-period side, competing structure becomes more prominent, especially around periods near 100 d.\n",
        "\n",
        "This means that, in this example, the improved sampling of the selected band helps the dominant component much more than the weaker one. For the secondary signal, the local periodogram structure remains ambiguous and may even become slightly harder to interpret because nearby competing power is enhanced.\n",
        "\n",
        "### Short-period region\n",
        "\n",
        "A key difference appears at short periods:\n",
        "\n",
        "- the default multiband periodogram shows substantial power and structure,\n",
        "- while the `use_best_band_init=True` curve is strongly suppressed in this region.\n",
        "\n",
        "This suggests that the frequency grid inherited from the high-sampling band reduces spurious short-period structure that is present when the combined multiband sampling is used directly.\n",
        "\n",
        "### Overall interpretation\n",
        "\n",
        "In this case, `use_best_band_init=True` provides a selective improvement:\n",
        "\n",
        "- the dominant peak is better localized,\n",
        "- the short-period region is cleaner,\n",
        "- but the weaker component near 66 d is not clearly improved and remains entangled with nearby competing structure.\n",
        "\n",
        "This is an important practical lesson. Even when one band is substantially better sampled than the others, `use_best_band_init=True` does not guarantee uniformly better recovery of all periodic components. It can sharpen the strongest signal while leaving weaker components ambiguous, or even shifting the balance among nearby competing peaks.\n",
        "\n",
        "This example therefore illustrates both the utility and the limitations of the option in a realistic multicomponent setting."
      ],
      "metadata": {
        "id": "ADA1iwJeKeGN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comparing sampling metrics for the multiband light curve and the high-sampling band\n",
        "\n",
        "To understand the behavior of `use_best_band_init=True` in this modified example, we compare the sampling properties of:\n",
        "\n",
        "- the full multiband light curve, and  \n",
        "- the high-sampling band that we explicitly added.\n",
        "\n",
        "Unlike the earlier version of this example, the dataset now contains one band with substantially more observations than the others. In the current implementation, `use_best_band_init=True` selects the band with the largest number of observations and uses it to construct the initial frequency grid.\n",
        "\n",
        "This makes it important to verify that the selected band is indeed distinct in its sampling properties, and to understand how its cadence compares to that of the full dataset.\n",
        "\n",
        "In the cell below, we compute and print sampling metrics for:\n",
        "\n",
        "- the full multiband light curve, and  \n",
        "- the high-sampling band alone.\n",
        "\n",
        "We will examine:\n",
        "\n",
        "- `n_points` — total number of observations,  \n",
        "- `baseline` — total time span,  \n",
        "- `median_cadence` and `mean_cadence`,  \n",
        "- `nyquist_period` and `nyquist_frequency`,  \n",
        "- `longest_detectable_period`,  \n",
        "- `max_gap_fraction`,  \n",
        "- `duty_cycle`,  \n",
        "- `sampling_uniformity`.\n",
        "\n",
        "These quantities help clarify whether the selected band provides genuinely finer temporal resolution, and whether the resulting frequency grid is better matched to the dominant signal or potentially misaligned with the rest of the dataset.\n",
        "\n",
        "In particular, the comparison allows us to determine whether:\n",
        "\n",
        "- the high-sampling band supports shorter timescales than the combined dataset,  \n",
        "- or whether the combined multiband sampling already provides comparable or superior coverage.\n",
        "\n",
        "This distinction is crucial for interpreting how `use_best_band_init=True` affects both the dominant peak and the surrounding periodogram structure."
      ],
      "metadata": {
        "id": "Yj8hAGjZNPcV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compare sampling metrics for:\n",
        "#   (1) the full multiband light curve\n",
        "#   (2) the high-sampling band\n",
        "\n",
        "lc2d = lc2d_synth_2comp_hs\n",
        "\n",
        "# Metrics for the full multiband light curve\n",
        "metrics_full = lc2d.compute_sampling_metrics()\n",
        "\n",
        "# Explicitly select the high-sampling band\n",
        "hs_band = \"band 3\"\n",
        "lc_hs_only = lc2d.select_bands([hs_band])\n",
        "\n",
        "metrics_hs = lc_hs_only.compute_sampling_metrics()\n",
        "\n",
        "# Count points per band (sanity check)\n",
        "bands = np.unique(lc2d.band)\n",
        "band_counts = {band: int(np.sum(lc2d.band == band)) for band in bands}\n",
        "\n",
        "print(\"Band counts:\")\n",
        "for k, v in band_counts.items():\n",
        "    print(f\"  {k}: {v}\")\n",
        "\n",
        "print(f\"\\nHigh-sampling band used for initialization: {hs_band}\")\n",
        "\n",
        "keys_to_show = [\n",
        "    \"n_points\",\n",
        "    \"baseline\",\n",
        "    \"median_cadence\",\n",
        "    \"mean_cadence\",\n",
        "    \"cadence_std\",\n",
        "    \"nyquist_period\",\n",
        "    \"nyquist_frequency\",\n",
        "    \"longest_detectable_period\",\n",
        "    \"max_gap_fraction\",\n",
        "    \"duty_cycle\",\n",
        "    \"sampling_uniformity\",\n",
        "]\n",
        "\n",
        "print(\"\\nSampling metrics: full multiband light curve\")\n",
        "for key in keys_to_show:\n",
        "    value = metrics_full.get(key, None)\n",
        "    if isinstance(value, (int, np.integer)):\n",
        "        print(f\"  {key}: {value}\")\n",
        "    elif isinstance(value, (float, np.floating)):\n",
        "        print(f\"  {key}: {value:.6f}\")\n",
        "    else:\n",
        "        print(f\"  {key}: {value}\")\n",
        "\n",
        "print(\"\\nSampling metrics: high-sampling band only\")\n",
        "for key in keys_to_show:\n",
        "    value = metrics_hs.get(key, None)\n",
        "    if isinstance(value, (int, np.integer)):\n",
        "        print(f\"  {key}: {value}\")\n",
        "    elif isinstance(value, (float, np.floating)):\n",
        "        print(f\"  {key}: {value:.6f}\")\n",
        "    else:\n",
        "        print(f\"  {key}: {value}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JwOVOU6fKDb2",
        "outputId": "6fc2a89b-8604-4854-cfce-73b6fc5888d4"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Band counts:\n",
            "  band 0: 38\n",
            "  band 1: 35\n",
            "  band 2: 33\n",
            "  band 3: 171\n",
            "\n",
            "High-sampling band used for initialization: band 3\n",
            "\n",
            "Sampling metrics: full multiband light curve\n",
            "  n_points: 277\n",
            "  baseline: 343.092621\n",
            "  median_cadence: 0.876945\n",
            "  mean_cadence: 1.243089\n",
            "  cadence_std: 1.300868\n",
            "  nyquist_period: 1.753891\n",
            "  nyquist_frequency: 0.570161\n",
            "  longest_detectable_period: 171.546310\n",
            "  max_gap_fraction: 0.027257\n",
            "  duty_cycle: 0.708013\n",
            "  sampling_uniformity: 0.000000\n",
            "\n",
            "Sampling metrics: high-sampling band only\n",
            "  n_points: 171\n",
            "  baseline: 341.659210\n",
            "  median_cadence: 1.448767\n",
            "  mean_cadence: 2.009760\n",
            "  cadence_std: 1.820683\n",
            "  nyquist_period: 2.897533\n",
            "  nyquist_frequency: 0.345121\n",
            "  longest_detectable_period: 170.829605\n",
            "  max_gap_fraction: 0.027371\n",
            "  duty_cycle: 0.725106\n",
            "  sampling_uniformity: 0.094079\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## How to interpret these sampling metrics\n",
        "\n",
        "These metrics show that the added high-sampling band is indeed the most heavily observed individual band in the dataset:\n",
        "\n",
        "- it has 171 points,\n",
        "- whereas the original bands have only 33--38 points each.\n",
        "\n",
        "This confirms that `use_best_band_init=True` is selecting a band that is genuinely distinct in terms of the number of observations.\n",
        "\n",
        "However, the cadence-based metrics show a more subtle result.\n",
        "\n",
        "Although the high-sampling band is much denser than any of the original bands individually, the **full multiband light curve** still has:\n",
        "\n",
        "- a smaller `median_cadence`*,\n",
        "- a smaller `nyquist_period`,\n",
        "- and therefore a higher `nyquist_frequency`\n",
        "\n",
        "than the high-sampling band alone.\n",
        "\n",
        "This happens because the multiband dataset combines observations from all bands, so the joint sampling can interleave measurements in time and effectively probe shorter timescales than any one band by itself.\n",
        "\n",
        "This is important for interpreting `use_best_band_init=True`.\n",
        "\n",
        "In the current implementation, that option does **not** choose the band with the finest cadence or the highest Nyquist frequency. It chooses the band with the largest number of observations. In this example, that is the high-sampling band we added, but that band still does not surpass the full multiband dataset in terms of cadence-based frequency reach.\n",
        "\n",
        "This helps explain the behavior seen in the comparison plot.\n",
        "\n",
        "Using `use_best_band_init=True` still sharpens the dominant peak near 150 d, which suggests that the initialization inherited from the high-sampling band is beneficial for localizing the strongest signal. However, this improvement does not come from extending the accessible high-frequency range beyond that of the full dataset. Instead, it likely reflects the fact that the selected band provides a cleaner or more stable basis for constructing the initial frequency grid around the dominant variability timescale.\n",
        "\n",
        "At the same time, the weaker component near 66 d is not clearly improved, and nearby competing structure remains significant. This is consistent with the idea that selecting the most-observed band can help the dominant signal without guaranteeing uniformly better recovery across the whole periodogram.\n",
        "\n",
        "The broader lesson is therefore:\n",
        "\n",
        "- `use_best_band_init=True` selects the most-observed band,\n",
        "- not necessarily the band with the finest cadence,\n",
        "- and not necessarily the band that supports the highest frequencies.\n",
        "\n",
        "Its effect depends on how the sampling pattern of that band interacts with the structure of the signal of interest. In this example, it helps the dominant period, but the sampling metrics show that its advantage is more subtle than simply providing the finest temporal resolution in the dataset.\n",
        "\n",
        "\n",
        "* Note: if a light curve has many repeated timestamps, the median cadence is artifically estimated to be very low or even zero. In such cases, it is better to use the mean cadence."
      ],
      "metadata": {
        "id": "ZuUrbym9Njsw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## How `fit_LS()` determines significance\n",
        "\n",
        "The boolean significance mask returned by `fit_LS()` is not a generic by-product of Lomb--Scargle. It is constructed explicitly by the current PGMUVI implementation.\n",
        "\n",
        "The logic differs slightly between single-band and multiband light curves, but both follow the same overall structure:\n",
        "\n",
        "1. compute the full periodogram,  \n",
        "2. identify candidate peaks,  \n",
        "3. test whether the strongest peak is significant as a **global detection**,  \n",
        "4. and, if so, assess the returned peaks individually using a multiple-testing correction.\n",
        "\n",
        "### Single-band case\n",
        "\n",
        "For a 1D light curve, the implementation proceeds as follows:\n",
        "\n",
        "- the Lomb--Scargle periodogram is computed,\n",
        "- peaks are identified,\n",
        "- the false-alarm probability (FAP) of the **maximum peak** is evaluated using:\n",
        "\n",
        "  - `astropy.timeseries.LombScargle.false_alarm_probability()`  \n",
        "  - with the default global method: `fap_method='davies'`\n",
        "\n",
        "If the global FAP of the highest peak exceeds `single_threshold`, then:\n",
        "\n",
        "- all returned peaks are marked as not significant.\n",
        "\n",
        "If the highest peak passes the global test, then:\n",
        "\n",
        "- FAP values are computed for each detected peak using `method='single'`,  \n",
        "- and a **Benjamini--Hochberg false-discovery-rate correction** is applied across those peaks.\n",
        "\n",
        "This is important:\n",
        "\n",
        "- the significance mask is not based directly on power,  \n",
        "- and it is not obtained by applying a single global threshold to all peaks.\n",
        "\n",
        "Instead, it combines:\n",
        "\n",
        "- a global detection test on the strongest peak,  \n",
        "- followed by a multiple-testing correction across the candidate peaks.\n",
        "\n",
        "### Multiband case\n",
        "\n",
        "For multiband light curves, the logic is analogous but uses the multiband significance wrapper.\n",
        "\n",
        "By default:\n",
        "\n",
        "- the global false-alarm probability is computed using `fap_method='phase_scramble'`.\n",
        "\n",
        "As in the single-band case:\n",
        "\n",
        "- if the strongest peak fails the global test, all peaks are marked insignificant,  \n",
        "- if it passes, per-peak FAP values are computed and a **Benjamini--Hochberg correction** is applied.\n",
        "\n",
        "### Practical implication\n",
        "\n",
        "The returned significance mask should be interpreted as:\n",
        "\n",
        "- a **code-level screening result** based on the current PGMUVI procedure,\n",
        "\n",
        "not as a definitive statement that a peak is physically real.\n",
        "\n",
        "A peak can be marked significant and still be scientifically dubious if:\n",
        "\n",
        "- the sampling is poor,  \n",
        "- aliases are present,  \n",
        "- long-timescale structure contaminates the periodogram,  \n",
        "- or nearby competing peaks make the interpretation ambiguous.\n",
        "\n",
        "In the next cell, we inspect the significance masks returned for the examples developed above."
      ],
      "metadata": {
        "id": "2QzcTapK20kZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Inspect the significance masks returned by fit_LS()\n",
        "# for the 1D example and for the multiband two-component example\n",
        "\n",
        "print(\"1D example\")\n",
        "peak_freqs_1d, signif_1d = lc1d.fit_LS(\n",
        "    freq_only=False,\n",
        "    num_peaks=5,\n",
        "    return_full=False,\n",
        ")\n",
        "\n",
        "peak_periods_1d = 1.0 / peak_freqs_1d\n",
        "\n",
        "for i, (f, p, s) in enumerate(zip(peak_freqs_1d, peak_periods_1d, signif_1d), start=1):\n",
        "    print(\n",
        "        f\"  Peak {i}: \"\n",
        "        f\"frequency = {float(f):.6f}, \"\n",
        "        f\"period = {float(p):.3f} d, \"\n",
        "        f\"significant = {bool(s)}\"\n",
        "    )\n",
        "\n",
        "print(\"\\nMultiband two-component example\")\n",
        "peak_freqs_mb, signif_mb = lc2d.fit_LS(\n",
        "    freq_only=False,\n",
        "    num_peaks=8,\n",
        "    return_full=False,\n",
        ")\n",
        "\n",
        "peak_periods_mb = 1.0 / peak_freqs_mb\n",
        "\n",
        "for i, (f, p, s) in enumerate(zip(peak_freqs_mb, peak_periods_mb, signif_mb), start=1):\n",
        "    print(\n",
        "        f\"  Peak {i}: \"\n",
        "        f\"frequency = {float(f):.6f}, \"\n",
        "        f\"period = {float(p):.3f} d, \"\n",
        "        f\"significant = {bool(s)}\"\n",
        "    )"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ubRiAjtTNSOj",
        "outputId": "878c87cd-93a5-4b53-b75e-6c4ccc82140c"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1D example\n",
            "  Peak 1: frequency = 0.006704, period = 149.171 d, significant = True\n",
            "  Peak 2: frequency = 0.039931, period = 25.043 d, significant = False\n",
            "  Peak 3: frequency = 0.061499, period = 16.260 d, significant = False\n",
            "  Peak 4: frequency = 0.248038, period = 4.032 d, significant = False\n",
            "  Peak 5: frequency = 0.069660, period = 14.355 d, significant = False\n",
            "\n",
            "Multiband two-component example\n",
            "  Peak 1: frequency = 0.006704, period = 149.171 d, significant = True\n",
            "  Peak 2: frequency = 1.908814, period = 0.524 d, significant = False\n",
            "  Peak 3: frequency = 1.112528, period = 0.899 d, significant = False\n",
            "  Peak 4: frequency = 1.148086, period = 0.871 d, significant = False\n",
            "  Peak 5: frequency = 1.134096, period = 0.882 d, significant = False\n",
            "  Peak 6: frequency = 1.381843, period = 0.724 d, significant = False\n",
            "  Peak 7: frequency = 0.787834, period = 1.269 d, significant = False\n",
            "  Peak 8: frequency = 0.014865, period = 67.273 d, significant = False\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Interpreting these significance masks\n",
        "\n",
        "These outputs show which peaks pass the current significance procedure implemented in `fit_LS()`. They are useful for quickly screening candidate periods, but they should not be treated as a substitute for scientific judgment.\n",
        "\n",
        "In particular:\n",
        "\n",
        "- a peak marked significant is not automatically the physically correct solution,\n",
        "- a peak marked insignificant is not always scientifically irrelevant,\n",
        "- and the interpretation becomes especially delicate in multicomponent or irregularly sampled datasets.\n",
        "\n",
        "This is why, throughout this notebook, the significance mask should be interpreted together with:\n",
        "\n",
        "- the visual structure of the periodogram,\n",
        "- the known injected periods in the synthetic examples,\n",
        "- and the temporal sampling metrics of the data."
      ],
      "metadata": {
        "id": "HH5SJHhJ25ba"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Relationship to Gaussian Process (GP) modeling in PGMUVI\n",
        "\n",
        "In PGMUVI, Lomb--Scargle analysis is not typically the final step in period inference. Instead, it is most useful as a **diagnostic and initialization tool** for more flexible models based on Gaussian processes (GPs).\n",
        "\n",
        "### Different roles of LS and GP models\n",
        "\n",
        "Lomb--Scargle and GP models answer related but distinct questions:\n",
        "\n",
        "- **Lomb--Scargle**:\n",
        "  - identifies periodic structure through sinusoidal decomposition,\n",
        "  - is fast and interpretable,\n",
        "  - but assumes relatively simple signal structure.\n",
        "\n",
        "- **GP models** (e.g., spectral mixture kernels):\n",
        "  - model the full covariance structure of the variability,\n",
        "  - can represent multiple timescales and quasi-periodic behavior,\n",
        "  - and can account for noise and irregular sampling more flexibly.\n",
        "\n",
        "### Using LS to initialize GP models\n",
        "\n",
        "A common workflow in PGMUVI is:\n",
        "\n",
        "1. run `fit_LS()` on the light curve,\n",
        "2. extract the strongest candidate frequencies,\n",
        "3. use those frequencies to initialize the GP kernel (e.g., mixture means in a spectral mixture model).\n",
        "\n",
        "This can significantly improve:\n",
        "\n",
        "- convergence speed,\n",
        "- stability of the optimization,\n",
        "- and interpretability of the resulting GP model.\n",
        "\n",
        "### Important caveat\n",
        "\n",
        "The periods identified by Lomb--Scargle are **not guaranteed to match** the dominant timescales inferred by the GP model.\n",
        "\n",
        "This is especially true when:\n",
        "\n",
        "- the signal is multi-component,\n",
        "- the data are irregularly sampled,\n",
        "- or long-timescale structure is present.\n",
        "\n",
        "In such cases:\n",
        "\n",
        "- LS may identify a broad or shifted peak,\n",
        "- while the GP model may converge to a different effective timescale.\n",
        "\n",
        "### Practical takeaway\n",
        "\n",
        "Lomb--Scargle should be used as:\n",
        "\n",
        "- a **guide to candidate periodicities**,  \n",
        "- not as a definitive answer.\n",
        "\n",
        "In practice, it is best to:\n",
        "\n",
        "- compare LS-derived periods with GP-inferred timescales,  \n",
        "- examine multiple candidate peaks,  \n",
        "- and interpret both in the context of the sampling properties of the data."
      ],
      "metadata": {
        "id": "UkF5r07VPIR4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: using LS peaks as candidate periods for further modeling\n",
        "\n",
        "peak_freqs, signif = lc2d_synth_2comp_hs.fit_LS(\n",
        "    freq_only=False,\n",
        "    num_peaks=5,\n",
        ")\n",
        "\n",
        "peak_periods = 1.0 / peak_freqs\n",
        "\n",
        "print(\"Candidate periods from LS (for GP initialization):\")\n",
        "for p, s in zip(peak_periods, signif):\n",
        "    print(f\"  period = {float(p):.3f} d, significant = {bool(s)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "heLlGpOt23Op",
        "outputId": "4b6c0b4f-828f-4f3d-fd3c-847fb7419db7"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Candidate periods from LS (for GP initialization):\n",
            "  period = 149.171 d, significant = True\n",
            "  period = 0.524 d, significant = False\n",
            "  period = 0.899 d, significant = False\n",
            "  period = 0.871 d, significant = False\n",
            "  period = 0.882 d, significant = False\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Summary and takeaways\n",
        "\n",
        "This notebook has explored the behavior of `Lightcurve.fit_LS()` in PGMUVI through a series of controlled examples.\n",
        "\n",
        "### What `fit_LS()` does well\n",
        "\n",
        "- Provides a fast and interpretable way to identify candidate periodicities.\n",
        "- Works for both single-band and multiband light curves.\n",
        "- Can recover dominant periodic components reliably, even in moderately noisy data.\n",
        "- Offers useful summary outputs (peak frequencies and significance masks) in addition to the full periodogram.\n",
        "\n",
        "### Key points about interpretation\n",
        "\n",
        "- All outputs are in **frequency space**; interpretation should be done in terms of periods.\n",
        "- Peaks are ordered by **power**, not by physical relevance.\n",
        "- The significance mask reflects a **specific statistical procedure**, not a guarantee of physical reality.\n",
        "- Multiple peaks should always be considered, especially in multicomponent signals.\n",
        "\n",
        "### Multiband-specific considerations\n",
        "\n",
        "- Multiband Lomb--Scargle combines information across bands and can improve sensitivity.\n",
        "- However, heterogeneous sampling can:\n",
        "  - broaden peaks,\n",
        "  - introduce competing structure,\n",
        "  - and complicate interpretation.\n",
        "\n",
        "- The option `use_best_band_init=True`:\n",
        "  - selects the band with the largest number of observations,\n",
        "  - can sharpen the dominant peak,\n",
        "  - but does not guarantee improved recovery of weaker components,\n",
        "  - and its effect depends on how that band’s sampling compares to the full dataset.\n",
        "\n",
        "### Role of sampling\n",
        "\n",
        "- Sampling properties strongly influence the periodogram.\n",
        "- Important diagnostics include:\n",
        "  - cadence,\n",
        "  - Nyquist frequency,\n",
        "  - baseline,\n",
        "  - and gap structure.\n",
        "\n",
        "- Combining multiple bands can sometimes provide **better effective cadence** than any individual band.\n",
        "\n",
        "### Relationship to GP modeling\n",
        "\n",
        "- Lomb--Scargle is best used as a **diagnostic and initialization step**.\n",
        "- GP models provide a more flexible and physically meaningful description of variability.\n",
        "- LS-derived periods should be treated as **candidate timescales**, not final answers.\n",
        "\n",
        "### Final takeaway\n",
        "\n",
        "`fit_LS()` is a powerful and convenient tool within PGMUVI, but its outputs must be interpreted carefully.\n",
        "\n",
        "In practice:\n",
        "\n",
        "- inspect the full periodogram,\n",
        "- examine multiple peaks,\n",
        "- consider sampling metrics,\n",
        "- and compare results with more flexible models.\n",
        "\n",
        "Used in this way, Lomb--Scargle analysis provides a strong foundation for more advanced time-series modeling."
      ],
      "metadata": {
        "id": "KrGyAY6rXFe2"
      }
    }
  ]
}