{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 2 — Reading a Star with Linear Algebra\n",
    "\n",
    "## Goal\n",
    "\n",
    "Create a calibrated toy spectrum, infer absorption-feature strengths with least squares, and see how noise and blended features limit the claim.\n",
    "\n",
    "This is a simplified forward-modeling exercise—not a full abundance analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "A real detector starts with counts on pixels. Here we begin after wavelength and continuum calibration. The synthetic spectrum contains sodium-like and hydrogen-alpha-like absorption features plus Gaussian measurement noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.430051Z",
     "iopub.status.busy": "2026-07-29T07:42:48.429882Z",
     "iopub.status.idle": "2026-07-29T07:42:48.632838Z",
     "shell.execute_reply": "2026-07-29T07:42:48.632420Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "RNG = np.random.default_rng(20260729)\n",
    "\n",
    "def gaussian_profile(wavelength, center, width):\n",
    "    return np.exp(-0.5 * ((wavelength - center) / width) ** 2)\n",
    "\n",
    "wavelength_nm = np.linspace(575.0, 665.0, 1400)\n",
    "sodium_profile = gaussian_profile(wavelength_nm, 589.2, 0.22)\n",
    "hydrogen_profile = gaussian_profile(wavelength_nm, 656.28, 0.34)\n",
    "\n",
    "true_continuum = 1.0\n",
    "true_depths = np.array([0.14, 0.24])\n",
    "noise_sigma = 0.008\n",
    "noiseless_flux = (\n",
    "    true_continuum\n",
    "    - true_depths[0] * sodium_profile\n",
    "    - true_depths[1] * hydrogen_profile\n",
    ")\n",
    "observed_flux = noiseless_flux + RNG.normal(0.0, noise_sigma, wavelength_nm.size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steps\n",
    "\n",
    "### 1. Inspect the measurement\n",
    "\n",
    "Never fit before looking. Ask whether the wavelength range, sampling, and flux scale are plausible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.634254Z",
     "iopub.status.busy": "2026-07-29T07:42:48.634130Z",
     "iopub.status.idle": "2026-07-29T07:42:48.694406Z",
     "shell.execute_reply": "2026-07-29T07:42:48.693932Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axis = plt.subplots(figsize=(10, 4))\n",
    "axis.plot(wavelength_nm, observed_flux, color=\"slateblue\", linewidth=1, label=\"observed\")\n",
    "axis.set(xlabel=\"wavelength [nm]\", ylabel=\"continuum-normalized flux\",\n",
    "         title=\"Synthetic stellar spectrum\")\n",
    "axis.set_ylim(0.70, 1.04)\n",
    "axis.grid(alpha=0.2)\n",
    "axis.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Build the design matrix and fit\n",
    "\n",
    "The model is `continuum - sodium_depth * sodium_profile - hydrogen_depth * hydrogen_profile`. Each model component is one matrix column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.695685Z",
     "iopub.status.busy": "2026-07-29T07:42:48.695587Z",
     "iopub.status.idle": "2026-07-29T07:42:48.698549Z",
     "shell.execute_reply": "2026-07-29T07:42:48.698143Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continuum                  : 1.0005\n",
      "sodium-like depth          : 0.1406\n",
      "hydrogen-alpha-like depth  : 0.2404\n",
      "matrix rank: 3\n",
      "condition number: 15.3\n"
     ]
    }
   ],
   "source": [
    "design_matrix = np.column_stack([\n",
    "    np.ones_like(wavelength_nm),\n",
    "    -sodium_profile,\n",
    "    -hydrogen_profile,\n",
    "])\n",
    "fit_parameters, residual_sum, rank, singular_values = np.linalg.lstsq(\n",
    "    design_matrix, observed_flux, rcond=None\n",
    ")\n",
    "fitted_flux = design_matrix @ fit_parameters\n",
    "\n",
    "parameter_names = [\"continuum\", \"sodium-like depth\", \"hydrogen-alpha-like depth\"]\n",
    "for name, value in zip(parameter_names, fit_parameters):\n",
    "    print(f\"{name:27s}: {value:.4f}\")\n",
    "print(f\"matrix rank: {rank}\")\n",
    "print(f\"condition number: {np.linalg.cond(design_matrix):.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Examine model and residuals\n",
    "\n",
    "Residuals should look structureless if the signal model is adequate and the noise model is reasonable. Patterns would be evidence that the model omitted physics or calibration effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.699613Z",
     "iopub.status.busy": "2026-07-29T07:42:48.699517Z",
     "iopub.status.idle": "2026-07-29T07:42:48.765837Z",
     "shell.execute_reply": "2026-07-29T07:42:48.765429Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "residual standard deviation: 0.0079\n",
      "injected noise standard deviation: 0.0080\n"
     ]
    }
   ],
   "source": [
    "residuals = observed_flux - fitted_flux\n",
    "fig, axes = plt.subplots(2, 1, figsize=(10, 6), sharex=True, height_ratios=[3, 1])\n",
    "axes[0].plot(wavelength_nm, observed_flux, color=\"slateblue\", linewidth=0.8, label=\"observed\")\n",
    "axes[0].plot(wavelength_nm, fitted_flux, color=\"darkorange\", linewidth=2, label=\"fit\")\n",
    "axes[0].set(ylabel=\"normalized flux\", title=\"Forward model and fitted spectrum\")\n",
    "axes[0].legend()\n",
    "axes[1].plot(wavelength_nm, residuals, color=\"black\", linewidth=0.7)\n",
    "axes[1].axhline(0, color=\"darkorange\", linewidth=1)\n",
    "axes[1].set(xlabel=\"wavelength [nm]\", ylabel=\"residual\")\n",
    "for axis in axes:\n",
    "    axis.grid(alpha=0.2)\n",
    "plt.show()\n",
    "\n",
    "print(f\"residual standard deviation: {np.std(residuals, ddof=3):.4f}\")\n",
    "print(f\"injected noise standard deviation: {noise_sigma:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Turn noise into parameter uncertainty\n",
    "\n",
    "For independent equal-variance Gaussian noise, the covariance estimate is $\\sigma^2(A^TA)^{-1}$. This assumption is convenient; real spectra may have correlated noise and additional systematics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.767127Z",
     "iopub.status.busy": "2026-07-29T07:42:48.767035Z",
     "iopub.status.idle": "2026-07-29T07:42:48.769120Z",
     "shell.execute_reply": "2026-07-29T07:42:48.768744Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continuum                  : 1.0005 ± 0.0002\n",
      "sodium-like depth          : 0.1406 ± 0.0032\n",
      "hydrogen-alpha-like depth  : 0.2404 ± 0.0026\n"
     ]
    }
   ],
   "source": [
    "degrees_of_freedom = len(observed_flux) - design_matrix.shape[1]\n",
    "estimated_variance = np.sum(residuals**2) / degrees_of_freedom\n",
    "covariance = estimated_variance * np.linalg.inv(design_matrix.T @ design_matrix)\n",
    "parameter_errors = np.sqrt(np.diag(covariance))\n",
    "\n",
    "for name, value, error in zip(parameter_names, fit_parameters, parameter_errors):\n",
    "    print(f\"{name:27s}: {value:.4f} ± {error:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Make two features hard to distinguish\n",
    "\n",
    "Move the two component centers together. A rising condition number warns that the individual depths are becoming poorly identifiable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.770125Z",
     "iopub.status.busy": "2026-07-29T07:42:48.770037Z",
     "iopub.status.idle": "2026-07-29T07:42:48.925064Z",
     "shell.execute_reply": "2026-07-29T07:42:48.924635Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def condition_for_separation(separation_nm):\n",
    "    first = gaussian_profile(wavelength_nm, 600.0 - separation_nm / 2, 0.35)\n",
    "    second = gaussian_profile(wavelength_nm, 600.0 + separation_nm / 2, 0.35)\n",
    "    matrix = np.column_stack([np.ones_like(wavelength_nm), -first, -second])\n",
    "    return np.linalg.cond(matrix)\n",
    "\n",
    "separations = np.geomspace(0.01, 3.0, 80)\n",
    "conditions = np.array([condition_for_separation(value) for value in separations])\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(7, 4))\n",
    "axis.loglog(separations, conditions)\n",
    "axis.set(xlabel=\"line-center separation [nm]\", ylabel=\"design-matrix condition number\",\n",
    "         title=\"Blending makes component strengths degenerate\")\n",
    "axis.grid(alpha=0.25, which=\"both\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Checks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:48.926174Z",
     "iopub.status.busy": "2026-07-29T07:42:48.926108Z",
     "iopub.status.idle": "2026-07-29T07:42:48.928131Z",
     "shell.execute_reply": "2026-07-29T07:42:48.927744Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checks passed: the injected features are recovered within uncertainty.\n"
     ]
    }
   ],
   "source": [
    "assert rank == 3\n",
    "assert abs(fit_parameters[1] - true_depths[0]) < 4 * parameter_errors[1]\n",
    "assert abs(fit_parameters[2] - true_depths[1]) < 4 * parameter_errors[2]\n",
    "assert 0.7 * noise_sigma < np.std(residuals) < 1.3 * noise_sigma\n",
    "print(\"Checks passed: the injected features are recovered within uncertainty.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next Steps\n",
    "\n",
    "1. Add a Doppler shift to both line centers and fit radial velocity.\n",
    "2. Generate 200 noise realizations and plot the distribution of fitted depths.\n",
    "3. Add an unmodeled third feature. Does the residual plot reveal it?\n",
    "4. Replace the toy Gaussians with a public calibrated spectrum only after recording its source and reduction steps.\n",
    "\n",
    "**Frontier connection:** exoplanet-atmosphere retrieval uses the same forward-model logic at much higher complexity. Clouds, chemistry, temperature structure, stellar contamination, and instrument systematics can be degenerate."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
