{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "setup-md",
   "metadata": {},
   "source": [
    "## 1. Imports + cosmology"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "imports",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Da(z_cl=0.22) = 732.0 Mpc\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.integrate as integrate\n",
    "import treecorr\n",
    "from astropy.table import Table, vstack\n",
    "\n",
    "# Manual flat-LCDM angular diameter distance for the cluster-radius\n",
    "# conversion (no external cosmology dependency).\n",
    "z_cl = 0.22\n",
    "H0, c_light = 70.0, 3e5\n",
    "omega_m, omega_de = 0.31, 0.69\n",
    "Hz = lambda z: c_light / (H0 * np.sqrt(omega_de + omega_m * (1 + z) ** 3))\n",
    "chi_dl = lambda z, z0=0: integrate.quad(Hz, z0, z)[0]\n",
    "Da = lambda z: chi_dl(z) / (1 + z)\n",
    "Da_lens = Da(z_cl)\n",
    "print(f'Da(z_cl={z_cl}) = {Da_lens:.1f} Mpc')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "load-md",
   "metadata": {},
   "source": [
    "## 2. Load the merged tract catalog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "butler-load",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  tract=10463: 45176 objects (a360_merged_tract10463.parq)\n",
      "  tract=10464: 25104 objects (a360_merged_tract10464.parq)\n",
      "  tract=10704: 3861 objects (a360_merged_tract10704.parq)\n",
      "\n",
      "Total merged objects: 74141\n"
     ]
    }
   ],
   "source": [
    "DATA_DIR = '/home/xiangchong/work/DP1'\n",
    "TRACT_FILES = {\n",
    "    10463: 'a360_merged_tract10463.parq',\n",
    "    10464: 'a360_merged_tract10464.parq',\n",
    "    10704: 'a360_merged_tract10704.parq',\n",
    "}\n",
    "\n",
    "cluster_coords = (37.865017, 6.982205)\n",
    "ra_bcg, dec_bcg = cluster_coords\n",
    "\n",
    "tables = []\n",
    "for tid, fname in TRACT_FILES.items():\n",
    "    path = os.path.join(DATA_DIR, fname)\n",
    "    if not os.path.isfile(path):\n",
    "        print(f'  tract={tid}: NO file at {path}')\n",
    "        continue\n",
    "    t = Table.read(path)\n",
    "    tables.append(t)\n",
    "    print(f'  tract={tid}: {len(t)} objects ({fname})')\n",
    "\n",
    "anacal_table = vstack(tables)\n",
    "print(f'\\nTotal merged objects: {len(anacal_table)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mags-md",
   "metadata": {},
   "source": [
    "## 3. Per-band magnitudes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "compute-mags",
   "metadata": {},
   "outputs": [],
   "source": [
    "mag_zero = 31.4\n",
    "for band in 'griz':\n",
    "    flux = np.asarray(anacal_table[f'{band}_flux_fpfs1'])\n",
    "    mag = np.full(len(anacal_table), 40.0)\n",
    "    pos = flux > 0\n",
    "    mag[pos] = mag_zero - 2.5 * np.log10(flux[pos])\n",
    "    anacal_table[f'{band}_mag'] = mag"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "selection-md",
   "metadata": {},
   "source": [
    "## 4. Selection (with shear-perturbed observables)\n",
    "\n",
    "Cuts (matching the old notebook + new ``zbest`` cut):\n",
    "\n",
    "- ``mask_value < 40``\n",
    "- ``wsel > 1e-5``\n",
    "- per-band magnitude limits ``g/r/z < 25.5``, ``i < 24.0``\n",
    "- size-like cut ``(m00 + m20) / m00 > 0.1`` — uses the band-combined\n",
    "  ``fpfs1_m00`` / ``fpfs1_m20`` since per-band ``i_fpfs1_m00`` /\n",
    "  ``i_fpfs1_m20`` are not surfaced in the merged catalog\n",
    "- red-sequence colour count < 3 (``g-i``, ``r-i``, ``g-r``, $r$-mag)\n",
    "- photo-z ``Z_MIN < zbest < Z_MAX``\n",
    "\n",
    "When ``dg_eff != 0`` the per-band fluxes, ``m00``, ``m20`` and the\n",
    "photo-z column are all replaced by their first-order Taylor expansions\n",
    "in the chosen shear component, mirroring ``selection.get_cut`` in\n",
    "``HSC_S23B_Shapes``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "selection-fns",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fiducial selected: 17051/74141\n",
      "  cut_1p: 17055\n",
      "  cut_1m: 17040\n",
      "  cut_2p: 17045\n",
      "  cut_2m: 17048\n"
     ]
    }
   ],
   "source": [
    "DG = 0.01\n",
    "Z_MIN, Z_MAX = 0.2, 10.0\n",
    "MAG_CUTS = {'g': 25.5, 'r': 25.5, 'i': 23.5, 'z': 25.5}\n",
    "MAG_LIM_REDSEQ = 24.0\n",
    "\n",
    "\n",
    "def _flux_to_mag(flux):\n",
    "    mag = np.full(len(flux), 40.0)\n",
    "    pos = flux > 0\n",
    "    mag[pos] = mag_zero - 2.5 * np.log10(flux[pos])\n",
    "    return mag\n",
    "\n",
    "\n",
    "def _band_mag(t, band, dg_eff, comp):\n",
    "    flux = np.asarray(t[f'{band}_flux_fpfs1'])\n",
    "    if dg_eff != 0.0:\n",
    "        flux = flux + dg_eff * np.asarray(t[f'{band}_dflux_fpfs1_dg{comp}'])\n",
    "    return _flux_to_mag(flux)\n",
    "\n",
    "\n",
    "def _redseq_count(g_mag, r_mag, i_mag):\n",
    "    color_gi = g_mag - i_mag\n",
    "    color_ri = r_mag - i_mag\n",
    "    color_gr = g_mag - r_mag\n",
    "    gi_line = (r_mag - 18) * (-0.20 / 5) + 2.15\n",
    "    ri_line = (r_mag - 18) * (-0.10 / 5) + 0.85\n",
    "    gr_line = (r_mag - 18) * (-0.12 / 5) + 1.35\n",
    "    gi_lims, ri_lims, gr_lims = (0.20, -0.20), (0.12, -0.15), (0.15, -0.16)\n",
    "    in_redseq = lambda c, line, lims: (\n",
    "        (c < line + lims[0]) & (c > line + lims[1]) & (r_mag < MAG_LIM_REDSEQ)\n",
    "    )\n",
    "    return (\n",
    "        in_redseq(color_gi, gi_line, gi_lims).astype(int)\n",
    "        + in_redseq(color_ri, ri_line, ri_lims).astype(int)\n",
    "        + in_redseq(color_gr, gr_line, gr_lims).astype(int)\n",
    "    )\n",
    "\n",
    "\n",
    "def get_cut(t, *, comp=1, dg_eff=0.0, zkey='zbest'):\n",
    "    \"\"\"Boolean mask for the standard selection.\n",
    "\n",
    "    The merged catalog is already filtered by ``wsel > 1e-5`` in\n",
    "    ``MergePipe._finalize_columns``; ``dg_eff != 0`` perturbs every\n",
    "    other shear-dependent observable by its first-order response so the\n",
    "    resulting cut feeds the selection-response finite difference.\n",
    "    \"\"\"\n",
    "    mags = {b: _band_mag(t, b, dg_eff, comp) for b in 'griz'}\n",
    "\n",
    "    mask = np.asarray(t['mask_value']) < 40\n",
    "    for b, lim in MAG_CUTS.items():\n",
    "        mask &= mags[b] < lim\n",
    "\n",
    "    m00 = np.asarray(t['fpfs1_m00'])\n",
    "    m20 = np.asarray(t['fpfs1_m20'])\n",
    "    if dg_eff != 0.0:\n",
    "        m00 = m00 + dg_eff * np.asarray(t[f'fpfs1_dm00_dg{comp}'])\n",
    "        m20 = m20 + dg_eff * np.asarray(t[f'fpfs1_dm20_dg{comp}'])\n",
    "    mask &= (m00 + m20) / m00 > 0.1\n",
    "\n",
    "    counts = _redseq_count(mags['g'], mags['r'], mags['i'])\n",
    "    mask &= counts < 3\n",
    "\n",
    "    if dg_eff == 0.0:\n",
    "        zcol = np.asarray(t[f'{zkey}_0'])\n",
    "    else:\n",
    "        suffix = 'p' if dg_eff > 0 else 'm'\n",
    "        zcol = np.asarray(t[f'{zkey}_{comp}{suffix}'])\n",
    "    mask &= (zcol > Z_MIN) & (zcol < Z_MAX)\n",
    "    return mask\n",
    "\n",
    "\n",
    "fid_cut = get_cut(anacal_table, dg_eff=0.0)\n",
    "cut_p1 = get_cut(anacal_table, comp=1, dg_eff=+DG)\n",
    "cut_m1 = get_cut(anacal_table, comp=1, dg_eff=-DG)\n",
    "cut_p2 = get_cut(anacal_table, comp=2, dg_eff=+DG)\n",
    "cut_m2 = get_cut(anacal_table, comp=2, dg_eff=-DG)\n",
    "print(f'Fiducial selected: {int(fid_cut.sum())}/{len(anacal_table)}')\n",
    "for tag, c in [('1p', cut_p1), ('1m', cut_m1), ('2p', cut_p2), ('2m', cut_m2)]:\n",
    "    print(f'  cut_{tag}: {int(c.sum())}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "treecorr-run",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N selected = 17051\n",
      "  R_shape  = +0.4481\n",
      "  R_weight = -0.0233\n",
      "  R_sel    = -0.0109\n",
      "  R_total  = +0.4140\n"
     ]
    }
   ],
   "source": [
    "# --- response components (computed *before* TreeCorr so the calibrated\n",
    "# ellipticities can be fed directly to it) ---\n",
    "nc = int(fid_cut.sum())\n",
    "sub = anacal_table[fid_cut]\n",
    "wsel = np.asarray(sub['wsel'])\n",
    "e1 = np.asarray(sub['fpfs1_e1'])\n",
    "e2 = np.asarray(sub['fpfs1_e2'])\n",
    "de1_dg1 = np.asarray(sub['fpfs1_de1_dg1'])\n",
    "de2_dg2 = np.asarray(sub['fpfs1_de2_dg2'])\n",
    "dwsel_dg1 = np.asarray(sub['dwsel_dg1'])\n",
    "dwsel_dg2 = np.asarray(sub['dwsel_dg2'])\n",
    "\n",
    "# Shape (pure-shear) response: <w * de_i/dg_i> averaged over i = 1, 2\n",
    "R_shape = 0.5 * (np.mean(wsel * de1_dg1) + np.mean(wsel * de2_dg2))\n",
    "# Weight-bias response: <dw/dg_i * e_i> averaged over i = 1, 2\n",
    "R_weight = 0.5 * (np.mean(dwsel_dg1 * e1) + np.mean(dwsel_dg2 * e2))\n",
    "\n",
    "\n",
    "def _sum_we(t, cut, comp):\n",
    "    s = t[cut]\n",
    "    e_col = 'fpfs1_e1' if comp == 1 else 'fpfs1_e2'\n",
    "    return float(np.sum(np.asarray(s['wsel']) * np.asarray(s[e_col])))\n",
    "\n",
    "\n",
    "R_sel_1 = (_sum_we(anacal_table, cut_p1, 1) - _sum_we(anacal_table, cut_m1, 1)) / (2.0 * DG) / nc\n",
    "R_sel_2 = (_sum_we(anacal_table, cut_p2, 2) - _sum_we(anacal_table, cut_m2, 2)) / (2.0 * DG) / nc\n",
    "R_sel = 0.5 * (R_sel_1 + R_sel_2)\n",
    "\n",
    "R_total = R_shape + R_weight + R_sel\n",
    "print(f'N selected = {nc}')\n",
    "print(f'  R_shape  = {R_shape:+.4f}')\n",
    "print(f'  R_weight = {R_weight:+.4f}')\n",
    "print(f'  R_sel    = {R_sel:+.4f}')\n",
    "print(f'  R_total  = {R_total:+.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "response-calc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min/max sep: 2.35 / 28.18 arcmin\n",
      "Mpc bin edges: [0.5   0.757 1.145 1.732 2.621 3.965 6.   ]\n",
      "mean_r (Mpc): [0.633 0.956 1.445 2.183 3.309 5.121]\n"
     ]
    }
   ],
   "source": [
    "# --- TreeCorr: pre-calibrate the ellipticities by feeding\n",
    "#     g1 = e1 * wsel / R_total\n",
    "#     g2 = e2 * wsel / R_total\n",
    "# (no sign flip on e2 -- merge.py keeps the WCS-corrected ellipticities\n",
    "# in the GalSim u=W convention, which is what TreeCorr expects for the\n",
    "# tangential / cross decomposition around the cluster centre)\n",
    "# and pass w=None so TreeCorr does not re-weight. The resulting\n",
    "# xi / xi_im are already the response- and weight-corrected tangential\n",
    "# and cross shears.\n",
    "bins_mpc = np.logspace(np.log10(0.5), np.log10(6.0), 7)\n",
    "nbins = len(bins_mpc) - 1\n",
    "mpc_to_arcmin = (1.0 / Da_lens) * (180.0 / np.pi) * 60.0\n",
    "min_sep_arcmin = bins_mpc[0] * mpc_to_arcmin\n",
    "max_sep_arcmin = bins_mpc[-1] * mpc_to_arcmin\n",
    "print(f'min/max sep: {min_sep_arcmin:.2f} / {max_sep_arcmin:.2f} arcmin')\n",
    "print(f'Mpc bin edges: {bins_mpc.round(3)}')\n",
    "\n",
    "lens_cat = treecorr.Catalog(\n",
    "    ra=[ra_bcg], dec=[dec_bcg], ra_units='deg', dec_units='deg',\n",
    ")\n",
    "\n",
    "\n",
    "def make_source_cat(t, cut, R_final):\n",
    "    sub = t[cut]\n",
    "    wsel_sub = np.asarray(sub['wsel'])\n",
    "    g1 = np.asarray(sub['fpfs1_e1']) * wsel_sub / R_final\n",
    "    g2 = np.asarray(sub['fpfs1_e2']) * wsel_sub / R_final\n",
    "    return treecorr.Catalog(\n",
    "        ra=np.asarray(sub['ra']),\n",
    "        dec=np.asarray(sub['dec']),\n",
    "        g1=g1, g2=g2, w=None,\n",
    "        ra_units='deg', dec_units='deg',\n",
    "    )\n",
    "\n",
    "\n",
    "src_cat = make_source_cat(anacal_table, fid_cut, R_total)\n",
    "ng = treecorr.NGCorrelation(\n",
    "    min_sep=min_sep_arcmin, max_sep=max_sep_arcmin,\n",
    "    nbins=nbins, sep_units='arcmin', bin_type='Log',\n",
    ")\n",
    "ng.process(lens_cat, src_cat)\n",
    "mean_r_arcmin = ng.meanr\n",
    "mean_r_mpc = mean_r_arcmin / mpc_to_arcmin\n",
    "print('mean_r (Mpc):', np.round(mean_r_mpc, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "plot-md",
   "metadata": {},
   "source": [
    "## 7. Tangential / cross shear profile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "plot",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 667
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# xi / xi_im are already calibrated (no /R_total here -- the input\n",
    "# ellipticities were pre-divided by R_total).\n",
    "gT = ng.xi\n",
    "gX = ng.xi_im\n",
    "err = np.sqrt(ng.varxi)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "ax.errorbar(mean_r_mpc, gT, yerr=err, fmt='o', label='tangential', color='C0')\n",
    "ax.errorbar(mean_r_mpc * 1.05, gX, yerr=err, fmt='s', label='cross', color='C3', alpha=0.8)\n",
    "ax.axhline(0, ls='--', color='k', alpha=0.5)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('$R$ [Mpc]')\n",
    "ax.set_ylabel('reduced shear')\n",
    "ax.set_xlim(0.4, 7.0)\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.13.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}