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March 10, 2026 22:42
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healpy harmonic_ud_grade aliasing demo notebook
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "id": "ecaee865", | |
| "metadata": {}, | |
| "source": [ | |
| "# Aliasing demo: synthetic small-scale input map\n", | |
| "\n", | |
| "This notebook isolates aliasing in downgrade workflows using a synthetic map whose power is concentrated mostly above the target output bandlimit.\n", | |
| "\n", | |
| "Instead of an artificial narrow spike, the input spectrum is a broad smooth bump centered at high multipoles. This makes the example closer to a realistic map with substantial small-scale structure.\n", | |
| "\n", | |
| "If the output NSIDE is `nside_out`, then the target harmonic content should live below `lmax_out = 3*nside_out - 1`. Any large-scale structure created by downgrade from the unresolved high-ell part is aliasing." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "72bb758c", | |
| "metadata": { | |
| "execution": { | |
| "iopub.execute_input": "2026-03-10T21:55:09.349835Z", | |
| "iopub.status.busy": "2026-03-10T21:55:09.349617Z", | |
| "iopub.status.idle": "2026-03-10T21:55:10.312991Z", | |
| "shell.execute_reply": "2026-03-10T21:55:10.312388Z" | |
| } | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "from pathlib import Path\n", | |
| "import numpy as np\n", | |
| "import healpy as hp\n", | |
| "import matplotlib.pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "id": "79f655dd", | |
| "metadata": { | |
| "execution": { | |
| "iopub.execute_input": "2026-03-10T21:55:10.314571Z", | |
| "iopub.status.busy": "2026-03-10T21:55:10.314354Z", | |
| "iopub.status.idle": "2026-03-10T21:55:10.321469Z", | |
| "shell.execute_reply": "2026-03-10T21:55:10.320791Z" | |
| } | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def _round_sig(x, sig=2):\n", | |
| " if x == 0 or not np.isfinite(x):\n", | |
| " return float(x)\n", | |
| " return float(np.round(x, sig - int(np.floor(np.log10(abs(x)))) - 1))\n", | |
| "\n", | |
| "def rounded_limits(*maps, q=(0.5, 99.5)):\n", | |
| " vals = np.concatenate([m[np.isfinite(m)] for m in maps])\n", | |
| " lo, hi = np.percentile(vals, q)\n", | |
| " vmin = _round_sig(float(lo), sig=2)\n", | |
| " vmax = _round_sig(float(hi), sig=2)\n", | |
| " if vmin == vmax:\n", | |
| " vmax = vmin + 1.0\n", | |
| " return vmin, vmax\n", | |
| "\n", | |
| "def proj_panels(maps, titles, cmap='RdBu_r', q=(0.5, 99.5), ncol=3, xsize=2200, symmetric=False):\n", | |
| " vmin, vmax = rounded_limits(*maps, q=q)\n", | |
| " if symmetric:\n", | |
| " lim = max(abs(vmin), abs(vmax))\n", | |
| " vmin, vmax = -lim, lim\n", | |
| " print(f'vmin={vmin}, vmax={vmax}')\n", | |
| " n = len(maps)\n", | |
| " ncol = min(ncol, n)\n", | |
| " nrow = int(np.ceil(n / ncol))\n", | |
| " plt.figure(figsize=(6.8*ncol, 4.8*nrow))\n", | |
| " for i, (m, t) in enumerate(zip(maps, titles), start=1):\n", | |
| " hp.projview(\n", | |
| " m,\n", | |
| " sub=(nrow, ncol, i),\n", | |
| " title=t,\n", | |
| " min=vmin,\n", | |
| " max=vmax,\n", | |
| " cmap=cmap,\n", | |
| " graticule=True,\n", | |
| " xsize=xsize,\n", | |
| " cb_orientation='horizontal',\n", | |
| " )\n", | |
| " plt.tight_layout()\n", | |
| "\n", | |
| "def moll_diff_panels(diff_maps, titles, unit='', q=(0.2, 99.8)):\n", | |
| " vmin, vmax = rounded_limits(*diff_maps, q=q)\n", | |
| " lim = max(abs(vmin), abs(vmax))\n", | |
| " vmin, vmax = -lim, lim\n", | |
| " print(f'moll diff scale: vmin={vmin}, vmax={vmax}')\n", | |
| " n = len(diff_maps)\n", | |
| " plt.figure(figsize=(6.8*n, 4.8))\n", | |
| " for i, (m, t) in enumerate(zip(diff_maps, titles), start=1):\n", | |
| " hp.mollview(m, sub=(1, n, i), title=t, min=vmin, max=vmax, cmap='RdBu_r', unit=unit)\n", | |
| " hp.graticule()\n", | |
| " plt.tight_layout()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f69d1288", | |
| "metadata": {}, | |
| "source": [ | |
| "## Build a map with a broad high-ell bump\n", | |
| "\n", | |
| "The synthetic input map is generated at high resolution, with most of its power placed above the output bandlimit in a broad smooth feature rather than a sharp line.\n", | |
| "\n", | |
| "This gives a more realistic stress test: the correct target-bandlimited output is still strongly suppressed, but the setup no longer depends on an extreme spectral spike." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "id": "92a6d197", | |
| "metadata": { | |
| "execution": { | |
| "iopub.execute_input": "2026-03-10T21:55:10.322712Z", | |
| "iopub.status.busy": "2026-03-10T21:55:10.322570Z", | |
| "iopub.status.idle": "2026-03-10T21:55:10.378525Z", | |
| "shell.execute_reply": "2026-03-10T21:55:10.377856Z" | |
| } | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Input bump center ell = 150\n", | |
| "Input bump width sigma_ell = 28.0\n", | |
| "Output bandlimit lmax_out = 95\n", | |
| "Injected floor amplitude ~ 1e-4 of peak with random jitter\n", | |
| "Reference low-resolution map std = 0.803241478580098\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "nside_in = 256\n", | |
| "nside_out = 32\n", | |
| "lmax_in = 3 * nside_in - 1\n", | |
| "lmax_out = 3 * nside_out - 1\n", | |
| "\n", | |
| "ell = np.arange(lmax_in + 1)\n", | |
| "ell0 = lmax_out + 55\n", | |
| "sigma_ell = 28.0\n", | |
| "# Broad, smooth high-ell bump with a soft low-ell cutoff.\n", | |
| "bump = np.exp(-0.5 * ((ell - ell0) / sigma_ell) ** 2)\n", | |
| "cut = 1.0 / (1.0 + np.exp(-(ell - (lmax_out + 10)) / 4.0))\n", | |
| "cl_hi = bump * cut\n", | |
| "cl_hi[:2] = 0.0\n", | |
| "cl_hi /= cl_hi.max()\n", | |
| "# Add a small random floor instead of clipping to zero so the spectrum stays realistic.\n", | |
| "rng_floor = np.random.default_rng(2026)\n", | |
| "floor = 1.0e-4 * 10.0 ** rng_floor.uniform(-0.3, 0.3, size=cl_hi.size)\n", | |
| "floor[:2] = 0.0\n", | |
| "cl_hi = np.maximum(cl_hi, floor)\n", | |
| "\n", | |
| "np.random.seed(4321)\n", | |
| "alm_in = hp.synalm(cl_hi, lmax=lmax_in)\n", | |
| "m_in = hp.alm2map(alm_in, nside=nside_in, lmax=lmax_in, pixwin=False)\n", | |
| "\n", | |
| "alm_ref = hp.resize_alm(alm_in, lmax_in, lmax_in, lmax_out, lmax_out)\n", | |
| "m_ref = hp.alm2map(alm_ref, nside=nside_out, lmax=lmax_out, pixwin=False)\n", | |
| "\n", | |
| "print('Input bump center ell =', int(ell0))\n", | |
| "print('Input bump width sigma_ell =', sigma_ell)\n", | |
| "print('Output bandlimit lmax_out =', lmax_out)\n", | |
| "print('Injected floor amplitude ~ 1e-4 of peak with random jitter')\n", | |
| "print('Reference low-resolution map std =', np.std(m_ref))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "1d06704e", | |
| "metadata": {}, | |
| "source": [ | |
| "## Input spectrum\n", | |
| "\n", | |
| "This panel shows the high-resolution input spectrum together with the output bandlimit. The signal is a broad smooth bump concentrated above the target low-resolution band, so the test still highlights aliasing without relying on an extreme spike." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "id": "032469a1", | |
| "metadata": { | |
| "execution": { | |
| "iopub.execute_input": "2026-03-10T21:55:10.380347Z", | |
| "iopub.status.busy": "2026-03-10T21:55:10.380187Z", | |
| "iopub.status.idle": "2026-03-10T21:55:11.017271Z", | |
| "shell.execute_reply": "2026-03-10T21:55:11.016676Z" | |
| } | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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", | |
| "text/plain": [ | |
| "<Figure size 800x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "cl_in = hp.anafast(m_in, lmax=lmax_in)\n", | |
| "plt.figure(figsize=(8, 4.8))\n", | |
| "plt.semilogy(ell[2:], cl_in[2:], label='input spectrum', linewidth=2.0)\n", | |
| "plt.axvline(lmax_out, color='black', linestyle='--', linewidth=1.5, label=f'output bandlimit = {lmax_out}')\n", | |
| "plt.xlabel(r'$\\ell$')\n", | |
| "plt.ylabel(r'$C_\\ell$')\n", | |
| "plt.title('Synthetic input spectrum for the aliasing stress test')\n", | |
| "plt.grid(alpha=0.25)\n", | |
| "plt.legend()\n", | |
| "plt.tight_layout()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "id": "1b943b91", | |
| "metadata": { | |
| "execution": { | |
| "iopub.execute_input": "2026-03-10T21:55:11.018538Z", | |
| "iopub.status.busy": "2026-03-10T21:55:11.018393Z", | |
| "iopub.status.idle": "2026-03-10T21:55:11.298936Z", | |
| "shell.execute_reply": "2026-03-10T21:55:11.298272Z" | |
| } | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "m_ud = hp.ud_grade(m_in, nside_out=nside_out)\n", | |
| "m_harm = hp.harmonic_ud_grade(m_in, nside_out=nside_out, use_pixel_weights=False)\n", | |
| "m_smooth_ud = hp.ud_grade(hp.smoothing(m_in, fwhm=np.radians(30/60)), nside_out=nside_out)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "id": "1ea8b133", | |
| "metadata": { | |
| "execution": { | |
| "iopub.execute_input": "2026-03-10T21:55:11.300429Z", | |
| "iopub.status.busy": "2026-03-10T21:55:11.300284Z", | |
| "iopub.status.idle": "2026-03-10T21:55:58.985599Z", | |
| "shell.execute_reply": "2026-03-10T21:55:58.984716Z" | |
| } | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "vmin=-100.0, vmax=100.0\n" | |
| ] | |
| }, | |
| { | |
| "data": { |
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