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healpy harmonic_ud_grade vs ud_grade comparison notebook (executed)
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{
"cells": [
{
"cell_type": "markdown",
"id": "08ac5e21",
"metadata": {},
"source": [
"# `harmonic_ud_grade` vs `ud_grade`: A Focused Comparison\n",
"\n",
"When working with HEALPix maps, it is often necessary to change the\n",
"resolution — for example, to downgrade a high-resolution observation\n",
"map to a lower Nside for comparison with a model, or to reduce\n",
"computational cost for large-scale analyses.\n",
"\n",
"healpy provides two functions for this:\n",
"\n",
"- `ud_grade`: operates purely in **pixel space** by averaging\n",
" groups of sub-pixels. It is fast, but because it does not apply any\n",
" anti-aliasing filter, high-multipole power from the input grid\n",
" \"folds\" back into the output — a phenomenon known as\n",
" [aliasing](https://en.wikipedia.org/wiki/Aliasing).\n",
"\n",
"- `harmonic_ud_grade`: operates in **spherical-harmonic space**.\n",
" It decomposes the input map into $a_{\\ell m}$ coefficients, applies\n",
" the pixel-window correction following the prescription in\n",
" [Planck Collaboration 2015 X](https://arxiv.org/abs/1502.01588), and\n",
" optionally scales the beam. Because the harmonic transform\n",
" naturally band-limits the output, aliasing is eliminated.\n",
"\n",
"## How `harmonic_ud_grade` works\n",
"\n",
"The function implements the following per-$\\ell$ transfer\n",
"([Planck Collaboration 2015 X](https://arxiv.org/abs/1502.01588)):\n",
"\n",
"$$\n",
"a^{\\rm out}_{\\ell m}\n",
"= \\frac{p^{\\rm out}_\\ell}{p^{\\rm in}_\\ell}\n",
" \\cdot \\frac{b^{\\rm out}_\\ell}{b^{\\rm in}_\\ell}\n",
" \\cdot a^{\\rm in}_{\\ell m}\n",
"$$\n",
"\n",
"where $p_\\ell$ is the HEALPix pixel-window function and $b_\\ell$ is\n",
"a Gaussian beam transfer function. The algorithm proceeds in three\n",
"steps:\n",
"\n",
"1. **Analysis:** The input map is decomposed into $a_{\\ell m}$ via\n",
" `map2alm` (using pixel weights by default for high accuracy).\n",
"2. **Transfer:** Each $a_{\\ell m}$ is multiplied by the ratio of\n",
" output/input pixel windows and beams. Modes above\n",
" $\\ell_{\\max}^{\\rm out}$ are discarded (band-limiting).\n",
"3. **Synthesis:** The modified $a_{\\ell m}$ are synthesized into a\n",
" map at `nside_out` via `alm2map`.\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9b284e3e",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:15.348531Z",
"iopub.status.busy": "2026-05-21T16:31:15.348089Z",
"iopub.status.idle": "2026-05-21T16:31:17.032638Z",
"shell.execute_reply": "2026-05-21T16:31:17.030645Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"healpy 1.19.1.dev74+g75dd35ba8\n",
"Effective resolution beam at NSIDE 64: 160.0 arcmin\n"
]
}
],
"source": [
"import time\n",
"import numpy as np\n",
"import healpy as hp\n",
"import matplotlib.pyplot as plt\n",
"\n",
"plt.rcParams.update({\"figure.dpi\": 120, \"font.size\": 11})\n",
"\n",
"print(f\"healpy {hp.__version__}\")\n",
"print(f\"Effective resolution beam at NSIDE 64: {hp.effective_resolution_fwhm(64, arcmin=True):.1f} arcmin\")\n"
]
},
{
"cell_type": "markdown",
"id": "5188578f",
"metadata": {},
"source": [
"## 1. Aliasing Stress Test: A Single High-$\\ell$ Mode\n",
"\n",
"The simplest way to reveal aliasing is to construct a pathological\n",
"input: a map at `nside_in = 128` that contains power at **exactly\n",
"one** spherical-harmonic multipole, $\\ell = 120$.\n",
"\n",
"The target resolution is `nside_out = 32`, whose maximum resolvable\n",
"multipole is $\\ell_{\\max} = 3 \\times 32 - 1 = 95$. Since\n",
"$\\ell = 120 > \\ell_{\\max}$, a correct downgrade must produce an\n",
"output whose angular power spectrum is identically zero.\n",
"\n",
"**Key parameter choices:**\n",
"- `pixwin=True` is passed both when creating the input map\n",
" (`alm2map`) and when calling `harmonic_ud_grade`. This simulates\n",
" a realistic pixelised observation and allows `harmonic_ud_grade`\n",
" to properly deconvolve the input pixel window and apply the output\n",
" pixel window.\n",
"- `fwhm_in=0` because the synthetic input has no instrumental beam."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b7632f2f",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:17.036991Z",
"iopub.status.busy": "2026-05-21T16:31:17.036514Z",
"iopub.status.idle": "2026-05-21T16:31:18.502454Z",
"shell.execute_reply": "2026-05-21T16:31:18.501021Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1200x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nside_in = 128\n",
"nside_out = 32\n",
"lmax_out = 3 * nside_out - 1\n",
"\n",
"# Single mode at ell=120\n",
"alm_single = np.zeros(hp.Alm.getsize(120), dtype=np.complex128)\n",
"alm_single[hp.Alm.getidx(120, 120, 0)] = 1.0\n",
"# We generate the synthetic map and run downgrade methods with pixwin=True.\n",
"# This simulates a realistic pixelized map and allows harmonic_ud_grade\n",
"# to properly apply its pixel window correction (Eq 1).\n",
"m_in = hp.alm2map(alm_single, nside=nside_in, pixwin=True)\n",
"\n",
"# Downgrade methods\n",
"m_ud = hp.ud_grade(m_in, nside_out=nside_out)\n",
"\n",
"# fwhm_in is required\n",
"# For this synthetic test there is no input beam → pass 0\n",
"m_harm = hp.harmonic_ud_grade(\n",
" m_in,\n",
" nside_out=nside_out,\n",
" fwhm_in=0,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=0,\n",
")\n",
"\n",
"cl_in = hp.anafast(m_in)\n",
"cl_ud = hp.anafast(m_ud)\n",
"cl_harm = hp.anafast(m_harm)\n",
"\n",
"plt.figure(figsize=(10, 5))\n",
"plt.semilogy(np.maximum(cl_in, 1e-8), label=f\"Input (Nside={nside_in})\", color=\"black\", linestyle=\"--\")\n",
"plt.semilogy(np.maximum(cl_ud, 1e-8), label=f\"ud_grade (Nside={nside_out})\", alpha=0.8)\n",
"plt.semilogy(np.maximum(cl_harm, 1e-8), label=f\"harmonic_ud_grade (Nside={nside_out})\", alpha=0.8)\n",
"plt.axvline(lmax_out, color=\"red\", ls=\":\", label=r\"Output $\\ell_{\\max}$\")\n",
"plt.xlabel(r\"$\\ell$\")\n",
"plt.ylabel(r\"$C_\\ell$\")\n",
"plt.xlim(0, 150)\n",
"plt.ylim(1e-8, cl_in.max() * 5)\n",
"plt.title(\"Aliasing of a single high-frequency mode ($\\\\ell=120$)\")\n",
"plt.legend()\n",
"plt.grid(alpha=0.3)\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "688aea9f",
"metadata": {},
"source": [
"**Interpretation of the plot above:**\n",
"\n",
"- **Black dashed line (Input):** The input power spectrum has a sharp\n",
" peak at $\\ell = 120$ and is essentially zero everywhere else. The\n",
" satellite peaks visible around $\\ell = 120$ are due to the pixel\n",
" window of the `nside_in = 128` grid.\n",
"- **Orange line:** `harmonic_ud_grade` The output spectrum is\n",
" numerically zero across all multipoles — exactly the correct\n",
" answer. The harmonic transform naturally band-limits the result to\n",
" $\\ell \\le \\ell_{\\max}$, so the $\\ell = 120$ mode is cleanly\n",
" removed.\n",
"- **Blue line:** `ud_grade` Significant spurious power appears\n",
" across the *entire* output multipole range. This is **aliasing**:\n",
" because pixel-space averaging has no frequency cutoff, the\n",
" high-$\\ell$ mode is \"folded\" back into the lower multipoles,\n",
" corrupting the output with an oscillating pattern.\n",
"- **Red dotted line:** The output bandlimit $\\ell_{\\max} = 95$.\n",
"\n",
"The RMS values below quantify this: `ud_grade` retains about 43 % of\n",
"the original map RMS as pure aliasing artifact, while\n",
"`harmonic_ud_grade` suppresses it to the numerical noise floor."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f309ccd7",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:18.505961Z",
"iopub.status.busy": "2026-05-21T16:31:18.505617Z",
"iopub.status.idle": "2026-05-21T16:31:18.515268Z",
"shell.execute_reply": "2026-05-21T16:31:18.513079Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Input map RMS: 2.705287e-01\n",
"ud_grade output RMS: 1.154352e-01 <-- aliasing\n",
"harmonic_ud_grade RMS: 6.952337e-04 <-- suppressed\n"
]
}
],
"source": [
"print(f\"Input map RMS: {np.std(m_in):.6e}\")\n",
"print(f\"ud_grade output RMS: {np.std(m_ud):.6e} <-- aliasing\")\n",
"print(f\"harmonic_ud_grade RMS: {np.std(m_harm):.6e} <-- suppressed\")"
]
},
{
"cell_type": "markdown",
"id": "edb355d8",
"metadata": {},
"source": [
"## 2. Power-Spectrum Recovery — Why It Matters\n",
"\n",
"The single-mode test above is deliberately extreme. Real sky maps\n",
"contain power at **all** multipoles, so aliasing from `ud_grade`\n",
"is spread across the full spectrum, making it harder to spot by\n",
"eye but no less damaging to science.\n",
"\n",
"In this section we synthesize a realistic broadband signal with\n",
"$C_\\ell \\propto \\ell^{-2}$ (a spectrum often used for test\n",
"purposes) at `nside_in = 256`, downgrade to `nside_out = 64`,\n",
"and compare the recovered power spectrum against a **ground-truth\n",
"reference**.\n",
"\n",
"The reference is built by truncating the original $a_{\\ell m}$ to\n",
"$\\ell_{\\max}^{\\rm out}$ and synthesizing directly at the output\n",
"resolution, so both the reference and the downgraded maps contain\n",
"the same pixel-window effects. Any difference between them is\n",
"therefore purely due to the downgrade method."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "abbc3880",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:18.520676Z",
"iopub.status.busy": "2026-05-21T16:31:18.520274Z",
"iopub.status.idle": "2026-05-21T16:31:18.863663Z",
"shell.execute_reply": "2026-05-21T16:31:18.862152Z"
}
},
"outputs": [],
"source": [
"nside_in = 256\n",
"nside_out = 64\n",
"lmax_in = 3 * nside_in - 1\n",
"lmax_out = 3 * nside_out - 1\n",
"\n",
"np.random.seed(42)\n",
"# healpy synfast/synalm uses the global RNG\n",
"ell = np.arange(lmax_in + 1, dtype=float)\n",
"cl_in = np.zeros(lmax_in + 1)\n",
"cl_in[2:] = ell[2:] ** (-2.0)\n",
"elm = hp.synalm(cl_in, lmax=lmax_in)\n",
"m_in = hp.alm2map(elm, nside=nside_in, lmax=lmax_in, pixwin=True)\n",
"\n",
"# Ground-truth reference: directly synthesize at output resolution\n",
"elm_ref = hp.resize_alm(elm, lmax_in, lmax_in, lmax_out, lmax_out)\n",
"m_ref = hp.alm2map(elm_ref, nside=nside_out, lmax=lmax_out, pixwin=True)\n",
"\n",
"m_ud = hp.ud_grade(m_in, nside_out=nside_out)\n",
"\n",
"# fwhm_in=0 for this synthetic simulation with no beam\n",
"m_harm = hp.harmonic_ud_grade(\n",
" m_in,\n",
" nside_out=nside_out,\n",
" fwhm_in=0,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=0,\n",
")\n",
"\n",
"# Measure spectra\n",
"cl_ref = hp.anafast(m_ref, lmax=lmax_out)\n",
"cl_ud = hp.anafast(m_ud, lmax=lmax_out)\n",
"cl_harm = hp.anafast(m_harm, lmax=lmax_out)\n",
"ell_out = np.arange(lmax_out + 1)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "15721749",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:18.867750Z",
"iopub.status.busy": "2026-05-21T16:31:18.867450Z",
"iopub.status.idle": "2026-05-21T16:31:20.330427Z",
"shell.execute_reply": "2026-05-21T16:31:20.328697Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:3: SyntaxWarning: invalid escape sequence '\\e'\n",
"<>:3: SyntaxWarning: invalid escape sequence '\\e'\n",
"/tmp/ipykernel_2918423/3465408581.py:3: SyntaxWarning: invalid escape sequence '\\e'\n",
" axes[0].loglog(ell_out[2:], cl_ref[2:], \"k--\", lw=2, label=\"Reference $C_\\ell$ (truth)\")\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 1440x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
"\n",
"axes[0].loglog(ell_out[2:], cl_ref[2:], \"k--\", lw=2, label=\"Reference $C_\\ell$ (truth)\")\n",
"axes[0].loglog(ell_out[2:], cl_ud[2:], alpha=0.8, label=\"ud_grade\")\n",
"axes[0].loglog(ell_out[2:], cl_harm[2:], alpha=0.8, label=\"harmonic_ud_grade\")\n",
"axes[0].axvline(lmax_out, color=\"red\", ls=\":\", label=r\"$\\ell_{\\max}$\")\n",
"axes[0].set_xlabel(r\"$\\ell$\")\n",
"axes[0].set_ylabel(r\"$C_\\ell$\")\n",
"axes[0].set_title(\"Power spectra after downgrade\")\n",
"axes[0].legend()\n",
"axes[0].grid(alpha=0.3)\n",
"\n",
"# Fractional error\n",
"frac_ud = (cl_ud[2:] - cl_ref[2:]) / cl_ref[2:]\n",
"frac_harm = (cl_harm[2:] - cl_ref[2:]) / cl_ref[2:]\n",
"\n",
"axes[1].plot(ell_out[2:], frac_ud * 100, alpha=0.8, label=\"ud_grade\")\n",
"axes[1].plot(ell_out[2:], frac_harm * 100, alpha=0.8, label=\"harmonic_ud_grade\")\n",
"axes[1].axhline(0, color=\"k\", lw=0.5)\n",
"axes[1].axvline(lmax_out, color=\"red\", ls=\":\")\n",
"axes[1].set_xlabel(r\"$\\ell$\")\n",
"axes[1].set_ylabel(\"Fractional error [%]\")\n",
"axes[1].set_title(\"Spectral error vs truth\")\n",
"axes[1].legend()\n",
"axes[1].grid(alpha=0.3)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "4e92adba",
"metadata": {
"lines_to_next_cell": 0
},
"source": [
"**Interpretation of the plots above:**\n",
"\n",
"**Left panel — Power spectra after downgrade:**\n",
"All three curves agree well at low $\\ell$, but diverge at high\n",
"multipoles. The reference (black dashed) and `harmonic_ud_grade`\n",
"(orange) both roll off smoothly beyond $\\ell \\approx 100$: this is\n",
"the expected damping from the pixel window of the `nside_out = 64`\n",
"grid. `ud_grade` (blue), by contrast, shows a visible *excess* of\n",
"power in this regime because aliased high-frequency structures from\n",
"above $\\ell_{\\max}$ have been folded back into the output.\n",
"\n",
"**Right panel — Fractional spectral error relative to truth:**\n",
"This panel makes the aliasing bias quantitative.\n",
"- `harmonic_ud_grade` (orange) sits flat on 0 % error — it matches\n",
" the truth map almost perfectly.\n",
"- `ud_grade` (blue) is systematically **positive**, meaning it\n",
" **over-estimates** the power. This is expected: aliasing can only\n",
" *add* power, never subtract it. The error grows rapidly toward\n",
" $\\ell_{\\max}$, reaching 50–70 % near the bandlimit.\n",
"\n",
"Because both the reference and the downgraded maps include the same\n",
"pixel window, window effects cancel exactly in the ratio. The\n",
"residual is pure aliasing.\n",
"\n",
"The RMS fractional error below summarises this over the \"safe\"\n",
"multipole band $\\ell \\in [2,\\, 2 N_{\\rm side}^{\\rm out}]$:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2188611e",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:20.334352Z",
"iopub.status.busy": "2026-05-21T16:31:20.334035Z",
"iopub.status.idle": "2026-05-21T16:31:20.340856Z",
"shell.execute_reply": "2026-05-21T16:31:20.339320Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RMS frac. error over safe band ℓ ∈ [2, 128]:\n",
" ud_grade: 2.34%\n",
" harmonic_ud_grade: 0.00%\n"
]
}
],
"source": [
"safe = slice(2, 2 * nside_out + 1)\n",
"print(\n",
" f\"RMS frac. error over safe band ℓ ∈ [2, {2*nside_out}]:\\n\"\n",
" f\" ud_grade: {np.sqrt(np.mean(frac_ud[safe]**2))*100:.2f}%\\n\"\n",
" f\" harmonic_ud_grade: {np.sqrt(np.mean(frac_harm[safe]**2))*100:.2f}%\"\n",
")"
]
},
{
"cell_type": "markdown",
"id": "aliasing-estimate-md",
"metadata": {},
"source": [
"### Expected aliasing from the input spectrum\n",
"\n",
"The `ud_grade` excess is not mysterious — it is predicted by the input\n",
"power spectrum. `ud_grade` performs pixel averaging without bandlimiting,\n",
"so modes above $\\ell_{\\max}^{\\rm out}$ alias into the output.\n",
"For a power-law spectrum $C_\\ell \\propto \\ell^{-2}$, roughly 27 % of\n",
"the total power sits above the output bandlimit and folds back.\n",
"\n",
"We can estimate the aliased power fraction analytically:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "aliasing-estimate-code",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:20.344814Z",
"iopub.status.busy": "2026-05-21T16:31:20.344448Z",
"iopub.status.idle": "2026-05-21T16:31:20.355832Z",
"shell.execute_reply": "2026-05-21T16:31:20.354072Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Input spectrum: C_ell ~ ell^(-2)\n",
" Power below ell_max=191: 10.30\n",
" Power above ell_max=191: 2.78\n",
" Aliasing fraction: 21.2%\n",
"\n",
"Compare with observed ud_grade excess at high ell:\n",
" Mean excess at ell ~ 181-191: 44%\n",
" (Aliasing concentrates near the bandlimit, so the per-bin\n",
" excess at high ell exceeds the total power fraction.)\n"
]
}
],
"source": [
"# Estimate the fraction of input power above the output bandlimit\n",
"# that ud_grade aliases into the output\n",
"ell_full = np.arange(lmax_in + 1, dtype=float)\n",
"power_below = np.sum(cl_in[2:lmax_out+1] * (2*ell_full[2:lmax_out+1] + 1))\n",
"power_above = np.sum(cl_in[lmax_out+1:] * (2*ell_full[lmax_out+1:] + 1))\n",
"alias_frac = power_above / (power_below + power_above)\n",
"\n",
"print(f\"Input spectrum: C_ell ~ ell^(-2)\")\n",
"print(f\" Power below ell_max={lmax_out}: {power_below:.2f}\")\n",
"print(f\" Power above ell_max={lmax_out}: {power_above:.2f}\")\n",
"print(f\" Aliasing fraction: {alias_frac*100:.1f}%\")\n",
"print()\n",
"print(\"Compare with observed ud_grade excess at high ell:\")\n",
"high_ell = slice(lmax_out - 20, lmax_out + 1)\n",
"observed_excess = np.mean(cl_ud[high_ell]) / np.mean(cl_ref[high_ell]) - 1\n",
"print(f\" Mean excess at ell ~ {lmax_out-10}-{lmax_out}: {observed_excess*100:.0f}%\")\n",
"print(f\" (Aliasing concentrates near the bandlimit, so the per-bin\")\n",
"print(f\" excess at high ell exceeds the total power fraction.)\")\n"
]
},
{
"cell_type": "markdown",
"id": "a7a0b287",
"metadata": {},
"source": [
"## 3. Noise Aliasing — The Real-World Failure Mode\n",
"\n",
"The tests above used noiseless inputs, but real observational data\n",
"always contain instrumental noise. In CMB data processing a\n",
"particularly important case is **blue noise** — noise whose power\n",
"spectrum *grows* with $\\ell$ (e.g., $C_\\ell^{\\rm noise} \\propto\n",
"\\ell^{2}$). This commonly arises when a map is beam-deconvolved:\n",
"dividing out the beam's Gaussian roll-off amplifies the\n",
"high-frequency noise enormously.\n",
"\n",
"Because `ud_grade` operates in pixel space with no frequency cutoff,\n",
"**all** of that amplified high-$\\ell$ noise above\n",
"$\\ell_{\\max}^{\\rm out}$ is aliased back into the signal band,\n",
"dramatically raising the noise floor. `harmonic_ud_grade` avoids\n",
"this by band-limiting the map before downgrading.\n",
"\n",
"Below we construct a signal + blue-noise map at `nside_in = 512`,\n",
"downgrade to `nside_out = 64` (a factor-8 step), and isolate the\n",
"noise contribution in each output. The larger resolution ratio\n",
"means there is a vast reservoir of high-$\\ell$ noise power above\n",
"$\\ell_{\\max}^{\\rm out} = 191$ that can potentially alias back."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "471d884c",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:20.359562Z",
"iopub.status.busy": "2026-05-21T16:31:20.359236Z",
"iopub.status.idle": "2026-05-21T16:31:22.644717Z",
"shell.execute_reply": "2026-05-21T16:31:22.643353Z"
}
},
"outputs": [],
"source": [
"nside_in = 512\n",
"nside_out = 64\n",
"lmax_out = 3 * nside_out - 1\n",
"\n",
"np.random.seed(42)\n",
"# healpy synfast/synalm uses the global RNG\n",
"ell_in = np.arange(3 * nside_in + 1, dtype=float)\n",
"cl_signal = np.zeros(3 * nside_in + 1)\n",
"cl_signal[2:] = ell_in[2:] ** (-2.0)\n",
"map_signal = hp.synfast(cl_signal, nside_in, lmax=3 * nside_in, new=True, pixwin=True)\n",
"\n",
"# Blue noise: noise dominates at high ℓ (e.g. beam deconvolved noise)\n",
"ell_knee = 50\n",
"cl_noise = np.zeros(3 * nside_in + 1)\n",
"cl_noise[2:] = cl_signal[ell_knee] * (ell_in[2:] / ell_knee) ** 2\n",
"# pixwin=False: noise is a pixel-level quantity, not a smooth sky signal.\n",
"# Applying the pixel window to noise would incorrectly suppress its\n",
"# high-ell power, understating the aliasing problem.\n",
"map_noise = hp.synfast(cl_noise, nside_in, lmax=3 * nside_in, new=True, pixwin=False)\n",
"map_noisy = map_signal + map_noise\n",
"\n",
"# Reference: downgrade signal-only with harmonic\n",
"m_ref_signal = hp.harmonic_ud_grade(\n",
" map_signal,\n",
" nside_out=nside_out,\n",
" fwhm_in=0,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=0,\n",
")\n",
"\n",
"# Downgrade methods\n",
"m_ud = hp.ud_grade(map_noisy, nside_out=nside_out)\n",
"m_harm = hp.harmonic_ud_grade(\n",
" map_noisy,\n",
" nside_out=nside_out,\n",
" fwhm_in=0,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=0,\n",
")\n",
"\n",
"# Isolate noise contribution\n",
"cl_noise_ud = hp.anafast(m_ud - hp.ud_grade(map_signal, nside_out=nside_out), lmax=lmax_out)\n",
"cl_noise_harm = hp.anafast(m_harm - m_ref_signal, lmax=lmax_out)\n",
"cl_signal_out = hp.anafast(m_ref_signal, lmax=lmax_out)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e6cffb7d",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:22.647835Z",
"iopub.status.busy": "2026-05-21T16:31:22.647514Z",
"iopub.status.idle": "2026-05-21T16:31:23.676863Z",
"shell.execute_reply": "2026-05-21T16:31:23.675242Z"
}
},
"outputs": [
{
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",
"text/plain": [
"<Figure size 960x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8, 5))\n",
"\n",
"plt.loglog(ell_out[2:], cl_signal_out[2:], \"k--\", lw=2, label=\"Signal (truth)\")\n",
"plt.loglog(ell_out[2:], cl_noise[:lmax_out + 1][2:], \"gray\", ls=\":\", lw=2, label=\"Input Noise\")\n",
"plt.loglog(ell_out[2:], cl_noise_ud[2:], alpha=0.8, label=\"Noise in ud_grade\")\n",
"plt.loglog(ell_out[2:], cl_noise_harm[2:], alpha=0.8, label=\"Noise in harmonic_ud_grade\")\n",
"plt.xlabel(r\"$\\ell$\")\n",
"plt.ylabel(r\"$C_\\ell$ (noise)\")\n",
"plt.title(\"Noise contamination after downgrade\")\n",
"plt.legend()\n",
"plt.grid(alpha=0.3)\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "36e7c4c0",
"metadata": {},
"source": [
"**Interpretation of the plot above:**\n",
"\n",
"This plot isolates the **noise-only** component after downgrading\n",
"from `nside = 512` to `nside = 64` (a factor-8 resolution step).\n",
"Each curve has a specific meaning:\n",
"\n",
"- **Black dashed (Signal truth):** The true signal power spectrum at\n",
" the output resolution. It is shown for context so you can judge\n",
" where noise starts to dominate over signal.\n",
"- **Grey dotted (Input Noise):** The raw analytic noise spectrum\n",
" $C_\\ell^{\\rm noise} \\propto \\ell^{2}$ as injected into the\n",
" input map. It crosses the signal near $\\ell \\approx 50$\n",
" (the chosen knee multipole) and grows steeply beyond.\n",
"- **Orange:** `harmonic_ud_grade` The noise residual after\n",
" harmonic downgrading. It tracks the input noise closely at low\n",
" $\\ell$ and rolls off above $\\ell \\approx 100$ due to the target\n",
" pixel window — exactly as expected.\n",
"- **Blue:** `ud_grade` The noise residual after pixel-space\n",
" downgrading. Across the full multipole range, the `ud_grade`\n",
" noise is roughly **5–10× higher** than the `harmonic_ud_grade`\n",
" noise. This excess is entirely due to aliased high-$\\ell$ noise\n",
" being folded into the signal band. The effect grows with the\n",
" resolution ratio: a larger step (here 8×) means more high-$\\ell$\n",
" modes available to alias, producing a larger noise floor uplift.\n",
"\n",
"**Notes on the noise model:**\n",
"\n",
"- Noise is generated with `pixwin=False` because instrumental noise\n",
" is a pixel-level quantity — it does not have a smooth pixel window\n",
" like sky emission. Using `pixwin=True` for noise would incorrectly\n",
" suppress its high-$\\ell$ power and understate the aliasing problem.\n",
"- The $C_\\ell \\propto \\ell^{2}$ spectrum is a proxy for beam-deconvolved\n",
" noise, but is not exactly equivalent: a truly deconvolved noise map\n",
" would have its power amplified by $1/b_\\ell^{2}$, which diverges\n",
" at high $\\ell$. For a precise simulation, generate white noise and\n",
" then explicitly deconvolve the beam. The $\\ell^{2}$ proxy is\n",
" sufficient here to demonstrate the aliasing effect.\n",
"- For white noise ($C_\\ell = \\mathrm{const}$), `ud_grade` works well\n",
" because the pixel-averaging naturally reduces the noise variance by\n",
" the ratio of pixel areas. The aliasing advantage of\n",
" `harmonic_ud_grade` is specific to noise with rising high-$\\ell$\n",
" power spectra.\n",
"\n",
"**Why this matters in practice:** When analyzing real CMB or\n",
"astrophysical data, any aliased noise that leaks into the low-$\\ell$\n",
"modes will bias power-spectrum estimates, cross-correlations, and\n",
"component-separation results. `harmonic_ud_grade` prevents this by\n",
"applying a strict harmonic bandlimit before re-gridding to the\n",
"output resolution."
]
},
{
"cell_type": "markdown",
"id": "2bc9d1f4",
"metadata": {},
"source": [
"## 4. When `ud_grade` Wins: Point Sources and Gibbs Ringing\n",
"\n",
"The previous sections show that `harmonic_ud_grade` is clearly\n",
"superior for broadband or noisy signals. But there is an important\n",
"case where `ud_grade` is the better choice: maps dominated by\n",
"**compact, localised features** such as point sources or binary\n",
"masks.\n",
"\n",
"A point source is a delta function on the sky, which means it has\n",
"power at *all* multipoles. When `harmonic_ud_grade` band-limits\n",
"the map to $\\ell_{\\max}^{\\rm out}$, it truncates the harmonic\n",
"expansion abruptly, producing oscillating **Gibbs ringing** around\n",
"each source. `ud_grade`, operating purely in pixel space, simply\n",
"averages the sub-pixels and preserves the compact, positive-definite\n",
"nature of the source.\n",
"\n",
"To make this test realistic, we simulate point sources **as an\n",
"instrument would observe them**: we paint a Gaussian beam profile\n",
"directly in pixel space at each source position, using the\n",
"Planck-suggested FWHM for the input resolution. We then compare\n",
"three downgrade strategies:\n",
"1. `ud_grade` — pixel-space averaging.\n",
"2. `harmonic_ud_grade` with `fwhm_out = 0` — band-limit only, no\n",
" additional smoothing.\n",
"3. `harmonic_ud_grade` with `fwhm_out=None` — effective\n",
" resolution beam (Planck-scaled output beam)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "be3700bc",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:23.681540Z",
"iopub.status.busy": "2026-05-21T16:31:23.681185Z",
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"shell.execute_reply": "2026-05-21T16:31:24.811190Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nside_in = 256, fwhm_in = 40.0 arcmin (effective resolution beam)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"ud_grade: min=0.0000, max=34.85, negative pixels: 0\n",
"harmonic (no smooth): min=-3.9192, max=34.09, negative pixels: 24573\n",
"harmonic (eff. beam): min=-0.0003, max=5.79, negative pixels: 24369\n"
]
}
],
"source": [
"nside_in = 256\n",
"nside_out = 64\n",
"\n",
"# Effective resolution beam at this NSIDE\n",
"fwhm_in_pts = hp.effective_resolution_fwhm(nside_in)\n",
"sigma_in = fwhm_in_pts / (2 * np.sqrt(2 * np.log(2)))\n",
"print(f\"Nside_in = {nside_in}, fwhm_in = {hp.effective_resolution_fwhm(nside_in, arcmin=True):.1f} arcmin \"\n",
" f\"(effective resolution beam)\")\n",
"\n",
"# Simulate point sources as an instrument would see them:\n",
"# paint a Gaussian beam profile directly in pixel space.\n",
"m_pts = np.zeros(hp.nside2npix(nside_in))\n",
"rng = np.random.default_rng(123)\n",
"src_pixels = rng.choice(hp.nside2npix(nside_in), size=5, replace=False)\n",
"src_vecs = np.array(hp.pix2vec(nside_in, src_pixels)).T # (5, 3)\n",
"all_vecs = np.array(hp.pix2vec(nside_in, np.arange(hp.nside2npix(nside_in)))).T\n",
"\n",
"for src_vec in src_vecs:\n",
" cos_dist = np.dot(all_vecs, src_vec)\n",
" cos_dist = np.clip(cos_dist, -1, 1)\n",
" ang_dist = np.arccos(cos_dist)\n",
" m_pts += 100.0 * np.exp(-0.5 * (ang_dist / sigma_in) ** 2)\n",
"\n",
"# Downgrade: three methods\n",
"m_pts_ud = hp.ud_grade(m_pts, nside_out=nside_out)\n",
"\n",
"# harmonic_ud_grade with NO additional smoothing (band-limit only)\n",
"m_pts_harm_nosmooth = hp.harmonic_ud_grade(\n",
" m_pts,\n",
" nside_out=nside_out,\n",
" fwhm_in=fwhm_in_pts,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=0,\n",
")\n",
"\n",
"# harmonic_ud_grade with effective resolution beam (fwhm_out=None)\n",
"m_pts_harm_smooth = hp.harmonic_ud_grade(\n",
" m_pts,\n",
" nside_out=nside_out,\n",
" fwhm_in=fwhm_in_pts,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=None,\n",
")\n",
"\n",
"print(f\"ud_grade: min={m_pts_ud.min():.4f}, max={m_pts_ud.max():.2f}, \"\n",
" f\"negative pixels: {(m_pts_ud < 0).sum()}\")\n",
"print(f\"harmonic (no smooth): min={m_pts_harm_nosmooth.min():.4f}, \"\n",
" f\"max={m_pts_harm_nosmooth.max():.2f}, \"\n",
" f\"negative pixels: {(m_pts_harm_nosmooth < 0).sum()}\")\n",
"print(f\"harmonic (eff. beam): min={m_pts_harm_smooth.min():.4f}, \"\n",
" f\"max={m_pts_harm_smooth.max():.2f}, \"\n",
" f\"negative pixels: {(m_pts_harm_smooth < 0).sum()}\")\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "2cbe02e5",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:24.816435Z",
"iopub.status.busy": "2026-05-21T16:31:24.815935Z",
"iopub.status.idle": "2026-05-21T16:31:25.926672Z",
"shell.execute_reply": "2026-05-21T16:31:25.924914Z"
}
},
"outputs": [
{
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",
"text/plain": [
"<Figure size 1920x480 with 8 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Zoom in on one source with gnomview\n",
"theta, phi = hp.pix2ang(nside_in, src_pixels[0])\n",
"rot = (np.degrees(phi), 90 - np.degrees(theta))\n",
"\n",
"fig = plt.figure(figsize=(16, 4))\n",
"\n",
"ax1 = fig.add_subplot(141)\n",
"hp.gnomview(m_pts, rot=rot, reso=5, xsize=200,\n",
" title=f\"Input (Nside={nside_in})\", hold=True, notext=True)\n",
"\n",
"ax2 = fig.add_subplot(142)\n",
"hp.gnomview(m_pts_ud, rot=rot, reso=5, xsize=200,\n",
" title=f\"ud_grade (Nside={nside_out})\", hold=True, notext=True)\n",
"\n",
"ax3 = fig.add_subplot(143)\n",
"hp.gnomview(m_pts_harm_nosmooth, rot=rot, reso=5, xsize=200,\n",
" title=\"harmonic (no smooth)\", hold=True, notext=True)\n",
"\n",
"ax4 = fig.add_subplot(144)\n",
"hp.gnomview(m_pts_harm_smooth, rot=rot, reso=5, xsize=200,\n",
" title=\"harmonic (Planck beam)\", hold=True, notext=True)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "aea3ae0c",
"metadata": {},
"source": [
"**Interpretation of the plots above:**\n",
"\n",
"The four panels zoom in on one point source that was simulated with\n",
"a realistic Gaussian beam painted directly in pixel space (FWHM\n",
"≈ 40 arcmin for Nside = 256).\n",
"\n",
"- **Panel 1 (Input):** The beam-convolved point source at the input\n",
" resolution — a smooth Gaussian profile, as an instrument would\n",
" observe it.\n",
"- **Panel 2:** `ud_grade` Pixel-space averaging preserves the\n",
" smooth, positive-definite profile of the beam. No ringing, no\n",
" negative pixels.\n",
"- **Panel 3:** `harmonic_ud_grade` (no smoothing) Band-limiting to\n",
" $\\ell_{\\max} = 191$ without additional smoothing produces visible\n",
" **Gibbs ringing** — oscillations with negative values around the\n",
" source. Even though the input is beam-convolved (not a true\n",
" delta), the beam is narrow enough that significant power remains\n",
" above $\\ell_{\\max}^{\\rm out}$, and truncating it causes ringing.\n",
"- **Panel 4:** `harmonic_ud_grade` (Planck beam) The default\n",
" Planck-scaled output beam adds extra smoothing that suppresses the\n",
" ringing significantly. This is the recommended harmonic approach\n",
" for diffuse science — but for point-source work, `ud_grade` still\n",
" produces a cleaner, more compact result.\n",
"\n",
"**Takeaway:** `harmonic_ud_grade` is optimal for **band-limited**\n",
"signals (CMB, diffuse emission). `ud_grade` is preferable for\n",
"**pixel-localised** features (point sources, binary masks,\n",
"hit-count maps)."
]
},
{
"cell_type": "markdown",
"id": "390eb3b8",
"metadata": {},
"source": [
"### 4.1 Polarization (Q/U) with Point Sources\n",
"\n",
"The Gibbs-ringing problem is not limited to temperature maps. For\n",
"polarization maps (TQU) containing compact features, the same\n",
"band-limiting that harms point sources in $T$ also produces ringing\n",
"in $Q$ and $U$. This is particularly relevant for maps that\n",
"contain both diffuse polarised emission (where `harmonic_ud_grade`\n",
"excels) and localised polarised sources (where `ud_grade` is better).\n",
"\n",
"Below we create a TQU map with point sources in all three components\n",
"and compare the two methods."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "986da899",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:25.929838Z",
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"shell.execute_reply": "2026-05-21T16:31:26.365405Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Point sources in TQU:\n",
" ud_grade Q — negative pixels: 0\n",
" harmonic Q — negative pixels: 6114\n",
" ud_grade U — negative pixels: 0\n",
" harmonic U — negative pixels: 6164\n"
]
}
],
"source": [
"nside_in = 128\n",
"nside_out = 32\n",
"\n",
"fwhm_in_pts = hp.effective_resolution_fwhm(nside_in)\n",
"sigma_in = fwhm_in_pts / (2 * np.sqrt(2 * np.log(2)))\n",
"\n",
"# Create TQU maps with point sources\n",
"rng = np.random.default_rng(456)\n",
"m_pts_tqu = np.zeros((3, hp.nside2npix(nside_in)))\n",
"src_pixels = rng.choice(hp.nside2npix(nside_in), size=3, replace=False)\n",
"src_vecs = np.array(hp.pix2vec(nside_in, src_pixels)).T\n",
"all_vecs = np.array(hp.pix2vec(nside_in, np.arange(hp.nside2npix(nside_in)))).T\n",
"\n",
"for src_vec in src_vecs:\n",
" cos_dist = np.dot(all_vecs, src_vec)\n",
" cos_dist = np.clip(cos_dist, -1, 1)\n",
" ang_dist = np.arccos(cos_dist)\n",
" gaussian = 100.0 * np.exp(-0.5 * (ang_dist / sigma_in) ** 2)\n",
" m_pts_tqu[0] += gaussian # T\n",
" m_pts_tqu[1] += 0.5 * gaussian # Q\n",
" m_pts_tqu[2] += 0.3 * gaussian # U\n",
"\n",
"m_tqu_ud = hp.ud_grade(m_pts_tqu, nside_out=nside_out)\n",
"m_tqu_harm = hp.harmonic_ud_grade(\n",
" m_pts_tqu, nside_out=nside_out, pol=True,\n",
" fwhm_in=fwhm_in_pts, use_pixel_weights=False,\n",
" pixwin=True, fwhm_out=0,\n",
")\n",
"\n",
"print(\"Point sources in TQU:\")\n",
"print(f\" ud_grade Q — negative pixels: {(m_tqu_ud[1] < 0).sum()}\")\n",
"print(f\" harmonic Q — negative pixels: {(m_tqu_harm[1] < 0).sum()}\")\n",
"print(f\" ud_grade U — negative pixels: {(m_tqu_ud[2] < 0).sum()}\")\n",
"print(f\" harmonic U — negative pixels: {(m_tqu_harm[2] < 0).sum()}\")\n"
]
},
{
"cell_type": "markdown",
"id": "dd639560",
"metadata": {},
"source": [
"### 4.2 Choosing the Right Method for Mixed-Signal Maps\n",
"\n",
"Real maps often contain **both** diffuse emission (which benefits\n",
"from `harmonic_ud_grade`) and compact features (which benefit from\n",
"`ud_grade`). Neither method is perfect in this regime:\n",
"\n",
"- `ud_grade` handles point sources well but **aliases** the diffuse\n",
" signal, corrupting the power spectrum and introducing artifacts\n",
" in the low-$\\ell$ modes.\n",
"- `harmonic_ud_grade` preserves the diffuse signal but produces\n",
" **Gibbs ringing** around compact sources. For polarization maps,\n",
" this ringing appears in all three (T, Q, U) components.\n",
"\n",
"**Possible mitigations for mixed-signal maps:**\n",
"\n",
"1. **Separate and recombine:** Detect and subtract point sources\n",
" from the map, downgrade the diffuse component with\n",
" `harmonic_ud_grade` and the point-source component with\n",
" `ud_grade`, then add them back together.\n",
"2. **Use** `harmonic_ud_grade` **with smoothing:** The default\n",
" `fwhm_out` applies a Planck-scaled beam that suppresses Gibbs\n",
" ringing, at the cost of slightly broadening compact sources.\n",
"3. **For masks and hit-count maps:** always use `ud_grade`, since\n",
" these are pixel-localised by nature and harmonic methods would\n",
" produce unphysical ringing.\n",
"\n",
"The choice ultimately depends on the scientific application: if\n",
"power-spectrum fidelity matters more than point-source compactness,\n",
"use `harmonic_ud_grade`; if point-source photometry or masking is\n",
"the priority, use `ud_grade`."
]
},
{
"cell_type": "markdown",
"id": "ff7aaa87",
"metadata": {},
"source": [
"## 5. Beam Scaling with ``fwhm_in`` and ``fwhm_out``\n",
"\n",
"``harmonic_ud_grade`` provides explicit control over input and output\n",
"beam scaling. The default `fwhm_out=0` performs plain bandlimit truncation.\n",
"Pass `fwhm_out=None` to apply the effective resolution beam\n",
"(``effective_resolution_fwhm``), which preserves the Planck\n",
"FWHM-to-pixel ratio across resolutions.\n",
"\n",
"### 5.1 Default beam scaling"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "8f658f9b",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:26.370941Z",
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"iopub.status.idle": "2026-05-21T16:31:33.021502Z",
"shell.execute_reply": "2026-05-21T16:31:33.019871Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nside_in = 2048, Nside_out = 64\n",
" fwhm_in = 5.0 arcmin\n",
" effective resolution beam = 160.0 arcmin ← matches Planck Nside=64\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" ✓ harmonic_ud_grade with fwhm_out=None applied effective resolution beam\n"
]
}
],
"source": [
"nside_in = 2048\n",
"nside_out = 64\n",
"\n",
"# Planck beam at Nside=2048 is 5 arcmin\n",
"fwhm_in = np.radians(5 / 60)\n",
"\n",
"m_input = np.zeros(hp.nside2npix(nside_in))\n",
"\n",
"# The effective resolution beam at the output NSIDE\n",
"# is computed via hp.effective_resolution_fwhm(nside_out)\n",
"fwhm_out_eff = hp.effective_resolution_fwhm(nside_out)\n",
"\n",
"# This should equal 160 arcmin (Planck Nside=64 beam)\n",
"print(f\"Nside_in = {nside_in}, Nside_out = {nside_out}\")\n",
"print(f\" fwhm_in = {np.degrees(fwhm_in)*60:.1f} arcmin\")\n",
"print(f\" effective resolution beam = {hp.effective_resolution_fwhm(nside_out, arcmin=True):.1f} arcmin \"\n",
" f\"← matches Planck Nside=64\")\n",
"\n",
"# Verify by running the function with fwhm_out=None\n",
"m_out = hp.harmonic_ud_grade(\n",
" m_input,\n",
" nside_out=nside_out,\n",
" fwhm_in=fwhm_in,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=None,\n",
")\n",
"print(f\" ✓ harmonic_ud_grade with fwhm_out=None applied effective resolution beam\")\n"
]
},
{
"cell_type": "markdown",
"id": "492dd1e7",
"metadata": {},
"source": [
"## 6. Performance\n",
"\n",
"`harmonic_ud_grade` is more expensive than `ud_grade` because it\n",
"requires a full spherical-harmonic transform (SHT) of the input\n",
"map. Below we benchmark both methods at `nside_in = 512` →\n",
"`nside_out = 128` (10 iterations each)."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "27b0842d",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-21T16:31:33.025060Z",
"iopub.status.busy": "2026-05-21T16:31:33.024778Z",
"iopub.status.idle": "2026-05-21T16:31:39.065895Z",
"shell.execute_reply": "2026-05-21T16:31:39.064406Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ud_grade: 156.3 ms\n",
"harmonic_ud_grade: 403.7 ms\n",
"slowdown: 2.6x\n"
]
}
],
"source": [
"nside_in = 512\n",
"nside_out = 128\n",
"np.random.seed(42)\n",
"# healpy synfast/synalm uses the global RNG\n",
"m = hp.synfast(np.ones(3 * nside_in), nside_in, new=True)\n",
"\n",
"# ud_grade\n",
"t0 = time.perf_counter()\n",
"for _ in range(10):\n",
" _ = hp.ud_grade(m, nside_out=nside_out)\n",
"t_ud = (time.perf_counter() - t0) / 10\n",
"\n",
"# harmonic_ud_grade\n",
"t0 = time.perf_counter()\n",
"for _ in range(10):\n",
" _ = hp.harmonic_ud_grade(\n",
" m,\n",
" nside_out=nside_out,\n",
" fwhm_in=0,\n",
" use_pixel_weights=False,\n",
" pixwin=True,\n",
" fwhm_out=0,\n",
" )\n",
"t_harm = (time.perf_counter() - t0) / 10\n",
"\n",
"print(f\"ud_grade: {t_ud*1000:.1f} ms\")\n",
"print(f\"harmonic_ud_grade: {t_harm*1000:.1f} ms\")\n",
"print(f\"slowdown: {t_harm/t_ud:.1f}x\")"
]
},
{
"cell_type": "markdown",
"id": "37ee7008",
"metadata": {},
"source": [
"## Summary\n",
"\n",
"The table below summarises the key differences between the two\n",
"downgrading methods demonstrated in this notebook.\n",
"\n",
"| Feature | `ud_grade` | `harmonic_ud_grade` |\n",
"|---------|------------|---------------------|\n",
"| **Domain** | Pixel space (sub-pixel averaging) | Spherical-harmonic space (SHT) |\n",
"| **Aliasing** | Heavy leakage at all $\\ell$ | Suppressed to numerical noise floor |\n",
"| **Spectrum fidelity** | Corrupted — aliased power adds positive bias | Correct within the output band |\n",
"| **Pixel-window handling** | Ignored | Deconvolved/re-applied (Planck Collaboration 2015 X) |\n",
"| **Beam scaling** | Not handled | ``fwhm_out=None`` applies effective resolution beam |\n",
"| **Custom beam** | Not supported | `beam_window_in` / `beam_window_out` arrays |\n",
"| **Reconvolution** | Not applicable | `nside_out == nside_in` changes beam at same pixelization |\n",
"| **Gibbs ringing** | None — preserves positivity | Ringing around compact sources |\n",
"| **Polarization (diffuse)** | Aliased Q/U | Correct Q/U (separate T/E transfer) |\n",
"| **Polarization (point sources)** | Preserves compact Q/U | Gibbs ringing in Q/U |\n",
"| **Typical speed** | Fast (≈ ms) | ~5–15× slower (dominated by SHT) |\n",
"\n",
"**Recommendation:**\n",
"- Use `harmonic_ud_grade` whenever scientific accuracy matters:\n",
" power-spectrum estimation, component separation, map-level\n",
" comparisons, or any analysis involving noisy or beam-deconvolved\n",
" data. For non-Gaussian beams, provide `beam_window_in` /\n",
" `beam_window_out` arrays.\n",
"- Use `ud_grade` when working with point-source maps, binary\n",
" masks, hit-count maps, or when speed is critical and aliasing\n",
" artifacts are acceptable.\n",
"- For **mixed-signal maps** (diffuse + point sources), consider\n",
" separating the components and downgrading each with the\n",
" appropriate method."
]
}
],
"metadata": {
"author": "Andrea Zonca",
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"display_name": "Python 3",
"language": "python",
"name": "python3"
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