{ "cells": [ { "cell_type": "markdown", "id": "fc194bf0", "metadata": {}, "source": [ "# Local HEALPix FFT: projection and reconstruction tests\n", "\n", "This notebook validates the gnomonic projection, the fast FFT/IFFT round trip, pole handling, the 0/360-degree meridian and PyTorch autograd. The HEALPix-to-grid reprojection is bilinear, so the final reconstruction is expected to be approximate." ] }, { "cell_type": "code", "execution_count": 1, "id": "4bec8eb0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "device: cuda\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import torch\n", "import matplotlib.pyplot as plt\n", "import healpix_geo\n", "\n", "from healpix_analyse.fft_local import LocalFFT, fft, ifft, ps\n", "\n", "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", "print(\"device:\", device)\n", "torch.manual_seed(0)" ] }, { "cell_type": "code", "execution_count": 2, "id": "aaf411e7", "metadata": {}, "outputs": [], "source": [ "def make_patch(lon_deg, lat_deg, *, level=7, radius_deg=5.0):\n", " cell_ids, _, _ = healpix_geo.nested.cone_coverage(\n", " (lon_deg, lat_deg), radius_deg, level, ellipsoid=\"sphere\"\n", " )\n", " return np.asarray(cell_ids, dtype=np.int64)\n", "\n", "\n", "def relative_rms(reference, estimate):\n", " reference = torch.as_tensor(reference)\n", " estimate = torch.as_tensor(estimate)\n", " return (\n", " torch.linalg.vector_norm(estimate - reference)\n", " / torch.linalg.vector_norm(reference)\n", " ).item()" ] }, { "cell_type": "markdown", "id": "f7361e3c", "metadata": {}, "source": [ "## Geometry and FFT/IFFT reconstruction\n", "\n", "The four cases exercise a regular equatorial patch, a patch crossing the longitude discontinuity, and both poles." ] }, { "cell_type": "code", "execution_count": 3, "id": "a6b00241", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'case': 'equator', 'cells': 434, 'grid': 32, 'radius_deg': 5.345987578998197, 'smooth_rel_rms': 0.009681833550991233, 'constant_max_abs': 4.440892098500626e-16}\n", "{'case': 'meridian_0', 'cells': 428, 'grid': 32, 'radius_deg': 5.341431499616129, 'smooth_rel_rms': 0.010064204688898055, 'constant_max_abs': 3.3306690738754696e-16}\n", "{'case': 'north_pole', 'cells': 420, 'grid': 32, 'radius_deg': 5.118462097772193, 'smooth_rel_rms': 0.016842954587225012, 'constant_max_abs': 4.440892098500626e-16}\n", "{'case': 'south_pole', 'cells': 420, 'grid': 32, 'radius_deg': 5.118462097772193, 'smooth_rel_rms': 0.01684295458722501, 'constant_max_abs': 4.440892098500626e-16}\n" ] } ], "source": [ "cases = {\n", " \"equator\": (45.0, 0.0),\n", " \"meridian_0\": (359.0, 20.0),\n", " \"north_pole\": (0.0, 90.0),\n", " \"south_pole\": (0.0, -90.0),\n", "}\n", "\n", "results = []\n", "transforms = {}\n", "for name, centre in cases.items():\n", " cell_ids = make_patch(*centre)\n", " transform = LocalFFT(\n", " cell_ids, level=7, device=device, dtype=torch.float64\n", " )\n", " transforms[name] = transform\n", "\n", " # A smooth signal defined directly in the local tangent plane.\n", " x = transform.projected_x\n", " y = transform.projected_y\n", " data = torch.sin(25.0 * x) + 0.4 * torch.cos(17.0 * y)\n", " spectrum = transform.fft(data)\n", " reconstructed = transform.ifft(spectrum)\n", "\n", " constant = torch.ones_like(data)\n", " constant_reconstructed = transform.ifft(transform.fft(constant))\n", " results.append({\n", " \"case\": name,\n", " \"cells\": transform.n_cells,\n", " \"grid\": transform.grid_size,\n", " \"radius_deg\": transform.patch_radius_deg,\n", " \"smooth_rel_rms\": relative_rms(data, reconstructed),\n", " \"constant_max_abs\": (constant_reconstructed - constant).abs().max().item(),\n", " })\n", "\n", "for result in results:\n", " print(result)" ] }, { "cell_type": "code", "execution_count": 4, "id": "840f1f2a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Visual inspection of the most singular geographic case.\n", "transform = transforms[\"north_pole\"]\n", "data = torch.sin(25.0 * transform.projected_x) + 0.4 * torch.cos(17.0 * transform.projected_y)\n", "grid = transform.project(data).detach().cpu()\n", "reconstructed = transform.ifft(transform.fft(data)).detach().cpu()\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n", "axes[0].scatter(transform.projected_x.cpu(), transform.projected_y.cpu(), c=data.cpu(), s=8)\n", "axes[0].set_title(\"HEALPix centres in tangent plane\")\n", "axes[0].set_aspect(\"equal\")\n", "axes[1].imshow(grid, origin=\"lower\", cmap=\"viridis\")\n", "axes[1].set_title(\"Projected square grid\")\n", "axes[2].scatter(data.cpu(), reconstructed, s=8, alpha=0.6)\n", "limits = [float(data.min().cpu()), float(data.max().cpu())]\n", "axes[2].plot(limits, limits, \"k--\")\n", "axes[2].set_xlabel(\"input\")\n", "axes[2].set_ylabel(\"reconstructed\")\n", "axes[2].set_title(\"FFT/IFFT round trip\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "9fa5e1a5", "metadata": {}, "source": [ "## Circular one-dimensional power spectrum" ] }, { "cell_type": "code", "execution_count": 5, "id": "03bb8148", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "transform = transforms[\"equator\"]\n", "data = torch.sin(25.0 * transform.projected_x) + 0.4 * torch.cos(17.0 * transform.projected_y)\n", "spectrum = transform.fft(data)\n", "frequency, power = transform.ps(spectrum)\n", "\n", "assert frequency.shape == (transform.grid_size // 2,)\n", "assert power.shape == frequency.shape\n", "assert torch.isfinite(power).all()\n", "assert torch.all(frequency[1:] > frequency[:-1])\n", "assert frequency[-1] < 0.5 / transform.pixel_size_rad\n", "\n", "# A Fourier plane with unit power must have unit power in every annulus.\n", "flat_spectrum = torch.ones_like(spectrum)\n", "_, flat_power = transform.ps(flat_spectrum)\n", "assert torch.allclose(flat_power, torch.ones_like(flat_power))\n", "corner_frequency, corner_power = transform.ps(spectrum, include_corners=True)\n", "assert corner_frequency.numel() > frequency.numel()\n", "assert corner_power.shape == corner_frequency.shape\n", "plt.loglog(frequency.cpu(), power.detach().cpu())\n", "plt.xlabel(\"spatial frequency [cycles per tangent unit]\")\n", "plt.ylabel(\"circularly averaged power\")\n", "plt.grid(True, which=\"both\", alpha=0.25)" ] }, { "cell_type": "markdown", "id": "89289b9d", "metadata": {}, "source": [ "## Batched tensors, CUDA and autograd" ] }, { "cell_type": "code", "execution_count": 6, "id": "a627df30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "batch spectrum shape: (3, 32, 32)\n", "batch power shape: (3, 16)\n", "batch reconstruction shape: (3, 434)\n", "finite gradient: True\n", "gradient norm: 0.06853051345715866\n" ] } ], "source": [ "transform = transforms[\"equator\"].to(device)\n", "batch = torch.randn(3, transform.n_cells, device=device, dtype=torch.float64, requires_grad=True)\n", "spectrum = transform.fft(batch)\n", "reconstructed = transform.ifft(spectrum)\n", "frequency, batch_power = transform.ps(spectrum)\n", "loss = reconstructed.square().mean() + torch.nan_to_num(batch_power).mean()\n", "loss.backward()\n", "\n", "print(\"batch spectrum shape:\", tuple(spectrum.shape))\n", "print(\"batch power shape:\", tuple(batch_power.shape))\n", "print(\"batch reconstruction shape:\", tuple(reconstructed.shape))\n", "print(\"finite gradient:\", bool(torch.isfinite(batch.grad).all()))\n", "print(\"gradient norm:\", batch.grad.norm().item())" ] }, { "cell_type": "markdown", "id": "ff3cd602", "metadata": {}, "source": [ "## Functional API and radius guard" ] }, { "cell_type": "code", "execution_count": 7, "id": "93838fb7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "functional API relative RMS: 0.5946385112854626\n", "functional PS shapes: (16,) (16,)\n", "expected radius error: The patch radius is 12.6701 degrees, greater than max_patch_radius_deg=10. Split the cells into smaller local patches.\n" ] } ], "source": [ "cell_ids = make_patch(10.0, 30.0, level=7, radius_deg=4.0)\n", "data = np.random.default_rng(0).standard_normal(len(cell_ids))\n", "spectrum, transform = fft(\n", " cell_ids, 7, data, return_transform=True, device=device\n", ")\n", "reconstructed = ifft(spectrum, transform)\n", "frequency, power = ps(spectrum, transform)\n", "print(\"functional API relative RMS:\", relative_rms(data, reconstructed))\n", "print(\"functional PS shapes:\", frequency.shape, power.shape)\n", "\n", "large_patch = make_patch(0.0, 0.0, level=6, radius_deg=12.0)\n", "try:\n", " LocalFFT(large_patch, level=6, max_patch_radius_deg=10.0, device=device)\n", "except ValueError as error:\n", " print(\"expected radius error:\", error)\n", "else:\n", " raise AssertionError(\"A patch larger than 10 degrees should be rejected\")" ] } ], "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": "3.13.13" } }, "nbformat": 4, "nbformat_minor": 5 }