spherical_signal.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0e003b6f",
   "metadata": {},
   "source": [
    "## Recovery of spherical harmonic signal generated from points using power spectrum and bispectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08344252",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Optional, Union, Callable, Tuple\n",
    "\n",
    "import jax\n",
    "jax.config.update(\"jax_enable_x64\", True)\n",
    "\n",
    "import e3nn_jax as e3nn\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "import optax\n",
    "import chex\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "78e4721b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Irreps: 1x0e+1x1o+1x2e+1x3o+1x4e+1x5o+1x6e\n"
     ]
    }
   ],
   "source": [
    "lmax = 6\n",
    "p_val = 1\n",
    "p_arg = -1\n",
    "\n",
    "print(f\"Irreps: {e3nn.s2_irreps(lmax=lmax, p_val=p_val, p_arg=p_arg)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d67a57ba",
   "metadata": {},
   "source": [
    "## Define power and bispectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "611dbd5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Direct translation of the PyTorch implementation linked above to JAX.\n",
    "def powerspectrum(coeffs: e3nn.IrrepsArray) -> jnp.ndarray:\n",
    "    return e3nn.tensor_square(coeffs).filter([\"0e\", \"0o\"]).array\n",
    "\n",
    "\n",
    "def bispectrum(x: e3nn.IrrepsArray) -> jnp.ndarray:\n",
    "    rtp = e3nn.reduced_symmetric_tensor_product_basis(x.irreps, 3, keep_ir=['0e', '0o'])\n",
    "    return jnp.einsum(\"ijkz,i,j,k->z\", rtp.array, x.array, x.array, x.array)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b01ca329",
   "metadata": {},
   "source": [
    "## Define random points that are sufficiently far enough away from center\n",
    "\n",
    "Atoms don't like to be too close to each other. This fact can be used to bound the configurations we are optimizing over."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0ddcb1cd",
   "metadata": {},
   "outputs": [
    {
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        "plotlyServerURL": "https://plot.ly"
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",
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",
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     "metadata": {},
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   ],
   "source": [
    "N = 5\n",
    "rng = jax.random.PRNGKey(0)\n",
    "true_vec_rng, rng = jax.random.split(rng)\n",
    "true_vec = jax.random.normal(true_vec_rng, (N, 3))\n",
    "true_vec /= jnp.linalg.norm(true_vec, axis=-1, keepdims=True)\n",
    "true_vec_rng, _ = jax.random.split(true_vec_rng)\n",
    "true_vec *= jax.random.normal(true_vec_rng, (N, 1)) * 0.5 + 1.0\n",
    "true_sig = e3nn.sum(e3nn.s2_dirac(\n",
    "    true_vec, lmax=lmax, p_val=p_val, p_arg=p_arg\n",
    "))\n",
    "\n",
    "go.Figure(\n",
    "    [\n",
    "        go.Surface(\n",
    "            e3nn.to_s2grid(\n",
    "                true_sig, 100, 99, quadrature=\"gausslegendre\"\n",
    "            ).plotly_surface(scale_radius_by_amplitude=True)\n",
    "        )\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "530131bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def colorplot(arr: jnp.ndarray):\n",
    "    \"\"\"Helper to plot a 1D array as a color plot.\"\"\"\n",
    "    plt.figure(figsize=(15, 1))\n",
    "    plt.axis(\"off\")\n",
    "    return plt.imshow(arr[None, :], cmap=\"RdBu\", vmin=-1e-1, vmax=1e-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a23752ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "true_spectrum, true_bispectrum = powerspectrum(true_sig), bispectrum(true_sig)\n",
    "\n",
    "colorplot(true_spectrum);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "09e3c509",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<Figure size 1500x100 with 1 Axes>"
      ]
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     "metadata": {},
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   ],
   "source": [
    "\n",
    "colorplot(true_bispectrum);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50f3c90d",
   "metadata": {},
   "source": [
    "## Optimize trial points to match power- and bi- specta.\n",
    "Using trial points makes optimization smoother. We won't actually care which points are recovered since we really care about the signal, but ensuring that our signal is always generated from a projection of points helps restrict the space of possible spherical harmonic signals.\n",
    "\n",
    "This optimization is not guaranteed to be perfect -- but it does pretty well and you can quickly tell whether its a good fit or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9b76dc56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 0, loss: 0.15349754691123962\n",
      "step 100, loss: 0.002825145609676838\n",
      "step 200, loss: 0.0007376660942099988\n",
      "step 300, loss: 0.0003766111913137138\n",
      "step 400, loss: 0.00026535181677900255\n",
      "step 500, loss: 0.0002094511000905186\n",
      "step 600, loss: 0.00016849409439601004\n",
      "step 700, loss: 0.00013254705118015409\n",
      "step 800, loss: 0.0001069381833076477\n",
      "step 900, loss: 8.533837535651401e-05\n",
      "step 1000, loss: 6.873224629089236e-05\n",
      "step 1100, loss: 5.6177690566983074e-05\n",
      "step 1200, loss: 4.667642497224733e-05\n",
      "step 1300, loss: 3.9579073927598074e-05\n",
      "step 1400, loss: 3.4307013265788555e-05\n",
      "step 1500, loss: 3.0381612305063754e-05\n",
      "step 1600, loss: 2.7449865228845738e-05\n",
      "step 1700, loss: 2.5255521904909983e-05\n",
      "step 1800, loss: 2.3605147362104617e-05\n",
      "step 1900, loss: 2.234931343991775e-05\n",
      "step 2000, loss: 2.1375604774220847e-05\n",
      "step 2100, loss: 2.0602221411536448e-05\n",
      "step 2200, loss: 1.9969780623796396e-05\n",
      "step 2300, loss: 1.9435030480963178e-05\n",
      "step 2400, loss: 1.8967813957715407e-05\n"
     ]
    }
   ],
   "source": [
    "def signal_from_params(params: optax.Params) -> e3nn.IrrepsArray:\n",
    "    \"\"\"Creates signal from current parameters.\"\"\"\n",
    "    other_vec = params[\"other_vec\"]\n",
    "    diracs = e3nn.s2_dirac(\n",
    "        other_vec, lmax=lmax, p_val=p_val, p_arg=p_arg\n",
    "    )\n",
    "    weights = jnp.linalg.norm(other_vec, axis=-1)\n",
    "    return e3nn.sum(diracs * weights[:, None])\n",
    "\n",
    "\n",
    "def loss(\n",
    "    params: optax.Params, true_spectrum: chex.Array, true_bispectrum: chex.Array\n",
    ") -> chex.Array:\n",
    "    \"\"\"Computes the loss corresponding to the current parameters.\"\"\"\n",
    "    # Compute signal.\n",
    "    pred_sig = signal_from_params(params)\n",
    "\n",
    "    # Compute spectrum and bispectrum.\n",
    "    pred_spectrum = powerspectrum(pred_sig)\n",
    "    pred_bispectrum = bispectrum(pred_sig)\n",
    "\n",
    "    # Compute loss.\n",
    "    loss_value = (\n",
    "        optax.l2_loss(true_spectrum, pred_spectrum).mean()\n",
    "        + optax.l2_loss(true_bispectrum, pred_bispectrum).mean()\n",
    "    )\n",
    "    return loss_value\n",
    "\n",
    "\n",
    "def fit(\n",
    "    params: optax.Params,\n",
    "    optimizer: optax.GradientTransformation,\n",
    "    true_spectrum: chex.Array,\n",
    "    true_bispectrum: chex.Array,\n",
    "    max_iter: int = 2500,\n",
    ") -> optax.Params:\n",
    "    opt_state = optimizer.init(params)\n",
    "\n",
    "    @jax.jit\n",
    "    def step(params, opt_state, true_spectrum, true_bispectrum):\n",
    "        loss_value, grads = jax.value_and_grad(loss)(\n",
    "            params, true_spectrum, true_bispectrum\n",
    "        )\n",
    "        updates, opt_state = optimizer.update(grads, opt_state, params)\n",
    "        params = optax.apply_updates(params, updates)\n",
    "        return params, opt_state, loss_value\n",
    "\n",
    "    for iter in range(max_iter):\n",
    "        params, opt_state, loss_value = step(\n",
    "            params, opt_state, true_spectrum, true_bispectrum\n",
    "        )\n",
    "        if iter % 100 == 0:\n",
    "            print(f\"step {iter}, loss: {loss_value}\")\n",
    "\n",
    "    return params\n",
    "\n",
    "\n",
    "# Finally, we can fit our parametrized function using the Adam optimizer\n",
    "# provided by optax.\n",
    "init_rng, rng = jax.random.split(rng)\n",
    "init_params = {\"other_vec\": jax.random.normal(init_rng, (10, 3))}\n",
    "optimizer = optax.adam(learning_rate=1e-2)\n",
    "params = fit(init_params, optimizer, true_spectrum, true_bispectrum)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06f1b537",
   "metadata": {},
   "source": [
    "## If the optimization goes well, we should recover the same signal modulo a rotation"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "40871deb",
   "metadata": {},
   "source": [
    "We can try to align the predicted and true signals by finding a rotation matrix that maps one to the other!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5275bc97",
   "metadata": {},
   "outputs": [],
   "source": [
    "align_signals = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7791c4fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ameyad/Downloads/b15272323164f6d2ab2bff57e6c5e65e-8263bd3cb63d9b3b853d5565d6c87d5a26ff2d07/.venv/lib/python3.13/site-packages/jax/_src/numpy/array_methods.py:122: UserWarning:\n",
      "\n",
      "Explicitly requested dtype float64 requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/jax-ml/jax#current-gotchas for more.\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Alignment loss = 0.06580092012882233\n"
     ]
    }
   ],
   "source": [
    "def mse_rot_closest(\n",
    "    w: chex.Array, sig1: e3nn.SphericalSignal, sig2: e3nn.SphericalSignal\n",
    "):\n",
    "    \"\"\"Mean distance between each point in rotated sig1 to its closest point in sig2.\"\"\"\n",
    "    assert w.shape == (4,)\n",
    "    # w is normalized to unit norm inside transform_by_quaternion().\n",
    "    sig1_rot = sig1.transform_by_quaternion(w, lmax=lmax)\n",
    "    r1_rot = sig1_rot.grid_vectors * sig1_rot.grid_values[..., None]\n",
    "    r2 = sig2.grid_vectors * sig2.grid_values[..., None]\n",
    "    r1_rot = r1_rot.reshape((-1, 3))\n",
    "    r2 = r2.reshape((-1, 3))\n",
    "    distances = jnp.linalg.norm(r1_rot[:, None, :] - r2[None, :, :], axis=-1) ** 2\n",
    "    return jnp.min(distances, axis=-1).mean()\n",
    "\n",
    "\n",
    "@jax.jit\n",
    "def optimal_rotation(\n",
    "    sig1: e3nn.SphericalSignal,\n",
    "    sig2: e3nn.SphericalSignal,\n",
    "    *,\n",
    "    steps: int = 256,\n",
    "    lr: float = 1e-2,\n",
    "    rng: chex.PRNGKey,\n",
    ") -> Tuple[chex.Array, chex.Numeric]:\n",
    "    \"\"\"Returns the rotation matrix and corresponding alignment error to rotate sig1 onto sig2.\"\"\"\n",
    "\n",
    "    def optimize(w):\n",
    "        optimizer = optax.adam(lr)\n",
    "        opt_state = optimizer.init(w)\n",
    "\n",
    "        def update(_, state):\n",
    "            w, opt_state = state\n",
    "            loss, grad = jax.value_and_grad(mse_rot_closest)(w, sig1, sig2)\n",
    "            u, s = optimizer.update(grad, opt_state, w)\n",
    "            w = optax.apply_updates(w, u)\n",
    "            return w, opt_state\n",
    "\n",
    "        w, s = jax.lax.fori_loop(0, steps, update, (w, opt_state))\n",
    "        return w\n",
    "\n",
    "    ws = jax.random.normal(rng, (10, 4))\n",
    "    optimal_ws = jax.vmap(optimize)(ws)\n",
    "    ls = jax.vmap(mse_rot_closest, (0, None, None))(optimal_ws, sig1, sig2)\n",
    "    optimal_l = jnp.nanmin(ls)\n",
    "    optimal_w = optimal_ws[jnp.nanargmin(ls)]\n",
    "    optimal_R = e3nn.quaternion_to_matrix(optimal_w)\n",
    "    return optimal_R, optimal_l\n",
    "\n",
    "\n",
    "# Compute optimal rotation.\n",
    "pred_sig = signal_from_params(params)\n",
    "if align_signals:\n",
    "    w_rng, rng = jax.random.split(rng)\n",
    "    R, loss = optimal_rotation(\n",
    "        e3nn.to_s2grid(pred_sig, 30, 29, quadrature=\"soft\"),\n",
    "        e3nn.to_s2grid(true_sig, 30, 29, quadrature=\"soft\"),\n",
    "        rng=w_rng,\n",
    "    )\n",
    "    pred_sig = pred_sig.transform_by_matrix(R)\n",
    "    print(f\"Alignment loss = {loss}\")\n",
    "else:\n",
    "    print(\"No alignment performed.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f647d248",
   "metadata": {},
   "outputs": [
    {
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            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "go.Figure(\n",
    "    [\n",
    "        go.Surface(\n",
    "            e3nn.to_s2grid(true_sig, 30, 29, quadrature=\"soft\").plotly_surface(\n",
    "                scale_radius_by_amplitude=True\n",
    "            )\n",
    "        )\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "546d3ea1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "surfacecolor": {
          "bdata": 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XCz7CVws+wlcLPsJXCz7CVws+wlcLPsJXCz7CVws+wlcLPsJXCz7CVws+wlcLPsJXCz7CVws+wlcLPsJXCz7CVws+wlcLPsJXCz7CVws+wlcLPsJXCz7CVws+",
          "dtype": "f4",
          "shape": "32, 30"
         },
         "type": "surface",
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            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "go.Figure(\n",
    "    [\n",
    "        go.Surface(\n",
    "            e3nn.to_s2grid(pred_sig, 30, 29, quadrature=\"soft\").plotly_surface(\n",
    "                scale_radius_by_amplitude=True\n",
    "            )\n",
    "        )\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8ee0e746",
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_spectrum, pred_bispectrum = powerspectrum(pred_sig), bispectrum(pred_sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ad2d2991",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colorplot(true_spectrum), colorplot(pred_spectrum);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a6644fde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colorplot(true_bispectrum), colorplot(pred_bispectrum);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a3c0b01c",
   "metadata": {},
   "outputs": [],
   "source": [
    "xyz_pred, r_pred = e3nn.to_s2grid(pred_sig, 100, 99, quadrature=\"soft\").find_peaks(lmax)\n",
    "xyz_tru, r_tru = e3nn.to_s2grid(true_sig, 100, 99, quadrature=\"soft\").find_peaks(lmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "752fec24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 0.98989904, -0.14090124, -0.01570773],\n",
       "        [ 0.9034191 ,  0.32391742,  0.280912  ],\n",
       "        [-0.09504421, -0.01570732, -0.9953491 ],\n",
       "        [ 0.9817719 ,  0.0784591 ,  0.17311291],\n",
       "        [ 0.60042024,  0.60436136,  0.523682  ],\n",
       "        [ 0.6730125 ,  0.5740621 , -0.46637636],\n",
       "        [ 0.35347486, -0.5304528 ,  0.77050334],\n",
       "        [ 0.78043044, -0.4852798 , -0.39424857],\n",
       "        [-0.94608533,  0.13921812, -0.29247358],\n",
       "        [-0.26387304,  0.8196089 , -0.50853914],\n",
       "        [ 0.9645574 , -0.2400274 , -0.1096169 ],\n",
       "        [ 0.993961  , -0.01043095,  0.10923739],\n",
       "        [ 0.57500523,  0.65105236,  0.49547935],\n",
       "        [-0.60042024,  0.533205  ,  0.5959766 ],\n",
       "        [-0.32391742,  0.6949865 , -0.6419278 ],\n",
       "        [ 0.14090118, -0.9453758 , -0.2939583 ],\n",
       "        [-0.29404032,  0.778566  , -0.5544143 ],\n",
       "        [-0.23344533,  0.85709876, -0.45922208],\n",
       "        [ 0.9969173 , -0.03595209,  0.06973718],\n",
       "        [-0.6959128 , -0.59789026,  0.39778453],\n",
       "        [-0.20278727,  0.8907324 , -0.40678385],\n",
       "        [ 0.64944804,  0.6194084 , -0.44107872]], dtype=float32),\n",
       " array([[ 0.6959128 , -0.55737114, -0.45281664],\n",
       "        [-0.86863154,  0.45068505, -0.20582092],\n",
       "        [-0.01570727,  0.9967318 ,  0.07924019],\n",
       "        [-0.5224985 ,  0.18784562,  0.83169067],\n",
       "        [-0.3826835 , -0.3970787 , -0.8341953 ],\n",
       "        [-0.78043044, -0.5908548 ,  0.20449673],\n",
       "        [ 0.78043044,  0.56874067, -0.2597352 ],\n",
       "        [-0.04710641,  0.9987641 ,  0.01584845],\n",
       "        [ 0.3826835 ,  0.6584436 ,  0.64807826],\n",
       "        [ 0.35347486, -0.5304528 ,  0.77050334]], dtype=float32))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xyz_pred[r_pred > 0.5], xyz_tru[r_tru > 0.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b9f074ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "mode": "markers",
         "name": "Predicted Peaks",
         "type": "scatter3d",
         "x": {
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        {
         "mode": "markers",
         "name": "True Peaks",
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         "x": {
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       ],
       "layout": {
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
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            "marker": {
             "line": {
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             },
             "pattern": {
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             }
            },
            "type": "bar"
           }
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          "barpolar": [
           {
            "marker": {
             "line": {
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             "pattern": {
              "fillmode": "overlay",
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            },
            "type": "barpolar"
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          "carpet": [
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            "aaxis": {
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             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
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            "baxis": {
             "endlinecolor": "#2a3f5f",
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             "linecolor": "white",
             "minorgridcolor": "white",
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          "choropleth": [
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            "colorscale": [
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             ],
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             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
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             ],
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              "#46039f"
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             [
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             ],
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             ],
             [
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             ],
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            ],
            "type": "heatmap"
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          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
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            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
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            "colorscale": [
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            "type": "histogram2d"
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          "histogram2dcontour": [
           {
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             "ticks": ""
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            "colorscale": [
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            ],
            "type": "histogram2dcontour"
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          ],
          "mesh3d": [
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             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
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          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
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            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
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            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
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            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
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            "marker": {
             "colorbar": {
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              "ticks": ""
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            },
            "type": "scattergeo"
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          ],
          "scattergl": [
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            },
            "type": "scattergl"
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          ],
          "scattermap": [
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            "marker": {
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              "outlinewidth": 0,
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            },
            "type": "scattermap"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
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            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
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            },
            "type": "scatterpolargl"
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          "scatterternary": [
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            },
            "type": "scatterternary"
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          ],
          "surface": [
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            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
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            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
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            },
            "type": "table"
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          ]
         },
         "layout": {
          "annotationdefaults": {
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           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
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          },
          "colorscale": {
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            [
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            [
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            [
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            [
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           ],
           "sequential": [
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           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "go.Figure(\n",
    "    [\n",
    "        go.Scatter3d(\n",
    "            x=xyz_pred[r_pred > 0.5][:, 0],\n",
    "            y=xyz_pred[r_pred > 0.5][:, 1],\n",
    "            z=xyz_pred[r_pred > 0.5][:, 2],\n",
    "            mode=\"markers\",\n",
    "            name=\"Predicted Peaks\",\n",
    "        ),\n",
    "        go.Scatter3d(\n",
    "            x=xyz_tru[r_tru > 0.5][:, 0],\n",
    "            y=xyz_tru[r_tru > 0.5][:, 1],\n",
    "            z=xyz_tru[r_tru > 0.5][:, 2],\n",
    "            mode=\"markers\",\n",
    "            name=\"True Peaks\",\n",
    "        ),\n",
    "    ]\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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