probability_mcmc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "561591e9-feaa-4b66-a9d5-915ea0b58ff0",
   "metadata": {},
   "source": [
    "SPDX-License-Identifier: GPL-3.0-or-later"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1da63fd9-569b-496c-b8b5-95416bf5e90b",
   "metadata": {},
   "source": [
    "# Init"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a339425e-30ac-4643-b3d5-ba00aec4ed78",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 964,
   "id": "afbb7abb-759c-4e3a-887c-e0c6e43c98f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.special\n",
    "import os\n",
    "import sys\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import tqdm\n",
    "import torch\n",
    "\n",
    "# from scipy.special import erfc\n",
    "# from scipy.stats import uniform\n",
    "\n",
    "_IPYTHON_PATH = os.path.expanduser(\"~/.ipython/\")\n",
    "_MY_PKG_PATHS = [_IPYTHON_PATH]\n",
    "for my_pkg_path in _MY_PKG_PATHS:\n",
    "    my_pkg_paths = [my_pkg_path, os.path.expanduser(my_pkg_path)]\n",
    "    my_pkg_paths.append(os.path.realpath(my_pkg_paths[-1]))\n",
    "    if all(x not in sys.path for x in my_pkg_paths):\n",
    "        sys.path.append(my_pkg_paths[-1])\n",
    "import my.utils as mu"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9c18a7-381e-45f1-8e92-1b98273f5541",
   "metadata": {},
   "source": [
    "## GPU memory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8c8e5194-d510-4b62-a07e-5a3343556adf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "import gc\n",
    "\n",
    "def del_models():\n",
    "    \"\"\"Delete the previous models.\"\"\"\n",
    "    models_var_names = {'opt_problem'}\n",
    "    for key in models_var_names:\n",
    "        if key in globals():\n",
    "            del globals()[key]\n",
    "            \n",
    "def del_jupyter_output():\n",
    "    \"\"\"Delete all global variables matching r'^_[0-9]*$' and keys of 'Out'.\n",
    "\n",
    "    These names are typically used for output cells in jupyter-lab.\n",
    "    This function followed by gc.collect() helps to free up memory\n",
    "    or other resources occupied by unused vars.\n",
    "    \n",
    "    Usually, this duplicates the work of '%reset out', hence no\n",
    "    additional variables are expected to be freed this way.\n",
    "    If for some reason the magic '%reset out' is not working,\n",
    "    this function could be used as an alternative.\n",
    "    \"\"\"\n",
    "    globals_keys = list(globals().keys())\n",
    "    for key in globals_keys:\n",
    "        if re.match(r'^_[0-9]*$', key):\n",
    "            del globals()[key]\n",
    "    if 'Out' in globals_keys:\n",
    "        out_keys = list(globals()['Out'].keys())\n",
    "        for key in out_keys:\n",
    "            del globals()['Out'][key]\n",
    "\n",
    "def free_gpu_memory(delete_models=False):\n",
    "    if delete_models:\n",
    "        del_models()\n",
    "    del_jupyter_output()\n",
    "    gc.collect()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "eb0648b2-656e-49df-a0f7-5f5ef2b520d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(torch.cuda.memory_allocated(0) / 1024**3)\n",
    "free_gpu_memory()\n",
    "print(torch.cuda.memory_allocated(0) / 1024**3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7069ee5-7fee-4a1a-b8fa-fecd6ca64fcf",
   "metadata": {},
   "source": [
    "## Zero temperature GinOE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e300d48e-6985-4ed6-8f89-826a4861be5d",
   "metadata": {},
   "source": [
    "### Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6b1d6d77-cc29-40c8-9e08-5fc33575a8bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ginoe_ypotential(ys):\n",
    "    \"\"\"\n",
    "    Compute the function $-2 y^2 - ln(erfc(\\sqrt{2} y))$ for y >= 0.\n",
    "    \n",
    "    We use direct formula (using scipy) for y <= 5 and a 2-point Pade approximant for y > 5.\n",
    "    \"\"\"\n",
    "    ys = np.array(ys)\n",
    "    # Initialize output array with the same shape as ys\n",
    "    output = np.empty_like(ys, dtype=np.float64)\n",
    "    \n",
    "    # For y > 5 (the absolute error is under $2 * 10^{-13}$ for y > 4):\n",
    "    mask1 = ys > 5\n",
    "    ys1 = ys[mask1]\n",
    "    y2 = ys1**2\n",
    "    y4 = y2 * y2\n",
    "    y6 = y4 * y2\n",
    "    y8 = y4 * y4\n",
    "    \n",
    "    numerator = (-0.8904519590478536430137744382884281115310 - \n",
    "                 9.869261681191832701731724404616295971553/y6 - \n",
    "                 16.90359050157721106889984300899829825369/y4 - \n",
    "                 7.423694049765192486628066963007045221308/y2)\n",
    "    \n",
    "    denominator = (1.000000000000000000000000000000000000000 +\n",
    "                   2.174258030977644555812272331973294792748/y8 +\n",
    "                   15.74732873975124317572963943709831902318/y6 +\n",
    "                   21.22717377517984141370472593958542366059/y4 +\n",
    "                   8.617751886323607565086681753902613859088/y2)\n",
    "                  \n",
    "    result1 = 0.8904519590478536430137744382884281115310 + numerator / denominator - \\\n",
    "              np.log(0.3989422804014326779399460599343818684759 / ys1)\n",
    "    \n",
    "    output[mask1] = result1\n",
    "    \n",
    "    # For y <= 5 (should work for y <= 18)\n",
    "    mask2 = ~mask1\n",
    "    ys2 = ys[mask2]\n",
    "    result2 = -2 * ys2**2 - np.log(scipy.special.erfc(np.sqrt(2) * ys2))\n",
    "    \n",
    "    output[mask2] = result2\n",
    "    \n",
    "    return output\n",
    "\n",
    "def ginoe_potentials(density0, density1, xs, ys, dx):\n",
    "    k = np.sum(density0)\n",
    "    k1 = np.sum(density1)\n",
    "    xs1 = xs[:, np.newaxis]\n",
    "    assert ys[0] == 0\n",
    "    ys1 = ys[np.newaxis, 1:]\n",
    "    nx = len(xs)\n",
    "    ny0 = len(ys)\n",
    "    ny1 = len(ys1[0])\n",
    "    \n",
    "    J = 2 * k1 + k\n",
    "    dk_ln_coeff = 0 # - math.log(2) / 2 - scipy.special.digamma(k + 1) + scipy.special.digamma((J-k)/2 + 1) / 2\n",
    "    potential0 = xs**2 /  2\n",
    "    potential1 = xs1**2 / 2 + ys1**2 / 2 + ginoe_ypotential(ys1) / 2\n",
    "    \n",
    "    interaction_00 = -np.sum(density0[np.newaxis, :] * np.log(np.maximum(dx, np.abs(xs[:, np.newaxis] - xs[np.newaxis, :]))), axis=1)\n",
    "    interaction_01 = -np.sum(density1[np.newaxis, :, :] * np.log((xs[:, np.newaxis, np.newaxis] - xs1[np.newaxis, :, :])**2 + ys1[np.newaxis, :, :]**2), axis=(1, 2))\n",
    "    interaction_10 = -np.sum(density0[np.newaxis, np.newaxis, :] * np.log((xs1[:, :, np.newaxis] - xs[np.newaxis, np.newaxis, :])**2 + ys1[:, :, np.newaxis]**2), axis=2) / 2\n",
    "    dx1_2 = (xs1[:, :, np.newaxis, np.newaxis] - xs1[np.newaxis, np.newaxis, :, :])**2\n",
    "    interaction_11 = -np.sum(density1[np.newaxis, np.newaxis, :, :] * (\n",
    "            np.log(np.maximum(dx**2, dx1_2 + (ys1[:, :, np.newaxis, np.newaxis] - ys1[np.newaxis, np.newaxis, :, :])**2))\n",
    "            + np.log(dx1_2 + (ys1[:, :, np.newaxis, np.newaxis] + ys1[np.newaxis, np.newaxis, :, :])**2)\n",
    "        ) / 2, axis=(2, 3))\n",
    "    assert interaction_11.shape == density1.shape\n",
    "    \n",
    "    potential0 = dk_ln_coeff * (k / J - 1) + potential0 + interaction_00 + interaction_01\n",
    "    potential1 = dk_ln_coeff * k / J + potential1 + interaction_10 + interaction_11\n",
    "    \n",
    "    return potential0, potential1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fd2834d4-310d-452f-92a2-195971340837",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GinOEOptimizationProblem:\n",
    "    def __init__(self, xs, ys, J):\n",
    "        self.xs = xs\n",
    "        self.ys = ys\n",
    "        self.J = J\n",
    "        self.learning_rate = 1.0\n",
    "        dx = min((xs[-1] - xs[0]) / (xs.shape[0] - 1), (ys[-1] - ys[0]) / (ys.shape[0] - 1))\n",
    "        \n",
    "        xs1 = xs[:, np.newaxis]\n",
    "        ys1 = ys[np.newaxis, 1:]\n",
    "        nx = xs.shape[0]\n",
    "        ny = ys.shape[0]\n",
    "        ny1 = ys.shape[0] - 1\n",
    "        potential0 = xs**2 /  2\n",
    "        potential1 = xs1**2 / 2 + ys1**2 / 2 + ginoe_ypotential(ys1) / 2\n",
    "        assert potential1.shape == (nx, ny1)\n",
    "        potential1_flat = potential1.reshape(nx * ny1)\n",
    "        self.potential_flat = np.concatenate([potential0, potential1_flat])\n",
    "        assert self.potential_flat.shape == (nx * ny,)\n",
    "        \n",
    "        coupling_00 = -np.log(np.maximum(dx / (2 * np.exp(1)), np.abs(xs[:, np.newaxis] - xs[np.newaxis, :])))\n",
    "        coupling_01 = -np.log((xs[:, np.newaxis, np.newaxis] - xs1[np.newaxis, :, :])**2 + ys1[np.newaxis, :, :]**2) / 2\n",
    "        dx1_2 = (xs1[:, :, np.newaxis, np.newaxis] - xs1[np.newaxis, np.newaxis, :, :])**2\n",
    "        coupling_11 = (\n",
    "                - np.log(np.maximum((dx / 2)**2 / np.exp(1), dx1_2 + (ys1[:, :, np.newaxis, np.newaxis] - ys1[np.newaxis, np.newaxis, :, :])**2))\n",
    "                - np.log(dx1_2 + (ys1[:, :, np.newaxis, np.newaxis] + ys1[np.newaxis, np.newaxis, :, :])**2)\n",
    "            ) / 4\n",
    "        assert coupling_01.shape == (nx, nx, ny1)\n",
    "        coupling_01_flat = coupling_01.reshape((nx, nx * ny1))\n",
    "        assert coupling_11.shape == (nx, ny1, nx, ny1)\n",
    "        coupling_11_flat = coupling_11.reshape((nx * ny1, nx * ny1))\n",
    "        self.coupling_flat = np.block([[coupling_00, coupling_01_flat], [coupling_01_flat.T, coupling_11_flat]])\n",
    "        assert self.coupling_flat.shape == (nx * ny, nx * ny)\n",
    "    \n",
    "    def flatten_density(self, density0, density1):\n",
    "        nx = self.xs.shape[0]\n",
    "        ny = self.ys.shape[0]\n",
    "        ny1 = self.ys.shape[0] - 1\n",
    "        assert density0.shape == (nx,)\n",
    "        assert density1.shape == (nx, ny1)\n",
    "        return np.concatenate([density0, density1.reshape(nx * ny1)])\n",
    "    \n",
    "    def unflatten_density(self, density_flat):\n",
    "        nx = self.xs.shape[0]\n",
    "        ny = self.ys.shape[0]\n",
    "        ny1 = self.ys.shape[0] - 1\n",
    "        assert density_flat.shape == (nx * ny,)\n",
    "        density0 = density_flat[:nx]\n",
    "        density1 = density_flat[nx:].reshape(nx, ny1)\n",
    "        return density0, density1\n",
    "    \n",
    "    def get_energy_flat(self, density_flat):\n",
    "        res = density_flat @ self.potential_flat + density_flat @ self.coupling_flat @ density_flat / 2\n",
    "        return res\n",
    "    \n",
    "    @torch.no_grad()\n",
    "    def optimize(self, density_flat, device=None, epochs=100, snapshot_every=10, snapshots=None):\n",
    "        if device is None:\n",
    "            device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "        density_flat = torch.from_numpy(density_flat).to(device)\n",
    "        potential_flat = torch.from_numpy(self.potential_flat).to(device)\n",
    "        coupling_flat = torch.from_numpy(self.coupling_flat).to(device)\n",
    "        get_objective = lambda x: (\n",
    "            torch.dot(x, potential_flat)\n",
    "            + torch.matmul(torch.matmul(x, coupling_flat), x) / 2)\n",
    "        objective = get_objective(density_flat)\n",
    "        grad_new = None\n",
    "        lr_decayed = False\n",
    "        for epoch in range(epochs):\n",
    "            if grad_new is None:\n",
    "                energy_grad = potential_flat + coupling_flat @ density_flat\n",
    "                grad_new = energy_grad - torch.mean(energy_grad[density_flat > 0])\n",
    "            \n",
    "            grad_new = grad_new - torch.mean(grad_new[(density_flat > 0) | (grad_new <= 0)])\n",
    "            print(f\"[{torch.std(energy_grad[density_flat > 0]):.3g}, {objective:.3f}, {self.learning_rate:.3g}]\", end=\"\")\n",
    "            \n",
    "            new_density_flat = density_flat - self.learning_rate * grad_new\n",
    "            new_density_flat[new_density_flat < 0] = 0\n",
    "            new_density_flat *= self.J / torch.sum(new_density_flat)\n",
    "            new_objective = get_objective(new_density_flat)\n",
    "            if lr_decayed or new_objective <= objective:\n",
    "                density_flat = new_density_flat\n",
    "                objective = new_objective\n",
    "                grad_new = None\n",
    "                self.learning_rate *= 1.01\n",
    "                lr_decayed = False\n",
    "            else:\n",
    "                self.learning_rate *= 0.5\n",
    "                lr_decayed = True\n",
    "            \n",
    "            if snapshots is not None and epoch % snapshot_every == 0:\n",
    "                snapshots.append(density_flat.data.cpu().numpy())\n",
    "        print(\"\")\n",
    "        return density_flat.data.cpu().numpy()\n",
    "    \n",
    "    def get_energy(self, density0, density1):\n",
    "        return self.get_energy_flat(self.flatten_density(density0, density1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7f6103a-262b-4986-beb7-7e1ed2577fb7",
   "metadata": {},
   "source": [
    "### Compute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a587ec56-15f5-4d39-b4b2-0c7e0efd5e06",
   "metadata": {},
   "outputs": [],
   "source": [
    "nx = 129\n",
    "ny = 129\n",
    "J = 255\n",
    "evals_scale = 1.6 * J**0.5\n",
    "xs = np.linspace(0, evals_scale, nx)\n",
    "ys = np.linspace(0, evals_scale, ny)\n",
    "dx = (xs[-1] - xs[0]) / (len(xs) - 1)\n",
    "all_ys = np.concatenate((-ys[::-1], ys[1:]))\n",
    "\n",
    "avg_density = J / (nx * (2 * ny - 1))\n",
    "circle_r = 1.25 * J**0.5\n",
    "circle_r2 = circle_r**2\n",
    "density_0 = (xs**2 <= circle_r2) * 1.0\n",
    "density_1 = (xs[:, np.newaxis]**2 + ys[np.newaxis, 1:]**2 <= circle_r2) * 1.0\n",
    "density_1[0, :] = 0.4 * (np.maximum(0, circle_r2 - ys[np.newaxis, 1:]**2)**0.5)\n",
    "total = np.sum(density_0) + np.sum(density_1)\n",
    "density_0 = density_0 / total * J\n",
    "density_1 = density_1 / total * J\n",
    "density_results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8f22b4ef-46c4-4ae3-8e5d-ba2e3003dd2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_problem = GinOEOptimizationProblem(xs=xs, ys=ys, J=J)\n",
    "density_flat = opt_problem.flatten_density(density_0, density_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7e0373bd-6ad8-4557-86c4-0265a74c6463",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: -60341.691\n",
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      "5: -60341.694\n",
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      "7: -60341.695\n",
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      "8: -60341.695\n",
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      "9: -60341.695\n",
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      "10: -60341.695\n",
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      "11: -60341.695\n",
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      "12: -60341.695\n",
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      "13: -60341.696\n",
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      "15: -60341.696\n",
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      "17: -60341.696\n",
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      "18: -60341.696\n",
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      "19: -60341.696\n",
      "[0.000197, -60341.696, 0.00101][0.000196, -60341.696, 0.00102][0.000196, -60341.696, 0.00103][0.000196, -60341.696, 0.00104][0.000196, -60341.696, 0.00105][0.000196, -60341.696, 0.00106][0.000196, -60341.696, 0.00108][0.000195, -60341.696, 0.00109][0.000195, -60341.696, 0.0011][0.000195, -60341.696, 0.00111][0.000195, -60341.696, 0.00112][0.000195, -60341.696, 0.00113][0.000195, -60341.696, 0.00114][0.000195, -60341.696, 0.00115][0.000195, -60341.696, 0.00116][0.000194, -60341.696, 0.00118][0.000194, -60341.696, 0.00119][0.000194, -60341.696, 0.0012][0.000194, -60341.696, 0.00121][0.000194, -60341.696, 0.00122][0.000194, -60341.696, 0.00124][0.000194, -60341.696, 0.00125][0.000194, -60341.696, 0.00126][0.000193, -60341.696, 0.00127][0.000193, -60341.696, 0.00129][0.000193, -60341.696, 0.0013][0.000193, -60341.696, 0.00131][0.000193, -60341.696, 0.00132][0.000193, -60341.696, 0.00134][0.000193, -60341.696, 0.00135][0.000193, -60341.696, 0.00137][0.000192, -60341.696, 0.00138][0.000192, -60341.696, 0.00139][0.000192, -60341.696, 0.00141][0.000192, -60341.696, 0.00142][0.000192, -60341.696, 0.00143][0.000192, -60341.696, 0.00145][0.000192, -60341.696, 0.00146][0.000191, -60341.696, 0.00148][0.000191, -60341.696, 0.00149][0.000191, -60341.696, 0.00151][0.000191, -60341.696, 0.00152][0.000191, -60341.696, 0.00154][0.000191, -60341.696, 0.00155][0.00019, -60341.696, 0.00157][0.00019, -60341.696, 0.00158][0.00019, -60341.696, 0.0016][0.00019, -60341.696, 0.00162][0.00019, -60341.696, 0.00163][0.00019, -60341.696, 0.00165][0.000189, -60341.696, 0.00167][0.000189, -60341.696, 0.00168][0.000189, -60341.696, 0.0017][0.000189, -60341.696, 0.00172][0.000189, -60341.696, 0.00173][0.000189, -60341.696, 0.00175][0.000188, -60341.696, 0.00177][0.000188, -60341.696, 0.00179][0.000188, -60341.696, 0.0018][0.000188, -60341.696, 0.00182][0.000188, -60341.696, 0.00184][0.000187, -60341.696, 0.00186][0.000187, -60341.696, 0.00188][0.000187, -60341.696, 0.0019][0.000187, -60341.696, 0.00191][0.000187, -60341.696, 0.00193][0.000187, -60341.696, 0.00195][0.000186, -60341.696, 0.00197][0.000186, -60341.696, 0.00199][0.000186, -60341.696, 0.00201][0.000186, -60341.696, 0.00203][0.000186, -60341.696, 0.00205][0.000188, -60341.696, 0.00207][0.000194, -60341.696, 0.00209][0.000216, -60341.696, 0.00211][0.000292, -60341.696, 0.00214][0.000498, -60341.696, 0.00216][0.000498, -60341.696, 0.00108][0.000309, -60341.696, 0.00109][0.000229, -60341.696, 0.0011][0.0002, -60341.696, 0.00111][0.00019, -60341.696, 0.00112][0.000186, -60341.696, 0.00113][0.000185, -60341.696, 0.00115][0.000184, -60341.696, 0.00116][0.000184, -60341.696, 0.00117][0.000184, -60341.696, 0.00118][0.000183, -60341.696, 0.00119][0.000183, -60341.696, 0.0012][0.000183, -60341.696, 0.00122][0.000183, -60341.696, 0.00123][0.000183, -60341.696, 0.00124][0.000183, -60341.696, 0.00125][0.000183, -60341.696, 0.00126][0.000183, -60341.696, 0.00128][0.000182, -60341.696, 0.00129][0.000182, -60341.696, 0.0013][0.000182, -60341.696, 0.00132][0.000182, -60341.696, 0.00133][0.000182, -60341.696, 0.00134]\n"
     ]
    }
   ],
   "source": [
    "for i in range(20):\n",
    "    print(f\"{i}: {opt_problem.get_energy_flat(density_flat):.3f}\")\n",
    "    density_flat = opt_problem.optimize(density_flat, snapshots=density_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3932b091-aa99-43b2-9142-55b3c4b17c5a",
   "metadata": {},
   "source": [
    "### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4f16511b-fe84-498e-b8a1-2153a48aeecc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x500 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=7, figsize=(20, 5))\n",
    "max_val = []\n",
    "imax = len(axs)\n",
    "imshow_lst = []\n",
    "for i in range(imax):\n",
    "    ax = axs[i]\n",
    "    density_i = len(density_results) - 1 - (imax - i - 1) * (len(density_results) - 1) // (imax - 1)\n",
    "    density0, density1 = opt_problem.unflatten_density(density_results[density_i])\n",
    "    density = np.hstack([density1[:, ::-1] / 2, density0[:, np.newaxis], density1 / 2])\n",
    "    assert density.shape == (xs.shape[0], all_ys.shape[0])\n",
    "    imshow_lst.append(ax.imshow(np.vstack([np.zeros((1, density.shape[1])), density]).T, cmap='gray_r', origin='lower', extent=[2 * xs[0] - xs[1], xs[-1], all_ys[0], all_ys[-1]]))\n",
    "    ax.set_title(density_i)\n",
    "    max_val.append(density)\n",
    "    \n",
    "max_val = np.percentile(max_val, 99)\n",
    "for c in imshow_lst:\n",
    "    c.set_clim(0, max_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "caf084e0-54a7-4368-811e-1d9e8955dcbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=5, figsize=(20, 5))\n",
    "max_density = np.max(np.concatenate([d.flatten() for d in density_results]))\n",
    "imax = len(axs)\n",
    "max_val = 0\n",
    "for i in range(imax):\n",
    "    ax = axs[i]\n",
    "    density_i = len(density_results) - 1 - (imax - i - 1) * (len(density_results) - 1) // (imax - 1)\n",
    "    density0, density1 = opt_problem.unflatten_density(density_results[density_i])\n",
    "    density = np.hstack([density1[:, ::-1] / 2, density0[:, np.newaxis], density1 / 2])\n",
    "    ax.plot(all_ys, density[0, :], '.')\n",
    "    ax.plot(all_ys, density[1, :], '.')\n",
    "    ax.plot(all_ys, density[2, :], '.')\n",
    "    ax.set_title(density_i)\n",
    "    max_val = max(max_val, np.max(density[:3, :]))\n",
    "\n",
    "for ax in axs:\n",
    "    ax.set_ylim((0,1.016 * max_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d67a9a22-f6db-468e-8d5f-4b1fddda0bf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x500 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=5, figsize=(20, 5))\n",
    "max_density = np.max(np.concatenate([d.flatten() for d in density_results]))\n",
    "imax = len(axs)\n",
    "max_val = 0\n",
    "for i in range(imax):\n",
    "    ax = axs[i]\n",
    "    density_i = len(density_results) - 1 - (imax - i - 1) * (len(density_results) - 1) // (imax - 1)\n",
    "    density0, density1 = opt_problem.unflatten_density(density_results[density_i])\n",
    "    ax.plot(xs, density0[:], '.')\n",
    "    ax.plot(xs, density1[:, 0] / 2, '.')\n",
    "    ax.plot(xs, density1[:, 1] / 2, '.')\n",
    "    ax.set_title(density_i)\n",
    "    max_val = max(max_val, np.max(density0))\n",
    "    max_val = max(max_val, np.max(density1[:, :2])/2)\n",
    "\n",
    "for ax in axs:\n",
    "    ax.set_ylim((0,1.016 * max_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "192a3096-2618-4da1-8b49-7c641a44ed96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=5, figsize=(20, 5))\n",
    "max_density = np.max(np.concatenate([d.flatten() for d in density_results]))\n",
    "imax = len(axs)\n",
    "max_val = 0\n",
    "for i in range(imax):\n",
    "    ax = axs[i]\n",
    "    density_i = len(density_results) - 1 - (imax - i - 1) * (len(density_results) - 1) // (imax - 1)\n",
    "    _, density1 = opt_problem.unflatten_density(density_results[density_i])\n",
    "    median_density = np.median(density1[density1 > 0])\n",
    "    density1_cs = np.cumsum(density1, axis=0)\n",
    "    max_indices = np.argmax(density1_cs, axis=0)\n",
    "    density1_boundary = xs[max_indices]\n",
    "    dx = (xs[-1] - xs[0]) / (len(xs) - 1)\n",
    "    density1_boundary += dx * np.minimum(1, density1[max_indices, np.arange(len(max_indices))] / median_density)\n",
    "    ax.plot(ys[1:], density1_boundary, '.')\n",
    "    top = 1.06 * J**0.5\n",
    "    scale = 1.22\n",
    "    right = 1.17 * J**0.5\n",
    "    offset = (scale**2 * right**2 - top**2) / (2 * top)\n",
    "    boundary_fit = np.maximum(0,(top + offset)**2 - (scale * ys[1:])**2)**0.5 - offset\n",
    "    boundary_fit = np.maximum(0, boundary_fit)\n",
    "    ax.plot(ys[1:], boundary_fit)\n",
    "    ax.set_title(density_i)\n",
    "    ax.set_ylabel('x')\n",
    "    ax.set_xlabel('y')\n",
    "    max_val = max(max_val, np.max(density1_boundary))\n",
    "\n",
    "for ax in axs:\n",
    "    ax.set_ylim((0,1.016 * max_val))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24ea08b8-4e11-45f0-93b0-6b9594712b88",
   "metadata": {},
   "source": [
    "### Fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "91a364ee-54bb-4b7b-9a46-53d52e1c3b6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9947429950785028"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median_density / (2 * dx**2) / (1 / math.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "6124a28f-4738-48b2-82b7-d0329eb40617",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 25.5499510762741)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20, 5))\n",
    "_, density1 = opt_problem.unflatten_density(density_results[-1])\n",
    "median_density = np.median(density1[density1 > 0])\n",
    "density1_cs = np.cumsum(density1, axis=0)\n",
    "max_indices = np.argmax(density1_cs, axis=0)\n",
    "density1_boundary = xs[max_indices]\n",
    "dx = (xs[-1] - xs[0]) / (len(xs) - 1)\n",
    "density1_boundary += dx * np.minimum(1, density1[max_indices, np.arange(len(max_indices))] / median_density)\n",
    "top = 1.06 * J**0.5\n",
    "scale = 1.22\n",
    "right = 1.17 * J**0.5\n",
    "offset = (scale**2 * right**2 - top**2) / (2 * top)\n",
    "boundary_fit = np.maximum(0,(top + offset)**2 - (scale * ys[1:])**2)**0.5 - offset\n",
    "boundary_fit = np.maximum(0, boundary_fit)\n",
    "ax.plot(ys[1:], density1_boundary - boundary_fit, '.')\n",
    "ax_ymax = ys[-1]*2 - ys[-1]\n",
    "ax.plot([0, ax_ymax], np.zeros(2))\n",
    "ax.set_title(density_i)\n",
    "ax.set_ylabel('delta x')\n",
    "ax.set_xlabel('y')\n",
    "ax.set_xlim((0, ax_ymax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "5d4d72a8-df8e-452d-9ef1-9c0cb5139d9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7466370697507463\n"
     ]
    }
   ],
   "source": [
    "J0 = J\n",
    "J = 3\n",
    "top = 1.06 * J**0.5\n",
    "scale = 1.22\n",
    "right = 1.17 * J**0.5\n",
    "offset = (scale**2 * right**2 - top**2) / (2 * top)\n",
    "print(offset)\n",
    "J = J0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "45fd1d55-04b0-44b8-9070-99b40d38b86e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.995\n"
     ]
    }
   ],
   "source": [
    "# Median density in the bulk is approximately 1 / pi:\n",
    "print(f\"{median_density / dx**2 / 2 * math.pi:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "cd300462-f90e-4a85-b36b-bdfc3b9e44aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'y')"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20, 5))\n",
    "density0, density1 = opt_problem.unflatten_density(density_results[-1])\n",
    "ax.plot(ys[1:], density1[0, :] / dx, '.')\n",
    "ax.plot(ys[1:], density1[1, :] / dx, '.')\n",
    "\n",
    "top = 1.4 * J**0.5 / math.pi\n",
    "scale = top / right\n",
    "right = 1.25 * J**0.5\n",
    "offset = (scale**2 * right**2 - top**2) / (2 * top)\n",
    "y_charge_fit = np.maximum(0,(top + offset)**2 - (scale * ys[1:])**2)**0.5 - offset\n",
    "y_charge_fit = np.maximum(0, y_charge_fit)\n",
    "ax.plot(ys[1:], y_charge_fit)\n",
    "\n",
    "ax.set_title(density_i)\n",
    "ax.set_ylabel('delta x')\n",
    "ax.set_xlabel('y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "4e1d0ab7-a68c-4c26-bd75-b3e11860252b",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'NoneType' object is not a mapping",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[154], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m {\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m}\n",
      "\u001b[0;31mTypeError\u001b[0m: 'NoneType' object is not a mapping"
     ]
    }
   ],
   "source": [
    "{**None}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "f3742106-de88-4229-b137-ee83bcec9a3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9800638973959295"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.sum(density1[0, :5]) - 5 * density1[0, 5]) / (1 - 2 * math.exp(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "3386a5a0-aa5f-4c5e-8bca-bfa8633aeac6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9938938790077979"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "density0[0] / (2 / math.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "b2a26f70-ea06-4e40-a6e0-88787fc4d4aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'x')"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20, 5))\n",
    "density0, density1 = opt_problem.unflatten_density(density_results[-1])\n",
    "ax.plot(xs, density0 / dx, '.')\n",
    "\n",
    "top = 1 / math.pi\n",
    "right = 1.06 * J**0.5\n",
    "zero_charge = 2 / math.pi\n",
    "x_charge_fit = top * np.exp(-np.maximum(0, xs - right)) + zero_charge * np.exp(-xs)\n",
    "ax.plot(xs, x_charge_fit)\n",
    "\n",
    "ax.set_title(density_i)\n",
    "ax.set_ylabel('density')\n",
    "ax.set_xlabel('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "06a5465e-a8d3-4ead-83a6-b178d1f6ac39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.022238887202981186"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(density0) / J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "b707db1d-31d2-4758-a38d-503f5aea47c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5203790150750273"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(density1[1:, :]) / J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "fc3cb871-5c41-4e11-8f78-dbbb35a01887",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45738209772199184"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(density1[0, :]) / J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "356b4da8-801f-4ebe-8f40-1f80b0f0ad1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.7244696742907646, 2.7244696742907615)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "right = (top**2 + 2 * top * offset)**0.5 / scale / J**0.5\n",
    "offset = (scale**2 * right**2 - top**2) / (2 * top)\n",
    "(offset, offset1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "97c23b2f-8dc8-48e6-9ada-43313342ed7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1590595383095876"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(top**2 + 2 * top * offset)**0.5 / scale / J**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8acff41f-a6fe-4707-b22b-1d3ebf59d95f",
   "metadata": {},
   "source": [
    "## MCMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 735,
   "id": "89ebcfc1-26d4-4a98-892c-961140995e07",
   "metadata": {},
   "outputs": [],
   "source": [
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 738,
   "id": "77517a30-491b-4d17-b921-7beaacb92183",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_posd(a):\n",
    "    try:\n",
    "        scipy.linalg.cholesky(a, lower=True)\n",
    "        return True\n",
    "    except np.linalg.LinAlgError:\n",
    "        return False\n",
    "    \n",
    "def is_a_posd(mcmc_state, rng):\n",
    "    real_evals = np.array(mcmc_state.real_evals, dtype=np.float64)\n",
    "    complex_evals = ginoe_mcmc.GinOEStableMCMC._np_array(mcmc_state.complex_evals, 'C')\n",
    "    G, c = ginoe_mcmc.GSampler.sample_Gc(real_evals, complex_evals, rng)\n",
    "    a = sgm.gc_to_a(G, c)\n",
    "    a_c0 = sgm.gc_to_a(G, c * 0)\n",
    "    return is_posd(a), is_posd(a_c0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 751,
   "id": "5363de4f-ac2e-42da-b048-fec6b0d741cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23-09-05 14:10:48: d=2\n",
      "0\n",
      "0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........\n",
      "23-09-05 14:24:16: d=3\n",
      "0\n",
      "0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........0.........1.........2.........3.........4.........5.........6.........7.........8.........9.........\n",
      "23-09-05 14:54:20\n"
     ]
    }
   ],
   "source": [
    "importlib.reload(ginoe_mcmc)\n",
    "a_stats = {}\n",
    "mcmc_stats = {}\n",
    "def mcmc_callback(state, rng):\n",
    "    cur_a_stats = a_stats.get(state.J, None)\n",
    "    if cur_a_stats is None:\n",
    "        cur_a_stats = []\n",
    "        a_stats[state.J] = cur_a_stats\n",
    "    cur_a_stats.append(is_a_posd(state, rng))\n",
    "\n",
    "for d in range(2, 4):\n",
    "    print(f\"{datetime.datetime.now():%y-%m-%d %H:%M:%S}: {d=}\")\n",
    "    J = d**2 - 1\n",
    "    sgm = ginoe_mcmc.SparseGellMann(d=d)\n",
    "\n",
    "    mcmc = ginoe_mcmc.GinOEStableMCMC(J=J, seed=44)\n",
    "    cur_mcmc_stats = {}\n",
    "    mcmc_stats[J] = cur_mcmc_stats\n",
    "    cur_mcmc_stats[\"burn_in\"] = mcmc.run(n_epochs=40)\n",
    "    cur_mcmc_stats[\"compute\"] = mcmc.run(n_epochs=500000, callback=mcmc_callback)\n",
    "print(f\"{datetime.datetime.now():%y-%m-%d %H:%M:%S}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 762,
   "id": "a5d9b0df-3394-4fe5-97cd-a72ee9b7b788",
   "metadata": {},
   "outputs": [],
   "source": [
    "a_stats = {k: np.array(v) for k, v in a_stats.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 763,
   "id": "c32e64ae-2b32-4d79-9016-b7cf43110640",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ 2220, 17729]), (1000000, 2)]"
      ]
     },
     "execution_count": 763,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.sum(a_stats[2**2-1], axis=0), a_stats[2**2-1].shape]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 926,
   "id": "89db6af6-50c8-498e-877a-1a81f4d39cd2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      0: 0.000000 0.000002 0.000004\n",
      "   2220: 0.002129 0.002222 0.002315\n",
      "  17729: 0.017472 0.017731 0.017990\n"
     ]
    }
   ],
   "source": [
    "for k in [0, 2220, 17729]:\n",
    "    lb, ub = ginoe_mcmc.wilson_interval(1000000, k)\n",
    "    mu = (lb + ub) / 2\n",
    "    print(f\"{k: 7d}: {lb:.6f} {mu:.6f} {ub:.6f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 765,
   "id": "acbb2330-e523-4421-ae75-ab20dbcd8538",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0021291605654800245, 0.002314693224288863)"
      ]
     },
     "execution_count": 765,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ginoe_mcmc.wilson_interval(1000000, 2220)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 768,
   "id": "3a06f7a8-cc62-4888-89f0-899aa599f545",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9.088566293361466e-08, 4.7893920079154094e-06)"
      ]
     },
     "execution_count": 768,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ginoe_mcmc.wilson_interval(1000000, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 817,
   "id": "a5d62f78-9ba4-4c7f-bf7e-ea0b2450260a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(0.), array(3.68887265e-06))"
      ]
     },
     "execution_count": 817,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ginoe_mcmc.wilson_interval(10**6, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 845,
   "id": "04944f1b-5c7a-4c2d-82f8-e4b086aef74b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(0.9491708), array(0.95002939))"
      ]
     },
     "execution_count": 845,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ginoe_mcmc.wilson_interval(10**6, 0.9496 * 10**6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 855,
   "id": "727ad973-85dc-4c95-a4b6-9ecbde04d62d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 855,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.array(res_w) < 0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 798,
   "id": "86e58d47-f9de-42ad-b7c4-86d665738c4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(array(0.), array(4.78939201e-06)), (0, 2.9957277863923437e-06)]"
      ]
     },
     "execution_count": 798,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[ginoe_mcmc.wilson_interval(10**6, 0), (0, 1 - 0.05**(10**-6))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7302b19b-f14c-4e6b-9772-f39a6bf51045",
   "metadata": {},
   "outputs": [],
   "source": [
    "ginoe_mcmc.wilson_interval(10**6, 17729)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 757,
   "id": "01e0d777-3e02-4282-a626-0cb423204080",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.017730886742512747"
      ]
     },
     "execution_count": 757,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(ginoe_mcmc.wilson_interval(10**6, 17729))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 754,
   "id": "2428a874-b9d1-42a8-9cc1-2ba5e531ac12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0])"
      ]
     },
     "execution_count": 754,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a_stats[3**2-1], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 747,
   "id": "dbe61ea3-f897-4f1c-800f-ccf295b3fde5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0021 , 0.01769])"
      ]
     },
     "execution_count": 747,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(a_stats[2**2-1], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 749,
   "id": "83e7dbab-cc1a-49c5-9d2f-ef70e26de3be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 2)"
      ]
     },
     "execution_count": 749,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_stats[2**2-1].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 750,
   "id": "7fe7af91-2a3f-4e89-adcb-fcaab7cb29e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01510628699971843"
      ]
     },
     "execution_count": 750,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 0.01769\n",
    "n = 10000\n",
    "z = 1.96\n",
    "p - z * (p * (1-p) / n)**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 700,
   "id": "023930e6-cf08-4f11-bace-51fc38b82735",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "322400"
      ]
     },
     "execution_count": 700,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "400 * sum(d**2 - 1 for d in range(2, 14))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 706,
   "id": "1a53e16e-e4f2-42f2-8ea0-58bb0fa93a6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "800: 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000100000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000001100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000\n"
     ]
    }
   ],
   "source": [
    "s = \"\".join(str(a[1]+0) for a in a_stats[3])\n",
    "print(f\"{len(s)}: {s}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 690,
   "id": "059c447e-04de-49b0-886c-f2d026d1cce5",
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_state = mcmc.state\n",
    "real_evals = np.array(mcmc_state.real_evals, dtype=np.float64)\n",
    "complex_evals = ginoe_mcmc.GinOEStableMCMC._np_array(mcmc_state.complex_evals, 'C')\n",
    "G, c = ginoe_mcmc.GSampler.sample_Gc(real_evals, complex_evals, rng)\n",
    "a = sgm.gc_to_a(G, c)\n",
    "a_c0 = sgm.gc_to_a(G, c * 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 694,
   "id": "5a7c8846-6ae9-4868-ad74-e7f7449829e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True])"
      ]
     },
     "execution_count": 694,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigvals(G).real < 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 628,
   "id": "0c631302-7673-4e04-b867-e5ea1379e286",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "756 ms ± 2.09 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 10\n",
    "a = sgm.gc_to_a(G, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 663,
   "id": "93c30492-1c74-48c4-9370-013aaf7ffae6",
   "metadata": {},
   "outputs": [],
   "source": [
    "ts = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 660,
   "id": "afdf6178-792c-4158-bbdc-eadd93406d97",
   "metadata": {},
   "outputs": [],
   "source": [
    "importlib.reload(ginoe_mcmc)\n",
    "sgm = ginoe_mcmc.SparseGellMann(d=d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 664,
   "id": "f011bb97-fa37-45cb-b74e-b4099876a740",
   "metadata": {},
   "outputs": [],
   "source": [
    "for _ in range(10):\n",
    "    t0 = time.time()\n",
    "    res = (\n",
    "        sgm.times_F(G)\n",
    "       + c[:, np.newaxis, np.newaxis] * np.eye(d)[np.newaxis, :, :]) # (i, a, b)\n",
    "    t1 = time.time()\n",
    "    res = sgm.times_newF(res) # (i, a, m, c)\n",
    "    t2 = time.time()\n",
    "    res = np.moveaxis(res, 0, 3) # (a, m, c, i)\n",
    "    t3 = time.time()\n",
    "    res = sgm.times_F(res) # (a, m, c, c, d)\n",
    "    t4 = time.time()\n",
    "    res = np.einsum('amccd->mad', res)\n",
    "    t5 = time.time()\n",
    "    res = sgm.times_newF(res)\n",
    "    t6 = time.time()\n",
    "    res = np.einsum('mana->mn', res)\n",
    "    t7 = time.time()\n",
    "    ts.append([t0, t1, t2, t3, t4, t5, t6, t7])\n",
    "    assert np.allclose(res, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 665,
   "id": "19c94cfa-0ffc-4d6c-8678-f5fe1f6745d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: 0.003s +/- 0.002s\n",
      "1: 0.155s +/- 0.005s\n",
      "2: 0.000s +/- 0.000s\n",
      "3: 0.414s +/- 0.003s\n",
      "4: 0.018s +/- 0.000s\n",
      "5: 0.137s +/- 0.003s\n",
      "6: 0.028s +/- 0.001s\n"
     ]
    }
   ],
   "source": [
    "dts = np.diff(ts, axis=1)\n",
    "for i in range(dts.shape[1]):\n",
    "    mu = np.mean(dts[:, i])\n",
    "    std = np.std(dts[:, i])\n",
    "    print(f\"{i}: {mu:.3f}s +/- {std:.3f}s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 644,
   "id": "bed18141-b947-4cdd-9b81-66a8618906db",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9bdfc1f-99b9-4365-9489-35006bd6045f",
   "metadata": {},
   "source": [
    "## Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "758a22c2-7b72-4c68-9a51-69f9d4d2f0c2",
   "metadata": {},
   "source": [
    "### MCMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "id": "0465e79a-b414-47ea-a4b6-b76f8e0ec54f",
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_seed = 1\n",
    "stats = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "id": "70a6da75-8213-42a9-a059-a3af11b3cc21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'ginoe_mcmc' from '/home/victor/Dropbox (Lidar group)/qc4ml_work/ode2qme/ode2qme/ginoe_mcmc.py'>"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import ginoe_mcmc\n",
    "import importlib\n",
    "importlib.reload(ginoe_mcmc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "id": "109c3ca8-0fa3-4c1b-b325-2235f13e27b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed: 356\n",
      "[0: 0.469][1: 0.289][2: 0.203][3: 0.188][4: 0.180][5: 0.148][6: 0.109][7: 0.086][8: 0.070][9: 0.148][10: 0.055][11: 0.125][12: 0.109][13: 0.109][14: 0.109][15: 0.109][16: 0.109][17: 0.141][18: 0.078][19: 0.125][20: 0.102][21: 0.086][22: 0.117][23: 0.078][24: 0.117][25: 0.078][26: 0.102][27: 0.102][28: 0.102][29: 0.047][30: 0.094][31: 0.062][32: 0.031][33: 0.078][34: 0.062][35: 0.055][36: 0.047][37: 0.133][38: 0.117][39: 0.094][40: 0.148]\n"
     ]
    }
   ],
   "source": [
    "print(f\"seed: {mcmc_seed}\")\n",
    "mcmc = ginoe_mcmc.GinOEStableMCMC(J=255, seed=mcmc_seed)\n",
    "cur_stats = mcmc.run(n_epochs=41)\n",
    "cur_stats['evals'] = (mcmc.state.real_evals, mcmc.state.complex_evals)\n",
    "stats.append(cur_stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "id": "0bcc704c-0515-49e5-aab7-de7d28c4cf23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "456"
      ]
     },
     "execution_count": 341,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max([s['seed'] for s in stats])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "id": "e21407ed-e8c4-4d65-854d-f720a48d0874",
   "metadata": {},
   "outputs": [],
   "source": [
    "mcmc_seed = 456"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "id": "04627a92-595d-4a05-a70d-a44749647879",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed: 457\n",
      "[0: 0.500][1: 0.500][2: 1.000][3: 0.500][4: 0.500][5: 0.000][6: 0.500][7: 0.500][8: 1.000][9: 0.500][10: 0.250][11: 0.500][12: 1.000][13: 0.000][14: 0.000][15: 0.500][16: 0.500][17: 0.500][18: 0.000][19: 1.000][20: 0.500][21: 0.000][22: 0.250][23: 0.500][24: 0.500][25: 0.000][26: 0.500][27: 0.000][28: 0.000][29: 0.000][30: 0.000][31: 0.500][32: 0.250][33: 0.000][34: 0.500][35: 1.000][36: 0.500][37: 0.500][38: 0.500][39: 0.500][40: 0.500]\n",
      "seed: 458\n",
      "[0: 1.000][1: 0.500][2: 0.500][3: 0.000][4: 0.500][5: 0.000][6: 0.500][7: 0.500][8: 0.500][9: 0.500][10: 0.500][11: 1.000][12: 0.000][13: 1.000][14: 1.000][15: 1.000][16: 0.500][17: 0.500][18: 0.500][19: 1.000][20: 0.500][21: 0.000][22: 1.000][23: 1.000][24: 0.500][25: 0.250][26: 1.000][27: 1.000][28: 0.500][29: 0.500][30: 1.000][31: 0.500][32: 0.000][33: 0.500][34: 0.500][35: 0.500][36: 0.500][37: 0.500][38: 0.500][39: 1.000][40: 0.000]\n",
      "seed: 459\n",
      "[0: 0.500][1: 0.500][2: 0.500][3: 0.500][4: 0.500][5: 0.000][6: 0.500][7: 0.500][8: 0.500][9: 0.500][10: 1.000][11: 0.000][12: 0.500][13: 0.500][14: 1.000][15: 0.500][16: 0.500][17: 0.000][18: 1.000][19: 0.500][20: 0.500][21: 0.500][22: 0.500][23: 1.000][24: 0.500][25: 0.500][26: 0.500][27: 0.500][28: 1.000][29: 1.000][30: 0.500][31: 0.500][32: 1.000][33: 0.500][34: 0.000][35: 1.000][36: 0.500][37: 0.000][38: 0.500][39: 0.500][40: 0.500]\n",
      "seed: 460\n",
      "[0: 1.000][1: 1.000][2: 0.500][3: 1.000][4: 0.500][5: 0.500][6: 0.500][7: 1.000][8: 0.500][9: 0.500][10: 1.000][11: 1.000][12: 1.000][13: 1.000][14: 0.500][15: 0.500][16: 0.000][17: 0.500][18: 0.500][19: 0.500][20: 0.500][21: 1.000][22: 0.500][23: 1.000][24: 0.500][25: 0.000][26: 0.000][27: 0.500][28: 0.500][29: 0.500][30: 0.000][31: 0.500][32: 0.500][33: 1.000][34: 0.500][35: 0.500][36: 1.000][37: 0.000][38: 0.500][39: 0.500][40: 1.000]\n",
      "seed: 461\n",
      "[0: 1.000][1: 1.000][2: 1.000][3: 0.500][4: 0.500][5: 0.500][6: 0.500][7: 0.500][8: 0.750][9: 0.250][10: 0.500][11: 0.000][12: 0.500][13: 0.000][14: 0.500][15: 0.500][16: 0.500][17: 0.500][18: 0.500][19: 0.500][20: 0.500][21: 0.500][22: 1.000][23: 0.000][24: 0.500][25: 0.000][26: 0.500][27: 1.000][28: 0.500][29: 0.500][30: 0.000][31: 0.000][32: 0.500][33: 0.500][34: 0.500][35: 1.000][36: 0.500][37: 1.000][38: 1.000][39: 0.000][40: 0.000]\n",
      "seed: 462\n",
      "[0: 0.500][1: 0.500][2: 0.500][3: 0.500][4: 0.500][5: 0.500][6: 1.000][7: 0.500][8: 1.000][9: 0.500][10: 0.500][11: 0.500][12: 0.500][13: 1.000][14: 1.000][15: 1.000][16: 0.500][17: 0.000][18: 0.500][19: 0.500][20: 0.500][21: 1.000][22: 1.000][23: 1.000][24: 0.500][25: 0.500][26: 0.500][27: 0.500][28: 0.500][29: 0.500][30: 0.500][31: 1.000][32: 0.500][33: 0.500][34: 0.500][35: 0.000][36: 0.500][37: 1.000][38: 0.500][39: 1.000][40: 0.000]\n",
      "seed: 463\n",
      "[0: 1.000][1: 1.000][2: 0.000][3: 1.000][4: 1.000][5: 1.000][6: 1.000][7: 0.500][8: 1.000][9: 1.000][10: 1.000][11: 0.500][12: 1.000][13: 1.000][14: 0.500][15: 1.000][16: 0.500][17: 0.500][18: 1.000][19: 0.500][20: 1.000][21: 1.000][22: 0.500][23: 0.500][24: 1.000][25: 0.500][26: 0.500][27: 0.500][28: 0.500][29: 0.000][30: 0.000][31: 1.000][32: 0.500][33: 1.000][34: 1.000][35: 1.000][36: 0.500][37: 1.000][38: 0.000][39: 1.000][40: 1.000]\n",
      "seed: 464\n",
      "[0: 1.000][1: 0.500][2: 0.500][3: 0.500][4: 1.000][5: 0.500][6: 1.000][7: 0.500][8: 1.000][9: 0.500][10: 0.000][11: 0.500][12: 0.500][13: 0.500][14: 0.500][15: 1.000][16: 0.500][17: 0.000][18: 0.000][19: 1.000][20: 0.000][21: 0.500][22: 0.500][23: 0.500][24: 0.000][25: 0.000][26: 0.500][27: 1.000][28: 1.000][29: 1.000][30: 0.000][31: 1.000][32: 1.000][33: 0.500][34: 0.500][35: 0.500][36: 1.000][37: 0.500][38: 0.500][39: 0.500][40: 1.000]\n",
      "seed: 465\n",
      "[0: 0.000][1: 0.500][2: 0.500][3: 1.000][4: 0.500][5: 0.500][6: 1.000][7: 0.500][8: 0.500][9: 0.500][10: 0.500][11: 1.000][12: 1.000][13: 1.000][14: 0.500][15: 0.500][16: 0.500][17: 0.000][18: 0.500][19: 0.000][20: 0.500][21: 0.500][22: 0.000][23: 0.500][24: 0.500][25: 0.500][26: 0.500][27: 0.500][28: 0.000][29: 0.500][30: 0.500][31: 0.000][32: 0.000][33: 0.000][34: 0.500][35: 0.500][36: 0.500][37: 0.500][38: 1.000][39: 0.500][40: 1.000]\n",
      "seed: 466\n",
      "[0: 1.000][1: 0.500][2: 0.500][3: 0.500][4: 1.000][5: 0.000][6: 0.500][7: 0.000][8: 0.000][9: 1.000][10: 0.500][11: 0.500][12: 0.000][13: 0.500][14: 1.000][15: 1.000][16: 0.500][17: 1.000][18: 0.000][19: 0.000][20: 0.500][21: 0.500][22: 1.000][23: 0.500][24: 0.500][25: 0.500][26: 0.500][27: 1.000][28: 0.000][29: 0.500][30: 0.500][31: 0.500][32: 1.000][33: 0.500][34: 1.000][35: 0.500][36: 1.000][37: 0.500][38: 1.000][39: 0.500][40: 1.000]\n",
      "seed: 467\n",
      "[0: 1.000][1: 0.500][2: 0.500][3: 1.000][4: 0.000][5: 0.500][6: 0.000][7: 0.000][8: 0.500][9: 0.000][10: 0.000][11: 0.500][12: 1.000][13: 0.500][14: 1.000][15: 0.500][16: 1.000][17: 0.500][18: 0.000][19: 0.500][20: 0.500][21: 0.500][22: 1.000][23: 0.500][24: 0.500][25: 0.000][26: 1.000][27: 0.000][28: 0.500][29: 0.500][30: 1.000][31: 0.000][32: 1.000][33: 0.000][34: 0.500][35: 1.000][36: 0.250][37: 0.000][38: 0.500][39: 0.500][40: 0.500]\n",
      "seed: 468\n",
      "[0: 1.000][1: 1.000][2: 0.500][3: 1.000][4: 1.000][5: 1.000][6: 0.250][7: 1.000][8: 1.000][9: 0.000][10: 0.500][11: 1.000][12: 1.000][13: 0.000][14: 0.500][15: 0.500][16: 0.000][17: 0.500][18: 0.500][19: 0.500][20: 1.000][21: 0.500][22: 0.000][23: 0.000][24: 0.500][25: 0.500][26: 0.500][27: 0.500][28: 0.500][29: 0.500][30: 1.000][31: 1.000][32: 1.000][33: 1.000][34: 1.000][35: 0.000][36: 0.500][37: 0.500][38: 0.500][39: 1.000][40: 0.500]\n",
      "seed: 469\n",
      "[0: 0.500][1: 0.500][2: 0.500][3: 0.500][4: 0.500][5: 0.500][6: 0.500][7: 0.500][8: 0.500][9: 0.500][10: 0.500][11: 1.000][12: 0.000][13: 0.500][14: 1.000][15: 1.000][16: 0.500][17: 0.500][18: 0.500][19: 0.000][20: 1.000][21: 1.000][22: 0.750][23: 1.000][24: 1.000][25: 1.000][26: 1.000][27: 1.000][28: 0.500][29: 0.500][30: 0.500][31: 0.500][32: 1.000][33: 0.500][34: 0.500][35: 1.000][36: 0.500][37: 0.000][38: 0.000][39: 0.500][40: 1.000]\n",
      "seed: 470\n",
      "[0: 1.000][1: 0.500][2: 0.500][3: 0.500][4: 0.500][5: 0.500][6: 0.500][7: 0.500][8: 0.500][9: 0.500][10: 1.000][11: 1.000][12: 1.000][13: 1.000][14: 0.500][15: 0.500][16: 0.500][17: 0.500][18: 0.000][19: 1.000][20: 1.000][21: 0.500][22: 1.000][23: 1.000][24: 0.500][25: 0.500][26: 0.500][27: 1.000][28: 0.000][29: 1.000][30: 1.000][31: 0.500][32: 0.500][33: 1.000][34: 0.500][35: 0.000][36: 0.500][37: 0.500][38: 0.000][39: 0.500][40: 0.000]\n",
      "seed: 471\n",
      "[0: 0.500][1: 0.500][2: 0.000][3: 0.000][4: 1.000][5: 0.500][6: 0.500][7: 0.000][8: 1.000][9: 0.500][10: 0.500][11: 0.500][12: 0.500][13: 0.000][14: 0.000][15: 1.000][16: 1.000][17: 0.500][18: 0.500][19: 1.000][20: 0.000][21: 0.000][22: 0.000][23: 0.500][24: 0.750][25: 0.000][26: 0.500][27: 0.000][28: 0.500][29: 1.000][30: 0.500][31: 1.000][32: 0.500][33: 0.500][34: 0.500][35: 0.500][36: 0.500][37: 0.500][38: 1.000][39: 0.000][40: 0.500]\n",
      "seed: 472\n",
      "[0: 0.500][1: 0.000][2: 0.500][3: 0.500][4: 1.000][5: 1.000][6: 0.500][7: 1.000][8: 1.000][9: 0.500][10: 0.500][11: 1.000][12: 0.500][13: 0.500][14: 1.000][15: 0.500][16: 0.500][17: 0.500][18: 1.000][19: 1.000][20: 1.000][21: 1.000][22: 1.000][23: 0.500][24: 0.500][25: 0.500][26: 0.500][27: 0.500][28: 0.500][29: 1.000][30: 0.500][31: 0.000][32: 1.000][33: 0.500][34: 1.000][35: 0.000][36: 1.000][37: 0.500][38: 0.500][39: 0.000][40: 0.000]\n",
      "seed: 473\n",
      "[0: 0.500][1: 0.500][2: 1.000][3: 0.500][4: 0.500][5: 0.000][6: 0.000][7: 0.500][8: 0.250][9: 1.000][10: 1.000][11: 0.500][12: 1.000][13: 0.500][14: 0.500][15: 1.000][16: 1.000][17: 0.500][18: 0.500][19: 1.000][20: 0.500][21: 0.500][22: 0.500][23: 0.500][24: 1.000][25: 0.750][26: 1.000][27: 1.000][28: 1.000][29: 0.500][30: 0.000][31: 1.000][32: 0.500][33: 0.500][34: 0.000][35: 1.000][36: 1.000][37: 1.000][38: 1.000][39: 0.000][40: 0.500]\n",
      "seed: 474\n",
      "[0: 0.500][1: 0.500][2: 1.000][3: 0.500][4: 0.500][5: 0.000][6: 0.500][7: 0.500][8: 0.500][9: 0.500][10: 1.000][11: 0.000][12: 0.000][13: 0.500][14: 0.500][15: 0.500][16: 0.500][17: 1.000][18: 0.500][19: 1.000][20: 0.500][21: 0.000][22: 0.000][23: 0.000][24: 0.000][25: 0.250][26: 1.000][27: 1.000][28: 0.500][29: 0.500][30: 1.000][31: 1.000][32: 0.500][33: 0.500][34: 1.000][35: 1.000][36: 0.500][37: 1.000][38: 0.500][39: 1.000][40: 0.500]\n",
      "seed: 475\n",
      "[0: 0.500][1: 0.000][2: 0.500][3: 0.000][4: 0.500][5: 0.500][6: 0.500][7: 0.500][8: 0.500][9: 1.000][10: 1.000][11: 1.000][12: 1.000][13: 1.000][14: 0.500][15: 0.250][16: 0.250][17: 0.500][18: 1.000][19: 1.000][20: 1.000][21: 0.500][22: 0.500][23: 0.000][24: 0.500][25: 0.500][26: 1.000][27: 0.500][28: 0.500][29: 0.500][30: 0.500][31: 1.000][32: 0.500][33: 0.500][34: 0.500][35: 0.500][36: 0.500][37: 0.500][38: 0.500][39: 0.000][40: 0.500]\n",
      "seed: 476\n",
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      "seed: 540\n",
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      "seed: 541\n",
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      "seed: 544\n",
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      "seed: 545\n",
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      "seed: 546\n",
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      "seed: 547\n",
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      "seed: 548\n",
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      "seed: 549\n",
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      "seed: 550\n",
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      "seed: 551\n",
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      "seed: 552\n",
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      "seed: 553\n",
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      "seed: 555\n",
      "[0: 1.000][1: 0.000][2: 1.000][3: 0.000][4: 1.000][5: 1.000][6: 0.000][7: 0.000][8: 0.500][9: 0.500][10: 0.500][11: 1.000][12: 0.500][13: 0.000][14: 0.500][15: 0.000][16: 1.000][17: 0.500][18: 0.500][19: 0.500][20: 0.500][21: 0.000][22: 0.000][23: 0.500][24: 0.000][25: 0.000][26: 0.000][27: 0.500][28: 0.500][29: 0.500][30: 0.000][31: 1.000][32: 0.500][33: 0.500][34: 1.000][35: 0.500][36: 0.000][37: 0.500][38: 1.000][39: 0.500][40: 0.500]\n",
      "seed: 556\n",
      "[0: 0.000][1: 1.000][2: 1.000][3: 1.000][4: 0.500][5: 1.000][6: 0.000][7: 0.500][8: 1.000][9: 1.000][10: 0.000][11: 1.000][12: 0.500][13: 0.500][14: 0.500][15: 0.500][16: 1.000][17: 0.500][18: 1.000][19: 0.000][20: 0.500][21: 0.500][22: 1.000][23: 0.500][24: 0.500][25: 0.500][26: 1.000][27: 0.000][28: 1.000][29: 0.500][30: 0.000][31: 0.000][32: 0.000][33: 0.500][34: 0.500][35: 1.000][36: 0.500][37: 1.000][38: 0.000][39: 1.000][40: 0.500]\n"
     ]
    }
   ],
   "source": [
    "for _ in range(100):\n",
    "    mcmc_seed += 1\n",
    "    print(f\"seed: {mcmc_seed}\")\n",
    "    mcmc = ginoe_mcmc.GinOEStableMCMC(J=3, seed=mcmc_seed)\n",
    "    cur_stats = mcmc.run(n_epochs=41)\n",
    "    cur_stats['evals'] = (mcmc.state.real_evals, mcmc.state.complex_evals)\n",
    "    stats.append(cur_stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "id": "2da209be-3ac1-49ba-b125-3b09487843f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "ars = np.array([s[\"acceptance_rate\"] for s in stats if \"J\" in s and s[\"J\"] == 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "id": "85423232-da8f-41fd-b5a3-97caf741e44f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5, 0.5, 1. , ..., 0.5, 0.5, 0.5],\n",
       "       [1. , 0.5, 0.5, ..., 0.5, 1. , 0. ],\n",
       "       [0.5, 0.5, 0.5, ..., 0.5, 0.5, 0.5],\n",
       "       ...,\n",
       "       [0.5, 0.5, 0.5, ..., 0.5, 0. , 0.5],\n",
       "       [1. , 0. , 1. , ..., 1. , 0.5, 0.5],\n",
       "       [0. , 1. , 1. , ..., 0. , 1. , 0.5]])"
      ]
     },
     "execution_count": 347,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "id": "fc77b888-9ff9-4572-94c4-9eb03d582cd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.688)"
      ]
     },
     "execution_count": 349,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=1, figsize=(11, 5))\n",
    "xs = np.arange(ars.shape[1])\n",
    "ars_mu = np.mean(ars, axis=0)\n",
    "ars_ste = np.std(ars, axis=0) / ars.shape[0]**0.5\n",
    "ax.plot(xs, ars_mu)\n",
    "ax.fill_between(xs, ars_mu - 2 * ars_ste, ars_mu + 2 * ars_ste, alpha=0.3)\n",
    "ax.set_xlim((0, len(ars_mu) - 1))\n",
    "ax.set_ylim((0, max(ars_mu[10:] + 2 * ars_ste[10:])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "id": "cf4ef5c1-8e6c-46f7-8e38-fe2999723c97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20: (0.08212458442026874, 0.08929085675620185\n",
      "40: (0.07746568159654081, 0.08495553689085415\n"
     ]
    }
   ],
   "source": [
    "for i in (20, 40):\n",
    "    print(f\"{i}: ({ars_mu[i] - 2 * ars_ste[i]}, {ars_mu[i] + 2 * ars_ste[i]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "id": "64b1b426-5f3d-462e-a424-2befbd489c08",
   "metadata": {},
   "outputs": [],
   "source": [
    "evals = []\n",
    "for s in stats:\n",
    "    if s.get(\"epoch_range\", (None, -1))[1] < 40 or s.get(\"J\", 0) != 3:\n",
    "        continue\n",
    "    real_evals, complex_evals = s[\"evals\"]\n",
    "    evals.append([(r, 0) for r in real_evals])\n",
    "    evals.append(complex_evals)\n",
    "evals = [vi for v in evals for vi in v]\n",
    "evals = np.array(evals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "id": "bc555748-82e2-44ef-9620-079632d64b20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "J = 3\n",
    "pp = ginoe_mcmc.GinOEStablePairProposal(J=J)\n",
    "\n",
    "# Define or import your sample_p and pdf_q functions here\n",
    "# For demonstration, I'll use a 2D Gaussian distribution for both\n",
    "def sample_p():\n",
    "    return pp._complex_model.sample(rng)\n",
    "\n",
    "def pdf_q(x, y):\n",
    "    return pp._complex_model.get_pdf(x, y)\n",
    "\n",
    "# Sampling from P\n",
    "n_samples = 100000\n",
    "samples_p = np.array([sample_p() for _ in range(n_samples)])\n",
    "\n",
    "# Get vmax for plotting region\n",
    "vmax = 1.01 * np.max(samples_p)\n",
    "\n",
    "# Plotting\n",
    "fig, (ax_p, ax_q) = plt.subplots(ncols=2, figsize=(13, 5))\n",
    "\n",
    "# Plot 2D histogram for P\n",
    "h = ax_p.hist2d(samples_p[:, 0], samples_p[:, 1], bins=50, range=[[0, vmax], [0, vmax]], density=True, cmap='gray_r')\n",
    "plt.colorbar(h[3], ax=ax_p)\n",
    "ax_p.set_title('Density of P')\n",
    "\n",
    "# Plot density for Q\n",
    "x, y = np.meshgrid(np.linspace(0, vmax, 100), np.linspace(0, vmax, 100))\n",
    "z = np.array([pdf_q(x_, y_) for x_, y_ in zip(np.ravel(x), np.ravel(y))])\n",
    "z = np.minimum(0.5 / (1.25 * J**0.5)**2 , z.reshape(x.shape))\n",
    "im = ax_q.imshow(z, extent=[0, vmax, 0, vmax], origin='lower', aspect='auto', cmap='gray_r')\n",
    "plt.colorbar(im, ax=ax_q)\n",
    "ax_q.set_title('Samples from MCMC on top of overexposed proposal distribution')\n",
    "ax_q.scatter(evals[:, 0], evals[:, 1], c='red', marker='o', s=5, alpha=0.5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04c5a234-8867-4371-bb0c-46184e741288",
   "metadata": {},
   "source": [
    "### Proposal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "id": "7fb3f6da-ba7b-465d-8a4b-789048fedd33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp = ginoe_mcmc.GinOEStablePairProposal(J=255)\n",
    "\n",
    "# Define or import your sample_p and pdf_q functions here\n",
    "# For demonstration, I'll use a 2D Gaussian distribution for both\n",
    "def sample_p():\n",
    "    return pp._complex_model.sample(rng)\n",
    "\n",
    "def pdf_q(x, y):\n",
    "    return pp._complex_model.get_pdf(x, y)\n",
    "\n",
    "# Sampling from P\n",
    "n_samples = 100000\n",
    "samples_p = np.array([sample_p() for _ in range(n_samples)])\n",
    "\n",
    "# Get vmax for plotting region\n",
    "vmax = 1.01 * np.max(samples_p)\n",
    "\n",
    "# Plotting\n",
    "fig, (ax_p, ax_q) = plt.subplots(ncols=2, figsize=(13, 5))\n",
    "\n",
    "# Plot 2D histogram for P\n",
    "h = ax_p.hist2d(samples_p[:, 0], samples_p[:, 1], bins=50, range=[[0, vmax], [0, vmax]], density=True, cmap='gray_r')\n",
    "plt.colorbar(h[3], ax=ax_p)\n",
    "ax_p.set_title('Density of P')\n",
    "\n",
    "# Plot density for Q\n",
    "x, y = np.meshgrid(np.linspace(0, vmax, 100), np.linspace(0, vmax, 100))\n",
    "z = np.array([pdf_q(x_, y_) for x_, y_ in zip(np.ravel(x), np.ravel(y))])\n",
    "z = z.reshape(x.shape)\n",
    "im = ax_q.imshow(z, extent=[0, vmax, 0, vmax], origin='lower', aspect='auto', cmap='gray_r')\n",
    "plt.colorbar(im, ax=ax_q)\n",
    "ax_q.set_title('Density of Q')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7be47fc-167b-4824-9012-3e026d2ff258",
   "metadata": {},
   "source": [
    "### Truncated normal sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "id": "03b28cda-efad-4370-a58d-0827f75f5d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "importlib.reload(ginoe_mcmc)\n",
    "xs = ginoe_mcmc.GSampler.truncated_normal_sample(threshold=np.full(fill_value=5, shape=40000, dtype=np.float64), rng=rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "id": "024c50ab-d545-48a9-8195-1577133078f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5afc5c0100>]"
      ]
     },
     "execution_count": 409,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=1, figsize=(13, 5))\n",
    "xmin = 5\n",
    "xmax = max(xs)\n",
    "ax.hist(xs, range=(xmin, xmax), bins=100, alpha=0.3, density=True)\n",
    "ax.set_xlim(xmin, xmax)\n",
    "xvals = np.linspace(xmin, xmax, 101)\n",
    "yvals = (2/math.pi)**0.5 * np.exp(-xvals**2/2) / scipy.special.erfc(xmin / 2**0.5)\n",
    "ax.plot(xvals, yvals)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c569ef33-87ce-4a0c-8ff1-397702c995a8",
   "metadata": {},
   "source": [
    "### Conversions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 578,
   "id": "768d14bf-9947-4fb8-bfd2-98d6d7403a08",
   "metadata": {},
   "outputs": [],
   "source": [
    "importlib.reload(ginoe_mcmc)\n",
    "d = 2\n",
    "J = d**2 - 1\n",
    "G = rng.normal(size=(J, J))\n",
    "c = rng.normal(size=J)\n",
    "sgm = ginoe_mcmc.SparseGellMann(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 513,
   "id": "7523f348-668a-4b5c-8c71-bcc4dc821a5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5j"
      ]
     },
     "execution_count": 513,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G1 = np.zeros(shape=(3, 3), dtype=np.float64)\n",
    "G1[1, 2] = 1.0\n",
    "a = sgm.gc_to_a(G1, c * 0)\n",
    "a[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "id": "c0fdd8f5-634a-4777-9cfe-e62935aafd0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 514,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eye1 = np.eye(3)[1]\n",
    "eye2 = np.eye(3)[2]\n",
    "res1 = sgm.times_F(G1)\n",
    "res1_expected = eye1[:, np.newaxis, np.newaxis] * sigma_matrices[2]\n",
    "np.allclose(res1, res1_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "id": "f4e0bbff-7f79-4da6-b160-f6de5cf0e637",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 515,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res2 = sgm.times_newF(res1)\n",
    "res2_expected = eye1[:, None, None, None] * np.moveaxis([sigma_matrices[2] @ sigma_matrices[m] for m in range(3)], 0, 1)[None, ...]\n",
    "np.allclose(res2, res2_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "id": "b15cf561-fd63-4a78-835a-cce87a302193",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 516,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res3 = np.moveaxis(res2, 0, 3) # a, m, c, i\n",
    "res3_expected = np.moveaxis([sigma_matrices[2] @ sigma_matrices[m] for m in range(3)], 0, 1)[..., None] * eye1[None, None, None, :]\n",
    "np.allclose(res3, res3_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 580,
   "id": "a02ea019-63b8-4d75-8aa6-8787212caa66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[True, True, True]"
      ]
     },
     "execution_count": 580,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res4 = sgm.times_F(res3) # (a, m, c, c, d)\n",
    "res4_expected = np.moveaxis([sigma_matrices[2] @ sigma_matrices[m] for m in range(3)], 0, 1)[..., None, None] * sigma_matrices[1][None, None, None, ...]\n",
    "res4_v2 = sum(res3[:, :, :, i, None, None] * sigma_matrices[i][None, None, None, :, :] for i in range(3))\n",
    "[np.allclose(res4, res4_expected), np.allclose(res4_v2, res4_expected), np.allclose(res4, res4_v2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 586,
   "id": "ffa01020-06b7-4b90-b4a8-68d4ec01effa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 586,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.zeros(shape=(2, 3, 2, 3), dtype=np.complex128)\n",
    "x[0, 0, 1, 1] = 1j\n",
    "y = sgm.times_F(x)\n",
    "y_expected = sum(x[:, :, :, i, None, None] * sigma_matrices[i][None, None, None, :, :] for i in range(3))\n",
    "np.allclose(y, y_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "id": "2864ce02-9fc6-4453-8a86-6a0ce309c6f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 504,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res5 = np.einsum('amccd->mad', res4)\n",
    "res5_expected = np.array([sigma_matrices[0] @ sigma_matrices[m] @ sigma_matrices[0] for m in range(3)])\n",
    "np.allclose(res5, res5_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 505,
   "id": "bae975bb-1602-4c23-b965-35ac88411c2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 505,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res6 = sgm.times_newF(res5)\n",
    "res6_expected = np.moveaxis([[sigma_matrices[0] @ sigma_matrices[m] @ sigma_matrices[0] @ sigma_matrices[n] for n in range(3)] for m in range(3)], 1, 2)\n",
    "np.allclose(res6, res6_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 506,
   "id": "91a71458-2ba2-4319-a413-ed3a6b669a9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[ 0.25+0.j  , -0.  +0.j  ],\n",
       "         [ 0.  +0.j  ,  0.25+0.j  ],\n",
       "         [ 0.  +0.j  ,  0.  -0.25j]],\n",
       "\n",
       "        [[ 0.  +0.j  ,  0.25-0.j  ],\n",
       "         [-0.25+0.j  ,  0.  +0.j  ],\n",
       "         [-0.  -0.25j,  0.  -0.j  ]]],\n",
       "\n",
       "\n",
       "       [[[ 0.  +0.j  ,  0.25-0.j  ],\n",
       "         [-0.25+0.j  ,  0.  +0.j  ],\n",
       "         [-0.  -0.25j,  0.  -0.j  ]],\n",
       "\n",
       "        [[-0.25+0.j  , -0.  +0.j  ],\n",
       "         [ 0.  +0.j  , -0.25+0.j  ],\n",
       "         [ 0.  +0.j  ,  0.  +0.25j]]],\n",
       "\n",
       "\n",
       "       [[[ 0.  +0.j  , -0.  -0.25j],\n",
       "         [ 0.  +0.25j,  0.  +0.j  ],\n",
       "         [-0.25+0.j  ,  0.  -0.j  ]],\n",
       "\n",
       "        [[ 0.  -0.25j, -0.  +0.j  ],\n",
       "         [ 0.  +0.j  ,  0.  -0.25j],\n",
       "         [ 0.  +0.j  , -0.25+0.j  ]]]])"
      ]
     },
     "execution_count": 506,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.einsum('mana->mn', res6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 582,
   "id": "bd9a782c-c62e-4758-93f9-5198a725d5e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6.21 ms, sys: 2.35 ms, total: 8.57 ms\n",
      "Wall time: 5.81 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "a = sgm.gc_to_a(G, c * 0)\n",
    "H = sgm.gc_to_h(G, c)\n",
    "G1 = sgm.ah_to_g(a, H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 583,
   "id": "bce9fc00-f153-436e-b2ad-cd20edbddd25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 583,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(a, a.T.conj())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 584,
   "id": "3e33e604-94e8-4e9c-b9b8-f4ae01e79271",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 584,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(H, H.T.conj())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 585,
   "id": "7b7d5fc1-b697-4fe0-a5b6-8c9dc1bc3c9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 585,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(G, G1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b897796-6d3b-438e-a08a-5de75b19c351",
   "metadata": {},
   "source": [
    "### Binomial CI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 919,
   "id": "1bbe4494-d32d-4e98-be01-b3922383ca7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ci_gpt3_f(n, k):\n",
    "    alpha = 0.05\n",
    "    p_hat = k / n\n",
    "    q1 = (1 - alpha) / 2\n",
    "    q2 = 1 - q1\n",
    "    lower_endpoint = scipy.stats.beta.ppf(q1, k, n - k + 1)\n",
    "    upper_endpoint = scipy.stats.beta.ppf(q2, k + 1, n - k)\n",
    "\n",
    "    return lower_endpoint, upper_endpoint\n",
    "\n",
    "def ci_gpt4_f(n, x, alpha=0.05):\n",
    "    \"\"\"\n",
    "    Calculate exact binomial confidence interval.\n",
    "    \n",
    "    Parameters:\n",
    "    n (int): Number of trials\n",
    "    x (int): Number of successes\n",
    "    alpha (float): Significance level\n",
    "    \n",
    "    Returns:\n",
    "    tuple: Lower and upper confidence limits\n",
    "    \"\"\"\n",
    "    \n",
    "    def lower_func(c):\n",
    "        return scipy.special.betainc(x, n - x + 1, c) - alpha / 2\n",
    "    \n",
    "    def upper_func(c):\n",
    "        return 1 - scipy.special.betainc(x + 1, n - x, c) - alpha / 2\n",
    "    \n",
    "    # Initial guesses for lower and upper bounds\n",
    "    lower_guess = x / n\n",
    "    upper_guess = x / n\n",
    "    \n",
    "    # Bisect to find lower and upper confidence bounds\n",
    "    lower_bound = scipy.optimize.bisect(lower_func, 0, lower_guess)\n",
    "    upper_bound = scipy.optimize.bisect(upper_func, upper_guess, 1)\n",
    "    \n",
    "    return lower_bound, upper_bound\n",
    "\n",
    "def ci_gpt4_f_lb(n, x, alpha=0.05):\n",
    "    lower_bound = scipy.special.betaincinv(x, n - x + 1, alpha / 2)\n",
    "    return np.nan_to_num(lower_bound, nan=0)\n",
    "\n",
    "def ci_gpt4_f_v2(n, x, alpha=0.05):\n",
    "    lower_bound = ci_gpt4_f_lb(n, x, alpha)\n",
    "    upper_bound = 1 - ci_gpt4_f_lb(n, n - x, alpha)\n",
    "    return lower_bound, upper_bound\n",
    "\n",
    "def add_ci_test(p, samples, ci_lookup, results):\n",
    "    try:\n",
    "        lb, ub = tuple(c[samples] for c in ci_lookup)\n",
    "    except:\n",
    "        print(f\"{type(ci_lookup)} {type(ci_lookup[0])}\")\n",
    "        raise\n",
    "    results.append(np.mean((lb < p) & (p < ub)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 864,
   "id": "f6958192-ddad-4d79-9288-5b0d30d03494",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_trials = 10**6\n",
    "ci_wilson = ginoe_mcmc.wilson_interval(n_trials, np.arange(n_trials + 1))\n",
    "ci_gpt = ci_gpt3_f(n_trials, np.arange(n_trials + 1))\n",
    "ci_gpt = np.nan_to_num(ci_gpt[0], nan=0), np.nan_to_num(ci_gpt[1], nan=1)\n",
    "ci_gpt4 = [ci_gpt4_f(n_trials, k) for k in np.arange(n_trials + 1)]\n",
    "ci_gpt4 = np.array(ci_gpt4).T\n",
    "ci_gpt4_v2 = ci_gpt4_f_v2(n_trials, np.arange(n_trials + 1))\n",
    "ci_gpt4_v2 = np.nan_to_num(ci_gpt4_v2[0], nan=0), np.nan_to_num(ci_gpt4_v2[1], nan=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 917,
   "id": "578c632a-b783-4d82-87b5-d0ff9bc95139",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 10**6\n",
    "pmin = 36e-7\n",
    "pmax = 38e-7\n",
    "ps = np.linspace(pmin, pmax, 101)\n",
    "# ps = ps[np.minimum(res_gpt4, res_wilson) < 0.951]\n",
    "res_wilson = []\n",
    "res_gpt = []\n",
    "res_gpt4 = []\n",
    "for p in ps:\n",
    "    samples = rng.binomial(n=n_trials, p=p, size=n_samples)\n",
    "    add_ci_test(p, samples, ci_wilson, res_wilson)\n",
    "    add_ci_test(p, samples, ci_gpt, res_gpt)\n",
    "    add_ci_test(p, samples, ci_gpt4, res_gpt4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 918,
   "id": "fc4de26b-1192-47d6-bb4f-ef9aeb0a4542",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.939483, 0.9887688499999999)"
      ]
     },
     "execution_count": 918,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(ps, res_wilson)\n",
    "# ax.plot(ps, res_gpt)\n",
    "ax.plot(ps, res_gpt4)\n",
    "ax.set_xlim((pmin, pmax))\n",
    "ymin = np.min([res_wilson, res_gpt4])\n",
    "if ymin < 0.1:\n",
    "    ymin = 0\n",
    "ymax = 0.95 + 1.01 * (np.max([res_wilson, res_gpt4]) - 0.95)\n",
    "if ymax > 0.99:\n",
    "    ymax = 1\n",
    "ax.set_ylim((ymin, ymax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 965,
   "id": "8617ee83-101d-4a01-8d12-490fe464a8a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a, b, badvalue, cdf, entropy, expect, extradoc, freeze, generic_moment, inc, interval, isf, logcdf, logpmf, logsf,\n",
      "mean, median, moment, moment_tol, name, nnlf, numargs, pmf, ppf, random_state, rvs, sf, shapes, stats, std, support,\n",
      "var, vecentropy\n"
     ]
    }
   ],
   "source": [
    "mu.print_dir(scipy.stats.poisson.ppf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 966,
   "id": "b76de3ca-3e41-4cd8-95a7-78abab0625b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpoisson\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mppf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Percent point function (inverse of `cdf`) at q of the given RV.\n",
       "\n",
       "Parameters\n",
       "----------\n",
       "q : array_like\n",
       "    Lower tail probability.\n",
       "arg1, arg2, arg3,... : array_like\n",
       "    The shape parameter(s) for the distribution (see docstring of the\n",
       "    instance object for more information).\n",
       "loc : array_like, optional\n",
       "    Location parameter (default=0).\n",
       "\n",
       "Returns\n",
       "-------\n",
       "k : array_like\n",
       "    Quantile corresponding to the lower tail probability, q.\n",
       "\u001b[0;31mFile:\u001b[0m      ~/.local/lib/mambaforge/envs/bitchifc_minimal/lib/python3.10/site-packages/scipy/stats/_distn_infrastructure.py\n",
       "\u001b[0;31mType:\u001b[0m      method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "?scipy.stats.poisson.ppf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 987,
   "id": "684b437f-f60b-4204-b99e-0542eabc6581",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.160,2.266\n"
     ]
    }
   ],
   "source": [
    "x_min = 0.16\n",
    "x0 = 0.7755\n",
    "x_max = 2.27\n",
    "k = 3\n",
    "alpha = 0.05\n",
    "lower_bound = 0.5 * scipy.stats.chi2.ppf(alpha / 2, 2 * k) * x0 / k\n",
    "upper_bound = 0.5 * scipy.stats.chi2.ppf(1 - alpha / 2, 2 * k + 2) * x0 / k\n",
    "print(\",\".join(f\"{v:.3f}\" for v in [lower_bound, upper_bound]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 982,
   "id": "91f7a094-9a51-4478-898c-b582bd0373d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[81.36399125092314, 121.62679379242638]"
      ]
     },
     "execution_count": 982,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[0.5 * scipy.stats.chi2.ppf(alpha / 2, 200), 0.5 * scipy.stats.chi2.ppf(1 - alpha / 2, 200 + 2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 977,
   "id": "5d93a798-3822-4867-851f-996ae54b2b28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a, b, badvalue, cdf, entropy, expect, extradoc, fit, fit_loc_scale, freeze, generic_moment, interval, isf, logcdf,\n",
      "logpdf, logsf, mean, median, moment, moment_type, name, nnlf, numargs, pdf, ppf, random_state, rvs, sf, shapes, stats,\n",
      "std, support, var, vecentropy, xtol\n"
     ]
    }
   ],
   "source": [
    "mu.print_dir(scipy.stats.gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "edfff9e2-820a-4162-a640-d1088818e6bc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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