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    "# Lecture 21.4: NEMO 3-D — eigenvalues: Lanczos\n",
    "\n",
    "*From* [Nanoelectronic Modeling — From Atoms to Devices](https://nanohub.org/resources/45001),\n",
    "*Gerhard Klimeck, Purdue University. Lecture page:* [nanoHUB resource 45240](https://nanohub.org/resources/45240)\n",
    "— [video](https://nanohub.org/resources/45270) · [slides](https://nanohub.org/resources/45269)\n",
    "\n",
    "**In this lecture**\n",
    "\n",
    "- The size of the problem: a dot of 50 million atoms with 20 orbitals each gives a Hamiltonian of\n",
    "  order $10^9$, whose dense storage would take some 16,000 PB.\n",
    "- Stored sparsely it is \"only\" tens of GB, and a Lanczos solver never needs $H$ itself, only\n",
    "  products $H\\mathbf{q}$.\n",
    "- The Lanczos idea: a few thousand products build a small tridiagonal matrix $T_k$ whose\n",
    "  eigenvalues approach those of $H$ — extreme eigenvalues first.\n",
    "- The wanted states lie in the middle of the spectrum, near the band gap; NEMO 3-D runs the\n",
    "  recurrence as an open-ended loop until they emerge.\n",
    "- The Lanczos vectors form an orthonormal basis $Q_k$; the factorization $HQ_k = Q_kT_k +\n",
    "  \\mathbf{f}_k\\mathbf{e}_k^T$ gives Ritz values, Ritz vectors and a free error estimate.\n",
    "- Eigenvectors without storing $Q_k$: a second sweep regenerates the Lanczos vectors.\n",
    "\n",
    "**In this notebook**\n",
    "\n",
    "- Redo the storage estimates of the slides.\n",
    "- Write the Lanczos recurrence of slide 6 in a few lines of numpy, apply it to the tight-binding\n",
    "  Hamiltonian of a small GaAs nanocrystal built with open-nemo, and watch the Ritz values converge:\n",
    "  extremes first, gap states last, with spurious copies from the lost orthogonality.\n",
    "- Compute eigenvectors with the second sweep and check the residual formula\n",
    "  $\\|H\\mathbf{x}-\\lambda\\mathbf{x}\\| = \\|\\mathbf{f}_k\\|\\,|y_k|$.\n",
    "- Compare with open-nemo's NEMO 3-D-style solver `lanczos_window_eigenstates`."
   ]
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   "id": "63d21b98",
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   "source": [
    "%matplotlib inline\n",
    "import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import opennemo as nemo\n",
    "from opennemo.visualization import style\n",
    "from opennemo.structures.structure import cluster\n",
    "from opennemo.structures.shapes import Sphere\n",
    "from opennemo.solvers.eigen import lanczos_window_eigenstates\n",
    "\n",
    "style.use(notebook=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23f32f92",
   "metadata": {},
   "source": [
    "## 1. How large is the problem?\n",
    "\n",
    "A realistic dot involves millions of atoms: $N \\approx 50$ million atoms with a block of $B = 20$\n",
    "orbitals (sp3d5s\\* with spin) gives a Hamiltonian of size $(NB)^2$, i.e. $NB = 10^9$ rows. Stored\n",
    "dense in double-precision complex numbers (16 bytes each) it would need\n",
    "\n",
    "$$S = 10^9 \\times 10^9 \\times 16\\ \\text{bytes} \\approx 2\\times10^{4}\\ \\text{PB}$$\n",
    "\n",
    "(the slides compare this with the storage of the largest internet companies, an infrastructure of\n",
    "hundreds of millions of dollars). It is also too much *information*: that is the size of the full\n",
    "eigenvector space, and nobody wants all $10^9$ eigenvectors — only a few states in the middle of the\n",
    "spectrum, near the band gap. Stored sparsely, with only the diagonal block and the four neighbour\n",
    "blocks of each atom, the matrix shrinks enormously; and Lanczos never needs $H$ itself, only its\n",
    "product with a vector, which can be recomputed on the fly (lecture 21.5)."
   ]
  },
  {
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   "execution_count": 2,
   "id": "1e98ab22",
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    "execution": {
     "iopub.execute_input": "2026-10-24T22:30:55.197040Z",
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     "shell.execute_reply": "2026-10-24T22:30:55.199426Z"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dense storage:              16,000 PB\n",
      "sparse, slide's estimate:   80 GB\n",
      "sparse, every non-zero (CSR, 41 per row): 1.0 TB\n",
      "three Lanczos vectors:      48 GB\n"
     ]
    }
   ],
   "source": [
    "N, B = 50e6, 20\n",
    "dense = (N * B)**2 * 16\n",
    "slide_sparse = N * B * 5 * 16                         # the slide's count: N x B x n(=5 blocks) x 16 bytes\n",
    "nnz_row = 41                                          # measured for sp3d5s* + spin in lecture 21.3\n",
    "every_nnz = N * B * nnz_row * (16 + 8)                # value + column index for every non-zero\n",
    "print(f\"dense storage:              {dense / 1e15:,.0f} PB\")\n",
    "print(f\"sparse, slide's estimate:   {slide_sparse / 1e9:,.0f} GB\")\n",
    "print(f\"sparse, every non-zero (CSR, 41 per row): {every_nnz / 1e12:.1f} TB\")\n",
    "print(f\"three Lanczos vectors:      {3 * N * B * 16 / 1e9:,.0f} GB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23958c67",
   "metadata": {},
   "source": [
    "The slide's 80 GB counts one 16-byte number per row and neighbour block; storing every non-zero of\n",
    "the sp3d5s\\* matrix with its column index takes about 1 TB. Either way the matrix must be spread\n",
    "over many processors, while the Lanczos recurrence itself only needs three vectors of 16 GB each.\n",
    "\n",
    "## 2. The Lanczos idea\n",
    "\n",
    "![Slide 5: trade a 10^9 matrix for a 10^3 one](attachment:slide_005_crop.png)\n",
    "\n",
    "*Slide 5: a sparse $H$ of order $10^9$, never stored densely nor inverted, is touched only through\n",
    "products $H\\mathbf{q}$; $k \\approx 10^3$ products build a tridiagonal $T_k$ whose dense\n",
    "eigenvalues approximate those of $H$. Extreme eigenvalues converge first; the states we want lie\n",
    "in the middle.*\n",
    "\n",
    "Starting from a random unit vector $\\mathbf{q}_1$, each step applies $H$ once, projects the result on\n",
    "the current vector, subtracts the components along the last two vectors, and normalizes (slide 6):\n",
    "\n",
    "$$\\mathbf{w}_j = H\\mathbf{q}_j,\\qquad \\alpha_j = \\mathbf{q}_j^\\dagger\\mathbf{w}_j,\\qquad\n",
    "\\mathbf{f}_j = \\mathbf{w}_j - \\alpha_j\\mathbf{q}_j - \\beta_{j-1}\\mathbf{q}_{j-1},\\qquad\n",
    "\\beta_j = \\|\\mathbf{f}_j\\|,\\qquad \\mathbf{q}_{j+1} = \\mathbf{f}_j/\\beta_j .$$\n",
    "\n",
    "Only the numbers $\\alpha_j$ (the projection of $H\\mathbf{q}_j$ on $\\mathbf{q}_j$) and $\\beta_j$ (the\n",
    "norm of the residual) are kept. They form the tridiagonal matrix\n",
    "\n",
    "$$T_k = \\begin{pmatrix}\\alpha_1 & \\beta_1 & & \\\\ \\beta_1 & \\alpha_2 & \\ddots & \\\\\n",
    "& \\ddots & \\ddots & \\beta_{k-1} \\\\ & & \\beta_{k-1} & \\alpha_k\\end{pmatrix}.$$\n",
    "\n",
    "The test object is the sp3d5s\\* Hamiltonian (no spin) of a GaAs nanocrystal of 2.6 nm diameter,\n",
    "passivated at the surface, small enough to be diagonalized densely for comparison."
   ],
   "attachments": {
    "slide_005_crop.png": {
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"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6a739e27",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-24T22:30:55.200848Z",
     "iopub.status.busy": "2026-10-24T22:30:55.200788Z",
     "iopub.status.idle": "2026-10-24T22:31:02.063189Z",
     "shell.execute_reply": "2026-10-24T22:31:02.062840Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "399 atoms, H of order 3990 with 142202 non-zeros; dense eigvalsh 6.8 s\n",
      "spectrum -12.07 to 37.62 eV (passivated levels near 30 eV); gap states: HOMO -0.4179 eV, LUMO 2.3452 eV\n",
      "mean level spacing 12.5 meV\n"
     ]
    }
   ],
   "source": [
    "GAAS = nemo.structures.materials.load(\"klimeck2002_sp3d5s\")[\"GaAs\"]\n",
    "lat = nemo.structures.lattice.from_material(GAAS)\n",
    "dot = cluster(lat, Sphere([0.05, 0.07, 0.03], 1.3))\n",
    "H = nemo.models.tb.SlaterKoster(GAAS, passivation=30.0).build(dot).at(np.zeros(3)).tocsr()\n",
    "n = H.shape[0]\n",
    "t0 = time.perf_counter()\n",
    "exact = np.linalg.eigvalsh(H.toarray())\n",
    "print(f\"{dot.num_atoms} atoms, H of order {n} with {H.nnz} non-zeros; \"\n",
    "      f\"dense eigvalsh {time.perf_counter() - t0:.1f} s\")\n",
    "gap_lo = exact[exact < 0.8].max()                     # highest occupied level near the GaAs valence band\n",
    "gap_hi = exact[exact > 0.8].min()                     # lowest empty level\n",
    "print(f\"spectrum {exact[0]:.2f} to {exact[-1]:.2f} eV (passivated levels near 30 eV); \"\n",
    "      f\"gap states: HOMO {gap_lo:.4f} eV, LUMO {gap_hi:.4f} eV\")\n",
    "print(f\"mean level spacing {(exact[-1] - exact[0]) / n * 1000:.1f} meV\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "884ed747",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-24T22:31:02.064346Z",
     "iopub.status.busy": "2026-10-24T22:31:02.064273Z",
     "iopub.status.idle": "2026-10-24T22:31:02.226711Z",
     "shell.execute_reply": "2026-10-24T22:31:02.226292Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1500 Lanczos steps in 0.16 s (1500 products H q)\n"
     ]
    }
   ],
   "source": [
    "def lanczos(H, k, seed=0):\n",
    "    # plain Lanczos of slide 6, no reorthogonalization: returns alpha, beta (and the start vector)\n",
    "    rng = np.random.default_rng(seed)\n",
    "    q = rng.standard_normal(H.shape[0]) + 0j\n",
    "    q /= np.linalg.norm(q)\n",
    "    q0 = q.copy()\n",
    "    q_prev, b_prev = np.zeros_like(q), 0.0\n",
    "    alpha, beta = np.zeros(k), np.zeros(k)\n",
    "    for j in range(k):\n",
    "        w = H @ q\n",
    "        alpha[j] = np.vdot(q, w).real\n",
    "        f = w - alpha[j] * q - b_prev * q_prev\n",
    "        beta[j] = np.linalg.norm(f)\n",
    "        q_prev, q, b_prev = q, f / beta[j], beta[j]\n",
    "    return alpha, beta, q0\n",
    "\n",
    "\n",
    "K = 1500\n",
    "t0 = time.perf_counter()\n",
    "alpha, beta, q_start = lanczos(H, K)\n",
    "print(f\"{K} Lanczos steps in {time.perf_counter() - t0:.2f} s ({K} products H q)\")\n",
    "\n",
    "\n",
    "def ritz(k):\n",
    "    return np.linalg.eigvalsh(np.diag(alpha[:k]) + np.diag(beta[:k - 1], 1) + np.diag(beta[:k - 1], -1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e435d3bf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-24T22:31:02.227887Z",
     "iopub.status.busy": "2026-10-24T22:31:02.227811Z",
     "iopub.status.idle": "2026-10-24T22:31:09.386810Z",
     "shell.execute_reply": "2026-10-24T22:31:09.386388Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lowest level  -12.0680 eV: converged to 1e-8 eV after 80 steps\n",
      "HOMO           -0.4179 eV: converged to 1e-8 eV after 580 steps\n",
      "LUMO            2.3452 eV: converged to 1e-8 eV after 480 steps\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1210x484 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps = np.arange(20, K + 1, 20)\n",
    "fig, (a1, a2) = plt.subplots(1, 2, figsize=(11, 4.4))\n",
    "for k in steps:\n",
    "    t = ritz(k)\n",
    "    a1.plot(np.full(t.size, k), t, \",\", color=style.OPEN_NEMO)\n",
    "a1.set(xlabel=\"Lanczos steps k\", ylabel=\"Ritz values (eV)\", title=\"eigenvalues of T_k\", ylim=(-14, 16))\n",
    "a1.axhspan(gap_lo, gap_hi, color=style.CONTEXT, alpha=0.25, lw=0)\n",
    "targets = {\"lowest level\": exact[0], \"HOMO\": gap_lo, \"LUMO\": gap_hi}\n",
    "err = {name: [] for name in targets}\n",
    "for k in steps:\n",
    "    t = ritz(k)\n",
    "    for name, e in targets.items():\n",
    "        err[name].append(np.min(np.abs(t - e)))\n",
    "for (name, e), c in zip(err.items(), style.sweep(3)):\n",
    "    a2.semilogy(steps, np.maximum(e, 1e-15), color=c, label=name)\n",
    "a2.set(xlabel=\"Lanczos steps k\", ylabel=\"|nearest Ritz value − exact| (eV)\", title=\"convergence\")\n",
    "a2.legend(frameon=False, fontsize=8)\n",
    "fig.tight_layout()\n",
    "for name in targets:\n",
    "    conv = steps[np.argmax(np.array(err[name]) < 1e-8)] if min(err[name]) < 1e-8 else None\n",
    "    print(f\"{name:12s} {targets[name]:9.4f} eV: converged to 1e-8 eV after {conv} steps\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df7a1324",
   "metadata": {},
   "source": [
    "The picture is the one of slide 5. The lowest eigenvalue, at the edge of the spectrum, converges to\n",
    "$10^{-8}$ eV in 80 steps; the HOMO and LUMO, which lie in the middle of a spectrum about 50 eV wide\n",
    "(from $-12.1$ to $37.6$ eV, the top part being the passivation levels near 30 eV) where the levels are\n",
    "on average 12.5 meV apart, need 580 and 480 steps. Ordinary\n",
    "Lanczos codes stop after the extreme eigenvalues; NEMO 3-D instead keeps the loop open, monitors\n",
    "the Ritz values in the band gap, and peels out the gap states when they have converged.\n",
    "\n",
    "The recurrence is run without reorthogonalization, so the computed vectors lose their\n",
    "orthogonality as soon as an eigenvalue converges, and converged eigenvalues reappear as copies\n",
    "(\"ghosts\") in $T_k$. Counting the Ritz values that agree with the lowest eigenvalue shows it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "806d149b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-24T22:31:09.387938Z",
     "iopub.status.busy": "2026-10-24T22:31:09.387848Z",
     "iopub.status.idle": "2026-10-24T22:31:09.613370Z",
     "shell.execute_reply": "2026-10-24T22:31:09.612967Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k =  100: copies of the lowest eigenvalue in T_k: 1, Ritz values inside the gap (-0.418, 2.345) eV, strictly between: 0\n",
      "k =  500: copies of the lowest eigenvalue in T_k: 3, Ritz values inside the gap (-0.418, 2.345) eV, strictly between: 0\n",
      "k = 1000: copies of the lowest eigenvalue in T_k: 7, Ritz values inside the gap (-0.418, 2.345) eV, strictly between: 1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k = 1500: copies of the lowest eigenvalue in T_k: 11, Ritz values inside the gap (-0.418, 2.345) eV, strictly between: 1\n"
     ]
    }
   ],
   "source": [
    "for k in (100, 500, 1000, 1500):\n",
    "    t = ritz(k)\n",
    "    print(f\"k = {k:4d}: copies of the lowest eigenvalue in T_k: {np.sum(np.abs(t - exact[0]) < 1e-6)}, \"\n",
    "          f\"Ritz values inside the gap ({gap_lo:.3f}, {gap_hi:.3f}) eV, strictly between: \"\n",
    "          f\"{np.sum((t > gap_lo + 1e-4) & (t < gap_hi - 1e-4))}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6439aef4",
   "metadata": {},
   "source": [
    "Copies multiply with the number of steps; they are harmless (they are exact eigenvalues, only\n",
    "repeated) and are removed by the test of Cullum and Willoughby that open-nemo's solver applies: a\n",
    "simple eigenvalue of $T_k$ that is also an eigenvalue of $T_k$ with its first row and column removed\n",
    "is spurious. Values strictly inside the gap that appear and disappear while converging are also\n",
    "discarded by that test and by the convergence check.\n",
    "\n",
    "## 3. The Lanczos basis and the factorization\n",
    "\n",
    "![Slide 7: the Lanczos basis Q_k](attachment:slide_007_crop.png)\n",
    "\n",
    "*Slide 7: the $k$ Lanczos vectors are the columns of $Q_k$, tall ($N \\approx 10^9$ rows) and thin\n",
    "($k \\approx 10^3$ columns).*\n",
    "\n",
    "The vectors $\\mathbf{q}_1 \\dots \\mathbf{q}_k$ are orthonormal (in exact arithmetic) and span the\n",
    "Krylov space $\\{\\mathbf{q}_1, H\\mathbf{q}_1, H^2\\mathbf{q}_1, \\dots\\}$. In this basis $H$ becomes\n",
    "$T_k = Q_k^\\dagger H Q_k$, and the recurrence reads, as one matrix equation (slide 9),\n",
    "\n",
    "$$HQ_k = Q_kT_k + \\mathbf{f}_k\\mathbf{e}_k^T ,$$\n",
    "\n",
    "where $\\mathbf{e}_k$ is the last unit vector: $H$ acting on the Lanczos vectors is tridiagonal apart\n",
    "from one leftover direction $\\mathbf{f}_k$. If $T_k\\mathbf{y} = \\lambda\\mathbf{y}$, then $\\lambda$ is\n",
    "a **Ritz value** (an estimate of an eigenvalue of $H$) and $\\mathbf{x} = Q_k\\mathbf{y} =\n",
    "\\sum_j y_j\\mathbf{q}_j$ a **Ritz vector**, and multiplying the factorization by $\\mathbf{y}$ gives the\n",
    "error for free:\n",
    "\n",
    "$$H\\mathbf{x} - \\lambda\\mathbf{x} = (\\mathbf{e}_k^T\\mathbf{y})\\,\\mathbf{f}_k ,\\qquad\n",
    "\\|H\\mathbf{x} - \\lambda\\mathbf{x}\\| = \\|\\mathbf{f}_k\\|\\,|y_k| = \\beta_k\\,|y_k| .$$\n",
    "\n",
    "The convergence of an eigenvalue can thus be monitored from $T_k$ alone, without any vector.\n",
    "Storing all $N \\times k$ entries of $Q_k$ is exactly what NEMO 3-D avoids: since the recurrence is\n",
    "deterministic, a **second sweep** from the same start vector regenerates the $\\mathbf{q}_j$ one by\n",
    "one and accumulates $\\mathbf{x} = \\sum_j y_j\\mathbf{q}_j$ on the fly, at the price of a second set\n",
    "of $k$ products."
   ],
   "attachments": {
    "slide_007_crop.png": {
     "image/png": 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"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0ed74a5b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-24T22:31:09.614539Z",
     "iopub.status.busy": "2026-10-24T22:31:09.614458Z",
     "iopub.status.idle": "2026-10-24T22:31:09.827869Z",
     "shell.execute_reply": "2026-10-24T22:31:09.827472Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lowest  Ritz value -12.06802 eV (exact -12.06802), beta_k |y_k| = 2.2e-18, ||Hx - lx||/||x|| = 3.3e-14, ||x|| = 1.000\n",
      "HOMO    Ritz value  -0.41791 eV (exact  -0.41791), beta_k |y_k| = 1.0e-11, ||Hx - lx||/||x|| = 1.0e-11, ||x|| = 1.000\n",
      "LUMO    Ritz value   2.34517 eV (exact   2.34517), beta_k |y_k| = 6.6e-11, ||Hx - lx||/||x|| = 6.6e-11, ||x|| = 1.000\n"
     ]
    }
   ],
   "source": [
    "def second_sweep(H, q, k, Y):\n",
    "    # regenerate q_1..q_k from the same start and accumulate x = sum_j y_j q_j for each column of Y\n",
    "    X = np.zeros((H.shape[0], Y.shape[1]), complex)\n",
    "    q_prev, b_prev = np.zeros_like(q), 0.0\n",
    "    for j in range(k):\n",
    "        X += np.outer(q, Y[j])\n",
    "        w = H @ q\n",
    "        f = w - alpha[j] * q - b_prev * q_prev\n",
    "        q_prev, q, b_prev = q, f / beta[j], beta[j]\n",
    "    return X\n",
    "\n",
    "\n",
    "k = 1000\n",
    "Tk = np.diag(alpha[:k]) + np.diag(beta[:k - 1], 1) + np.diag(beta[:k - 1], -1)\n",
    "theta, Y = np.linalg.eigh(Tk)\n",
    "pick = [np.argmin(np.abs(theta - e)) for e in (exact[0], gap_lo, gap_hi)]\n",
    "X = second_sweep(H, q_start, k, Y[:, pick])\n",
    "for i, name in zip(range(3), (\"lowest\", \"HOMO\", \"LUMO\")):\n",
    "    x = X[:, i]\n",
    "    lam = theta[pick[i]]\n",
    "    true_res = np.linalg.norm(H @ x - lam * x) / np.linalg.norm(x)\n",
    "    print(f\"{name:7s} Ritz value {lam:9.5f} eV (exact {[exact[0], gap_lo, gap_hi][i]:9.5f}), \"\n",
    "          f\"beta_k |y_k| = {beta[k - 1] * abs(Y[-1, pick[i]]):.1e}, ||Hx - lx||/||x|| = {true_res:.1e}, \"\n",
    "          f\"||x|| = {np.linalg.norm(x):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cab118d0",
   "metadata": {},
   "source": [
    "The free estimate $\\beta_k|y_k|$ and the residual of the vector built by the second sweep agree for\n",
    "the converged states, to round-off, and $\\|\\mathbf{x}\\| = 1.000$ for all three. (Because the\n",
    "computed $\\mathbf{q}_j$ are not exactly orthogonal, the norm need not be 1 in general; the solver\n",
    "normalizes the vectors at the end.) Where\n",
    "the estimate is not yet small, the eigenvalue has not converged and the vector is a mixture.\n",
    "\n",
    "## 4. The NEMO 3-D solver in open-nemo\n",
    "\n",
    "`lanczos_window_eigenstates` implements this algorithm as NEMO 3-D did (Klimeck et al. 2002,\n",
    "§III F): the recurrence without reorthogonalization, Ritz values in an energy window checked every\n",
    "200 steps with their error bounds, the Cullum–Willoughby test against spurious values, an\n",
    "open-ended loop with a minimum number of steps, and the second pass for the eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "455eb176",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-24T22:31:09.828880Z",
     "iopub.status.busy": "2026-10-24T22:31:09.828813Z",
     "iopub.status.idle": "2026-10-24T22:31:10.555690Z",
     "shell.execute_reply": "2026-10-24T22:31:10.555193Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "window (-0.718, 2.645) eV: 2000 steps, 0.7 s\n",
      "Lanczos: [-0.70355 -0.64727 -0.6384  -0.63399 -0.62896 -0.60608 -0.59849 -0.57235\n",
      " -0.4544  -0.43997 -0.41791  2.34517  2.44501  2.44796  2.45545  2.45664\n",
      "  2.47278  2.48138  2.48318  2.56643  2.58118  2.58475  2.58739  2.62476\n",
      "  2.63284  2.64015]\n",
      "dense:   [-0.70355 -0.64727 -0.6384  -0.63399 -0.62896 -0.60608 -0.59849 -0.57235\n",
      " -0.4544  -0.43997 -0.41791  2.34517  2.44501  2.44796  2.45545  2.45664\n",
      "  2.47278  2.48138  2.48318  2.56643  2.58118  2.58475  2.58739  2.62476\n",
      "  2.63284  2.64015]\n",
      "residuals ||Hx - lx||: [1.7e-10 5.6e-09 1.7e-10 7.7e-11 6.3e-09 2.5e-10 1.6e-11 2.2e-10 2.9e-10\n",
      " 3.1e-10 7.4e-12 9.2e-09 1.4e-11 1.1e-11 2.9e-10 1.3e-10 8.4e-10 2.1e-10\n",
      " 1.5e-09 5.2e-09 2.0e-09 2.6e-09 2.0e-09 4.8e-09 1.2e-09 6.4e-09]\n"
     ]
    }
   ],
   "source": [
    "t0 = time.perf_counter()\n",
    "res = lanczos_window_eigenstates(H, (gap_lo - 0.3, gap_hi + 0.3), tol=1e-8, min_steps=1000)\n",
    "dt = time.perf_counter() - t0\n",
    "inwin = exact[(exact > gap_lo - 0.3) & (exact < gap_hi + 0.3)]\n",
    "print(f\"window ({gap_lo - 0.3:.3f}, {gap_hi + 0.3:.3f}) eV: {res.attrs['steps']} steps, {dt:.1f} s\")\n",
    "print(\"Lanczos:\", np.round(np.sort(res[\"energies\"]), 5))\n",
    "print(\"dense:  \", np.round(np.unique(np.round(inwin, 5)), 5))\n",
    "print(\"residuals ||Hx - lx||:\", np.array2string(np.asarray(res.attrs[\"residuals\"]), precision=1))"
   ]
  },
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    "The solver returns the distinct eigenvalues of the window, the gap states of the nanocrystal, with\n",
    "residuals between $10^{-11}$ and $10^{-8}$ eV, and all 26 match the dense diagonalization. This\n",
    "off-centre sphere has no degenerate levels in the window. Had it any (a nanocrystal centred on an\n",
    "atom has threefold levels from its cubic symmetry), they would be returned once: a single Lanczos\n",
    "recurrence only sees the start vector's component in each eigenspace, and nothing in $\\alpha$ and\n",
    "$\\beta$ distinguishes a degenerate eigenvalue from a simple one; open-nemo's `block` option runs\n",
    "several recurrences at once to recover the multiplicities.\n",
    "\n",
    "The scaling argument of the lecture is now concrete: each step costs one sparse product, linear in\n",
    "the number of atoms; the memory is three vectors plus the $\\alpha$'s and $\\beta$'s; and the number\n",
    "of steps, $10^3$–$10^4$ for gap states, depends on how wide the spectrum is and how close the wanted\n",
    "states are to their neighbours, not directly on the size of the matrix.\n",
    "\n",
    "## Summary\n",
    "\n",
    "- An sp3d5s\\* Hamiltonian of 50 million atoms has order $10^9$: about 16,000 PB dense, 80 GB to 1 TB\n",
    "  sparse, and Lanczos needs only products $H\\mathbf{q}$ and three vectors.\n",
    "- The Lanczos recurrence keeps only $\\alpha_j$ and $\\beta_j$; the eigenvalues of the tridiagonal $T_k$\n",
    "  converge to those of $H$, extremes first. The gap states of a GaAs nanocrystal need about 500\n",
    "  steps; the lowest level needs 80.\n",
    "- Without reorthogonalization converged eigenvalues reappear as copies, removed by the\n",
    "  Cullum–Willoughby test.\n",
    "- $HQ_k = Q_kT_k + \\mathbf{f}_k\\mathbf{e}_k^T$ gives Ritz pairs and the residual $\\beta_k|y_k|$ for free;\n",
    "  a second sweep builds the eigenvectors without storing $Q_k$.\n",
    "- open-nemo's `lanczos_window_eigenstates` reproduces the NEMO 3-D solver and agrees with dense\n",
    "  diagonalization.\n",
    "\n",
    "## Exercises\n",
    "\n",
    "1. Start the recurrence from a different random vector (`seed=1`). Do the convergence curves and the\n",
    "   number of ghost copies change?\n",
    "2. Add full reorthogonalization to `lanczos` (store the vectors and orthogonalize each new one against\n",
    "   all previous ones). How do the ghosts and the convergence of the HOMO change, and what does it\n",
    "   cost in memory for $10^9$ rows?\n",
    "3. Shift the spectrum: run Lanczos on $(H - \\sigma)^2$ with $\\sigma$ in the gap (\"folded spectrum\",\n",
    "   lecture 21.5). The gap states are now the lowest eigenvalues; how many products does their\n",
    "   convergence take, counting two per step?\n",
    "\n",
    "## Further reading\n",
    "\n",
    "- [Silicon quantum dot](../../book/07_quantum_dots/07_01_dot_levels_and_strain/07_01_01_silicon_quantum_dot.ipynb):\n",
    "  dense versus shift-invert eigensolvers for dots.\n",
    "- [FP32 block Lanczos](../../book/14_performance/14_01_kernels_and_solver_options/14_01_06_fp32_block_lanczos.ipynb)\n",
    "  and [cost scaling](../../book/14_performance/14_01_kernels_and_solver_options/14_01_01_cost_scaling.ipynb).\n",
    "- [Usman et al. 2009 dot](../../book/15_benchmarks/15_03_nemo3d/15_03_02_usman2009_dot.ipynb): the Lanczos\n",
    "  solver on a NEMO 3-D benchmark.\n",
    "- [API: electronic structure](../../book/18_api/18_03_electronic_structure.md).\n",
    "- Previous: [sp3d5s\\* tight binding](21_3_sp3d5s_tight_binding.ipynb); next:\n",
    "  [parallel computing](21_5_parallel_computing.ipynb).\n",
    "- C. Lanczos, *J. Res. Natl. Bur. Stand.* **45**, 255 (1950).\n",
    "- J. K. Cullum and R. A. Willoughby, *Lanczos Algorithms for Large Symmetric Eigenvalue Computations*\n",
    "  (Birkhäuser, 1985).\n",
    "- G. Klimeck, F. Oyafuso, T. B. Boykin, R. C. Bowen, P. von Allmen, *CMES* **3**, 601 (2002)."
   ]
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