Unbalanced_Optimal_Transport.ipynb

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      "cell_type": "markdown",
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      "source": [
        "# Introduction\n",
        "\n",
        "- Results on OT:\n",
        "    - Linear programming: $\\tilde{\\mathcal{O}}(n^3), \\tilde{\\mathcal{O}}(n^{5/2})$\n",
        "    - Entropic regularization: \n",
        "        - $\\tilde{\\mathcal{O}}(n^2/\\varepsilon^3), \\tilde{\\mathcal{O}}(n^2/\\varepsilon^2), \\tilde{\\mathcal{O}}(n^{7/3}/\\varepsilon)$\n",
        "        - $\\tilde{\\mathcal{O}}(n^{2.5}/\\varepsilon), \\tilde{\\mathcal{O}}(n^2/\\varepsilon)$: hard to implement."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IyiZ9exWtZUF",
        "colab_type": "text"
      },
      "source": [
        "# Contribution\n",
        "\n",
        "- Complexity for Sinkhorn for entropic-regulazized UOT is\n",
        "$$\n",
        "\\mathcal{O} \\Big( \\frac{n^2}{\\varepsilon} \\log(n) [\\log(\\| C \\|_\\infty ) + \\log(\\log(n)) + \\log (\\frac{1}{\\varepsilon})] \\Big).\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RD3oLFALoYc3",
        "colab_type": "text"
      },
      "source": [
        "# Implementation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ATdH9qXRCOUB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from numpy.linalg import norm\n",
        "from copy import copy\n",
        "import cvxpy as cp\n",
        "from tqdm.notebook import tqdm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "np.random.seed(999)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I3Kq3t0woLpx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "smallest_float = np.nextafter(np.float32(0), np.float32(1))\n",
        "float_type = np.longdouble\n",
        "\n",
        "def max_norm(x):\n",
        "    return np.amax(np.abs(x))\n",
        "\n",
        "def compute_entropy(P):\n",
        "    logP = np.log(P + 1e-20)\n",
        "    return -1 * np.sum(logP * P - P)\n",
        "\n",
        "\n",
        "def compute_KL(P, Q):\n",
        "    log_ratio = np.log(P) - np.log(Q)\n",
        "    return np.sum(P * log_ratio - P + Q)\n",
        "\n",
        "\n",
        "def dot(x, y):\n",
        "    return np.sum(x * y)\n",
        "\n",
        "\n",
        "def compute_B(C, u, v, eta):\n",
        "    return np.exp((u + v.T - C) / eta)\n",
        "\n",
        "\n",
        "def compute_f(C, X, a, b, tau1, tau2):\n",
        "    Xa = X.sum(axis=1).reshape(-1, 1)\n",
        "    Xb = X.sum(axis=0).reshape(-1, 1)\n",
        "\n",
        "    return dot(C, X) + tau1 * compute_KL(Xa, a) + tau2 * compute_KL(Xb, b)\n",
        "\n",
        "\n",
        "def compute_g_primal(C, u, v, a, b, eta, tau1, tau2):\n",
        "    B = compute_B(C, u, v, eta)\n",
        "\n",
        "    Ba = B.sum(axis=1).reshape(-1, 1)\n",
        "    Bb = B.sum(axis=0).reshape(-1, 1)\n",
        "\n",
        "    return dot(C, B) + tau1 * compute_KL(Ba, a) + tau2 * compute_KL(Bb, b) - eta * compute_entropy(B)\n",
        "\n",
        "\n",
        "def compute_g_dual(C, u, v, a, b, eta, tau1, tau2):\n",
        "    B = compute_B(C, u, v, eta)\n",
        "    f = eta * np.sum(B) + tau1 * dot(np.exp(- u / tau1), a) + tau2 * dot(np.exp(- v / tau2), b)\n",
        "\n",
        "    return f\n",
        "\n",
        "\n",
        "def solve_g_dual_cp(C, a, b, eta, tau):\n",
        "    dim_a = a.shape[0]\n",
        "    dim_b = b.shape[0]\n",
        "\n",
        "    u = cp.Variable(shape=a.shape)\n",
        "    v = cp.Variable(shape=b.shape)\n",
        "\n",
        "    u_stack = cp.vstack([u.T for _ in range(dim_b)])\n",
        "    v_stack = cp.hstack([v for _ in range(dim_a)])\n",
        "\n",
        "    obj = eta * cp.sum(cp.exp((u_stack + v_stack - C) / eta))\n",
        "    obj += tau * cp.sum(cp.multiply(cp.exp(- u / tau), a))\n",
        "    obj += tau * cp.sum(cp.multiply(cp.exp(- v / tau), b))\n",
        "\n",
        "    prob = cp.Problem(cp.Minimize(obj))\n",
        "    # prob.solve(solver=cp.SCS, eps=smallest_float)\n",
        "    prob.solve()\n",
        "\n",
        "    return prob.value, u.value, v.value\n",
        "\n",
        "\n",
        "def solve_f_cp(C, a, b, tau1=1.0, tau2=1.0):\n",
        "    \"\"\"\n",
        "    Convex programming solver for standard Unbalanced Optimal Transport.\n",
        "\n",
        "    :param C:\n",
        "    :param a:\n",
        "    :param b:\n",
        "    :param tau1:\n",
        "    :param tau2:\n",
        "    :return:\n",
        "    \"\"\"\n",
        "\n",
        "    X = cp.Variable((a.shape[0], b.shape[0]), nonneg=True)\n",
        "\n",
        "    row_sums = cp.sum(X, axis=1)\n",
        "    col_sums = cp.sum(X, axis=0)\n",
        "\n",
        "    obj = cp.sum(cp.multiply(X, C))\n",
        "\n",
        "    obj -= tau1 * cp.sum(cp.entr(row_sums))\n",
        "    obj -= tau2 * cp.sum(cp.entr(col_sums))\n",
        "\n",
        "    obj -= tau1 * cp.sum(cp.multiply(row_sums, cp.log(a.reshape(-1, ))))\n",
        "    obj -= tau2 * cp.sum(cp.multiply(col_sums, cp.log(b.reshape(-1, ))))\n",
        "\n",
        "    obj -= (tau1 + tau2) * cp.sum(X)\n",
        "    obj += tau1 * cp.sum(a.reshape(-1, )) + tau2 * cp.sum(b.reshape(-1, ))\n",
        "\n",
        "    prob = cp.Problem(cp.Minimize(obj))\n",
        "    # prob.solve(solver=cp.SCS, max_iters=10000, eps=1e-6)\n",
        "    prob.solve()\n",
        "\n",
        "    return prob.value, X.value\n",
        "    \n",
        "\n",
        "def sinkhorn_uot(C, a, b, eta=1.0, tau1=1.0, tau2=1.0, k=100, compute_optimal=True):\n",
        "    \"\"\"\n",
        "    Sinkhorn algorithm for entropic-regularized Unbalanced Optimal Transport.\n",
        "\n",
        "    :param C:\n",
        "    :param a:\n",
        "    :param b:\n",
        "    :param eta:\n",
        "    :param tau1:\n",
        "    :param tau2:\n",
        "    :param k:\n",
        "    :param epsilon:\n",
        "    :return:\n",
        "    \"\"\"\n",
        "\n",
        "    output = {\n",
        "        \"u\": list(),\n",
        "        \"v\": list(),\n",
        "        \"f\": list(),\n",
        "        \"g_dual\": list()\n",
        "    }\n",
        "\n",
        "    # Compute optimal value and X for unregularized UOT\n",
        "    if compute_optimal:\n",
        "        f_optimal, X_optimal = solve_f_cp(C, a, b, tau1=tau1, tau2=tau2)\n",
        "        output[\"f_optimal\"] = f_optimal\n",
        "        output[\"X_optimal\"] = X_optimal\n",
        "\n",
        "    # Initialization\n",
        "    u = np.zeros_like(a).astype(float_type)\n",
        "    v = np.zeros_like(b).astype(float_type)\n",
        "\n",
        "    output[\"u\"].append(copy(u))\n",
        "    output[\"v\"].append(copy(v))\n",
        "\n",
        "    # # Compute initial value of f\n",
        "    # B = compute_B(C, u, v, eta)\n",
        "    # f = compute_f_primal(C=C, X=B, a=a, b=b, tau1=tau1, tau2=tau2)\n",
        "    # output[\"f\"].append(f)\n",
        "\n",
        "    for i in range(k):\n",
        "        u_old = copy(u)\n",
        "        v_old = copy(v)\n",
        "        B = compute_B(C, u, v, eta)\n",
        "\n",
        "        f = compute_f(C=C, X=B, a=a, b=b, tau1=tau1, tau2=tau2)\n",
        "\n",
        "        output[\"f\"].append(f)\n",
        "\n",
        "        # Sinkhorn update\n",
        "        if i % 2 == 0:\n",
        "            Ba = B.sum(axis=1).reshape(-1, 1)\n",
        "            u = (u / eta + np.log(a) - np.log(Ba)) * (tau1 * eta / (eta + tau1))\n",
        "        else:\n",
        "            Bb = B.sum(axis=0).reshape(-1, 1)\n",
        "            v = (v / eta + np.log(b) - np.log(Bb)) * (tau2 * eta / (eta + tau2))\n",
        "\n",
        "        g_dual = compute_g_dual(C=C, u=u, v=v, a=a, b=b, eta=eta, tau1=tau1, tau2=tau2)\n",
        "\n",
        "        output[\"u\"].append(copy(u))\n",
        "        output[\"v\"].append(copy(v))\n",
        "        output[\"g_dual\"].append(g_dual)\n",
        "\n",
        "        # err = norm(u - u_old, ord=1) + norm(v - v_old, ord=1)\n",
        "\n",
        "        # if err < 1e-10:\n",
        "        #     break\n",
        "        #\n",
        "        # if np.abs(f - output[\"f_optimal\"]) < epsilon:\n",
        "        #     break\n",
        "\n",
        "    return output\n",
        "\n",
        "\n",
        "def find_k_sinkhorn(C, a, b, epsilon, f_optimal, eta=1.0, tau1=1.0, tau2=1.0, momentum=100, max_trial=100000):\n",
        "    # Initialization\n",
        "    u = np.zeros_like(a)\n",
        "    v = np.zeros_like(b)\n",
        "\n",
        "    i = 0\n",
        "    count = 0\n",
        "    trial = 0\n",
        "    start_trial = False\n",
        "\n",
        "    while True:\n",
        "        B = compute_B(C, u, v, eta)\n",
        "\n",
        "        f_primal = compute_f(C=C, X=B, a=a, b=b, tau1=tau1, tau2=tau2)\n",
        "\n",
        "        # Sinkhorn update\n",
        "        if i % 2 == 0:\n",
        "            Ba = B.sum(axis=1).reshape(-1, 1)\n",
        "            u = (u / eta + np.log(a) - np.log(Ba)) * (tau1 * eta / (eta + tau1))\n",
        "        else:\n",
        "            Bb = B.sum(axis=0).reshape(-1, 1)\n",
        "            v = (v / eta + np.log(b) - np.log(Bb)) * (tau2 * eta / (eta + tau2))\n",
        "\n",
        "        if np.abs(f_primal - f_optimal) < epsilon:\n",
        "            # print(f\"{i} ------ {np.abs(f_primal - f_optimal)}\")\n",
        "            if count == 0:\n",
        "                true_flag = i\n",
        "\n",
        "            counting_flag = i\n",
        "            count += 1\n",
        "            start_trial = True\n",
        "\n",
        "            if count > momentum:\n",
        "                return true_flag\n",
        "\n",
        "            # if start_trial:\n",
        "            #     print(\"X.\")\n",
        "        else:\n",
        "            if start_trial:\n",
        "                counting_flag = -np.inf\n",
        "                count = 0\n",
        "                trial += 1\n",
        "\n",
        "        if trial > max_trial:\n",
        "            break\n",
        "\n",
        "        i += 1\n",
        "\n",
        "    return counting_flag\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1KZVnB96ofan",
        "colab_type": "text"
      },
      "source": [
        "# Experiment (Checking theorems and lemmas)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ODfHLct2o_31",
        "colab_type": "text"
      },
      "source": [
        "## Hyperparameters"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "duPwVWS0oSw8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "range_a = 10\n",
        "range_b = 10\n",
        "range_C = 100\n",
        "dim_a = 100\n",
        "dim_b = 100\n",
        "eta = 0.05\n",
        "tau1 = 1.0\n",
        "tau2 = 1.0\n",
        "k = 500\n",
        "\n",
        "C = np.random.uniform(low=1, high=range_C, size=(dim_a, dim_b)).astype(\"float128\")\n",
        "C = (C + C.T) / 2\n",
        "a = np.random.uniform(low=0.1, high=range_a, size=(dim_a, 1)).astype(\"float128\")\n",
        "b = np.random.uniform(low=0.1, high=range_b, size=(dim_b, 1)).astype(\"float128\")\n",
        "\n",
        "n = dim_a\n",
        "tau = tau1\n",
        "\n",
        "alpha = np.sum(a)\n",
        "beta = np.sum(b)\n",
        "\n",
        "exp_name = f\"[n={dim_a}]_[tau={'{0:.1f}'.format(np.mean(tau1))}]_[rC={range_C}]_[ra={range_a}]_[rb={range_b}]_[eta={'{0:.2f}'.format(np.mean(eta))}]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7heU44w_p2fe",
        "colab_type": "text"
      },
      "source": [
        "## Solving UOT"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D2fnKv8DqFx-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "g_dual_optimal, u_optimal, v_optimal = solve_g_dual_cp(C=C, a=a, b=b, eta=eta, tau=tau)\n",
        "output = sinkhorn_uot(C=C, a=a, b=b, eta=eta, tau1=tau1, tau2=tau2, k=k)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZFZRoFIOxvct",
        "colab_type": "text"
      },
      "source": [
        "## Checking convergence of Sinkhorn algorithm"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PbmENTafCb9X",
        "colab_type": "code",
        "outputId": "8f046c26-0396-4ce9-ccc1-02c9b2e26d17",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 801
        }
      },
      "source": [
        "delta_u = [max_norm(u - u_optimal) for u in output[\"u\"]]\n",
        "delta_v = [max_norm(v - v_optimal) for v in output[\"v\"]]\n",
        "\n",
        "\"\"\"\n",
        "PLOTTING\n",
        "\"\"\"\n",
        "fig, axs = plt.subplots(2, 2, figsize=(18, 12))\n",
        "plt.subplots_adjust(hspace=0.5)\n",
        "\n",
        "fig.suptitle(exp_name)\n",
        "\n",
        "axs[0, 0].plot(list(range(k)), output[\"f\"], \"r\", label=\"f\")\n",
        "axs[0, 0].plot([0, k - 1], [output[\"f_optimal\"], output[\"f_optimal\"]], \"b\", label=\"f optimal\")\n",
        "axs[0, 0].set_xlabel(\"k (iterations)\")\n",
        "axs[0, 0].set_title(\"f\")\n",
        "axs[0, 0].legend()\n",
        "axs[0, 0].text(x=0.5, y=0.7, s=f\"min_f={'{0:.2f}'.format(min(output['f']))}\\noptimal_f={'{0:.2f}'.format(output['f_optimal'])}\", horizontalalignment='center', verticalalignment='center', transform=axs[0, 0].transAxes)\n",
        "\n",
        "b1 = 500\n",
        "b2 = 750\n",
        "axs[0, 1].plot(list(range(k)), output[\"g_dual\"], \"r\", label=\"g dual\")\n",
        "axs[0, 1].plot([0, k - 1], [g_dual_optimal, g_dual_optimal], \"b\", label=\"g dual optimal\")\n",
        "axs[0, 1].set_xlabel(\"k (iterations)\")\n",
        "axs[0, 1].set_title(\"g dual\")\n",
        "axs[0, 1].legend()\n",
        "axs[0, 1].text(x=0.5, y=0.7, s=f\"min_g={'{0:.2f}'.format(min(output['g_dual']))}\\noptimal_g={'{0:.2f}'.format(g_dual_optimal)}\", horizontalalignment='center', verticalalignment='center', transform=axs[0, 1].transAxes)\n",
        "\n",
        "axs[1, 0].plot(list(range(k + 1)), delta_u, \"r\", label=\"f optimal\")\n",
        "axs[1, 0].set_xlabel(\"k (iterations)\")\n",
        "axs[1, 0].set_title(r\"$\\| u - u^* \\|_\\infty$\")\n",
        "axs[1, 0].text(x=0.7, y=0.7, s=f\"min={'{0:.2f}'.format(delta_u[-1])}\", horizontalalignment='center', verticalalignment='center', transform=axs[1, 0].transAxes)\n",
        "\n",
        "axs[1, 1].plot(list(range(k + 1)), delta_v, \"r\", label=\"f optimal\")\n",
        "axs[1, 1].set_xlabel(\"k (iterations)\")\n",
        "axs[1, 1].set_title(r\"$\\| v - v^* \\|_\\infty$\")\n",
        "axs[1, 1].text(x=0.7, y=0.7, s=f\"min={'{0:.2f}'.format(delta_v[-1])}\", horizontalalignment='center', verticalalignment='center', transform=axs[1, 1].transAxes)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1296x864 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QHSUX0YWBFDa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "B_star = compute_B(C=C, u=u_optimal, v=v_optimal, eta=eta)\n",
        "a_star = np.sum(B_star, axis=1, keepdims=True)\n",
        "b_star = np.sum(B_star, axis=0, keepdims=True).T\n",
        "\n",
        "R = max(max_norm(np.log(a)), max_norm(np.log(b))) + max(np.log(n), 1 / eta * max_norm(C) - np.log(n))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Oyaum6ClqMFO",
        "colab_type": "text"
      },
      "source": [
        "## Lemma 1\n",
        "\n",
        "$$\n",
        "\\frac{u^*}{\\tau} = \\log(a) - \\log(a^*) \\\\\n",
        "\\frac{v^*}{\\tau} = \\log(b) - \\log(b^*)\n",
        "$$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eD3CGcrQqQ49",
        "colab_type": "code",
        "outputId": "2c492c9c-a3ef-4368-b444-ade18619d65c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "lhs = list(u_optimal / tau)\n",
        "rhs = list(np.log(a) - np.log(a_star))\n",
        "\n",
        "plt.figure(figsize=(12, 8))\n",
        "plt.plot(list(range(n)), lhs, \"r\", label=\"lhs\")\n",
        "plt.plot(list(range(n)), rhs, \"b\", label=\"rhs\")\n",
        "plt.xlabel(\"k (-th iteration)\")\n",
        "plt.title(\"Lemma 1\")\n",
        "plt.legend()\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BQXZsl_TCnk7",
        "colab_type": "text"
      },
      "source": [
        "## Lemma 2\n",
        "\n",
        "$$\n",
        "\\Big| \\log\\left( \\frac{a_i^*}{a_i^k} \\right) -  \\frac{u_i^* - u_i^k}{\\eta}\\Big| \\leq  \\max_{1 \\leq j \\leq n} \\frac{|v^*_j - v^{k}_j|}{\\eta}\n",
        "$$\n",
        "\n",
        "$$\n",
        "\\Big| \\log\\left( \\frac{b_j^*}{b_j^k} \\right) -  \\frac{v_j^* - v_j^k}{\\eta}\\Big| \\leq  \\max_{1 \\leq i \\leq n} \\frac{|u^*_i - u^{k}_i|}{\\eta}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ySD4R4JmBJME",
        "colab_type": "code",
        "outputId": "6341faf9-4cb3-447d-c3c3-bfa1f94acdf3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "B_k_list = [compute_B(C=C, u=output[\"u\"][i], v=output[\"v\"][i], eta=eta) for i in range(k)]\n",
        "a_k_list = [np.sum(B_k_list[i], axis=1, keepdims=True) for i in range(k)]\n",
        "b_k_list = [np.sum(B_k_list[i], axis=0, keepdims=True).T for i in range(k)]\n",
        "lhs = [max_norm(np.log(a_star / a_k_list[i]) - (u_optimal - output[\"u\"][i]) / eta) for i in range(k)]\n",
        "rhs = [max_norm((v_optimal - output[\"v\"][i]) / eta) for i in range(k)]\n",
        "\n",
        "plt.figure(figsize=(12, 8))\n",
        "\n",
        "plt.plot(list(range(k)), lhs, \"r\", label=\"lhs\")\n",
        "plt.plot(list(range(k)), rhs, \"b\", label=\"rhs\")\n",
        "plt.xlabel(\"k (iterations)\")\n",
        "plt.title(\"Lemma 2\")\n",
        "plt.legend()\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H6xNGpmCEJJ8",
        "colab_type": "text"
      },
      "source": [
        "## Lemma 3\n",
        "\n",
        "$$\n",
        "\\max \\{ \\|u^*\\|_{\\infty},\\|v^*\\|_\\infty \\} \\le \\tau R\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rywo8PfHD0yc",
        "colab_type": "text"
      },
      "source": [
        "## Theorem 1\n",
        "\n",
        "$$\n",
        "\\max \\{ \\| u^{k} -  u^*\\|_\\infty, \\| v^{k} -  v^*\\|_\\infty \\} \\le \\Big( \\frac{\\tau}{\\tau + \\eta} \\Big)^k \\times \\tau \\times R\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2YjmZ_N0pQa9",
        "colab_type": "code",
        "outputId": "339a26c5-83a7-4cea-b72c-6b93ccb0f9d3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "delta_k_list = [max(delta_u[i], delta_v[i]) for i in range(k)]\n",
        "bound_list = [np.power(tau / (tau + eta), i) * tau * R for i in range(k)]\n",
        "\n",
        "plt.figure(figsize=(12, 8))\n",
        "plt.plot(list(range(k)), delta_k_list, \"r\", label=r\"$\\Delta_{k}$\")\n",
        "plt.plot(list(range(k)), bound_list, \"b\", label=r\"$(\\frac{\\tau}{\\tau + \\eta})^k \\times \\tau \\times R$\")\n",
        "plt.xlabel(\"k (iterations)\")\n",
        "plt.title(\"Theorem 1\")\n",
        "plt.legend()\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ],
            "image/png": 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K6QOlxxHxdeDlsvMfSynN6uQ6FwKnAbcD1wJHAdf1vOSBtfXW9jBLkiQ1s832MKeUfgt02sea9xK/H5hX6RoRMRHYMqX0h5RSIgvfx/W83IE3bpyBWZIkqZn1dQzzgcBzKaVHy9qmR8S9EXFLRByYt00C2srOacvbap6BWZIkqbl1Z0hGJSfy5t7lZcCUlNLKiNgL+FlE7Ax0Nl45dXXRiDiNbPgGU6ZM6WOJfeMYZkmSpObW6x7miBgMvBf4caktpbQupbQyf3w38BjwFrIe5cllL58MLO3q2imli1JKs1NKs1tbW3tbYlVsvTW8/DJs2FBoGZIkSSpIX4ZkHAY8lFJ6fahFRLRGREv+eAdgBvB4SmkZsCoi9svHPZ8C/LwP7z1gXO1PkiSpuXVnWrl5wB+At0ZEW0R8ND90Apt+2e8gYGFE3AdcAXw8pVSKmp8AvgssIet5rvkZMuCNwOw4ZkmSpOa02THMKaUTu2j/607argSu7OL8+cAuPayvcPYwS5IkNTdX+tuMrbfO9vYwS5IkNScD82Y4JEOSJKm5GZg3w8AsSZLU3AzMmzF6NAwe7BhmSZKkZmVg3oyIbByzPcySJEnNycDcDS6PLUmS1LwMzN1gYJYkSWpeBuZuGDfOMcySJEnNysDcDY5hliRJal4G5m5wSIYkSVLzMjB3w7hxsHYtrF5ddCWSJEkaaAbmbigtXuI4ZkmSpOZjYO6GrbfO9g7LkCRJaj4G5m5weWxJkqTmZWDuBgOzJElS8zIwd4NjmCVJkpqXgbkbHMMsSZLUvAzM3TB8OIwcaWCWJElqRgbmbnLxEkmSpOZkYO6m8ePh+eeLrkKSJEkDzcDcTePHw4oVRVchSZKkgWZg7qbWVnuYJUmSmpGBuZtaW+1hliRJakYG5m4aPx5WrYJ164quRJIkSQPJwNxNra3Z3mEZkiRJzcXA3E2lwOywDEmSpOZiYO6m8eOzvT3MkiRJzcXA3E32MEuSJDUnA3M3GZglSZKak4G5m8aOhQiHZEiSJDUbA3M3tbTAuHH2MEuSJDUbA3MPuDy2JElS8zEw94DLY0uSJDUfA3MPuDy2JElS8zEw98D48fYwS5IkNRsDcw+0tsLKldDRUXQlkiRJGigG5h5obYX2dnjxxaIrkSRJ0kAxMPeAy2NLkiQ1HwNzD7janyRJUvMxMPdAqYfZwCxJktQ8DMw9UOphdkiGJElS89hsYI6IuRGxPCIWlbWdGRHPRMSCfDum7NgXImJJRDwcEUeWtR+Vty2JiDOq/1H6nz3MkiRJzac7Pcw/AI7qpP2bKaVZ+XYtQETsBJwA7Jy/5n8ioiUiWoD/Bo4GdgJOzM+tKyNGwKhRBmZJkqRmMnhzJ6SUfhsR07p5vWOBy1JK64AnImIJsE9+bElK6XGAiLgsP/fBHldcMJfHliRJai59GcP8yYhYmA/ZGJu3TQKeLjunLW/rqr3uuDy2JElSc+ltYL4Q2BGYBSwDvp63RyfnpgrtnYqI0yJifkTMX1Fj6dTlsSVJkppLrwJzSum5lFJ7SqkDmMMbwy7agO3LTp0MLK3Q3tX1L0opzU4pzW4tTU1RI+xhliRJai69CswRMbHs6fFAaQaNq4ETImJYREwHZgB3AncBMyJiekQMJfti4NW9L7s4BmZJkqTmstkv/UXEPOBgYHxEtAFfAg6OiFlkwyqeBP4WIKX0QERcTvZlvg3A6Sml9vw6nwSuB1qAuSmlB6r+aQbA+PGwZg28+mo2Y4YkSZIaW3dmyTixk+bvVTj/HOCcTtqvBa7tUXU1aJttsv2KFQZmSZKkZuBKfz1UCszPPVdsHZIkSRoYBuYemjAh2xuYJUmSmoOBuYcMzJIkSc3FwNxDpSEZy5cXW4ckSZIGhoG5h4YPh622sodZkiSpWRiYe2GbbQzMkiRJzcLA3AsTJhiYJUmSmoWBuRcmTHAMsyRJUrMwMPeCPcySJEnNw8DcC9tsAy+8AK+9VnQlkiRJ6m8G5l4ozcXssAxJkqTGZ2DuBQOzJElS8zAw94Kr/UmSJDUPA3MvGJglSZKah4G5F0rLYxuYJUmSGp+BuRe22AJGjHAMsyRJUjMwMPdChHMxS5IkNQsDcy8ZmCVJkpqDgbmXttnGwCxJktQMDMy9NGGCY5glSZKagYG5lyZMgBUroKOj6EokSZLUnwzMvTRhArS3w8qVRVciSZKk/mRg7iUXL5EkSWoOBuZeKi1e4jhmSZKkxmZg7iV7mCVJkpqDgbmXDMySJEnNwcDcS2PHwpAhBmZJkqRGZ2DupQjYdltYtqzoSiRJktSfDMx9MHGigVmSJKnRGZj7wMAsSZLU+AzMfTBxIixdWnQVkiRJ6k8G5j6YODFb6W/9+qIrkSRJUn8xMPfBxInZ/tlni61DkiRJ/cfA3AelwOw4ZkmSpMZlYO6D7bbL9gZmSZKkxmVg7gN7mCVJkhqfgbkPttkGBg0yMEuSJDUyA3MftLRkodnALEmS1LgMzH3kXMySJEmNzcDcR672J0mS1NgMzH1kYJYkSWpsmw3METE3IpZHxKKytv+IiIciYmFEXBURY/L2aRGxJiIW5Nu3y16zV0TcHxFLIuL8iIj++UgDa+JEWL4c2tuLrkSSJEn9oTs9zD8Ajtqo7QZgl5TSbsAjwBfKjj2WUpqVbx8va78QOA2YkW8bX7MuTZwIHR1ZaJYkSVLj2WxgTin9Fnhho7ZfpZQ25E9vByZXukZETAS2TCn9IaWUgEuA43pXcm1x8RJJkqTGVo0xzB8Brit7Pj0i7o2IWyLiwLxtEtBWdk5b3lb3XLxEkiSpsQ3uy4sj4l+ADcCledMyYEpKaWVE7AX8LCJ2Bjobr5wqXPc0suEbTJkypS8l9rtSYHZqOUmSpMbU6x7miDgVeBfwoXyYBSmldSmllfnju4HHgLeQ9SiXD9uYDHQZMVNKF6WUZqeUZre2tva2xAGx7bbZ3h5mSZKkxtSrwBwRRwGfB96TUlpd1t4aES354x3Ivtz3eEppGbAqIvbLZ8c4Bfh5n6uvAUOHwrhxBmZJkqRGtdkhGRExDzgYGB8RbcCXyGbFGAbckM8Od3s+I8ZBwNkRsQFoBz6eUip9YfATZDNujCAb81w+7rmuORezJElS49psYE4pndhJ8/e6OPdK4Moujs0HdulRdXXCwCxJktS4XOmvCgzMkiRJjcvAXAXbbZcF5o6OoiuRJElStRmYq2DyZNiwAVasKLoSSZIkVZuBuQom5UuwtLVVPk+SJEn1x8BcBZPzGaYNzJIkSY3HwFwFpcD8zDPF1iFJkqTqMzBXwTbbwODB9jBLkiQ1IgNzFQwalM2UYWCWJElqPAbmKpk82SEZkiRJjcjAXCWTJ9vDLEmS1IgMzFUyaVIWmFMquhJJkiRVk4G5SiZPhtWr4eWXi65EkiRJ1WRgrhLnYpYkSWpMBuYqcbU/SZKkxmRgrhIXL5EkSWpMBuYqmTgRIuxhliRJajQG5ioZOjRb8c/ALEmS1FgMzFXk4iWSJEmNx8BcRS5eIkmS1HgMzFVUWrxEkiRJjcPAXEWTJ8OLL2YLmEiSJKkxGJiryKnlJEmSGo+BuYpc7U+SJKnxGJiryNX+JEmSGo+BuYpKPcxPP11sHZIkSaoeA3MVjRwJra3wxz8WXYkkSZKqxcBcZVOmwFNPFV2FJEmSqsXAXGVTp9rDLEmS1EgMzFVW6mFOqehKJEmSVA0G5iqbOhVefRVeeKHoSiRJklQNBuYqmzIl2zuOWZIkqTEYmKts6tRs7zhmSZKkxmBgrjJ7mCVJkhqLgbnKxo+HESPsYZYkSWoUBuYqi8h6mQ3MkiRJjcHA3A+mTnVIhiRJUqMwMPcDe5glSZIah4G5H0yZAsuXw5o1RVciSZKkvjIw94PS1HJPP11sHZIkSeo7A3M/cGo5SZKkxmFg7gcuXiJJktQ4uhWYI2JuRCyPiEVlbVtHxA0R8Wi+H5u3R0ScHxFLImJhROxZ9ppT8/MfjYhTq/9xasOkSdn0cvYwS5Ik1b/u9jD/ADhqo7YzgBtTSjOAG/PnAEcDM/LtNOBCyAI28CVgX2Af4EulkN1ohg6F7bazh1mSJKkRdCswp5R+C7ywUfOxwMX544uB48raL0mZ24ExETEROBK4IaX0QkrpReAGNg3hDcOp5SRJkhpDX8YwT0gpLQPI99vk7ZOA8vkh2vK2rtob0tSpBmZJkqRG0B9f+otO2lKF9k0vEHFaRMyPiPkrVqyoanEDZYcdsjHMGzYUXYkkSZL6oi+B+bl8qAX5fnne3gZsX3beZGBphfZNpJQuSinNTinNbm1t7UOJxZk+HdrbnYtZkiSp3vUlMF8NlGa6OBX4eVn7KflsGfsBL+dDNq4HjoiIsfmX/Y7I2xrSDjtk+8cfL7YOSZIk9c3g7pwUEfOAg4HxEdFGNtvFecDlEfFR4Cngffnp1wLHAEuA1cCHAVJKL0TEl4G78vPOTilt/EXChlEKzE88UWwdkiRJ6ptuBeaU0oldHDq0k3MTcHoX15kLzO12dXVs8mRoabGHWZIkqd650l8/GTw4mynDHmZJkqT6ZmDuRzvsYA+zJElSvTMw96Pp0w3MkiRJ9c7A3I922AGefx5WrSq6EkmSJPWWgbkfOVOGJElS/TMw96Pp07O9wzIkSZLql4G5H9nDLEmSVP8MzP1o661h9Gh7mCVJkuqZgbkfRTi1nCRJUr0zMPezHXZwSIYkSVI9MzD3s+nTs8CcUtGVSJIkqTcMzP1shx1g7Vp49tmiK5EkSVJvGJj7WWmmjMceK7YOSZIk9Y6BuZ/tuGO2NzBLkiTVJwNzP5s+HVpa4NFHi65EkiRJvWFg7mdDhsC0aQZmSZKkemVgHgAzZsAjjxRdhSRJknrDwDwAZszIepidWk6SJKn+GJgHwIwZ8OqrTi0nSZJUjwzMA2DGjGzvOGZJkqT6Y2AeAAZmSZKk+mVgHgBTp2azZRiYJUmS6o+BeQAMHpyt+GdgliRJqj8G5gFSmilDkiRJ9cXAPEBmzIAlS6Cjo+hKJEmS1BMG5gEyYwasWQNLlxZdiSRJknrCwDxAnClDkiSpPhmYB4iBWZIkqT4ZmAfI9tvDsGHwyCNFVyJJkqSeMDAPkEGDYMcd7WGWJEmqNwbmAfS2t8FDDxVdhSRJknrCwDyAZs6Exx6D9euLrkSSJEndZWAeQDNnQnu7wzIkSZLqiYF5AL3tbdl+8eJi65AkSVL3GZgHUCkwO45ZkiSpfhiYB9CoUTBlij3MkiRJ9cTAPMBmzjQwS5Ik1RMD8wCbOTMbktHRUXQlkiRJ6g4D8wCbORPWrIGnniq6EkmSJHWHgXmAzZyZ7R2WIUmSVB8MzAPMwCxJklRfeh2YI+KtEbGgbHslIj4TEWdGxDNl7ceUveYLEbEkIh6OiCOr8xHqy/jx2WZgliRJqg+De/vClNLDwCyAiGgBngGuAj4MfDOl9LXy8yNiJ+AEYGdgO+DXEfGWlFJ7b2uoV297m4FZkiSpXlRrSMahwGMppT9WOOdY4LKU0rqU0hPAEmCfKr1/XSnNlCFJkqTaV63AfAIwr+z5JyNiYUTMjYixedsk4Omyc9rytk1ExGkRMT8i5q9YsaJKJdaOmTNh5UpowI8mSZLUcPocmCNiKPAe4Cd504XAjmTDNZYBXy+d2snLU2fXTCldlFKanVKa3dra2tcSa87OO2f7RYuKrUOSJEmbV40e5qOBe1JKzwGklJ5LKbWnlDqAObwx7KIN2L7sdZOBpVV4/7qz667Z/v77i61DkiRJm1eNwHwiZcMxImJi2bHjgVI/6tXACRExLCKmAzOAO6vw/nVn221h3DgDsyRJUj3o9SwZABExEjgc+Nuy5n+PiFlkwy2eLB1LKT0QEZcDDwIbgNObcYYMgIisl9nALEmSVPv6FJhTSquBcRu1nVzh/HOAc/ryno1i111h7lzo6IBBLh8jSZJUs4xqBdl1V3j1VXjyyaIrkSRJUiUG5oLstlu2d1iGJElSbTMwF6Q0tZyBWZIkqbYZmAuyxRawww4GZkmSpFpnYC7QrrvCwoVFVyFJkqRKDMwF2nVXePRRWLu26EokSZLUFQNzgXbdFdrbYfHioiuRJElSVwzMBXKJbEmSpCVRD9MAABj0SURBVNpnYC7QjBkwbJiBWZIkqZYZmAs0eDDssgssWFB0JZIkSeqKgblge+4J99wDKRVdiSRJkjpjYC7YnnvCCy/AU08VXYkkSZI6Y2Au2B57ZPt77y22DkmSJHXOwFyw3XaDlpZsWIYkSZJqj4G5YCNGwMyZBmZJkqRaZWCuAXvs4ZAMSZKkWmVgrgF77glLl8KzzxZdiSRJkjZmYK4Be+6Z7e1lliRJqj0G5howa1a2dxyzJElS7TEw14Att4Q/+zN7mCVJkmqRgblGlFb8kyRJUm0xMNeIPfeEJ57IVv2TJElS7TAw14h99sn2d95ZbB2SJEl6MwNzjdhrL4iAO+4ouhJJkiSVMzDXiC23hJ12MjBLkiTVGgNzDdl332xIRkpFVyJJkqQSA3MN2XdfWLkSHn+86EokSZJUYmCuIaUv/jksQ5IkqXYYmGvILrvAyJEGZkmSpFpiYK4hgwdns2UYmCVJkmqHgbnG7LtvtkT2+vVFVyJJkiQwMNecffbJwvJ99xVdiSRJksDAXHP23Tfb3357sXVIkiQpY2CuMdtvD5Mmwe9/X3QlkiRJAgNzzYmAAw6AW291ARNJkqRaYGCuQQceCM88A3/8Y9GVSJIkycBcgw44INvfdluxdUiSJMnAXJN22QW22iobliFJkqRiGZhrUEsL7L+/PcySJEm1wMBcow48EB58EFauLLoSSZKk5mZgrlGlccy/+12xdUiSJDW7PgfmiHgyIu6PiAURMT9v2zoiboiIR/P92Lw9IuL8iFgSEQsjYs++vn+j2ntvGDrUYRmSJElFq1YP8ztTSrNSSrPz52cAN6aUZgA35s8BjgZm5NtpwIVVev+GM3x4FpoNzJIkScXqryEZxwIX548vBo4ra78kZW4HxkTExH6qoe4ddBDcdRf86U9FVyJJktS8qhGYE/CriLg7Ik7L2yaklJYB5Ptt8vZJwNNlr23L294kIk6LiPkRMX/FihVVKLE+HXIIbNjg9HKSJElFqkZgfntKaU+y4RanR8RBFc6NTto2WQA6pXRRSml2Sml2a2trFUqsT/vvn41j/s1viq5EkiSpefU5MKeUlub75cBVwD7Ac6WhFvl+eX56G7B92csnA0v7WkOjGjkyC8033lh0JZIkSc2rT4E5IkZFxOjSY+AIYBFwNXBqftqpwM/zx1cDp+SzZewHvFwauqHOHXIILFjgfMySJElF6WsP8wTgtoi4D7gTuCal9EvgPODwiHgUODx/DnAt8DiwBJgD/F0f37/hHXoopAQ331x0JZIkSc1pcF9enFJ6HNi9k/aVwKGdtCfg9L68Z7PZe2/YYotsWMZf/mXR1UiSJDUfV/qrcUOGZNPLOY5ZkiSpGAbmOnDoofDII9DWVnQlkiRJzcfAXAcOOSTb//rXxdYhSZLUjAzMdWC33WDbbeG664quRJIkqfkYmOvAoEFw1FHwq19lK/9JkiRp4BiY68Qxx8BLL8EddxRdiSRJUnMxMNeJww+Hlha49tqiK5EkSWouBuY6MWZMtky245glSZIGloG5jhx9NNx7LyxzMXFJkqQBY2CuI0cfne1/+cti65AkSWomBuY6svvuMHGi45glSZIGkoG5jkTAX/wFXH89rFtXdDWSJEnNwcBcZ44/HlatghtvLLoSSZKk5mBgrjOHHgqjR8NVVxVdiSRJUnMwMNeZYcOyRUx+/nNoby+6GkmSpMZnYK5Dxx8PK1bA739fdCWSJEmNz8Bch44+GoYOdViGJEnSQDAw16Ett4TDDssCc0pFVyNJktTYDMx16r3vhSefhAULiq5EkiSpsRmY69Rxx8HgwXDZZUVXIkmS1NgMzHVq3Dg44ogsMHd0FF2NJElS4zIw17ETT4SnnoI//KHoSiRJkhqXgbmOHXssDB8OP/pR0ZVIkiQ1LgNzHRs9Gt79bvjJT2DDhqKrkSRJakwG5jr3wQ9mi5jceGPRlUiSJDUmA3OdO/po2GoruPTSoiuRJElqTAbmOjdsGLz//XDllfDKK0VXI0mS1HgMzA3gox+F1avhxz8uuhJJkqTGY2BuAPvsAzvtBHPnFl2JJElS4zEwN4CIrJf59tvhwQeLrkaSJKmxGJgbxEknZUtl28ssSZJUXQbmBrHNNtmczJdcAuvXF12NJElS4zAwN5CPfSybk/mqq4quRJIkqXEYmBvIkUfCjjvCf/1X0ZVIkiQ1DgNzAxk0CE4/HX73O7j33qKrkSRJagwG5gbz4Q/DyJFwwQVFVyJJktQYDMwNZswYOPlk+NGPYOXKoquRJEmqfwbmBnT66bB2LcyZU3QlkiRJ9c/A3IB23RUOOwz+8z+z4CxJkqTeMzA3qM9/Hp59Fv73f4uuRJIkqb71OjBHxPYRcVNELI6IByLi03n7mRHxTEQsyLdjyl7zhYhYEhEPR8SR1fgA6tyhh8Jee8F//Ae0txddjSRJUv3qSw/zBuBzKaWZwH7A6RGxU37smymlWfl2LUB+7ARgZ+Ao4H8ioqUP768KIuCMM+DRR13IRJIkqS96HZhTSstSSvfkj1cBi4FJFV5yLHBZSmldSukJYAmwT2/fX5t3/PEwYwacdx6kVHQ1kiRJ9akqY5gjYhqwB3BH3vTJiFgYEXMjYmzeNgl4uuxlbVQO2OqjlpZsLPPdd8M11xRdjSRJUn3qc2COiC2AK4HPpJReAS4EdgRmAcuAr5dO7eTlnfZ7RsRpETE/IuavWLGiryU2tVNOyZbL/td/hY6OoquRJEmqP30KzBExhCwsX5pS+ilASum5lFJ7SqkDmMMbwy7agO3LXj4ZWNrZdVNKF6WUZqeUZre2tvalxKY3ZAiceSYsWAA//WnR1UiSJNWfvsySEcD3gMUppW+UtU8sO+14YFH++GrghIgYFhHTgRnAnb19f3XfiSfCzJnw//6fM2ZIkiT1VF96mN8OnAwcstEUcv8eEfdHxELgncA/AKSUHgAuBx4EfgmcnlIyvg2AlhY4+2xYvBguvbToaiRJkupLpBqfPmH27Nlp/vz5RZdR9zo6YN99YdkyePhhGDWq6IokSZJqR0TcnVKa3dkxV/prEoMGwTe/Cc88A1/7WtHVSJIk1Q8DcxM54AB43/vg3/8d2tqKrkaSJKk+GJibzFe/Chs2wBe+UHQlkiRJ9cHA3GSmT4fPfQ5++EO4+eaiq5EkSap9BuYm9MUvZsH54x+HdeuKrkaSJKm2GZib0MiRcOGF2WwZ551XdDWSJEm1zcDcpI48MlvQ5Nxzs/mZJUmS1DkDcxP75jdh9Gg45RR47bWiq5EkSapNBuYmNmECfPvbMH9+1tMsSZKkTRmYm9xf/RWcdBJ8+ctw111FVyNJklR7DMziv/4LJk6ED34QXnml6GokSZJqi4FZjBkDP/oRPPEE/M3fQEpFVyRJklQ7DMwC4MADs3HMP/kJXHBB0dVIkiTVDgOzXveP/wjvfne2EuBttxVdjSRJUm0wMOt1gwbBxRdnqwAefzw8/njRFUmSJBXPwKw3GTsWfvELaG/PeptffrnoiiRJkoplYNYm3vIWuOIKeOSRbNq5deuKrkiSJKk4BmZ16pBD4LvfhV//Gk4+OetxliRJakaDiy5AtevUU2HlyuxLgGPGwHe+AxFFVyVJkjSwDMyq6LOfhRdegHPOgZYW+O//zr4cKEmS1CwMzNqsL385G5Jx3nnw2mtw0UWGZkmS1DwMzNqsiGxRkyFDsvD86qvwgx/AsGFFVyZJktT/DMzqlgg4+2wYNQrOOAOeew6uugq22qroyiRJkvqX/7CuHvn85+GSS+DWW+GAA+Cxx4quSJIkqX8ZmNVjJ58M110HzzwDs2fDtdcWXZEkSVL/MTCrVw47DO6+G6ZNg3e9C846Czo6iq5KkiSp+gzM6rXp0+F3v4OTToIzz4SjjoK2tqKrkiRJqi4Ds/pk5Ei4+OJsUZPf/Q522SUb45xS0ZVJkiRVh4FZfRYBp50GCxfCrrtmKwQef3w2xlmSJKneGZhVNTvuCDffDF/7Gvzyl/DWt2aLnaxbV3RlkiRJvWdgVlW1tMDnPgeLF8Phh8MXvgA77wxXX+0wDUmSVJ8MzOoX06dnC5tcf322QuCxx8J++2XPDc6SJKmeGJjVr444IhvbPGcOPPtsNpPGAQdk8zg7DZ0kSaoHBmb1uyFD4G/+Bh59FC68EJ56Co45Jhuq8e1vw6uvFl2hJElS1wzMGjBDh8LHP54tp/3DH8KoUfCJT8DkyfD3fw/33ONwDUmSVHsMzBpwQ4fChz4Ed90Ft92WDdOYMwf22gtmzYKvfx2efLLoKiVJkjIGZhUmAt7+dpg3D5Ytg//5Hxg2DP7xH7MvDe65J3zlK/Dgg/Y8S5Kk4kSq8SQye/bsNH/+/KLL0AB67LFsho2f/hT+8Iesbccd4dBDs+2QQ2D8+GJrlCRJjSUi7k4pze70mIFZtWzpUvjZz7KFUG6+GVatytpnzYKDDsqmqtt336xHOqLQUiVJUh0zMKshbNgA8+fDjTdm2x13wOrV2bHW1iw477EH7LJLtkT3jBkweHCxNUuSpPpgYFZD2rABFi3KgvPtt2f7hx9+Y37noUNh5swsQL/tbdmwjtK29db2SEuSpDfUVGCOiKOA/wRagO+mlM6rdH4hgfmee+DFF2H77eEtbxnY91afrF2bLcu9aBHcf/8b2zPPvPm8rbbKgvPUqTBpUrZtt92bH2+5ZTGfQZIkDbyaCcwR0QI8AhwOtAF3ASemlB7s6jWFBOZDD4Xf/AZaWuD88+E974GxY2HkSLsl69Tq1fD449n22GNvbE89lY2TfumlTV8zalT25cJx47rejxmTBevRo9/Yjx6dLdYiSZLqRy0F5j8HzkwpHZk//wJASunfunpNIYF54cIsQZ17Llx//RvtQ4Zkwbm0jRyZbSNGdL5159jgwVkw78k2yNkAq+3VV7PgvHRp1hv9zDPZVHcrV8Lzz79531m43tjw4W8O0SNHZm3lfwU2fl7eNnRo9tett1v5X5VBg978eNAgf++TJGljlQLzQH8lahLwdNnzNmDfAa5h83bbLdv/+Z/DddfBs89mQzTKt5deyrotX3oJ1qzJHq9Z88a2YUP/1lgpUEe8sZXSUXe27p7b3fM6U2vt+bFRwIx86/Q1o/JtKmxILbywYUueX78lL7eP4pUNo1i1YQSvtI9iVftIXtkwklXtI7L2V0fwysujWNMxlDXtw3ipY+jrj9d0DGVtx1DWtA9lfRradX39IOigJToYRAeDInX6uCWy5xs/HhQpv0ai9CcUkQje3B6dnUfapL2755W/z2bPozodAaVr9/k61aqnKldp4M9VpXokFeuUD6zjg//99qLLeJOBDsyd/Vzc5CdcRJwGnAYwZcqU/q6pa0OGZMMxemPDhs6D9MZtGzZAe3t1t5TevHV0bNrW2dbd87pzbmeKbO/sWKV/XalwrcHANqxmm8HPZv8FDet7re1p0OvheU3HMF5LgzeztfBaR9fH29MgstgbtKcWOlLQTrbvYNAbx8va2xlER96eHQ860qCy9uxapWhciqcpvRFVS+0plZ5veqz8NZWOddpe6dib2vsuVSnG5b8W9P06qZr1VOM61VG1eqr05yOpeGtXrym6hE0MdGBuA7Yvez4ZWLrxSSmli4CLIBuSMTClVdngwW8MaJU2o4U3OrElSVJtGejBsHcBMyJiekQMBU4Arh7gGiRJkqRuG9Ae5pTShoj4JHA9Wafa3JTSAwNZgyRJktQTA74OWkrpWuDagX5fSZIkqTecn0ySJEmqwMAsSZIkVWBgliRJkiowMEuSJEkVGJglSZKkCgzMkiRJUgUGZkmSJKkCA7MkSZJUgYFZkiRJqsDALEmSJFVgYJYkSZIqMDBLkiRJFRiYJUmSpAoMzJIkSVIFBmZJkiSpgkgpFV1DRRGxAvhjAW89Hni+gPfVwPI+Nwfvc3PwPjcH73NzKOI+T00ptXZ2oOYDc1EiYn5KaXbRdah/eZ+bg/e5OXifm4P3uTnU2n12SIYkSZJUgYFZkiRJqsDA3LWLii5AA8L73By8z83B+9wcvM/Noabus2OYJUmSpArsYZYkSZIqMDB3IiKOioiHI2JJRJxRdD3qvYiYGxHLI2JRWdvWEXFDRDya78fm7RER5+f3fWFE7Flc5equiNg+Im6KiMUR8UBEfDpv9z43kIgYHhF3RsR9+X0+K2+fHhF35Pf5xxExNG8flj9fkh+fVmT96pmIaImIeyPi//Ln3ucGExFPRsT9EbEgIubnbTX7c9vAvJGIaAH+Gzga2Ak4MSJ2KrYq9cEPgKM2ajsDuDGlNAO4MX8O2T2fkW+nARcOUI3qmw3A51JKM4H9gNPz/2a9z41lHXBISml3YBZwVETsB3wV+GZ+n18EPpqf/1HgxZTSnwHfzM9T/fg0sLjsufe5Mb0zpTSrbPq4mv25bWDe1D7AkpTS4yml9cBlwLEF16ReSin9Fnhho+ZjgYvzxxcDx5W1X5IytwNjImLiwFSq3kopLUsp3ZM/XkX2P9lJeJ8bSn6//pQ/HZJvCTgEuCJv3/g+l+7/FcChEREDVK76ICImA38BfDd/Hnifm0XN/tw2MG9qEvB02fO2vE2NY0JKaRlkYQvYJm/33te5/J9j9wDuwPvccPJ/pl8ALAduAB4DXkopbchPKb+Xr9/n/PjLwLiBrVi99C3gn4CO/Pk4vM+NKAG/ioi7I+K0vK1mf24PHsg3qxOd/WbqVCLNwXtfxyJiC+BK4DMppVcqdDJ5n+tUSqkdmBURY4CrgJmdnZbvvc91KCLeBSxPKd0dEQeXmjs51ftc/96eUloaEdsAN0TEQxXOLfw+28O8qTZg+7Lnk4GlBdWi/vFc6Z9y8v3yvN17X6ciYghZWL40pfTTvNn73KBSSi8BN5ONWR8TEaXOn/J7+fp9zo9vxabDs1R73g68JyKeJBsSeQhZj7P3ucGklJbm++VkvwDvQw3/3DYwb+ouYEb+jdyhwAnA1QXXpOq6Gjg1f3wq8POy9lPyb+PuB7xc+qch1a58vOL3gMUppW+UHfI+N5CIaM17lomIEcBhZOPVbwL+Kj9t4/tcuv9/BfwmufBAzUspfSGlNDmlNI3s/7+/SSl9CO9zQ4mIURExuvQYOAJYRA3/3Hbhkk5ExDFkv9G2AHNTSucUXJJ6KSLmAQcD44HngC8BPwMuB6YATwHvSym9kAevC8hm1VgNfDilNL+IutV9EXEAcCtwP2+MefxnsnHM3ucGERG7kX0JqIWss+fylNLZEbEDWU/k1sC9wEkppXURMRz4X7Ix7S8AJ6SUHi+mevVGPiTjH1NK7/I+N5b8fl6VPx0M/CildE5EjKNGf24bmCVJkqQKHJIhSZIkVWBgliRJkiowMEuSJEkVGJglSZKkCgzMkiRJUgUGZkmSJKkCA7MkVVlETIuIRd04b2JE/F/+eHZEnJ8/Pjgi9q9yPR8se/76e1XxPS6LiBnVvKYk1QoDsyQV57PAHICU0vyU0qfy9oOBHgXmsmWDOzMNeD0wb/Re1XIh8E9VvqYk1QQDsyT1o4jYISLujYi9Ozn8l8Av8/MOjoj/i4hpwMeBf4iIBRFxYL4s9JURcVe+vT1/zZkRcVFE/Aq4JO9JvjUi7sm3Uug+Dzgwv94/lN4rv8bWEfGziFgYEbfnK+qVrj03Im6OiMcj4lN5+6iIuCYi7ouIRRHxgfw9bgUO20xwl6S65A82SeonEfFWsuV8P5xSWrDRsenAiymldeXtKaUnI+LbwJ9SSl/Lz/0R8M2U0m0RMQW4HpiZv2Qv4ICU0pqIGAkcnlJamw+PmAfMBs4gX2I4v97BZW95FnBvSum4iDgEuASYlR97G/BOYDTwcERcSLY07dKU0l/k19oqr7sjIpYAuwN39+GPTZJqjoFZkvpHK/Bz4C9TSg90cnwisKKb1zoM2CkiSs+3jIjR+eOrU0pr8sdDgAsiYhbQDrylG9c+gKynm5TSbyJiXCkEA9fkgX5dRCwHJgD3A1+LiK8C/5dSurXsWsuB7TAwS2owBmZJ6h8vA08Dbwc6C8xrgOHdvNYg4M/LgjEAeYB+tazpH4DnyHp5BwFru3Ht6KQt5fvy3u92YHBK6ZGI2As4Bvi3iPhVSuns/JzhZJ9LkhqKY5glqX+sB44DTimfoaLMI2RfxuvMKrJhECW/Aj5ZepL3IHdmK2BZSqkDOBlo6eJ65X4LfCi/7sHA8ymlV7o4l4jYDlidUvoh8DVgz7LDb6HzXw4kqa4ZmCWpn6SUXgXeRfYFvmM7OfZYRPxZJy/9BXB86Ut/wKeA2fkX8x4k+1JgZ/4HODUibicLr6Xe54XAhvyLev+w0WvOLF2b7MuBp27mY+0K3BkRC4B/Ab4CEBETgDUppWWbeb0k1Z1IKW3+LElS1UXE8cBeKaUvFl1LX+VB/JWU0veKrkWSqs0xzJJUkJTSVRExrug6quQl4H+LLkKS+oM9zJIkSVIFjmGWJEmSKjAwS5IkSRUYmCVJkqQKDMySJElSBQZmSZIkqYL/H38W9cQjA/wMAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VAUI4oCiFGnP",
        "colab_type": "text"
      },
      "source": [
        "As the plot suggests, the inequality is quite loose when $k$ is small."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-kTptS1YjCV0",
        "colab_type": "text"
      },
      "source": [
        "## Lemma 4\n",
        "\n",
        "$$\n",
        "g(X^*) + (2 \\tau + \\eta) x^* = \\tau (\\alpha + \\beta) \\\\\n",
        "f(\\hat{X}) + 2 \\tau \\hat{x} = \\tau (\\alpha + \\beta)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5rozUwvpjFup",
        "colab_type": "code",
        "outputId": "670b3f8f-2f59-4e41-95ee-0b52fdac024f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "g_X_star = compute_g_primal(C=C, u=u_optimal, v=v_optimal, a=a, b=b, eta=eta, tau1=tau, tau2=tau)\n",
        "X_star = compute_B(C=C, u=u_optimal, v=v_optimal, eta=eta)\n",
        "x_star = np.sum(X_star)\n",
        "\n",
        "print(\"LHS 1: \", g_X_star + (2 * tau + eta) * x_star)\n",
        "print(\"RHS 1: \", tau * (alpha + beta))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LHS 1:  980.774417631171918\n",
            "RHS 1:  980.7746274968506354\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7yagi6GJlkgr",
        "colab_type": "code",
        "outputId": "57685dd9-b3f0-4520-ff82-91617be76a67",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "f_X_hat = output[\"f_optimal\"]\n",
        "X_hat = output[\"X_optimal\"]\n",
        "x_hat = np.sum(X_hat)\n",
        "\n",
        "print(\"LHS 2: \", f_X_hat + 2 * tau * x_hat)\n",
        "print(\"RHS 2: \", tau * (alpha + beta))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LHS 2:  980.7746277081164\n",
            "RHS 2:  980.7746274968506354\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fLuMpMaEDZZj",
        "colab_type": "text"
      },
      "source": [
        "# Experiment (Synthetic data)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fSkBNl70CHoH",
        "colab_type": "text"
      },
      "source": [
        "## Varyinng $\\varepsilon$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZttWIVHtID9b",
        "colab_type": "text"
      },
      "source": [
        "### Computation of quantities\n",
        "\n",
        "$\\newcommand{\\mnorm}[1]{\\|{#1}\\|_{\\scriptscriptstyle \\infty}}$\n",
        "\n",
        "$$\n",
        "\\begin{align}\n",
        "R &= \\max \\left\\{ \\mnorm{\\log(a)}, \\mnorm{\\log(a)} \\right\\} + \\max \\left\\{ \\log(n), \\frac{1}{\\eta} \\mnorm{\\log(C)} - \\log(n) \\right\\} \\\\\n",
        "S &=  \\frac{1}{2} (\\alpha + \\beta) + \\frac{1}{2} + \\frac{1}{4 \\log(n)} \\\\\n",
        "T &= \\frac{1}{2} (\\alpha + \\beta) \\left[ \\log\\left( \\frac{\\alpha + \\beta}{2} \\right) + 2 \\log(n) - 1 \\right] + \\log(n) + \\frac{5}{2} \\\\\n",
        "U &= \\max \\left\\{ S + T, 2 \\varepsilon, \\frac{4 \\varepsilon \\log(n)}{\\tau}, \\frac{4 \\varepsilon (\\alpha + \\beta) \\log(n)}{\\tau} \\right\\}\n",
        "\\end{align}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xXjcmNpJEtiV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Hyperparameters\n",
        "dim_a = 10\n",
        "dim_b = 10\n",
        "tau = 5\n",
        "\n",
        "n = dim_a\n",
        "\n",
        "alpha = 2\n",
        "beta = 4\n",
        "\n",
        "# Initialize UOT parameters\n",
        "C = np.random.uniform(low=1, high=50, size=(dim_a, dim_b)).astype(\"float128\")\n",
        "C = (C + C.T) / 2\n",
        "a = np.random.uniform(low=0.1, high=1, size=(dim_a, 1)).astype(\"float128\")\n",
        "b = np.random.uniform(low=0.1, high=1, size=(dim_b, 1)).astype(\"float128\")\n",
        "\n",
        "# Rescaling\n",
        "a = a / a.sum() * alpha\n",
        "b = b / b.sum() * beta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mEW8z3yEOviM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "num_eps = 20\n",
        "\n",
        "# Set epsilon\n",
        "epsilon_list = np.linspace(start=1, stop=0.05, num=num_eps).astype(\"float128\")\n",
        "epsilons = np.array(epsilon_list)\n",
        "\n",
        "# Calculate quantities\n",
        "S = 1 / 2 * (alpha + beta) + 1 / 2 + 1 / (4 * np.log(n))\n",
        "T = 1 / 2 * (alpha + beta) * (np.log((alpha + beta) / 2) + 2 * np.log(n) - 1) + np.log(n) + 5 / 2\n",
        "U_list = [max(S + T, epsilon, 4 * epsilon * np.log(n) / tau, 4 * epsilon * (alpha + beta) * np.log(n) / tau) for epsilon in epsilon_list]\n",
        "\n",
        "# Calculate eta from the formula\n",
        "eta_list = [epsilon_list[i] / U_list[i] for i in range(num_eps)]\n",
        "\n",
        "R_list = [max(max_norm(np.log(a)), max_norm(np.log(b))) + max(np.log(n), 1 / eta_list[i] * max_norm(C) - np.log(n)) for i in range(num_eps)]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LmMKE8aYEm98",
        "colab_type": "code",
        "outputId": "0e5797cc-153f-46f1-f923-c665c6cb1ac8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 114,
          "referenced_widgets": [
            "174d6adc54134f0a893402aad033df42",
            "e151df18f0da4f43a753c4818bfcfb5c",
            "00df3a85032d44e18f2407939568ffb8",
            "7e9e4d4d14cd4e459a62a2f220d15a6e",
            "20ea07af01c345708a6a9fd753634a13",
            "2847bfe466b24daca0cb2c60dfea9066",
            "4eb176e5889b4b929c8a7f1cbfaf9b3e",
            "6a35ff4abd4240a0a8ab530d8b9cad43",
            "491eb84c3cee4c51aa0069af2f0d3da0",
            "9326145c83dc408f9f2fac5b2e4d1d6f",
            "1b1b5d4bbed5430bafe94ab3f8d84128",
            "e7f0dac066584575b5dac513450ba5df",
            "7f18e00d20984b96b5e48d709402cfd8",
            "d1963c600d9d446b8fd8ad459c749853",
            "c90bbab6269741ed9ee0d9c65144e528",
            "46f489d3afcc4ad4a567edfd2c37a698"
          ]
        }
      },
      "source": [
        "# Solve UOT problem exactly\n",
        "f_optimal, _ = solve_f_cp(C, a, b, tau1=tau, tau2=tau)\n",
        "\n",
        "k_list_empirical_true = list()\n",
        "for i in tqdm(range(num_eps)):\n",
        "    k_list_empirical_true.append(find_k_sinkhorn(C=C, a=a, b=b, epsilon=epsilon_list[i], f_optimal=f_optimal, eta=eta_list[i], tau1=tau, tau2=tau, momentum=1000))\n",
        "\n",
        "k_list_empirical_first = list()\n",
        "for i in tqdm(range(num_eps)):\n",
        "    k_list_empirical_first.append(find_k_sinkhorn(C=C, a=a, b=b, epsilon=epsilon_list[i], f_optimal=f_optimal, eta=eta_list[i], tau1=tau, tau2=tau, momentum=0))\n",
        "\n",
        "k_list_formula = [(tau * U_list[i] / epsilon_list[i] + 1) * (np.log(8 * eta_list[i] * R_list[i]) + np.log(tau * (tau + 1)) + 3 * np.log(U_list[i] / epsilon_list[i])) for i in range(num_eps)]"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=20.0), HTML(value='')))"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "174d6adc54134f0a893402aad033df42"
            }
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=20.0), HTML(value='')))"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "491eb84c3cee4c51aa0069af2f0d3da0"
            }
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iaXP0LNE6wmC",
        "colab_type": "code",
        "outputId": "92340b56-1f95-46df-cc6a-e62e1a73238e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        }
      },
      "source": [
        "print(\"alpha: \", alpha)\n",
        "print(\"beta: \", beta)\n",
        "print(\"S: \", S)\n",
        "print(\"T: \", T)\n",
        "print(\"U: \", U_list)\n",
        "print(\"R: \", R_list)\n",
        "print(\"epsilon: \", epsilon_list)\n",
        "print(\"eta: \", eta_list)\n",
        "print(\"f_optimal: \", f_optimal)\n",
        "print(\"K empirical true: \", k_list_empirical_true)\n",
        "print(\"K empirical first: \", k_list_empirical_first)\n",
        "print(\"K formula: \", k_list_formula)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "alpha:  2\n",
            "beta:  4\n",
            "S:  3.6085736204758128\n",
            "T:  18.913932516962653\n",
            "U:  [22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466, 22.522506137438466]\n",
            "R:  [1113.154549287106107, 1171.7024804123989561, 1236.7557372182797534, 1309.462318354264334, 1391.2572221322468029, 1483.9581130806271377, 1589.9019884502046759, 1712.1449215689477136, 1854.7616768741478941, 2023.3087513257484739, 2225.5652406676691992, 2472.7676165300161872, 2781.770586357950591, 3179.0601189938653288, 3708.7794958417527733, 4450.3866234287934076, 5562.7973148093566236, 7416.815133776962532, 11124.850771712164057, 22248.957685517803625]\n",
            "epsilon:  [1.   0.95 0.9  0.85 0.8  0.75 0.7  0.65 0.6  0.55 0.5  0.45 0.4  0.35\n",
            " 0.3  0.25 0.2  0.15 0.1  0.05]\n",
            "eta:  [0.044400032300922804798, 0.042180030685876662586, 0.039960029070830525305, 0.03774002745578438309, 0.03552002584073824581, 0.033300024225692103598, 0.031080022610645961387, 0.028860020995599824104, 0.026640019380553686823, 0.02442001776550754461, 0.022200016150461402399, 0.019980014535415265116, 0.017760012920369122905, 0.0155400113053229856224, 0.013320009690276843411, 0.011100008075230706129, 0.008880006460184563917, 0.0066600048451384217057, 0.0044400032300922844235, 0.002220001615046140363]\n",
            "f_optimal:  22.66687847952826\n",
            "K empirical true:  [125, 133, 143, 155, 169, 183, 201, 223, 247, 277, 315, 361, 419, 499, 607, 765, 1013, 1451, 2363, 5461]\n",
            "K empirical first:  [65, 73, 81, 91, 103, 117, 131, 151, 173, 199, 233, 275, 329, 401, 503, 651, 887, 1305, 2211, 5213]\n",
            "K formula:  [2127.3517242297760255, 2256.7228290911949107, 2401.500991834351947, 2564.5306874222435487, 2749.3918323913852044, 2960.6516425886391253, 3204.2269153723617419, 3487.9173887268170913, 3822.2119911492167588, 4221.5451888654100374, 4706.325017258539779, 5306.3456061381200635, 6066.821583060301494, 7059.7238136101112866, 8406.741692662337966, 10330.534992979760535, 13285.029964847480383, 18354.292525042863423, 28890.223352012634251, 62440.24252556354704]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UJ1iGaw_goW8",
        "colab_type": "code",
        "outputId": "0e9956e4-f16d-4054-9e0e-b7e8eee5885f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 654
        }
      },
      "source": [
        "fig, axs = plt.subplots(1, 2, figsize=(16, 8), sharex=True)\n",
        "\n",
        "plt.rcParams.update({'font.size': 22})\n",
        "\n",
        "axs[0].plot(epsilon_list, [np.log(tmp) for tmp in k_list_formula], color=\"#990000\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\log$ $\\mathrm{k}_\\mathrm{f}$\")\n",
        "axs[0].plot(epsilon_list, [np.log(tmp) for tmp in k_list_empirical_true], color=\"#2F6276\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\log$ $\\mathrm{k}_\\mathrm{c}$\")\n",
        "axs[0].set_xlim(1.05, 0)\n",
        "axs[0].yaxis.set_label_coords(-0.1, 0.5)\n",
        "axs[0].set_ylabel(r\"log iteration\")\n",
        "axs[0].legend(prop={'size': 30})\n",
        "\n",
        "# ratio_k_first_true = [k_list_empirical_first[i] / k_list_empirical_true[i] for i in range(num_eps)]\n",
        "ratio_k_true_formula = [k_list_formula[i] / k_list_empirical_true[i] for i in range(num_eps)]\n",
        "\n",
        "\n",
        "axs[1].plot(epsilon_list, ratio_k_true_formula, color=\"#66892B\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\mathrm{k}_\\mathrm{f}$ / $\\mathrm{k}_\\mathrm{c}$\")\n",
        "axs[1].set_xlim(1.05, 0)\n",
        "axs[1].yaxis.tick_right()\n",
        "axs[1].yaxis.set_label_position(\"right\")\n",
        "axs[1].yaxis.set_label_coords(1.17, 0.5)\n",
        "axs[1].set_ylabel(\"ratio\", rotation=\"-90\")\n",
        "axs[1].legend(prop={'size': 30})\n",
        "\n",
        "fig.text(0.5, 0.04, 'epsilon', ha='center')\n",
        "\n",
        "plt.savefig('k_comparison.eps', bbox_inches='tight')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x576 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PoWhjNYfOGZj",
        "colab_type": "text"
      },
      "source": [
        "## $\\Delta_k / \\Delta_{k + 1}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qyjoRz9zOBSd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(999)\n",
        "\n",
        "# Hyperparameters\n",
        "dim_a = 10\n",
        "dim_b = 10\n",
        "tau = 5\n",
        "eta = 0.5\n",
        "k = 200\n",
        "\n",
        "n = dim_a\n",
        "\n",
        "alpha = 2\n",
        "beta = 4\n",
        "\n",
        "# Initialize UOT parameters\n",
        "C = np.random.uniform(low=1, high=50, size=(dim_a, dim_b)).astype(float_type)\n",
        "C = (C + C.T) / 2\n",
        "a = np.random.uniform(low=0.1, high=1, size=(dim_a, 1)).astype(float_type)\n",
        "b = np.random.uniform(low=0.1, high=1, size=(dim_b, 1)).astype(float_type)\n",
        "\n",
        "# Rescaling\n",
        "a = a / a.sum() * alpha\n",
        "b = b / b.sum() * beta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A0NuttZrONB8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "g_dual_optimal, u_optimal, v_optimal = solve_g_dual_cp(C=C, a=a, b=b, eta=eta, tau=tau)\n",
        "output = sinkhorn_uot(C=C, a=a, b=b, eta=eta, tau1=tau, tau2=tau, k=k)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ORVnFyV1PcIe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "k_fixed = k + 1\n",
        "\n",
        "delta_u = [max_norm(u - u_optimal) for u in output[\"u\"]]\n",
        "delta_v = [max_norm(v - v_optimal) for v in output[\"v\"]]\n",
        "\n",
        "odd_ids = [i for i in range(k_fixed) if i % 2 == 1]\n",
        "even_ids = [i for i in range(k_fixed) if i % 2 == 0]\n",
        "\n",
        "even_ids_1 = [i for i in even_ids if i < k_fixed - 1]\n",
        "ratio_k_even_uv_list = [delta_v[i] / delta_u[i + 1] for i in even_ids_1]\n",
        "\n",
        "even_ids_2 = [i for i in even_ids if i > 0]\n",
        "ratio_k_even_vu_list = [delta_u[i - 1] / delta_v[i]  for i in even_ids_2]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UDcOPg-1ExBY",
        "colab_type": "code",
        "outputId": "5dd20e10-8811-482a-b052-fd46d3cceead",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        }
      },
      "source": [
        "plt.figure(figsize=(16, 6))\n",
        "plt.rcParams.update({'font.size': 22})\n",
        "\n",
        "plt.plot(even_ids_1[:50], ratio_k_even_uv_list[:50], color=\"#2F6276\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\frac{|| v^{k} - v^* ||_\\infty}{|| u^{k + 1} - u^* ||_\\infty}$\")\n",
        "plt.plot(even_ids_2[:50], ratio_k_even_vu_list[:50], color=\"#66892B\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\frac{|| u^{k - 1} - u^* ||_\\infty}{|| v^{k} - v^* ||_\\infty}$\")\n",
        "plt.plot([0, 100], [((tau + eta) / tau), ((tau + eta) / tau)], \"#990000\", linewidth=4, label=r\"$\\frac{\\tau + \\eta}{\\tau}$\")\n",
        "# plt.ylim(bottom=1.0)\n",
        "plt.xlabel(r\"k (iterations)\")\n",
        "plt.ylabel(r\"ratio\")\n",
        "plt.yticks(np.arange(1.0, 2.0, 0.1), [\"1.0\", \"1.1\", \"1.2\", \"1.3\", \"1.4\", \"1.5\", \"1.6\", \"1.7\", \"1.8\", \"1.9\", \"2.0\"])\n",
        "plt.tick_params(axis=\"y\", labelsize=16)\n",
        "plt.legend(prop={'size': 30})\n",
        "\n",
        "fig.text(0.5, 0.04, 'epsilon', ha='center')\n",
        "\n",
        "plt.savefig('uv_ratio.eps', bbox_inches='tight')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AxTQyrEZuxdR",
        "colab_type": "text"
      },
      "source": [
        "# Experiment (MNIST)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OhzKWWeNQEX1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt \n",
        "from copy import copy\n",
        "import random\n",
        "import pdb\n",
        "import os \n",
        "import gzip\n",
        "import pickle as pkl\n",
        "from urllib import request\n",
        "import torch\n",
        "from time import time\n",
        "import cvxpy as cp\n",
        "\n",
        "os.environ[\"CUDA_VISIBLE_DEVICES\"] = \"0\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aeZjv9Bzu0VU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def _download_mnist(root_dir):\n",
        "    data_loc = os.path.join(root_dir, 'mnist.pkl.gz')\n",
        "    if not os.path.exists(data_loc):\n",
        "        url = 'http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz'\n",
        "        print(\"Downloading data from:\", url)\n",
        "        data_loc = os.path.join(root_dir, 'mnist.pkl.gz')\n",
        "        data_loc, _ = request.urlretrieve(url, data_loc)\n",
        "    else: print('WARNING: data might already exist')\n",
        "    return data_loc\n",
        "\n",
        "def _load_mnist(root_dir,  split_type, download):\n",
        "    if download:\n",
        "        data_loc = _download_mnist(root_dir)\n",
        "    else:\n",
        "        data_loc = os.path.join(root_dir, 'mnist.pkl.gz')\n",
        "    f = gzip.open(data_loc, 'rb')\n",
        "\n",
        "    train, valid, test = pkl.load(f, encoding='bytes')\n",
        "    f.close()\n",
        "    if split_type == 'train':\n",
        "        x, y = train[0], train[1]\n",
        "    if split_type == 'valid':\n",
        "        x, y = valid[0], valid[1]\n",
        "    if split_type == 'test':\n",
        "        x, y = test[0], test[1]\n",
        "    return x, y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fYiYmMl5PGWn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def get_entropy(P):\n",
        "    logP = torch.log(P + 1e-20)\n",
        "    return -1 * torch.sum(logP * P - P)\n",
        "\n",
        "def get_KL(P, Q):\n",
        "    log_ratio = torch.log(P + 1e-20) - torch.log(Q + 1e-20)\n",
        "    return torch.sum(P * log_ratio - P + Q)\n",
        "\n",
        "def dotp(x, y):\n",
        "    return torch.sum(x * y)\n",
        "\n",
        "def norm1(X):\n",
        "    return torch.sum(torch.abs(X))\n",
        "\n",
        "def supnorm(X):\n",
        "    return torch.max(torch.abs(X))\n",
        "\n",
        "\n",
        "# main funcs\n",
        "def get_B(C, u, v, eta):\n",
        "    n, m = C.shape\n",
        "    K = - C + u + v.T\n",
        "    return torch.exp(K / eta)\n",
        "\n",
        "\n",
        "def f_dual(B, u, v, r, c, eta, t1, t2):\n",
        "    \"\"\"\n",
        "    the dual of the entropic-regularized unbalanced OT\n",
        "    \"\"\"\n",
        "    f = eta * torch.sum(B) + t1 * dotp(torch.exp(- u / t1), r) + t2 * dotp(torch.exp(- v / t2), c)\n",
        "\n",
        "    return f\n",
        "\n",
        "\n",
        "def unreg_f(B, C, r, c, eta, t1, t2):\n",
        "    \"\"\"\n",
        "    the unregularized objective with solutions u, v\n",
        "    \"\"\"\n",
        "    a = B.sum(dim=1).reshape(-1, 1)\n",
        "    b = B.sum(dim=0).reshape(-1, 1)\n",
        "    return dotp(C, B) + t1 * get_KL(a, r) + t2 * get_KL(b, c)\n",
        "\n",
        "\n",
        "def f_primal(unreg_f_val, B, eta):\n",
        "    ent = get_entropy(B) \n",
        "    return unreg_f_val - eta * ent\n",
        "\n",
        "\n",
        "\n",
        "def sinkhorn_uot(C, r, c, eta=1.0, t1=1.0, t2=1.0, n_iter=100, eps=None, opt_val=None, vbo=False):\n",
        "    \"\"\"\n",
        "    :arg C: cost matrix\n",
        "    :arg r: first marginal\n",
        "    :arg c: second marginal\n",
        "    :arg eta: entropic-regularizer\n",
        "    :arg t1: first KL regularizer\n",
        "    :arg t2: second Kl regularizer\n",
        "    :n_iter: number of Sinkhorn iterations\n",
        "    \"\"\"\n",
        "\n",
        "    # convert numpy variables to torch\n",
        "    C = torch.from_numpy(C)\n",
        "    r = torch.from_numpy(r)\n",
        "    c = torch.from_numpy(c)\n",
        "\n",
        "    # collect some stats\n",
        "    f_val_list = []\n",
        "    unreg_f_val_list = []\n",
        "    f_primal_val_list = []\n",
        "    sum_B_list = []\n",
        "\n",
        "    # initial solution\n",
        "    u = torch.zeros(r.shape, dtype=torch.float64)\n",
        "    v = torch.zeros(c.shape, dtype=torch.float64)\n",
        "\n",
        "    # compute before any updates\n",
        "    B = get_B(C, u, v, eta)\n",
        "    f_val = f_dual(B, u, v, r, c, eta, t1, t2)\n",
        "    f_val_list.append(f_val)\n",
        "\n",
        "    unreg_f_val = unreg_f(B, C, r, c, eta, t1, t2)\n",
        "    unreg_f_val_list.append(unreg_f_val)\n",
        "\n",
        "    f_primal_val = f_primal(unreg_f_val, B, eta)\n",
        "    f_primal_val_list.append(f_primal_val)\n",
        "\n",
        "    sum_B_list.append(B.sum())\n",
        "\n",
        "\n",
        "    stop_iter = n_iter\n",
        "    start = time()\n",
        "    for i in range(n_iter):\n",
        "        # update\n",
        "        if i % 2 == 0:\n",
        "            a = B.sum(dim=1).reshape(-1, 1)\n",
        "            u = (u / eta + torch.log(r) - torch.log(a)) * (t1 * eta / (eta + t1))\n",
        "        else:\n",
        "            b = B.sum(dim=0).reshape(-1, 1)\n",
        "            v = (v / eta + torch.log(c) - torch.log(b)) * (t2 * eta / (eta + t2))\n",
        "\n",
        "\t    # compute stats\n",
        "        B = get_B(C, u, v, eta)\n",
        "\n",
        "        f_val = f_dual(B, u, v, r, c, eta, t1, t2)\n",
        "        f_val_list.append(f_val)\n",
        "\n",
        "        unreg_f_val = unreg_f(B, C, r, c, eta, t1, t2)\n",
        "        unreg_f_val_list.append(unreg_f_val)\n",
        "\n",
        "        f_primal_val = f_primal(unreg_f_val, B, eta)\n",
        "        f_primal_val_list.append(f_primal_val)\n",
        "\n",
        "        sum_B_list.append(B.sum())\n",
        "\n",
        "\n",
        "        if eps is not None and unreg_f_val_list[-1] <= opt_val + eps:\n",
        "            stop_iter = i + 1\n",
        "            break\n",
        "\n",
        "        if vbo and (i + 1) % 1000 == 0:\n",
        "            stop = time()\n",
        "            print(f'iteration={i+1}, elapsed={stop-start:.3f}, f_dual={f_val:.3f}, f_primal={f_primal_val:.3f}, f_unreg={unreg_f_val:.3f}')\n",
        "            start = time()\n",
        "\n",
        "\n",
        "    info = {}\n",
        "    info['f_val_list'] = f_val_list\n",
        "    info['unreg_f_val_list'] = unreg_f_val_list\n",
        "    info['f_primal_val_list'] = f_primal_val_list\n",
        "    info['sum_B_list'] = sum_B_list\n",
        "    info['stop_iter'] = stop_iter\n",
        "\n",
        "    return u, v, info\n",
        "\n",
        "def exact_uot(C, a, b, tau, vbo=False):\n",
        "    nr = len(a)\n",
        "    nc = len(b)\n",
        "    X = cp.Variable((nr,nc), nonneg=True)\n",
        "\n",
        "    row_sums = cp.sum(X, axis=1)\n",
        "    col_sums = cp.sum(X, axis=0)\n",
        "\n",
        "    obj = cp.sum(cp.multiply(X, C))\n",
        "\n",
        "    obj -= tau * cp.sum(cp.entr(row_sums))\n",
        "    obj -= tau * cp.sum(cp.entr(col_sums))\n",
        "\n",
        "    obj -= tau * cp.sum(cp.multiply(row_sums, cp.log(a)))\n",
        "    obj -= tau * cp.sum(cp.multiply(col_sums, cp.log(b)))\n",
        "\n",
        "    obj -= 2 * tau * cp.sum(X)\n",
        "    obj += tau * cp.sum(a) + tau * cp.sum(b)\n",
        "\n",
        "    prob = cp.Problem(cp.Minimize(obj))\n",
        "\n",
        "    prob.solve(solver='SCS', verbose=vbo)\n",
        "\n",
        "    # print('UOT optimal value:', prob.value)\n",
        "\n",
        "    return prob.value"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EdFKZF61OanL",
        "colab_type": "code",
        "outputId": "6801f2e3-67bf-446b-8f49-bc174222a56d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "USE_PRESET_PAIRS = True\n",
        "\n",
        "\n",
        "# USE_PRECOMPUTED_OPTVAL = True\n",
        "\n",
        "def repeat_newdim(x, n_repeat, newdim):\n",
        "    x = np.expand_dims(x, axis=newdim)\n",
        "    x = np.repeat(x, n_repeat, newdim)\n",
        "    return x\n",
        "\n",
        "\n",
        "def get_L1_C(dim):\n",
        "    xv, yv = np.meshgrid(np.arange(dim), np.arange(dim), indexing='ij')\n",
        "    vv1 = np.concatenate((xv.reshape(-1, 1), yv.reshape(-1, 1)), axis=1)\n",
        "\n",
        "    vv2 = copy(vv1)\n",
        "    vv1 = repeat_newdim(vv1, dim ** 2, 1)\n",
        "    vv2 = repeat_newdim(vv2, dim ** 2, 0)\n",
        "    # print(vv1.shape, vv2.shape)\n",
        "    C = vv1 - vv2\n",
        "    C = np.abs(C).sum(axis=-1)\n",
        "    return C\n",
        "\n",
        "\n",
        "def get_eta_k(eps, a, b, tau, nr):\n",
        "    alpha = np.sum(a)\n",
        "    beta = np.sum(b)\n",
        "    # S = (alpha + beta + 1 / np.log(nr)) * (2 * tau + 2)\n",
        "    S = 0.5 * (alpha + beta) + 0.5 + 0.25 / np.log(nr)\n",
        "    # T = 4 * ((alpha + beta) * (np.log(alpha + beta) + np.log(nr)) + 1)\n",
        "    T = 0.5 * (alpha + beta) * (np.log(alpha + beta) - np.log(2) + np.log(nr) - 0.5) + np.log(nr) + 5 / 2\n",
        "\n",
        "    U = np.max([S + T, 2 * eps, 4 * eps * np.log(nr) / tau, 4 * eps * (alpha + beta) * np.log(nr) / tau])\n",
        "    eta = eps / U\n",
        "\n",
        "    # print('S, T, U, eps, eta:', S, T, U, eps, eta)\n",
        "\n",
        "    def supnorm(X):\n",
        "        return np.max(np.abs(X))\n",
        "\n",
        "    R = np.log(a).max() + np.log(b).max() + np.max([np.log(nr), supnorm(C) / eta - np.log(nr)])\n",
        "    k = (tau * U / eps + 1) * (\n",
        "            np.log(8) + np.log(eta) + np.log(R) + np.log(tau) + np.log(tau + 1) + 3 * np.log(U) - 3 * np.log(eps))\n",
        "\n",
        "    return eta, k\n",
        "\n",
        "\n",
        "C = get_L1_C(28).astype(np.float64)\n",
        "# print(C)\n",
        "\n",
        "x, y = _load_mnist('.', split_type='train', download=True)\n",
        "pairs = ((3, 5), (20562, 12428), (2564, 12380), (48485, 7605), (26428, 42698), (6152, 25061), (13168, 7506), (40816, 39370), (846, 16727), (31169, 7144))\n",
        "\n",
        "k_list_empirical_first = []\n",
        "k_list_formula = []\n",
        "uot_opt_val_list = []\n",
        "eps_list = np.linspace(5.0, 0.5, 10)\n",
        "tau = 10\n",
        "\n",
        "print(\"COMPUTE OPTIMAL VALUES\")\n",
        "for (id1, id2) in pairs:\n",
        "    print('pair', id1, id2)\n",
        "    a = x[id1].astype(np.float64)\n",
        "    b = x[id2].astype(np.float64)\n",
        "    a = a.reshape(-1, 1)\n",
        "    b = b.reshape(-1, 1)\n",
        "    a[a == 0] = 1e-6\n",
        "    b[b == 0] = 1e-6\n",
        "\n",
        "    start = time()\n",
        "    uot_opt_val = exact_uot(C, a.flatten(), b.flatten(), tau, vbo=True)\n",
        "    print('time elapsed:', time() - start)\n",
        "    print('exact val:', uot_opt_val)\n",
        "    uot_opt_val_list.append(uot_opt_val)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING: data might already exist\n",
            "COMPUTE OPTIMAL VALUES\n",
            "pair 3 5\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 6.11e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.46e+25 -2.13e+20  2.37e+28  1.44e-01 \n",
            "   100| 7.48e-04  2.30e-02  8.48e-01 -1.06e+03 -8.71e+01  1.84e-10  3.02e+01 \n",
            "   200| 3.28e-04  6.71e-03  6.68e-02 -1.48e+03 -1.29e+03  2.34e-10  5.92e+01 \n",
            "   300| 1.53e-04  3.80e-03  2.66e-02 -1.49e+03 -1.41e+03  1.35e-10  8.95e+01 \n",
            "   400| 1.25e-04  1.78e-03  1.66e-02 -1.49e+03 -1.45e+03  2.09e-10  1.19e+02 \n",
            "   500| 8.44e-05  2.59e-03  8.65e-03 -1.50e+03 -1.47e+03  2.14e-10  1.47e+02 \n",
            "   600| 1.17e-04  1.86e-03  1.53e-02 -1.50e+03 -1.45e+03  3.76e-10  1.76e+02 \n",
            "   700| 1.03e-04  1.38e-03  6.78e-03 -1.50e+03 -1.48e+03  2.81e-10  2.05e+02 \n",
            "   800| 7.87e-05  8.99e-04  9.95e-03 -1.50e+03 -1.47e+03  5.41e-10  2.33e+02 \n",
            "   900| 8.91e-05  8.82e-04  5.63e-03 -1.50e+03 -1.48e+03  2.47e-10  2.62e+02 \n",
            "  1000| 6.26e-05  6.46e-04  7.61e-03 -1.50e+03 -1.48e+03  3.27e-10  2.91e+02 \n",
            "  1100| 6.99e-05  1.11e-03  9.22e-03 -1.50e+03 -1.47e+03  4.73e-10  3.20e+02 \n",
            "  1200| 7.23e-05  1.99e-03  1.07e-02 -1.50e+03 -1.47e+03  5.49e-10  3.50e+02 \n",
            "  1300| 4.14e-05  5.82e-04  5.89e-03 -1.50e+03 -1.48e+03  7.83e-11  3.79e+02 \n",
            "  1400| 4.43e-05  3.89e-04  2.24e-03 -1.50e+03 -1.50e+03  2.07e-10  4.08e+02 \n",
            "  1500| 6.65e-05  4.67e-04  2.43e-03 -1.50e+03 -1.49e+03  5.01e-10  4.37e+02 \n",
            "  1600| 6.54e-05  1.49e-03  6.58e-03 -1.50e+03 -1.48e+03  2.95e-11  4.67e+02 \n",
            "  1700| 8.17e-05  9.31e-04  4.15e-03 -1.50e+03 -1.49e+03  2.22e-10  4.96e+02 \n",
            "  1800| 6.36e-05  1.54e-03  3.12e-03 -1.50e+03 -1.51e+03  7.01e-11  5.26e+02 \n",
            "  1900| 4.43e-05  1.05e-03  3.83e-03 -1.50e+03 -1.49e+03  1.08e-10  5.54e+02 \n",
            "  2000| 6.29e-05  1.49e-03  7.30e-03 -1.50e+03 -1.48e+03  2.17e-11  5.83e+02 \n",
            "  2100| 4.28e-05  1.12e-03  6.91e-04 -1.50e+03 -1.50e+03  1.18e-10  6.13e+02 \n",
            "  2200| 6.01e-05  7.59e-04  2.23e-03 -1.50e+03 -1.50e+03  1.68e-10  6.43e+02 \n",
            "  2300| 3.08e-05  1.12e-03  3.24e-03 -1.50e+03 -1.49e+03  4.74e-10  6.72e+02 \n",
            "  2400| 3.77e-05  8.88e-04  5.06e-04 -1.50e+03 -1.51e+03  3.06e-10  7.00e+02 \n",
            "  2500| 2.35e-05  2.36e-04  1.49e-03 -1.50e+03 -1.50e+03  1.30e-10  7.30e+02 \n",
            "  2600| 2.48e-05  3.60e-04  1.37e-03 -1.50e+03 -1.50e+03  9.54e-11  7.58e+02 \n",
            "  2700| 2.28e-05  3.66e-04  9.78e-04 -1.50e+03 -1.50e+03  2.63e-10  7.86e+02 \n",
            "  2800| 2.87e-05  5.88e-04  2.09e-03 -1.50e+03 -1.50e+03  1.98e-10  8.14e+02 \n",
            "  2900| 1.97e-05  3.84e-04  2.33e-03 -1.50e+03 -1.50e+03  3.01e-10  8.42e+02 \n",
            "  3000| 2.12e-05  6.67e-04  1.30e-03 -1.50e+03 -1.51e+03  5.56e-10  8.69e+02 \n",
            "  3100| 1.62e-05  3.59e-04  1.47e-03 -1.50e+03 -1.50e+03  2.94e-10  8.96e+02 \n",
            "  3200| 9.73e-06  2.53e-04  1.18e-03 -1.50e+03 -1.50e+03  1.35e-10  9.25e+02 \n",
            "  3300| 1.13e-05  2.37e-04  9.65e-04 -1.50e+03 -1.50e+03  3.12e-10  9.54e+02 \n",
            "  3400| 8.24e-06  1.32e-04  8.35e-04 -1.50e+03 -1.50e+03  1.22e-10  9.82e+02 \n",
            "  3500| 1.50e-05  2.59e-04  1.05e-03 -1.50e+03 -1.50e+03  6.84e-10  1.01e+03 \n",
            "  3600| 1.33e-05  1.90e-04  4.51e-05 -1.50e+03 -1.50e+03  6.79e-10  1.04e+03 \n",
            "  3700| 1.09e-05  2.61e-04  3.37e-04 -1.50e+03 -1.50e+03  2.38e-11  1.07e+03 \n",
            "  3800| 1.06e-05  2.14e-04  2.67e-04 -1.50e+03 -1.50e+03  1.39e-11  1.10e+03 \n",
            "  3900| 6.10e-06  1.46e-04  2.32e-04 -1.50e+03 -1.50e+03  1.98e-10  1.12e+03 \n",
            "  4000| 4.54e-06  1.16e-04  2.36e-04 -1.50e+03 -1.50e+03  5.71e-10  1.15e+03 \n",
            "  4100| 5.19e-06  1.59e-04  2.22e-04 -1.50e+03 -1.50e+03  6.47e-10  1.18e+03 \n",
            "  4200| 4.36e-06  7.70e-05  4.24e-04 -1.50e+03 -1.50e+03  5.58e-10  1.21e+03 \n",
            "  4240| 3.50e-06  8.45e-05  5.31e-05 -1.50e+03 -1.50e+03  7.29e-11  1.22e+03 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved\n",
            "Timing: Solve time: 1.22e+03s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 4.54e-02s\n",
            "\tCones: avg projection time: 1.82e-02s\n",
            "\tAcceleration: avg step time: 1.74e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.1921e-07, dist(y, K*) = 1.2089e-05, s'y/|s||y| = 1.0045e-14\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.5032e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 8.4514e-05\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.3062e-05\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1503.7984, -b'y = -1503.9580\n",
            "============================================================================\n",
            "time elapsed: 1229.4001519680023\n",
            "exact val: 321.83947656441\n",
            "pair 20562 12428\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 5.96e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.41e+25 -1.30e+20  2.44e+28  1.60e-01 \n",
            "   100| 6.82e-04  1.33e-02  9.38e-01 -8.09e+02 -2.55e+01  2.81e-10  2.87e+01 \n",
            "   200| 5.97e-04  1.05e-02  8.20e-04 -1.18e+03 -1.18e+03  6.44e-11  5.65e+01 \n",
            "   300| 2.68e-04  3.59e-03  1.64e-02 -1.19e+03 -1.15e+03  7.25e-11  8.44e+01 \n",
            "   400| 1.64e-04  4.07e-03  1.58e-02 -1.19e+03 -1.16e+03  2.26e-10  1.13e+02 \n",
            "   500| 1.82e-04  3.30e-03  1.05e-02 -1.20e+03 -1.17e+03  2.51e-10  1.41e+02 \n",
            "   600| 2.35e-04  3.78e-03  7.95e-03 -1.20e+03 -1.18e+03  2.93e-10  1.70e+02 \n",
            "   700| 1.72e-04  4.98e-03  3.62e-03 -1.20e+03 -1.19e+03  3.97e-10  1.97e+02 \n",
            "   800| 1.32e-04  1.82e-03  1.33e-02 -1.20e+03 -1.17e+03  2.88e-10  2.26e+02 \n",
            "   900| 1.41e-04  2.90e-03  1.13e-02 -1.20e+03 -1.17e+03  2.40e-10  2.54e+02 \n",
            "  1000| 8.14e-05  1.76e-03  8.64e-03 -1.20e+03 -1.18e+03  1.68e-10  2.82e+02 \n",
            "  1100| 1.55e-04  3.32e-03  1.30e-02 -1.20e+03 -1.17e+03  1.39e-10  3.11e+02 \n",
            "  1200| 6.89e-05  1.12e-03  7.01e-03 -1.20e+03 -1.19e+03  5.21e-11  3.39e+02 \n",
            "  1300| 6.63e-05  1.72e-03  8.38e-03 -1.20e+03 -1.18e+03  6.69e-10  3.68e+02 \n",
            "  1400| 5.43e-05  8.57e-04  6.18e-03 -1.20e+03 -1.19e+03  2.24e-10  3.97e+02 \n",
            "  1500| 7.38e-05  1.45e-03  6.71e-03 -1.20e+03 -1.19e+03  1.31e-10  4.27e+02 \n",
            "  1600| 6.42e-05  1.09e-03  5.50e-03 -1.21e+03 -1.19e+03  1.43e-10  4.55e+02 \n",
            "  1700| 4.59e-05  8.87e-04  3.10e-03 -1.21e+03 -1.20e+03  5.73e-10  4.84e+02 \n",
            "  1800| 5.49e-05  1.94e-03  5.23e-03 -1.21e+03 -1.19e+03  3.73e-11  5.12e+02 \n",
            "  1900| 5.90e-05  1.33e-03  1.79e-03 -1.21e+03 -1.20e+03  4.71e-10  5.40e+02 \n",
            "  2000| 3.02e-05  4.18e-04  1.62e-03 -1.21e+03 -1.20e+03  8.44e-11  5.68e+02 \n",
            "  2100| 4.37e-05  9.60e-04  9.42e-04 -1.20e+03 -1.20e+03  2.05e-10  5.95e+02 \n",
            "  2200| 4.71e-05  6.46e-04  1.49e-06 -1.21e+03 -1.21e+03  6.07e-10  6.22e+02 \n",
            "  2300| 1.67e-05  4.88e-04  2.01e-03 -1.21e+03 -1.20e+03  3.50e-10  6.49e+02 \n",
            "  2400| 2.85e-05  1.02e-03  3.45e-04 -1.21e+03 -1.21e+03  9.95e-12  6.77e+02 \n",
            "  2500| 4.75e-05  8.71e-04  1.36e-03 -1.21e+03 -1.21e+03  6.73e-10  7.06e+02 \n",
            "  2600| 2.99e-05  4.75e-04  7.67e-04 -1.21e+03 -1.20e+03  1.37e-10  7.35e+02 \n",
            "  2700| 3.44e-05  6.79e-04  1.65e-03 -1.21e+03 -1.21e+03  1.59e-10  7.62e+02 \n",
            "  2800| 2.78e-05  6.61e-04  4.16e-04 -1.21e+03 -1.21e+03  2.26e-10  7.91e+02 \n",
            "  2900| 2.05e-05  2.83e-04  2.36e-04 -1.21e+03 -1.21e+03  5.87e-10  8.19e+02 \n",
            "  3000| 5.27e-05  1.35e-03  2.26e-03 -1.21e+03 -1.20e+03  1.58e-10  8.47e+02 \n",
            "  3100| 3.49e-05  4.25e-04  1.67e-03 -1.21e+03 -1.20e+03  2.30e-11  8.75e+02 \n",
            "  3200| 3.09e-05  6.92e-04  1.01e-03 -1.21e+03 -1.20e+03  1.81e-10  9.02e+02 \n",
            "  3300| 7.50e-06  1.73e-04  9.11e-04 -1.21e+03 -1.20e+03  3.06e-10  9.30e+02 \n",
            "  3400| 1.89e-05  3.87e-04  5.47e-04 -1.21e+03 -1.20e+03  2.49e-11  9.58e+02 \n",
            "  3500| 1.29e-05  2.83e-04  2.98e-04 -1.21e+03 -1.21e+03  6.40e-10  9.87e+02 \n",
            "  3600| 1.66e-05  3.77e-04  6.85e-04 -1.21e+03 -1.20e+03  9.17e-11  1.01e+03 \n",
            "  3700| 1.84e-05  4.53e-04  6.56e-05 -1.21e+03 -1.21e+03  3.33e-11  1.04e+03 \n",
            "  3800| 1.34e-05  3.89e-04  4.51e-04 -1.21e+03 -1.21e+03  6.98e-10  1.07e+03 \n",
            "  3900| 1.12e-05  3.14e-04  7.34e-05 -1.21e+03 -1.21e+03  3.68e-10  1.10e+03 \n",
            "  4000| 1.21e-05  2.44e-04  5.25e-04 -1.21e+03 -1.21e+03  3.89e-10  1.13e+03 \n",
            "  4100| 1.64e-05  2.18e-04  2.10e-04 -1.21e+03 -1.21e+03  3.33e-11  1.15e+03 \n",
            "  4200| 7.78e-06  1.79e-04  2.77e-04 -1.21e+03 -1.21e+03  8.05e-11  1.18e+03 \n",
            "  4300| 1.17e-05  2.02e-04  6.33e-04 -1.21e+03 -1.21e+03  6.81e-10  1.21e+03 \n",
            "  4400| 1.35e-05  1.82e-04  9.39e-04 -1.21e+03 -1.20e+03  5.99e-10  1.24e+03 \n",
            "  4500| 1.36e-05  2.94e-04  2.48e-04 -1.21e+03 -1.21e+03  1.83e-10  1.27e+03 \n",
            "  4560| 4.74e-06  7.50e-05  1.55e-05 -1.21e+03 -1.21e+03  4.05e-10  1.28e+03 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved\n",
            "Timing: Solve time: 1.28e+03s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 3.69e-02s\n",
            "\tCones: avg projection time: 2.15e-02s\n",
            "\tAcceleration: avg step time: 1.73e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.2219e-06, dist(y, K*) = 1.2405e-05, s'y/|s||y| = -6.1814e-11\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.7419e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.5026e-05\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.5486e-05\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1206.3522, -b'y = -1206.3148\n",
            "============================================================================\n",
            "time elapsed: 1291.4287762641907\n",
            "exact val: 167.64555073518932\n",
            "pair 2564 12380\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 6.00e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.41e+25 -1.17e+20  2.45e+28  1.29e-01 \n",
            "   100| 4.89e-04  1.16e-02  9.23e-01 -6.82e+02 -2.69e+01  3.69e-10  2.87e+01 \n",
            "   200| 5.39e-04  1.30e-02  8.37e-01 -1.02e+03 -9.03e+01  4.61e-10  5.74e+01 \n",
            "   300| 3.07e-04  5.61e-03  2.56e-02 -1.12e+03 -1.06e+03  2.71e-10  8.58e+01 \n",
            "   400| 1.78e-04  4.17e-03  2.48e-02 -1.13e+03 -1.08e+03  5.98e-10  1.15e+02 \n",
            "   500| 1.51e-04  2.13e-03  2.03e-02 -1.13e+03 -1.09e+03  5.12e-10  1.44e+02 \n",
            "   600| 1.42e-04  1.59e-03  1.39e-02 -1.14e+03 -1.11e+03  2.57e-10  1.74e+02 \n",
            "   700| 1.88e-04  1.25e-03  1.16e-02 -1.14e+03 -1.11e+03  3.05e-11  2.02e+02 \n",
            "   800| 7.07e-05  9.80e-04  1.35e-02 -1.14e+03 -1.11e+03  3.88e-10  2.31e+02 \n",
            "   900| 7.90e-05  1.25e-03  9.33e-03 -1.14e+03 -1.12e+03  2.11e-10  2.61e+02 \n",
            "  1000| 8.72e-05  8.60e-04  6.42e-03 -1.14e+03 -1.13e+03  3.28e-10  2.89e+02 \n",
            "  1100| 7.48e-05  8.03e-04  6.72e-03 -1.14e+03 -1.13e+03  7.87e-11  3.17e+02 \n",
            "  1200| 8.30e-05  1.68e-03  6.35e-03 -1.14e+03 -1.13e+03  3.46e-10  3.47e+02 \n",
            "  1300| 7.28e-05  1.84e-03  5.20e-03 -1.14e+03 -1.13e+03  3.29e-10  3.75e+02 \n",
            "  1400| 5.58e-05  1.97e-03  2.96e-03 -1.14e+03 -1.14e+03  6.02e-10  4.05e+02 \n",
            "  1500| 6.55e-05  1.72e-03  5.17e-03 -1.14e+03 -1.13e+03  2.94e-10  4.35e+02 \n",
            "  1600| 3.53e-05  8.05e-04  4.22e-03 -1.14e+03 -1.13e+03  3.94e-10  4.63e+02 \n",
            "  1700| 2.98e-05  5.80e-04  4.83e-03 -1.14e+03 -1.13e+03  2.43e-10  4.93e+02 \n",
            "  1800| 6.30e-05  7.94e-04  1.24e-03 -1.14e+03 -1.14e+03  4.01e-11  5.22e+02 \n",
            "  1900| 2.72e-05  6.41e-04  2.39e-03 -1.14e+03 -1.14e+03  1.90e-10  5.51e+02 \n",
            "  2000| 2.58e-05  7.28e-04  1.96e-03 -1.14e+03 -1.14e+03  1.53e-10  5.80e+02 \n",
            "  2100| 3.74e-05  9.18e-04  2.49e-03 -1.14e+03 -1.14e+03  1.54e-10  6.08e+02 \n",
            "  2200| 2.43e-05  6.11e-04  1.35e-03 -1.14e+03 -1.14e+03  1.16e-11  6.36e+02 \n",
            "  2300| 3.10e-05  1.08e-03  1.39e-03 -1.14e+03 -1.14e+03  3.27e-10  6.66e+02 \n",
            "  2400| 2.47e-05  3.68e-04  1.05e-03 -1.14e+03 -1.14e+03  7.48e-11  6.95e+02 \n",
            "  2500| 3.17e-05  7.79e-04  1.29e-03 -1.15e+03 -1.14e+03  2.59e-11  7.25e+02 \n",
            "  2600| 3.98e-05  6.68e-04  1.95e-03 -1.15e+03 -1.14e+03  5.22e-10  7.53e+02 \n",
            "  2700| 1.60e-05  4.56e-04  1.48e-03 -1.14e+03 -1.14e+03  7.81e-11  7.83e+02 \n",
            "  2800| 1.66e-05  3.02e-04  4.93e-04 -1.15e+03 -1.14e+03  2.37e-10  8.12e+02 \n",
            "  2900| 1.11e-05  1.71e-04  1.37e-03 -1.14e+03 -1.14e+03  7.80e-11  8.41e+02 \n",
            "  3000| 1.97e-05  3.44e-04  1.24e-03 -1.15e+03 -1.14e+03  2.59e-11  8.70e+02 \n",
            "  3100| 2.15e-05  2.82e-04  1.29e-03 -1.15e+03 -1.14e+03  1.58e-10  9.00e+02 \n",
            "  3200| 1.07e-05  1.82e-04  5.11e-04 -1.14e+03 -1.14e+03  8.73e-11  9.28e+02 \n",
            "  3300| 2.43e-05  2.63e-04  6.26e-05 -1.14e+03 -1.14e+03  3.35e-10  9.57e+02 \n",
            "  3400| 3.55e-05  7.45e-04  1.01e-03 -1.14e+03 -1.14e+03  1.17e-11  9.88e+02 \n",
            "  3500| 1.03e-05  2.54e-04  6.02e-05 -1.14e+03 -1.15e+03  4.09e-11  1.02e+03 \n",
            "  3600| 8.09e-06  1.45e-04  2.18e-04 -1.14e+03 -1.14e+03  3.26e-10  1.04e+03 \n",
            "  3700| 1.12e-05  2.22e-04  2.19e-04 -1.15e+03 -1.14e+03  2.17e-10  1.07e+03 \n",
            "  3800| 1.06e-05  1.53e-04  1.78e-04 -1.15e+03 -1.14e+03  3.41e-10  1.10e+03 \n",
            "  3900| 9.96e-06  1.42e-04  2.87e-04 -1.15e+03 -1.14e+03  2.08e-10  1.13e+03 \n",
            "  4000| 7.14e-06  1.41e-04  6.89e-04 -1.15e+03 -1.14e+03  5.57e-10  1.16e+03 \n",
            "  4100| 9.91e-06  2.04e-04  6.08e-05 -1.14e+03 -1.15e+03  3.26e-10  1.19e+03 \n",
            "  4200| 7.75e-06  1.85e-04  1.36e-04 -1.14e+03 -1.15e+03  8.72e-11  1.22e+03 \n",
            "  4300| 9.49e-06  1.81e-04  3.65e-04 -1.14e+03 -1.14e+03  3.22e-10  1.25e+03 \n",
            "  4400| 9.11e-06  1.92e-04  3.65e-04 -1.15e+03 -1.15e+03  1.59e-10  1.28e+03 \n",
            "  4500| 1.19e-05  4.39e-04  2.04e-04 -1.15e+03 -1.14e+03  2.82e-10  1.31e+03 \n",
            "  4600| 7.66e-06  1.16e-04  5.54e-04 -1.14e+03 -1.14e+03  3.56e-11  1.33e+03 \n",
            "  4700| 8.55e-06  2.59e-04  2.71e-04 -1.15e+03 -1.14e+03  2.12e-10  1.36e+03 \n",
            "  4800| 5.84e-06  2.20e-04  6.12e-04 -1.14e+03 -1.14e+03  3.47e-10  1.39e+03 \n",
            "  4900| 1.16e-05  1.80e-04  2.16e-04 -1.15e+03 -1.14e+03  1.72e-10  1.41e+03 \n",
            "  5000| 4.79e-06  1.50e-04  9.64e-05 -1.15e+03 -1.14e+03  2.24e-10  1.44e+03 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved/Inaccurate\n",
            "Hit max_iters, solution may be inaccurate\n",
            "Timing: Solve time: 1.44e+03s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 4.56e-02s\n",
            "\tCones: avg projection time: 2.01e-02s\n",
            "\tAcceleration: avg step time: 1.73e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.2219e-06, dist(y, K*) = 1.2424e-05, s'y/|s||y| = -5.2472e-10\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.7871e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 1.5046e-04\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 9.6416e-05\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1145.0850, -b'y = -1144.8641\n",
            "============================================================================\n",
            "time elapsed: 1445.5877101421356\n",
            "exact val: 207.3502556064093\n",
            "pair 48485 7605\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 5.01e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  6.00e+21  1.00e+00 -3.49e+25 -1.79e+20  2.33e+28  1.50e-01 \n",
            "   100| 1.42e-02  2.90e-01  8.92e-01 -1.94e+03 -3.40e+04  3.31e-10  2.61e+01 \n",
            "   200| 1.00e-03  1.71e-02  2.78e-02 -1.83e+03 -1.93e+03  4.25e-10  5.16e+01 \n",
            "   300| 2.58e-04  3.84e-03  3.05e-02 -1.85e+03 -1.74e+03  6.15e-11  7.74e+01 \n",
            "   400| 2.83e-04  4.24e-03  2.73e-02 -1.86e+03 -1.76e+03  2.40e-10  1.04e+02 \n",
            "   500| 3.12e-04  9.58e-03  4.49e-03 -1.86e+03 -1.87e+03  4.69e-10  1.30e+02 \n",
            "   600| 2.37e-04  2.95e-03  1.28e-02 -1.86e+03 -1.81e+03  5.49e-10  1.56e+02 \n",
            "   700| 1.51e-04  1.96e-03  1.02e-02 -1.86e+03 -1.83e+03  1.34e-10  1.82e+02 \n",
            "   800| 2.21e-04  2.98e-03  6.83e-03 -1.87e+03 -1.84e+03  5.66e-10  2.08e+02 \n",
            "   900| 1.94e-04  4.39e-03  9.65e-04 -1.87e+03 -1.87e+03  1.83e-10  2.35e+02 \n",
            "  1000| 1.14e-04  3.88e-03  1.71e-02 -1.87e+03 -1.81e+03  2.23e-10  2.62e+02 \n",
            "  1100| 1.73e-04  2.08e-03  5.08e-03 -1.87e+03 -1.85e+03  2.87e-10  2.89e+02 \n",
            "  1200| 1.20e-04  2.86e-03  1.60e-02 -1.87e+03 -1.81e+03  1.05e-10  3.16e+02 \n",
            "  1300| 1.61e-04  2.07e-03  1.08e-02 -1.87e+03 -1.83e+03  1.42e-10  3.42e+02 \n",
            "  1400| 1.10e-04  1.51e-03  7.96e-03 -1.88e+03 -1.85e+03  5.18e-10  3.68e+02 \n",
            "  1500| 1.04e-04  1.63e-03  2.65e-03 -1.88e+03 -1.87e+03  2.01e-10  3.97e+02 \n",
            "  1600| 1.03e-04  2.30e-03  9.17e-03 -1.88e+03 -1.84e+03  3.16e-10  4.26e+02 \n",
            "  1700| 7.09e-05  8.17e-04  7.45e-03 -1.88e+03 -1.85e+03  7.78e-11  4.52e+02 \n",
            "  1800| 8.32e-05  1.77e-03  8.63e-03 -1.88e+03 -1.84e+03  2.54e-10  4.77e+02 \n",
            "  1900| 6.42e-05  1.72e-03  8.92e-03 -1.88e+03 -1.84e+03  5.05e-11  5.04e+02 \n",
            "  2000| 9.88e-05  1.27e-03  2.18e-03 -1.88e+03 -1.87e+03  4.91e-10  5.30e+02 \n",
            "  2100| 5.12e-05  1.55e-03  9.45e-04 -1.88e+03 -1.88e+03  2.59e-10  5.56e+02 \n",
            "  2200| 4.51e-05  1.31e-03  1.61e-04 -1.88e+03 -1.88e+03  3.44e-10  5.82e+02 \n",
            "  2300| 4.46e-05  1.19e-03  5.20e-03 -1.88e+03 -1.86e+03  2.43e-10  6.10e+02 \n",
            "  2400| 3.33e-05  8.69e-04  1.85e-03 -1.88e+03 -1.87e+03  4.43e-11  6.36e+02 \n",
            "  2500| 3.24e-05  8.78e-04  4.56e-03 -1.88e+03 -1.86e+03  6.42e-10  6.62e+02 \n",
            "  2600| 3.58e-05  1.38e-03  2.57e-04 -1.88e+03 -1.88e+03  1.32e-12  6.88e+02 \n",
            "  2700| 3.14e-05  1.13e-03  7.36e-04 -1.88e+03 -1.88e+03  1.90e-12  7.15e+02 \n",
            "  2800| 5.00e-05  6.87e-04  3.47e-04 -1.88e+03 -1.88e+03  3.20e-10  7.40e+02 \n",
            "  2900| 2.63e-05  3.23e-04  1.15e-03 -1.88e+03 -1.87e+03  1.22e-10  7.67e+02 \n",
            "  3000| 2.60e-05  5.11e-04  2.33e-03 -1.88e+03 -1.87e+03  1.39e-10  7.93e+02 \n",
            "  3100| 4.33e-05  8.66e-04  1.42e-04 -1.88e+03 -1.88e+03  3.36e-10  8.20e+02 \n",
            "  3200| 1.62e-05  2.70e-04  7.13e-04 -1.88e+03 -1.88e+03  1.41e-10  8.47e+02 \n",
            "  3300| 6.84e-05  1.30e-03  2.93e-03 -1.88e+03 -1.89e+03  1.18e-10  8.72e+02 \n",
            "  3400| 3.33e-05  8.27e-04  9.32e-04 -1.88e+03 -1.88e+03  2.49e-10  8.98e+02 \n",
            "  3500| 3.65e-05  5.51e-04  1.72e-03 -1.88e+03 -1.87e+03  1.90e-10  9.24e+02 \n",
            "  3600| 1.30e-05  2.42e-04  6.82e-04 -1.88e+03 -1.88e+03  4.12e-10  9.50e+02 \n",
            "  3700| 2.18e-05  4.33e-04  2.93e-04 -1.88e+03 -1.88e+03  1.75e-10  9.76e+02 \n",
            "  3800| 1.58e-05  3.06e-04  3.04e-04 -1.88e+03 -1.88e+03  6.30e-10  1.00e+03 \n",
            "  3900| 2.26e-05  4.92e-04  5.36e-04 -1.88e+03 -1.88e+03  1.61e-10  1.03e+03 \n",
            "  4000| 1.73e-05  4.45e-04  1.98e-03 -1.88e+03 -1.87e+03  2.22e-10  1.06e+03 \n",
            "  4100| 1.16e-05  2.17e-04  5.38e-04 -1.88e+03 -1.88e+03  4.14e-10  1.08e+03 \n",
            "  4200| 2.14e-05  6.45e-04  1.64e-03 -1.88e+03 -1.87e+03  2.59e-10  1.11e+03 \n",
            "  4300| 2.10e-05  4.19e-04  3.57e-04 -1.88e+03 -1.88e+03  5.63e-10  1.14e+03 \n",
            "  4400| 1.13e-05  2.85e-04  1.18e-03 -1.88e+03 -1.88e+03  6.56e-10  1.16e+03 \n",
            "  4500| 2.01e-05  3.66e-04  2.81e-04 -1.88e+03 -1.88e+03  4.98e-10  1.19e+03 \n",
            "  4600| 2.16e-05  4.56e-04  1.13e-03 -1.88e+03 -1.88e+03  3.31e-10  1.22e+03 \n",
            "  4700| 9.55e-06  2.05e-04  3.21e-04 -1.88e+03 -1.88e+03  3.12e-10  1.24e+03 \n",
            "  4800| 1.27e-05  4.28e-04  1.60e-03 -1.88e+03 -1.87e+03  4.12e-10  1.27e+03 \n",
            "  4900| 1.59e-05  2.75e-04  3.63e-04 -1.88e+03 -1.88e+03  7.69e-11  1.29e+03 \n",
            "  5000| 1.29e-05  2.97e-04  1.08e-03 -1.88e+03 -1.88e+03  6.18e-10  1.31e+03 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved/Inaccurate\n",
            "Hit max_iters, solution may be inaccurate\n",
            "Timing: Solve time: 1.31e+03s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 4.01e-02s\n",
            "\tCones: avg projection time: 1.52e-02s\n",
            "\tAcceleration: avg step time: 1.62e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.0471e-06, dist(y, K*) = 1.2149e-05, s'y/|s||y| = 1.5304e-11\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 1.2904e-05\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.9657e-04\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.0786e-03\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1880.0548, -b'y = -1876.0023\n",
            "============================================================================\n",
            "time elapsed: 1311.268438577652\n",
            "exact val: 423.35617236431176\n",
            "pair 26428 42698\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 3.92e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.98e+21  1.00e+00 -3.38e+25 -1.18e+20  2.48e+28  9.18e-02 \n",
            "   100| 3.83e-03  1.13e-01  2.02e-01 -6.75e+02 -1.02e+03  2.98e-11  1.50e+01 \n",
            "   200| 8.27e-04  5.13e-03  3.98e-02 -9.08e+02 -8.38e+02  1.88e-10  3.01e+01 \n",
            "   300| 1.06e-04  2.59e-03  5.98e-03 -9.37e+02 -9.48e+02  5.16e-10  4.54e+01 \n",
            "   400| 1.28e-04  1.86e-03  6.41e-03 -9.41e+02 -9.53e+02  6.09e-10  6.08e+01 \n",
            "   500| 1.20e-04  1.38e-03  9.44e-04 -9.41e+02 -9.39e+02  1.84e-10  7.69e+01 \n",
            "   600| 1.09e-04  2.28e-03  1.52e-03 -9.43e+02 -9.46e+02  4.85e-10  9.23e+01 \n",
            "   700| 1.29e-04  1.86e-03  3.78e-03 -9.45e+02 -9.52e+02  2.01e-10  1.08e+02 \n",
            "   800| 1.53e-04  1.56e-03  3.17e-03 -9.46e+02 -9.52e+02  3.15e-10  1.23e+02 \n",
            "   900| 7.27e-05  2.28e-03  8.79e-04 -9.46e+02 -9.44e+02  1.24e-10  1.39e+02 \n",
            "  1000| 4.43e-05  5.21e-04  2.86e-03 -9.45e+02 -9.39e+02  3.94e-10  1.55e+02 \n",
            "  1100| 8.56e-05  2.80e-03  2.92e-03 -9.45e+02 -9.40e+02  3.30e-10  1.70e+02 \n",
            "  1200| 7.49e-05  6.79e-04  2.71e-03 -9.44e+02 -9.39e+02  6.07e-10  1.85e+02 \n",
            "  1300| 5.72e-05  1.20e-03  1.03e-03 -9.46e+02 -9.44e+02  2.25e-10  2.00e+02 \n",
            "  1400| 4.95e-05  1.27e-03  2.58e-03 -9.46e+02 -9.41e+02  5.11e-10  2.16e+02 \n",
            "  1500| 5.00e-05  1.39e-03  1.88e-03 -9.46e+02 -9.42e+02  1.99e-10  2.31e+02 \n",
            "  1600| 5.31e-05  1.04e-03  1.92e-03 -9.46e+02 -9.42e+02  3.67e-10  2.49e+02 \n",
            "  1700| 6.57e-05  1.02e-03  1.82e-03 -9.47e+02 -9.43e+02  3.01e-10  2.67e+02 \n",
            "  1800| 2.34e-05  3.69e-04  2.51e-03 -9.46e+02 -9.41e+02  6.07e-10  2.84e+02 \n",
            "  1900| 4.27e-05  5.24e-04  7.33e-04 -9.46e+02 -9.48e+02  3.76e-11  3.01e+02 \n",
            "  2000| 2.72e-05  5.04e-04  2.15e-03 -9.47e+02 -9.43e+02  4.49e-11  3.19e+02 \n",
            "  2100| 3.23e-05  5.45e-04  2.26e-03 -9.47e+02 -9.43e+02  1.60e-10  3.37e+02 \n",
            "  2200| 3.64e-05  7.74e-04  2.47e-03 -9.47e+02 -9.43e+02  1.73e-11  3.56e+02 \n",
            "  2300| 1.88e-05  5.19e-04  1.99e-03 -9.47e+02 -9.43e+02  1.43e-10  3.74e+02 \n",
            "  2400| 2.34e-05  7.47e-04  6.72e-04 -9.47e+02 -9.46e+02  2.93e-10  3.92e+02 \n",
            "  2500| 1.94e-05  4.60e-04  1.50e-03 -9.47e+02 -9.44e+02  6.17e-11  4.10e+02 \n",
            "  2600| 1.79e-05  5.33e-04  1.45e-03 -9.47e+02 -9.44e+02  3.55e-10  4.28e+02 \n",
            "  2700| 1.78e-05  2.82e-04  8.47e-04 -9.47e+02 -9.46e+02  2.29e-10  4.47e+02 \n",
            "  2800| 2.30e-05  2.30e-04  1.09e-03 -9.47e+02 -9.45e+02  3.31e-10  4.66e+02 \n",
            "  2900| 3.42e-05  4.49e-04  3.74e-04 -9.47e+02 -9.46e+02  6.96e-10  4.84e+02 \n",
            "  3000| 2.04e-05  2.67e-04  6.87e-04 -9.47e+02 -9.46e+02  2.78e-11  5.02e+02 \n",
            "  3100| 1.23e-05  1.30e-04  1.27e-03 -9.47e+02 -9.45e+02  6.73e-10  5.20e+02 \n",
            "  3200| 1.87e-05  1.58e-04  4.08e-04 -9.47e+02 -9.46e+02  3.22e-10  5.39e+02 \n",
            "  3300| 1.73e-05  2.89e-04  1.04e-03 -9.47e+02 -9.45e+02  3.23e-11  5.56e+02 \n",
            "  3400| 1.79e-05  3.81e-04  1.33e-03 -9.47e+02 -9.45e+02  3.01e-10  5.74e+02 \n",
            "  3500| 1.35e-05  1.66e-04  1.44e-03 -9.47e+02 -9.45e+02  3.07e-10  5.92e+02 \n",
            "  3600| 1.49e-05  1.72e-04  4.29e-04 -9.47e+02 -9.46e+02  9.91e-11  6.10e+02 \n",
            "  3700| 1.12e-05  1.57e-04  2.74e-04 -9.47e+02 -9.47e+02  9.38e-11  6.28e+02 \n",
            "  3800| 8.61e-06  1.82e-04  4.55e-04 -9.47e+02 -9.48e+02  3.04e-10  6.45e+02 \n",
            "  3900| 1.28e-05  2.52e-04  1.06e-03 -9.47e+02 -9.45e+02  4.08e-10  6.62e+02 \n",
            "  4000| 6.01e-06  1.02e-04  1.76e-04 -9.47e+02 -9.47e+02  4.64e-11  6.80e+02 \n",
            "  4100| 1.08e-05  1.76e-04  7.32e-04 -9.47e+02 -9.46e+02  1.52e-10  6.99e+02 \n",
            "  4180| 9.02e-06  9.34e-05  6.12e-05 -9.47e+02 -9.47e+02  1.03e-10  7.13e+02 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved\n",
            "Timing: Solve time: 7.13e+02s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 2.28e-02s\n",
            "\tCones: avg projection time: 9.42e-03s\n",
            "\tAcceleration: avg step time: 1.13e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.2219e-06, dist(y, K*) = 1.2539e-05, s'y/|s||y| = 3.6700e-10\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 9.0249e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 9.3439e-05\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 6.1175e-05\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -947.3336, -b'y = -947.2176\n",
            "============================================================================\n",
            "time elapsed: 717.4669678211212\n",
            "exact val: 117.52384257739209\n",
            "pair 6152 25061\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 4.05e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  6.00e+21  1.00e+00 -3.48e+25 -2.64e+20  2.34e+28  9.46e-02 \n",
            "   100| 6.96e-04  1.71e-02  8.86e-01 -1.05e+03 -6.29e+01  7.12e-11  1.78e+01 \n",
            "   200| 1.18e-03  2.45e-02  8.66e-01 -1.46e+03 -1.04e+02  1.86e-10  3.55e+01 \n",
            "   300| 2.67e-04  4.38e-03  3.18e-02 -1.62e+03 -1.52e+03  3.10e-10  5.39e+01 \n",
            "   400| 2.21e-04  3.39e-03  1.14e-02 -1.63e+03 -1.60e+03  4.06e-10  7.16e+01 \n",
            "   500| 1.77e-04  2.16e-03  1.19e-02 -1.64e+03 -1.60e+03  8.65e-11  8.88e+01 \n",
            "   600| 1.70e-04  2.90e-03  2.18e-02 -1.64e+03 -1.57e+03  6.15e-11  1.07e+02 \n",
            "   700| 2.32e-04  4.58e-03  1.88e-04 -1.64e+03 -1.64e+03  5.46e-10  1.25e+02 \n",
            "   800| 1.54e-04  3.22e-03  5.14e-04 -1.65e+03 -1.65e+03  2.94e-10  1.43e+02 \n",
            "   900| 1.58e-04  4.60e-03  3.11e-02 -1.65e+03 -1.55e+03  2.35e-10  1.62e+02 \n",
            "  1000| 1.39e-04  3.35e-03  9.50e-04 -1.65e+03 -1.66e+03  3.23e-10  1.81e+02 \n",
            "  1100| 1.03e-04  1.22e-03  7.49e-03 -1.65e+03 -1.63e+03  2.80e-10  1.99e+02 \n",
            "  1200| 1.20e-04  1.71e-03  1.21e-02 -1.65e+03 -1.61e+03  5.04e-10  2.17e+02 \n",
            "  1300| 1.05e-04  1.93e-03  4.12e-03 -1.65e+03 -1.64e+03  2.01e-10  2.35e+02 \n",
            "  1400| 8.95e-05  2.61e-03  5.03e-04 -1.66e+03 -1.66e+03  3.90e-11  2.53e+02 \n",
            "  1500| 1.06e-04  2.19e-03  1.62e-02 -1.65e+03 -1.60e+03  2.57e-10  2.70e+02 \n",
            "  1600| 8.23e-05  1.80e-03  1.68e-03 -1.66e+03 -1.65e+03  1.34e-10  2.88e+02 \n",
            "  1700| 4.96e-05  9.66e-04  6.21e-03 -1.66e+03 -1.64e+03  4.54e-10  3.06e+02 \n",
            "  1800| 1.16e-04  2.50e-03  1.05e-03 -1.66e+03 -1.66e+03  1.36e-10  3.25e+02 \n",
            "  1900| 7.27e-05  8.43e-04  4.69e-03 -1.66e+03 -1.64e+03  4.33e-10  3.44e+02 \n",
            "  2000| 4.75e-05  1.27e-03  5.65e-04 -1.66e+03 -1.65e+03  1.58e-10  3.62e+02 \n",
            "  2100| 3.80e-05  7.55e-04  1.41e-03 -1.66e+03 -1.65e+03  1.10e-10  3.80e+02 \n",
            "  2200| 5.93e-05  1.50e-03  9.15e-03 -1.66e+03 -1.63e+03  1.36e-10  3.98e+02 \n",
            "  2300| 5.33e-05  1.27e-03  6.50e-03 -1.66e+03 -1.64e+03  1.09e-10  4.16e+02 \n",
            "  2400| 4.53e-05  1.11e-03  1.32e-03 -1.66e+03 -1.66e+03  6.24e-10  4.35e+02 \n",
            "  2500| 4.79e-05  7.28e-04  6.70e-04 -1.66e+03 -1.66e+03  1.04e-10  4.52e+02 \n",
            "  2600| 4.22e-05  6.59e-04  2.58e-03 -1.66e+03 -1.65e+03  2.82e-10  4.70e+02 \n",
            "  2700| 1.85e-05  7.67e-04  1.18e-03 -1.66e+03 -1.66e+03  4.04e-10  4.87e+02 \n",
            "  2800| 2.38e-05  5.43e-04  2.90e-03 -1.66e+03 -1.65e+03  3.08e-10  5.05e+02 \n",
            "  2900| 3.02e-05  3.49e-04  1.77e-03 -1.66e+03 -1.65e+03  2.54e-10  5.22e+02 \n",
            "  3000| 3.62e-05  7.58e-04  2.72e-04 -1.66e+03 -1.66e+03  2.25e-10  5.40e+02 \n",
            "  3100| 2.00e-05  4.67e-04  2.75e-03 -1.66e+03 -1.65e+03  3.29e-10  5.58e+02 \n",
            "  3200| 3.95e-05  1.25e-03  4.73e-03 -1.66e+03 -1.64e+03  1.04e-10  5.76e+02 \n",
            "  3300| 2.24e-05  8.61e-04  4.11e-03 -1.66e+03 -1.65e+03  4.79e-11  5.94e+02 \n",
            "  3400| 1.27e-05  3.33e-04  4.25e-04 -1.66e+03 -1.66e+03  1.21e-10  6.10e+02 \n",
            "  3500| 1.55e-05  2.36e-04  1.23e-03 -1.66e+03 -1.65e+03  1.83e-10  6.27e+02 \n",
            "  3600| 1.41e-05  4.36e-04  3.58e-04 -1.66e+03 -1.66e+03  6.21e-13  6.44e+02 \n",
            "  3700| 1.98e-05  7.13e-04  3.33e-03 -1.66e+03 -1.65e+03  2.35e-10  6.61e+02 \n",
            "  3800| 2.97e-05  5.95e-04  1.07e-03 -1.66e+03 -1.66e+03  6.01e-10  6.76e+02 \n",
            "  3900| 3.66e-05  6.85e-04  4.69e-04 -1.66e+03 -1.66e+03  1.93e-10  6.91e+02 \n",
            "  4000| 1.19e-05  2.36e-04  3.29e-04 -1.66e+03 -1.66e+03  1.13e-10  7.06e+02 \n",
            "  4100| 1.72e-05  1.90e-04  1.50e-04 -1.66e+03 -1.66e+03  3.25e-10  7.21e+02 \n",
            "  4200| 1.28e-05  2.00e-04  3.82e-04 -1.66e+03 -1.66e+03  1.90e-10  7.36e+02 \n",
            "  4300| 6.38e-06  1.06e-04  7.31e-04 -1.66e+03 -1.66e+03  6.18e-10  7.52e+02 \n",
            "  4400| 1.28e-05  1.37e-04  1.37e-04 -1.66e+03 -1.66e+03  5.47e-10  7.67e+02 \n",
            "  4500| 9.69e-06  1.81e-04  1.00e-04 -1.66e+03 -1.66e+03  2.31e-10  7.83e+02 \n",
            "  4600| 9.63e-06  2.91e-04  1.37e-03 -1.66e+03 -1.65e+03  7.45e-11  7.97e+02 \n",
            "  4700| 1.55e-05  2.46e-04  4.33e-05 -1.66e+03 -1.66e+03  8.03e-12  8.12e+02 \n",
            "  4800| 1.20e-05  3.60e-04  1.02e-03 -1.66e+03 -1.66e+03  8.91e-11  8.28e+02 \n",
            "  4900| 8.91e-06  2.30e-04  1.12e-03 -1.66e+03 -1.66e+03  6.28e-10  8.43e+02 \n",
            "  5000| 4.78e-06  1.63e-04  8.34e-04 -1.66e+03 -1.66e+03  3.02e-10  8.59e+02 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved/Inaccurate\n",
            "Hit max_iters, solution may be inaccurate\n",
            "Timing: Solve time: 8.59e+02s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 2.32e-02s\n",
            "\tCones: avg projection time: 8.65e-03s\n",
            "\tAcceleration: avg step time: 1.13e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.1921e-07, dist(y, K*) = 1.2152e-05, s'y/|s||y| = 1.3807e-10\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.7832e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 1.6339e-04\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 8.3385e-04\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1658.9574, -b'y = -1656.1922\n",
            "============================================================================\n",
            "time elapsed: 863.4114470481873\n",
            "exact val: 459.297428039594\n",
            "pair 13168 7506\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 3.93e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.45e+25 -1.10e+20  2.38e+28  8.79e-02 \n",
            "   100| 1.09e-03  2.24e-02  9.72e-01 -1.46e+03 -2.04e+01  1.52e-10  1.53e+01 \n",
            "   200| 1.79e-03  1.61e-02  1.83e-01 -1.81e+03 -2.63e+03  2.25e-10  3.02e+01 \n",
            "   300| 3.09e-04  4.91e-03  2.18e-02 -1.84e+03 -1.76e+03  3.73e-11  4.56e+01 \n",
            "   400| 3.63e-04  4.01e-03  2.02e-02 -1.85e+03 -1.78e+03  2.66e-10  6.04e+01 \n",
            "   500| 2.03e-04  3.34e-03  1.78e-02 -1.85e+03 -1.78e+03  1.08e-10  7.56e+01 \n",
            "   600| 1.77e-04  5.07e-03  1.99e-02 -1.85e+03 -1.78e+03  2.25e-10  9.05e+01 \n",
            "   700| 2.66e-04  3.48e-03  1.02e-02 -1.85e+03 -1.81e+03  5.08e-10  1.05e+02 \n",
            "   800| 1.82e-04  4.71e-03  6.59e-03 -1.85e+03 -1.83e+03  2.30e-10  1.19e+02 \n",
            "   900| 1.87e-04  2.62e-03  1.03e-02 -1.85e+03 -1.82e+03  3.21e-10  1.34e+02 \n",
            "  1000| 1.65e-04  2.34e-03  1.26e-02 -1.86e+03 -1.81e+03  2.88e-10  1.49e+02 \n",
            "  1100| 1.69e-04  2.33e-03  1.20e-02 -1.86e+03 -1.81e+03  2.35e-10  1.64e+02 \n",
            "  1200| 2.25e-04  4.41e-03  1.33e-02 -1.86e+03 -1.81e+03  2.33e-10  1.79e+02 \n",
            "  1300| 2.07e-04  4.41e-03  1.06e-03 -1.86e+03 -1.85e+03  2.73e-10  1.95e+02 \n",
            "  1400| 1.86e-04  2.34e-03  5.57e-03 -1.86e+03 -1.84e+03  5.32e-11  2.09e+02 \n",
            "  1500| 1.06e-04  1.31e-03  3.28e-03 -1.86e+03 -1.85e+03  3.16e-10  2.24e+02 \n",
            "  1600| 7.87e-05  1.35e-03  4.74e-03 -1.86e+03 -1.84e+03  2.01e-10  2.39e+02 \n",
            "  1700| 5.84e-05  1.65e-03  3.10e-03 -1.86e+03 -1.85e+03  4.71e-10  2.54e+02 \n",
            "  1800| 1.51e-04  3.76e-03  2.71e-03 -1.86e+03 -1.87e+03  3.21e-10  2.69e+02 \n",
            "  1900| 1.75e-04  1.82e-03  3.80e-04 -1.86e+03 -1.87e+03  2.82e-10  2.84e+02 \n",
            "  2000| 5.70e-05  7.59e-04  2.35e-03 -1.86e+03 -1.85e+03  2.79e-10  2.98e+02 \n",
            "  2100| 3.98e-05  6.61e-04  3.11e-03 -1.86e+03 -1.85e+03  7.29e-11  3.13e+02 \n",
            "  2200| 8.14e-05  8.47e-04  1.91e-03 -1.87e+03 -1.86e+03  1.44e-10  3.28e+02 \n",
            "  2300| 7.95e-05  1.58e-03  3.49e-03 -1.86e+03 -1.85e+03  2.68e-10  3.44e+02 \n",
            "  2400| 8.65e-05  1.02e-03  9.76e-04 -1.86e+03 -1.86e+03  5.01e-10  3.59e+02 \n",
            "  2500| 6.51e-05  9.01e-04  2.82e-03 -1.86e+03 -1.85e+03  2.49e-10  3.73e+02 \n",
            "  2600| 6.00e-05  1.06e-03  2.56e-03 -1.86e+03 -1.85e+03  3.33e-10  3.89e+02 \n",
            "  2700| 5.01e-05  7.64e-04  1.75e-03 -1.87e+03 -1.86e+03  1.81e-10  4.04e+02 \n",
            "  2800| 4.05e-05  8.04e-04  2.10e-03 -1.87e+03 -1.86e+03  1.14e-10  4.19e+02 \n",
            "  2900| 4.07e-05  4.19e-04  1.47e-03 -1.87e+03 -1.86e+03  3.15e-10  4.34e+02 \n",
            "  3000| 3.57e-05  5.04e-04  1.22e-03 -1.87e+03 -1.86e+03  5.14e-11  4.48e+02 \n",
            "  3100| 4.17e-05  1.02e-03  2.35e-03 -1.86e+03 -1.86e+03  3.91e-11  4.62e+02 \n",
            "  3200| 7.72e-05  9.56e-04  7.39e-04 -1.87e+03 -1.86e+03  1.68e-10  4.77e+02 \n",
            "  3300| 3.45e-05  1.10e-03  2.57e-04 -1.87e+03 -1.86e+03  3.01e-10  4.93e+02 \n",
            "  3400| 3.03e-05  6.06e-04  2.21e-03 -1.87e+03 -1.86e+03  5.80e-11  5.14e+02 \n",
            "  3500| 4.21e-05  4.52e-04  9.90e-04 -1.87e+03 -1.86e+03  2.31e-10  5.34e+02 \n",
            "  3600| 4.79e-05  9.29e-04  2.58e-03 -1.87e+03 -1.86e+03  1.24e-10  5.49e+02 \n",
            "  3700| 1.72e-05  5.92e-04  1.86e-03 -1.87e+03 -1.86e+03  6.37e-10  5.65e+02 \n",
            "  3800| 1.49e-05  2.61e-04  1.27e-03 -1.87e+03 -1.86e+03  6.34e-11  5.85e+02 \n",
            "  3900| 3.18e-05  4.65e-04  1.37e-03 -1.87e+03 -1.86e+03  2.21e-10  6.09e+02 \n",
            "  4000| 2.67e-05  8.32e-04  1.62e-03 -1.87e+03 -1.86e+03  2.16e-11  6.37e+02 \n",
            "  4100| 3.43e-05  5.19e-04  6.63e-04 -1.87e+03 -1.86e+03  5.10e-10  6.67e+02 \n",
            "  4200| 3.14e-05  6.06e-04  1.71e-03 -1.87e+03 -1.86e+03  2.30e-10  6.98e+02 \n",
            "  4300| 2.94e-05  5.51e-04  1.33e-03 -1.87e+03 -1.86e+03  1.13e-10  7.30e+02 \n",
            "  4400| 1.71e-05  1.91e-04  8.58e-04 -1.87e+03 -1.86e+03  1.71e-10  7.60e+02 \n",
            "  4500| 2.06e-05  2.38e-04  1.02e-03 -1.87e+03 -1.86e+03  1.38e-10  7.92e+02 \n",
            "  4600| 1.40e-05  2.02e-04  1.07e-03 -1.87e+03 -1.86e+03  3.03e-10  8.24e+02 \n",
            "  4700| 3.21e-05  6.08e-04  1.44e-03 -1.87e+03 -1.86e+03  3.35e-10  8.54e+02 \n",
            "  4800| 3.72e-05  4.69e-04  6.92e-04 -1.87e+03 -1.86e+03  3.01e-10  8.73e+02 \n",
            "  4900| 1.74e-05  5.00e-04  6.33e-04 -1.87e+03 -1.86e+03  3.38e-10  8.88e+02 \n",
            "  5000| 1.73e-05  5.36e-04  2.49e-04 -1.87e+03 -1.87e+03  3.36e-10  9.03e+02 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved/Inaccurate\n",
            "Hit max_iters, solution may be inaccurate\n",
            "Timing: Solve time: 9.03e+02s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 2.08e-02s\n",
            "\tCones: avg projection time: 1.15e-02s\n",
            "\tAcceleration: avg step time: 1.19e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.2219e-06, dist(y, K*) = 1.2393e-05, s'y/|s||y| = 3.9932e-10\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 1.7314e-05\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.3632e-04\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.4872e-04\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1866.5007, -b'y = -1867.4297\n",
            "============================================================================\n",
            "time elapsed: 907.516428232193\n",
            "exact val: 138.082535273433\n",
            "pair 40816 39370\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 3.91e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.45e+25 -1.72e+20  2.39e+28  9.34e-02 \n",
            "   100| 1.19e-03  1.87e-02  8.99e-01 -9.29e+02 -4.90e+01  2.45e-10  1.48e+01 \n",
            "   200| 7.46e-04  1.41e-02  9.13e-01 -1.11e+03 -4.96e+01  5.24e-11  3.03e+01 \n",
            "   300| 2.81e-04  3.81e-03  2.89e-02 -1.33e+03 -1.26e+03  2.66e-10  4.64e+01 \n",
            "   400| 2.76e-04  3.93e-03  3.17e-02 -1.34e+03 -1.26e+03  6.36e-11  6.16e+01 \n",
            "   500| 1.77e-04  1.88e-03  1.73e-02 -1.34e+03 -1.30e+03  6.56e-10  8.27e+01 \n",
            "   600| 1.47e-04  3.53e-03  2.00e-02 -1.35e+03 -1.30e+03  6.07e-10  1.09e+02 \n",
            "   700| 1.12e-04  1.42e-03  1.48e-02 -1.35e+03 -1.31e+03  4.24e-10  1.30e+02 \n",
            "   800| 1.02e-04  1.17e-03  1.15e-02 -1.36e+03 -1.32e+03  3.96e-10  1.45e+02 \n",
            "   900| 1.36e-04  1.85e-03  1.06e-02 -1.36e+03 -1.33e+03  1.28e-10  1.70e+02 \n",
            "  1000| 6.98e-05  7.65e-04  5.39e-03 -1.36e+03 -1.34e+03  8.87e-11  1.96e+02 \n",
            "  1100| 1.22e-04  1.61e-03  6.57e-03 -1.36e+03 -1.34e+03  3.78e-12  2.26e+02 \n",
            "  1200| 4.78e-05  1.16e-03  2.73e-03 -1.36e+03 -1.35e+03  5.87e-10  2.57e+02 \n",
            "  1300| 6.02e-05  1.45e-03  2.43e-03 -1.36e+03 -1.35e+03  5.34e-10  2.88e+02 \n",
            "  1400| 7.77e-05  9.76e-04  3.07e-03 -1.36e+03 -1.35e+03  1.08e-10  3.19e+02 \n",
            "  1500| 5.27e-05  1.57e-03  1.01e-03 -1.36e+03 -1.35e+03  8.43e-11  3.49e+02 \n",
            "  1600| 6.74e-05  8.48e-04  4.43e-03 -1.36e+03 -1.35e+03  2.66e-13  3.81e+02 \n",
            "  1700| 9.20e-05  1.27e-03  2.08e-03 -1.36e+03 -1.35e+03  5.73e-11  4.14e+02 \n",
            "  1800| 4.84e-05  1.24e-03  3.64e-03 -1.36e+03 -1.35e+03  1.87e-10  4.45e+02 \n",
            "  1900| 5.40e-05  1.76e-03  1.98e-03 -1.36e+03 -1.35e+03  4.42e-10  4.61e+02 \n",
            "  2000| 1.71e-05  2.68e-04  9.82e-04 -1.36e+03 -1.36e+03  6.69e-10  4.76e+02 \n",
            "  2100| 2.64e-05  8.36e-04  6.62e-04 -1.36e+03 -1.36e+03  1.53e-10  4.91e+02 \n",
            "  2200| 3.13e-05  4.86e-04  9.43e-04 -1.36e+03 -1.36e+03  2.51e-10  5.07e+02 \n",
            "  2300| 2.02e-05  4.75e-04  2.71e-03 -1.36e+03 -1.35e+03  5.19e-10  5.22e+02 \n",
            "  2400| 2.19e-05  4.36e-04  9.82e-04 -1.36e+03 -1.36e+03  1.53e-10  5.37e+02 \n",
            "  2500| 2.37e-05  2.45e-04  3.17e-04 -1.36e+03 -1.36e+03  9.62e-11  5.53e+02 \n",
            "  2600| 2.75e-05  4.44e-04  1.41e-03 -1.36e+03 -1.36e+03  1.36e-10  5.68e+02 \n",
            "  2700| 1.95e-05  3.79e-04  3.65e-04 -1.36e+03 -1.36e+03  2.32e-10  5.83e+02 \n",
            "  2800| 3.02e-05  4.67e-04  3.47e-04 -1.36e+03 -1.36e+03  2.20e-10  5.98e+02 \n",
            "  2900| 2.18e-05  1.72e-04  4.69e-04 -1.36e+03 -1.36e+03  3.05e-10  6.14e+02 \n",
            "  3000| 2.54e-05  3.65e-04  4.83e-04 -1.36e+03 -1.36e+03  1.35e-10  6.29e+02 \n",
            "  3100| 3.30e-05  3.58e-04  9.34e-04 -1.36e+03 -1.36e+03  1.81e-10  6.45e+02 \n",
            "  3200| 1.16e-05  2.46e-04  7.15e-04 -1.36e+03 -1.36e+03  5.02e-10  6.60e+02 \n",
            "  3300| 1.90e-05  3.44e-04  1.24e-04 -1.36e+03 -1.36e+03  3.35e-10  6.76e+02 \n",
            "  3400| 1.74e-05  1.77e-04  6.58e-04 -1.36e+03 -1.36e+03  3.00e-10  6.92e+02 \n",
            "  3500| 1.60e-05  2.64e-04  7.55e-04 -1.36e+03 -1.36e+03  2.12e-11  7.07e+02 \n",
            "  3600| 1.68e-05  3.97e-04  1.09e-04 -1.36e+03 -1.36e+03  1.79e-10  7.22e+02 \n",
            "  3700| 1.15e-05  3.48e-04  7.35e-04 -1.36e+03 -1.36e+03  6.45e-10  7.38e+02 \n",
            "  3800| 1.37e-05  3.46e-04  4.69e-04 -1.36e+03 -1.36e+03  2.32e-10  7.53e+02 \n",
            "  3900| 8.09e-06  1.11e-04  2.75e-04 -1.36e+03 -1.36e+03  1.72e-10  7.68e+02 \n",
            "  4000| 7.75e-06  2.50e-04  5.71e-04 -1.36e+03 -1.36e+03  6.85e-10  7.84e+02 \n",
            "  4100| 5.93e-06  7.37e-05  1.53e-04 -1.36e+03 -1.36e+03  2.34e-11  8.00e+02 \n",
            "  4200| 1.77e-05  2.09e-04  4.17e-04 -1.36e+03 -1.36e+03  1.27e-10  8.15e+02 \n",
            "  4300| 1.00e-05  2.58e-04  7.58e-04 -1.36e+03 -1.36e+03  2.10e-10  8.31e+02 \n",
            "  4400| 7.00e-06  1.05e-04  2.69e-04 -1.36e+03 -1.36e+03  1.54e-10  8.47e+02 \n",
            "  4500| 8.63e-06  1.55e-04  1.06e-04 -1.36e+03 -1.36e+03  1.45e-10  8.63e+02 \n",
            "  4600| 1.69e-05  2.69e-04  5.43e-04 -1.36e+03 -1.36e+03  5.85e-10  8.78e+02 \n",
            "  4660| 5.17e-06  9.21e-05  7.80e-05 -1.36e+03 -1.36e+03  2.29e-10  8.87e+02 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved\n",
            "Timing: Solve time: 8.87e+02s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 2.64e-02s\n",
            "\tCones: avg projection time: 1.16e-02s\n",
            "\tAcceleration: avg step time: 1.23e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.2219e-06, dist(y, K*) = 1.2172e-05, s'y/|s||y| = 3.4090e-10\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.1725e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 9.2063e-05\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 7.8031e-05\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1359.6040, -b'y = -1359.3917\n",
            "============================================================================\n",
            "time elapsed: 891.7790441513062\n",
            "exact val: 256.3855206718765\n",
            "pair 846 16727\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 3.81e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.46e+25 -1.26e+20  2.37e+28  9.14e-02 \n",
            "   100| 1.11e-03  2.35e-02  9.68e-01 -1.36e+03 -2.19e+01  1.22e-10  1.60e+01 \n",
            "   200| 6.18e-04  7.99e-03  2.64e-02 -1.67e+03 -1.58e+03  2.50e-10  3.14e+01 \n",
            "   300| 2.16e-04  5.75e-03  3.80e-02 -1.69e+03 -1.57e+03  2.85e-10  4.61e+01 \n",
            "   400| 1.88e-04  3.43e-03  2.48e-02 -1.70e+03 -1.62e+03  6.15e-10  6.17e+01 \n",
            "   500| 1.47e-04  3.11e-03  1.59e-02 -1.70e+03 -1.65e+03  3.36e-10  7.78e+01 \n",
            "   600| 1.35e-04  2.49e-03  1.53e-02 -1.71e+03 -1.65e+03  3.12e-10  9.29e+01 \n",
            "   700| 1.55e-04  2.61e-03  1.24e-02 -1.71e+03 -1.66e+03  1.59e-10  1.08e+02 \n",
            "   800| 1.58e-04  3.96e-03  1.35e-02 -1.71e+03 -1.67e+03  4.69e-11  1.24e+02 \n",
            "   900| 1.07e-04  2.64e-03  8.09e-03 -1.71e+03 -1.68e+03  1.12e-10  1.39e+02 \n",
            "  1000| 1.31e-04  3.86e-03  9.26e-03 -1.72e+03 -1.68e+03  3.11e-10  1.55e+02 \n",
            "  1100| 1.32e-04  2.60e-03  8.49e-03 -1.71e+03 -1.68e+03  2.69e-10  1.71e+02 \n",
            "  1200| 9.26e-05  1.38e-03  6.38e-03 -1.71e+03 -1.69e+03  1.41e-11  1.86e+02 \n",
            "  1300| 8.25e-05  2.51e-03  3.02e-03 -1.72e+03 -1.71e+03  2.55e-10  2.02e+02 \n",
            "  1400| 1.37e-04  2.98e-03  9.24e-03 -1.72e+03 -1.69e+03  3.13e-10  2.18e+02 \n",
            "  1500| 6.24e-05  8.01e-04  5.90e-03 -1.72e+03 -1.70e+03  4.35e-10  2.34e+02 \n",
            "  1600| 7.83e-05  1.96e-03  4.78e-03 -1.72e+03 -1.70e+03  3.34e-10  2.50e+02 \n",
            "  1700| 1.25e-04  2.34e-03  8.06e-03 -1.72e+03 -1.69e+03  3.14e-10  2.66e+02 \n",
            "  1800| 8.68e-05  1.78e-03  2.48e-03 -1.72e+03 -1.71e+03  6.01e-11  2.82e+02 \n",
            "  1900| 5.19e-05  7.47e-04  4.03e-03 -1.72e+03 -1.70e+03  2.99e-10  2.97e+02 \n",
            "  2000| 7.30e-05  1.22e-03  3.12e-03 -1.72e+03 -1.71e+03  8.70e-11  3.12e+02 \n",
            "  2100| 4.63e-05  5.18e-04  2.13e-03 -1.72e+03 -1.71e+03  3.51e-10  3.28e+02 \n",
            "  2200| 3.87e-05  1.31e-03  4.54e-03 -1.72e+03 -1.70e+03  2.64e-11  3.43e+02 \n",
            "  2300| 2.38e-05  5.87e-04  2.35e-03 -1.72e+03 -1.71e+03  1.25e-10  3.58e+02 \n",
            "  2400| 3.09e-05  3.98e-04  1.95e-03 -1.72e+03 -1.71e+03  1.27e-10  3.74e+02 \n",
            "  2500| 3.47e-05  5.94e-04  1.81e-03 -1.72e+03 -1.71e+03  2.59e-10  3.90e+02 \n",
            "  2600| 3.22e-05  7.58e-04  2.41e-03 -1.72e+03 -1.71e+03  6.76e-10  4.05e+02 \n",
            "  2700| 3.74e-05  5.19e-04  1.03e-03 -1.72e+03 -1.71e+03  6.25e-12  4.21e+02 \n",
            "  2800| 2.08e-05  2.81e-04  1.04e-03 -1.72e+03 -1.71e+03  6.60e-10  4.36e+02 \n",
            "  2900| 3.68e-05  5.80e-04  1.75e-03 -1.72e+03 -1.71e+03  2.92e-10  4.51e+02 \n",
            "  3000| 2.78e-05  6.99e-04  1.33e-03 -1.72e+03 -1.71e+03  8.02e-11  4.66e+02 \n",
            "  3100| 2.18e-05  4.25e-04  8.52e-04 -1.72e+03 -1.72e+03  4.53e-10  4.82e+02 \n",
            "  3200| 1.74e-05  5.64e-04  1.97e-04 -1.72e+03 -1.72e+03  1.39e-10  4.99e+02 \n",
            "  3300| 6.90e-05  1.41e-03  2.19e-03 -1.72e+03 -1.71e+03  6.28e-12  5.15e+02 \n",
            "  3400| 2.61e-05  3.72e-04  1.51e-03 -1.72e+03 -1.71e+03  6.53e-10  5.31e+02 \n",
            "  3500| 3.04e-05  4.74e-04  1.46e-04 -1.72e+03 -1.72e+03  4.26e-10  5.47e+02 \n",
            "  3600| 2.60e-05  7.16e-04  1.15e-03 -1.72e+03 -1.71e+03  2.08e-10  5.63e+02 \n",
            "  3700| 2.10e-05  3.78e-04  9.28e-04 -1.72e+03 -1.72e+03  2.69e-11  5.79e+02 \n",
            "  3800| 1.73e-05  1.99e-04  4.63e-04 -1.72e+03 -1.72e+03  1.93e-10  5.95e+02 \n",
            "  3900| 1.48e-05  1.35e-04  3.27e-04 -1.72e+03 -1.72e+03  6.12e-10  6.11e+02 \n",
            "  4000| 2.19e-05  7.62e-04  1.03e-03 -1.72e+03 -1.72e+03  8.94e-11  6.29e+02 \n",
            "  4100| 1.35e-05  1.32e-04  3.43e-04 -1.72e+03 -1.72e+03  2.48e-10  6.45e+02 \n",
            "  4200| 1.34e-05  1.69e-04  3.16e-04 -1.72e+03 -1.72e+03  2.25e-11  6.60e+02 \n",
            "  4300| 2.34e-05  3.78e-04  9.78e-05 -1.72e+03 -1.72e+03  5.56e-11  6.77e+02 \n",
            "  4400| 1.10e-05  1.61e-04  4.21e-04 -1.72e+03 -1.72e+03  3.54e-10  6.94e+02 \n",
            "  4500| 1.50e-05  2.05e-04  1.10e-04 -1.72e+03 -1.72e+03  1.46e-10  7.09e+02 \n",
            "  4600| 1.63e-05  2.58e-04  3.71e-04 -1.72e+03 -1.72e+03  4.57e-10  7.27e+02 \n",
            "  4700| 1.03e-05  2.02e-04  5.89e-04 -1.72e+03 -1.72e+03  6.33e-10  7.44e+02 \n",
            "  4800| 1.60e-05  3.31e-04  8.58e-05 -1.72e+03 -1.72e+03  1.71e-11  7.60e+02 \n",
            "  4900| 9.54e-06  1.11e-04  3.01e-04 -1.72e+03 -1.72e+03  2.02e-10  7.77e+02 \n",
            "  5000| 8.54e-06  2.10e-04  7.29e-05 -1.72e+03 -1.72e+03  2.11e-10  7.93e+02 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved/Inaccurate\n",
            "Hit max_iters, solution may be inaccurate\n",
            "Timing: Solve time: 7.93e+02s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 2.06e-02s\n",
            "\tCones: avg projection time: 9.48e-03s\n",
            "\tAcceleration: avg step time: 1.05e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 5.0366e-07, dist(y, K*) = 1.2238e-05, s'y/|s||y| = 1.2473e-09\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 8.5415e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.1014e-04\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 7.2880e-05\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1719.0736, -b'y = -1719.3242\n",
            "============================================================================\n",
            "time elapsed: 797.5517008304596\n",
            "exact val: 221.13453306061183\n",
            "pair 31169 7144\n",
            "----------------------------------------------------------------------------\n",
            "\tSCS v2.1.1 - Splitting Conic Solver\n",
            "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
            "----------------------------------------------------------------------------\n",
            "Lin-sys: sparse-direct, nnz in A = 1845536\n",
            "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
            "acceleration_lookback = 10, rho_x = 1.00e-03\n",
            "Variables n = 616224, constraints m = 619360\n",
            "Cones:\tlinear vars: 614656\n",
            "\texp vars: 4704, dual exp vars: 0\n",
            "Setup time: 3.94e+00s\n",
            "----------------------------------------------------------------------------\n",
            " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
            "----------------------------------------------------------------------------\n",
            "     0| 5.76e+21  5.99e+21  1.00e+00 -3.44e+25 -1.21e+20  2.41e+28  9.37e-02 \n",
            "   100| 6.56e-04  1.65e-02  9.29e-01 -1.17e+03 -4.28e+01  2.43e-10  1.59e+01 \n",
            "   200| 6.52e-04  8.65e-03  6.93e-02 -1.47e+03 -1.28e+03  1.64e-10  3.19e+01 \n",
            "   300| 2.07e-04  3.84e-03  2.13e-02 -1.49e+03 -1.43e+03  3.91e-10  4.85e+01 \n",
            "   400| 1.32e-04  2.39e-03  1.81e-02 -1.49e+03 -1.44e+03  1.46e-11  6.37e+01 \n",
            "   500| 1.08e-04  3.13e-03  1.70e-02 -1.49e+03 -1.44e+03  7.25e-11  8.08e+01 \n",
            "   600| 1.21e-04  3.70e-03  5.80e-04 -1.49e+03 -1.49e+03  1.50e-10  9.76e+01 \n",
            "   700| 9.45e-05  2.61e-03  1.75e-03 -1.50e+03 -1.49e+03  5.48e-10  1.14e+02 \n",
            "   800| 8.24e-05  1.15e-03  7.61e-03 -1.50e+03 -1.47e+03  8.30e-12  1.30e+02 \n",
            "   900| 7.98e-05  2.57e-03  4.29e-04 -1.50e+03 -1.50e+03  2.25e-10  1.47e+02 \n",
            "  1000| 8.99e-05  8.93e-04  5.26e-03 -1.50e+03 -1.48e+03  1.79e-10  1.64e+02 \n",
            "  1100| 5.14e-05  1.58e-03  8.21e-03 -1.50e+03 -1.47e+03  5.39e-10  1.80e+02 \n",
            "  1200| 3.74e-05  6.23e-04  5.21e-03 -1.50e+03 -1.48e+03  1.94e-10  1.96e+02 \n",
            "  1300| 3.65e-05  1.27e-03  1.46e-04 -1.50e+03 -1.50e+03  3.74e-10  2.13e+02 \n",
            "  1400| 4.34e-05  1.07e-03  1.64e-03 -1.50e+03 -1.49e+03  2.23e-10  2.29e+02 \n",
            "  1500| 4.28e-05  8.87e-04  1.92e-03 -1.50e+03 -1.49e+03  3.16e-10  2.46e+02 \n",
            "  1600| 4.23e-05  1.61e-03  6.34e-03 -1.50e+03 -1.48e+03  3.07e-10  2.63e+02 \n",
            "  1700| 5.06e-05  9.97e-04  3.87e-03 -1.50e+03 -1.49e+03  3.22e-10  2.78e+02 \n",
            "  1800| 3.26e-05  8.87e-04  3.93e-03 -1.50e+03 -1.49e+03  6.84e-10  2.94e+02 \n",
            "  1900| 2.36e-05  5.40e-04  3.42e-04 -1.50e+03 -1.50e+03  1.34e-10  3.11e+02 \n",
            "  2000| 3.48e-05  4.17e-04  1.78e-03 -1.50e+03 -1.49e+03  2.21e-10  3.26e+02 \n",
            "  2100| 2.94e-05  3.95e-04  9.34e-04 -1.50e+03 -1.50e+03  5.24e-10  3.41e+02 \n",
            "  2200| 5.90e-05  1.18e-03  3.89e-04 -1.50e+03 -1.50e+03  3.18e-10  3.57e+02 \n",
            "  2300| 3.29e-05  9.56e-04  2.86e-04 -1.50e+03 -1.50e+03  5.60e-10  3.72e+02 \n",
            "  2400| 2.42e-05  9.96e-04  3.47e-03 -1.50e+03 -1.49e+03  3.47e-10  3.87e+02 \n",
            "  2500| 4.68e-05  8.42e-04  1.31e-03 -1.50e+03 -1.50e+03  4.06e-10  4.03e+02 \n",
            "  2600| 2.84e-05  3.99e-04  3.46e-04 -1.50e+03 -1.50e+03  4.13e-10  4.18e+02 \n",
            "  2700| 3.29e-05  7.67e-04  2.45e-03 -1.50e+03 -1.49e+03  3.20e-10  4.33e+02 \n",
            "  2800| 3.93e-05  4.80e-04  1.01e-04 -1.50e+03 -1.50e+03  5.04e-10  4.49e+02 \n",
            "  2900| 2.01e-05  3.02e-04  1.27e-03 -1.50e+03 -1.50e+03  1.85e-10  4.64e+02 \n",
            "  3000| 2.22e-05  4.21e-04  3.10e-04 -1.50e+03 -1.50e+03  1.56e-10  4.80e+02 \n",
            "  3100| 2.80e-05  3.74e-04  1.13e-03 -1.50e+03 -1.50e+03  1.42e-10  4.95e+02 \n",
            "  3200| 1.88e-05  4.79e-04  1.10e-05 -1.50e+03 -1.50e+03  1.76e-10  5.10e+02 \n",
            "  3300| 3.51e-05  9.05e-04  6.69e-04 -1.50e+03 -1.50e+03  8.40e-11  5.26e+02 \n",
            "  3400| 2.09e-05  2.64e-04  1.17e-03 -1.50e+03 -1.50e+03  3.35e-10  5.41e+02 \n",
            "  3500| 2.43e-05  3.07e-04  4.56e-04 -1.50e+03 -1.50e+03  4.45e-10  5.57e+02 \n",
            "  3600| 1.75e-05  2.50e-04  1.01e-03 -1.50e+03 -1.50e+03  4.36e-10  5.74e+02 \n",
            "  3700| 2.77e-05  7.18e-04  2.00e-03 -1.50e+03 -1.49e+03  1.27e-10  5.89e+02 \n",
            "  3800| 1.60e-05  5.92e-04  1.04e-03 -1.50e+03 -1.50e+03  2.16e-10  6.05e+02 \n",
            "  3900| 3.04e-05  4.27e-04  7.49e-05 -1.50e+03 -1.50e+03  2.27e-10  6.21e+02 \n",
            "  4000| 1.53e-05  1.48e-04  6.40e-04 -1.50e+03 -1.50e+03  2.16e-11  6.37e+02 \n",
            "  4100| 1.29e-05  3.81e-04  9.20e-04 -1.50e+03 -1.50e+03  5.43e-10  6.52e+02 \n",
            "  4200| 8.84e-06  1.91e-04  2.13e-04 -1.50e+03 -1.50e+03  3.80e-10  6.67e+02 \n",
            "  4300| 1.05e-05  3.65e-04  1.26e-03 -1.50e+03 -1.50e+03  5.32e-10  6.82e+02 \n",
            "  4400| 1.11e-05  1.85e-04  2.95e-04 -1.50e+03 -1.50e+03  1.54e-10  6.97e+02 \n",
            "  4500| 1.56e-05  2.23e-04  4.05e-04 -1.50e+03 -1.50e+03  3.20e-10  7.13e+02 \n",
            "  4600| 1.35e-05  2.24e-04  2.62e-04 -1.50e+03 -1.50e+03  4.64e-10  7.29e+02 \n",
            "  4700| 1.55e-05  1.67e-04  1.23e-04 -1.50e+03 -1.50e+03  1.22e-10  7.44e+02 \n",
            "  4800| 1.23e-05  1.53e-04  7.07e-04 -1.50e+03 -1.50e+03  5.50e-10  7.60e+02 \n",
            "  4900| 9.55e-06  1.51e-04  4.41e-04 -1.50e+03 -1.50e+03  5.39e-10  7.75e+02 \n",
            "  5000| 6.91e-06  1.07e-04  3.62e-04 -1.50e+03 -1.50e+03  6.32e-10  7.91e+02 \n",
            "----------------------------------------------------------------------------\n",
            "Status: Solved/Inaccurate\n",
            "Hit max_iters, solution may be inaccurate\n",
            "Timing: Solve time: 7.91e+02s\n",
            "\tLin-sys: nnz in L factor: 4002712, avg solve time: 2.06e-02s\n",
            "\tCones: avg projection time: 8.39e-03s\n",
            "\tAcceleration: avg step time: 1.06e-01s\n",
            "----------------------------------------------------------------------------\n",
            "Error metrics:\n",
            "dist(s, K) = 1.1921e-07, dist(y, K*) = 1.2315e-05, s'y/|s||y| = 1.0649e-10\n",
            "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.9055e-06\n",
            "dual res:   |A'y + c|_2 / (1 + |c|_2) = 1.0748e-04\n",
            "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.6159e-04\n",
            "----------------------------------------------------------------------------\n",
            "c'x = -1500.8218, -b'y = -1499.7364\n",
            "============================================================================\n",
            "time elapsed: 795.8019144535065\n",
            "exact val: 348.8398254732447\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7RRShOgMVsjZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "4b956d90-e074-444d-d65d-d593ce1b2c22"
      },
      "source": [
        "print(\"COMPUTE REGULARIZED VALUES\")\n",
        "for (id1, id2), uot_opt_val in zip(pairs, uot_opt_val_list):\n",
        "    print('pair', id1, id2)\n",
        "    a = x[id1].astype(np.float64)\n",
        "    b = x[id2].astype(np.float64)\n",
        "    a = a.reshape(-1, 1)\n",
        "    b = b.reshape(-1, 1)\n",
        "    a[a == 0] = 1e-6\n",
        "    b[b == 0] = 1e-6\n",
        "    k_list_empirical_eps = []\n",
        "    k_list_formula_eps = []\n",
        "    for eps in eps_list:\n",
        "        start = time()\n",
        "        eta, k = get_eta_k(eps, a, b, tau, 784)\n",
        "        k_list_empirical_eps.append(k)\n",
        "        print('eps:', eps, 'eta:', eta, 'k:', k)\n",
        "        u, v, info = sinkhorn_uot(C, a, b, eta=eta, t1=tau, t2=tau, n_iter=10000000, eps=eps, opt_val=uot_opt_val,\n",
        "                                  vbo=True)\n",
        "        print('time elapsed:', time() - start)\n",
        "        print('approx val:', info['unreg_f_val_list'][-1])\n",
        "        print(info['stop_iter'])\n",
        "        k_list_formula_eps.append(info['stop_iter'])\n",
        "        \n",
        "    k_list_empirical_first.append(k_list_empirical_eps)\n",
        "    k_list_formula.append(k_list_empirical_eps)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "COMPUTE REGULARIZED VALUES\n",
            "pair 3 5\n",
            "eps: 5.0 eta: 0.002054772460377554 k: 142777.12022134647\n",
            "iteration=1000, elapsed=10.117, f_dual=1542.339, f_primal=457.316, f_unreg=457.796\n",
            "iteration=2000, elapsed=10.126, f_dual=1525.653, f_primal=356.341, f_unreg=356.837\n",
            "iteration=3000, elapsed=9.606, f_dual=1517.510, f_primal=339.715, f_unreg=340.218\n",
            "iteration=4000, elapsed=10.597, f_dual=1512.846, f_primal=330.644, f_unreg=331.153\n",
            "iteration=5000, elapsed=11.402, f_dual=1509.963, f_primal=327.409, f_unreg=327.912\n",
            "time elapsed: 53.16999077796936\n",
            "approx val: tensor(326.8374, dtype=torch.float64)\n",
            "5115\n",
            "eps: 4.5 eta: 0.0020547724603775545 k: 142777.12022134644\n",
            "iteration=1000, elapsed=11.983, f_dual=1542.339, f_primal=457.316, f_unreg=457.796\n",
            "iteration=2000, elapsed=10.386, f_dual=1525.653, f_primal=356.341, f_unreg=356.837\n",
            "iteration=3000, elapsed=8.515, f_dual=1517.510, f_primal=339.715, f_unreg=340.218\n",
            "iteration=4000, elapsed=10.375, f_dual=1512.846, f_primal=330.644, f_unreg=331.153\n",
            "iteration=5000, elapsed=11.446, f_dual=1509.963, f_primal=327.409, f_unreg=327.912\n",
            "time elapsed: 57.29464268684387\n",
            "approx val: tensor(326.3362, dtype=torch.float64)\n",
            "5379\n",
            "eps: 4.0 eta: 0.002054772460377554 k: 142777.1202213465\n",
            "iteration=1000, elapsed=11.988, f_dual=1542.339, f_primal=457.316, f_unreg=457.796\n",
            "iteration=2000, elapsed=10.827, f_dual=1525.653, f_primal=356.341, f_unreg=356.837\n",
            "iteration=3000, elapsed=10.947, f_dual=1517.510, f_primal=339.715, f_unreg=340.218\n",
            "iteration=4000, elapsed=10.873, f_dual=1512.846, f_primal=330.644, f_unreg=331.153\n",
            "iteration=5000, elapsed=10.748, f_dual=1509.963, f_primal=327.409, f_unreg=327.912\n",
            "time elapsed: 60.88124203681946\n",
            "approx val: tensor(325.8390, dtype=torch.float64)\n",
            "5671\n",
            "eps: 3.5 eta: 0.0020547724603775545 k: 142777.12022134647\n",
            "iteration=1000, elapsed=10.440, f_dual=1542.339, f_primal=457.316, f_unreg=457.796\n",
            "iteration=2000, elapsed=11.421, f_dual=1525.653, f_primal=356.341, f_unreg=356.837\n",
            "iteration=3000, elapsed=10.804, f_dual=1517.510, f_primal=339.715, f_unreg=340.218\n",
            "iteration=4000, elapsed=11.265, f_dual=1512.846, f_primal=330.644, f_unreg=331.153\n",
            "iteration=5000, elapsed=10.760, f_dual=1509.963, f_primal=327.409, f_unreg=327.912\n",
            "iteration=6000, elapsed=10.444, f_dual=1508.053, f_primal=325.311, f_unreg=325.810\n",
            "time elapsed: 65.1809401512146\n",
            "approx val: tensor(325.3389, dtype=torch.float64)\n",
            "6003\n",
            "eps: 3.0 eta: 0.0020547724603775545 k: 142777.12022134644\n",
            "iteration=1000, elapsed=9.800, f_dual=1542.339, f_primal=457.316, f_unreg=457.796\n",
            "iteration=2000, elapsed=9.944, f_dual=1525.653, f_primal=356.341, f_unreg=356.837\n",
            "iteration=3000, elapsed=10.085, f_dual=1517.510, f_primal=339.715, f_unreg=340.218\n",
            "iteration=4000, elapsed=11.580, f_dual=1512.846, f_primal=330.644, f_unreg=331.153\n",
            "iteration=5000, elapsed=11.467, f_dual=1509.963, f_primal=327.409, f_unreg=327.912\n",
            "iteration=6000, elapsed=11.630, f_dual=1508.053, f_primal=325.311, f_unreg=325.810\n",
            "time elapsed: 69.06056308746338\n",
            "approx val: tensor(324.8388, dtype=torch.float64)\n",
            "6385\n",
            "eps: 2.5 eta: 0.002054772460377554 k: 142777.1202213465\n",
            "iteration=1000, elapsed=11.577, f_dual=1542.339, f_primal=457.316, f_unreg=457.796\n",
            "iteration=2000, elapsed=9.580, f_dual=1525.653, f_primal=356.341, f_unreg=356.837\n",
            "iteration=3000, elapsed=10.760, f_dual=1517.510, f_primal=339.715, f_unreg=340.218\n",
            "iteration=4000, elapsed=11.121, f_dual=1512.846, f_primal=330.644, f_unreg=331.153\n",
            "iteration=5000, elapsed=10.460, f_dual=1509.963, f_primal=327.409, f_unreg=327.912\n",
            "iteration=6000, elapsed=10.890, f_dual=1508.053, f_primal=325.311, f_unreg=325.810\n",
            "time elapsed: 72.851487159729\n",
            "approx val: tensor(324.3388, dtype=torch.float64)\n",
            "6835\n",
            "eps: 2.0 eta: 0.0018592114878061314 k: 159406.25343007708\n",
            "iteration=1000, elapsed=8.805, f_dual=1545.171, f_primal=467.029, f_unreg=467.466\n",
            "iteration=2000, elapsed=10.173, f_dual=1527.760, f_primal=362.529, f_unreg=362.973\n",
            "iteration=3000, elapsed=11.223, f_dual=1519.376, f_primal=343.583, f_unreg=344.036\n",
            "iteration=4000, elapsed=8.148, f_dual=1514.298, f_primal=334.155, f_unreg=334.614\n",
            "iteration=5000, elapsed=5.516, f_dual=1511.141, f_primal=328.819, f_unreg=329.277\n",
            "iteration=6000, elapsed=5.445, f_dual=1509.001, f_primal=326.442, f_unreg=326.896\n",
            "iteration=7000, elapsed=5.327, f_dual=1507.526, f_primal=324.834, f_unreg=325.284\n",
            "iteration=8000, elapsed=5.341, f_dual=1506.509, f_primal=323.741, f_unreg=324.188\n",
            "time elapsed: 60.85450792312622\n",
            "approx val: tensor(323.8392, dtype=torch.float64)\n",
            "8161\n",
            "eps: 1.5 eta: 0.0013944086158545986 k: 218722.40421980343\n",
            "iteration=1000, elapsed=5.487, f_dual=1556.017, f_primal=701.717, f_unreg=702.023\n",
            "iteration=2000, elapsed=5.523, f_dual=1534.294, f_primal=386.045, f_unreg=386.376\n",
            "iteration=3000, elapsed=5.476, f_dual=1525.130, f_primal=355.848, f_unreg=356.185\n",
            "iteration=4000, elapsed=5.460, f_dual=1519.275, f_primal=343.692, f_unreg=344.032\n",
            "iteration=5000, elapsed=5.521, f_dual=1515.251, f_primal=335.495, f_unreg=335.841\n",
            "iteration=6000, elapsed=5.491, f_dual=1512.444, f_primal=330.516, f_unreg=330.861\n",
            "iteration=7000, elapsed=5.487, f_dual=1510.422, f_primal=328.245, f_unreg=328.587\n",
            "iteration=8000, elapsed=5.813, f_dual=1508.893, f_primal=326.551, f_unreg=326.891\n",
            "iteration=9000, elapsed=5.530, f_dual=1507.737, f_primal=325.288, f_unreg=325.626\n",
            "iteration=10000, elapsed=5.509, f_dual=1506.862, f_primal=324.344, f_unreg=324.680\n",
            "iteration=11000, elapsed=5.511, f_dual=1506.201, f_primal=323.636, f_unreg=323.971\n",
            "time elapsed: 65.93122243881226\n",
            "approx val: tensor(323.3389, dtype=torch.float64)\n",
            "11925\n",
            "eps: 1.0 eta: 0.0009296057439030657 k: 341155.26016233454\n",
            "iteration=1000, elapsed=5.495, f_dual=1577.032, f_primal=1170.395, f_unreg=1170.585\n",
            "iteration=2000, elapsed=5.511, f_dual=1544.982, f_primal=467.212, f_unreg=467.430\n",
            "iteration=3000, elapsed=5.480, f_dual=1534.191, f_primal=386.738, f_unreg=386.958\n",
            "iteration=4000, elapsed=5.526, f_dual=1527.561, f_primal=362.716, f_unreg=362.938\n",
            "iteration=5000, elapsed=5.482, f_dual=1522.830, f_primal=351.092, f_unreg=351.319\n",
            "iteration=6000, elapsed=5.523, f_dual=1519.169, f_primal=343.795, f_unreg=344.022\n",
            "iteration=7000, elapsed=5.874, f_dual=1516.305, f_primal=336.961, f_unreg=337.193\n",
            "iteration=8000, elapsed=5.506, f_dual=1514.084, f_primal=334.371, f_unreg=334.601\n",
            "iteration=9000, elapsed=5.506, f_dual=1512.335, f_primal=330.624, f_unreg=330.854\n",
            "iteration=10000, elapsed=5.505, f_dual=1510.925, f_primal=329.036, f_unreg=329.265\n",
            "iteration=11000, elapsed=5.529, f_dual=1509.755, f_primal=327.733, f_unreg=327.960\n",
            "iteration=12000, elapsed=5.498, f_dual=1508.784, f_primal=326.659, f_unreg=326.886\n",
            "iteration=13000, elapsed=5.513, f_dual=1507.978, f_primal=325.777, f_unreg=326.003\n",
            "iteration=14000, elapsed=5.486, f_dual=1507.309, f_primal=325.051, f_unreg=325.275\n",
            "iteration=15000, elapsed=5.513, f_dual=1506.754, f_primal=324.452, f_unreg=324.676\n",
            "iteration=16000, elapsed=5.474, f_dual=1506.293, f_primal=323.958, f_unreg=324.181\n",
            "iteration=17000, elapsed=5.517, f_dual=1505.910, f_primal=323.550, f_unreg=323.773\n",
            "iteration=18000, elapsed=6.037, f_dual=1505.592, f_primal=323.214, f_unreg=323.436\n",
            "iteration=19000, elapsed=5.487, f_dual=1505.328, f_primal=322.936, f_unreg=323.157\n",
            "iteration=20000, elapsed=5.508, f_dual=1505.109, f_primal=322.706, f_unreg=322.927\n",
            "time elapsed: 111.38105797767639\n",
            "approx val: tensor(322.8394, dtype=torch.float64)\n",
            "20069\n",
            "eps: 0.5 eta: 0.00046480287195153284 k: 727020.2633245726\n",
            "iteration=1000, elapsed=5.429, f_dual=1631.948, f_primal=3480.629, f_unreg=3480.707\n",
            "iteration=2000, elapsed=5.487, f_dual=1576.947, f_primal=1170.466, f_unreg=1170.561\n",
            "iteration=3000, elapsed=5.434, f_dual=1555.832, f_primal=701.882, f_unreg=701.984\n",
            "iteration=4000, elapsed=5.469, f_dual=1544.887, f_primal=467.310, f_unreg=467.419\n",
            "iteration=5000, elapsed=5.510, f_dual=1538.508, f_primal=410.025, f_unreg=410.133\n",
            "iteration=6000, elapsed=5.569, f_dual=1534.093, f_primal=387.744, f_unreg=387.853\n",
            "iteration=7000, elapsed=5.489, f_dual=1530.484, f_primal=371.291, f_unreg=371.403\n",
            "iteration=8000, elapsed=5.558, f_dual=1527.463, f_primal=362.820, f_unreg=362.932\n",
            "iteration=9000, elapsed=5.763, f_dual=1524.926, f_primal=356.173, f_unreg=356.285\n",
            "iteration=10000, elapsed=5.699, f_dual=1522.728, f_primal=351.199, f_unreg=351.313\n",
            "iteration=11000, elapsed=5.600, f_dual=1520.776, f_primal=346.013, f_unreg=346.126\n",
            "iteration=12000, elapsed=5.569, f_dual=1519.066, f_primal=343.902, f_unreg=344.015\n",
            "iteration=13000, elapsed=5.641, f_dual=1517.522, f_primal=340.804, f_unreg=340.918\n",
            "iteration=14000, elapsed=5.595, f_dual=1516.199, f_primal=337.070, f_unreg=337.186\n",
            "iteration=15000, elapsed=5.363, f_dual=1515.036, f_primal=335.710, f_unreg=335.825\n",
            "iteration=16000, elapsed=5.318, f_dual=1513.978, f_primal=334.480, f_unreg=334.595\n",
            "iteration=17000, elapsed=5.312, f_dual=1513.037, f_primal=331.652, f_unreg=331.767\n",
            "iteration=18000, elapsed=5.342, f_dual=1512.227, f_primal=330.733, f_unreg=330.848\n",
            "iteration=19000, elapsed=5.303, f_dual=1511.489, f_primal=329.900, f_unreg=330.014\n",
            "iteration=20000, elapsed=5.589, f_dual=1510.817, f_primal=329.145, f_unreg=329.259\n",
            "iteration=21000, elapsed=5.300, f_dual=1510.205, f_primal=328.461, f_unreg=328.575\n",
            "iteration=22000, elapsed=5.344, f_dual=1509.648, f_primal=327.841, f_unreg=327.955\n",
            "iteration=23000, elapsed=5.302, f_dual=1509.139, f_primal=327.279, f_unreg=327.392\n",
            "iteration=24000, elapsed=5.351, f_dual=1508.676, f_primal=326.768, f_unreg=326.881\n",
            "iteration=25000, elapsed=5.327, f_dual=1508.255, f_primal=326.305, f_unreg=326.418\n",
            "iteration=26000, elapsed=5.344, f_dual=1507.870, f_primal=325.885, f_unreg=325.998\n",
            "iteration=27000, elapsed=5.301, f_dual=1507.520, f_primal=325.505, f_unreg=325.617\n",
            "iteration=28000, elapsed=5.344, f_dual=1507.201, f_primal=325.159, f_unreg=325.271\n",
            "iteration=29000, elapsed=5.317, f_dual=1506.911, f_primal=324.845, f_unreg=324.957\n",
            "iteration=30000, elapsed=5.355, f_dual=1506.646, f_primal=324.560, f_unreg=324.672\n",
            "iteration=31000, elapsed=5.962, f_dual=1506.405, f_primal=324.301, f_unreg=324.413\n",
            "iteration=32000, elapsed=5.486, f_dual=1506.185, f_primal=324.066, f_unreg=324.178\n",
            "iteration=33000, elapsed=5.341, f_dual=1505.984, f_primal=323.853, f_unreg=323.964\n",
            "iteration=34000, elapsed=5.300, f_dual=1505.802, f_primal=323.659, f_unreg=323.770\n",
            "iteration=35000, elapsed=5.342, f_dual=1505.635, f_primal=323.482, f_unreg=323.593\n",
            "iteration=36000, elapsed=5.328, f_dual=1505.484, f_primal=323.322, f_unreg=323.433\n",
            "iteration=37000, elapsed=5.313, f_dual=1505.346, f_primal=323.176, f_unreg=323.287\n",
            "iteration=38000, elapsed=5.266, f_dual=1505.220, f_primal=323.044, f_unreg=323.155\n",
            "iteration=39000, elapsed=5.309, f_dual=1505.105, f_primal=322.924, f_unreg=323.034\n",
            "iteration=40000, elapsed=5.271, f_dual=1505.001, f_primal=322.814, f_unreg=322.925\n",
            "iteration=41000, elapsed=5.313, f_dual=1504.906, f_primal=322.715, f_unreg=322.825\n",
            "iteration=42000, elapsed=5.365, f_dual=1504.819, f_primal=322.624, f_unreg=322.735\n",
            "iteration=43000, elapsed=5.298, f_dual=1504.740, f_primal=322.542, f_unreg=322.652\n",
            "iteration=44000, elapsed=5.297, f_dual=1504.668, f_primal=322.467, f_unreg=322.577\n",
            "iteration=45000, elapsed=5.287, f_dual=1504.602, f_primal=322.399, f_unreg=322.509\n",
            "iteration=46000, elapsed=5.302, f_dual=1504.542, f_primal=322.337, f_unreg=322.447\n",
            "iteration=47000, elapsed=5.296, f_dual=1504.488, f_primal=322.281, f_unreg=322.391\n",
            "time elapsed: 256.94957160949707\n",
            "approx val: tensor(322.3394, dtype=torch.float64)\n",
            "47473\n",
            "pair 20562 12428\n",
            "eps: 5.0 eta: 0.0027301867501687686 k: 104339.01480785808\n",
            "iteration=1000, elapsed=5.334, f_dual=1215.063, f_primal=184.765, f_unreg=185.154\n",
            "iteration=2000, elapsed=5.302, f_dual=1210.325, f_primal=175.415, f_unreg=175.822\n",
            "time elapsed: 13.354761123657227\n",
            "approx val: tensor(172.6277, dtype=torch.float64)\n",
            "2492\n",
            "eps: 4.5 eta: 0.002730186750168769 k: 104339.01480785805\n",
            "iteration=1000, elapsed=5.299, f_dual=1215.063, f_primal=184.765, f_unreg=185.154\n",
            "iteration=2000, elapsed=5.350, f_dual=1210.325, f_primal=175.415, f_unreg=175.822\n",
            "time elapsed: 13.43196988105774\n",
            "approx val: tensor(172.1419, dtype=torch.float64)\n",
            "2523\n",
            "eps: 4.0 eta: 0.002730186750168769 k: 104339.01480785807\n",
            "iteration=1000, elapsed=5.335, f_dual=1215.063, f_primal=184.765, f_unreg=185.154\n",
            "iteration=2000, elapsed=5.220, f_dual=1210.325, f_primal=175.415, f_unreg=175.822\n",
            "time elapsed: 13.932687520980835\n",
            "approx val: tensor(171.6441, dtype=torch.float64)\n",
            "2643\n",
            "eps: 3.5 eta: 0.002730186750168769 k: 104339.01480785805\n",
            "iteration=1000, elapsed=5.265, f_dual=1215.063, f_primal=184.765, f_unreg=185.154\n",
            "iteration=2000, elapsed=5.264, f_dual=1210.325, f_primal=175.415, f_unreg=175.822\n",
            "time elapsed: 14.801139116287231\n",
            "approx val: tensor(171.1227, dtype=torch.float64)\n",
            "2807\n",
            "eps: 3.0 eta: 0.0027301867501687686 k: 104339.01480785808\n",
            "iteration=1000, elapsed=5.241, f_dual=1215.063, f_primal=184.765, f_unreg=185.154\n",
            "iteration=2000, elapsed=5.276, f_dual=1210.325, f_primal=175.415, f_unreg=175.822\n",
            "time elapsed: 14.853228330612183\n",
            "approx val: tensor(170.6241, dtype=torch.float64)\n",
            "2827\n",
            "eps: 2.5 eta: 0.0027301867501687686 k: 104339.01480785807\n",
            "iteration=1000, elapsed=5.300, f_dual=1215.063, f_primal=184.765, f_unreg=185.154\n",
            "iteration=2000, elapsed=5.286, f_dual=1210.325, f_primal=175.415, f_unreg=175.822\n",
            "time elapsed: 15.249555110931396\n",
            "approx val: tensor(170.1197, dtype=torch.float64)\n",
            "2875\n",
            "eps: 2.0 eta: 0.0025237256222535387 k: 113807.5302402654\n",
            "iteration=1000, elapsed=5.885, f_dual=1215.612, f_primal=186.155, f_unreg=186.512\n",
            "iteration=2000, elapsed=5.451, f_dual=1210.824, f_primal=176.235, f_unreg=176.610\n",
            "iteration=3000, elapsed=5.479, f_dual=1208.417, f_primal=170.957, f_unreg=171.342\n",
            "time elapsed: 17.87650227546692\n",
            "approx val: tensor(169.6451, dtype=torch.float64)\n",
            "3193\n",
            "eps: 1.5 eta: 0.0018927942166901538 k: 156294.71823730165\n",
            "iteration=1000, elapsed=5.267, f_dual=1217.560, f_primal=189.682, f_unreg=189.946\n",
            "iteration=2000, elapsed=5.316, f_dual=1212.692, f_primal=178.600, f_unreg=178.879\n",
            "iteration=3000, elapsed=5.286, f_dual=1209.945, f_primal=175.306, f_unreg=175.588\n",
            "iteration=4000, elapsed=5.327, f_dual=1208.321, f_primal=171.077, f_unreg=171.366\n",
            "time elapsed: 23.697467803955078\n",
            "approx val: tensor(169.1219, dtype=torch.float64)\n",
            "4471\n",
            "eps: 1.0 eta: 0.0012618628111267694 k: 244068.80249720297\n",
            "iteration=1000, elapsed=5.503, f_dual=1220.118, f_primal=197.058, f_unreg=197.233\n",
            "iteration=2000, elapsed=5.459, f_dual=1215.438, f_primal=186.657, f_unreg=186.835\n",
            "iteration=3000, elapsed=5.498, f_dual=1212.597, f_primal=178.738, f_unreg=178.924\n",
            "iteration=4000, elapsed=5.541, f_dual=1210.636, f_primal=176.426, f_unreg=176.614\n",
            "iteration=5000, elapsed=5.507, f_dual=1209.163, f_primal=174.764, f_unreg=174.952\n",
            "iteration=6000, elapsed=5.462, f_dual=1208.223, f_primal=171.197, f_unreg=171.389\n",
            "iteration=7000, elapsed=5.506, f_dual=1207.783, f_primal=168.573, f_unreg=168.775\n",
            "time elapsed: 39.764066219329834\n",
            "approx val: tensor(168.6450, dtype=torch.float64)\n",
            "7233\n",
            "eps: 0.5 eta: 0.0006309314055633847 k: 521068.4083730001\n",
            "iteration=1000, elapsed=5.348, f_dual=1224.933, f_primal=325.018, f_unreg=325.098\n",
            "iteration=2000, elapsed=5.349, f_dual=1220.040, f_primal=197.147, f_unreg=197.235\n",
            "iteration=3000, elapsed=5.366, f_dual=1217.389, f_primal=189.864, f_unreg=189.952\n",
            "iteration=4000, elapsed=5.320, f_dual=1215.355, f_primal=186.756, f_unreg=186.845\n",
            "iteration=5000, elapsed=5.413, f_dual=1213.756, f_primal=180.619, f_unreg=180.711\n",
            "iteration=6000, elapsed=5.384, f_dual=1212.507, f_primal=178.878, f_unreg=178.971\n",
            "iteration=7000, elapsed=5.397, f_dual=1211.456, f_primal=177.597, f_unreg=177.691\n",
            "iteration=8000, elapsed=5.973, f_dual=1210.546, f_primal=176.525, f_unreg=176.619\n",
            "iteration=9000, elapsed=5.356, f_dual=1209.757, f_primal=175.498, f_unreg=175.592\n",
            "iteration=10000, elapsed=5.564, f_dual=1209.071, f_primal=174.861, f_unreg=174.955\n",
            "iteration=11000, elapsed=5.302, f_dual=1208.503, f_primal=171.975, f_unreg=172.071\n",
            "iteration=12000, elapsed=5.317, f_dual=1208.129, f_primal=171.300, f_unreg=171.396\n",
            "iteration=13000, elapsed=5.313, f_dual=1207.862, f_primal=169.617, f_unreg=169.715\n",
            "iteration=14000, elapsed=5.337, f_dual=1207.682, f_primal=168.676, f_unreg=168.777\n",
            "iteration=15000, elapsed=5.295, f_dual=1207.544, f_primal=168.532, f_unreg=168.633\n",
            "iteration=16000, elapsed=5.341, f_dual=1207.423, f_primal=168.405, f_unreg=168.506\n",
            "iteration=17000, elapsed=5.301, f_dual=1207.316, f_primal=168.294, f_unreg=168.395\n",
            "iteration=18000, elapsed=5.340, f_dual=1207.221, f_primal=168.196, f_unreg=168.297\n",
            "iteration=19000, elapsed=5.666, f_dual=1207.138, f_primal=168.110, f_unreg=168.211\n",
            "time elapsed: 105.6606616973877\n",
            "approx val: tensor(168.1455, dtype=torch.float64)\n",
            "19543\n",
            "pair 2564 12380\n",
            "eps: 5.0 eta: 0.0027737152569132476 k: 102530.8995087205\n",
            "iteration=1000, elapsed=5.306, f_dual=1167.835, f_primal=262.180, f_unreg=262.597\n",
            "iteration=2000, elapsed=5.347, f_dual=1155.803, f_primal=219.961, f_unreg=220.429\n",
            "iteration=3000, elapsed=5.308, f_dual=1151.255, f_primal=213.084, f_unreg=213.546\n",
            "time elapsed: 16.35292887687683\n",
            "approx val: tensor(212.3499, dtype=torch.float64)\n",
            "3065\n",
            "eps: 4.5 eta: 0.0027737152569132476 k: 102530.8995087205\n",
            "iteration=1000, elapsed=5.495, f_dual=1167.835, f_primal=262.180, f_unreg=262.597\n",
            "iteration=2000, elapsed=5.471, f_dual=1155.803, f_primal=219.961, f_unreg=220.429\n",
            "iteration=3000, elapsed=5.481, f_dual=1151.255, f_primal=213.084, f_unreg=213.546\n",
            "time elapsed: 17.891801357269287\n",
            "approx val: tensor(211.8456, dtype=torch.float64)\n",
            "3263\n",
            "eps: 4.0 eta: 0.0027737152569132476 k: 102530.89950872048\n",
            "iteration=1000, elapsed=5.511, f_dual=1167.835, f_primal=262.180, f_unreg=262.597\n",
            "iteration=2000, elapsed=5.467, f_dual=1155.803, f_primal=219.961, f_unreg=220.429\n",
            "iteration=3000, elapsed=5.503, f_dual=1151.255, f_primal=213.084, f_unreg=213.546\n",
            "time elapsed: 18.934767484664917\n",
            "approx val: tensor(211.3443, dtype=torch.float64)\n",
            "3447\n",
            "eps: 3.5 eta: 0.0027737152569132476 k: 102530.89950872048\n",
            "iteration=1000, elapsed=5.566, f_dual=1167.835, f_primal=262.180, f_unreg=262.597\n",
            "iteration=2000, elapsed=5.519, f_dual=1155.803, f_primal=219.961, f_unreg=220.429\n",
            "iteration=3000, elapsed=5.503, f_dual=1151.255, f_primal=213.084, f_unreg=213.546\n",
            "time elapsed: 20.15040373802185\n",
            "approx val: tensor(210.8464, dtype=torch.float64)\n",
            "3645\n",
            "eps: 3.0 eta: 0.002773715256913248 k: 102530.89950872048\n",
            "iteration=1000, elapsed=5.493, f_dual=1167.835, f_primal=262.180, f_unreg=262.597\n",
            "iteration=2000, elapsed=5.493, f_dual=1155.803, f_primal=219.961, f_unreg=220.429\n",
            "iteration=3000, elapsed=5.512, f_dual=1151.255, f_primal=213.084, f_unreg=213.546\n",
            "time elapsed: 21.5512855052948\n",
            "approx val: tensor(210.3472, dtype=torch.float64)\n",
            "3921\n",
            "eps: 2.5 eta: 0.0027737152569132476 k: 102530.89950872051\n",
            "iteration=1000, elapsed=5.335, f_dual=1167.835, f_primal=262.180, f_unreg=262.597\n",
            "iteration=2000, elapsed=5.297, f_dual=1155.803, f_primal=219.961, f_unreg=220.429\n",
            "iteration=3000, elapsed=5.348, f_dual=1151.255, f_primal=213.084, f_unreg=213.546\n",
            "iteration=4000, elapsed=5.349, f_dual=1148.851, f_primal=210.191, f_unreg=210.652\n",
            "time elapsed: 22.662267208099365\n",
            "approx val: tensor(209.8499, dtype=torch.float64)\n",
            "4243\n",
            "eps: 2.0 eta: 0.002566981312785127 k: 111691.58288858103\n",
            "iteration=1000, elapsed=5.296, f_dual=1169.306, f_primal=266.853, f_unreg=267.236\n",
            "iteration=2000, elapsed=5.261, f_dual=1156.758, f_primal=226.775, f_unreg=227.194\n",
            "iteration=3000, elapsed=5.280, f_dual=1151.976, f_primal=213.975, f_unreg=214.404\n",
            "iteration=4000, elapsed=5.274, f_dual=1149.394, f_primal=210.858, f_unreg=211.286\n",
            "iteration=5000, elapsed=5.292, f_dual=1147.877, f_primal=209.189, f_unreg=209.613\n",
            "time elapsed: 26.422414302825928\n",
            "approx val: tensor(209.3487, dtype=torch.float64)\n",
            "5001\n",
            "eps: 1.5 eta: 0.0019252359845888453 k: 153396.63849883166\n",
            "iteration=1000, elapsed=5.286, f_dual=1174.766, f_primal=293.152, f_unreg=293.427\n",
            "iteration=2000, elapsed=5.277, f_dual=1161.503, f_primal=238.795, f_unreg=239.098\n",
            "iteration=3000, elapsed=5.296, f_dual=1155.182, f_primal=219.508, f_unreg=219.832\n",
            "iteration=4000, elapsed=5.275, f_dual=1151.878, f_primal=214.081, f_unreg=214.403\n",
            "iteration=5000, elapsed=5.311, f_dual=1149.812, f_primal=211.676, f_unreg=211.995\n",
            "iteration=6000, elapsed=5.266, f_dual=1148.437, f_primal=210.023, f_unreg=210.342\n",
            "iteration=7000, elapsed=5.531, f_dual=1147.503, f_primal=209.000, f_unreg=209.318\n",
            "time elapsed: 39.275073528289795\n",
            "approx val: tensor(208.8494, dtype=torch.float64)\n",
            "7385\n",
            "eps: 1.0 eta: 0.0012834906563925635 k: 239559.2720660304\n",
            "iteration=1000, elapsed=5.290, f_dual=1182.572, f_primal=331.127, f_unreg=331.301\n",
            "iteration=2000, elapsed=5.258, f_dual=1169.127, f_primal=267.036, f_unreg=267.228\n",
            "iteration=3000, elapsed=5.268, f_dual=1161.416, f_primal=238.955, f_unreg=239.157\n",
            "iteration=4000, elapsed=5.265, f_dual=1156.572, f_primal=227.014, f_unreg=227.224\n",
            "iteration=5000, elapsed=5.276, f_dual=1153.826, f_primal=217.920, f_unreg=218.137\n",
            "iteration=6000, elapsed=5.241, f_dual=1151.781, f_primal=214.188, f_unreg=214.402\n",
            "iteration=7000, elapsed=5.280, f_dual=1150.316, f_primal=212.526, f_unreg=212.739\n",
            "iteration=8000, elapsed=5.240, f_dual=1149.193, f_primal=211.069, f_unreg=211.282\n",
            "iteration=9000, elapsed=5.284, f_dual=1148.337, f_primal=210.127, f_unreg=210.340\n",
            "iteration=10000, elapsed=5.256, f_dual=1147.674, f_primal=209.398, f_unreg=209.610\n",
            "iteration=11000, elapsed=5.946, f_dual=1147.163, f_primal=208.847, f_unreg=209.058\n",
            "iteration=12000, elapsed=5.242, f_dual=1146.767, f_primal=208.425, f_unreg=208.636\n",
            "time elapsed: 66.76540875434875\n",
            "approx val: tensor(208.3498, dtype=torch.float64)\n",
            "12545\n",
            "eps: 0.5 eta: 0.0006417453281962818 k: 511494.0250524103\n",
            "iteration=1000, elapsed=5.301, f_dual=1201.429, f_primal=713.397, f_unreg=713.476\n",
            "iteration=2000, elapsed=5.339, f_dual=1182.481, f_primal=330.843, f_unreg=330.930\n",
            "iteration=3000, elapsed=5.322, f_dual=1174.593, f_primal=293.325, f_unreg=293.416\n",
            "iteration=4000, elapsed=5.342, f_dual=1169.038, f_primal=267.128, f_unreg=267.223\n",
            "iteration=5000, elapsed=5.371, f_dual=1164.705, f_primal=255.335, f_unreg=255.432\n",
            "iteration=6000, elapsed=5.534, f_dual=1161.323, f_primal=239.056, f_unreg=239.157\n",
            "iteration=7000, elapsed=5.498, f_dual=1158.666, f_primal=234.412, f_unreg=234.515\n",
            "iteration=8000, elapsed=5.554, f_dual=1156.476, f_primal=227.114, f_unreg=227.219\n",
            "iteration=9000, elapsed=5.638, f_dual=1154.986, f_primal=219.720, f_unreg=219.828\n",
            "iteration=10000, elapsed=5.538, f_dual=1153.725, f_primal=218.025, f_unreg=218.133\n",
            "iteration=11000, elapsed=5.557, f_dual=1152.621, f_primal=216.739, f_unreg=216.847\n",
            "iteration=12000, elapsed=5.517, f_dual=1151.681, f_primal=214.292, f_unreg=214.399\n",
            "iteration=13000, elapsed=5.564, f_dual=1150.901, f_primal=213.404, f_unreg=213.511\n",
            "iteration=14000, elapsed=5.522, f_dual=1150.216, f_primal=212.630, f_unreg=212.736\n",
            "iteration=15000, elapsed=5.561, f_dual=1149.613, f_primal=211.954, f_unreg=212.060\n",
            "iteration=16000, elapsed=5.517, f_dual=1149.092, f_primal=211.172, f_unreg=211.279\n",
            "iteration=17000, elapsed=5.557, f_dual=1148.636, f_primal=210.670, f_unreg=210.776\n",
            "iteration=18000, elapsed=5.338, f_dual=1148.235, f_primal=210.231, f_unreg=210.337\n",
            "iteration=19000, elapsed=5.301, f_dual=1147.882, f_primal=209.846, f_unreg=209.953\n",
            "iteration=20000, elapsed=5.802, f_dual=1147.572, f_primal=209.507, f_unreg=209.613\n",
            "iteration=21000, elapsed=5.594, f_dual=1147.300, f_primal=209.207, f_unreg=209.313\n",
            "iteration=22000, elapsed=5.626, f_dual=1147.061, f_primal=208.950, f_unreg=209.056\n",
            "iteration=23000, elapsed=5.597, f_dual=1146.850, f_primal=208.725, f_unreg=208.831\n",
            "iteration=24000, elapsed=5.637, f_dual=1146.665, f_primal=208.528, f_unreg=208.634\n",
            "iteration=25000, elapsed=5.616, f_dual=1146.502, f_primal=208.356, f_unreg=208.461\n",
            "iteration=26000, elapsed=5.637, f_dual=1146.359, f_primal=208.205, f_unreg=208.309\n",
            "iteration=27000, elapsed=5.633, f_dual=1146.233, f_primal=208.072, f_unreg=208.177\n",
            "iteration=28000, elapsed=5.623, f_dual=1146.122, f_primal=207.956, f_unreg=208.060\n",
            "iteration=29000, elapsed=5.628, f_dual=1146.025, f_primal=207.854, f_unreg=207.958\n",
            "time elapsed: 164.46618795394897\n",
            "approx val: tensor(207.8502, dtype=torch.float64)\n",
            "29749\n",
            "pair 48485 7605\n",
            "eps: 5.0 eta: 0.0016285718632240947 k: 184417.717256823\n",
            "iteration=1000, elapsed=6.068, f_dual=1989.763, f_primal=585.923, f_unreg=586.200\n",
            "iteration=2000, elapsed=5.561, f_dual=1951.279, f_primal=502.261, f_unreg=502.579\n",
            "iteration=3000, elapsed=5.602, f_dual=1929.466, f_primal=471.353, f_unreg=471.694\n",
            "iteration=4000, elapsed=5.560, f_dual=1914.762, f_primal=455.479, f_unreg=455.832\n",
            "iteration=5000, elapsed=5.611, f_dual=1904.943, f_primal=445.317, f_unreg=445.684\n",
            "iteration=6000, elapsed=5.594, f_dual=1898.046, f_primal=439.099, f_unreg=439.474\n",
            "iteration=7000, elapsed=5.590, f_dual=1893.111, f_primal=434.563, f_unreg=434.944\n",
            "iteration=8000, elapsed=5.607, f_dual=1889.645, f_primal=431.050, f_unreg=431.440\n",
            "iteration=9000, elapsed=5.571, f_dual=1887.155, f_primal=428.797, f_unreg=429.190\n",
            "time elapsed: 53.30390524864197\n",
            "approx val: tensor(428.3529, dtype=torch.float64)\n",
            "9444\n",
            "eps: 4.5 eta: 0.0016285718632240945 k: 184417.7172568231\n",
            "iteration=1000, elapsed=5.275, f_dual=1989.763, f_primal=585.923, f_unreg=586.200\n",
            "iteration=2000, elapsed=5.329, f_dual=1951.279, f_primal=502.261, f_unreg=502.579\n",
            "iteration=3000, elapsed=5.258, f_dual=1929.466, f_primal=471.353, f_unreg=471.694\n",
            "iteration=4000, elapsed=5.262, f_dual=1914.762, f_primal=455.479, f_unreg=455.832\n",
            "iteration=5000, elapsed=5.261, f_dual=1904.943, f_primal=445.317, f_unreg=445.684\n",
            "iteration=6000, elapsed=5.308, f_dual=1898.046, f_primal=439.099, f_unreg=439.474\n",
            "iteration=7000, elapsed=5.324, f_dual=1893.111, f_primal=434.563, f_unreg=434.944\n",
            "iteration=8000, elapsed=5.323, f_dual=1889.645, f_primal=431.050, f_unreg=431.440\n",
            "iteration=9000, elapsed=5.275, f_dual=1887.155, f_primal=428.797, f_unreg=429.190\n",
            "time elapsed: 51.67096400260925\n",
            "approx val: tensor(427.8548, dtype=torch.float64)\n",
            "9756\n",
            "eps: 4.0 eta: 0.0016285718632240945 k: 184417.71725682306\n",
            "iteration=1000, elapsed=5.352, f_dual=1989.763, f_primal=585.923, f_unreg=586.200\n",
            "iteration=2000, elapsed=5.393, f_dual=1951.279, f_primal=502.261, f_unreg=502.579\n",
            "iteration=3000, elapsed=5.349, f_dual=1929.466, f_primal=471.353, f_unreg=471.694\n",
            "iteration=4000, elapsed=5.477, f_dual=1914.762, f_primal=455.479, f_unreg=455.832\n",
            "iteration=5000, elapsed=5.347, f_dual=1904.943, f_primal=445.317, f_unreg=445.684\n",
            "iteration=6000, elapsed=5.385, f_dual=1898.046, f_primal=439.099, f_unreg=439.474\n",
            "iteration=7000, elapsed=5.347, f_dual=1893.111, f_primal=434.563, f_unreg=434.944\n",
            "iteration=8000, elapsed=5.369, f_dual=1889.645, f_primal=431.050, f_unreg=431.440\n",
            "iteration=9000, elapsed=5.269, f_dual=1887.155, f_primal=428.797, f_unreg=429.190\n",
            "iteration=10000, elapsed=5.303, f_dual=1885.364, f_primal=427.101, f_unreg=427.499\n",
            "time elapsed: 54.16411733627319\n",
            "approx val: tensor(427.3560, dtype=torch.float64)\n",
            "10104\n",
            "eps: 3.5 eta: 0.0016285718632240943 k: 184417.7172568231\n",
            "iteration=1000, elapsed=5.295, f_dual=1989.763, f_primal=585.923, f_unreg=586.200\n",
            "iteration=2000, elapsed=5.274, f_dual=1951.279, f_primal=502.261, f_unreg=502.579\n",
            "iteration=3000, elapsed=5.312, f_dual=1929.466, f_primal=471.353, f_unreg=471.694\n",
            "iteration=4000, elapsed=5.261, f_dual=1914.762, f_primal=455.479, f_unreg=455.832\n",
            "iteration=5000, elapsed=5.366, f_dual=1904.943, f_primal=445.317, f_unreg=445.684\n",
            "iteration=6000, elapsed=5.251, f_dual=1898.046, f_primal=439.099, f_unreg=439.474\n",
            "iteration=7000, elapsed=5.297, f_dual=1893.111, f_primal=434.563, f_unreg=434.944\n",
            "iteration=8000, elapsed=5.261, f_dual=1889.645, f_primal=431.050, f_unreg=431.440\n",
            "iteration=9000, elapsed=5.299, f_dual=1887.155, f_primal=428.797, f_unreg=429.190\n",
            "iteration=10000, elapsed=5.271, f_dual=1885.364, f_primal=427.101, f_unreg=427.499\n",
            "time elapsed: 55.55706596374512\n",
            "approx val: tensor(426.8544, dtype=torch.float64)\n",
            "10498\n",
            "eps: 3.0 eta: 0.0016285718632240943 k: 184417.71725682312\n",
            "iteration=1000, elapsed=5.276, f_dual=1989.763, f_primal=585.923, f_unreg=586.200\n",
            "iteration=2000, elapsed=5.278, f_dual=1951.279, f_primal=502.261, f_unreg=502.579\n",
            "iteration=3000, elapsed=5.273, f_dual=1929.466, f_primal=471.353, f_unreg=471.694\n",
            "iteration=4000, elapsed=5.297, f_dual=1914.762, f_primal=455.479, f_unreg=455.832\n",
            "iteration=5000, elapsed=5.259, f_dual=1904.943, f_primal=445.317, f_unreg=445.684\n",
            "iteration=6000, elapsed=5.681, f_dual=1898.046, f_primal=439.099, f_unreg=439.474\n",
            "iteration=7000, elapsed=5.254, f_dual=1893.111, f_primal=434.563, f_unreg=434.944\n",
            "iteration=8000, elapsed=5.295, f_dual=1889.645, f_primal=431.050, f_unreg=431.440\n",
            "iteration=9000, elapsed=5.260, f_dual=1887.155, f_primal=428.797, f_unreg=429.190\n",
            "iteration=10000, elapsed=5.291, f_dual=1885.364, f_primal=427.101, f_unreg=427.499\n",
            "time elapsed: 57.94484519958496\n",
            "approx val: tensor(426.3547, dtype=torch.float64)\n",
            "10904\n",
            "eps: 2.5 eta: 0.0016285718632240947 k: 184417.71725682306\n",
            "iteration=1000, elapsed=5.281, f_dual=1989.763, f_primal=585.923, f_unreg=586.200\n",
            "iteration=2000, elapsed=5.239, f_dual=1951.279, f_primal=502.261, f_unreg=502.579\n",
            "iteration=3000, elapsed=5.275, f_dual=1929.466, f_primal=471.353, f_unreg=471.694\n",
            "iteration=4000, elapsed=5.254, f_dual=1914.762, f_primal=455.479, f_unreg=455.832\n",
            "iteration=5000, elapsed=5.265, f_dual=1904.943, f_primal=445.317, f_unreg=445.684\n",
            "iteration=6000, elapsed=5.336, f_dual=1898.046, f_primal=439.099, f_unreg=439.474\n",
            "iteration=7000, elapsed=5.268, f_dual=1893.111, f_primal=434.563, f_unreg=434.944\n",
            "iteration=8000, elapsed=5.280, f_dual=1889.645, f_primal=431.050, f_unreg=431.440\n",
            "iteration=9000, elapsed=5.243, f_dual=1887.155, f_primal=428.797, f_unreg=429.190\n",
            "iteration=10000, elapsed=5.289, f_dual=1885.364, f_primal=427.101, f_unreg=427.499\n",
            "iteration=11000, elapsed=5.269, f_dual=1884.074, f_primal=425.854, f_unreg=426.255\n",
            "time elapsed: 60.238532304763794\n",
            "approx val: tensor(425.8548, dtype=torch.float64)\n",
            "11422\n",
            "eps: 2.0 eta: 0.0014477248561269077 k: 209890.79151938987\n",
            "iteration=1000, elapsed=5.300, f_dual=1996.343, f_primal=604.600, f_unreg=604.838\n",
            "iteration=2000, elapsed=5.270, f_dual=1957.808, f_primal=506.845, f_unreg=507.124\n",
            "iteration=3000, elapsed=5.282, f_dual=1935.587, f_primal=475.957, f_unreg=476.258\n",
            "iteration=4000, elapsed=5.281, f_dual=1920.524, f_primal=464.687, f_unreg=464.994\n",
            "iteration=5000, elapsed=5.270, f_dual=1909.842, f_primal=449.602, f_unreg=449.924\n",
            "iteration=6000, elapsed=5.362, f_dual=1902.329, f_primal=443.220, f_unreg=443.547\n",
            "iteration=7000, elapsed=5.268, f_dual=1896.756, f_primal=438.070, f_unreg=438.404\n",
            "iteration=8000, elapsed=5.554, f_dual=1892.617, f_primal=433.935, f_unreg=434.276\n",
            "iteration=9000, elapsed=5.231, f_dual=1889.596, f_primal=431.093, f_unreg=431.440\n",
            "iteration=10000, elapsed=5.290, f_dual=1887.345, f_primal=429.059, f_unreg=429.408\n",
            "iteration=11000, elapsed=5.242, f_dual=1885.665, f_primal=427.469, f_unreg=427.822\n",
            "iteration=12000, elapsed=5.273, f_dual=1884.410, f_primal=426.303, f_unreg=426.659\n",
            "iteration=13000, elapsed=5.229, f_dual=1883.476, f_primal=425.381, f_unreg=425.739\n",
            "time elapsed: 71.77466082572937\n",
            "approx val: tensor(425.3553, dtype=torch.float64)\n",
            "13548\n",
            "eps: 1.5 eta: 0.0010857936420951807 k: 287794.06530426437\n",
            "iteration=1000, elapsed=5.252, f_dual=2013.907, f_primal=725.974, f_unreg=726.124\n",
            "iteration=2000, elapsed=5.267, f_dual=1973.937, f_primal=540.376, f_unreg=540.572\n",
            "iteration=3000, elapsed=5.245, f_dual=1951.101, f_primal=502.383, f_unreg=502.595\n",
            "iteration=4000, elapsed=6.187, f_dual=1935.470, f_primal=476.024, f_unreg=476.250\n",
            "iteration=5000, elapsed=5.250, f_dual=1923.774, f_primal=467.314, f_unreg=467.543\n",
            "iteration=6000, elapsed=5.292, f_dual=1914.605, f_primal=455.595, f_unreg=455.830\n",
            "iteration=7000, elapsed=5.255, f_dual=1907.650, f_primal=447.827, f_unreg=448.070\n",
            "iteration=8000, elapsed=5.305, f_dual=1902.228, f_primal=443.301, f_unreg=443.547\n",
            "iteration=9000, elapsed=5.373, f_dual=1897.897, f_primal=439.225, f_unreg=439.474\n",
            "iteration=10000, elapsed=5.469, f_dual=1894.434, f_primal=436.229, f_unreg=436.481\n",
            "iteration=11000, elapsed=5.312, f_dual=1891.677, f_primal=433.277, f_unreg=433.533\n",
            "iteration=12000, elapsed=5.330, f_dual=1889.499, f_primal=431.182, f_unreg=431.442\n",
            "iteration=13000, elapsed=5.327, f_dual=1887.752, f_primal=429.605, f_unreg=429.867\n",
            "iteration=14000, elapsed=5.320, f_dual=1886.348, f_primal=428.280, f_unreg=428.544\n",
            "iteration=15000, elapsed=5.670, f_dual=1885.222, f_primal=427.236, f_unreg=427.501\n",
            "iteration=16000, elapsed=5.287, f_dual=1884.316, f_primal=426.394, f_unreg=426.660\n",
            "iteration=17000, elapsed=5.332, f_dual=1883.590, f_primal=425.669, f_unreg=425.937\n",
            "iteration=18000, elapsed=5.289, f_dual=1883.008, f_primal=425.119, f_unreg=425.388\n",
            "time elapsed: 101.56427836418152\n",
            "approx val: tensor(424.8558, dtype=torch.float64)\n",
            "18894\n",
            "eps: 1.0 eta: 0.0007238624280634539 k: 448481.543185832\n",
            "iteration=1000, elapsed=5.325, f_dual=2044.445, f_primal=936.296, f_unreg=936.388\n",
            "iteration=2000, elapsed=5.344, f_dual=1996.084, f_primal=605.264, f_unreg=605.383\n",
            "iteration=3000, elapsed=5.306, f_dual=1973.834, f_primal=540.440, f_unreg=540.571\n",
            "iteration=4000, elapsed=5.347, f_dual=1957.576, f_primal=506.974, f_unreg=507.114\n",
            "iteration=5000, elapsed=5.306, f_dual=1945.049, f_primal=488.488, f_unreg=488.634\n",
            "iteration=6000, elapsed=5.340, f_dual=1935.371, f_primal=476.104, f_unreg=476.254\n",
            "iteration=7000, elapsed=5.394, f_dual=1927.293, f_primal=470.116, f_unreg=470.267\n",
            "iteration=8000, elapsed=5.332, f_dual=1920.318, f_primal=464.840, f_unreg=464.994\n",
            "iteration=9000, elapsed=5.332, f_dual=1914.510, f_primal=455.679, f_unreg=455.836\n",
            "iteration=10000, elapsed=5.316, f_dual=1909.641, f_primal=449.661, f_unreg=449.822\n",
            "iteration=11000, elapsed=5.329, f_dual=1905.613, f_primal=446.314, f_unreg=446.476\n",
            "iteration=12000, elapsed=5.345, f_dual=1902.133, f_primal=443.388, f_unreg=443.552\n",
            "iteration=13000, elapsed=5.353, f_dual=1899.136, f_primal=440.465, f_unreg=440.631\n",
            "iteration=14000, elapsed=5.301, f_dual=1896.563, f_primal=438.246, f_unreg=438.413\n",
            "iteration=15000, elapsed=5.344, f_dual=1894.340, f_primal=436.317, f_unreg=436.485\n",
            "iteration=16000, elapsed=5.303, f_dual=1892.425, f_primal=434.113, f_unreg=434.284\n",
            "iteration=17000, elapsed=5.336, f_dual=1890.801, f_primal=432.670, f_unreg=432.842\n",
            "iteration=18000, elapsed=5.902, f_dual=1889.405, f_primal=431.272, f_unreg=431.446\n",
            "iteration=19000, elapsed=5.637, f_dual=1888.199, f_primal=430.186, f_unreg=430.360\n",
            "iteration=20000, elapsed=5.574, f_dual=1887.156, f_primal=429.239, f_unreg=429.413\n",
            "iteration=21000, elapsed=5.259, f_dual=1886.254, f_primal=428.372, f_unreg=428.548\n",
            "iteration=22000, elapsed=5.266, f_dual=1885.476, f_primal=427.650, f_unreg=427.827\n",
            "iteration=23000, elapsed=5.484, f_dual=1884.804, f_primal=427.027, f_unreg=427.204\n",
            "iteration=24000, elapsed=5.522, f_dual=1884.222, f_primal=426.486, f_unreg=426.663\n",
            "iteration=25000, elapsed=5.490, f_dual=1883.721, f_primal=425.971, f_unreg=426.150\n",
            "iteration=26000, elapsed=5.526, f_dual=1883.289, f_primal=425.565, f_unreg=425.744\n",
            "iteration=27000, elapsed=5.483, f_dual=1882.915, f_primal=425.211, f_unreg=425.391\n",
            "iteration=28000, elapsed=5.525, f_dual=1882.591, f_primal=424.904, f_unreg=425.084\n",
            "iteration=29000, elapsed=5.812, f_dual=1882.321, f_primal=424.434, f_unreg=424.615\n",
            "iteration=30000, elapsed=5.530, f_dual=1882.092, f_primal=424.215, f_unreg=424.397\n",
            "time elapsed: 163.82607555389404\n",
            "approx val: tensor(424.3560, dtype=torch.float64)\n",
            "30202\n",
            "eps: 0.5 eta: 0.0003619312140317269 k: 954387.9937240625\n",
            "iteration=1000, elapsed=5.630, f_dual=2113.577, f_primal=1717.287, f_unreg=1717.330\n",
            "iteration=2000, elapsed=5.576, f_dual=2044.300, f_primal=936.329, f_unreg=936.375\n",
            "iteration=3000, elapsed=5.624, f_dual=2013.669, f_primal=725.909, f_unreg=725.959\n",
            "iteration=4000, elapsed=5.599, f_dual=1995.970, f_primal=605.389, f_unreg=605.448\n",
            "iteration=5000, elapsed=5.623, f_dual=1983.611, f_primal=562.462, f_unreg=562.526\n",
            "iteration=6000, elapsed=5.598, f_dual=1973.725, f_primal=540.501, f_unreg=540.566\n",
            "iteration=7000, elapsed=5.607, f_dual=1965.005, f_primal=527.929, f_unreg=527.997\n",
            "iteration=8000, elapsed=5.603, f_dual=1957.470, f_primal=507.043, f_unreg=507.113\n",
            "iteration=9000, elapsed=5.590, f_dual=1950.895, f_primal=502.528, f_unreg=502.599\n",
            "iteration=10000, elapsed=5.678, f_dual=1944.944, f_primal=488.559, f_unreg=488.631\n",
            "iteration=11000, elapsed=5.568, f_dual=1939.849, f_primal=483.972, f_unreg=484.045\n",
            "iteration=12000, elapsed=5.610, f_dual=1935.267, f_primal=476.179, f_unreg=476.254\n",
            "iteration=13000, elapsed=5.565, f_dual=1931.080, f_primal=473.088, f_unreg=473.164\n",
            "iteration=14000, elapsed=5.614, f_dual=1927.191, f_primal=470.193, f_unreg=470.268\n",
            "iteration=15000, elapsed=5.597, f_dual=1923.576, f_primal=467.473, f_unreg=467.549\n",
            "iteration=16000, elapsed=5.578, f_dual=1920.218, f_primal=464.919, f_unreg=464.995\n",
            "iteration=17000, elapsed=5.617, f_dual=1917.137, f_primal=458.237, f_unreg=458.315\n",
            "iteration=18000, elapsed=5.562, f_dual=1914.410, f_primal=455.760, f_unreg=455.839\n",
            "iteration=19000, elapsed=5.604, f_dual=1911.885, f_primal=453.750, f_unreg=453.829\n",
            "iteration=20000, elapsed=5.641, f_dual=1909.542, f_primal=449.709, f_unreg=449.790\n",
            "iteration=21000, elapsed=5.876, f_dual=1907.455, f_primal=447.997, f_unreg=448.078\n",
            "iteration=22000, elapsed=5.565, f_dual=1905.515, f_primal=446.398, f_unreg=446.479\n",
            "iteration=23000, elapsed=5.590, f_dual=1903.712, f_primal=444.873, f_unreg=444.955\n",
            "iteration=24000, elapsed=5.813, f_dual=1902.036, f_primal=443.473, f_unreg=443.555\n",
            "iteration=25000, elapsed=5.937, f_dual=1900.477, f_primal=442.162, f_unreg=442.244\n",
            "iteration=26000, elapsed=6.009, f_dual=1899.039, f_primal=440.551, f_unreg=440.634\n",
            "iteration=27000, elapsed=5.900, f_dual=1897.707, f_primal=439.399, f_unreg=439.482\n",
            "iteration=28000, elapsed=5.943, f_dual=1896.468, f_primal=438.335, f_unreg=438.419\n",
            "iteration=29000, elapsed=5.927, f_dual=1895.316, f_primal=437.334, f_unreg=437.418\n",
            "iteration=30000, elapsed=5.920, f_dual=1894.245, f_primal=436.404, f_unreg=436.489\n",
            "iteration=31000, elapsed=6.013, f_dual=1893.249, f_primal=435.536, f_unreg=435.620\n",
            "iteration=32000, elapsed=5.895, f_dual=1892.329, f_primal=434.205, f_unreg=434.290\n",
            "iteration=33000, elapsed=5.934, f_dual=1891.488, f_primal=433.455, f_unreg=433.541\n",
            "iteration=34000, elapsed=5.926, f_dual=1890.706, f_primal=432.760, f_unreg=432.845\n",
            "iteration=35000, elapsed=5.807, f_dual=1889.982, f_primal=431.964, f_unreg=432.050\n",
            "iteration=36000, elapsed=5.593, f_dual=1889.310, f_primal=431.362, f_unreg=431.449\n",
            "iteration=37000, elapsed=5.550, f_dual=1888.685, f_primal=430.800, f_unreg=430.887\n",
            "iteration=38000, elapsed=5.593, f_dual=1888.104, f_primal=430.276, f_unreg=430.363\n",
            "iteration=39000, elapsed=5.568, f_dual=1887.564, f_primal=429.786, f_unreg=429.873\n",
            "iteration=40000, elapsed=5.602, f_dual=1887.061, f_primal=429.329, f_unreg=429.416\n",
            "iteration=41000, elapsed=5.639, f_dual=1886.594, f_primal=428.902, f_unreg=428.990\n",
            "iteration=42000, elapsed=5.585, f_dual=1886.159, f_primal=428.462, f_unreg=428.550\n",
            "iteration=43000, elapsed=5.576, f_dual=1885.757, f_primal=428.092, f_unreg=428.180\n",
            "iteration=44000, elapsed=5.571, f_dual=1885.382, f_primal=427.741, f_unreg=427.829\n",
            "iteration=45000, elapsed=5.597, f_dual=1885.034, f_primal=427.419, f_unreg=427.507\n",
            "iteration=46000, elapsed=5.583, f_dual=1884.710, f_primal=427.118, f_unreg=427.207\n",
            "iteration=47000, elapsed=5.596, f_dual=1884.409, f_primal=426.838, f_unreg=426.927\n",
            "iteration=48000, elapsed=5.554, f_dual=1884.129, f_primal=426.577, f_unreg=426.666\n",
            "iteration=49000, elapsed=5.593, f_dual=1883.868, f_primal=426.333, f_unreg=426.422\n",
            "iteration=50000, elapsed=5.581, f_dual=1883.627, f_primal=426.063, f_unreg=426.152\n",
            "iteration=51000, elapsed=5.593, f_dual=1883.403, f_primal=425.852, f_unreg=425.942\n",
            "iteration=52000, elapsed=5.669, f_dual=1883.195, f_primal=425.656, f_unreg=425.746\n",
            "iteration=53000, elapsed=5.553, f_dual=1883.001, f_primal=425.474, f_unreg=425.563\n",
            "iteration=54000, elapsed=5.597, f_dual=1882.821, f_primal=425.303, f_unreg=425.393\n",
            "iteration=55000, elapsed=5.556, f_dual=1882.654, f_primal=425.144, f_unreg=425.234\n",
            "iteration=56000, elapsed=5.598, f_dual=1882.498, f_primal=424.996, f_unreg=425.086\n",
            "iteration=57000, elapsed=5.558, f_dual=1882.354, f_primal=424.659, f_unreg=424.750\n",
            "iteration=58000, elapsed=5.595, f_dual=1882.227, f_primal=424.526, f_unreg=424.617\n",
            "iteration=59000, elapsed=5.579, f_dual=1882.108, f_primal=424.413, f_unreg=424.504\n",
            "iteration=60000, elapsed=5.572, f_dual=1881.998, f_primal=424.307, f_unreg=424.398\n",
            "iteration=61000, elapsed=5.612, f_dual=1881.896, f_primal=424.209, f_unreg=424.300\n",
            "iteration=62000, elapsed=5.570, f_dual=1881.800, f_primal=424.117, f_unreg=424.209\n",
            "iteration=63000, elapsed=6.425, f_dual=1881.712, f_primal=424.032, f_unreg=424.123\n",
            "iteration=64000, elapsed=5.548, f_dual=1881.629, f_primal=423.953, f_unreg=424.044\n",
            "iteration=65000, elapsed=5.586, f_dual=1881.553, f_primal=423.879, f_unreg=423.970\n",
            "iteration=66000, elapsed=5.576, f_dual=1881.481, f_primal=423.810, f_unreg=423.901\n",
            "time elapsed: 378.05074095726013\n",
            "approx val: tensor(423.8561, dtype=torch.float64)\n",
            "66692\n",
            "pair 26428 42698\n",
            "eps: 5.0 eta: 0.003522791207347895 k: 78698.21669077412\n",
            "iteration=1000, elapsed=5.596, f_dual=953.804, f_primal=128.420, f_unreg=128.833\n",
            "time elapsed: 8.847062587738037\n",
            "approx val: tensor(122.4892, dtype=torch.float64)\n",
            "1556\n",
            "eps: 4.5 eta: 0.0035227912073478944 k: 78698.21669077412\n",
            "iteration=1000, elapsed=5.276, f_dual=953.804, f_primal=128.420, f_unreg=128.833\n",
            "time elapsed: 8.596520185470581\n",
            "approx val: tensor(122.0217, dtype=torch.float64)\n",
            "1620\n",
            "eps: 4.0 eta: 0.0035227912073478944 k: 78698.21669077412\n",
            "iteration=1000, elapsed=5.282, f_dual=953.804, f_primal=128.420, f_unreg=128.833\n",
            "time elapsed: 8.851407051086426\n",
            "approx val: tensor(121.5076, dtype=torch.float64)\n",
            "1670\n",
            "eps: 3.5 eta: 0.003522791207347894 k: 78698.21669077412\n",
            "iteration=1000, elapsed=5.261, f_dual=953.804, f_primal=128.420, f_unreg=128.833\n",
            "time elapsed: 10.014925956726074\n",
            "approx val: tensor(121.0234, dtype=torch.float64)\n",
            "1826\n",
            "eps: 3.0 eta: 0.0035227912073478944 k: 78698.21669077415\n",
            "iteration=1000, elapsed=5.253, f_dual=953.804, f_primal=128.420, f_unreg=128.833\n",
            "iteration=2000, elapsed=5.256, f_dual=950.175, f_primal=120.218, f_unreg=120.656\n",
            "time elapsed: 10.632554531097412\n",
            "approx val: tensor(120.5074, dtype=torch.float64)\n",
            "2022\n",
            "eps: 2.5 eta: 0.003522791207347895 k: 78698.21669077412\n",
            "iteration=1000, elapsed=5.264, f_dual=953.804, f_primal=128.420, f_unreg=128.833\n",
            "iteration=2000, elapsed=5.277, f_dual=950.175, f_primal=120.218, f_unreg=120.656\n",
            "time elapsed: 11.221705913543701\n",
            "approx val: tensor(120.0231, dtype=torch.float64)\n",
            "2128\n",
            "eps: 2.0 eta: 0.0033179117139832243 k: 84098.10839861784\n",
            "iteration=1000, elapsed=5.242, f_dual=954.165, f_primal=128.953, f_unreg=129.342\n",
            "iteration=2000, elapsed=5.276, f_dual=950.392, f_primal=120.493, f_unreg=120.905\n",
            "time elapsed: 13.902526140213013\n",
            "approx val: tensor(119.5236, dtype=torch.float64)\n",
            "2644\n",
            "eps: 1.5 eta: 0.002488433785487418 k: 115591.01903184612\n",
            "iteration=1000, elapsed=5.336, f_dual=956.154, f_primal=137.935, f_unreg=138.215\n",
            "iteration=2000, elapsed=5.290, f_dual=951.632, f_primal=123.216, f_unreg=123.517\n",
            "iteration=3000, elapsed=5.328, f_dual=949.821, f_primal=119.725, f_unreg=120.035\n",
            "time elapsed: 20.574812412261963\n",
            "approx val: tensor(119.0117, dtype=torch.float64)\n",
            "3872\n",
            "eps: 1.0 eta: 0.0016589558569916122 k: 180706.2792550925\n",
            "iteration=1000, elapsed=5.445, f_dual=959.299, f_primal=155.518, f_unreg=155.692\n",
            "iteration=2000, elapsed=5.311, f_dual=953.953, f_primal=129.122, f_unreg=129.317\n",
            "iteration=3000, elapsed=5.349, f_dual=951.526, f_primal=123.318, f_unreg=123.518\n",
            "iteration=4000, elapsed=5.315, f_dual=950.176, f_primal=120.700, f_unreg=120.906\n",
            "iteration=5000, elapsed=5.360, f_dual=949.345, f_primal=119.490, f_unreg=119.697\n",
            "iteration=6000, elapsed=5.330, f_dual=948.779, f_primal=118.645, f_unreg=118.852\n",
            "time elapsed: 34.214983224868774\n",
            "approx val: tensor(118.5233, dtype=torch.float64)\n",
            "6388\n",
            "eps: 0.5 eta: 0.0008294779284958061 k: 386455.18161569803\n",
            "iteration=1000, elapsed=5.321, f_dual=967.185, f_primal=321.599, f_unreg=321.682\n",
            "iteration=2000, elapsed=5.340, f_dual=959.194, f_primal=155.602, f_unreg=155.689\n",
            "iteration=3000, elapsed=5.298, f_dual=955.943, f_primal=138.163, f_unreg=138.256\n",
            "iteration=4000, elapsed=5.340, f_dual=953.846, f_primal=129.216, f_unreg=129.313\n",
            "iteration=5000, elapsed=5.300, f_dual=952.383, f_primal=124.396, f_unreg=124.496\n",
            "iteration=6000, elapsed=5.424, f_dual=951.419, f_primal=123.417, f_unreg=123.518\n",
            "iteration=7000, elapsed=5.290, f_dual=950.640, f_primal=121.849, f_unreg=121.951\n",
            "iteration=8000, elapsed=5.329, f_dual=950.068, f_primal=120.803, f_unreg=120.906\n",
            "iteration=9000, elapsed=5.294, f_dual=949.605, f_primal=119.933, f_unreg=120.036\n",
            "iteration=10000, elapsed=5.333, f_dual=949.237, f_primal=119.594, f_unreg=119.697\n",
            "iteration=11000, elapsed=5.340, f_dual=948.925, f_primal=119.305, f_unreg=119.408\n",
            "iteration=12000, elapsed=5.355, f_dual=948.672, f_primal=118.749, f_unreg=118.853\n",
            "iteration=13000, elapsed=5.350, f_dual=948.477, f_primal=118.383, f_unreg=118.487\n",
            "iteration=14000, elapsed=5.338, f_dual=948.320, f_primal=118.236, f_unreg=118.340\n",
            "iteration=15000, elapsed=5.616, f_dual=948.188, f_primal=118.110, f_unreg=118.214\n",
            "iteration=16000, elapsed=5.306, f_dual=948.076, f_primal=118.004, f_unreg=118.108\n",
            "time elapsed: 86.93849682807922\n",
            "approx val: tensor(118.0235, dtype=torch.float64)\n",
            "16238\n",
            "pair 6152 25061\n",
            "eps: 5.0 eta: 0.001770924965001721 k: 168176.0714604547\n",
            "iteration=1000, elapsed=5.314, f_dual=1738.406, f_primal=589.282, f_unreg=589.517\n",
            "iteration=2000, elapsed=5.281, f_dual=1707.474, f_primal=510.766, f_unreg=511.073\n",
            "iteration=3000, elapsed=5.322, f_dual=1691.569, f_primal=493.314, f_unreg=493.641\n",
            "iteration=4000, elapsed=5.280, f_dual=1681.578, f_primal=480.110, f_unreg=480.457\n",
            "iteration=5000, elapsed=5.318, f_dual=1674.803, f_primal=473.104, f_unreg=473.463\n",
            "iteration=6000, elapsed=5.329, f_dual=1670.173, f_primal=468.822, f_unreg=469.188\n",
            "iteration=7000, elapsed=5.293, f_dual=1666.952, f_primal=465.929, f_unreg=466.301\n",
            "time elapsed: 42.11896467208862\n",
            "approx val: tensor(464.2972, dtype=torch.float64)\n",
            "7932\n",
            "eps: 4.5 eta: 0.0017709249650017208 k: 168176.0714604547\n",
            "iteration=1000, elapsed=5.285, f_dual=1738.406, f_primal=589.282, f_unreg=589.517\n",
            "iteration=2000, elapsed=5.287, f_dual=1707.474, f_primal=510.766, f_unreg=511.073\n",
            "iteration=3000, elapsed=5.276, f_dual=1691.569, f_primal=493.314, f_unreg=493.641\n",
            "iteration=4000, elapsed=5.757, f_dual=1681.578, f_primal=480.110, f_unreg=480.457\n",
            "iteration=5000, elapsed=5.265, f_dual=1674.803, f_primal=473.104, f_unreg=473.463\n",
            "iteration=6000, elapsed=5.298, f_dual=1670.173, f_primal=468.822, f_unreg=469.188\n",
            "iteration=7000, elapsed=5.255, f_dual=1666.952, f_primal=465.929, f_unreg=466.301\n",
            "iteration=8000, elapsed=5.297, f_dual=1664.708, f_primal=463.802, f_unreg=464.179\n",
            "time elapsed: 43.96208477020264\n",
            "approx val: tensor(463.7973, dtype=torch.float64)\n",
            "8232\n",
            "eps: 4.0 eta: 0.0017709249650017208 k: 168176.07146045472\n",
            "iteration=1000, elapsed=5.369, f_dual=1738.406, f_primal=589.282, f_unreg=589.517\n",
            "iteration=2000, elapsed=5.397, f_dual=1707.474, f_primal=510.766, f_unreg=511.073\n",
            "iteration=3000, elapsed=5.377, f_dual=1691.569, f_primal=493.314, f_unreg=493.641\n",
            "iteration=4000, elapsed=5.365, f_dual=1681.578, f_primal=480.110, f_unreg=480.457\n",
            "iteration=5000, elapsed=5.392, f_dual=1674.803, f_primal=473.104, f_unreg=473.463\n",
            "iteration=6000, elapsed=5.358, f_dual=1670.173, f_primal=468.822, f_unreg=469.188\n",
            "iteration=7000, elapsed=5.754, f_dual=1666.952, f_primal=465.929, f_unreg=466.301\n",
            "iteration=8000, elapsed=5.347, f_dual=1664.708, f_primal=463.802, f_unreg=464.179\n",
            "time elapsed: 46.44875693321228\n",
            "approx val: tensor(463.2947, dtype=torch.float64)\n",
            "8568\n",
            "eps: 3.5 eta: 0.001770924965001721 k: 168176.0714604547\n",
            "iteration=1000, elapsed=5.361, f_dual=1738.406, f_primal=589.282, f_unreg=589.517\n",
            "iteration=2000, elapsed=5.355, f_dual=1707.474, f_primal=510.766, f_unreg=511.073\n",
            "iteration=3000, elapsed=5.376, f_dual=1691.569, f_primal=493.314, f_unreg=493.641\n",
            "iteration=4000, elapsed=5.375, f_dual=1681.578, f_primal=480.110, f_unreg=480.457\n",
            "iteration=5000, elapsed=5.336, f_dual=1674.803, f_primal=473.104, f_unreg=473.463\n",
            "iteration=6000, elapsed=5.378, f_dual=1670.173, f_primal=468.822, f_unreg=469.188\n",
            "iteration=7000, elapsed=5.334, f_dual=1666.952, f_primal=465.929, f_unreg=466.301\n",
            "iteration=8000, elapsed=5.396, f_dual=1664.708, f_primal=463.802, f_unreg=464.179\n",
            "time elapsed: 48.52901911735535\n",
            "approx val: tensor(462.7966, dtype=torch.float64)\n",
            "8944\n",
            "eps: 3.0 eta: 0.001770924965001721 k: 168176.0714604547\n",
            "iteration=1000, elapsed=5.315, f_dual=1738.406, f_primal=589.282, f_unreg=589.517\n",
            "iteration=2000, elapsed=5.210, f_dual=1707.474, f_primal=510.766, f_unreg=511.073\n",
            "iteration=3000, elapsed=5.243, f_dual=1691.569, f_primal=493.314, f_unreg=493.641\n",
            "iteration=4000, elapsed=5.210, f_dual=1681.578, f_primal=480.110, f_unreg=480.457\n",
            "iteration=5000, elapsed=5.325, f_dual=1674.803, f_primal=473.104, f_unreg=473.463\n",
            "iteration=6000, elapsed=5.277, f_dual=1670.173, f_primal=468.822, f_unreg=469.188\n",
            "iteration=7000, elapsed=5.259, f_dual=1666.952, f_primal=465.929, f_unreg=466.301\n",
            "iteration=8000, elapsed=5.380, f_dual=1664.708, f_primal=463.802, f_unreg=464.179\n",
            "iteration=9000, elapsed=5.569, f_dual=1663.135, f_primal=462.347, f_unreg=462.728\n",
            "time elapsed: 49.88839364051819\n",
            "approx val: tensor(462.2967, dtype=torch.float64)\n",
            "9372\n",
            "eps: 2.5 eta: 0.001770924965001721 k: 168176.07146045472\n",
            "iteration=1000, elapsed=5.306, f_dual=1738.406, f_primal=589.282, f_unreg=589.517\n",
            "iteration=2000, elapsed=5.322, f_dual=1707.474, f_primal=510.766, f_unreg=511.073\n",
            "iteration=3000, elapsed=5.255, f_dual=1691.569, f_primal=493.314, f_unreg=493.641\n",
            "iteration=4000, elapsed=5.237, f_dual=1681.578, f_primal=480.110, f_unreg=480.457\n",
            "iteration=5000, elapsed=5.259, f_dual=1674.803, f_primal=473.104, f_unreg=473.463\n",
            "iteration=6000, elapsed=5.265, f_dual=1670.173, f_primal=468.822, f_unreg=469.188\n",
            "iteration=7000, elapsed=5.257, f_dual=1666.952, f_primal=465.929, f_unreg=466.301\n",
            "iteration=8000, elapsed=5.249, f_dual=1664.708, f_primal=463.802, f_unreg=464.179\n",
            "iteration=9000, elapsed=5.425, f_dual=1663.135, f_primal=462.347, f_unreg=462.728\n",
            "time elapsed: 52.09273624420166\n",
            "approx val: tensor(461.7966, dtype=torch.float64)\n",
            "9818\n",
            "eps: 2.0 eta: 0.0015843660871516126 k: 190083.55364736175\n",
            "iteration=1000, elapsed=5.269, f_dual=1743.773, f_primal=616.964, f_unreg=617.165\n",
            "iteration=2000, elapsed=5.302, f_dual=1711.965, f_primal=521.507, f_unreg=521.765\n",
            "iteration=3000, elapsed=5.259, f_dual=1695.828, f_primal=497.050, f_unreg=497.339\n",
            "iteration=4000, elapsed=5.655, f_dual=1685.262, f_primal=483.374, f_unreg=483.681\n",
            "iteration=5000, elapsed=5.261, f_dual=1677.980, f_primal=476.584, f_unreg=476.900\n",
            "iteration=6000, elapsed=5.279, f_dual=1672.862, f_primal=471.439, f_unreg=471.763\n",
            "iteration=7000, elapsed=5.420, f_dual=1669.171, f_primal=468.012, f_unreg=468.341\n",
            "iteration=8000, elapsed=5.349, f_dual=1666.501, f_primal=465.532, f_unreg=465.866\n",
            "iteration=9000, elapsed=5.265, f_dual=1664.570, f_primal=463.755, f_unreg=464.093\n",
            "iteration=10000, elapsed=5.300, f_dual=1663.164, f_primal=462.454, f_unreg=462.795\n",
            "iteration=11000, elapsed=5.276, f_dual=1662.145, f_primal=461.433, f_unreg=461.777\n",
            "time elapsed: 62.14376735687256\n",
            "approx val: tensor(461.2966, dtype=torch.float64)\n",
            "11656\n",
            "eps: 1.5 eta: 0.0011882745653637094 k: 260698.99628955475\n",
            "iteration=1000, elapsed=5.290, f_dual=1763.526, f_primal=677.074, f_unreg=677.210\n",
            "iteration=2000, elapsed=5.302, f_dual=1724.112, f_primal=561.359, f_unreg=561.529\n",
            "iteration=3000, elapsed=5.659, f_dual=1707.075, f_primal=509.908, f_unreg=510.115\n",
            "iteration=4000, elapsed=5.541, f_dual=1695.729, f_primal=497.138, f_unreg=497.355\n",
            "iteration=5000, elapsed=5.281, f_dual=1687.386, f_primal=485.258, f_unreg=485.486\n",
            "iteration=6000, elapsed=5.270, f_dual=1681.228, f_primal=480.052, f_unreg=480.286\n",
            "iteration=7000, elapsed=5.282, f_dual=1676.435, f_primal=474.824, f_unreg=475.063\n",
            "iteration=8000, elapsed=5.300, f_dual=1672.768, f_primal=471.522, f_unreg=471.765\n",
            "iteration=9000, elapsed=5.297, f_dual=1669.890, f_primal=468.816, f_unreg=469.062\n",
            "iteration=10000, elapsed=5.514, f_dual=1667.638, f_primal=466.809, f_unreg=467.057\n",
            "iteration=11000, elapsed=5.275, f_dual=1665.867, f_primal=465.112, f_unreg=465.363\n",
            "iteration=12000, elapsed=5.387, f_dual=1664.479, f_primal=463.842, f_unreg=464.095\n",
            "iteration=13000, elapsed=5.274, f_dual=1663.384, f_primal=462.831, f_unreg=463.085\n",
            "iteration=14000, elapsed=5.470, f_dual=1662.521, f_primal=462.026, f_unreg=462.282\n",
            "iteration=15000, elapsed=5.502, f_dual=1661.848, f_primal=461.326, f_unreg=461.584\n",
            "iteration=16000, elapsed=5.240, f_dual=1661.318, f_primal=460.824, f_unreg=461.083\n",
            "time elapsed: 89.59020113945007\n",
            "approx val: tensor(460.7974, dtype=torch.float64)\n",
            "16694\n",
            "eps: 1.0 eta: 0.0007921830435758063 k: 406389.8195418092\n",
            "iteration=1000, elapsed=5.222, f_dual=1815.324, f_primal=807.119, f_unreg=807.195\n",
            "iteration=2000, elapsed=5.257, f_dual=1743.566, f_primal=617.057, f_unreg=617.157\n",
            "iteration=3000, elapsed=5.223, f_dual=1724.015, f_primal=561.413, f_unreg=561.527\n",
            "iteration=4000, elapsed=5.275, f_dual=1711.769, f_primal=521.633, f_unreg=521.762\n",
            "iteration=5000, elapsed=5.213, f_dual=1702.820, f_primal=505.490, f_unreg=505.630\n",
            "iteration=6000, elapsed=5.249, f_dual=1695.633, f_primal=497.220, f_unreg=497.364\n",
            "iteration=7000, elapsed=5.219, f_dual=1689.725, f_primal=489.243, f_unreg=489.392\n",
            "iteration=8000, elapsed=5.281, f_dual=1685.070, f_primal=483.531, f_unreg=483.684\n",
            "iteration=9000, elapsed=5.893, f_dual=1681.134, f_primal=480.133, f_unreg=480.289\n",
            "iteration=10000, elapsed=5.236, f_dual=1677.792, f_primal=476.747, f_unreg=476.905\n",
            "iteration=11000, elapsed=5.259, f_dual=1675.019, f_primal=473.753, f_unreg=473.914\n",
            "iteration=12000, elapsed=5.220, f_dual=1672.675, f_primal=471.606, f_unreg=471.768\n",
            "iteration=13000, elapsed=5.811, f_dual=1670.679, f_primal=469.859, f_unreg=470.022\n",
            "iteration=14000, elapsed=5.241, f_dual=1668.987, f_primal=468.182, f_unreg=468.346\n",
            "iteration=15000, elapsed=5.332, f_dual=1667.547, f_primal=466.894, f_unreg=467.060\n",
            "iteration=16000, elapsed=5.412, f_dual=1666.318, f_primal=465.727, f_unreg=465.893\n",
            "iteration=17000, elapsed=5.718, f_dual=1665.276, f_primal=464.743, f_unreg=464.911\n",
            "iteration=18000, elapsed=5.367, f_dual=1664.388, f_primal=463.929, f_unreg=464.098\n",
            "iteration=19000, elapsed=5.277, f_dual=1663.630, f_primal=463.230, f_unreg=463.399\n",
            "iteration=20000, elapsed=5.616, f_dual=1662.983, f_primal=462.629, f_unreg=462.800\n",
            "iteration=21000, elapsed=5.506, f_dual=1662.431, f_primal=462.114, f_unreg=462.285\n",
            "iteration=22000, elapsed=5.621, f_dual=1661.964, f_primal=461.609, f_unreg=461.781\n",
            "iteration=23000, elapsed=5.397, f_dual=1661.567, f_primal=461.234, f_unreg=461.406\n",
            "iteration=24000, elapsed=5.697, f_dual=1661.228, f_primal=460.912, f_unreg=461.085\n",
            "iteration=25000, elapsed=5.677, f_dual=1660.938, f_primal=460.636, f_unreg=460.810\n",
            "iteration=26000, elapsed=5.649, f_dual=1660.691, f_primal=460.400, f_unreg=460.574\n",
            "iteration=27000, elapsed=5.515, f_dual=1660.480, f_primal=460.198, f_unreg=460.372\n",
            "time elapsed: 148.75197100639343\n",
            "approx val: tensor(460.2972, dtype=torch.float64)\n",
            "27414\n",
            "eps: 0.5 eta: 0.00039609152178790314 k: 865249.7800012412\n",
            "iteration=1000, elapsed=5.524, f_dual=1923.418, f_primal=1103.786, f_unreg=1103.821\n",
            "iteration=2000, elapsed=5.566, f_dual=1815.106, f_primal=807.155, f_unreg=807.193\n",
            "iteration=3000, elapsed=5.788, f_dual=1763.264, f_primal=677.096, f_unreg=677.141\n",
            "iteration=4000, elapsed=5.714, f_dual=1743.465, f_primal=617.104, f_unreg=617.154\n",
            "iteration=5000, elapsed=5.520, f_dual=1732.663, f_primal=585.708, f_unreg=585.761\n",
            "iteration=6000, elapsed=5.654, f_dual=1723.920, f_primal=561.469, f_unreg=561.526\n",
            "iteration=7000, elapsed=5.520, f_dual=1717.058, f_primal=528.894, f_unreg=528.957\n",
            "iteration=8000, elapsed=5.530, f_dual=1711.674, f_primal=521.698, f_unreg=521.763\n",
            "iteration=9000, elapsed=5.532, f_dual=1706.881, f_primal=510.051, f_unreg=510.120\n",
            "iteration=10000, elapsed=5.497, f_dual=1702.724, f_primal=505.562, f_unreg=505.632\n",
            "iteration=11000, elapsed=5.514, f_dual=1698.953, f_primal=501.583, f_unreg=501.654\n",
            "iteration=12000, elapsed=5.511, f_dual=1695.538, f_primal=497.295, f_unreg=497.367\n",
            "iteration=13000, elapsed=5.534, f_dual=1692.445, f_primal=494.752, f_unreg=494.824\n",
            "iteration=14000, elapsed=5.854, f_dual=1689.631, f_primal=489.330, f_unreg=489.405\n",
            "iteration=15000, elapsed=5.478, f_dual=1687.196, f_primal=485.416, f_unreg=485.492\n",
            "iteration=16000, elapsed=5.505, f_dual=1684.976, f_primal=483.610, f_unreg=483.687\n",
            "iteration=17000, elapsed=5.474, f_dual=1682.927, f_primal=481.775, f_unreg=481.852\n",
            "iteration=18000, elapsed=5.624, f_dual=1681.041, f_primal=480.214, f_unreg=480.292\n",
            "iteration=19000, elapsed=5.465, f_dual=1679.299, f_primal=478.762, f_unreg=478.840\n",
            "iteration=20000, elapsed=6.004, f_dual=1677.699, f_primal=476.829, f_unreg=476.908\n",
            "iteration=21000, elapsed=5.476, f_dual=1676.249, f_primal=474.983, f_unreg=475.063\n",
            "iteration=22000, elapsed=5.516, f_dual=1674.926, f_primal=473.837, f_unreg=473.917\n",
            "iteration=23000, elapsed=5.853, f_dual=1673.707, f_primal=472.666, f_unreg=472.747\n",
            "iteration=24000, elapsed=5.539, f_dual=1672.583, f_primal=471.691, f_unreg=471.772\n",
            "iteration=25000, elapsed=5.986, f_dual=1671.546, f_primal=470.785, f_unreg=470.866\n",
            "iteration=26000, elapsed=5.532, f_dual=1670.588, f_primal=469.944, f_unreg=470.025\n",
            "iteration=27000, elapsed=5.581, f_dual=1669.706, f_primal=468.986, f_unreg=469.068\n",
            "iteration=28000, elapsed=5.504, f_dual=1668.896, f_primal=468.267, f_unreg=468.349\n",
            "iteration=29000, elapsed=5.571, f_dual=1668.147, f_primal=467.600, f_unreg=467.682\n",
            "iteration=30000, elapsed=5.525, f_dual=1667.456, f_primal=466.980, f_unreg=467.063\n",
            "iteration=31000, elapsed=5.522, f_dual=1666.817, f_primal=466.406, f_unreg=466.489\n",
            "iteration=32000, elapsed=5.520, f_dual=1666.227, f_primal=465.871, f_unreg=465.954\n",
            "iteration=33000, elapsed=5.484, f_dual=1665.685, f_primal=465.286, f_unreg=465.370\n",
            "iteration=34000, elapsed=5.502, f_dual=1665.186, f_primal=464.830, f_unreg=464.914\n",
            "iteration=35000, elapsed=5.520, f_dual=1664.724, f_primal=464.408, f_unreg=464.492\n",
            "iteration=36000, elapsed=5.630, f_dual=1664.298, f_primal=464.016, f_unreg=464.101\n",
            "iteration=37000, elapsed=5.501, f_dual=1663.904, f_primal=463.654, f_unreg=463.738\n",
            "iteration=38000, elapsed=5.542, f_dual=1663.540, f_primal=463.317, f_unreg=463.402\n",
            "iteration=39000, elapsed=5.491, f_dual=1663.204, f_primal=463.006, f_unreg=463.091\n",
            "iteration=40000, elapsed=5.585, f_dual=1662.893, f_primal=462.717, f_unreg=462.802\n",
            "iteration=41000, elapsed=5.559, f_dual=1662.606, f_primal=462.450, f_unreg=462.535\n",
            "iteration=42000, elapsed=5.534, f_dual=1662.341, f_primal=462.202, f_unreg=462.287\n",
            "iteration=43000, elapsed=5.559, f_dual=1662.098, f_primal=461.908, f_unreg=461.994\n",
            "iteration=44000, elapsed=5.786, f_dual=1661.874, f_primal=461.697, f_unreg=461.783\n",
            "iteration=45000, elapsed=5.532, f_dual=1661.668, f_primal=461.503, f_unreg=461.589\n",
            "iteration=46000, elapsed=7.381, f_dual=1661.477, f_primal=461.322, f_unreg=461.408\n",
            "iteration=47000, elapsed=6.279, f_dual=1661.301, f_primal=461.155, f_unreg=461.242\n",
            "iteration=48000, elapsed=5.570, f_dual=1661.138, f_primal=461.001, f_unreg=461.087\n",
            "iteration=49000, elapsed=5.476, f_dual=1660.987, f_primal=460.857, f_unreg=460.944\n",
            "iteration=50000, elapsed=5.552, f_dual=1660.849, f_primal=460.725, f_unreg=460.812\n",
            "iteration=51000, elapsed=5.506, f_dual=1660.720, f_primal=460.602, f_unreg=460.689\n",
            "iteration=52000, elapsed=5.523, f_dual=1660.602, f_primal=460.489, f_unreg=460.576\n",
            "iteration=53000, elapsed=5.418, f_dual=1660.492, f_primal=460.384, f_unreg=460.471\n",
            "iteration=54000, elapsed=5.473, f_dual=1660.391, f_primal=460.287, f_unreg=460.374\n",
            "iteration=55000, elapsed=6.068, f_dual=1660.297, f_primal=460.197, f_unreg=460.284\n",
            "iteration=56000, elapsed=5.487, f_dual=1660.211, f_primal=460.114, f_unreg=460.201\n",
            "iteration=57000, elapsed=5.605, f_dual=1660.131, f_primal=460.037, f_unreg=460.124\n",
            "iteration=58000, elapsed=5.431, f_dual=1660.057, f_primal=459.965, f_unreg=460.053\n",
            "iteration=59000, elapsed=5.466, f_dual=1659.989, f_primal=459.900, f_unreg=459.987\n",
            "iteration=60000, elapsed=5.432, f_dual=1659.926, f_primal=459.839, f_unreg=459.926\n",
            "iteration=61000, elapsed=5.484, f_dual=1659.868, f_primal=459.782, f_unreg=459.870\n",
            "iteration=62000, elapsed=5.471, f_dual=1659.815, f_primal=459.730, f_unreg=459.818\n",
            "time elapsed: 350.1585998535156\n",
            "approx val: tensor(459.7974, dtype=torch.float64)\n",
            "62414\n",
            "pair 13168 7506\n",
            "eps: 5.0 eta: 0.001871346769461299 k: 158268.40509734268\n",
            "iteration=1000, elapsed=5.431, f_dual=1880.303, f_primal=179.531, f_unreg=179.861\n",
            "iteration=2000, elapsed=5.485, f_dual=1873.880, f_primal=152.557, f_unreg=152.908\n",
            "iteration=3000, elapsed=5.433, f_dual=1870.874, f_primal=146.428, f_unreg=146.787\n",
            "time elapsed: 20.647765636444092\n",
            "approx val: tensor(143.0818, dtype=torch.float64)\n",
            "3757\n",
            "eps: 4.5 eta: 0.0018713467694612992 k: 158268.40509734265\n",
            "iteration=1000, elapsed=5.415, f_dual=1880.303, f_primal=179.531, f_unreg=179.861\n",
            "iteration=2000, elapsed=5.945, f_dual=1873.880, f_primal=152.557, f_unreg=152.908\n",
            "iteration=3000, elapsed=5.390, f_dual=1870.874, f_primal=146.428, f_unreg=146.787\n",
            "time elapsed: 22.10822033882141\n",
            "approx val: tensor(142.5818, dtype=torch.float64)\n",
            "3977\n",
            "eps: 4.0 eta: 0.0018713467694612994 k: 158268.4050973426\n",
            "iteration=1000, elapsed=5.368, f_dual=1880.303, f_primal=179.531, f_unreg=179.861\n",
            "iteration=2000, elapsed=5.419, f_dual=1873.880, f_primal=152.557, f_unreg=152.908\n",
            "iteration=3000, elapsed=5.372, f_dual=1870.874, f_primal=146.428, f_unreg=146.787\n",
            "iteration=4000, elapsed=5.360, f_dual=1869.100, f_primal=142.415, f_unreg=142.783\n",
            "time elapsed: 22.391668796539307\n",
            "approx val: tensor(142.0782, dtype=torch.float64)\n",
            "4161\n",
            "eps: 3.5 eta: 0.001871346769461299 k: 158268.40509734268\n",
            "iteration=1000, elapsed=5.424, f_dual=1880.303, f_primal=179.531, f_unreg=179.861\n",
            "iteration=2000, elapsed=5.766, f_dual=1873.880, f_primal=152.557, f_unreg=152.908\n",
            "iteration=3000, elapsed=5.464, f_dual=1870.874, f_primal=146.428, f_unreg=146.787\n",
            "iteration=4000, elapsed=5.825, f_dual=1869.100, f_primal=142.415, f_unreg=142.783\n",
            "time elapsed: 23.874664306640625\n",
            "approx val: tensor(141.5812, dtype=torch.float64)\n",
            "4249\n",
            "eps: 3.0 eta: 0.0018713467694612992 k: 158268.40509734265\n",
            "iteration=1000, elapsed=5.435, f_dual=1880.303, f_primal=179.531, f_unreg=179.861\n",
            "iteration=2000, elapsed=5.840, f_dual=1873.880, f_primal=152.557, f_unreg=152.908\n",
            "iteration=3000, elapsed=5.351, f_dual=1870.874, f_primal=146.428, f_unreg=146.787\n",
            "iteration=4000, elapsed=5.749, f_dual=1869.100, f_primal=142.415, f_unreg=142.783\n",
            "time elapsed: 24.285306692123413\n",
            "approx val: tensor(141.0818, dtype=torch.float64)\n",
            "4355\n",
            "eps: 2.5 eta: 0.001871346769461299 k: 158268.40509734265\n",
            "iteration=1000, elapsed=5.383, f_dual=1880.303, f_primal=179.531, f_unreg=179.861\n",
            "iteration=2000, elapsed=5.400, f_dual=1873.880, f_primal=152.557, f_unreg=152.908\n",
            "iteration=3000, elapsed=5.386, f_dual=1870.874, f_primal=146.428, f_unreg=146.787\n",
            "iteration=4000, elapsed=5.815, f_dual=1869.100, f_primal=142.415, f_unreg=142.783\n",
            "time elapsed: 23.971946477890015\n",
            "approx val: tensor(140.5263, dtype=torch.float64)\n",
            "4369\n",
            "eps: 2.0 eta: 0.001681256608355792 k: 178071.4018442675\n",
            "iteration=1000, elapsed=5.392, f_dual=1881.438, f_primal=192.702, f_unreg=192.995\n",
            "iteration=2000, elapsed=5.682, f_dual=1874.729, f_primal=156.180, f_unreg=156.491\n",
            "iteration=3000, elapsed=5.464, f_dual=1871.597, f_primal=147.698, f_unreg=148.019\n",
            "iteration=4000, elapsed=6.521, f_dual=1869.653, f_primal=144.275, f_unreg=144.601\n",
            "time elapsed: 28.30805277824402\n",
            "approx val: tensor(140.0804, dtype=torch.float64)\n",
            "4963\n",
            "eps: 1.5 eta: 0.001260942456266844 k: 244264.2866832352\n",
            "iteration=1000, elapsed=5.871, f_dual=1884.993, f_primal=224.457, f_unreg=224.668\n",
            "iteration=2000, elapsed=5.559, f_dual=1877.289, f_primal=165.919, f_unreg=166.147\n",
            "iteration=3000, elapsed=5.569, f_dual=1873.682, f_primal=152.518, f_unreg=152.754\n",
            "iteration=4000, elapsed=5.539, f_dual=1871.517, f_primal=147.776, f_unreg=148.017\n",
            "iteration=5000, elapsed=5.554, f_dual=1869.982, f_primal=145.092, f_unreg=145.336\n",
            "iteration=6000, elapsed=5.536, f_dual=1868.927, f_primal=142.248, f_unreg=142.497\n",
            "iteration=7000, elapsed=5.525, f_dual=1868.343, f_primal=139.471, f_unreg=139.725\n",
            "time elapsed: 39.673743724823\n",
            "approx val: tensor(139.5825, dtype=torch.float64)\n",
            "7091\n",
            "eps: 1.0 eta: 0.000840628304177896 k: 380852.9395090108\n",
            "iteration=1000, elapsed=5.649, f_dual=1890.593, f_primal=313.837, f_unreg=313.970\n",
            "iteration=2000, elapsed=5.513, f_dual=1881.287, f_primal=192.842, f_unreg=192.988\n",
            "iteration=3000, elapsed=5.563, f_dual=1877.213, f_primal=165.992, f_unreg=166.145\n",
            "iteration=4000, elapsed=5.502, f_dual=1874.574, f_primal=156.332, f_unreg=156.487\n",
            "iteration=5000, elapsed=5.963, f_dual=1872.767, f_primal=151.465, f_unreg=151.623\n",
            "iteration=6000, elapsed=5.478, f_dual=1871.437, f_primal=147.855, f_unreg=148.016\n",
            "iteration=7000, elapsed=5.494, f_dual=1870.352, f_primal=145.867, f_unreg=146.029\n",
            "iteration=8000, elapsed=5.482, f_dual=1869.491, f_primal=144.488, f_unreg=144.651\n",
            "iteration=9000, elapsed=5.436, f_dual=1868.845, f_primal=142.330, f_unreg=142.496\n",
            "iteration=10000, elapsed=5.491, f_dual=1868.399, f_primal=139.771, f_unreg=139.940\n",
            "iteration=11000, elapsed=5.511, f_dual=1868.131, f_primal=139.420, f_unreg=139.589\n",
            "iteration=12000, elapsed=5.468, f_dual=1867.905, f_primal=139.151, f_unreg=139.320\n",
            "time elapsed: 66.98720145225525\n",
            "approx val: tensor(139.0797, dtype=torch.float64)\n",
            "12077\n",
            "eps: 0.5 eta: 0.000420314152088948 k: 811150.6889674953\n",
            "iteration=1000, elapsed=5.383, f_dual=1904.120, f_primal=833.708, f_unreg=833.768\n",
            "iteration=2000, elapsed=5.449, f_dual=1890.521, f_primal=313.902, f_unreg=313.969\n",
            "iteration=3000, elapsed=5.402, f_dual=1884.850, f_primal=224.595, f_unreg=224.666\n",
            "iteration=4000, elapsed=5.438, f_dual=1881.214, f_primal=192.913, f_unreg=192.986\n",
            "iteration=5000, elapsed=5.404, f_dual=1878.910, f_primal=176.365, f_unreg=176.440\n",
            "iteration=6000, elapsed=5.408, f_dual=1877.137, f_primal=166.067, f_unreg=166.143\n",
            "iteration=7000, elapsed=5.457, f_dual=1875.662, f_primal=164.314, f_unreg=164.390\n",
            "iteration=8000, elapsed=5.367, f_dual=1874.498, f_primal=156.409, f_unreg=156.486\n",
            "iteration=9000, elapsed=5.526, f_dual=1873.526, f_primal=152.669, f_unreg=152.748\n",
            "iteration=10000, elapsed=5.703, f_dual=1872.689, f_primal=151.544, f_unreg=151.623\n",
            "iteration=11000, elapsed=5.507, f_dual=1871.985, f_primal=148.622, f_unreg=148.702\n",
            "iteration=12000, elapsed=5.362, f_dual=1871.358, f_primal=147.935, f_unreg=148.015\n",
            "iteration=13000, elapsed=5.413, f_dual=1870.786, f_primal=146.907, f_unreg=146.988\n",
            "iteration=14000, elapsed=5.392, f_dual=1870.272, f_primal=145.984, f_unreg=146.065\n",
            "iteration=15000, elapsed=5.416, f_dual=1869.821, f_primal=145.253, f_unreg=145.334\n",
            "iteration=16000, elapsed=5.460, f_dual=1869.410, f_primal=144.733, f_unreg=144.814\n",
            "iteration=17000, elapsed=5.366, f_dual=1869.064, f_primal=143.207, f_unreg=143.289\n",
            "iteration=18000, elapsed=5.430, f_dual=1868.763, f_primal=142.416, f_unreg=142.499\n",
            "iteration=19000, elapsed=5.388, f_dual=1868.507, f_primal=141.610, f_unreg=141.693\n",
            "iteration=20000, elapsed=5.412, f_dual=1868.316, f_primal=139.862, f_unreg=139.946\n",
            "iteration=21000, elapsed=6.272, f_dual=1868.175, f_primal=139.638, f_unreg=139.723\n",
            "iteration=22000, elapsed=5.461, f_dual=1868.047, f_primal=139.504, f_unreg=139.589\n",
            "iteration=23000, elapsed=5.407, f_dual=1867.930, f_primal=139.381, f_unreg=139.465\n",
            "iteration=24000, elapsed=5.408, f_dual=1867.821, f_primal=139.236, f_unreg=139.321\n",
            "iteration=25000, elapsed=5.391, f_dual=1867.730, f_primal=138.941, f_unreg=139.026\n",
            "iteration=26000, elapsed=5.440, f_dual=1867.647, f_primal=138.854, f_unreg=138.939\n",
            "iteration=27000, elapsed=5.432, f_dual=1867.571, f_primal=138.614, f_unreg=138.700\n",
            "iteration=28000, elapsed=5.535, f_dual=1867.507, f_primal=138.545, f_unreg=138.631\n",
            "time elapsed: 154.44329595565796\n",
            "approx val: tensor(138.5825, dtype=torch.float64)\n",
            "28245\n",
            "pair 40816 39370\n",
            "eps: 5.0 eta: 0.0023213457741394455 k: 124807.63465139116\n",
            "iteration=1000, elapsed=5.656, f_dual=1378.783, f_primal=294.473, f_unreg=294.851\n",
            "iteration=2000, elapsed=5.640, f_dual=1369.473, f_primal=271.070, f_unreg=271.485\n",
            "iteration=3000, elapsed=5.622, f_dual=1365.327, f_primal=261.030, f_unreg=261.473\n",
            "time elapsed: 17.207849264144897\n",
            "approx val: tensor(261.3850, dtype=torch.float64)\n",
            "3040\n",
            "eps: 4.5 eta: 0.0023213457741394455 k: 124807.63465139111\n",
            "iteration=1000, elapsed=5.536, f_dual=1378.783, f_primal=294.473, f_unreg=294.851\n",
            "iteration=2000, elapsed=5.427, f_dual=1369.473, f_primal=271.070, f_unreg=271.485\n",
            "iteration=3000, elapsed=5.482, f_dual=1365.327, f_primal=261.030, f_unreg=261.473\n",
            "time elapsed: 17.971768140792847\n",
            "approx val: tensor(260.8837, dtype=torch.float64)\n",
            "3284\n",
            "eps: 4.0 eta: 0.002321345774139445 k: 124807.63465139116\n",
            "iteration=1000, elapsed=5.948, f_dual=1378.783, f_primal=294.473, f_unreg=294.851\n",
            "iteration=2000, elapsed=5.992, f_dual=1369.473, f_primal=271.070, f_unreg=271.485\n",
            "iteration=3000, elapsed=6.011, f_dual=1365.327, f_primal=261.030, f_unreg=261.473\n",
            "time elapsed: 21.241129159927368\n",
            "approx val: tensor(260.3816, dtype=torch.float64)\n",
            "3552\n",
            "eps: 3.5 eta: 0.002321345774139445 k: 124807.63465139117\n",
            "iteration=1000, elapsed=5.968, f_dual=1378.783, f_primal=294.473, f_unreg=294.851\n",
            "iteration=2000, elapsed=5.954, f_dual=1369.473, f_primal=271.070, f_unreg=271.485\n",
            "iteration=3000, elapsed=5.988, f_dual=1365.327, f_primal=261.030, f_unreg=261.473\n",
            "time elapsed: 22.54867935180664\n",
            "approx val: tensor(259.8841, dtype=torch.float64)\n",
            "3772\n",
            "eps: 3.0 eta: 0.0023213457741394455 k: 124807.63465139116\n",
            "iteration=1000, elapsed=5.458, f_dual=1378.783, f_primal=294.473, f_unreg=294.851\n",
            "iteration=2000, elapsed=5.309, f_dual=1369.473, f_primal=271.070, f_unreg=271.485\n",
            "iteration=3000, elapsed=5.373, f_dual=1365.327, f_primal=261.030, f_unreg=261.473\n",
            "iteration=4000, elapsed=5.311, f_dual=1363.332, f_primal=259.102, f_unreg=259.550\n",
            "time elapsed: 22.073757648468018\n",
            "approx val: tensor(259.3852, dtype=torch.float64)\n",
            "4114\n",
            "eps: 2.5 eta: 0.0023213457741394455 k: 124807.63465139113\n",
            "iteration=1000, elapsed=5.387, f_dual=1378.783, f_primal=294.473, f_unreg=294.851\n",
            "iteration=2000, elapsed=5.397, f_dual=1369.473, f_primal=271.070, f_unreg=271.485\n",
            "iteration=3000, elapsed=5.339, f_dual=1365.327, f_primal=261.030, f_unreg=261.473\n",
            "iteration=4000, elapsed=5.350, f_dual=1363.332, f_primal=259.102, f_unreg=259.550\n",
            "time elapsed: 23.769813299179077\n",
            "approx val: tensor(258.8847, dtype=torch.float64)\n",
            "4430\n",
            "eps: 2.0 eta: 0.002119876231719951 k: 137951.6140125189\n",
            "iteration=1000, elapsed=5.310, f_dual=1380.067, f_primal=298.497, f_unreg=298.839\n",
            "iteration=2000, elapsed=5.350, f_dual=1370.560, f_primal=272.403, f_unreg=272.778\n",
            "iteration=3000, elapsed=5.851, f_dual=1366.050, f_primal=263.573, f_unreg=263.967\n",
            "iteration=4000, elapsed=5.353, f_dual=1363.872, f_primal=259.666, f_unreg=260.074\n",
            "iteration=5000, elapsed=5.340, f_dual=1362.531, f_primal=258.324, f_unreg=258.736\n",
            "time elapsed: 28.64090347290039\n",
            "approx val: tensor(258.3836, dtype=torch.float64)\n",
            "5264\n",
            "eps: 1.5 eta: 0.0015899071737899635 k: 189355.29501810513\n",
            "iteration=1000, elapsed=5.451, f_dual=1383.897, f_primal=302.527, f_unreg=302.781\n",
            "iteration=2000, elapsed=5.471, f_dual=1374.105, f_primal=279.480, f_unreg=279.752\n",
            "iteration=3000, elapsed=5.423, f_dual=1368.997, f_primal=269.274, f_unreg=269.560\n",
            "iteration=4000, elapsed=5.534, f_dual=1365.941, f_primal=263.672, f_unreg=263.967\n",
            "iteration=5000, elapsed=5.492, f_dual=1364.205, f_primal=260.314, f_unreg=260.618\n",
            "iteration=6000, elapsed=5.471, f_dual=1363.015, f_primal=259.095, f_unreg=259.401\n",
            "iteration=7000, elapsed=5.443, f_dual=1362.171, f_primal=258.161, f_unreg=258.471\n",
            "time elapsed: 43.00734186172485\n",
            "approx val: tensor(257.8854, dtype=torch.float64)\n",
            "7862\n",
            "eps: 1.0 eta: 0.0010599381158599755 k: 295495.82399167604\n",
            "iteration=1000, elapsed=5.840, f_dual=1388.976, f_primal=330.775, f_unreg=330.940\n",
            "iteration=2000, elapsed=5.670, f_dual=1379.847, f_primal=298.754, f_unreg=298.925\n",
            "iteration=3000, elapsed=5.501, f_dual=1373.996, f_primal=279.582, f_unreg=279.764\n",
            "iteration=4000, elapsed=5.459, f_dual=1370.340, f_primal=272.585, f_unreg=272.773\n",
            "iteration=5000, elapsed=5.982, f_dual=1367.682, f_primal=267.920, f_unreg=268.112\n",
            "iteration=6000, elapsed=5.452, f_dual=1365.830, f_primal=263.769, f_unreg=263.966\n",
            "iteration=7000, elapsed=5.477, f_dual=1364.589, f_primal=260.854, f_unreg=261.057\n",
            "iteration=8000, elapsed=5.347, f_dual=1363.651, f_primal=259.869, f_unreg=260.073\n",
            "iteration=9000, elapsed=5.338, f_dual=1362.905, f_primal=259.197, f_unreg=259.402\n",
            "iteration=10000, elapsed=5.333, f_dual=1362.313, f_primal=258.532, f_unreg=258.737\n",
            "iteration=11000, elapsed=5.400, f_dual=1361.842, f_primal=257.960, f_unreg=258.167\n",
            "iteration=12000, elapsed=5.763, f_dual=1361.469, f_primal=257.612, f_unreg=257.820\n",
            "iteration=13000, elapsed=5.375, f_dual=1361.167, f_primal=257.329, f_unreg=257.538\n",
            "time elapsed: 75.11576294898987\n",
            "approx val: tensor(257.3855, dtype=torch.float64)\n",
            "13586\n",
            "eps: 0.5 eta: 0.0005299690579299878 k: 630200.6825791717\n",
            "iteration=1000, elapsed=5.411, f_dual=1406.088, f_primal=639.410, f_unreg=639.481\n",
            "iteration=2000, elapsed=5.443, f_dual=1388.870, f_primal=330.861, f_unreg=330.943\n",
            "iteration=3000, elapsed=5.448, f_dual=1383.685, f_primal=302.970, f_unreg=303.055\n",
            "iteration=4000, elapsed=5.456, f_dual=1379.745, f_primal=298.842, f_unreg=298.927\n",
            "iteration=5000, elapsed=5.885, f_dual=1376.429, f_primal=292.582, f_unreg=292.668\n",
            "iteration=6000, elapsed=5.419, f_dual=1373.891, f_primal=279.673, f_unreg=279.763\n",
            "iteration=7000, elapsed=5.383, f_dual=1371.875, f_primal=274.483, f_unreg=274.576\n",
            "iteration=8000, elapsed=5.426, f_dual=1370.234, f_primal=272.679, f_unreg=272.773\n",
            "iteration=9000, elapsed=5.455, f_dual=1368.780, f_primal=269.933, f_unreg=270.027\n",
            "iteration=10000, elapsed=5.438, f_dual=1367.574, f_primal=268.066, f_unreg=268.162\n",
            "iteration=11000, elapsed=5.397, f_dual=1366.574, f_primal=265.889, f_unreg=265.986\n",
            "iteration=12000, elapsed=5.471, f_dual=1365.722, f_primal=263.869, f_unreg=263.967\n",
            "iteration=13000, elapsed=5.644, f_dual=1365.029, f_primal=261.442, f_unreg=261.543\n",
            "iteration=14000, elapsed=5.709, f_dual=1364.479, f_primal=260.957, f_unreg=261.058\n",
            "iteration=15000, elapsed=5.418, f_dual=1363.984, f_primal=260.518, f_unreg=260.619\n",
            "iteration=16000, elapsed=5.391, f_dual=1363.542, f_primal=259.973, f_unreg=260.074\n",
            "iteration=17000, elapsed=5.919, f_dual=1363.149, f_primal=259.620, f_unreg=259.722\n",
            "iteration=18000, elapsed=5.737, f_dual=1362.796, f_primal=259.301, f_unreg=259.403\n",
            "iteration=19000, elapsed=5.276, f_dual=1362.483, f_primal=258.891, f_unreg=258.994\n",
            "iteration=20000, elapsed=5.633, f_dual=1362.204, f_primal=258.636, f_unreg=258.739\n",
            "iteration=21000, elapsed=5.236, f_dual=1361.953, f_primal=258.405, f_unreg=258.508\n",
            "iteration=22000, elapsed=5.252, f_dual=1361.733, f_primal=258.065, f_unreg=258.168\n",
            "iteration=23000, elapsed=5.242, f_dual=1361.537, f_primal=257.882, f_unreg=257.986\n",
            "iteration=24000, elapsed=5.541, f_dual=1361.360, f_primal=257.718, f_unreg=257.822\n",
            "iteration=25000, elapsed=5.213, f_dual=1361.201, f_primal=257.569, f_unreg=257.673\n",
            "iteration=26000, elapsed=5.258, f_dual=1361.058, f_primal=257.435, f_unreg=257.539\n",
            "iteration=27000, elapsed=5.209, f_dual=1360.930, f_primal=257.302, f_unreg=257.406\n",
            "iteration=28000, elapsed=5.419, f_dual=1360.815, f_primal=257.193, f_unreg=257.297\n",
            "iteration=29000, elapsed=5.571, f_dual=1360.712, f_primal=257.095, f_unreg=257.199\n",
            "iteration=30000, elapsed=5.620, f_dual=1360.619, f_primal=257.006, f_unreg=257.111\n",
            "iteration=31000, elapsed=5.657, f_dual=1360.536, f_primal=256.917, f_unreg=257.022\n",
            "iteration=32000, elapsed=5.596, f_dual=1360.461, f_primal=256.846, f_unreg=256.951\n",
            "iteration=33000, elapsed=5.597, f_dual=1360.394, f_primal=256.781, f_unreg=256.887\n",
            "time elapsed: 180.9125053882599\n",
            "approx val: tensor(256.8855, dtype=torch.float64)\n",
            "33018\n",
            "pair 846 16727\n",
            "eps: 5.0 eta: 0.0019334371050647608 k: 152680.12129586324\n",
            "iteration=1000, elapsed=5.637, f_dual=1751.250, f_primal=292.427, f_unreg=292.769\n",
            "iteration=2000, elapsed=5.638, f_dual=1737.506, f_primal=246.785, f_unreg=247.160\n",
            "iteration=3000, elapsed=5.602, f_dual=1730.713, f_primal=236.119, f_unreg=236.511\n",
            "iteration=4000, elapsed=5.629, f_dual=1726.522, f_primal=230.393, f_unreg=230.798\n",
            "time elapsed: 26.475358963012695\n",
            "approx val: tensor(226.1344, dtype=torch.float64)\n",
            "4698\n",
            "eps: 4.5 eta: 0.0019334371050647606 k: 152680.12129586324\n",
            "iteration=1000, elapsed=5.419, f_dual=1751.250, f_primal=292.427, f_unreg=292.769\n",
            "iteration=2000, elapsed=5.377, f_dual=1737.506, f_primal=246.785, f_unreg=247.160\n",
            "iteration=3000, elapsed=5.421, f_dual=1730.713, f_primal=236.119, f_unreg=236.511\n",
            "iteration=4000, elapsed=5.466, f_dual=1726.522, f_primal=230.393, f_unreg=230.798\n",
            "time elapsed: 26.169169664382935\n",
            "approx val: tensor(225.6314, dtype=torch.float64)\n",
            "4826\n",
            "eps: 4.0 eta: 0.0019334371050647606 k: 152680.1212958632\n",
            "iteration=1000, elapsed=5.322, f_dual=1751.250, f_primal=292.427, f_unreg=292.769\n",
            "iteration=2000, elapsed=5.334, f_dual=1737.506, f_primal=246.785, f_unreg=247.160\n",
            "iteration=3000, elapsed=5.296, f_dual=1730.713, f_primal=236.119, f_unreg=236.511\n",
            "iteration=4000, elapsed=5.339, f_dual=1726.522, f_primal=230.393, f_unreg=230.798\n",
            "iteration=5000, elapsed=5.325, f_dual=1723.972, f_primal=224.803, f_unreg=225.222\n",
            "time elapsed: 26.939022302627563\n",
            "approx val: tensor(225.1343, dtype=torch.float64)\n",
            "5056\n",
            "eps: 3.5 eta: 0.0019334371050647606 k: 152680.12129586324\n",
            "iteration=1000, elapsed=5.256, f_dual=1751.250, f_primal=292.427, f_unreg=292.769\n",
            "iteration=2000, elapsed=5.244, f_dual=1737.506, f_primal=246.785, f_unreg=247.160\n",
            "iteration=3000, elapsed=5.231, f_dual=1730.713, f_primal=236.119, f_unreg=236.511\n",
            "iteration=4000, elapsed=5.244, f_dual=1726.522, f_primal=230.393, f_unreg=230.798\n",
            "iteration=5000, elapsed=5.231, f_dual=1723.972, f_primal=224.803, f_unreg=225.222\n",
            "time elapsed: 27.742339611053467\n",
            "approx val: tensor(224.6343, dtype=torch.float64)\n",
            "5276\n",
            "eps: 3.0 eta: 0.0019334371050647606 k: 152680.12129586324\n",
            "iteration=1000, elapsed=5.259, f_dual=1751.250, f_primal=292.427, f_unreg=292.769\n",
            "iteration=2000, elapsed=5.216, f_dual=1737.506, f_primal=246.785, f_unreg=247.160\n",
            "iteration=3000, elapsed=5.285, f_dual=1730.713, f_primal=236.119, f_unreg=236.511\n",
            "iteration=4000, elapsed=5.218, f_dual=1726.522, f_primal=230.393, f_unreg=230.798\n",
            "iteration=5000, elapsed=5.262, f_dual=1723.972, f_primal=224.803, f_unreg=225.222\n",
            "time elapsed: 29.74188542366028\n",
            "approx val: tensor(224.1324, dtype=torch.float64)\n",
            "5664\n",
            "eps: 2.5 eta: 0.0019334371050647608 k: 152680.1212958632\n",
            "iteration=1000, elapsed=5.264, f_dual=1751.250, f_primal=292.427, f_unreg=292.769\n",
            "iteration=2000, elapsed=5.226, f_dual=1737.506, f_primal=246.785, f_unreg=247.160\n",
            "iteration=3000, elapsed=5.274, f_dual=1730.713, f_primal=236.119, f_unreg=236.511\n",
            "iteration=4000, elapsed=5.216, f_dual=1726.522, f_primal=230.393, f_unreg=230.798\n",
            "iteration=5000, elapsed=5.263, f_dual=1723.972, f_primal=224.803, f_unreg=225.222\n",
            "iteration=6000, elapsed=5.306, f_dual=1722.585, f_primal=223.332, f_unreg=223.756\n",
            "time elapsed: 32.193339347839355\n",
            "approx val: tensor(223.6344, dtype=torch.float64)\n",
            "6118\n",
            "eps: 2.0 eta: 0.0017413576756523026 k: 171321.23838825093\n",
            "iteration=1000, elapsed=5.314, f_dual=1753.395, f_primal=294.468, f_unreg=294.774\n",
            "iteration=2000, elapsed=5.299, f_dual=1739.369, f_primal=250.360, f_unreg=250.692\n",
            "iteration=3000, elapsed=5.286, f_dual=1732.361, f_primal=237.693, f_unreg=238.044\n",
            "iteration=4000, elapsed=5.294, f_dual=1727.929, f_primal=232.030, f_unreg=232.390\n",
            "iteration=5000, elapsed=5.293, f_dual=1724.967, f_primal=228.696, f_unreg=229.065\n",
            "iteration=6000, elapsed=5.322, f_dual=1723.298, f_primal=224.080, f_unreg=224.460\n",
            "iteration=7000, elapsed=5.285, f_dual=1722.218, f_primal=223.014, f_unreg=223.396\n",
            "time elapsed: 38.735435009002686\n",
            "approx val: tensor(223.1340, dtype=torch.float64)\n",
            "7308\n",
            "eps: 1.5 eta: 0.0013060182567392268 k: 235027.87523812012\n",
            "iteration=1000, elapsed=5.320, f_dual=1759.853, f_primal=354.653, f_unreg=354.860\n",
            "iteration=2000, elapsed=5.295, f_dual=1744.622, f_primal=272.038, f_unreg=272.277\n",
            "iteration=3000, elapsed=5.316, f_dual=1737.128, f_primal=246.704, f_unreg=246.957\n",
            "iteration=4000, elapsed=5.692, f_dual=1732.259, f_primal=237.780, f_unreg=238.044\n",
            "iteration=5000, elapsed=5.300, f_dual=1728.761, f_primal=232.963, f_unreg=233.232\n",
            "iteration=6000, elapsed=5.290, f_dual=1726.205, f_primal=230.280, f_unreg=230.554\n",
            "iteration=7000, elapsed=5.318, f_dual=1724.321, f_primal=225.548, f_unreg=225.829\n",
            "iteration=8000, elapsed=5.310, f_dual=1723.198, f_primal=224.176, f_unreg=224.461\n",
            "iteration=9000, elapsed=5.288, f_dual=1722.353, f_primal=223.390, f_unreg=223.676\n",
            "iteration=10000, elapsed=5.305, f_dual=1721.709, f_primal=222.708, f_unreg=222.996\n",
            "time elapsed: 57.428627252578735\n",
            "approx val: tensor(222.6338, dtype=torch.float64)\n",
            "10754\n",
            "eps: 1.0 eta: 0.0008706788378261513 k: 366498.9565448219\n",
            "iteration=1000, elapsed=5.304, f_dual=1769.541, f_primal=438.539, f_unreg=438.664\n",
            "iteration=2000, elapsed=5.267, f_dual=1753.186, f_primal=294.615, f_unreg=294.769\n",
            "iteration=3000, elapsed=5.330, f_dual=1744.525, f_primal=272.118, f_unreg=272.278\n",
            "iteration=4000, elapsed=5.281, f_dual=1739.169, f_primal=250.608, f_unreg=250.774\n",
            "iteration=5000, elapsed=5.857, f_dual=1735.183, f_primal=242.070, f_unreg=242.242\n",
            "iteration=6000, elapsed=5.259, f_dual=1732.161, f_primal=237.870, f_unreg=238.046\n",
            "iteration=7000, elapsed=5.305, f_dual=1729.693, f_primal=234.922, f_unreg=235.100\n",
            "iteration=8000, elapsed=5.257, f_dual=1727.730, f_primal=232.222, f_unreg=232.402\n",
            "iteration=9000, elapsed=5.303, f_dual=1726.106, f_primal=230.414, f_unreg=230.597\n",
            "iteration=10000, elapsed=5.273, f_dual=1724.768, f_primal=228.884, f_unreg=229.068\n",
            "iteration=11000, elapsed=5.282, f_dual=1723.809, f_primal=225.230, f_unreg=225.418\n",
            "iteration=12000, elapsed=5.314, f_dual=1723.098, f_primal=224.274, f_unreg=224.464\n",
            "iteration=13000, elapsed=5.320, f_dual=1722.511, f_primal=223.728, f_unreg=223.919\n",
            "iteration=14000, elapsed=5.333, f_dual=1722.018, f_primal=223.219, f_unreg=223.410\n",
            "iteration=15000, elapsed=5.315, f_dual=1721.610, f_primal=222.806, f_unreg=222.998\n",
            "iteration=16000, elapsed=6.074, f_dual=1721.267, f_primal=222.482, f_unreg=222.674\n",
            "iteration=17000, elapsed=5.299, f_dual=1720.979, f_primal=222.209, f_unreg=222.401\n",
            "iteration=18000, elapsed=5.380, f_dual=1720.737, f_primal=221.978, f_unreg=222.171\n",
            "time elapsed: 97.70626759529114\n",
            "approx val: tensor(222.1343, dtype=torch.float64)\n",
            "18174\n",
            "eps: 0.5 eta: 0.00043533941891307564 k: 780735.3048087221\n",
            "iteration=1000, elapsed=5.255, f_dual=1793.236, f_primal=835.437, f_unreg=835.491\n",
            "iteration=2000, elapsed=5.300, f_dual=1769.443, f_primal=438.974, f_unreg=439.037\n",
            "iteration=3000, elapsed=5.554, f_dual=1759.658, f_primal=354.783, f_unreg=354.852\n",
            "iteration=4000, elapsed=5.252, f_dual=1753.084, f_primal=294.688, f_unreg=294.765\n",
            "iteration=5000, elapsed=5.254, f_dual=1748.273, f_primal=288.507, f_unreg=288.584\n",
            "iteration=6000, elapsed=5.247, f_dual=1744.425, f_primal=272.196, f_unreg=272.276\n",
            "iteration=7000, elapsed=5.283, f_dual=1741.485, f_primal=253.728, f_unreg=253.810\n",
            "iteration=8000, elapsed=5.254, f_dual=1739.071, f_primal=250.694, f_unreg=250.777\n",
            "iteration=9000, elapsed=5.641, f_dual=1736.931, f_primal=246.876, f_unreg=246.960\n",
            "iteration=10000, elapsed=5.238, f_dual=1735.084, f_primal=242.151, f_unreg=242.237\n",
            "iteration=11000, elapsed=5.298, f_dual=1733.490, f_primal=239.900, f_unreg=239.987\n",
            "iteration=12000, elapsed=5.451, f_dual=1732.062, f_primal=237.960, f_unreg=238.048\n",
            "iteration=13000, elapsed=5.363, f_dual=1730.769, f_primal=236.801, f_unreg=236.890\n",
            "iteration=14000, elapsed=5.276, f_dual=1729.594, f_primal=235.013, f_unreg=235.102\n",
            "iteration=15000, elapsed=5.516, f_dual=1728.564, f_primal=233.146, f_unreg=233.236\n",
            "iteration=16000, elapsed=5.390, f_dual=1727.632, f_primal=232.314, f_unreg=232.404\n",
            "iteration=17000, elapsed=5.298, f_dual=1726.781, f_primal=231.436, f_unreg=231.527\n",
            "iteration=18000, elapsed=5.272, f_dual=1726.007, f_primal=230.566, f_unreg=230.657\n",
            "iteration=19000, elapsed=5.292, f_dual=1725.307, f_primal=229.788, f_unreg=229.879\n",
            "iteration=20000, elapsed=5.371, f_dual=1724.669, f_primal=228.978, f_unreg=229.070\n",
            "iteration=21000, elapsed=5.266, f_dual=1724.123, f_primal=225.710, f_unreg=225.804\n",
            "iteration=22000, elapsed=5.293, f_dual=1723.710, f_primal=225.331, f_unreg=225.425\n",
            "iteration=23000, elapsed=5.281, f_dual=1723.335, f_primal=224.863, f_unreg=224.958\n",
            "iteration=24000, elapsed=5.299, f_dual=1722.999, f_primal=224.371, f_unreg=224.466\n",
            "iteration=25000, elapsed=5.278, f_dual=1722.692, f_primal=224.087, f_unreg=224.182\n",
            "iteration=26000, elapsed=5.373, f_dual=1722.412, f_primal=223.825, f_unreg=223.921\n",
            "iteration=27000, elapsed=5.552, f_dual=1722.154, f_primal=223.585, f_unreg=223.680\n",
            "iteration=28000, elapsed=5.661, f_dual=1721.919, f_primal=223.330, f_unreg=223.425\n",
            "iteration=29000, elapsed=5.615, f_dual=1721.706, f_primal=223.088, f_unreg=223.183\n",
            "iteration=30000, elapsed=5.668, f_dual=1721.511, f_primal=222.904, f_unreg=223.000\n",
            "iteration=31000, elapsed=6.012, f_dual=1721.332, f_primal=222.735, f_unreg=222.831\n",
            "iteration=32000, elapsed=5.625, f_dual=1721.168, f_primal=222.580, f_unreg=222.676\n",
            "iteration=33000, elapsed=5.633, f_dual=1721.018, f_primal=222.437, f_unreg=222.534\n",
            "iteration=34000, elapsed=5.604, f_dual=1720.880, f_primal=222.306, f_unreg=222.403\n",
            "iteration=35000, elapsed=5.644, f_dual=1720.754, f_primal=222.186, f_unreg=222.282\n",
            "iteration=36000, elapsed=5.601, f_dual=1720.638, f_primal=222.076, f_unreg=222.172\n",
            "iteration=37000, elapsed=5.640, f_dual=1720.532, f_primal=221.974, f_unreg=222.071\n",
            "iteration=38000, elapsed=5.626, f_dual=1720.436, f_primal=221.856, f_unreg=221.953\n",
            "iteration=39000, elapsed=5.616, f_dual=1720.348, f_primal=221.771, f_unreg=221.868\n",
            "iteration=40000, elapsed=5.636, f_dual=1720.267, f_primal=221.694, f_unreg=221.791\n",
            "iteration=41000, elapsed=5.518, f_dual=1720.193, f_primal=221.622, f_unreg=221.719\n",
            "iteration=42000, elapsed=5.607, f_dual=1720.125, f_primal=221.557, f_unreg=221.654\n",
            "time elapsed: 230.64100670814514\n",
            "approx val: tensor(221.6344, dtype=torch.float64)\n",
            "42316\n",
            "pair 31169 7144\n",
            "eps: 5.0 eta: 0.0020280847058116304 k: 144848.99048872816\n",
            "iteration=1000, elapsed=5.522, f_dual=1521.437, f_primal=434.380, f_unreg=434.862\n",
            "iteration=2000, elapsed=5.508, f_dual=1511.476, f_primal=376.001, f_unreg=376.493\n",
            "iteration=3000, elapsed=5.519, f_dual=1507.146, f_primal=355.961, f_unreg=356.469\n",
            "time elapsed: 20.534497499465942\n",
            "approx val: tensor(353.8394, dtype=torch.float64)\n",
            "3709\n",
            "eps: 4.5 eta: 0.0020280847058116304 k: 144848.9904887282\n",
            "iteration=1000, elapsed=5.462, f_dual=1521.437, f_primal=434.380, f_unreg=434.862\n",
            "iteration=2000, elapsed=5.450, f_dual=1511.476, f_primal=376.001, f_unreg=376.493\n",
            "iteration=3000, elapsed=5.471, f_dual=1507.146, f_primal=355.961, f_unreg=356.469\n",
            "iteration=4000, elapsed=5.430, f_dual=1505.003, f_primal=353.459, f_unreg=353.963\n",
            "time elapsed: 21.91713237762451\n",
            "approx val: tensor(353.3391, dtype=torch.float64)\n",
            "4013\n",
            "eps: 4.0 eta: 0.0020280847058116304 k: 144848.99048872816\n",
            "iteration=1000, elapsed=5.279, f_dual=1521.437, f_primal=434.380, f_unreg=434.862\n",
            "iteration=2000, elapsed=5.242, f_dual=1511.476, f_primal=376.001, f_unreg=376.493\n",
            "iteration=3000, elapsed=5.358, f_dual=1507.146, f_primal=355.961, f_unreg=356.469\n",
            "iteration=4000, elapsed=5.234, f_dual=1505.003, f_primal=353.459, f_unreg=353.963\n",
            "time elapsed: 23.022504329681396\n",
            "approx val: tensor(352.8394, dtype=torch.float64)\n",
            "4357\n",
            "eps: 3.5 eta: 0.0020280847058116304 k: 144848.9904887282\n",
            "iteration=1000, elapsed=5.263, f_dual=1521.437, f_primal=434.380, f_unreg=434.862\n",
            "iteration=2000, elapsed=5.282, f_dual=1511.476, f_primal=376.001, f_unreg=376.493\n",
            "iteration=3000, elapsed=5.264, f_dual=1507.146, f_primal=355.961, f_unreg=356.469\n",
            "iteration=4000, elapsed=5.280, f_dual=1505.003, f_primal=353.459, f_unreg=353.963\n",
            "time elapsed: 25.057213068008423\n",
            "approx val: tensor(352.3386, dtype=torch.float64)\n",
            "4755\n",
            "eps: 3.0 eta: 0.0020280847058116304 k: 144848.99048872816\n",
            "iteration=1000, elapsed=5.281, f_dual=1521.437, f_primal=434.380, f_unreg=434.862\n",
            "iteration=2000, elapsed=5.270, f_dual=1511.476, f_primal=376.001, f_unreg=376.493\n",
            "iteration=3000, elapsed=5.276, f_dual=1507.146, f_primal=355.961, f_unreg=356.469\n",
            "iteration=4000, elapsed=5.266, f_dual=1505.003, f_primal=353.459, f_unreg=353.963\n",
            "time elapsed: 26.384330987930298\n",
            "approx val: tensor(351.8241, dtype=torch.float64)\n",
            "4937\n",
            "eps: 2.5 eta: 0.0020280847058116304 k: 144848.99048872816\n",
            "iteration=1000, elapsed=5.252, f_dual=1521.437, f_primal=434.380, f_unreg=434.862\n",
            "iteration=2000, elapsed=5.291, f_dual=1511.476, f_primal=376.001, f_unreg=376.493\n",
            "iteration=3000, elapsed=5.230, f_dual=1507.146, f_primal=355.961, f_unreg=356.469\n",
            "iteration=4000, elapsed=5.276, f_dual=1505.003, f_primal=353.459, f_unreg=353.963\n",
            "iteration=5000, elapsed=5.249, f_dual=1503.590, f_primal=351.348, f_unreg=351.851\n",
            "time elapsed: 27.406179904937744\n",
            "approx val: tensor(351.3379, dtype=torch.float64)\n",
            "5209\n",
            "eps: 2.0 eta: 0.001833244755674339 k: 161893.94573873648\n",
            "iteration=1000, elapsed=5.276, f_dual=1524.177, f_primal=496.556, f_unreg=496.971\n",
            "iteration=2000, elapsed=5.227, f_dual=1512.921, f_primal=377.695, f_unreg=378.141\n",
            "iteration=3000, elapsed=5.264, f_dual=1507.938, f_primal=357.928, f_unreg=358.385\n",
            "iteration=4000, elapsed=5.235, f_dual=1505.675, f_primal=354.301, f_unreg=354.758\n",
            "iteration=5000, elapsed=5.255, f_dual=1504.147, f_primal=352.618, f_unreg=353.071\n",
            "time elapsed: 30.995782375335693\n",
            "approx val: tensor(350.8330, dtype=torch.float64)\n",
            "5825\n",
            "eps: 1.5 eta: 0.0013749335667557541 k: 222126.9811782262\n",
            "iteration=1000, elapsed=5.285, f_dual=1532.799, f_primal=573.185, f_unreg=573.489\n",
            "iteration=2000, elapsed=5.276, f_dual=1516.910, f_primal=384.215, f_unreg=384.549\n",
            "iteration=3000, elapsed=5.257, f_dual=1511.078, f_primal=375.871, f_unreg=376.204\n",
            "iteration=4000, elapsed=5.271, f_dual=1507.830, f_primal=358.035, f_unreg=358.378\n",
            "iteration=5000, elapsed=5.262, f_dual=1506.045, f_primal=355.057, f_unreg=355.400\n",
            "iteration=6000, elapsed=5.539, f_dual=1504.732, f_primal=353.487, f_unreg=353.829\n",
            "iteration=7000, elapsed=5.214, f_dual=1503.736, f_primal=352.397, f_unreg=352.737\n",
            "iteration=8000, elapsed=5.279, f_dual=1503.050, f_primal=350.344, f_unreg=350.688\n",
            "time elapsed: 44.35928821563721\n",
            "approx val: tensor(350.3398, dtype=torch.float64)\n",
            "8375\n",
            "eps: 1.0 eta: 0.0009166223778371695 k: 346447.4460490379\n",
            "iteration=1000, elapsed=5.241, f_dual=1547.308, f_primal=901.092, f_unreg=901.271\n",
            "iteration=2000, elapsed=5.254, f_dual=1523.977, f_primal=496.731, f_unreg=496.938\n",
            "iteration=3000, elapsed=5.319, f_dual=1516.812, f_primal=384.322, f_unreg=384.545\n",
            "iteration=4000, elapsed=5.233, f_dual=1512.717, f_primal=377.903, f_unreg=378.127\n",
            "iteration=5000, elapsed=5.251, f_dual=1509.700, f_primal=365.967, f_unreg=366.191\n",
            "iteration=6000, elapsed=5.233, f_dual=1507.724, f_primal=358.145, f_unreg=358.374\n",
            "iteration=7000, elapsed=5.242, f_dual=1506.468, f_primal=355.760, f_unreg=355.989\n",
            "iteration=8000, elapsed=5.262, f_dual=1505.458, f_primal=354.520, f_unreg=354.749\n",
            "iteration=9000, elapsed=5.253, f_dual=1504.624, f_primal=353.597, f_unreg=353.825\n",
            "iteration=10000, elapsed=5.215, f_dual=1503.930, f_primal=352.836, f_unreg=353.063\n",
            "iteration=11000, elapsed=5.257, f_dual=1503.355, f_primal=351.652, f_unreg=351.879\n",
            "iteration=12000, elapsed=5.216, f_dual=1502.939, f_primal=350.455, f_unreg=350.685\n",
            "iteration=13000, elapsed=5.266, f_dual=1502.633, f_primal=350.130, f_unreg=350.358\n",
            "iteration=14000, elapsed=5.302, f_dual=1502.379, f_primal=349.860, f_unreg=350.088\n",
            "time elapsed: 77.27877020835876\n",
            "approx val: tensor(349.8397, dtype=torch.float64)\n",
            "14703\n",
            "eps: 0.5 eta: 0.00045831118891858475 k: 738238.2798433691\n",
            "iteration=1000, elapsed=5.285, f_dual=1602.997, f_primal=4288.544, f_unreg=4288.616\n",
            "iteration=2000, elapsed=5.321, f_dual=1547.232, f_primal=901.047, f_unreg=901.137\n",
            "iteration=3000, elapsed=5.388, f_dual=1532.627, f_primal=573.390, f_unreg=573.491\n",
            "iteration=4000, elapsed=5.320, f_dual=1523.887, f_primal=496.834, f_unreg=496.938\n",
            "iteration=5000, elapsed=5.279, f_dual=1519.184, f_primal=392.729, f_unreg=392.839\n",
            "iteration=6000, elapsed=5.321, f_dual=1516.716, f_primal=384.432, f_unreg=384.544\n",
            "iteration=7000, elapsed=5.274, f_dual=1514.545, f_primal=381.976, f_unreg=382.087\n",
            "iteration=8000, elapsed=5.329, f_dual=1512.621, f_primal=378.015, f_unreg=378.127\n",
            "iteration=9000, elapsed=5.281, f_dual=1510.881, f_primal=376.088, f_unreg=376.199\n",
            "iteration=10000, elapsed=5.318, f_dual=1509.601, f_primal=366.078, f_unreg=366.190\n",
            "iteration=11000, elapsed=5.347, f_dual=1508.496, f_primal=364.555, f_unreg=364.668\n",
            "iteration=12000, elapsed=5.602, f_dual=1507.621, f_primal=358.258, f_unreg=358.372\n",
            "iteration=13000, elapsed=5.273, f_dual=1506.944, f_primal=356.525, f_unreg=356.640\n",
            "iteration=14000, elapsed=5.265, f_dual=1506.362, f_primal=355.872, f_unreg=355.987\n",
            "iteration=15000, elapsed=5.273, f_dual=1505.832, f_primal=355.280, f_unreg=355.394\n",
            "iteration=16000, elapsed=5.288, f_dual=1505.352, f_primal=354.632, f_unreg=354.746\n",
            "iteration=17000, elapsed=5.289, f_dual=1504.916, f_primal=354.148, f_unreg=354.262\n",
            "iteration=18000, elapsed=5.247, f_dual=1504.517, f_primal=353.709, f_unreg=353.823\n",
            "iteration=19000, elapsed=5.296, f_dual=1504.154, f_primal=353.310, f_unreg=353.423\n",
            "iteration=20000, elapsed=5.245, f_dual=1503.823, f_primal=352.947, f_unreg=353.061\n",
            "iteration=21000, elapsed=5.291, f_dual=1503.520, f_primal=352.618, f_unreg=352.731\n",
            "iteration=22000, elapsed=5.328, f_dual=1503.246, f_primal=351.757, f_unreg=351.871\n",
            "iteration=23000, elapsed=5.282, f_dual=1503.018, f_primal=351.511, f_unreg=351.624\n",
            "iteration=24000, elapsed=5.244, f_dual=1502.829, f_primal=350.567, f_unreg=350.682\n",
            "iteration=25000, elapsed=5.325, f_dual=1502.669, f_primal=350.397, f_unreg=350.511\n",
            "iteration=26000, elapsed=5.300, f_dual=1502.523, f_primal=350.242, f_unreg=350.356\n",
            "iteration=27000, elapsed=5.264, f_dual=1502.390, f_primal=350.100, f_unreg=350.215\n",
            "iteration=28000, elapsed=5.291, f_dual=1502.268, f_primal=349.972, f_unreg=350.086\n",
            "iteration=29000, elapsed=5.271, f_dual=1502.157, f_primal=349.855, f_unreg=349.969\n",
            "iteration=30000, elapsed=5.285, f_dual=1502.056, f_primal=349.749, f_unreg=349.862\n",
            "iteration=31000, elapsed=5.266, f_dual=1501.964, f_primal=349.652, f_unreg=349.765\n",
            "iteration=32000, elapsed=5.293, f_dual=1501.880, f_primal=349.563, f_unreg=349.677\n",
            "iteration=33000, elapsed=5.254, f_dual=1501.803, f_primal=349.483, f_unreg=349.597\n",
            "iteration=34000, elapsed=5.816, f_dual=1501.733, f_primal=349.410, f_unreg=349.523\n",
            "iteration=35000, elapsed=5.260, f_dual=1501.669, f_primal=349.343, f_unreg=349.457\n",
            "iteration=36000, elapsed=5.302, f_dual=1501.610, f_primal=349.283, f_unreg=349.396\n",
            "time elapsed: 193.49386858940125\n",
            "approx val: tensor(349.3397, dtype=torch.float64)\n",
            "36407\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mMDonFWIPinZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 721
        },
        "outputId": "5a9b9c21-c0d1-4b52-dc50-e6970d64447e"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "eps_list = np.linspace(5.0, 0.5, 10)\n",
        "\n",
        "k_list_empirical_first = np.array(k_list_empirical_first)\n",
        "k_list_formula = np.array(k_list_formula)\n",
        "\n",
        "k_list_empirical_first = np.log(k_list_empirical_first)\n",
        "k_list_empirical_first = np.mean(k_list_empirical_first, axis=0)\n",
        "\n",
        "k_list_formula = np.log(k_list_formula)\n",
        "k_list_formula = np.mean(k_list_formula, axis=0)\n",
        "\n",
        "print(k_list_empirical_first)\n",
        "print(k_list_formula)\n",
        "\n",
        "fig, axs = plt.subplots(1, 2, figsize=(16, 8), sharex=True)\n",
        "plt.rcParams.update({'font.size': 22})\n",
        "\n",
        "axs[0].plot(eps_list, [tmp for tmp in k_list_formula], color=\"#990000\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\log$ $\\mathrm{k}_\\mathrm{f}$\")\n",
        "axs[0].plot(eps_list, [tmp for tmp in k_list_empirical_first], color=\"#2F6276\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\log$ $\\mathrm{k}_\\mathrm{c}$\")\n",
        "axs[0].set_xlim(5.5, 0.2)\n",
        "axs[0].yaxis.set_label_coords(-0.1, 0.5)\n",
        "axs[0].set_ylabel(r\"log iteration\")\n",
        "axs[0].legend(prop={'size': 30})\n",
        "\n",
        "axs[1].plot(eps_list, [k_list_formula[i] / k_list_empirical_first[i] for i in range(len(k_list_formula))], color=\"#66892B\", marker=\"o\", markersize=6, linewidth=4, label=r\"$\\mathrm{k}_\\mathrm{f}$ / $\\mathrm{k}_\\mathrm{c}$\")\n",
        "axs[1].set_xlim(5.5, 0.2)\n",
        "axs[1].yaxis.tick_right()\n",
        "axs[1].yaxis.set_label_position(\"right\")\n",
        "axs[1].yaxis.set_label_coords(1.20, 0.5)\n",
        "axs[1].set_ylabel(\"ratio\", rotation=\"-90\")\n",
        "axs[1].legend(prop={'size': 30})\n",
        "\n",
        "fig.text(0.5, 0.04, 'epsilon', ha='center')\n",
        "\n",
        "plt.savefig('k_comparison_mnist.eps', bbox_inches='tight')\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[ 8.27946441  8.32696356  8.37817522  8.43362342  8.4884619   8.54004307\n",
            "  8.69959015  9.06823141  9.58464746 10.4602251 ]\n",
            "[11.79195532 11.79195532 11.79195532 11.79195532 11.79195532 11.79195532\n",
            " 11.89648301 12.21306    12.65789705 13.41498175]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x576 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qXgLHv_4Wguh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}