minimal_VARX.ipynb

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        "<a href=\"https://colab.research.google.com/github/dnguyend/minimal_varx/blob/master/minimal_VARX.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "$\\newcommand{\\by}{\\boldsymbol{y}}}$\n",
        "$\\newcommand{\\R}{\\mathbb{R}}$ \n",
        "$\\newcommand{\\nmin}{n_{\\min}}$\n",
        "$\\newcommand{\\C}{\\mathbb{C}}$ $\\newcommand{\\Z}{\\mathbb{Z}}$\n",
        "$\\newcommand{\\V}{\\mathbb{V}}$\n",
        "$\\newcommand{\\cX}{\\mathcal{X}}$\n",
        "$\\newcommand{\\cC}{\\mathcal{C}}$\n",
        "$\\newcommand{\\cG}{\\mathcal{G}}$\n",
        "$\\newcommand{\\cH}{\\mathcal{H}}$\n",
        "$\\newcommand{\\cGO}{\\mathcal{GO}}$\n",
        "$\\newcommand{\\cF}{\\mathcal{F}}$\n",
        "$\\newcommand{\\bpi}{\\boldsymbol{\\pi}}$\n",
        "$\\newcommand{\\cK}{\\mathcal{K}}$\n",
        "$\\newcommand{\\cQ}{\\mathcal{Q}}$\n",
        "$\\newcommand{\\cR}{\\mathcal{R}}$\n",
        "$\\newcommand{\\cS}{\\mathcal{S}}$\n",
        "$\\newcommand{\\fll}{\\mathfrak{l}}$\n",
        "$\\newcommand{\\bF}{\\boldsymbol{F}}$\n",
        "$\\newcommand{\\bW}{\\boldsymbol{W}}$\n",
        "$\\newcommand{\\bQ}{\\boldsymbol{Q}}$\n",
        "$\\newcommand{\\bG}{\\boldsymbol{G}}$\n",
        "$\\newcommand{\\bS}{\\boldsymbol{S}}$\n",
        "$\\newcommand{\\bU}{\\boldsymbol{U}}$\n",
        "$\\newcommand{\\bx}{\\boldsymbol{x}}$\n",
        "$\\newcommand{\\by}{\\boldsymbol{y}}$\n",
        "$\\newcommand{\\bu}{\\boldsymbol{u}}$\n",
        "$\\newcommand{\\bv}{\\boldsymbol{v}}$\n",
        "$\\newcommand{\\bX}{\\boldsymbol{X}}$\n",
        "$\\newcommand{\\bI}{\\boldsymbol{I}}$\n",
        "$\\newcommand{\\bA}{\\boldsymbol{A}}$\n",
        "$\\newcommand{\\bB}{\\boldsymbol{B}}$\n",
        "$\\newcommand{\\bC}{\\boldsymbol{C}}$\n",
        "$\\newcommand{\\bO}{\\boldsymbol{O}}$\n",
        "$\\newcommand{\\bD}{\\boldsymbol{D}}$\n",
        "$\\newcommand{\\bJ}{\\boldsymbol{J}}$\n",
        "$\\newcommand{\\bK}{\\boldsymbol{K}}$\n",
        "$\\newcommand{\\bH}{\\boldsymbol{H}}$\n",
        "$\\newcommand{\\AR}{\\text{AR}}$\n",
        "$\\newcommand{\\Xlag}{\\boldsymbol{X}_{\\text{LAG}}}$\n",
        "$\\newcommand{\\hX}{\\hat{X}}$\n",
        "$\\newcommand{\\bY}{\\boldsymbol{Y}}$\n",
        "$\\newcommand{\\bH}{\\boldsymbol{H}}$\n",
        "$\\newcommand{\\bhH}{\\hat{\\boldsymbol{H}}}$\n",
        "$\\newcommand{\\bT}{\\boldsymbol{T}}$\n",
        "$\\newcommand{\\bq}{\\boldsymbol{q}}$\n",
        "$\\newcommand{\\bP}{\\boldsymbol{P}}$\n",
        "$\\newcommand{\\Gperp}{\\boldsymbol{G}_{\\perp}}$\n",
        "$\\newcommand{\\bone}{\\boldsymbol{1}}$\n",
        "$\\newcommand{\\bZ}{\\boldsymbol{Z}}$\n",
        "$\\newcommand{\\bhX}{\\hat{\\boldsymbol{X}}}$\n",
        "$\\newcommand{\\bhZ}{\\hat{\\boldsymbol{Z}}}$\n",
        "$\\newcommand{\\bep}{\\boldsymbol{\\epsilon}}$\n",
        "$\\newcommand{\\bsc}{\\boldsymbol{c}}$\n",
        "$\\newcommand{\\bhep}{\\hat{\\boldsymbol{\\epsilon}}}$\n",
        "$\\newcommand{\\hOmg}{\\hat{\\Omega}}$\n",
        "$\\newcommand{\\btheta}{\\boldsymbol{\\theta}}$\n",
        "$\\newcommand{\\blambda}{\\boldsymbol{\\lambda}}$\n",
        "$\\newcommand{\\bPhi}{\\boldsymbol{\\Phi}}$\n",
        "$\\newcommand{\\bpsi}{\\boldsymbol{\\psi}}$\n",
        "$\\newcommand{\\baP}{\\boldsymbol{\\bar{P}}}$\n",
        "$\\newcommand{\\baq}{\\boldsymbol{\\bar{q}}}$\n",
        "$\\newcommand{\\bXtheta}{\\boldsymbol{X}_{\\theta}}$\n",
        "$\\newcommand{\\bXthetaL}{\\boldsymbol{X}_{\\theta;}^L}$\n",
        "$\\newcommand{\\bXLag}{\\boldsymbol{X}_{\\text{LAG}}}$\n",
        "$\\newcommand{\\MA}{\\text{MA}}$\n",
        "$\\newcommand{\\VAR}{\\text{VAR}}$\n",
        "$\\newcommand{\\VARX}{\\text{VARX}}$\n",
        "$\\newcommand{\\VARMA}{\\text{VARMA}}$\n",
        "$\\DeclareMathOperator{\\diag}{diag}$\n",
        "$\\DeclareMathOperator{\\Tr}{Tr}$\n",
        "$\\DeclareMathOperator{\\Mat}{Mat}$\n",
        "\n",
        "\n",
        "# Minimal VARX: The $\\AR$-state-space approach to time series analysis.\n",
        "In this project we show implications an autoregressive state-space approach to time series and linear system identification.\n",
        "The traditional state-space approach expresses $\\by$ a function of inputs and innovations. This is the traditional approach in control theory, but in forecasting the link between past and future observation is not explicit, making it is difficult for both model fitting and forecasting.\n"
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        "We advocate the $\\AR$ state-space approach. It is expressed as\n",
        "$$\\by = \\bH(\\bI-\\bF L)^{-1}\\bG L \\by + \\bep$$\n",
        "By a theorem of Kalman, $\\VAR, \\VARMA$ and their exogenous counterparts are all expressible in this form. For the $\\VARX(1)$ the minimal $\\AR$ state-space approach is exactly the reduced rank regression, and the estimation procedure for reduced rank regression could be generalized. We show the (negative) likelhood function could be expressed as a determinant ratio. In the reduced-rank case maximizing this likelihood function leads to canonical- correlation-analysis. In the general case we must use a numerical procedure, but both the gradient and the Hessian could be computed explicitly for MLE.\n",
        "\n",
        "For the $\\VAR(p)$ case, $\\bF$ could be reduced to a Jordan matrix with $\\bF^p=0$. This allows an explicit classication of possible $minimal$ state-space. This helps providing a framework for parameter reductions going beyond reduced-rank regression. While in the $p=1$ case we factor the regression matrix $\\bPhi$ to a product $\\bH\\bG$, in the general case we distribute the ranks $d_i$ on to each power $1\\leq i\\leq p$. These ranks define the complexity of the model. The most expensive model in term of parameter is one with all the rank concentrated at the $\\Phi_p$ parameter, the least expensive is one where $\\Phi_p$ of rank $1$ (and no lower power get allocate any rank). This provides an intuitive look at complexity of state-space model.\n",
        "\n",
        "More interestingly, we can reduce the search space further by using matrices $\\bS$ that commute with $\\bF$. $\\bG$ could be made to satisfy two sets of orthogonal relations. Hence we can apply manifold optimization technique for high dimensional problem. It turns out the manifold in question is an interesting mathematical object by itself, a vector bundle over a flag manifold. However, there is no need to get to manifold optimization to use our model.\n",
        "\n",
        "This notebook is to illustrate the code. For details derivation please consult the paper.\n",
        "We summarize symbols here:"
      ]
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        "| Concept/Symbol                         | Reduced\\-Rank                                                                                                                            | $\\AR$\\-state\\-space                                                                                                                                                                                         |\n",
        "|----------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n",
        "| Dimension of $\\bx$                    | $m$                                                                                                                  | $m$                                                                                                                                                                                                          |\n",
        "| Dimension of $\\by$                    | $k$                                                                                                                  | $k$                                                                                                                                                                                                          |\n",
        "| $\\min(m, k)$                        | $h$                                                                                                                  | $h$                                                                                                                                                                                                          |\n",
        "| Lag                                    | $p=1$ or not applicable                                                                                              | $p$                                                                                                                                                                                                          |\n",
        "| Structure params                       | reduced rank $\\fll = d < m$                                                                                         | $\\hat{\\Psi} = [d_1,\\cdots,d_p], d_i \\geq 0; d_p > 0; \\sum d_i\\leq h$                                                                                                                          |\n",
        "| Total rank alloc.                     | $\\fll=d$                                                                                                            | $\\fll = \\sum d_i$                                                                                                                                                                                         |\n",
        "| Min\\. state-space dim.               | $\\fll=d$                                                                                                            | $\\sum jd_j$                                                                                                                                                                                                |\n",
        "| Alt. struct. params                  | $\\fll=d$ | $\\Psi = [(r_g, l_g), \\cdots,(r_1, l_1) )]_{r_g > \\cdots > r_1, 0 < l_i = d_{r_i}}$                                                                 |\n",
        "| Parameter reduction                    | $(m-d)(k-d)$                                                                                                   | $\\sum_{i=1}^p(m-\\sum_{j\\geq i}d_j) \\sum_{i=1}^p(k-\\sum_{j\\geq i}d_j)$                                                                                                              |\n",
        "| Jordan block                           | $\\bJ(\\lambda, r, l)$                                                                                             | $\\bJ(\\lambda, r, l)$                                                                                                                                                                                     |\n",
        "| $\\lambda=0$ Jordan block              | $\\bK(r, l)$                                                                                                       | $\\bK(r, l)$                                                                                                                                                                                               |\n",
        "| $\\bF$                                 | $\\bF= \\bK(1, l) = 0_{d, d}$                                                                                   | $\\bF = \\sum_\\{i=g\\}^1 \\bK(r_i, l_i)$                                                                                                                                                                 |\n",
        "| Factorization                          | $\\beta = \\bH\\bG$                                                                                                  | $\\bP(L) = \\bZ(L^{-1}) = \\bH(\\bI -\\bF L)^{-1} \\bG$                                                                                                                                         |\n",
        "| Minimal criteria                       | $\\bG, \\bH$ of size $(d, m), (k, d)$, rank $d$                                                                  | $\\bG_{r, 0}, \\bH_{r, 0}$ of size $(d_{r}, m), (k, d_r)$, rank $d_r$\\. $\\bG_{:, 0} = (\\bG_{r, 0})_r$ and $\\bH_{:, 0} = (\\bH_{r, 0})_r$ are of full row and column rank |\n",
        "| Gram\\-Schmidt                          | $\\bG\\bG' = \\bI_{\\fll}$                                                                                        | $\\bG_{:, 0}\\bG_{:, 0}' = \\bI_{\\fll}$; $\\bG_{r, l} \\bG_{r_1, 0}' = 0$ for $l>\\max(0, r-r_1-1)$                                                                                                            |\n",
        "| Numerator matrix ($\\bA$)            | $\\bX\\bX' -\\bX\\bY'(\\bY\\bY')^{-1}\\bY\\bX'$ | $\\bXLag\\bXLag' -\\bXLag\\bY'(\\bY\\bY')^{-1}\\bY\\bXLag'$                                                                                                                                         |\n",
        "| Denom\\. matrix ($\\bB$)              | $\\bX\\bX'$                                                                                                          | $\\bXLag\\bXLag'$                                                                                                                                                                                            |\n",
        "| $\\kappa$                              | $\\kappa(\\bG) = \\bG$                                                                                             | defined in \\cref\\{eq:kappa\\}                                                                                                                                                                                |\n",
        "| Neg Log Likelhood                      | $\\log(\\det(\\bG\\bA\\bG'))-\\log(\\det(\\bG\\bB\\bG'))$                                                   | $\\log(\\det(\\kappa(\\bG)\\bA\\kappa(\\bG)')-\\log(\\det(\\kappa(\\bG)\\bB\\kappa(\\bG)')$                                                                                                   |\n",
        "| Gradient                               | $2\\Tr(\\bG\\bA\\bG')^{-1}\\bG\\bA\\eta'-2\\Tr(\\bG\\bB\\bG')^{-1}\\bG\\bB\\eta'$ | $2\\Tr(\\kappa(\\bG)\\bA\\kappa(\\bG)')^{-1}\\kappa(\\bG)\\bA\\kappa(\\eta)'-2\\Tr(\\kappa(\\bG)\\bB\\kappa(\\bG)')^{-1}\\kappa(\\bG)\\bB\\kappa(\\eta)'$                         |\n",
        "| ($\\cH(\\bA, \\bG, \\psi, \\eta)$) | $2\\Tr((\\bG\\bA\\bG')^{-1}(\\bG\\bA\\psi' + \\psi\\bA\\bG') - (\\bG\\bA\\bG')^{-1}\\psi\\bA\\eta')$ |$2\\Tr((\\kappa(\\bG)\\bA\\kappa(\\bG)')^{-1}(\\kappa(\\bG)\\bA\\kappa(\\psi)' + \\kappa(\\psi)\\bA\\kappa(\\bG)') - (\\kappa(\\bG)\\bA\\kappa(\\bG)')^{-1}\\kappa(\\psi)\\bA\\kappa(\\eta)')$ \n",
        "| Hessian                                | $\\cH(\\bA, \\bG, \\psi, \\eta) - \\cH(\\bB, \\bG, \\psi, \\eta)$     | $\\cH(\\bA, \\bG, \\psi, \\eta) - \\cH(\\bB, \\bG, \\psi, \\eta)$                   |                                                        |\n",
        "| No. configs for $\\bF$                | $h$                                                                                                                  | $\\begin{pmatrix}p+h-1\\\\ p\\end{pmatrix}$                                                                                                                                                            |\n"
      ]
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      "cell_type": "markdown",
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        "id": "MK4JJ8yr9wiL",
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      "source": [
        "# The minimal_varx package\n",
        "We can first clone the github project to our environment"
      ]
    },
    {
      "cell_type": "code",
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        "id": "BGugcSpBUI8j",
        "colab_type": "code",
        "outputId": "836b5118-e645-4035-88eb-776d55caad37",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "!rm -rf minimal_varx/\n",
        "import os\n",
        "!git clone https://github.com/dnguyend/minimal_varx"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'minimal_varx'...\n",
            "remote: Enumerating objects: 59, done.\u001b[K\n",
            "remote: Counting objects: 100% (59/59), done.\u001b[K\n",
            "remote: Compressing objects: 100% (43/43), done.\u001b[K\n",
            "remote: Total 59 (delta 31), reused 26 (delta 14), pack-reused 0\u001b[K\n",
            "Unpacking objects: 100% (59/59), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "4xy4P3E6MmSw",
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      "source": [
        "Now we can import the modules and packages. \n",
        "\n",
        "We have a **polynomial_matrix** module built on the numpy polynomial package that provides basic functionality to multiply polynomial matrices, computing determinant and roots to check for stability. It can also do Smith normal form, with some caveats as decomposition could be sensitive to numerical tolerance.\n",
        "We will not go in to the package in any detail, but sometime the lag polynomial $\\Phi$ could be given as an object in the polynomial matrix class.\n",
        "\n",
        "**utils** contains a number of utility functions. VAR_sim is to simulate an autoregressive model, where the noise covariance matrix is given by $\\bO^T  \\bD  \\bO$ and autoregressive terms is given by Phi. There is a utility to generate a random orthogonal matrix. list_all_psi_hat and psi_hat_to_psi are functions to list all possible nilpotent Jordan matrix configurations.\n",
        "\n",
        "**minimal_varx** is the main module. Its main object is varx_minimal_estimator. Given $\\Psi$ and $m$, it constructs the basic structure, including aggregate rank ($\\sum d_i$), McMillan dimension. It can compute $\\kappa$. Set it up with some covariant matrices and $\\bG$ it computes the optimal negative log likelihood for that $\\bG$ via $calc\\_states$. That function also compute gradient. Hessian product is computed via a call to $hessian\\_product$.\n",
        "\n",
        "It has a few fit functions, $simple\\_fit$ does not use gradient, $gradient\\_fit$ uses gradient, $hessian\\_fit$ uses Hessian product and $manifold\\_fit$ uses manifold optimization (we set up the later for the manifold case only, not the vector bundle case - and not using the full symmetry.)"
      ]
    },
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      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from minimal_varx.minimal_varx import gen_random_stable, varx_minimal_estimator\n",
        "from minimal_varx.minimal_varx import calc_extended_covariance\n",
        "from minimal_varx.utils import VAR_sim, random_orthogonal, list_all_psi_hat, psi_hat_to_psi\n",
        "from minimal_varx import polynomial_matrix as pm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ez-OrE_ukDvY",
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      "source": [
        "Central to our set up is a Jordan matrix configuration $\\Psi$. For most of the paper we are assuming that a Jordan matrix configuration is picked. We will show a few operations we can perform with Jordan matrix configuration:"
      ]
    },
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      "source": [
        "Psi =  [(3, 2), (2, 1), (1, 2)]\n",
        "m = 5\n",
        "es = varx_minimal_estimator(Psi, m=m)\n",
        "# Jordan matrix\n",
        "print(pm.calc_Jordan_matrix(es.Psi, 0))\n",
        "# McMilan degree\n",
        "print('McMillan degree is %d' % es.mm_degree)\n",
        "# aggregate rank sum d_i\n",
        "print('Aggregate rank is %d' %es.agg_rnk)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "McMillan degree is 10\n",
            "Aggregate rank is 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
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      "source": [
        "In the above, $\\Psi$ specifies a Jordan matrix of form $\\bK(3,2)\\oplus \\bK(2, 1)\\oplus \\bK(1, 2)$. The total aggregate rank $\\fll$ is $5$, same as $m$. So in this case there is no extra dimension. The McMillan degree which is the dimension of $\\bF$ is $10$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vDLTjm4clRZ4",
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      "source": [
        "Another example is the LQ factorization applied to multi-lag system. Given a $\\Psi$, and $\\bG$ of size $\\nmin\\times m$ can be factorized to $\\bS, \\bW$ with $ \\bG = \\bS^{-1}\\bW$ where $\\bS$ communtes with $\\bF$ and $\\bW$ satisfies the orthogonal relations in the paper. We summarize the orthogonal relations as follow:\n",
        "\n",
        "*   The zero blocks can be made orthonormal\n",
        "*   The $(r, r-1)$ blocks are all orthogonal to the zero blocks.\n",
        "*   The $(r, j)$ blocks are orthogonal to the orthogonal to the $(p, 0), (p-1, 0),\\cdots, (r-j, 0)$ blocks.\n",
        "The following code demonstrates the theorem.\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OFddhy2KtEoM",
        "colab_type": "code",
        "outputId": "91ace52e-d05b-4a31-a22e-9cb40d028ed0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "from minimal_varx.minimal_varx import get_zero_blocks, LQ_multi_lags\n",
        "from numpy.linalg import qr\n",
        "\n",
        "def check_W(es, G):\n",
        "    W, S = LQ_multi_lags(es, G)\n",
        "    # print check decomposition:\n",
        "    print(\"Check decomposition sum(abs(W - S @ G)) %f\" % np.nansum(np.abs(W - S @ G)))\n",
        "    FF = pm.calc_Jordan_matrix(es.Psi, 0)\n",
        "    print(\"F:\")\n",
        "    print(FF)\n",
        "    # print check commutative:\n",
        "    print(\"check commutative sum(abs(FF @S - S @ FF)) %f\" % np.nansum(np.abs(FF @ S - S @ FF)))\n",
        "    W0 = get_zero_blocks(es, W)\n",
        "    print(\"check orthogonal W0\")\n",
        "    print(\"sum abs W0 @ W0.T - I=%f\" % np.nansum(np.abs(W0 @ W0.T - np.eye(es.agg_rnk))))\n",
        "    print(\"check orthorgonal individuals:\")\n",
        "    n_psi = len(es.Psi)\n",
        "\n",
        "    start_blk = 0\n",
        "    for r in range(n_psi):\n",
        "        rho, lx = es.Psi[r]\n",
        "        for j in range(rho-1, -1, -1):\n",
        "            if j == 0:\n",
        "                start_blk += lx\n",
        "                continue\n",
        "            n_j_col = sum([rr[1] for rr in es.Psi if rr[0] >= rho - j])\n",
        "            print(\n",
        "                \"rho=%d j=%d n_j_col=%d start=%d end=%d\" % (\n",
        "                    rho, j, n_j_col, start_blk, start_blk+lx))\n",
        "            ee = np.nansum(\n",
        "                np.abs(W[start_blk:start_blk+lx, :] @ W0[:n_j_col, :].T))\n",
        "            if ee > 1e-5:\n",
        "                print(\"BAD!!!\")\n",
        "            print(ee)\n",
        "            start_blk += lx\n",
        "    return W, S\n",
        "\n",
        "Psi =  [(3, 2), (2, 1), (1, 2)]\n",
        "d_0 = 1\n",
        "m = sum([rr[1] for rr in Psi]) + d_0\n",
        "es = varx_minimal_estimator(Psi, m=m)\n",
        "np.random.seed(0)\n",
        "\n",
        "G = np.random.randint(-10,10, (es.mm_degree, m))\n",
        "G0 = get_zero_blocks(es, G)\n",
        "# Check G0 is of full rank\n",
        "print(\"full rank check %f\" % np.prod(np.diagonal(qr(G0)[1])))\n",
        "print(\"G\")\n",
        "print(G)\n",
        "W, S = check_W(es, G)\n",
        "print(\"W=%s\" % str(W))\n",
        "print(\"S=%s\" % str(S))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "full rank check 107629.000000\n",
            "G\n",
            "[[  2   5 -10  -7  -7  -3]\n",
            " [ -1   9   8  -6  -4   2]\n",
            " [ -9  -4  -3   4   7  -5]\n",
            " [  3  -2  -1   9   6   9]\n",
            " [ -5   5   5 -10   8  -7]\n",
            " [  7   9   9   9   4  -3]\n",
            " [-10  -9  -1 -10   0  -7]\n",
            " [  1   8  -8 -10 -10  -6]\n",
            " [ -5  -4  -2   7   5  -6]\n",
            " [ -1   0  -9  -9  -3  -1]]\n",
            "Check decomposition sum(abs(W - S @ G)) 0.000000\n",
            "F:\n",
            "[[0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "check commutative sum(abs(FF @S - S @ FF)) 0.000000\n",
            "check orthogonal W0\n",
            "sum abs W0 @ W0.T - I=0.000000\n",
            "check orthorgonal individuals:\n",
            "rho=3 j=2 n_j_col=5 start=0 end=2\n",
            "9.536923669726823e-16\n",
            "rho=3 j=1 n_j_col=3 start=2 end=4\n",
            "3.7183917279385354e-16\n",
            "rho=2 j=1 n_j_col=5 start=6 end=7\n",
            "6.314393452555578e-16\n",
            "W=[[ 0.0328329  -0.03359505  0.01307958 -0.01176335 -0.00564292 -0.02775025]\n",
            " [ 0.05482424 -0.05609687  0.02184023 -0.01964239 -0.00942253 -0.04633725]\n",
            " [-0.29250158  0.01980605 -0.29831372  0.34068501  0.10119092 -0.36105044]\n",
            " [-0.07342636 -0.16856374  0.19615904  0.04518864 -0.2069576  -0.22891983]\n",
            " [-0.29462783  0.29462783  0.29462783 -0.58925565  0.47140452 -0.41247896]\n",
            " [-0.41144165 -0.48880675 -0.48880675 -0.54155567 -0.19692934  0.14418041]\n",
            " [ 0.12457129 -0.12746297  0.04962524 -0.04463131 -0.0214098  -0.10528721]\n",
            " [ 0.25313945  0.56196874 -0.33752236 -0.26494706 -0.58356873 -0.30893496]\n",
            " [ 0.33497986  0.10934275  0.3980086  -0.48723612 -0.11965434  0.68242627]\n",
            " [-0.49267086 -0.07965231  0.59192091  0.1009677  -0.61198862 -0.12584124]]\n",
            "S=[[ 0.05892557  0.         -0.01824336  0.01757805  0.00906368 -0.00223062\n",
            "   0.02356533 -0.01905263  0.00669348 -0.04716351]\n",
            " [ 0.0035166  -0.05626552 -0.02232565  0.00592619  0.05042335 -0.06971721\n",
            "  -0.02609198  0.05589205 -0.0121584  -0.13534948]\n",
            " [ 0.          0.          0.05892557  0.         -0.01824336  0.01757805\n",
            "   0.          0.02356533  0.          0.        ]\n",
            " [ 0.          0.          0.0035166  -0.05626552 -0.02232565  0.00592619\n",
            "   0.         -0.02609198  0.          0.        ]\n",
            " [ 0.          0.          0.          0.          0.05892557  0.\n",
            "   0.          0.          0.          0.        ]\n",
            " [ 0.          0.          0.          0.          0.0035166  -0.05626552\n",
            "   0.          0.          0.          0.        ]\n",
            " [ 0.          0.         -0.01233411  0.01932153 -0.02424277  0.05819374\n",
            "   0.05621819 -0.00855852 -0.00843643  0.04441203]\n",
            " [ 0.          0.          0.          0.         -0.01233411  0.01932153\n",
            "   0.          0.05621819  0.          0.        ]\n",
            " [ 0.          0.          0.          0.          0.00844824 -0.00677792\n",
            "   0.         -0.02939311 -0.09081193 -0.        ]\n",
            " [ 0.          0.          0.          0.          0.01646766 -0.11406885\n",
            "   0.          0.10634232 -0.00347263 -0.26444396]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ldo2OHQThXO7",
        "colab_type": "text"
      },
      "source": [
        "We see $\\bS$ has the perculiar form required so that it commutes with $\\bF$.\n",
        "Next we test generating a random stable matrix of a particular configuration $\\Psi$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2lQ8nuaEmkRx",
        "colab_type": "code",
        "outputId": "b8e83bd6-9e07-4387-a1f0-75360941a458",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        }
      },
      "source": [
        "def test_random_stable():\n",
        "    Psi = [(2, 1), (1, 2)]\n",
        "    k_zero = 2\n",
        "    k = sum([a[1] for a in Psi]) + k_zero\n",
        "    \n",
        "    es = varx_minimal_estimator(Psi, m=k)\n",
        "    stable, H, F, G, Phi = gen_random_stable(es, k)\n",
        "\n",
        "    p = Psi[0][0]\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "    D = np.arange(k) * 0.2 + 1\n",
        "    OO = random_orthogonal(k)\n",
        "    Y, e = VAR_sim(Phi, n, D, OO)\n",
        "    Y = Y.T\n",
        "    e = e.T\n",
        "    X = Y.copy()\n",
        "    print(Y[:, -5:])\n",
        "    print(X[:, -5:])\n",
        "    \n",
        "test_random_stable()    "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 6.39964614e+08  5.30547996e+08 -1.31242852e+08 -6.80138382e+08\n",
            "  -5.44672554e+08]\n",
            " [-1.47171982e+08  7.21864736e+07  2.24463846e+08  1.49888351e+08\n",
            "  -8.22469542e+07]\n",
            " [-3.44779346e+08 -6.74829679e+07  2.89151938e+08  3.59089322e+08\n",
            "   6.01286315e+07]\n",
            " [-3.67221094e+08  1.73815324e+08  5.53772500e+08  3.74210632e+08\n",
            "  -1.98486092e+08]\n",
            " [ 5.59996707e+08  3.96447889e+08 -1.82677749e+08 -5.92873178e+08\n",
            "  -4.04160688e+08]]\n",
            "[[ 6.39964614e+08  5.30547996e+08 -1.31242852e+08 -6.80138382e+08\n",
            "  -5.44672554e+08]\n",
            " [-1.47171982e+08  7.21864736e+07  2.24463846e+08  1.49888351e+08\n",
            "  -8.22469542e+07]\n",
            " [-3.44779346e+08 -6.74829679e+07  2.89151938e+08  3.59089322e+08\n",
            "   6.01286315e+07]\n",
            " [-3.67221094e+08  1.73815324e+08  5.53772500e+08  3.74210632e+08\n",
            "  -1.98486092e+08]\n",
            " [ 5.59996707e+08  3.96447889e+08 -1.82677749e+08 -5.92873178e+08\n",
            "  -4.04160688e+08]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OBCfWQ6VAvln",
        "colab_type": "text"
      },
      "source": [
        "## Example of orthogonal relations and reduction of parameters for $\\bG$.\n",
        "We now show an example of the orthogonal realtions and show how it reduce dimensions. This is the case of $m=k=2$. We generate $\\bG_a$, then perform a factorization to $\\bW_a$ and $\\bS_a$. We demonstrate that $\\kappa(\\bS_a \\bG_a) = \\bW_a$ so the likelihood function is unchanged, and verify that:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IPKhHHos7M5x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 646
        },
        "outputId": "ad677f64-92b7-4057-ce9e-007dc4a18f60"
      },
      "source": [
        "Psi =  [(3, 1), (1, 1)]\n",
        "d_0 = 0\n",
        "m = sum([rr[1] for rr in Psi]) + d_0\n",
        "es = varx_minimal_estimator(Psi, m=m)\n",
        "np.random.seed(2)\n",
        "\n",
        "G_a = np.random.randint(-10,10, (es.mm_degree, m))\n",
        "G0_a = get_zero_blocks(es, G_a)\n",
        "print(\"G_a=%s\" %str(G_a))\n",
        "W_a, S_a = check_W(es, G_a)\n",
        "print(\"W=%s\" % str(W_a))\n",
        "print(\"S=%s\" % str(S_a))\n",
        "\n",
        "k = sum([a[1] for a in Psi])\n",
        "p = Psi[0][0]\n",
        "T = 1000\n",
        "n = T + p\n",
        "\n",
        "for ii in range(5):\n",
        "    success = False\n",
        "    cnt = 0\n",
        "    while (not success) and (cnt < 10):\n",
        "      cnt += 1\n",
        "      try:\n",
        "        D = np.arange(k) * 0.2 + 1\n",
        "        OO = random_orthogonal(k)\n",
        "        es = varx_minimal_estimator(Psi, m=k)\n",
        "        stable, H, F, G, Phi = gen_random_stable(es, k)\n",
        "        Y, e = VAR_sim(Phi, n, D, OO)\n",
        "        Y = Y.T\n",
        "        e = e.T\n",
        "        X = Y.copy()\n",
        "        cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "\n",
        "        es_G = varx_minimal_estimator(Psi, m=k)\n",
        "        es_G.set_covs(cov_res, cov_xlag)\n",
        "        es_G.calc_states(G)\n",
        "\n",
        "        if ~np.isnan(es_G.neg_log_llk):\n",
        "          success = True          \n",
        "          es_G.calc_states(G_a)\n",
        "          es = varx_minimal_estimator(Psi, m=k)\n",
        "          es.set_covs(cov_res, cov_xlag)\n",
        "          es.calc_states(W_a)\n",
        "          print(\"doing ii=%d cnt=%d\" % (ii, cnt))\n",
        "          print('LLK for G=%f W=%f' % (es_G.neg_log_llk, es.neg_log_llk))\n",
        "          if ii == 0:\n",
        "            print(\"check S @kappa(G) = kappa(W) diff=%f\" % np.sum(np.abs(S_a @ es_G.kappa - es.kappa)))\n",
        "      except Exception as e:\n",
        "        pass\n",
        "        # print(e)\n",
        "\n",
        "  \n"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "G_a=[[-2  5]\n",
            " [ 3 -2]\n",
            " [ 1  8]\n",
            " [ 1 -2]]\n",
            "Check decomposition sum(abs(W - S @ G)) 0.000000\n",
            "F:\n",
            "[[0. 1. 0. 0.]\n",
            " [0. 0. 1. 0.]\n",
            " [0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]]\n",
            "check commutative sum(abs(FF @S - S @ FF)) 0.000000\n",
            "check orthogonal W0\n",
            "sum abs W0 @ W0.T - I=0.000000\n",
            "check orthorgonal individuals:\n",
            "rho=3 j=2 n_j_col=2 start=0 end=1\n",
            "3.098389909369715e-17\n",
            "rho=3 j=1 n_j_col=1 start=1 end=2\n",
            "4.163336342344337e-17\n",
            "W=[[ 2.77555756e-17  0.00000000e+00]\n",
            " [-3.96911151e-01  4.96138938e-02]\n",
            " [-1.24034735e-01 -9.92277877e-01]\n",
            " [-9.92277877e-01  1.24034735e-01]]\n",
            "S=[[-0.12403473 -0.02480695  0.02232625 -0.19597488]\n",
            " [ 0.         -0.12403473 -0.02480695  0.        ]\n",
            " [ 0.          0.         -0.12403473  0.        ]\n",
            " [ 0.          0.         -0.1860521  -0.80622577]]\n",
            "doing ii=0 cnt=1\n",
            "LLK for G=-0.367114 W=-0.367114\n",
            "check S @kappa(G) = kappa(W) diff=0.000000\n",
            "doing ii=1 cnt=1\n",
            "LLK for G=-1.556929 W=-1.556929\n",
            "doing ii=2 cnt=1\n",
            "LLK for G=-0.884369 W=-0.884369\n",
            "doing ii=3 cnt=1\n",
            "LLK for G=-3.754913 W=-3.754913\n",
            "doing ii=4 cnt=1\n",
            "LLK for G=-0.239516 W=-0.239516\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yCkkLDV3hg8f",
        "colab_type": "text"
      },
      "source": [
        "Now we go through the examples. First is the case $\\Psi = [(2, 1), (1, 1)]$ and $k=m=2$. In this case, we allocate one rank to exponent $2$ and one to expoment $1$, leaving $2-1-1=0$ rank free. We test for 10 simulations, the result in the table at the end shows the fitted results agree well with the original data. Here, we do not constraint $\\bG$, just vectorize $\\bG$ and use a standard optimizer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1hXIZufpo6fs",
        "colab_type": "code",
        "outputId": "85fb5211-1a3f-46b1-ed79-3bba6f197689",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "# The following cell shows a number of simulations for the case where configuration of G is a half circle.\n",
        "def k_2_p_2_sphere():\n",
        "    np.random.seed(0)\n",
        "    Psi = [(2, 1), (1, 1)]\n",
        "    k_zero = 0\n",
        "    k = sum([a[1] for a in Psi]) + k_zero\n",
        "    p = Psi[0][0]\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "    n_test = 10\n",
        "    results = np.zeros((n_test, 3))\n",
        "    for ii in range(n_test):\n",
        "        success = False\n",
        "        cnt = 0\n",
        "        while not success and cnt < 10:\n",
        "          cnt += 1\n",
        "          try:\n",
        "            D = np.arange(k) * 0.2 + 1\n",
        "            OO = random_orthogonal(k)\n",
        "            es = varx_minimal_estimator(Psi, m=k)\n",
        "            stable, H, F, G, Phi = gen_random_stable(es, k)\n",
        "            Y, e = VAR_sim(Phi, n, D, OO)\n",
        "            Y = Y.T\n",
        "            e = e.T\n",
        "            X = Y.copy()\n",
        "            cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "\n",
        "            es_G = varx_minimal_estimator(Psi, m=k)\n",
        "            es_G.set_covs(cov_res, cov_xlag)\n",
        "            es_G.calc_states(G)\n",
        "            if ~np.isnan(es_G.neg_log_llk):\n",
        "              success = True\n",
        "          except Exception:\n",
        "            continue\n",
        "          \n",
        "        results[ii, 0] = es_G.neg_log_llk\n",
        "        n_cnt = 0\n",
        "        success = False        \n",
        "        while (not success) and (n_cnt < 10):\n",
        "          n_cnt += 1\n",
        "          try:\n",
        "            opt = es.hessian_fit(Y, X)\n",
        "            if opt['success']:\n",
        "                print('orig_llk %s est_llk=%s' % (\n",
        "                    es_G.neg_log_llk, opt['fun']))                \n",
        "                print(Phi.PolynomialMatrix_to_3darray())\n",
        "                print(es.Phi)\n",
        "                success = True\n",
        "                results[ii, 1] = opt['fun']\n",
        "                results[ii, 2] = 1                    \n",
        "          except Exception as e:\n",
        "            continue            \n",
        "        if not success:\n",
        "            print(\"failed for ii=%d\" % ii)\n",
        "            results[ii, 1] = opt['fun']\n",
        "            results[ii, 2] = 0\n",
        "    print(pd.DataFrame(results, columns=['org_llk', 'fitted_llk', 'success']))\n",
        "                           \n",
        "k_2_p_2_sphere()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "orig_llk -1.5275612811492956 est_llk=-1.5336429203454474\n",
            "[[[-0.13954948 -0.13632018]\n",
            "  [ 0.07099343  0.68471271]]\n",
            "\n",
            " [[-0.07170538 -0.32448304]\n",
            "  [ 0.0364789  -0.91472841]]]\n",
            "[[[-0.18863503 -0.11991588]\n",
            "  [ 0.00147733  0.62950123]]\n",
            "\n",
            " [[-0.12773866 -0.32318168]\n",
            "  [ 0.00100041 -0.91994404]]]\n",
            "orig_llk -1.3009257030066925 est_llk=-1.3021348575403358\n",
            "[[[ 0.0948563   0.08103531]\n",
            "  [ 0.62161702 -0.10897317]]\n",
            "\n",
            " [[-0.07212174  0.40856505]\n",
            "  [-0.47263176 -0.26227015]]]\n",
            "[[[ 0.1198313   0.0461108 ]\n",
            "  [ 0.60599118 -0.14548534]]\n",
            "\n",
            " [[-0.08419285  0.45048081]\n",
            "  [-0.42576627 -0.23178044]]]\n",
            "orig_llk -4.2375244086469674 est_llk=-4.2383618386917625\n",
            "[[[-0.31996468 -0.58783334]\n",
            "  [ 0.34045303  0.41843011]]\n",
            "\n",
            " [[ 0.55580947 -0.04251673]\n",
            "  [-0.59139971 -0.4332968 ]]]\n",
            "[[[-0.30967438 -0.54425847]\n",
            "  [ 0.30967438  0.42770733]]\n",
            "\n",
            " [[ 0.55802751 -0.07439485]\n",
            "  [-0.55802751 -0.43364089]]]\n",
            "orig_llk -1.118878318082876 est_llk=-1.1193471358061333\n",
            "[[[ 0.16749775 -0.46734125]\n",
            "  [ 0.13063426 -0.03723419]]\n",
            "\n",
            " [[ 0.5179894   0.66133849]\n",
            "  [ 0.4039885  -0.40798825]]]\n",
            "[[[ 0.17140448 -0.43326115]\n",
            "  [ 0.1252449  -0.06012902]]\n",
            "\n",
            " [[ 0.5028066   0.65650421]\n",
            "  [ 0.36739977 -0.38967607]]]\n",
            "orig_llk -1.4851074710244905 est_llk=-1.4873193037289547\n",
            "[[[-0.11530714 -0.72074518]\n",
            "  [-0.16335292 -0.19044837]]\n",
            "\n",
            " [[-0.33589116  0.85640455]\n",
            "  [-0.47584915  0.25889728]]]\n",
            "[[[-0.12845817 -0.73171737]\n",
            "  [-0.15532764 -0.23309872]]\n",
            "\n",
            " [[-0.39414821  0.83129259]\n",
            "  [-0.47659179  0.28913746]]]\n",
            "orig_llk -1.6937787525291848 est_llk=-1.6971695454662399\n",
            "[[[-0.14466819  0.38934711]\n",
            "  [ 0.34537356  0.96556131]]\n",
            "\n",
            " [[-0.06069045  0.233879  ]\n",
            "  [ 0.14488933 -0.4482402 ]]]\n",
            "[[[-0.18078364  0.44881615]\n",
            "  [ 0.2929218   0.9819615 ]]\n",
            "\n",
            " [[-0.0624692   0.26254601]\n",
            "  [ 0.10121818 -0.47989334]]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/linalg/linalg.py:2093: RuntimeWarning: overflow encountered in det\n",
            "  r = _umath_linalg.det(a, signature=signature)\n",
            "/content/minimal_varx/minimal_varx.py:93: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  self.rayleigh_quotient = self._numerator_det / self._denominator_det\n",
            "/content/minimal_varx/minimal_varx.py:94: RuntimeWarning: invalid value encountered in log\n",
            "  self.neg_log_llk = log(self._numerator_det)-log(self._denominator_det)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "orig_llk -15.649076012284404 est_llk=-15.65305739665043\n",
            "[[[ 0.15755201 -0.82791427]\n",
            "  [ 0.7290189   0.03448568]]\n",
            "\n",
            " [[ 0.15545239  0.3885806 ]\n",
            "  [ 0.71930361 -0.18407493]]]\n",
            "[[[ 0.19214924 -0.80079825]\n",
            "  [ 0.71131067 -0.00744048]]\n",
            "\n",
            " [[ 0.19283759  0.42021699]\n",
            "  [ 0.71385884 -0.21125326]]]\n",
            "orig_llk -1.1733339556419362 est_llk=-1.1734581000538276\n",
            "[[[ 0.3475915   0.21438361]\n",
            "  [-0.16075141  0.42723564]]\n",
            "\n",
            " [[ 0.5715599  -0.30169449]\n",
            "  [-0.26433056 -0.16960751]]]\n",
            "[[[ 0.31873484  0.24935002]\n",
            "  [-0.14238439  0.41784877]]\n",
            "\n",
            " [[ 0.608375   -0.32142303]\n",
            "  [-0.27177168 -0.17776184]]]\n",
            "orig_llk -2.269574534861329 est_llk=-2.2695746812736584\n",
            "[[[ 0.07902385  0.89429155]\n",
            "  [ 0.41307228  0.25765305]]\n",
            "\n",
            " [[-0.09665286 -0.08390629]\n",
            "  [-0.50522236 -0.65695199]]]\n",
            "[[[ 0.07511543  0.8853464 ]\n",
            "  [ 0.3912652   0.23253625]]\n",
            "\n",
            " [[-0.10318147 -0.08947927]\n",
            "  [-0.53745704 -0.68777714]]]\n",
            "orig_llk -0.7398119121971161 est_llk=-0.7400982177687072\n",
            "[[[ 0.19149181 -0.15644406]\n",
            "  [ 0.15810495  0.14142782]]\n",
            "\n",
            " [[-0.32526829  0.09088141]\n",
            "  [-0.26855732 -0.76234884]]]\n",
            "[[[ 0.17350019 -0.14058875]\n",
            "  [ 0.15341837  0.16399227]]\n",
            "\n",
            " [[-0.30761889  0.09745394]\n",
            "  [-0.27201348 -0.74767212]]]\n",
            "     org_llk  fitted_llk  success\n",
            "0  -1.527561   -1.533643      1.0\n",
            "1  -1.300926   -1.302135      1.0\n",
            "2  -4.237524   -4.238362      1.0\n",
            "3  -1.118878   -1.119347      1.0\n",
            "4  -1.485107   -1.487319      1.0\n",
            "5  -1.693779   -1.697170      1.0\n",
            "6 -15.649076  -15.653057      1.0\n",
            "7  -1.173334   -1.173458      1.0\n",
            "8  -2.269575   -2.269575      1.0\n",
            "9  -0.739812   -0.740098      1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PK1HYJ48h833",
        "colab_type": "text"
      },
      "source": [
        "Let us try to apply the LQ theorem to this case. We note $\\nmin=3$ so original $G$ would have dimension $3\\times 2$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wXhPBY7viFy_",
        "colab_type": "code",
        "outputId": "e0fc404b-1750-4cd5-a0ce-71241dddf767",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        }
      },
      "source": [
        "Psi =  [(2, 1), (1, 1)]\n",
        "d_0 = 0\n",
        "m = sum([rr[1] for rr in Psi]) + d_0\n",
        "es = varx_minimal_estimator(Psi, m=m)\n",
        "np.random.seed(0)\n",
        "\n",
        "G = np.random.randint(-10,10, (es.mm_degree, m))\n",
        "G0 = get_zero_blocks(es, G)\n",
        "# Check G0 is of full rank\n",
        "print(\"full rank check %f\" % np.prod(np.diagonal(qr(G0)[1])))\n",
        "print(\"G\")\n",
        "print(G)\n",
        "W, S = check_W(es, G)\n",
        "print(\"W=%s\" % str(W))\n",
        "print(\"S=%s\" % str(S))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "full rank check 19.000000\n",
            "G\n",
            "[[  2   5]\n",
            " [-10  -7]\n",
            " [ -7  -3]]\n",
            "Check decomposition sum(abs(W - S @ G)) 0.000000\n",
            "F:\n",
            "[[0. 1. 0.]\n",
            " [0. 0. 0.]\n",
            " [0. 0. 0.]]\n",
            "check commutative sum(abs(FF @S - S @ FF)) 0.000000\n",
            "check orthogonal W0\n",
            "sum abs W0 @ W0.T - I=0.000000\n",
            "check orthorgonal individuals:\n",
            "rho=2 j=1 n_j_col=2 start=0 end=1\n",
            "5.911945914342813e-16\n",
            "W=[[-4.44089210e-16 -1.11022302e-16]\n",
            " [-8.19231921e-01 -5.73462344e-01]\n",
            " [-5.73462344e-01  8.19231921e-01]]\n",
            "S=[[ 0.08192319  0.12504066 -0.15522289]\n",
            " [ 0.          0.08192319  0.        ]\n",
            " [ 0.         -0.39236897  0.6424503 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1bOw2SlakdKi",
        "colab_type": "text"
      },
      "source": [
        "As explained in the paper, if we constraint $\\bG$ using the orthogonal relations, we are left with a sphere (with opposite points identified). By the orthogonalizing proposition, once we choose a vector of norm $1$ for $G_{1, 0}$, $G_{2, 0}$ must be orthogonal to it and is uniquely defined up to a scale of $\\pm 1$, which does not change the result. Next, we graph the $llk$ versus $t$, where we represent the circle coordinates by $\\cos t, \\sin t$. Note that in this case\n",
        "$$\\bG = \\begin{bmatrix} 0 & 0 \\\\ \\cos t & \\sin t \\\\ -\\sin t & \\cos t\\end{bmatrix}$$\n",
        "We see $\\bW= \\bS\\bG$ in the above example is indeed of this form, obtained from $\\bG$ without constraint."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aSelFjFfqy1f",
        "colab_type": "code",
        "outputId": "8581e382-8c57-4691-ca82-958dc79a9051",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        }
      },
      "source": [
        "# graphing llk vs the half circle\n",
        "def plot_circle():\n",
        "    np.random.seed(1)\n",
        "    Psi = [(2, 1), (1, 1)]\n",
        "    k_zero = 0\n",
        "    k = sum([a[1] for a in Psi]) + k_zero\n",
        "    p = Psi[0][0]\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "    D = np.arange(k) * 0.2 + 1\n",
        "    OO = random_orthogonal(k)\n",
        "    \n",
        "    es_gen = varx_minimal_estimator(Psi, m=k)\n",
        "    stable, H, F, G, Phi = gen_random_stable(es_gen, k)\n",
        "    Y, e = VAR_sim(Phi, n, D, OO)\n",
        "    Y = Y.T\n",
        "    e = e.T\n",
        "    X = Y.copy()\n",
        "    cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "    \n",
        "    es_G = varx_minimal_estimator(Psi, m=k)\n",
        "    es_G.set_covs(cov_res, cov_xlag)\n",
        "    es_G.calc_states(G)\n",
        "    \n",
        "    print('original llk %s' % es_G.neg_log_llk)    \n",
        "    \n",
        "    es_graph = varx_minimal_estimator(Psi, m=k)\n",
        "    es_graph.set_covs(cov_res, cov_xlag)\n",
        "    n_s = 100\n",
        "    Theta = np.arange(n_s) * 1 * np.pi / n_s - np.pi / 2\n",
        "    llks = np.zeros_like(Theta)\n",
        "    \n",
        "    def gen_gt(t):\n",
        "        vv = np.array([np.cos(t), np.sin(t)])        \n",
        "        return np.array([0, 0, vv[0], vv[1], -vv[1], vv[0]]).reshape(3, 2)\n",
        "\n",
        "    for i in range(Theta.shape[0]):\n",
        "        try:\n",
        "            es_graph.calc_states(gen_gt(Theta[i]))\n",
        "            llks[i] = es_graph.neg_log_llk\n",
        "        except Exception as e:\n",
        "            print(e)\n",
        "            pass\n",
        "    cosTheta = np.cos(Theta)\n",
        "    # import pandas as pd\n",
        "    # resDF = pd.DataFrame({'cosTheta': cosTheta, 'llk': llks}).sort_values('cosTheta')\n",
        "    plt.plot(Theta, llks)\n",
        "    plt.xlabel('Theta')\n",
        "    plt.ylabel('-log_llk')\n",
        "    plt.title('-log_llk vs Theta, org_llk=%f' % es_G.neg_log_llk)\n",
        "    es_graph.simple_fit(Y, X)\n",
        "    print(es_graph.Phi)\n",
        "    print(Phi.PolynomialMatrix_to_3darray())\n",
        "plot_circle()    "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "original llk -1.2723302685925293\n",
            "[[[-0.19686572 -0.53498222]\n",
            "  [ 0.42740042 -0.95142986]]\n",
            "\n",
            " [[ 0.12781235  0.05058104]\n",
            "  [-0.27748382  0.20364765]]]\n",
            "[[[-0.21712203 -0.5690077 ]\n",
            "  [ 0.43775564 -0.98005326]]\n",
            "\n",
            " [[ 0.12523273  0.04440429]\n",
            "  [-0.25249089  0.17464151]]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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86eP4O95BBt/C2yx1NdAVWAm8Boyt63DGmJMrLfdwx1srKTpWzju3DSY22rot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\nJ1Y4jDHG+MQKhzHGGJ/8Pz5tICSPhWAOAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8bfjnzINk3zZ",
        "colab_type": "text"
      },
      "source": [
        "For the next example, we look at the case $\\Psi= [(2, 1)]$. This means there is no rank allocated to exponent $1$. Note here we do not use the orthogonal relation to constraint $\\bG$. We just vectorize $G$ and optimize.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EcE66xBsq3Bh",
        "colab_type": "code",
        "outputId": "e00a3944-22cc-4ece-ff2e-60f3a96d8ce4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "# the example where the configuration space of G is a line and a sphere\n",
        "def k_2_p_2_sphere_line_bundle():\n",
        "    np.random.seed(1)\n",
        "    Psi = [(2, 1)]\n",
        "    k_zero = 1\n",
        "    k = sum([a[1] for a in Psi]) + k_zero\n",
        "    p = Psi[0][0]\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "    n_test = 10\n",
        "    results = np.zeros((n_test, 3))\n",
        "    for ii in range(n_test):\n",
        "        try:\n",
        "            D = np.arange(k) * 0.2 + 1\n",
        "            OO = random_orthogonal(k)\n",
        "            es = varx_minimal_estimator(Psi, m=k)\n",
        "            stable, H, F, G, Phi = gen_random_stable(es, k)\n",
        "            Y, e = VAR_sim(Phi, n, D, OO)\n",
        "            Y = Y.T\n",
        "            e = e.T\n",
        "            X = Y.copy()\n",
        "            cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "            es_G = varx_minimal_estimator(Psi, m=k)\n",
        "            es_G.set_covs(cov_res, cov_xlag)\n",
        "            es_G.calc_states(G)\n",
        "            if ~np.isnan(es_G.neg_log_llk):\n",
        "              success = True\n",
        "        except Exception:\n",
        "            continue\n",
        "\n",
        "        results[ii, 0] = es_G.neg_log_llk\n",
        "        n_cnt = 0\n",
        "        success = False        \n",
        "        while (not success) and (n_cnt < 10):\n",
        "            opt = es.hessian_fit(Y, X)\n",
        "            if opt['success']:\n",
        "                print('orig_llk %s est_llk=%s' % (\n",
        "                    es_G.neg_log_llk, es.neg_log_llk))                \n",
        "                print(Phi.PolynomialMatrix_to_3darray())\n",
        "                print(es.Phi)\n",
        "                success = True\n",
        "                results[ii, 1] = opt['fun']\n",
        "                results[ii, 2] = 1\n",
        "            n_cnt += 1\n",
        "        if not success:\n",
        "            print(\"failed for ii=%d\" % ii)\n",
        "            results[ii, 1] = opt['fun']\n",
        "            results[ii, 2] = 0\n",
        "    print(pd.DataFrame(results, columns=['org_llk', 'fitted_llk', 'success']))\n",
        "k_2_p_2_sphere_line_bundle()            "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "orig_llk -1.1019960013307275 est_llk=None\n",
            "[[[ 0.74186938 -0.05524596]\n",
            "  [-0.24536459  0.73052047]]\n",
            "\n",
            " [[ 0.12980835 -0.05497244]\n",
            "  [-0.04293259  0.14280693]]]\n",
            "[[[ 0.7414377  -0.03648238]\n",
            "  [-0.24914976  0.75543974]]\n",
            "\n",
            " [[ 0.1075042  -0.07386196]\n",
            "  [-0.03612528  0.13257716]]]\n",
            "orig_llk -1.3925935041177167 est_llk=None\n",
            "[[[-0.39620384  0.38145171]\n",
            "  [-0.52480875  0.4212764 ]]\n",
            "\n",
            " [[ 0.48581298  0.03613956]\n",
            "  [ 0.64350437  0.15085835]]]\n",
            "[[[-0.40190153  0.38112102]\n",
            "  [-0.54083358  0.42973515]]\n",
            "\n",
            " [[ 0.51159657  0.03885165]\n",
            "  [ 0.68844875  0.15810725]]]\n",
            "orig_llk -1.3435266967850292 est_llk=None\n",
            "[[[ 0.09457228  0.41805105]\n",
            "  [-0.35028818  0.35922678]]\n",
            "\n",
            " [[ 0.13345387  0.87845344]\n",
            "  [-0.49430248 -0.56177118]]]\n",
            "[[[ 0.10049616  0.39061511]\n",
            "  [-0.34318987  0.36680354]]\n",
            "\n",
            " [[ 0.14952114  0.90863136]\n",
            "  [-0.51060798 -0.57252934]]]\n",
            "orig_llk -0.7524715684243024 est_llk=None\n",
            "[[[ 0.06389573 -0.33411621]\n",
            "  [ 0.01887324 -0.08565621]]\n",
            "\n",
            " [[ 0.70648975 -0.30364179]\n",
            "  [ 0.20867984  0.0544227 ]]]\n",
            "[[[ 0.07836974 -0.31407356]\n",
            "  [ 0.02041271 -0.06463463]]\n",
            "\n",
            " [[ 0.74232998 -0.25625182]\n",
            "  [ 0.19335228  0.09590208]]]\n",
            "orig_llk -0.7361810231443848 est_llk=None\n",
            "[[[ 0.39955478 -0.139411  ]\n",
            "  [ 0.55132826 -0.0542898 ]]\n",
            "\n",
            " [[-0.18032572 -0.13526139]\n",
            "  [-0.24882361 -0.24895792]]]\n",
            "[[[ 0.41445634 -0.14058041]\n",
            "  [ 0.57547233 -0.05400744]]\n",
            "\n",
            " [[-0.17679787 -0.13011436]\n",
            "  [-0.24548371 -0.24089152]]]\n",
            "orig_llk -0.43460325588759485 est_llk=None\n",
            "[[[ 0.26191076 -0.27098645]\n",
            "  [ 0.41340608  0.11861365]]\n",
            "\n",
            " [[-0.09353545  0.25421292]\n",
            "  [-0.14763855  0.20614096]]]\n",
            "[[[ 0.263128   -0.27896834]\n",
            "  [ 0.43760703  0.10574752]]\n",
            "\n",
            " [[-0.06343539  0.23630638]\n",
            "  [-0.10549911  0.25565613]]]\n",
            "orig_llk -4.088476979939146 est_llk=None\n",
            "[[[ 0.29691302 -0.04151373]\n",
            "  [ 0.02354476  0.25074044]]\n",
            "\n",
            " [[ 0.57550855  0.53289666]\n",
            "  [ 0.04563697  0.5346507 ]]]\n",
            "[[[ 0.289758   -0.05489956]\n",
            "  [ 0.03782127  0.24748973]]\n",
            "\n",
            " [[ 0.52756576  0.50700265]\n",
            "  [ 0.06886162  0.52983201]]]\n",
            "orig_llk -0.9505111837630245 est_llk=None\n",
            "[[[-0.02454419  0.64572393]\n",
            "  [ 0.0033655  -0.07480608]]\n",
            "\n",
            " [[-0.50942038  0.88073468]\n",
            "  [ 0.06985168  0.16431795]]]\n",
            "[[[ 0.03112     0.65463405]\n",
            "  [-0.00409955 -0.1034404 ]]\n",
            "\n",
            " [[-0.51325958  0.87694278]\n",
            "  [ 0.06761361  0.16820459]]]\n",
            "orig_llk -0.6032340310857908 est_llk=None\n",
            "[[[ 0.38387933 -0.01902725]\n",
            "  [ 0.40408214  0.26322588]]\n",
            "\n",
            " [[-0.17143008  0.33669821]\n",
            "  [-0.1804521   0.22792421]]]\n",
            "[[[ 0.41467482 -0.08319979]\n",
            "  [ 0.40219065  0.20597108]]\n",
            "\n",
            " [[-0.16365101  0.32794453]\n",
            "  [-0.15872415  0.20493898]]]\n",
            "orig_llk -0.8389188095118252 est_llk=None\n",
            "[[[ 0.00542113  0.0867083 ]\n",
            "  [ 0.00983331  0.20425834]]\n",
            "\n",
            " [[-0.16498541  0.94101941]\n",
            "  [-0.29926439  0.27713629]]]\n",
            "[[[-0.00739677  0.10293187]\n",
            "  [-0.0268212   0.14461099]]\n",
            "\n",
            " [[-0.09702252  0.89472753]\n",
            "  [-0.35181027  0.24547199]]]\n",
            "    org_llk   opt_llk  success\n",
            "0 -1.101996 -1.102927      1.0\n",
            "1 -1.392594 -1.392807      1.0\n",
            "2 -1.343527 -1.343897      1.0\n",
            "3 -0.752472 -0.754267      1.0\n",
            "4 -0.736181 -0.736200      1.0\n",
            "5 -0.434603 -0.435047      1.0\n",
            "6 -4.088477 -4.091982      1.0\n",
            "7 -0.950511 -0.950550      1.0\n",
            "8 -0.603234 -0.604483      1.0\n",
            "9 -0.838919 -0.850620      1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BFfzkkr4jix0",
        "colab_type": "text"
      },
      "source": [
        "To illustrate the $LQ$ theorem in this case, we again show a general $G$ could be factorized to the $LQ$ form:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "akQxJaHDjhtn",
        "colab_type": "code",
        "outputId": "a7a41121-7f0a-45de-fccb-83c18e261743",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        }
      },
      "source": [
        "Psi =  [(2, 1)]\n",
        "d_0 = 1\n",
        "m = sum([rr[1] for rr in Psi]) + d_0\n",
        "es = varx_minimal_estimator(Psi, m=m)\n",
        "np.random.seed(0)\n",
        "\n",
        "G = np.random.randint(-10,10, (es.mm_degree, m))\n",
        "G0 = get_zero_blocks(es, G)\n",
        "# Check G0 is of full rank\n",
        "print(\"full rank check %f\" % np.prod(np.diagonal(qr(G0)[1])))\n",
        "print(\"G\")\n",
        "print(G)\n",
        "W, S = check_W(es, G)\n",
        "print(\"W=%s\" % str(W))\n",
        "print(\"S=%s\" % str(S))\n",
        "print(\"W @ W.T %s\" % str(W @ W.T))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "full rank check -10.000000\n",
            "G\n",
            "[[  2   5]\n",
            " [-10  -7]]\n",
            "Check decomposition sum(abs(W - S @ G)) 0.000000\n",
            "F:\n",
            "[[0. 1.]\n",
            " [0. 0.]]\n",
            "check commutative sum(abs(FF @S - S @ FF)) 0.000000\n",
            "check orthogonal W0\n",
            "sum abs W0 @ W0.T - I=0.000000\n",
            "check orthorgonal individuals:\n",
            "rho=2 j=1 n_j_col=1 start=0 end=1\n",
            "9.71445146547012e-17\n",
            "W=[[-0.13855466  0.19793523]\n",
            " [-0.81923192 -0.57346234]]\n",
            "S=[[0.08192319 0.0302401 ]\n",
            " [0.         0.08192319]]\n",
            "W @ W.T [[5.83757488e-02 9.74213778e-17]\n",
            " [9.74213778e-17 1.00000000e+00]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XCE1Z-fpmaOy",
        "colab_type": "text"
      },
      "source": [
        "So $\\bG$ could be orthogonalized. As explained in the paper this is the case of a circle and its tangent. In the example above we see the top row of $\\bW$ is orthogonal to the second row.\n",
        "The matrix $\\bG$ is\n",
        "$$\\begin{bmatrix}-c\\sin t & c\\cos t \\\\ \\cos t & \\sin t\n",
        "\\end{bmatrix}$$\n",
        "The likelihood ratio is a trigonometric function in $t$, and for fixed $t$ is a ratio of two polynomial function in $c$. We made a few plots, we see we recover the $llk$ as well as $\\Phi$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7Z-jlSJYq5ss",
        "colab_type": "code",
        "outputId": "3d741b8a-3c32-4f70-c007-7edb93a5a780",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 687
        }
      },
      "source": [
        "# graphing LLK vs the line bunle over the circle, in this case just a copy of a line ($G_{2,1}$) and a circle\n",
        "np.random.seed(1)\n",
        "Psi = [(2, 1)]\n",
        "k_zero = 1\n",
        "k = sum([a[1] for a in Psi]) + k_zero\n",
        "p = Psi[0][0]\n",
        "T = 1000\n",
        "n = T + p\n",
        "D = np.arange(k) * 0.2 + 1\n",
        "OO = random_orthogonal(k)\n",
        "\n",
        "es_gen = varx_minimal_estimator(Psi, m=k)\n",
        "stable, H, F, G, Phi = gen_random_stable(es_gen, k)\n",
        "Y, e = VAR_sim(Phi, n, D, OO)\n",
        "Y = Y.T\n",
        "e = e.T\n",
        "X = Y.copy()\n",
        "cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "\n",
        "es_G = varx_minimal_estimator(Psi, m=k)\n",
        "es_G.set_covs(cov_res, cov_xlag)\n",
        "es_G.calc_states(G)\n",
        "n_s = 20\n",
        "\n",
        "Theta = np.arange(n_s) * 1 * np.pi / n_s - np.pi / 2\n",
        "C = np.arange(n_s) * 20 / n_s\n",
        "C -= C[C.shape[0] // 2]\n",
        "\n",
        "es = varx_minimal_estimator(Psi, m=k)\n",
        "es.set_covs(cov_res, cov_xlag)\n",
        "es.gradient_fit(Y, X)\n",
        "llk_dat = np.zeros((n_s * n_s, 3))\n",
        "cnt = 0\n",
        "for i_theta in range(n_s):\n",
        "    G_20 = [np.cos(Theta[i_theta]), np.sin(Theta[i_theta])]\n",
        "\n",
        "    for i_c in range(n_s):\n",
        "        llk_dat[cnt, 0] = Theta[i_theta]\n",
        "        llk_dat[cnt, 1] = C[i_c]\n",
        "        G_21 = [C[i_c] * G_20[1], C[i_c] * G_20[0]]\n",
        "        G = np.array(G_21 + G_20).reshape(2, 2)\n",
        "        try:\n",
        "            es.calc_states(G)\n",
        "            llk_dat[cnt, 2] = es.neg_log_llk \n",
        "        except Exception as e:\n",
        "            print(e)\n",
        "            tt[cnt, 2] = np.nan\n",
        "        cnt += 1\n",
        "            \n",
        "\"\"\"\n",
        "    for ii in range(Theta.shape[0]):\n",
        "        G_20 = [np.cos(Theta[ii]), np.sin(Theta[ii])]\n",
        "        G_21 = [C[ii] * G_20[1], C[ii] * G_20[0]]\n",
        "        G = np.array(G_21 + G_20).reshape(2, 2)\n",
        "        es.calc_states(G)\n",
        "        llks[ii] = es.neg_log_llk\n",
        "\"\"\"\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "# llk_dat = np.concatenate([Theta.reshape(-1, 1), C.reshape(-1, 1), llks.reshape(-1, 1)], axis=1)\n",
        "# fig= plt.figure()\n",
        "fig = plt.figure(figsize=(5, 8))\n",
        "ax = plt.axes(projection='3d')\n",
        "ax.scatter(xs=llk_dat[:, 0], ys=llk_dat[:, 1], zs=llk_dat[:, 2])\n",
        "ax.set_xlabel('theta')\n",
        "ax.set_ylabel('C')\n",
        "ax.set_zlabel('-LLK');\n",
        "print('Original LLK %f' % es_G.neg_log_llk)\n",
        "pd.DataFrame(llk_dat, columns=['Theta', 'C', 'llk']).sort_values('llk').head()\n",
        "print(\"org Phi\")\n",
        "print(Phi.PolynomialMatrix_to_3darray())\n",
        "print(\"fitted Phi\")\n",
        "print(es.Phi)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Original LLK -1.101996\n",
            "org Phi\n",
            "[[[ 0.74186938 -0.05524596]\n",
            "  [-0.24536459  0.73052047]]\n",
            "\n",
            " [[ 0.12980835 -0.05497244]\n",
            "  [-0.04293259  0.14280693]]]\n",
            "fitted Phi\n",
            "[[[ 0.74142713 -0.03649409]\n",
            "  [-0.24909784  0.75546506]]\n",
            "\n",
            " [[ 0.10750374 -0.07386304]\n",
            "  [-0.03611811  0.13257722]]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9epTf//3f5+zZs7zwwgt88pOf5KMf/Si9vb00NTXxpS996b7m+IYRpfUKtVUE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j1NXV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weBXMysrKGDVqFNzc3HieYwUFBVJJTgwGAzQajU8DuzvESU4MBgPKysoC+8mePXuG/Px8LFu2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\n",
            "text/plain": [
              "<Figure size 360x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lJuRG9BAug5x",
        "colab_type": "code",
        "outputId": "8830630a-1f8a-47d3-9b30-275f8f9bf841",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "llk_dat[idx_m]"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.        , -3.        , -0.01322268]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9S6lNvYqq8om",
        "colab_type": "code",
        "outputId": "7f0a89de-5656-495e-ff27-0779798044d2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 729
        }
      },
      "source": [
        "n_plt = 5\n",
        "plt.figure(figsize=(5, 10))\n",
        "for ii in range(n_plt):\n",
        "    plt.subplot(n_plt+1, 1, ii+1)\n",
        "    idx = np.where(llk_dat[:, 0] == Theta[ii * n_s // n_plt])[0]\n",
        "    plt.plot(llk_dat[idx, 1], llk_dat[idx, 2])\n",
        "    plt.title('theta=%0.3f cos=%0.3f' % (Theta[ii * n_s // n_plt], np.cos(Theta[ii * n_s // n_plt])))\n",
        "idx_m = np.where(llk_dat[:, 2] == np.max(llk_dat[:, 2]))[0]\n",
        "idx = np.where(llk_dat[:, 0] == llk_dat[idx_m, 0])[0]\n",
        "plt.subplot(n_plt+1, 1, n_plt+1)\n",
        "plt.plot(llk_dat[idx, 1], llk_dat[idx, 2])\n",
        "plt.title('best llk theta=%0.3f cos=%0.3f' % (llk_dat[idx_m, 0], np.cos(llk_dat[idx_m, 0])))\n",
        "\n",
        "plt.tight_layout()\n",
        "# plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ND2y0g3gFeCZwj4/fA5wbrZCqvgTEfFFeRPoAJwHWAzbaZGddIzc/t5RPlPbj7MMGpdqc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\n7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q8cP4DfXT7ewgB1AewMGkYLuOqUPDLTknlgSce2gn/7r0/55asbuHDcQP73snEmvl0E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\nJsCGYRgxwgTYMAwjRpgAG4ZhxIj/A6tFoyqmWQMdAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 360x720 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CIbB-5RkAoxi",
        "colab_type": "text"
      },
      "source": [
        "# The configuration of $\\VAR(p)$ when m=k=2.\n",
        "This could be consider the next step after from $AR(p)$. To fully study this case we probably need an article but we can use the LQ factorization to look at the search space for the orthogonalized $\\bG^{o}$, which could be parametrized explicitly.\n",
        "\n",
        "As $d_p = 2$ is the full rank case, we will assume $d_p = 1$. There are two main cases\n",
        "*  $\\Psi = [(p, 1), (\\rho, 1)]$. Let $\\bW = \\bG^o$ be the orthogonalized $G$. For the first case, $\\bW_{p, 0}$ and $\\bW_{\\rho, 0}$ form an orthogonal basis, $\\bW_{\\rho, \\rho-1}\\cdots \\bW_{\\rho, 1}$ are orthogonal to both vectors and hence is zero, $\\bW_{p, p-1}\\cdots \\bW_{p, p-\\rho}$ are also zero. The remaining $p-\\rho-1$ vectors $\\bW_{p, 1}\\cdots \\bW_{p, p-\\rho-1}$ are proportional to $\\bW_{\\rho, 0}$. So this is a picture of the circle with $p-\\rho-1$ tangent vectors. The minimal state space dimension is $p+\\rho$. So the non reduced search space of $\\bG$ has dimension $2(p+\\rho)$, while the reduced one has dimension $2(p-\\rho)$\n",
        "*  $\\Psi = [(p, 1)]$. In this case the $\\bW_{p, p-1}\\cdots \\bW_{p, 1}$ are all orthogonal to $\\bW_{p, 0}$. This is the case of a circle and $p-1$ tangent vectors. Here, the minimal state-space dimension is $p$, hen the non-reduced search space for $\\bG$ is of dimension $2p$, while the reduced one has dimension $p$. \n",
        "\n",
        "We will not implement an optimizing routine here, but this case the search space could be parameterized explicitly as simple geometric object. The gradient on the reduced search space could be computed via the chain rule and we can use a standard optimzer to search. The next code segment illustrates the $LQ$ factorization discussed above."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "66VuiYRf7Zpz",
        "colab_type": "code",
        "outputId": "d71a0aa7-7c70-48a4-d85a-67608046b824",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 782
        }
      },
      "source": [
        "from minimal_varx.minimal_varx import LQ_multi_lags\n",
        "np.random.seed(1)\n",
        "m = 2\n",
        "p = 6\n",
        "rho = 2\n",
        "Psi = [(p, 1), (rho, 1)]\n",
        "es = varx_minimal_estimator(Psi, m = 2)\n",
        "G = np.random.randn(es.mm_degree, m)\n",
        "W, S = LQ_multi_lags(es, G)\n",
        "print(\"S=%s\" % str(S))\n",
        "print(\"W=%s\" % str(W))\n",
        "print(\"test factorization %s\" % str(W - S @ G))\n",
        "FF = pm.calc_Jordan_matrix(es.Psi, 0)\n",
        "print(\"test commutative %s\" % (FF @ S - S @ FF))\n",
        "for j in range(p-1):\n",
        "  print(\"ratio %d %s\" % (j, str(W[j, :] / W[-1, :])))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "S=[[-0.39584363  0.06079797  0.24616383  0.29552492  1.22441356  1.70493487\n",
            "  -2.27180826 -3.23652534]\n",
            " [ 0.         -0.39584363  0.06079797  0.24616383  0.29552492  1.22441356\n",
            "   0.         -2.27180826]\n",
            " [ 0.          0.         -0.39584363  0.06079797  0.24616383  0.29552492\n",
            "   0.          0.        ]\n",
            " [ 0.          0.          0.         -0.39584363  0.06079797  0.24616383\n",
            "   0.          0.        ]\n",
            " [ 0.          0.          0.          0.         -0.39584363  0.06079797\n",
            "   0.          0.        ]\n",
            " [ 0.          0.          0.          0.          0.         -0.39584363\n",
            "   0.          0.        ]\n",
            " [ 0.          0.          0.          0.         -2.13471232 -3.97045793\n",
            "   3.47219925  6.7084111 ]\n",
            " [ 0.          0.          0.          0.          0.         -2.13471232\n",
            "   0.          3.47219925]]\n",
            "W=[[ 4.44089210e-16 -8.88178420e-16]\n",
            " [ 4.44089210e-16 -8.88178420e-16]\n",
            " [ 2.74140130e-01  1.94560720e-01]\n",
            " [-3.11357608e-01 -2.20974435e-01]\n",
            " [-3.73963998e-02 -2.65406983e-02]\n",
            " [-5.78766117e-01  8.15493582e-01]\n",
            " [-8.88178420e-16  8.88178420e-16]\n",
            " [ 8.15493582e-01  5.78766117e-01]]\n",
            "test factorization [[ 3.48775446e-16 -6.44416606e-16]\n",
            " [-4.59991847e-17 -1.78541349e-16]\n",
            " [-5.55111512e-17  2.77555756e-17]\n",
            " [ 0.00000000e+00  0.00000000e+00]\n",
            " [-6.93889390e-18  6.93889390e-18]\n",
            " [ 1.11022302e-16  0.00000000e+00]\n",
            " [ 5.87918275e-17 -1.09999843e-15]\n",
            " [ 4.44089210e-16 -5.55111512e-16]]\n",
            "test commutative [[0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "ratio 0 [ 5.44564936e-16 -1.53460680e-15]\n",
            "ratio 1 [ 5.44564936e-16 -1.53460680e-15]\n",
            "ratio 2 [0.33616467 0.33616467]\n",
            "ratio 3 [-0.38180265 -0.38180265]\n",
            "ratio 4 [-0.04585738 -0.04585738]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NAjdAo04777R",
        "colab_type": "text"
      },
      "source": [
        "##Analyzing the number of configurations\n",
        "Dimension of the state space is one of the measures of the complexity of the system. From the parameter count, the higher exponents contribute more to to parameter count than the lower one. The minimal state-space dimension formula:\n",
        "$$\\sum d_i i = \\nmin$$\n",
        "could be thought of as a weighted sum of complexity: it gives more weight to higher dimesnion and less to the lower one.\n",
        "\n",
        "In the following, we plot how the number of configurations are distributed with respect to the minimal state-space: it is a bell-shape figure. The next block of code shows all posible $\\Psi$ for $m=k=5, p=3$. The block after plots number of distribution per minimal state space dimension."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ELnVPa22_f2D",
        "colab_type": "code",
        "outputId": "58417bb5-1473-454c-96ee-15375c7e2b16",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 629
        }
      },
      "source": [
        "print(pd.DataFrame(np.array([a for a in list_all_psi_hat(5, 3)]), columns=[str(j) for j in range(3, 0, -1)]))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "    3  2  1\n",
            "0   1  0  0\n",
            "1   1  0  1\n",
            "2   1  0  2\n",
            "3   1  0  3\n",
            "4   1  0  4\n",
            "5   1  1  0\n",
            "6   1  1  1\n",
            "7   1  1  2\n",
            "8   1  1  3\n",
            "9   1  2  0\n",
            "10  1  2  1\n",
            "11  1  2  2\n",
            "12  1  3  0\n",
            "13  1  3  1\n",
            "14  1  4  0\n",
            "15  2  0  0\n",
            "16  2  0  1\n",
            "17  2  0  2\n",
            "18  2  0  3\n",
            "19  2  1  0\n",
            "20  2  1  1\n",
            "21  2  1  2\n",
            "22  2  2  0\n",
            "23  2  2  1\n",
            "24  2  3  0\n",
            "25  3  0  0\n",
            "26  3  0  1\n",
            "27  3  0  2\n",
            "28  3  1  0\n",
            "29  3  1  1\n",
            "30  3  2  0\n",
            "31  4  0  0\n",
            "32  4  0  1\n",
            "33  4  1  0\n",
            "34  5  0  0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WLbq1fZRq_Nw",
        "colab_type": "code",
        "outputId": "e966a466-8389-4edc-ade7-afda4550ba49",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        }
      },
      "source": [
        "p = 5\n",
        "m = 10\n",
        "all_psi = np.array([a for a in list_all_psi_hat(m, p)])\n",
        "\n",
        "\n",
        "psiDF = pd.DataFrame(all_psi, columns=[str(a) for a in range(p,0,-1)])\n",
        "psiDF['mm'] = np.sum(all_psi * np.arange(p, 0, -1)[None, :], axis=1)\n",
        "# psiDF.groupby('mm').count()['1']\n",
        "ax = psiDF[['mm']].plot.hist(title='Number of configurations vs state-space dimension')\n",
        "ax.set_xlabel('Minimal state-space dimension')\n",
        "ax.set_ylabel('Number of Psi')\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Number of Psi')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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aBXwfmBgR2wBLgKObGGOjHQc8VOjvzm0BsFdE7Fi496HuvxUniAaKiL8Az7cq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\nSZdtwwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cPSgLkKYAj3g",
        "colab_type": "text"
      },
      "source": [
        "## Saving per different structural parameters\n",
        "The next block shows parameter saving per different structural parameters\n",
        "\n",
        "*   List item\n",
        "*   List item\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xeMQx5t8rBzQ",
        "colab_type": "code",
        "outputId": "234a5e25-ea5c-4ae9-a112-9a04786cb0e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 585
        }
      },
      "source": [
        "def calc_saving(m, k, p, psi_hat):\n",
        "    s = 0\n",
        "    \n",
        "    for i in range(1, p+1):\n",
        "        s += (k - np.sum(psi_hat[:i])) * (m - np.sum(psi_hat[:i]))\n",
        "    return s\n",
        "p = 5\n",
        "m = 10\n",
        "all_psi = np.array([a for a in list_all_psi_hat(m, p)])\n",
        "\n",
        "\n",
        "psiDF = pd.DataFrame(all_psi, columns=[str(a) for a in range(p,0,-1)])\n",
        "psiDF['mm'] = np.sum(all_psi * np.arange(p, 0, -1)[None, :], axis=1)\n",
        "psiDF['saving'] = psiDF.apply(lambda x: calc_saving(m, m, p, x[:p]), axis=1)\n",
        "plt.figure(figsize=(8, 8))\n",
        "n_plots = 2\n",
        "plt.subplot(3, 2, 1)\n",
        "ax = psiDF.groupby('mm').mean()['saving'].plot()\n",
        "ax.set_xlabel('McMillan dimension')\n",
        "ax.set_ylabel('Parameter saving')\n",
        "plt.title('average param saving vs McMillan dim')\n",
        "for jj in range(n_plots):\n",
        "    plt.subplot(3, 2, 2*jj+3)\n",
        "    ax = psiDF.groupby(str(p-jj)).mean()['saving'].plot()\n",
        "    ax.set_xlabel('d_%d' % (p-jj))    \n",
        "    ax.set_ylabel('Parameter saving')\n",
        "    plt.title('average param saving vs d%d' % (p-jj))\n",
        "\n",
        "jj = 5\n",
        "plt.subplot(3, 2, 2)\n",
        "ax = psiDF.loc[(psiDF['5'] >= -1 ) & (psiDF['4'] == 0 ) & (psiDF['3'] == 0 ) & (psiDF['2'] == 0 ) & (psiDF['1'] ==0 )].groupby('5').mean()['saving'].plot()\n",
        "ax.set_xlabel('d_%d' % (jj))\n",
        "ax.set_ylabel('Parameter saving')\n",
        "plt.title('param saving vs d%d, Psi=[0, 0, 0, 0, d_5]' % (jj))\n",
        "\n",
        "jj = 3\n",
        "plt.subplot(3, 2, 4)\n",
        "ax = psiDF.loc[(psiDF['5'] == 1 ) & (psiDF['4'] == 0 ) & (psiDF['3'] >= -1 ) & (psiDF['2'] == 0 ) & (psiDF['1'] ==0 )].groupby('3').mean()['saving'].plot()\n",
        "ax.set_xlabel('d_%d' % (jj))\n",
        "ax.set_ylabel('Parameter saving')\n",
        "plt.title('param saving vs d%d, Psi=[0, 0, d_3, 0, 1]' % (jj))\n",
        "plt.tight_layout()\n",
        "\n",
        "jj = 1\n",
        "plt.subplot(3, 2, 6)\n",
        "ax = psiDF.loc[(psiDF['5'] == 1 ) & (psiDF['4'] == 0 ) & (psiDF['3'] == 0 ) & (psiDF['2'] == 0 ) & (psiDF['1'] >= -1 )].groupby('1').mean()['saving'].plot()\n",
        "ax.set_xlabel('d_%d' % (jj))\n",
        "ax.set_ylabel('Parameter saving')\n",
        "plt.title('param saving vs d%d, Psi=[d_%d, 0, 0, 0, 1]' % (jj, jj))\n",
        "\n",
        "\n",
        "\n",
        "plt.tight_layout()    "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pKiJjRWSViGzI+iuJ4EJJxXJRjBjchYfPPo0flu7g0mGzSEhM9josYzxnOcZ/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\neP37kmtY7mRgHzBVVY9y0x4DdqvqIyJyH9BaVe8VkZHAz4GRwFDgSVU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zeHn+Br5Yv5v4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\nMcYYY0KGFTbGGGOMCRlW2BhjjDEmZPw/+z3ZVz3gl6kAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x576 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zfh0wMGEAyXT",
        "colab_type": "text"
      },
      "source": [
        "## Likelihood with respect to different $\\Psi$'s\n",
        "We next test how likelihood changes with respect to different $\\Psi$'s. Conceptually, there will be little improvements in likelihood in choosing a more complex $\\Psi$ than the data generation $\\Psi$. We see this in the table below. This shows the strategy is not to scan all $\\Psi$, but to get a $\\Psi$ that adequately *explains* the relationship."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Dq9aBpSrMTW",
        "colab_type": "code",
        "outputId": "ef59f66a-3422-4558-a6de-d10bb1ca5ff4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "def k_5_p_2_all_psi():\n",
        "    np.random.seed(1)\n",
        "    k = 5\n",
        "    m = k\n",
        "    p = 2\n",
        "    Psi0 = [(2, 2), (1, 2)]\n",
        "\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "    D = np.arange(k) * 0.2 + 1\n",
        "    OO = random_orthogonal(k)\n",
        "    found_good_stable = False\n",
        "    n_test = 10\n",
        "    n_cnt = 0\n",
        "    while (n_cnt < n_test) and (not found_good_stable):\n",
        "        try:\n",
        "            es = varx_minimal_estimator(Psi0, m=k)\n",
        "            stable, H, F, G, Phi = gen_random_stable(es, k)\n",
        "            Y, e = VAR_sim(Phi, n, D, OO)\n",
        "            Y = Y.T\n",
        "            e = e.T\n",
        "            X = Y.copy()\n",
        "            cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "            es_G = varx_minimal_estimator(Psi0, m=k)\n",
        "            es_G.set_covs(cov_res, cov_xlag)\n",
        "            es_G.calc_states(G)\n",
        "            found_good_stable = True\n",
        "        except Exception:\n",
        "            pass\n",
        "        n_cnt += 1\n",
        "    \n",
        "    all_psi = [a for a in list_all_psi_hat(m=m, p=p)]\n",
        "    results = np.zeros((len(all_psi), p+3))\n",
        "    header = [str(jj) for jj in range(p, 0, -1)]+['org_llk', 'fitted_llk', 'success']\n",
        "    for ii in range(len(all_psi)):        \n",
        "        Psi = psi_hat_to_psi(all_psi[ii])\n",
        "        results[ii, :p] = all_psi[ii]\n",
        "        es = varx_minimal_estimator(Psi, m=k)\n",
        "        # print('X.shape=%s Y.shape=%s' % (str(X.shape), str(Y.shape)))\n",
        "        # opt = es.gradient_fit(Y, X)\n",
        "        print('Psi=%s' % Psi)\n",
        "        results[ii, p] = es_G.neg_log_llk\n",
        "        success = False\n",
        "        n_cnt = 0\n",
        "        while (not success) and (n_cnt < 10):\n",
        "            opt = es.hessian_fit(Y, X)\n",
        "            if opt['success']:\n",
        "                print('orig_llk %s est_llk=%s' % (\n",
        "                    es_G.neg_log_llk, opt['fun']))\n",
        "                results[ii, p+2] = 1\n",
        "                success = True\n",
        "            results[ii, p+1] = opt['fun']\n",
        "            n_cnt += 1\n",
        "        if not opt['success']:\n",
        "            print(\"failed opt=%s\" % '\\n'.join([jjj + ': ' + str(opt[jjj]) for jjj in opt.keys() if jjj not in ['hess_inv', 'jac', 'x']]))\n",
        "            results[ii, p+1] = opt['fun']\n",
        "    return pd.DataFrame(results, columns=header)\n",
        "all_psi_table = k_5_p_2_all_psi()\n",
        "print(all_psi_table)\n",
        "print(all_psi_table.to_latex())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Psi=[(2, 1), (1, 0)]\n",
            "orig_llk -8.746827869107664 est_llk=-5.575983664362306\n",
            "Psi=[(2, 1), (1, 1)]\n",
            "orig_llk -8.746827869107664 est_llk=-6.7151786181629705\n",
            "Psi=[(2, 1), (1, 2)]\n",
            "orig_llk -8.746827869107664 est_llk=-7.614980596933654\n",
            "Psi=[(2, 1), (1, 3)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.290709571010836\n",
            "Psi=[(2, 1), (1, 4)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.342101767284555\n",
            "Psi=[(2, 2), (1, 0)]\n",
            "orig_llk -8.746827869107664 est_llk=-7.745143944525469\n",
            "Psi=[(2, 2), (1, 1)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.569491516144147\n",
            "Psi=[(2, 2), (1, 2)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.75407272577322\n",
            "Psi=[(2, 2), (1, 3)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.754606859037658\n",
            "Psi=[(2, 3), (1, 0)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.754916374685767\n",
            "Psi=[(2, 3), (1, 1)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.756863629683155\n",
            "Psi=[(2, 3), (1, 2)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.75957109028095\n",
            "Psi=[(2, 4), (1, 0)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.759829175735138\n",
            "Psi=[(2, 4), (1, 1)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.760025903708625\n",
            "Psi=[(2, 5), (1, 0)]\n",
            "orig_llk -8.746827869107664 est_llk=-8.760028105554845\n",
            "      2    1   org_llk  fitted_llk  success\n",
            "0   1.0  0.0 -8.746828   -5.575984      1.0\n",
            "1   1.0  1.0 -8.746828   -6.715179      1.0\n",
            "2   1.0  2.0 -8.746828   -7.614981      1.0\n",
            "3   1.0  3.0 -8.746828   -8.290710      1.0\n",
            "4   1.0  4.0 -8.746828   -8.342102      1.0\n",
            "5   2.0  0.0 -8.746828   -7.745144      1.0\n",
            "6   2.0  1.0 -8.746828   -8.569492      1.0\n",
            "7   2.0  2.0 -8.746828   -8.754073      1.0\n",
            "8   2.0  3.0 -8.746828   -8.754607      1.0\n",
            "9   3.0  0.0 -8.746828   -8.754916      1.0\n",
            "10  3.0  1.0 -8.746828   -8.756864      1.0\n",
            "11  3.0  2.0 -8.746828   -8.759571      1.0\n",
            "12  4.0  0.0 -8.746828   -8.759829      1.0\n",
            "13  4.0  1.0 -8.746828   -8.760026      1.0\n",
            "14  5.0  0.0 -8.746828   -8.760028      1.0\n",
            "\\begin{tabular}{lrrrrr}\n",
            "\\toprule\n",
            "{} &    2 &    1 &   org\\_llk &  fitted\\_llk &  success \\\\\n",
            "\\midrule\n",
            "0  &  1.0 &  0.0 & -8.746828 &   -5.575984 &      1.0 \\\\\n",
            "1  &  1.0 &  1.0 & -8.746828 &   -6.715179 &      1.0 \\\\\n",
            "2  &  1.0 &  2.0 & -8.746828 &   -7.614981 &      1.0 \\\\\n",
            "3  &  1.0 &  3.0 & -8.746828 &   -8.290710 &      1.0 \\\\\n",
            "4  &  1.0 &  4.0 & -8.746828 &   -8.342102 &      1.0 \\\\\n",
            "5  &  2.0 &  0.0 & -8.746828 &   -7.745144 &      1.0 \\\\\n",
            "6  &  2.0 &  1.0 & -8.746828 &   -8.569492 &      1.0 \\\\\n",
            "7  &  2.0 &  2.0 & -8.746828 &   -8.754073 &      1.0 \\\\\n",
            "8  &  2.0 &  3.0 & -8.746828 &   -8.754607 &      1.0 \\\\\n",
            "9  &  3.0 &  0.0 & -8.746828 &   -8.754916 &      1.0 \\\\\n",
            "10 &  3.0 &  1.0 & -8.746828 &   -8.756864 &      1.0 \\\\\n",
            "11 &  3.0 &  2.0 & -8.746828 &   -8.759571 &      1.0 \\\\\n",
            "12 &  4.0 &  0.0 & -8.746828 &   -8.759829 &      1.0 \\\\\n",
            "13 &  4.0 &  1.0 & -8.746828 &   -8.760026 &      1.0 \\\\\n",
            "14 &  5.0 &  0.0 & -8.746828 &   -8.760028 &      1.0 \\\\\n",
            "\\bottomrule\n",
            "\\end{tabular}\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zl7IQfD8CgNZ",
        "colab_type": "text"
      },
      "source": [
        "## Non autoregressive model\n",
        "We test for the case where $\\bx$ is not related to $\\by$. We use $m=7, k=5, p=2$ and test just one example. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t_zQNJoXrOR5",
        "colab_type": "code",
        "outputId": "4658ca18-c9b6-463a-83a4-54ffa366a7a5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "def k_5_p_2_x_not_autogressive():\n",
        "    from minimal_varx.polynomial_matrix import state_to_Phi\n",
        "    from minimal_varx.utils import random_innovation_series\n",
        "    \n",
        "    np.random.seed(0)\n",
        "    k = 5\n",
        "    m = 7\n",
        "    p = 2\n",
        "    Psi = [(2, 2), (1, 2)]\n",
        "    # first generate X\n",
        "    \n",
        "    es = varx_minimal_estimator(Psi, m=m)\n",
        "    stable, _, _, _, PhiX = gen_random_stable(es, m)\n",
        "    Dx = np.arange(m) * 0.2 + 1\n",
        "    OOx = random_orthogonal(m)\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "    X, ex = VAR_sim(PhiX, n, Dx, OOx)\n",
        "\n",
        "    # next generate Y\n",
        "    stable, _, F, G, _ = gen_random_stable(es, m, scale_range=(.4, .6))\n",
        "    H = np.random.randn(k, es.mm_degree)\n",
        "    Phi = state_to_Phi(H, F, G, Psi)\n",
        "    Phi_arr = Phi.PolynomialMatrix_to_3darray()\n",
        "    D = np.arange(k) * 0.2 + 1\n",
        "    OO = random_orthogonal(k)\n",
        "    e = random_innovation_series(D, OO, n)\n",
        "    Y = np.zeros_like(e)\n",
        "\n",
        "    for j in range(0, n):\n",
        "        for i in range(min(j, p)):\n",
        "            Y[j, :] += Phi_arr[:, :, p-i-1] @ X[j-i-1, :]\n",
        "        Y[j, :] += e[j, :]\n",
        "    X = X.T\n",
        "    Y = Y.T\n",
        "    es_G = varx_minimal_estimator(Psi, m=m)\n",
        "    cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "    es_G.set_covs(cov_res, cov_xlag)\n",
        "    es_G.calc_states(G)\n",
        "    n_cnt = 0\n",
        "    success = False\n",
        "    while (not success) and (n_cnt < 10):\n",
        "        opt = es.hessian_fit(Y, X)\n",
        "        if opt['success']:\n",
        "            print('orig_llk %s est_llk=%s' % (\n",
        "                es_G.neg_log_llk, opt['fun']))                \n",
        "            print(Phi.PolynomialMatrix_to_3darray())\n",
        "            print(es.Phi)\n",
        "            success = True\n",
        "        n_cnt += 1\n",
        "    if not success:\n",
        "        print(\"failed for ii=%d\" % ii)\n",
        "k_5_p_2_x_not_autogressive()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "orig_llk -19.87443073545531 est_llk=-19.90889577633093\n",
            "[[[-1.76184053e-01 -3.33552349e-01]\n",
            "  [-3.85800138e-01 -8.46683551e-01]\n",
            "  [-8.16573096e-02 -7.66910408e-01]\n",
            "  [ 9.98224373e-01 -1.08324789e+00]\n",
            "  [ 2.33844817e-01 -1.07290071e+00]\n",
            "  [ 2.44226628e-01  1.21924218e-01]\n",
            "  [ 1.44399121e-01  5.03759278e-02]]\n",
            "\n",
            " [[ 5.42958109e-02  1.93026461e+00]\n",
            "  [ 2.03133451e-01  3.01626878e-01]\n",
            "  [-7.22017320e-01 -1.21925635e+00]\n",
            "  [ 8.92217785e-01 -3.76112419e-01]\n",
            "  [ 2.22742604e-01 -3.73845961e-01]\n",
            "  [ 4.29410167e-01 -2.51167100e-02]\n",
            "  [-2.35720405e-01 -9.24978795e-01]]\n",
            "\n",
            " [[ 9.90745673e-03 -1.21602950e+00]\n",
            "  [-3.08248591e-02  5.19159790e-01]\n",
            "  [ 4.70432013e-01 -8.42831365e-01]\n",
            "  [-8.04193546e-01  5.83941677e-02]\n",
            "  [-1.96951752e-01 -1.66868794e+00]\n",
            "  [-3.28379774e-01  1.40558069e+00]\n",
            "  [ 1.11098416e-01 -2.18194692e-01]]\n",
            "\n",
            " [[ 2.78525469e-01 -6.65618837e-01]\n",
            "  [ 6.88381688e-01 -1.62967554e+00]\n",
            "  [-5.67001285e-01  4.98011169e-01]\n",
            "  [-4.60266506e-01  8.64103314e-01]\n",
            "  [-9.50303103e-02 -1.06225490e+00]\n",
            "  [ 8.40740645e-02 -2.55365790e-02]\n",
            "  [-4.06422140e-01  1.83570341e-01]]\n",
            "\n",
            " [[ 3.10244389e-01  7.26334571e-01]\n",
            "  [ 7.97055285e-01  1.05705482e-01]\n",
            "  [-9.00146456e-01 -1.07570988e+00]\n",
            "  [-8.13980489e-02  2.61893234e-01]\n",
            "  [ 1.16080235e-04  7.54368925e-02]\n",
            "  [ 2.75053703e-01 -5.25295250e-01]\n",
            "  [-5.21440031e-01 -1.00970776e+00]]]\n",
            "[[[-1.53409629e-01 -2.78940698e-01]\n",
            "  [-4.00615627e-01 -8.75572481e-01]\n",
            "  [-6.70719831e-02 -7.37964661e-01]\n",
            "  [ 1.00316730e+00 -1.07250986e+00]\n",
            "  [ 2.26838779e-01 -1.03535628e+00]\n",
            "  [ 2.25258262e-01  1.62588158e-01]\n",
            "  [ 1.60544539e-01  1.86736555e-02]]\n",
            "\n",
            " [[ 6.12392739e-02  1.95396919e+00]\n",
            "  [ 1.90427358e-01  2.77950559e-01]\n",
            "  [-7.16781673e-01 -1.26004762e+00]\n",
            "  [ 8.91799404e-01 -3.36756619e-01]\n",
            "  [ 2.23078132e-01 -3.90666258e-01]\n",
            "  [ 4.02948223e-01 -7.69756858e-02]\n",
            "  [-2.20195102e-01 -9.60824976e-01]]\n",
            "\n",
            " [[ 1.97836725e-04 -1.21536252e+00]\n",
            "  [-1.91496171e-02  5.49917535e-01]\n",
            "  [ 4.79426694e-01 -8.37688990e-01]\n",
            "  [-8.34355593e-01  5.16039577e-02]\n",
            "  [-2.02476625e-01 -1.65885549e+00]\n",
            "  [-3.18022761e-01  1.39299732e+00]\n",
            "  [ 1.00429196e-01 -2.26837075e-01]]\n",
            "\n",
            " [[ 2.54231977e-01 -6.63098172e-01]\n",
            "  [ 6.91136203e-01 -1.57533816e+00]\n",
            "  [-5.52592600e-01  5.07873554e-01]\n",
            "  [-5.08913584e-01  8.50975019e-01]\n",
            "  [-9.59540935e-02 -1.07599889e+00]\n",
            "  [ 6.66653361e-02 -2.09480700e-02]\n",
            "  [-4.05407560e-01  1.40977335e-01]]\n",
            "\n",
            " [[ 2.93432112e-01  7.06825090e-01]\n",
            "  [ 8.08954701e-01  1.16798060e-01]\n",
            "  [-9.12048481e-01 -1.04148692e+00]\n",
            "  [-1.10752193e-01  2.53467660e-01]\n",
            "  [ 4.92902767e-03  6.67692965e-02]\n",
            "  [ 2.58732956e-01 -5.22859697e-01]\n",
            "  [-5.25495892e-01 -1.03771975e+00]]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7omBv4SxDNG5",
        "colab_type": "text"
      },
      "source": [
        "### Higher dimension and order\n",
        "We test one with $k=8, p=3$. Convergence is slower, but this is because we optimize over the whole space instead of the reduced set satisfying the orthogonal relation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l0296CjCrQaS",
        "colab_type": "code",
        "outputId": "ee448f3a-a468-4ef3-cf51-d57583b5bcff",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "from minimal_varx.utils import _calc_var_sim\n",
        "def deautocorrel(e, p):\n",
        "  k = e.shape[0]\n",
        "  T = e.shape[1] - p\n",
        "  eStack = np.zeros((e.shape[0]* p, T))      \n",
        "  for i in range(p):\n",
        "      eStack[k*i:k*(i+1), :] = e[:, p-i:p-i+T]\n",
        "  Phi_e = np.linalg.solve(eStack @ eStack.T, eStack @ e[:, :T].T)\n",
        "  e_ = e[:, 3:] - Phi_e[:8, :] @ e[:, :T]- Phi_e[8:16, :] @ e[:, 1:T+1] - Phi_e[16:, :] @ e[:, 2:T+2]\n",
        "  return e_\n",
        "\n",
        "def k_8_p3_generic():\n",
        "    np.random.seed(2)\n",
        "    Psi = [(3, 1), (2, 1), (1, 2)]\n",
        "    k_zero = 4\n",
        "    k = sum([a[1] for a in Psi]) + k_zero\n",
        "    p = Psi[0][0]\n",
        "    T = 2000\n",
        "    n = T + p\n",
        "    n_test = 10\n",
        "    results = np.zeros((n_test, 4))\n",
        "\n",
        "    for ii in range(n_test):\n",
        "        n_tries = 10\n",
        "        n_cnt = 0\n",
        "        found_good_stable = False\n",
        "        while (n_cnt < n_tries) and (not found_good_stable):\n",
        "            try:\n",
        "                D = np.arange(k) * 0.2 + 1\n",
        "                OO = random_orthogonal(k)\n",
        "\n",
        "                es = varx_minimal_estimator(Psi, m=k)\n",
        "                stable, H, F, G, Phi = gen_random_stable(\n",
        "                    es, k, scale_range=(0.1, .6))\n",
        "                Y, e = VAR_sim(Phi, n, D, OO)\n",
        "                # e_ = deautocorrel(e.T, p).T                        \n",
        "                # Y = _calc_var_sim(Phi.PolynomialMatrix_to_3darray(), e_).T            \n",
        "                Y = Y.T\n",
        "                X = Y.copy()\n",
        "                cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "                found_good_stable = True\n",
        "            except Exception as ex:\n",
        "                print(ex)\n",
        "                pass\n",
        "            n_cnt += 1\n",
        "        print(\"found stable Phi for ii= %d\" % ii)\n",
        "        es_G = varx_minimal_estimator(Psi, m=k)\n",
        "        es_G.set_covs(cov_res, cov_xlag)\n",
        "        es_G.calc_states(G)\n",
        "        results[ii, 0] = es_G.neg_log_llk\n",
        "        results[ii, 2] = np.log(np.linalg.det(cov_res)) - np.log(np.linalg.det(cov_xlag))\n",
        "        success = False\n",
        "        n_cnt = 0\n",
        "        while (not success) and (n_cnt < 11):\n",
        "            opt = es.gradient_fit(Y, X)\n",
        "            if opt['success']:\n",
        "                print('orig_llk %s est_llk=%s' % (\n",
        "                    es_G.neg_log_llk, opt['fun']))                \n",
        "                print(Phi.PolynomialMatrix_to_3darray())\n",
        "                print(es.Phi)\n",
        "                success = True\n",
        "                results[ii, 1] = opt['fun']\n",
        "                results[ii, 3] = 1\n",
        "            n_cnt += 1\n",
        "        if not success:\n",
        "            print(\"failed for ii=%d\" % ii)\n",
        "            results[ii, 1] = opt['fun']\n",
        "            results[ii, 3] = 0\n",
        "    return pd.DataFrame(results, columns=['org_llk', 'fitted_llk', 'full_llk', 'success'])\n",
        "fitted_k8p3 = k_8_p3_generic()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "found stable Phi for ii= 0\n",
            "orig_llk -6.77897374326653 est_llk=-7.333461836462682\n",
            "[[[-2.94529065e-02 -1.17025490e-01  3.92336551e-02]\n",
            "  [ 8.94164701e-03  2.60358320e-02  8.15826072e-03]\n",
            "  [ 4.34803159e-04  1.06239946e-02 -2.34543988e-01]\n",
            "  [-1.15220878e-02 -6.35224869e-02  8.92181655e-02]\n",
            "  [ 8.46428223e-03  9.39677706e-02 -3.40779434e-01]\n",
            "  [ 1.37652265e-02  1.22932713e-01  7.67023270e-01]\n",
            "  [ 6.18157395e-03 -2.29286473e-03 -3.30636840e-01]\n",
            "  [ 4.24512735e-03 -1.49962456e-02 -2.65372744e-02]]\n",
            "\n",
            " [[-6.47696529e-02  8.90794746e-02  1.54337309e-01]\n",
            "  [ 1.96635050e-02 -4.79177400e-02  1.73252379e-01]\n",
            "  [ 9.56172176e-04  1.82489252e-02  4.04627884e-02]\n",
            "  [-2.53381319e-02 -4.16735122e-03 -2.54522886e-01]\n",
            "  [ 1.86137359e-02  1.07085680e-01  7.40006912e-02]\n",
            "  [ 3.02710003e-02  1.08431790e-01 -1.67830824e-01]\n",
            "  [ 1.35938502e-02 -7.77507778e-02  3.74065352e-01]\n",
            "  [ 9.33542587e-03 -8.29099201e-02 -1.91473477e-01]]\n",
            "\n",
            " [[ 1.33201760e-01 -4.72015503e-02  2.39331060e-01]\n",
            "  [-4.04388993e-02  5.72582862e-02  3.77397295e-01]\n",
            "  [-1.96641191e-03 -3.95373908e-02 -1.14349980e-01]\n",
            "  [ 5.21090298e-02  6.17718982e-02 -2.51942822e-01]\n",
            "  [-3.82800011e-02 -2.59309190e-01 -2.45978253e-01]\n",
            "  [-6.22536997e-02 -2.86553860e-01 -9.67525268e-02]\n",
            "  [-2.79563761e-02  1.31355528e-01 -1.62450259e-01]\n",
            "  [-1.91987312e-02  1.50906799e-01  3.47932454e-02]]\n",
            "\n",
            " [[-7.13974534e-02  1.52623982e-01  4.34226544e-02]\n",
            "  [ 2.16756477e-02 -6.93453110e-02 -3.20648558e-01]\n",
            "  [ 1.05401612e-03  1.93127973e-02  9.72927299e-02]\n",
            "  [-2.79309524e-02  1.66990822e-02 -4.01014479e-01]\n",
            "  [ 2.05184570e-02  1.02401594e-01 -4.40158178e-01]\n",
            "  [ 3.33685952e-02  9.40892803e-02  3.93691620e-02]\n",
            "  [ 1.49848925e-02 -9.71304993e-02 -6.32720084e-02]\n",
            "  [ 1.02907087e-02 -9.92390078e-02  6.30196523e-01]]\n",
            "\n",
            " [[-1.14909086e-01  1.80168220e-01 -6.66456038e-01]\n",
            "  [ 3.48854021e-02 -9.17304455e-02 -1.69881021e-01]\n",
            "  [ 1.69636343e-03  3.20490622e-02 -3.92360060e-02]\n",
            "  [-4.49528669e-02  1.26420086e-03  6.47024778e-01]\n",
            "  [ 3.30229866e-02  1.83622788e-01 -1.12482223e-01]\n",
            "  [ 5.37043634e-02  1.82027873e-01 -3.07329233e-01]\n",
            "  [ 2.41171109e-02 -1.42583921e-01 -8.97829933e-02]\n",
            "  [ 1.65621585e-02 -1.50281828e-01  1.82948060e-02]]\n",
            "\n",
            " [[ 6.75788337e-02 -2.83140371e-02  3.51023353e-01]\n",
            "  [-2.05163479e-02  3.03752237e-02  8.13868135e-02]\n",
            "  [-9.97643148e-04 -1.99945106e-02  9.74565527e-02]\n",
            "  [ 2.64370940e-02  2.96311975e-02 -7.75138679e-01]\n",
            "  [-1.94210484e-02 -1.30303495e-01  2.30040835e-02]\n",
            "  [-3.15839101e-02 -1.43339935e-01  2.77131315e-01]\n",
            "  [-1.41834409e-02  6.75586483e-02  4.55317028e-01]\n",
            "  [-9.74032072e-03  7.71907277e-02  3.03905972e-01]]\n",
            "\n",
            " [[-1.23060177e-01  2.71470408e-01  6.13395147e-01]\n",
            "  [ 3.73600027e-02 -1.22075934e-01  3.12843507e-01]\n",
            "  [ 1.81669520e-03  3.31632743e-02  1.32891866e-01]\n",
            "  [-4.81416044e-02  3.20719523e-02 -1.18930049e+00]\n",
            "  [ 3.53654765e-02  1.74082179e-01 -3.57273951e-01]\n",
            "  [ 5.75138895e-02  1.58241725e-01 -3.53670080e-01]\n",
            "  [ 2.58278614e-02 -1.69178307e-01  5.64096859e-01]\n",
            "  [ 1.77369974e-02 -1.72259668e-01  1.61745353e-01]]\n",
            "\n",
            " [[-9.30736690e-02 -3.01496497e-02  1.58332909e-01]\n",
            "  [ 2.82563588e-02 -2.08426389e-02 -2.25364821e-03]\n",
            "  [ 1.37401466e-03  2.85584235e-02  2.70678669e-02]\n",
            "  [-3.64107695e-02 -6.78598463e-02 -2.92542383e-01]\n",
            "  [ 2.67478459e-02  1.99333148e-01  1.76060416e-01]\n",
            "  [ 4.34992768e-02  2.29732547e-01  4.26106589e-01]\n",
            "  [ 1.95342951e-02 -7.85336243e-02  3.46666861e-01]\n",
            "  [ 1.34149605e-02 -9.63456297e-02 -1.82622968e-01]]]\n",
            "[[[-2.83866777e-02 -1.32257415e-01  3.42296765e-02]\n",
            "  [ 5.00375864e-03  6.58239002e-03  1.61322614e-02]\n",
            "  [ 1.14354806e-03  1.43464625e-02 -2.37013481e-01]\n",
            "  [-1.32370603e-02 -8.09792827e-02  7.90720123e-02]\n",
            "  [ 6.63064026e-03  8.69443502e-02 -3.71338019e-01]\n",
            "  [ 1.51820583e-02  1.39943064e-01  7.38439377e-01]\n",
            "  [ 4.74490883e-03 -6.28274073e-03 -3.22030319e-01]\n",
            "  [ 6.29137373e-03  4.55632937e-03 -5.39775912e-03]]\n",
            "\n",
            " [[-6.78135002e-02  7.75028141e-02  1.49199157e-01]\n",
            "  [ 1.19535787e-02 -5.36300834e-02  1.52634882e-01]\n",
            "  [ 2.73184474e-03  1.84223361e-02  2.49538794e-02]\n",
            "  [-3.16222771e-02 -9.97998279e-03 -2.39244738e-01]\n",
            "  [ 1.58400687e-02  1.15798718e-01  5.06098771e-02]\n",
            "  [ 3.62687217e-02  1.23880978e-01 -1.78770800e-01]\n",
            "  [ 1.13352073e-02 -8.07760478e-02  3.64497927e-01]\n",
            "  [ 1.50295881e-02 -7.63172436e-02 -2.09620797e-01]]\n",
            "\n",
            " [[ 1.30770541e-01 -3.00496699e-02  2.38508957e-01]\n",
            "  [-2.30511027e-02  8.23716629e-02  3.78588245e-01]\n",
            "  [-5.26804860e-03 -4.03355733e-02 -1.24326573e-01]\n",
            "  [ 6.09799267e-02  7.49255631e-02 -2.17163131e-01]\n",
            "  [-3.05457518e-02 -2.51195615e-01 -2.53372847e-01]\n",
            "  [-6.99400612e-02 -3.02751972e-01 -8.54094183e-02]\n",
            "  [-2.18586444e-02  1.35808360e-01 -1.41551508e-01]\n",
            "  [-2.89828332e-02  1.20705025e-01  5.28799644e-02]]\n",
            "\n",
            " [[-6.90229471e-02  1.40362193e-01  4.61407600e-02]\n",
            "  [ 1.21667696e-02 -6.54232274e-02 -3.10323812e-01]\n",
            "  [ 2.78056692e-03  1.62743107e-02  1.12126112e-01]\n",
            "  [-3.21862571e-02  1.85095713e-02 -4.11765880e-01]\n",
            "  [ 1.61225747e-02  1.03503976e-01 -4.41362035e-01]\n",
            "  [ 3.69155706e-02  9.32105474e-02  6.47408804e-02]\n",
            "  [ 1.15373695e-02 -9.24927455e-02 -4.61794969e-02]\n",
            "  [ 1.52976393e-02 -9.13036031e-02  6.30615277e-01]]\n",
            "\n",
            " [[-1.19201738e-01  1.65476069e-01 -6.69512028e-01]\n",
            "  [ 2.10118539e-02 -9.94249307e-02 -1.85578269e-01]\n",
            "  [ 4.80200315e-03  3.12045286e-02 -2.62689518e-02]\n",
            "  [-5.55852503e-02 -3.90651589e-03  6.52736889e-01]\n",
            "  [ 2.78434782e-02  1.96719002e-01 -9.97789270e-02]\n",
            "  [ 6.37527137e-02  2.02116644e-01 -3.03092899e-01]\n",
            "  [ 1.99248881e-02 -1.46875119e-01 -8.31743608e-02]\n",
            "  [ 2.64188254e-02 -1.40630581e-01  1.41525406e-02]]\n",
            "\n",
            " [[ 7.75696784e-02 -2.09158502e-02  3.69761491e-01]\n",
            "  [-1.36733137e-02  4.94056093e-02  5.85948518e-02]\n",
            "  [-3.12486920e-03 -2.38014847e-02  1.06716230e-01]\n",
            "  [ 3.61717041e-02  4.30024420e-02 -7.77146116e-01]\n",
            "  [-1.81189443e-02 -1.48280652e-01  1.95922580e-02]\n",
            "  [-4.14866224e-02 -1.77931332e-01  2.67655178e-01]\n",
            "  [-1.29659784e-02  8.10746786e-02  4.40063977e-01]\n",
            "  [-1.71918617e-02  7.22841762e-02  3.05412454e-01]]\n",
            "\n",
            " [[-1.14298030e-01  2.48251257e-01  6.08627988e-01]\n",
            "  [ 2.01474705e-02 -1.11125633e-01  2.87535145e-01]\n",
            "  [ 4.60445886e-03  2.63120372e-02  1.28568282e-01]\n",
            "  [-5.32985903e-02  3.80276334e-02 -1.22303705e+00]\n",
            "  [ 2.66980562e-02  1.67701458e-01 -3.89563911e-01]\n",
            "  [ 6.11300614e-02  1.45890533e-01 -3.62398892e-01]\n",
            "  [ 1.91052202e-02 -1.55806944e-01  6.01011320e-01]\n",
            "  [ 2.53320106e-02 -1.54699618e-01  1.78721732e-01]]\n",
            "\n",
            " [[-8.79778938e-02 -4.67982744e-02  1.55966455e-01]\n",
            "  [ 1.55079841e-02 -4.36040392e-02  8.78708703e-03]\n",
            "  [ 3.54416077e-03  2.98360411e-02  1.36275457e-02]\n",
            "  [-4.10251841e-02 -8.16570900e-02 -3.26430696e-01]\n",
            "  [ 2.05501246e-02  1.84649187e-01  1.47502875e-01]\n",
            "  [ 4.70532525e-02  2.39522522e-01  3.82525163e-01]\n",
            "  [ 1.47057394e-02 -8.01654865e-02  3.37811449e-01]\n",
            "  [ 1.94986471e-02 -6.63536248e-02 -2.11511384e-01]]]\n",
            "found stable Phi for ii= 1\n",
            "orig_llk -7.664919665767687 est_llk=-8.280116928459002\n",
            "[[[ 4.13588968e-02 -5.48181658e-03  6.74779582e-01]\n",
            "  [-4.88106559e-02  5.83686579e-02  5.76844330e-01]\n",
            "  [-1.62823227e-02  2.05042215e-01 -3.58201804e-01]\n",
            "  [ 4.74014987e-02  1.15644929e-01 -6.76241988e-01]\n",
            "  [ 1.24879837e-02 -1.58558117e-01  2.45911966e-01]\n",
            "  [-6.99913260e-03 -1.65955906e-02 -8.15515880e-01]\n",
            "  [-6.49657199e-02  1.24776603e-01  3.61465128e-02]\n",
            "  [ 9.53403041e-02 -5.27263868e-02  4.32952656e-01]]\n",
            "\n",
            " [[ 6.82093465e-03 -1.05832160e-02 -6.23459591e-01]\n",
            "  [-8.04988334e-03  2.10492687e-02 -7.03621478e-01]\n",
            "  [-2.68529067e-03  3.76262119e-02  1.52173884e-01]\n",
            "  [ 7.81748428e-03  7.97894159e-03  1.08299622e-01]\n",
            "  [ 2.05952594e-03 -2.90720434e-02  4.99964238e-01]\n",
            "  [-1.15430125e-03 -1.09896004e-03  7.27101934e-02]\n",
            "  [-1.07141864e-02  3.57820495e-02 -4.31847673e-01]\n",
            "  [ 1.57235815e-02 -3.10079953e-02 -3.61551585e-01]]\n",
            "\n",
            " [[ 1.23510219e-02 -2.72539292e-02 -2.31724190e-01]\n",
            "  [-1.45763434e-02  4.76630193e-02  1.35185552e-01]\n",
            "  [-4.86239578e-03  7.13167814e-02 -3.16113144e-01]\n",
            "  [ 1.41555263e-02  5.17552400e-03  1.63257025e-01]\n",
            "  [ 3.72929097e-03 -5.50850796e-02  3.46181632e-01]\n",
            "  [-2.09015344e-03 -6.20821129e-04  4.44115855e-01]\n",
            "  [-1.94007358e-02  7.75005782e-02  3.43945901e-01]\n",
            "  [ 2.84715087e-02 -7.47976207e-02  1.42499065e-01]]\n",
            "\n",
            " [[-3.99564869e-02 -1.66335145e-02  1.52290992e-01]\n",
            "  [ 4.71555696e-02 -3.05089275e-02 -1.21879441e-01]\n",
            "  [ 1.57302169e-02 -1.89456314e-01  3.60568487e-01]\n",
            "  [-4.57941945e-02 -1.36856987e-01 -4.44063087e-01]\n",
            "  [-1.20645374e-02  1.46560261e-01  6.22165532e-01]\n",
            "  [ 6.76180392e-03  1.97439658e-02 -4.69065061e-01]\n",
            "  [ 6.27628428e-02 -8.60993000e-02  8.63419720e-01]\n",
            "  [-9.21074765e-02  3.86871113e-04  5.13140079e-01]]\n",
            "\n",
            " [[ 1.65743437e-02  1.27389762e-02 -1.36264937e-01]\n",
            "  [-1.95605940e-02  5.76410026e-03 -1.25398934e-02]\n",
            "  [-6.52504866e-03  7.62895327e-02 -5.47670246e-02]\n",
            "  [ 1.89958823e-02  6.34619760e-02  1.30728562e-01]\n",
            "  [ 5.00448877e-03 -5.90315293e-02  1.69100138e-01]\n",
            "  [-2.80486277e-03 -9.17815948e-03  1.21574346e-01]\n",
            "  [-2.60346445e-02  2.65426906e-02  4.57769063e-02]\n",
            "  [ 3.82070871e-02  1.33000852e-02  4.84470507e-02]]\n",
            "\n",
            " [[-1.91879360e-02  2.26683160e-04  3.11734143e-01]\n",
            "  [ 2.26450852e-02 -2.43454855e-02  5.91404005e-01]\n",
            "  [ 7.55397729e-03 -9.42147545e-02 -2.45345737e-01]\n",
            "  [-2.19913246e-02 -5.63069852e-02  2.92149699e-01]\n",
            "  [-5.79364177e-03  7.28615699e-02 -2.36425643e-01]\n",
            "  [ 3.24715887e-03  8.09133950e-03  3.09893125e-01]\n",
            "  [ 3.01400224e-02 -5.42497553e-02  5.89309523e-01]\n",
            "  [-4.42319259e-02  1.91216724e-02  3.96406352e-01]]\n",
            "\n",
            " [[-4.29294605e-02  1.52510642e-02  2.50758469e-02]\n",
            "  [ 5.06641929e-02 -7.18688809e-02 -2.85299786e-01]\n",
            "  [ 1.69006280e-02 -2.16592534e-01  5.39916158e-01]\n",
            "  [-4.92015244e-02 -1.09078462e-01 -9.95005856e-02]\n",
            "  [-1.29622027e-02  1.67466098e-01 -1.62028310e-01]\n",
            "  [ 7.26491782e-03  1.56077780e-02 -1.58214710e-01]\n",
            "  [ 6.74327296e-02 -1.44533225e-01  2.53795856e-01]\n",
            "  [-9.89607590e-02  7.67687717e-02 -1.30251493e-02]]\n",
            "\n",
            " [[-3.81178786e-02  1.53981590e-02  1.74033434e-01]\n",
            "  [ 4.49856936e-02 -6.60046701e-02  4.95089498e-01]\n",
            "  [ 1.50063868e-02 -1.93047456e-01 -1.62432969e-01]\n",
            "  [-4.36869626e-02 -9.47251447e-02  4.34116829e-01]\n",
            "  [-1.15093845e-02  1.49256851e-01 -2.59362598e-01]\n",
            "  [ 6.45065773e-03  1.35442751e-02 -1.09170272e-01]\n",
            "  [ 5.98747941e-02 -1.31249856e-01  2.71915318e-02]\n",
            "  [-8.78691268e-02  7.24439231e-02 -1.72479870e-01]]]\n",
            "[[[ 1.09240990e-02  6.86904916e-02  6.76373631e-01]\n",
            "  [-8.82650119e-02 -3.78151433e-01  6.01584490e-01]\n",
            "  [-1.34557732e-02  1.39120208e-01 -3.88793517e-01]\n",
            "  [ 7.30016322e-02  4.73967766e-01 -6.82790024e-01]\n",
            "  [ 1.76754607e-02 -4.80859969e-02  2.38082298e-01]\n",
            "  [-2.50334764e-03 -3.17854162e-02 -8.08192499e-01]\n",
            "  [-9.47808855e-02 -3.19068383e-01  2.93951161e-02]\n",
            "  [ 6.77213215e-02  2.76883949e-01  4.31506704e-01]]\n",
            "\n",
            " [[ 1.30247576e-03 -1.48435953e-01 -6.48147396e-01]\n",
            "  [-1.05238005e-02  1.22042589e+00 -7.04955064e-01]\n",
            "  [-1.60432622e-03  2.09511392e-01  1.11022110e-01]\n",
            "  [ 8.70395412e-03 -9.90160770e-01  1.16424529e-01]\n",
            "  [ 2.10743780e-03 -2.59157818e-01  4.76528779e-01]\n",
            "  [-2.98473093e-04  3.21023569e-02  9.40877304e-02]\n",
            "  [-1.13006854e-02  1.32089264e+00 -4.44699871e-01]\n",
            "  [ 8.07438488e-03 -9.37951753e-01 -3.54887558e-01]]\n",
            "\n",
            " [[ 2.89575056e-03 -4.36724867e-02 -2.54020402e-01]\n",
            "  [-2.33972119e-02  3.99747965e-01  1.47978054e-01]\n",
            "  [-3.56684455e-03  1.13099745e-01 -3.30555844e-01]\n",
            "  [ 1.93512086e-02 -2.87887764e-01  1.62138790e-01]\n",
            "  [ 4.68539561e-03 -1.12871415e-01  3.34037004e-01]\n",
            "  [-6.63585195e-04  5.75487033e-03  4.62349833e-01]\n",
            "  [-2.51244340e-02  4.52319615e-01  3.40513356e-01]\n",
            "  [ 1.79515085e-02 -3.10219600e-01  1.38503705e-01]]\n",
            "\n",
            " [[-9.33927610e-03 -6.46050768e-01  1.67913308e-01]\n",
            "  [ 7.54598910e-02  5.06878989e+00 -1.53483857e-01]\n",
            "  [ 1.15036656e-02  6.04501859e-01  3.67787786e-01]\n",
            "  [-6.24108589e-02 -4.33008196e+00 -4.15177386e-01]\n",
            "  [-1.51111784e-02 -9.09197392e-01  6.39414025e-01]\n",
            "  [ 2.14017237e-03  1.61764641e-01 -4.76669654e-01]\n",
            "  [ 8.10304688e-02  5.36859920e+00  8.51245531e-01]\n",
            "  [-5.78965938e-02 -3.87769848e+00  5.06744476e-01]]\n",
            "\n",
            " [[ 4.55043122e-03  1.22724869e-02 -1.28734795e-01]\n",
            "  [-3.67667729e-02 -2.54900273e-02 -2.22749529e-02]\n",
            "  [-5.60499961e-03  7.80779557e-02 -6.24016346e-02]\n",
            "  [ 3.04088152e-02  8.82336231e-02  1.28320909e-01]\n",
            "  [ 7.36270959e-03 -4.64695811e-02  1.34976583e-01]\n",
            "  [-1.04276895e-03 -9.49564257e-03  1.29192353e-01]\n",
            "  [-3.94809588e-02  8.86760169e-03  2.95653305e-02]\n",
            "  [ 2.82093028e-02  1.40368116e-02  4.06560337e-02]]\n",
            "\n",
            " [[-4.33919993e-03  8.76978405e-02  3.32883534e-01]\n",
            "  [ 3.50600571e-02 -7.78834837e-01  6.14026022e-01]\n",
            "  [ 5.34481520e-03 -1.96890438e-01 -2.48197634e-01]\n",
            "  [-2.89972362e-02  5.80119151e-01  2.72492871e-01]\n",
            "  [-7.02093217e-03  2.05145136e-01 -2.30048365e-01]\n",
            "  [ 9.94363557e-04 -1.37236241e-02  3.10911359e-01]\n",
            "  [ 3.76482503e-02 -8.70886866e-01  5.94139208e-01]\n",
            "  [-2.68998253e-02  6.02825102e-01  3.81586425e-01]]\n",
            "\n",
            " [[-1.02019872e-02 -2.67943020e-01  6.08473097e-02]\n",
            "  [ 8.24304620e-02  1.99977143e+00 -3.03258074e-01]\n",
            "  [ 1.25663111e-02  1.21098485e-01  5.65766523e-01]\n",
            "  [-6.81760319e-02 -1.80450999e+00 -9.46821703e-02]\n",
            "  [-1.65070662e-02 -2.84834943e-01 -1.65834569e-01]\n",
            "  [ 2.33786976e-03  7.63852027e-02 -1.65333954e-01]\n",
            "  [ 8.85156193e-02  2.06614998e+00  2.47391332e-01]\n",
            "  [-6.32447637e-02 -1.52194777e+00 -1.61619249e-02]]\n",
            "\n",
            " [[-9.17200091e-03  2.58127458e-01  2.05203828e-01]\n",
            "  [ 7.41083336e-02 -2.23412071e+00  5.39906128e-01]\n",
            "  [ 1.12976241e-02 -5.05794993e-01 -1.52869479e-01]\n",
            "  [-6.12930219e-02  1.71242872e+00  4.23259724e-01]\n",
            "  [-1.48405230e-02  5.51347016e-01 -2.81754063e-01]\n",
            "  [ 2.10183988e-03 -4.56809584e-02 -9.34328141e-02]\n",
            "  [ 7.95791371e-02 -2.47209254e+00  2.88016439e-02]\n",
            "  [-5.68596115e-02  1.72525601e+00 -1.70538339e-01]]]\n",
            "found stable Phi for ii= 2\n",
            "orig_llk -7.909142967580796 est_llk=-9.150680844789775\n",
            "[[[-1.60293961e-03 -2.32964823e-02  5.91343691e-02]\n",
            "  [ 5.79811770e-05  6.99334096e-04  3.44314897e-01]\n",
            "  [ 3.01797143e-04  3.92044482e-03 -5.96096970e-01]\n",
            "  [ 7.01928356e-04  1.03942338e-02 -3.57442834e-01]\n",
            "  [-4.05271877e-04 -5.38860618e-03 -3.38297200e-01]\n",
            "  [ 1.39056645e-03  2.19545679e-02  1.94524423e-01]\n",
            "  [ 4.91397356e-04  6.03387708e-03 -2.39236921e-01]\n",
            "  [-1.57797436e-04 -2.06726786e-03 -3.84949761e-01]]\n",
            "\n",
            " [[-3.87315396e-02  7.60187054e-02 -4.93082101e-01]\n",
            "  [ 1.40098868e-03 -6.21325693e-03 -5.04487153e-01]\n",
            "  [ 7.29226970e-03 -2.55665252e-02  3.88550521e-01]\n",
            "  [ 1.69605677e-02 -2.86327533e-02  7.68181306e-01]\n",
            "  [-9.79251096e-03  3.13363568e-02  1.18594843e+00]\n",
            "  [ 3.36000053e-02 -2.37917710e-02 -8.05748228e-01]\n",
            "  [ 1.18735453e-02 -5.00741757e-02  9.44613010e-01]\n",
            "  [-3.81283087e-03  1.29466117e-02  1.11732313e+00]]\n",
            "\n",
            " [[ 5.64295764e-02 -1.19120228e-01  2.18843339e-01]\n",
            "  [-2.04115815e-03  9.35494306e-03 -6.55110966e-01]\n",
            "  [-1.06244083e-02  3.88239473e-02  6.32963123e-01]\n",
            "  [-2.47105502e-02  4.53794716e-02  4.74329134e-01]\n",
            "  [ 1.42671128e-02 -4.77702682e-02  2.02599761e-01]\n",
            "  [-4.89532326e-02  4.19203184e-02 -4.16025697e-03]\n",
            "  [-1.72990576e-02  7.55196416e-02  2.90029496e-01]\n",
            "  [ 5.55507045e-03 -1.96859675e-02  4.73109931e-01]]\n",
            "\n",
            " [[-6.30334827e-02  8.96853589e-02 -5.83964883e-02]\n",
            "  [ 2.28003319e-03 -8.88077852e-03  6.87310158e-01]\n",
            "  [ 1.18677739e-02 -3.52008764e-02 -1.15179850e+00]\n",
            "  [ 2.76024053e-02 -3.16960716e-02 -1.27952335e+00]\n",
            "  [-1.59367812e-02  4.23941602e-02 -1.38697687e+00]\n",
            "  [ 5.46821886e-02 -9.19760829e-03  4.66638681e-01]\n",
            "  [ 1.93235519e-02 -7.10604715e-02 -1.16857384e+00]\n",
            "  [-6.20517571e-03  1.77198147e-02 -1.09191455e+00]]\n",
            "\n",
            " [[-3.00762000e-02  1.09658107e-01 -4.77399032e-01]\n",
            "  [ 1.08790965e-03 -6.65605975e-03  7.65385473e-01]\n",
            "  [ 5.66266574e-03 -2.93851448e-02  1.67073845e-01]\n",
            "  [ 1.31703886e-02 -4.44039224e-02 -8.13532405e-01]\n",
            "  [-7.60417793e-03  3.71337418e-02 -8.86015573e-01]\n",
            "  [ 2.60914100e-02 -6.23947267e-02  1.71434738e-01]\n",
            "  [ 9.22016341e-03 -5.44044096e-02 -1.61220658e+00]\n",
            "  [-2.96077732e-03  1.50373118e-02 -8.01595397e-01]]\n",
            "\n",
            " [[-6.01789611e-03  3.67735530e-02 -9.23699238e-01]\n",
            "  [ 2.17678006e-04 -1.86830853e-03 -1.93518779e-01]\n",
            "  [ 1.13303323e-03 -8.67219952e-03  4.25340146e-02]\n",
            "  [ 2.63524083e-03 -1.53797572e-02  4.68806655e-01]\n",
            "  [-1.52150713e-03  1.11800709e-02  8.01295589e-01]\n",
            "  [ 5.22058620e-03 -2.53515813e-02 -8.34431667e-01]\n",
            "  [ 1.84484694e-03 -1.54326620e-02  2.04803655e-01]\n",
            "  [-5.92416937e-04  4.46891435e-03  9.91994217e-01]]\n",
            "\n",
            " [[ 4.97729595e-02  6.13966769e-02  2.44580879e-01]\n",
            "  [-1.80037648e-03  2.23006492e-03 -6.20392852e-01]\n",
            "  [-9.37111843e-03  2.90254933e-03  2.66529815e-01]\n",
            "  [-2.17956131e-02 -3.28688178e-02  7.63732491e-01]\n",
            "  [ 1.25841177e-02 -4.76938176e-05  6.74919924e-01]\n",
            "  [-4.31785496e-02 -1.07434905e-01 -3.10950689e-01]\n",
            "  [-1.52584043e-02  1.55795395e-02  1.22990088e+00]\n",
            "  [ 4.89977621e-03 -9.76501025e-04  6.82793590e-01]]\n",
            "\n",
            " [[ 6.01287132e-02  2.93308496e-02 -2.71209225e-01]\n",
            "  [-2.17496251e-03  4.31599476e-03 -9.59013637e-01]\n",
            "  [-1.13208718e-02  1.19488092e-02  4.97332999e-02]\n",
            "  [-2.63304048e-02 -2.00720276e-02  1.15031231e+00]\n",
            "  [ 1.52023671e-02 -1.13945349e-02  1.39517000e+00]\n",
            "  [-5.21622714e-02 -9.08886276e-02 -1.10923074e+00]\n",
            "  [-1.84330654e-02  3.25671745e-02  1.56360015e+00]\n",
            "  [ 5.91922284e-03 -5.59383580e-03  1.64987070e+00]]]\n",
            "[[[-1.18413985e-04 -2.83471097e-01  5.17490369e-02]\n",
            "  [ 1.06041037e-05  2.54209340e-02  3.17147136e-01]\n",
            "  [ 1.27405659e-05  3.03957722e-02 -5.84060730e-01]\n",
            "  [ 1.40186105e-05  3.34501240e-02 -3.22380764e-01]\n",
            "  [-5.36787089e-05 -1.28648670e-01 -3.36824679e-01]\n",
            "  [ 1.10812854e-04  2.65525032e-01  2.06067171e-01]\n",
            "  [-4.98330101e-06 -1.21094147e-02 -2.30421123e-01]\n",
            "  [-3.30575392e-05 -7.92608789e-02 -3.72286906e-01]]\n",
            "\n",
            " [[-3.79838749e-02  1.64132869e-01 -4.95598740e-01]\n",
            "  [ 3.40149813e-03 -3.22013015e-03 -4.83109229e-01]\n",
            "  [ 4.08681508e-03 -5.09727605e-02  3.90112981e-01]\n",
            "  [ 4.49677586e-03 -5.43987455e-02  7.49349697e-01]\n",
            "  [-1.72186196e-02  2.71625867e-02  1.19238879e+00]\n",
            "  [ 3.55456460e-02 -7.33164059e-02 -8.07896543e-01]\n",
            "  [-1.59850276e-03 -5.07983963e-02  9.38575104e-01]\n",
            "  [-1.06039285e-02  5.89259942e-03  1.11851590e+00]]\n",
            "\n",
            " [[ 5.73117678e-02  4.34715168e-01  2.20249538e-01]\n",
            "  [-5.13233237e-03 -5.62479716e-02 -6.71358442e-01]\n",
            "  [-6.16636921e-03  3.49186697e-03  6.14385032e-01]\n",
            "  [-6.78493636e-03  1.29635339e-03  4.35334693e-01]\n",
            "  [ 2.59802227e-02  2.68341968e-01  1.87711954e-01]\n",
            "  [-5.36328590e-02 -5.27941231e-01 -2.75937620e-03]\n",
            "  [ 2.41189240e-03  1.05363397e-01  3.20610332e-01]\n",
            "  [ 1.59996812e-02  1.81604612e-01  4.76941546e-01]]\n",
            "\n",
            " [[-6.41291094e-02 -5.72447265e-02 -6.52414311e-02]\n",
            "  [ 5.74283287e-03  2.45051720e-02  6.89244330e-01]\n",
            "  [ 6.89987032e-03 -5.00842427e-02 -1.15820411e+00]\n",
            "  [ 7.59201718e-03 -5.22597244e-02 -1.29787012e+00]\n",
            "  [-2.90706186e-02 -1.05708191e-01 -1.37382657e+00]\n",
            "  [ 6.00125875e-02  1.89109804e-01  4.64258833e-01]\n",
            "  [-2.69879149e-03 -9.98350527e-02 -1.19819740e+00]\n",
            "  [-1.79028731e-02 -8.33928021e-02 -1.06993725e+00]]\n",
            "\n",
            " [[-3.72434633e-02  4.21920445e-02 -4.83061602e-01]\n",
            "  [ 3.33519344e-03  7.47606479e-03  7.76056455e-01]\n",
            "  [ 4.00715166e-03 -3.72033639e-02  1.35818220e-01]\n",
            "  [ 4.40912116e-03 -3.92809882e-02 -7.98420220e-01]\n",
            "  [-1.68829807e-02 -2.71940264e-02 -8.76845765e-01]\n",
            "  [ 3.48527622e-02  3.92320035e-02  1.82697704e-01]\n",
            "  [-1.56734349e-03 -5.48052745e-02 -1.58614764e+00]\n",
            "  [-1.03972284e-02 -2.73712120e-02 -8.10980192e-01]]\n",
            "\n",
            " [[-9.88045749e-03  9.46755750e-02 -9.43869931e-01]\n",
            "  [ 8.84805926e-04 -5.49257849e-03 -1.89832042e-01]\n",
            "  [ 1.06307223e-03 -1.88519646e-02  3.74802927e-02]\n",
            "  [ 1.16971222e-03 -2.03041715e-02  4.62634583e-01]\n",
            "  [-4.47894901e-03  3.06292801e-02  8.07965736e-01]\n",
            "  [ 9.24621947e-03 -6.77154602e-02 -8.20607474e-01]\n",
            "  [-4.15806408e-04 -1.10262507e-02  1.88714348e-01]\n",
            "  [-2.75831956e-03  1.60442742e-02  9.88734509e-01]]\n",
            "\n",
            " [[ 5.19873242e-02  2.02877510e-01  2.47476713e-01]\n",
            "  [-4.65552254e-03 -3.38776861e-02 -5.92748016e-01]\n",
            "  [-5.59349410e-03  2.37663567e-02  2.86154674e-01]\n",
            "  [-6.15459441e-03  2.38411507e-02  7.68081430e-01]\n",
            "  [ 2.35665782e-02  1.56624636e-01  6.87986583e-01]\n",
            "  [-4.86501976e-02 -2.99732056e-01 -3.26478484e-01]\n",
            "  [ 2.18782000e-03  8.75178253e-02  1.18882574e+00]\n",
            "  [ 1.45132605e-02  1.11285677e-01  6.68703403e-01]]\n",
            "\n",
            " [[ 6.35659914e-02  3.16414792e-01 -2.58696877e-01]\n",
            "  [-5.69240503e-03 -4.75439731e-02 -9.62017575e-01]\n",
            "  [-6.83928253e-03  2.17053749e-02  6.24352105e-02]\n",
            "  [-7.52535165e-03  2.10591003e-02  1.17674235e+00]\n",
            "  [ 2.88153494e-02  2.22493234e-01  1.39731091e+00]\n",
            "  [-5.94856168e-02 -4.30453269e-01 -1.09882706e+00]\n",
            "  [ 2.67509339e-03  1.09886395e-01  1.57436594e+00]\n",
            "  [ 1.77456679e-02  1.55153162e-01  1.64457147e+00]]]\n",
            "found stable Phi for ii= 3\n",
            "orig_llk -14.679623435605322 est_llk=-15.425846400567236\n",
            "[[[ 5.39766230e-02 -9.06091144e-02 -8.47782236e-01]\n",
            "  [ 4.32474973e-02 -2.52015753e-03  1.05319649e+00]\n",
            "  [-3.91411790e-02 -6.45809749e-02  2.47976302e-01]\n",
            "  [ 2.67541617e-02 -5.31215225e-02  6.26545251e-01]\n",
            "  [-4.63317608e-03  5.54740310e-02  8.12278314e-01]\n",
            "  [-3.15867503e-02  5.19113401e-02  8.05475663e-01]\n",
            "  [ 4.64451176e-02 -5.92645031e-02  1.83973708e-01]\n",
            "  [ 7.98409024e-03  4.67526206e-03  6.77274519e-01]]\n",
            "\n",
            " [[-2.36834145e-02  7.03172675e-02 -4.24245724e-01]\n",
            "  [-1.89757778e-02  2.55916964e-02 -7.04510216e-02]\n",
            "  [ 1.71740415e-02  6.17530189e-03 -2.10219664e-01]\n",
            "  [-1.17389690e-02  3.84559257e-02  4.25172230e-01]\n",
            "  [ 2.03290653e-03 -2.69636523e-02  4.19552421e-01]\n",
            "  [ 1.38593720e-02 -4.06610530e-02 -5.91820996e-01]\n",
            "  [-2.03788031e-02  5.22999420e-02 -3.74492489e-01]\n",
            "  [-3.50319283e-03  2.46906962e-03 -1.79797627e-01]]\n",
            "\n",
            " [[ 2.77699959e-02 -1.24953282e-03 -6.37292341e-01]\n",
            "  [ 2.22500548e-02  3.50528382e-02  3.77904129e-01]\n",
            "  [-2.01374283e-02 -6.61238063e-02  7.34957462e-02]\n",
            "  [ 1.37645321e-02 -4.84325590e-03  2.21355961e-01]\n",
            "  [-2.38368526e-03  2.46462123e-02  5.17271843e-01]\n",
            "  [-1.62508115e-02  1.58860349e-04  3.55243516e-01]\n",
            "  [ 2.38951726e-02  8.54649101e-03  3.22251260e-01]\n",
            "  [ 4.10766996e-03  9.11594567e-03  5.02491968e-01]]\n",
            "\n",
            " [[ 4.37635048e-02 -5.63359122e-02 -8.33129959e-02]\n",
            "  [ 3.50644770e-02  1.16806690e-02  6.14061410e-01]\n",
            "  [-3.17351304e-02 -6.47822641e-02  3.63223115e-01]\n",
            "  [ 2.16919070e-02 -3.45801483e-02  2.79036162e-01]\n",
            "  [-3.75651554e-03  4.35073101e-02  7.12742356e-01]\n",
            "  [-2.56101034e-02  3.20653958e-02  3.11142031e-01]\n",
            "  [ 3.76570636e-02 -3.33121479e-02 -1.85259207e-01]\n",
            "  [ 6.47339074e-03  6.32427576e-03  2.53560321e-01]]\n",
            "\n",
            " [[-7.82326687e-03 -3.53726192e-02  6.81985766e-01]\n",
            "  [-6.26820824e-03 -3.84984845e-02 -8.30582622e-02]\n",
            "  [ 5.67304643e-03  4.45339074e-02  4.04371618e-02]\n",
            "  [-3.87769622e-03 -1.63429184e-02 -2.54681713e-01]\n",
            "  [ 6.71523539e-04 -3.87676018e-03 -6.63400849e-01]\n",
            "  [ 4.57812221e-03  2.08610572e-02  1.51149274e-01]\n",
            "  [-6.73166511e-03 -3.31475655e-02 -5.10089632e-01]\n",
            "  [-1.15719853e-03 -7.85241307e-03 -5.08589720e-01]]\n",
            "\n",
            " [[ 1.05406366e-02  5.98139159e-03  3.11784908e-01]\n",
            "  [ 8.44543669e-03  1.84774377e-02  6.61318552e-01]\n",
            "  [-7.64354863e-03 -2.97799008e-02  1.93589259e-01]\n",
            "  [ 5.22459317e-03  1.36148227e-03  3.60415921e-02]\n",
            "  [-9.04773632e-04  8.80081036e-03  2.06266053e-01]\n",
            "  [-6.16830837e-03 -3.71751880e-03  6.10232224e-01]\n",
            "  [ 9.06987282e-03  8.79888298e-03 -3.17831828e-01]\n",
            "  [ 1.55914522e-03  4.41504049e-03  4.31640123e-04]]\n",
            "\n",
            " [[-4.44985287e-02  5.80087583e-02  1.64302721e-01]\n",
            "  [-3.56533976e-02 -1.12946276e-02 -3.85779867e-01]\n",
            "  [ 3.22681334e-02  6.53433648e-02 -2.52229051e-01]\n",
            "  [-2.20562304e-02  3.55211142e-02 -1.36248102e-01]\n",
            "  [ 3.81960758e-03 -4.43004056e-02 -4.16770351e-01]\n",
            "  [ 2.60402343e-02 -3.30291845e-02 -3.09700752e-01]\n",
            "  [-3.82895276e-02  3.44969081e-02 -4.57420295e-02]\n",
            "  [-6.58211368e-03 -6.32300788e-03 -2.96219588e-01]]\n",
            "\n",
            " [[ 4.68692225e-02 -8.99081135e-02 -1.65920184e+00]\n",
            "  [ 3.75528602e-02 -1.11860892e-02  5.78040840e-01]\n",
            "  [-3.39872434e-02 -4.79337981e-02 -7.77677477e-01]\n",
            "  [ 2.32312933e-02 -5.16930034e-02  9.21273911e-01]\n",
            "  [-4.02310016e-03  4.91334051e-02 -4.20636111e-01]\n",
            "  [-2.74275482e-02  5.16476073e-02  4.08276692e-01]\n",
            "  [ 4.03294321e-02 -6.11238677e-02  5.48705565e-01]\n",
            "  [ 6.93278092e-03  2.39852992e-03  5.04631583e-01]]]\n",
            "[[[ 3.40614292e-02 -1.98418199e-01 -8.36342587e-01]\n",
            "  [ 6.05587127e-02 -1.79374494e-01  1.02294544e+00]\n",
            "  [-2.78957486e-02  1.42413920e-02  2.13282568e-01]\n",
            "  [ 1.84900889e-02 -8.27080555e-02  6.24060559e-01]\n",
            "  [ 9.57099316e-04  7.88775379e-02  8.18880136e-01]\n",
            "  [-1.01856811e-02  3.22683130e-02  7.99303153e-01]\n",
            "  [ 6.87218042e-02 -2.82501845e-01  1.70363219e-01]\n",
            "  [ 2.55817273e-02 -9.66171461e-02  6.79971954e-01]]\n",
            "\n",
            " [[-7.65581406e-03  1.47562048e-01 -4.03618323e-01]\n",
            "  [-1.36114736e-02  2.23380566e-01 -4.04895259e-02]\n",
            "  [ 6.26998541e-03 -8.75272731e-02 -2.53575837e-01]\n",
            "  [-4.15592316e-03  7.44837238e-02  4.20030290e-01]\n",
            "  [-2.15122341e-04 -1.48356786e-02  4.06016685e-01]\n",
            "  [ 2.28938369e-03 -3.80431709e-02 -5.85306852e-01]\n",
            "  [-1.54462501e-02  2.71236259e-01 -3.61312779e-01]\n",
            "  [-5.74987463e-03  9.90473765e-02 -1.94304572e-01]]\n",
            "\n",
            " [[ 2.50361760e-02 -4.44286629e-03 -6.43033655e-01]\n",
            "  [ 4.45124771e-02  1.19553994e-01  3.92528247e-01]\n",
            "  [-2.05042151e-02 -1.05336812e-01  4.32335252e-02]\n",
            "  [ 1.35907720e-02  1.59656861e-02  2.23898011e-01]\n",
            "  [ 7.03496813e-04  6.19506074e-02  5.15727624e-01]\n",
            "  [-7.48678226e-03 -1.85660169e-02  3.53040453e-01]\n",
            "  [ 5.05125952e-02  7.76400326e-02  2.54718007e-01]\n",
            "  [ 1.88033398e-02  3.51818694e-02  4.84249515e-01]]\n",
            "\n",
            " [[ 2.38630868e-02 -1.04620939e-01 -7.92080774e-02]\n",
            "  [ 4.24268110e-02 -6.45271530e-02  6.07678963e-01]\n",
            "  [-1.95434744e-02 -1.81864953e-02  3.74121290e-01]\n",
            "  [ 1.29539660e-02 -3.92766066e-02  2.73540000e-01]\n",
            "  [ 6.70533932e-04  5.62270899e-02  7.06399090e-01]\n",
            "  [-7.13598335e-03  1.23232675e-02  3.18159423e-01]\n",
            "  [ 4.81457889e-02 -1.28535563e-01 -2.01364803e-01]\n",
            "  [ 1.79222949e-02 -4.18613727e-02  2.42269254e-01]]\n",
            "\n",
            " [[-8.05113077e-03 -2.15746365e-01  6.73252119e-01]\n",
            "  [-1.43143176e-02 -4.24567497e-01 -7.85809820e-02]\n",
            "  [ 6.59374326e-03  2.11737025e-01  6.31633513e-02]\n",
            "  [-4.37051900e-03 -1.23026740e-01 -2.67272058e-01]\n",
            "  [-2.26230429e-04 -2.60245188e-02 -6.43286648e-01]\n",
            "  [ 2.40759863e-03  7.09141893e-02  1.43454409e-01]\n",
            "  [-1.62438349e-02 -4.63136544e-01 -5.08137088e-01]\n",
            "  [-6.04677598e-03 -1.74422446e-01 -5.20494622e-01]]\n",
            "\n",
            " [[ 3.15420603e-03 -2.07947897e-01  2.85816104e-01]\n",
            "  [ 5.60794603e-03 -3.53658751e-01  6.79523358e-01]\n",
            "  [-2.58324270e-03  1.56576524e-01  1.99290001e-01]\n",
            "  [ 1.71224612e-03 -1.10568248e-01  1.35383773e-02]\n",
            "  [ 8.86307035e-05  1.97746136e-03  2.30693712e-01]\n",
            "  [-9.43229260e-04  5.96780013e-02  6.31248476e-01]\n",
            "  [ 6.36387651e-03 -4.08641537e-01 -3.32251275e-01]\n",
            "  [ 2.36895634e-03 -1.51325792e-01 -1.30535820e-02]]\n",
            "\n",
            " [[-2.37913025e-02  7.69344833e-02  1.62166894e-01]\n",
            "  [-4.22991838e-02  1.56681104e-02 -3.87310830e-01]\n",
            "  [ 1.94846843e-02  4.05487887e-02 -2.60593251e-01]\n",
            "  [-1.29149983e-02  2.42998350e-02 -1.16450660e-01]\n",
            "  [-6.68516851e-04 -5.68270734e-02 -4.24284379e-01]\n",
            "  [ 7.11451708e-03 -4.10099172e-03 -3.35024921e-01]\n",
            "  [-4.80009581e-02  7.29241184e-02 -4.32809475e-02]\n",
            "  [-1.78683816e-02  2.11779906e-02 -3.00991016e-01]]\n",
            "\n",
            " [[ 2.75077535e-02 -2.56222222e-01 -1.64535643e+00]\n",
            "  [ 4.89067599e-02 -3.15508958e-01  5.72009855e-01]\n",
            "  [-2.25283962e-02  9.01082433e-02 -7.81843252e-01]\n",
            "  [ 1.49324564e-02 -1.18897340e-01  8.93451486e-01]\n",
            "  [ 7.72946192e-04  6.10039095e-02 -4.22684142e-01]\n",
            "  [-8.22587925e-03  5.47617210e-02  4.35435665e-01]\n",
            "  [ 5.54992110e-02 -4.21796480e-01  5.80984223e-01]\n",
            "  [ 2.06596101e-02 -1.50113636e-01  4.84666408e-01]]]\n",
            "found stable Phi for ii= 4\n",
            "orig_llk -9.291282764415168 est_llk=-10.05267766592375\n",
            "[[[-0.01485881  0.06632908 -0.24642789]\n",
            "  [ 0.05895396  0.02296358  0.1766284 ]\n",
            "  [-0.02697826  0.02400383  0.06219304]\n",
            "  [ 0.08126867 -0.00672632  0.13549388]\n",
            "  [ 0.02117463 -0.05848678 -0.06741007]\n",
            "  [-0.07549827  0.01959189  0.546621  ]\n",
            "  [ 0.01941712  0.0962931  -0.33574928]\n",
            "  [-0.01452668 -0.03932313 -0.74926617]]\n",
            "\n",
            " [[ 0.01219115 -0.0422307  -0.21290377]\n",
            "  [-0.04836975 -0.06720637  0.19413983]\n",
            "  [ 0.02213476  0.00243848 -0.15641327]\n",
            "  [-0.06667822 -0.06115368  0.14765271]\n",
            "  [-0.01737307  0.03061489  0.94663293]\n",
            "  [ 0.0619438   0.0458639   0.57268147]\n",
            "  [-0.01593109 -0.09493497 -0.09712981]\n",
            "  [ 0.01191865  0.04418093 -0.33559516]]\n",
            "\n",
            " [[-0.00447752  0.00979849  0.16854251]\n",
            "  [ 0.01776507  0.04734572  0.52773044]\n",
            "  [-0.00812957 -0.01126627  0.36918538]\n",
            "  [ 0.02448934  0.05370068 -0.42232282]\n",
            "  [ 0.00638072 -0.00310442 -0.36642696]\n",
            "  [-0.0227505  -0.04586691 -0.20356593]\n",
            "  [ 0.00585112  0.04233148 -0.19169336]\n",
            "  [-0.00437744 -0.02181079  0.61682322]]\n",
            "\n",
            " [[ 0.01459514 -0.07715837 -0.1212178 ]\n",
            "  [-0.05790784  0.02508014  0.56703239]\n",
            "  [ 0.02649954 -0.04537698 -0.57892342]\n",
            "  [-0.07982658  0.07227403 -0.36326956]\n",
            "  [-0.02079889  0.07455856 -0.13311581]\n",
            "  [ 0.07415857 -0.08024868 -0.16643805]\n",
            "  [-0.01907257 -0.07889491  0.06284448]\n",
            "  [ 0.01426891  0.02688745  0.5639116 ]]\n",
            "\n",
            " [[-0.00478152  0.02997445  0.20267507]\n",
            "  [ 0.01897123 -0.02685059  0.39637506]\n",
            "  [-0.00868153  0.02339323  0.04564665]\n",
            "  [ 0.02615204 -0.04936501 -0.34422298]\n",
            "  [ 0.00681394 -0.03111902  0.06695758]\n",
            "  [-0.02429514  0.05015369  0.03149009]\n",
            "  [ 0.00624838  0.01970948 -0.12936558]\n",
            "  [-0.00467465 -0.00421705  1.15225868]]\n",
            "\n",
            " [[-0.00170177 -0.01159184 -0.05013364]\n",
            "  [ 0.00675197  0.0787624   0.05627586]\n",
            "  [-0.00308981 -0.03209023  0.22835296]\n",
            "  [ 0.00930766  0.10417897  0.24786821]\n",
            "  [ 0.00242512  0.02064618  0.03370204]\n",
            "  [-0.00864678 -0.09525365  0.08219365]\n",
            "  [ 0.00222383  0.03610342  0.02816058]\n",
            "  [-0.00166373 -0.02326323 -0.75701027]]\n",
            "\n",
            " [[ 0.0175209  -0.07183426 -0.0691266 ]\n",
            "  [-0.0695161  -0.05238425  0.64657947]\n",
            "  [ 0.03181166 -0.01672367  0.17801684]\n",
            "  [-0.0958287  -0.02695393 -0.07544337]\n",
            "  [-0.02496826  0.05987581  1.16469918]\n",
            "  [ 0.08902447  0.00930637  0.5002087 ]\n",
            "  [-0.02289587 -0.12187987 -0.17718423]\n",
            "  [ 0.01712927  0.05260395  0.10521813]]\n",
            "\n",
            " [[-0.00454646 -0.00296563  0.36939091]\n",
            "  [ 0.01803857  0.09931621  0.40693431]\n",
            "  [-0.00825473 -0.03488867  0.69675719]\n",
            "  [ 0.02486637  0.1251645  -0.36784995]\n",
            "  [ 0.00647895  0.01525234 -0.31149726]\n",
            "  [-0.02310075 -0.1121946  -0.2881843 ]\n",
            "  [ 0.0059412   0.05986016 -0.0525468 ]\n",
            "  [-0.00444483 -0.03477287  0.59422377]]]\n",
            "[[[-1.20829174e-02  6.34346608e-02 -2.50363132e-01]\n",
            "  [ 6.20360611e-02  4.25691187e-02  2.05094391e-01]\n",
            "  [-1.64412667e-02  2.77902330e-02  7.34570257e-02]\n",
            "  [ 7.19951681e-02  1.05078811e-02  1.47979563e-01]\n",
            "  [ 5.80985903e-03 -6.93308064e-02 -9.58540376e-02]\n",
            "  [-7.69925641e-02 -7.54295130e-03  5.36866024e-01]\n",
            "  [ 1.17875583e-02  8.48820616e-02 -3.38056158e-01]\n",
            "  [ 9.03168130e-04 -2.44329875e-02 -6.78504600e-01]]\n",
            "\n",
            " [[ 1.14757551e-02 -5.17360922e-02 -2.13324330e-01]\n",
            "  [-5.89187711e-02 -8.41271718e-02  1.84556654e-01]\n",
            "  [ 1.56150989e-02 -1.48128378e-02 -1.35217904e-01]\n",
            "  [-6.83774366e-02 -6.06920240e-02  1.65399998e-01]\n",
            "  [-5.51791569e-03  6.17545932e-02  9.37742313e-01]\n",
            "  [ 7.31237152e-02  6.13961608e-02  5.83044406e-01]\n",
            "  [-1.11952377e-02 -8.89197219e-02 -1.11103334e-01]\n",
            "  [-8.57784253e-04  2.25690624e-02 -3.11116797e-01]]\n",
            "\n",
            " [[-5.10029570e-03  1.95015185e-02  1.40169686e-01]\n",
            "  [ 2.61859157e-02  5.53187910e-02  5.69008296e-01]\n",
            "  [-6.93998969e-03  1.83169186e-03  3.73489508e-01]\n",
            "  [ 3.03897342e-02  4.77815628e-02 -4.33154016e-01]\n",
            "  [ 2.45238779e-03 -2.57671463e-02 -3.57364122e-01]\n",
            "  [-3.24991748e-02 -4.95388225e-02 -1.91303009e-01]\n",
            "  [ 4.97562229e-03  4.29263252e-02 -2.05272697e-01]\n",
            "  [ 3.81234464e-04 -9.76958863e-03  6.22291026e-01]]\n",
            "\n",
            " [[ 1.40815293e-02 -9.02473417e-02 -1.19811056e-01]\n",
            "  [-7.22973257e-02  3.41800712e-02  5.51548030e-01]\n",
            "  [ 1.91607848e-02 -5.45937453e-02 -5.75032049e-01]\n",
            "  [-8.39037494e-02  8.49959982e-02 -3.74840916e-01]\n",
            "  [-6.77085655e-03  8.86459035e-02 -1.47696579e-01]\n",
            "  [ 8.97277549e-02 -9.52012017e-02 -1.84590838e-01]\n",
            "  [-1.37373155e-02 -8.30010960e-02  7.16240936e-02]\n",
            "  [-1.05255942e-03  2.96942859e-02  6.00316036e-01]]\n",
            "\n",
            " [[-3.71668796e-03  2.92174888e-02  1.93219993e-01]\n",
            "  [ 1.90822030e-02 -3.67335722e-02  3.97087838e-01]\n",
            "  [-5.05730994e-03  2.17539690e-02  3.82912176e-02]\n",
            "  [ 2.21456099e-02 -5.45947829e-02 -3.35958206e-01]\n",
            "  [ 1.78710426e-03 -2.59925731e-02  3.74831807e-02]\n",
            "  [-2.36828017e-02  5.95207323e-02  4.44495830e-02]\n",
            "  [ 3.62583595e-03  1.66417555e-02 -1.29204614e-01]\n",
            "  [ 2.77813215e-04 -8.24098231e-03  1.18100788e+00]]\n",
            "\n",
            " [[-7.67892603e-04 -1.43024448e-02 -5.48533054e-02]\n",
            "  [ 3.94251082e-03  9.68348663e-02  6.99448251e-02]\n",
            "  [-1.04487407e-03 -2.31807948e-02  2.57655651e-01]\n",
            "  [ 4.57543120e-03  1.09908620e-01  2.39205109e-01]\n",
            "  [ 3.69227699e-04  4.40939940e-03  3.47559972e-02]\n",
            "  [-4.89302531e-03 -1.17302919e-01  7.27216893e-02]\n",
            "  [ 7.49121968e-04  2.32800986e-02  2.15775244e-02]\n",
            "  [ 5.73980691e-05 -1.82354222e-04 -7.90939848e-01]]\n",
            "\n",
            " [[ 1.62469988e-02 -8.17554532e-02 -8.96554622e-02]\n",
            "  [-8.34152695e-02 -7.54166753e-02  6.23093375e-01]\n",
            "  [ 2.21073464e-02 -3.25500092e-02  1.84764704e-01]\n",
            "  [-9.68065388e-02 -3.52244303e-02 -7.38354830e-02]\n",
            "  [-7.81208459e-03  9.15216264e-02  1.15933626e+00]\n",
            "  [ 1.03526165e-01  3.27019945e-02  5.13624825e-01]\n",
            "  [-1.58498515e-02 -1.17588450e-01 -1.84887133e-01]\n",
            "  [-1.21442290e-03  3.25885811e-02  1.14161787e-01]]\n",
            "\n",
            " [[-5.78656231e-03  1.19457277e-02  3.61176404e-01]\n",
            "  [ 2.97093427e-02  1.15027274e-01  3.98157646e-01]\n",
            "  [-7.87379500e-03 -1.17735395e-02  6.80907241e-01]\n",
            "  [ 3.44788029e-02  1.14866382e-01 -3.66217200e-01]\n",
            "  [ 2.78236707e-03 -2.43394460e-02 -3.22005655e-01]\n",
            "  [-3.68720779e-02 -1.21070373e-01 -2.85482791e-01]\n",
            "  [ 5.64511356e-03  5.86332109e-02 -3.20431261e-02]\n",
            "  [ 4.32531193e-04 -1.03232135e-02  5.71247311e-01]]]\n",
            "found stable Phi for ii= 5\n",
            "orig_llk -12.626511120977398 est_llk=-13.004965581472732\n",
            "[[[ 5.40872377e-02 -4.78582216e-02 -5.57192925e-01]\n",
            "  [ 4.60808913e-02 -7.95049848e-02  2.18506060e-01]\n",
            "  [-2.39130622e-02  4.78128674e-02  4.76384274e-02]\n",
            "  [ 2.27871899e-03  4.80380086e-02  1.90872570e-01]\n",
            "  [ 1.36482130e-02 -2.54212233e-03  3.40034846e-01]\n",
            "  [ 9.30031535e-03 -3.88924360e-02  3.67410253e-02]\n",
            "  [-1.54724634e-02 -8.52298094e-04 -6.88226227e-01]\n",
            "  [ 5.52570206e-02  3.45151672e-02  3.01125049e-01]]\n",
            "\n",
            " [[-3.61755317e-02 -1.19958783e-02  1.17112021e-01]\n",
            "  [-3.08205931e-02  1.56845791e-02  1.40766969e-02]\n",
            "  [ 1.59939346e-02 -1.25234062e-02 -6.89230701e-01]\n",
            "  [-1.52409098e-03 -3.39835441e-02 -4.53775077e-01]\n",
            "  [-9.12842626e-03 -9.40388056e-03 -4.80635817e-01]\n",
            "  [-6.22039260e-03  1.84459813e-02 -7.41172286e-01]\n",
            "  [ 1.03485520e-02  1.31583983e-02  1.64878773e-01]\n",
            "  [-3.69579255e-02 -6.80419591e-02 -3.19581119e-01]]\n",
            "\n",
            " [[-6.17958280e-02 -1.93049875e-02 -1.10013077e-01]\n",
            "  [-5.26484057e-02  2.78037172e-02  9.28461661e-02]\n",
            "  [ 2.73211860e-02 -2.19173882e-02 -2.02542314e-01]\n",
            "  [-2.60348527e-03 -5.80014338e-02 -4.48680001e-01]\n",
            "  [-1.55933757e-02 -1.57644815e-02 -1.82640573e-01]\n",
            "  [-1.06258096e-02  3.17138670e-02 -8.08061459e-01]\n",
            "  [ 1.76776209e-02  2.21380076e-02 -1.43129558e-01]\n",
            "  [-6.31323300e-02 -1.15018454e-01 -6.13329679e-03]]\n",
            "\n",
            " [[ 4.83061344e-02 -6.53435669e-02 -1.93139971e-01]\n",
            "  [ 4.11555447e-02 -9.02622747e-02 -4.12864713e-01]\n",
            "  [-2.13571195e-02  5.26946087e-02 -4.17652609e-01]\n",
            "  [ 2.03515858e-03  4.19513002e-02 -1.87518519e-01]\n",
            "  [ 1.21894265e-02 -7.97339191e-03  4.61728970e-01]\n",
            "  [ 8.30625305e-03 -3.86216159e-02 -1.83205335e-01]\n",
            "  [-1.38186923e-02  5.70405689e-03  3.09453264e-01]\n",
            "  [ 4.93508853e-02  7.73655865e-03  2.80817091e-01]]\n",
            "\n",
            " [[ 4.55417457e-02 -5.80341090e-02  2.28173987e-01]\n",
            "  [ 3.88003589e-02 -8.20552737e-02  2.29153545e-01]\n",
            "  [-2.01349273e-02  4.81006797e-02  4.32627070e-01]\n",
            "  [ 1.91869368e-03  3.97009851e-02 -1.67345973e-01]\n",
            "  [ 1.14918689e-02 -6.61624024e-03  6.07884234e-01]\n",
            "  [ 7.83091567e-03 -3.57975621e-02  6.76378395e-02]\n",
            "  [-1.30278976e-02  4.35635989e-03  9.03215192e-01]\n",
            "  [ 4.65267093e-02  1.09411129e-02 -1.35704038e-01]]\n",
            "\n",
            " [[-5.79653956e-02 -4.20061550e-02  8.54804583e-01]\n",
            "  [-4.93849790e-02  5.72001042e-03  6.06385197e-02]\n",
            "  [ 2.56276743e-02 -9.99313477e-03  5.07294937e-01]\n",
            "  [-2.44210748e-03 -5.54130225e-02 -1.29127917e-01]\n",
            "  [-1.46268158e-02 -2.08176136e-02 -8.50635903e-02]\n",
            "  [-9.96716567e-03  2.56388417e-02  4.44861855e-01]\n",
            "  [ 1.65818685e-02  2.76020979e-02  9.56235959e-01]\n",
            "  [-5.92190542e-02 -1.32303649e-01 -3.52643265e-01]]\n",
            "\n",
            " [[-5.02777350e-02  3.20428635e-03 -8.09944719e-02]\n",
            "  [-4.28352961e-02  3.87330898e-02 -6.08374376e-01]\n",
            "  [ 2.22288040e-02 -2.61931651e-02 -1.50506243e-01]\n",
            "  [-2.11822298e-03 -4.63938462e-02 -4.78120303e-01]\n",
            "  [-1.26869344e-02 -8.05419542e-03  4.19281936e-01]\n",
            "  [-8.64527033e-03  2.90544918e-02 -6.77713192e-01]\n",
            "  [ 1.43826982e-02  1.26019335e-02  3.39145374e-01]\n",
            "  [-5.13651272e-02 -7.42601938e-02  5.58674055e-01]]\n",
            "\n",
            " [[ 7.11666759e-03 -6.35641709e-02  2.78633907e-01]\n",
            "  [ 6.06321195e-03 -5.92511245e-02 -2.07682207e-01]\n",
            "  [-3.14642275e-03  3.16100458e-02  2.01200504e-01]\n",
            "  [ 2.99828320e-04  3.90803663e-03 -1.00637502e-01]\n",
            "  [ 1.79579877e-03 -1.47850968e-02  3.30022489e-01]\n",
            "  [ 1.22371294e-03 -1.49644663e-02  2.61141661e-01]\n",
            "  [-2.03582922e-03  1.62699678e-02  6.91507617e-01]\n",
            "  [ 7.27058479e-03 -5.39642362e-02 -2.15033298e-02]]]\n",
            "[[[ 5.20383161e-02 -8.38933842e-02 -5.76491379e-01]\n",
            "  [ 3.57122664e-02 -8.16528318e-02  2.05040399e-01]\n",
            "  [-8.73542287e-03  4.46776198e-02  3.39565438e-02]\n",
            "  [ 5.08815931e-03  4.74623621e-02  1.77385138e-01]\n",
            "  [ 1.63365989e-02 -3.65561514e-02  3.39483913e-01]\n",
            "  [ 7.97444350e-03 -3.06132383e-02  4.93334436e-02]\n",
            "  [-8.35781464e-03 -8.86409639e-03 -7.01160679e-01]\n",
            "  [ 5.51815507e-02 -3.89257134e-02  2.89667491e-01]]\n",
            "\n",
            " [[-3.73452775e-02  2.41168759e-02  1.39695839e-01]\n",
            "  [-2.56288942e-02  3.38312501e-02  3.26790824e-02]\n",
            "  [ 6.26897286e-03 -2.60047590e-02 -6.94730941e-01]\n",
            "  [-3.65151557e-03 -3.75900437e-02 -4.18035440e-01]\n",
            "  [-1.17239539e-02  1.49048861e-02 -5.02758662e-01]\n",
            "  [-5.72285631e-03  1.64392091e-02 -7.35550658e-01]\n",
            "  [ 5.99798246e-03  1.21575573e-02  1.77319468e-01]\n",
            "  [-3.96010186e-02 -1.03340256e-02 -3.01310883e-01]]\n",
            "\n",
            " [[-6.61609513e-02 -4.40945406e-02 -1.04739019e-01]\n",
            "  [-4.54041886e-02  3.53624200e-04  1.03298629e-01]\n",
            "  [ 1.11061220e-02 -3.14960078e-02 -2.18194451e-01]\n",
            "  [-6.46903062e-03 -7.50835968e-02 -4.58819026e-01]\n",
            "  [-2.07701749e-02 -8.50245278e-04 -1.91509314e-01]\n",
            "  [-1.01386211e-02  1.58192727e-02 -7.97208522e-01]\n",
            "  [ 1.06260350e-02  3.54824141e-02 -1.47198988e-01]\n",
            "  [-7.01572257e-02 -1.10371942e-01  1.16828776e-02]]\n",
            "\n",
            " [[ 5.37648593e-02 -4.52540571e-02 -1.98071835e-01]\n",
            "  [ 3.68971390e-02 -5.59347866e-02 -4.16230056e-01]\n",
            "  [-9.02524942e-03  3.92065060e-02 -4.11475752e-01]\n",
            "  [ 5.25697582e-03  5.30872839e-02 -1.77889200e-01]\n",
            "  [ 1.68786196e-02 -2.47650058e-02  4.86818657e-01]\n",
            "  [ 8.23902204e-03 -2.52812356e-02 -2.04358979e-01]\n",
            "  [-8.63511279e-03 -1.58110556e-02  3.54883432e-01]\n",
            "  [ 5.70123811e-02  3.70759592e-03  2.71026380e-01]]\n",
            "\n",
            " [[ 5.15090990e-02 -7.47916622e-02  2.30711583e-01]\n",
            "  [ 3.53490813e-02 -7.51617232e-02  2.40171299e-01]\n",
            "  [-8.64658574e-03  4.28386152e-02  4.09939763e-01]\n",
            "  [ 5.03641396e-03  4.77862009e-02 -1.79659600e-01]\n",
            "  [ 1.61704597e-02 -3.35948847e-02  6.08932501e-01]\n",
            "  [ 7.89334535e-03 -2.90378872e-02  6.27274362e-02]\n",
            "  [-8.27281770e-03 -1.00987403e-02  9.43552770e-01]\n",
            "  [ 5.46203677e-02 -2.97830704e-02 -1.17164772e-01]]\n",
            "\n",
            " [[-5.40459750e-02 -3.32550597e-02  8.81069682e-01]\n",
            "  [-3.70900599e-02  2.18651802e-03  7.07566825e-02]\n",
            "  [ 9.07243896e-03 -2.61928327e-02  5.15783324e-01]\n",
            "  [-5.28446252e-03 -6.10643918e-02 -1.21070561e-01]\n",
            "  [-1.69668714e-02  1.73526215e-04 -9.67950915e-02]\n",
            "  [-8.28210071e-03  1.33462862e-02  4.45733290e-01]\n",
            "  [ 8.68026246e-03  2.85409879e-02  9.44110732e-01]\n",
            "  [-5.73104769e-02 -8.72291386e-02 -3.16472194e-01]]\n",
            "\n",
            " [[-5.16832078e-02 -2.66628791e-03 -9.88217941e-02]\n",
            "  [-3.54685667e-02  2.20853225e-02 -6.27269158e-01]\n",
            "  [ 8.67581255e-03 -2.99384837e-02 -1.32631557e-01]\n",
            "  [-5.05343783e-03 -5.55460637e-02 -4.72111406e-01]\n",
            "  [-1.62251184e-02  9.31238832e-03  4.16133391e-01]\n",
            "  [-7.92002608e-03  1.72275060e-02 -6.82215275e-01]\n",
            "  [ 8.30078111e-03  2.26139119e-02  3.18714651e-01]\n",
            "  [-5.48049931e-02 -5.25209252e-02  5.53485304e-01]]\n",
            "\n",
            " [[ 1.22975459e-02 -5.48539543e-02  2.89040176e-01]\n",
            "  [ 8.43942057e-03 -4.33349327e-02 -1.93621340e-01]\n",
            "  [-2.06433013e-03  1.64381554e-02  2.03846632e-01]\n",
            "  [ 1.20241924e-03  7.79118094e-03 -1.00179689e-01]\n",
            "  [ 3.86061829e-03 -1.96354868e-02  3.41340942e-01]\n",
            "  [ 1.88449766e-03 -1.26022636e-02  2.46925918e-01]\n",
            "  [-1.97509483e-03  3.53115118e-03  7.03844519e-01]\n",
            "  [ 1.30403461e-02 -4.63431261e-02 -6.01403262e-03]]]\n",
            "found stable Phi for ii= 6\n",
            "orig_llk -11.045051056787 est_llk=-12.250215291547448\n",
            "[[[ 3.58313455e-02  5.15452475e-02  4.44623058e-01]\n",
            "  [ 1.22499429e-02 -3.56048383e-02  1.64217763e-01]\n",
            "  [-4.71263909e-02  3.76247003e-02  1.58565427e-01]\n",
            "  [ 1.30222166e-02  1.01075427e-02 -2.53608312e-01]\n",
            "  [ 3.47048886e-02  2.46402681e-02  6.03584004e-01]\n",
            "  [-2.54764102e-02 -1.60725274e-02 -2.83500713e-02]\n",
            "  [ 8.53861692e-02 -1.42055611e-01  3.26050599e-01]\n",
            "  [ 5.77113260e-02  1.52194108e-01 -8.48166250e-01]]\n",
            "\n",
            " [[-3.80011773e-02  9.31946353e-04 -2.21939803e-01]\n",
            "  [-1.29917603e-02  5.67688858e-02 -1.44274961e-02]\n",
            "  [ 4.99802145e-02 -1.13027983e-01  1.27445151e-01]\n",
            "  [-1.38108004e-02  9.48662698e-03 -1.30897259e+00]\n",
            "  [-3.68065058e-02  2.77183101e-02  4.32212916e-01]\n",
            "  [ 2.70191802e-02 -2.24852850e-02 -2.11616816e-01]\n",
            "  [-9.05568828e-02  2.83149644e-01  6.97016209e-01]\n",
            "  [-6.12061395e-02 -7.18612653e-02 -5.66877918e-01]]\n",
            "\n",
            " [[-3.10768487e-02  1.63515980e-02 -6.99319242e-01]\n",
            "  [-1.06244858e-02  5.17545192e-02 -3.02427288e-01]\n",
            "  [ 4.08731432e-02 -1.12936457e-01 -8.10825128e-02]\n",
            "  [-1.12942857e-02  1.34237278e-02 -8.49460288e-01]\n",
            "  [-3.00998624e-02  3.77670262e-02  1.19631998e-01]\n",
            "  [ 2.20959200e-02 -2.94724121e-02  6.01246453e-02]\n",
            "  [-7.40561935e-02  2.68705675e-01  2.57009899e-01]\n",
            "  [-5.00535527e-02 -3.36581862e-02  2.71308580e-02]]\n",
            "\n",
            " [[ 4.49424733e-02  1.17406593e-01 -2.12697185e-01]\n",
            "  [ 1.53648355e-02 -2.66227705e-02 -4.04946797e-01]\n",
            "  [-5.91096017e-02 -2.21923800e-02  4.69656925e-01]\n",
            "  [ 1.63334815e-02  3.18502886e-02 -9.52636643e-01]\n",
            "  [ 4.35295830e-02  8.20017819e-02 -2.35626726e-01]\n",
            "  [-3.19545043e-02 -5.76683566e-02  2.27794670e-02]\n",
            "  [ 1.07098005e-01 -5.24631298e-02  3.60241570e-01]\n",
            "  [ 7.23860544e-02  2.75862169e-01 -8.71241504e-02]]\n",
            "\n",
            " [[ 3.47450851e-02  7.23503216e-02  7.83545754e-01]\n",
            "  [ 1.18785745e-02 -2.68784182e-02  2.96400633e-01]\n",
            "  [-4.56977106e-02  7.06542493e-03  2.60882792e-01]\n",
            "  [ 1.26274360e-02  1.79302414e-02 -1.88290909e-01]\n",
            "  [ 3.36527778e-02  4.55578009e-02  3.05448791e-01]\n",
            "  [-2.47040692e-02 -3.14889219e-02 -1.96946038e-01]\n",
            "  [ 8.27976083e-02 -8.44467511e-02  5.30862275e-02]\n",
            "  [ 5.59617536e-02  1.83606496e-01 -4.88538144e-01]]\n",
            "\n",
            " [[ 5.23399411e-02  5.42874811e-02  1.01578333e+00]\n",
            "  [ 1.78938658e-02 -5.91906418e-02  4.46922549e-01]\n",
            "  [-6.88389589e-02  8.25875410e-02  2.62614293e-01]\n",
            "  [ 1.90219496e-02  7.13008187e-03  1.80422891e-01]\n",
            "  [ 5.06944911e-02  1.56469445e-02 -3.06311413e-01]\n",
            "  [-3.72141707e-02 -8.54200781e-03 -2.18702661e-01]\n",
            "  [ 1.24726186e-01 -2.57562876e-01 -3.99136068e-01]\n",
            "  [ 8.43006971e-02  1.88481141e-01 -1.32709664e-01]]\n",
            "\n",
            " [[-4.03861536e-02 -1.36547763e-01 -1.06919333e+00]\n",
            "  [-1.38071308e-02  1.33104728e-02 -1.03330605e-01]\n",
            "  [ 5.31170022e-02  6.07724117e-02 -7.29384737e-01]\n",
            "  [-1.46775744e-02 -3.99036119e-02 -2.54504877e-01]\n",
            "  [-3.91165038e-02 -1.03756379e-01  2.28967633e-01]\n",
            "  [ 2.87149198e-02  7.38944262e-02  3.28921560e-01]\n",
            "  [-9.62402860e-02 -2.68335234e-02  3.26248113e-01]\n",
            "  [-6.50474729e-02 -2.97895567e-01 -3.11279445e-01]]\n",
            "\n",
            " [[-2.17491056e-02 -5.98550172e-02  1.53737343e-02]\n",
            "  [-7.43553716e-03  1.18449207e-02  2.94695723e-01]\n",
            "  [ 2.86050338e-02  1.47355284e-02 -4.00796088e-01]\n",
            "  [-7.90429606e-03 -1.65175521e-02  4.19521358e-02]\n",
            "  [-2.10653626e-02 -4.26259786e-02  8.51650231e-01]\n",
            "  [ 1.54638104e-02  3.00677553e-02  7.09454450e-02]\n",
            "  [-5.18281628e-02  1.81485606e-02  1.92347198e-01]\n",
            "  [-3.50299355e-02 -1.38391997e-01 -8.03831246e-01]]]\n",
            "[[[ 0.04646834 -0.13166195  0.44298804]\n",
            "  [ 0.01669601 -0.10285476  0.16008775]\n",
            "  [-0.04342906  0.21450484  0.17345885]\n",
            "  [ 0.02041375 -0.07395193 -0.26420135]\n",
            "  [ 0.04571603 -0.15241429  0.62940723]\n",
            "  [-0.02910724  0.09192732 -0.02524761]\n",
            "  [ 0.07978731 -0.4493581   0.34612307]\n",
            "  [ 0.05531094 -0.08491284 -0.85173491]]\n",
            "\n",
            " [[-0.05336292  0.13778788 -0.24647624]\n",
            "  [-0.01917322  0.11329767 -0.03833614]\n",
            "  [ 0.0498727  -0.23379932  0.13697434]\n",
            "  [-0.02344257  0.07903369 -1.31020946]\n",
            "  [-0.05249899  0.16183637  0.48350508]\n",
            "  [ 0.03342592 -0.09716751 -0.21739643]\n",
            "  [-0.09162549  0.49300656  0.72351703]\n",
            "  [-0.06351752  0.0815509  -0.58912129]]\n",
            "\n",
            " [[-0.042078    0.20558066 -0.68979129]\n",
            "  [-0.01511857  0.12416538 -0.30681823]\n",
            "  [ 0.03932587 -0.27494825 -0.09295704]\n",
            "  [-0.01848505  0.10490247 -0.82398121]\n",
            "  [-0.04139677  0.22297421  0.07651418]\n",
            "  [ 0.02635718 -0.13733577  0.03687852]\n",
            "  [-0.07224899  0.55518179  0.2262829 ]\n",
            "  [-0.05008515  0.17968179  0.04096673]]\n",
            "\n",
            " [[ 0.05597328  0.43329465 -0.21956783]\n",
            "  [ 0.02011112  0.08877103 -0.43395663]\n",
            "  [-0.05231233 -0.29479391  0.47692638]\n",
            "  [ 0.02458931  0.17094033 -0.97175948]\n",
            "  [ 0.0550671   0.39871503 -0.25542338]\n",
            "  [-0.03506103 -0.26002089  0.0200823 ]\n",
            "  [ 0.09610754  0.47501321  0.35738199]\n",
            "  [ 0.06662461  0.60223828 -0.11277089]]\n",
            "\n",
            " [[ 0.0451933  -0.0239517   0.75636271]\n",
            "  [ 0.01623789 -0.06263042  0.28659771]\n",
            "  [-0.04223742  0.11133001  0.27456875]\n",
            "  [ 0.01985362 -0.02619223 -0.17414668]\n",
            "  [ 0.04446164 -0.04581992  0.32529442]\n",
            "  [-0.02830857  0.02419939 -0.19269551]\n",
            "  [ 0.07759804 -0.25829001  0.0599852 ]\n",
            "  [ 0.05379327  0.04132372 -0.47880898]]\n",
            "\n",
            " [[ 0.06633196  0.02839983  0.96154596]\n",
            "  [ 0.02383298 -0.06909     0.4383882 ]\n",
            "  [-0.0619935   0.10400553  0.26264887]\n",
            "  [ 0.02913993 -0.01052351  0.1727503 ]\n",
            "  [ 0.06525807 -0.00472594 -0.25345517]\n",
            "  [-0.04154959 -0.00429153 -0.2180295 ]\n",
            "  [ 0.11389366 -0.26997732 -0.37270365]\n",
            "  [ 0.07895448  0.13630113 -0.13041358]]\n",
            "\n",
            " [[-0.04647569 -0.1864943  -1.03599302]\n",
            "  [-0.01669865 -0.01144955 -0.08586441]\n",
            "  [ 0.04343593  0.08282782 -0.77212937]\n",
            "  [-0.02041698 -0.06581299 -0.24748364]\n",
            "  [-0.04572327 -0.1605875   0.2207099 ]\n",
            "  [ 0.02911184  0.10736062  0.31626864]\n",
            "  [-0.07979994 -0.09688891  0.31047034]\n",
            "  [-0.05531969 -0.29379771 -0.29875717]]\n",
            "\n",
            " [[-0.0249511  -0.3983233   0.02895217]\n",
            "  [-0.00896489 -0.11329017  0.31457496]\n",
            "  [ 0.02331916  0.32316461 -0.40674375]\n",
            "  [-0.01096113 -0.16633377  0.05452913]\n",
            "  [-0.02454715 -0.37958712  0.8585537 ]\n",
            "  [ 0.01562908  0.2444279   0.06362927]\n",
            "  [-0.04284167 -0.56403536  0.19773104]\n",
            "  [-0.02969912 -0.51267625 -0.78313876]]]\n",
            "found stable Phi for ii= 7\n",
            "orig_llk -6.679380205553242 est_llk=-7.898204084160028\n",
            "[[[ 3.68831508e-02  7.89118398e-02  4.02169069e-01]\n",
            "  [ 5.32778339e-03  1.13624665e-01 -5.11214140e-01]\n",
            "  [-1.50089470e-02  5.87759647e-02 -5.10069466e-01]\n",
            "  [ 4.24753103e-02 -2.87134268e-02 -3.54606254e-01]\n",
            "  [ 5.93935572e-03 -4.18015391e-02  1.45422150e-01]\n",
            "  [ 2.20458772e-03 -8.34966055e-02  1.12738186e+00]\n",
            "  [-3.38842877e-04  3.49891292e-02 -5.11503680e-01]\n",
            "  [ 4.92302919e-02 -9.46163299e-02 -2.78245329e-01]]\n",
            "\n",
            " [[ 5.15433344e-02  1.91869872e-01 -3.19772410e-01]\n",
            "  [ 7.44545178e-03  1.70573848e-01  4.53899304e-01]\n",
            "  [-2.09746499e-02  4.89354252e-02  7.93019025e-01]\n",
            "  [ 5.93582456e-02  5.38370015e-02  2.68449883e-02]\n",
            "  [ 8.30010971e-03 -4.52776993e-02 -7.14691243e-01]\n",
            "  [ 3.08085941e-03 -1.11807579e-01 -1.34905148e+00]\n",
            "  [-4.73524939e-04  4.81468999e-02  6.03178898e-01]\n",
            "  [ 6.87981732e-02 -2.33174692e-02  6.91195098e-01]]\n",
            "\n",
            " [[ 4.03335388e-02  8.63101741e-02 -2.39183897e-01]\n",
            "  [ 5.82619308e-03  1.24256498e-01  1.22249869e-01]\n",
            "  [-1.64130215e-02  6.42678160e-02  5.02221138e-01]\n",
            "  [ 4.64488402e-02 -3.13808907e-02 -4.34028091e-01]\n",
            "  [ 6.49497750e-03 -4.57094299e-02 -2.34683746e-01]\n",
            "  [ 2.41082507e-03 -9.13066753e-02 -1.04497494e+00]\n",
            "  [-3.70541346e-04  3.82621843e-02  5.92820334e-02]\n",
            "  [ 5.38357447e-02 -1.03445989e-01  8.04701650e-01]]\n",
            "\n",
            " [[ 2.53419002e-02  6.87374878e-02 -4.97633960e-01]\n",
            "  [ 3.66064591e-03  8.01670956e-02  4.26453180e-01]\n",
            "  [-1.03124389e-02  3.44761990e-02 -1.13286400e-01]\n",
            "  [ 2.91841953e-02 -3.00910357e-03  4.98080488e-01]\n",
            "  [ 4.08084876e-03 -2.63833568e-02 -2.72763758e-01]\n",
            "  [ 1.51474158e-03 -5.65015685e-02 -5.73502221e-01]\n",
            "  [-2.32814231e-04  2.39071661e-02  4.76048106e-01]\n",
            "  [ 3.38254492e-02 -4.56311190e-02 -1.23122210e-01]]\n",
            "\n",
            " [[-2.92855125e-02 -7.29152716e-02 -3.36749542e-01]\n",
            "  [-4.23030201e-03 -9.17007452e-02  6.60434887e-01]\n",
            "  [ 1.19172223e-02 -4.24940033e-02 -6.45531498e-02]\n",
            "  [-3.37257312e-02  1.09846399e-02 -9.49046339e-02]\n",
            "  [-4.71589526e-03  3.15387841e-02  3.49244771e-01]\n",
            "  [-1.75046003e-03  6.56837808e-02 -1.05711084e+00]\n",
            "  [ 2.69043915e-04 -2.76873989e-02  5.94542552e-01]\n",
            "  [-3.90892398e-02  6.14332395e-02  2.38228939e-01]]\n",
            "\n",
            " [[ 1.11270238e-02  1.45411309e-02 -5.75295475e-01]\n",
            "  [ 1.60730228e-03  3.29402760e-02  7.15476490e-01]\n",
            "  [-4.52794587e-03  2.15020413e-02 -2.31363590e-01]\n",
            "  [ 1.28140839e-02 -1.93323741e-02  2.76604821e-01]\n",
            "  [ 1.79180332e-03 -1.41028154e-02  7.27049827e-02]\n",
            "  [ 6.65086888e-04 -2.57433198e-02 -1.13053476e+00]\n",
            "  [-1.02223174e-04  1.06407485e-02  6.67138945e-01]\n",
            "  [ 1.48519477e-02 -4.09110535e-02  2.07990144e-01]]\n",
            "\n",
            " [[ 6.68526339e-03 -4.72280453e-03  2.57953329e-01]\n",
            "  [ 9.65688518e-04  1.78467529e-02 -5.09690498e-01]\n",
            "  [-2.72044991e-03  1.83957395e-02  8.45713879e-02]\n",
            "  [ 7.69887146e-03 -2.71151325e-02 -1.80919984e-01]\n",
            "  [ 1.07653919e-03 -1.06405335e-02 -7.03921751e-02]\n",
            "  [ 3.99593020e-04 -1.62714205e-02  7.16328833e-01]\n",
            "  [-6.14170382e-05  6.51675248e-03 -3.07144598e-01]\n",
            "  [ 8.92324708e-03 -4.25449004e-02  4.60984859e-02]]\n",
            "\n",
            " [[ 2.18806027e-02  6.55523707e-02 -3.62723405e-01]\n",
            "  [ 3.16066033e-03  7.01136267e-02  1.70441780e-02]\n",
            "  [-8.90392496e-03  2.72429701e-02  8.92054164e-01]\n",
            "  [ 2.51981018e-02  4.54575126e-03  1.95191909e-01]\n",
            "  [ 3.52347020e-03 -2.17808815e-02 -7.50595715e-01]\n",
            "  [ 1.30785215e-03 -4.84135732e-02 -6.47508579e-01]\n",
            "  [-2.01015537e-04  2.05848408e-02  5.97419937e-01]\n",
            "  [ 2.92054348e-02 -3.11186694e-02  5.46243135e-01]]]\n",
            "[[[ 0.02953507  0.09792541  0.41376818]\n",
            "  [ 0.02043979  0.19571792 -0.52357541]\n",
            "  [-0.035415   -0.08835501 -0.56047062]\n",
            "  [ 0.04642947  0.14305409 -0.31102423]\n",
            "  [ 0.01625415 -0.00539668  0.15034598]\n",
            "  [ 0.02085132 -0.02457944  1.17438223]\n",
            "  [ 0.02237304  0.10394059 -0.53986217]\n",
            "  [ 0.01878062 -0.11886971 -0.28415034]]\n",
            "\n",
            " [[ 0.03957065  0.15243495 -0.33242779]\n",
            "  [ 0.02738493  0.27691635  0.48599554]\n",
            "  [-0.04744849 -0.14384038  0.79148139]\n",
            "  [ 0.06220552  0.22504488 -0.01035703]\n",
            "  [ 0.02177707  0.00445645 -0.70699991]\n",
            "  [ 0.02793629 -0.01793892 -1.32552516]\n",
            "  [ 0.02997508  0.15534445  0.63899484]\n",
            "  [ 0.025162   -0.14575648  0.6904775 ]]\n",
            "\n",
            " [[ 0.03696385  0.08003811 -0.27509558]\n",
            "  [ 0.02558089  0.21552113  0.07456631]\n",
            "  [-0.04432273 -0.05959594  0.50475281]\n",
            "  [ 0.0581076   0.11219702 -0.43547396]\n",
            "  [ 0.02034246 -0.03015312 -0.20316611]\n",
            "  [ 0.02609593 -0.06077876 -1.05100821]\n",
            "  [ 0.02800041  0.09787652  0.06099906]\n",
            "  [ 0.0235044  -0.17580439  0.82173954]]\n",
            "\n",
            " [[ 0.01608147  0.05452726 -0.50181374]\n",
            "  [ 0.01112921  0.10740201  0.42982697]\n",
            "  [-0.01928302 -0.04955681 -0.10735239]\n",
            "  [ 0.02528026  0.0797903   0.48989117]\n",
            "  [ 0.00885018 -0.00227356 -0.29694952]\n",
            "  [ 0.01135328 -0.01253029 -0.55780293]\n",
            "  [ 0.01218184  0.05750949  0.4813685 ]\n",
            "  [ 0.01022581 -0.06395485 -0.11201309]]\n",
            "\n",
            " [[-0.02650067 -0.08407965 -0.33294052]\n",
            "  [-0.01833983 -0.17299066  0.69032583]\n",
            "  [ 0.0317765   0.07473897 -0.07550374]\n",
            "  [-0.04165936 -0.12240678 -0.10801096]\n",
            "  [-0.01458421  0.00692526  0.3110572 ]\n",
            "  [-0.01870908  0.02472634 -1.02693341]\n",
            "  [-0.02007446 -0.09039467  0.6003075 ]\n",
            "  [-0.01685112  0.10906397  0.20274339]]\n",
            "\n",
            " [[ 0.0070756   0.01360848 -0.55144064]\n",
            "  [ 0.00489668  0.0400699   0.76535154]\n",
            "  [-0.00848423 -0.00935454 -0.24175968]\n",
            "  [ 0.01112293  0.01878482  0.28514506]\n",
            "  [ 0.00389394 -0.00671427  0.04633835]\n",
            "  [ 0.00499527 -0.01284315 -1.11848668]\n",
            "  [ 0.00535982  0.01743834  0.68304352]\n",
            "  [ 0.0044992  -0.03474125  0.18999087]]\n",
            "\n",
            " [[ 0.00425551 -0.00280778  0.24495475]\n",
            "  [ 0.00294503  0.0164921  -0.51379587]\n",
            "  [-0.00510271  0.00755463  0.06348687]\n",
            "  [ 0.00668971 -0.00598232 -0.15037075]\n",
            "  [ 0.00234195 -0.01008767 -0.06892574]\n",
            "  [ 0.00300432 -0.01548476  0.73292134]\n",
            "  [ 0.00322358  0.00216119 -0.30430027]\n",
            "  [ 0.00270597 -0.02788434  0.02444293]]\n",
            "\n",
            " [[ 0.01419264  0.03599289 -0.34544426]\n",
            "  [ 0.00982204  0.08639269  0.05650859]\n",
            "  [-0.01701815 -0.02919138  0.85635794]\n",
            "  [ 0.02231099  0.05135024  0.21652909]\n",
            "  [ 0.00781069 -0.00868203 -0.777345  ]\n",
            "  [ 0.01001979 -0.0196221  -0.62099706]\n",
            "  [ 0.01075104  0.04156626  0.58782016]\n",
            "  [ 0.00902475 -0.06415622  0.54866072]]]\n",
            "found stable Phi for ii= 8\n",
            "orig_llk -10.012286185538574 est_llk=-10.811004844419074\n",
            "[[[-0.00317138  0.039561   -0.97827813]\n",
            "  [-0.00354476  0.00551651 -0.07745482]\n",
            "  [-0.00932058  0.06572711 -0.16476954]\n",
            "  [-0.00586762  0.03834135  0.11270484]\n",
            "  [-0.00381055  0.01596507 -0.53019014]\n",
            "  [-0.00570403  0.03517945  0.73042245]\n",
            "  [ 0.00399028 -0.03071976  0.14041673]\n",
            "  [-0.00830599  0.065798    0.14009594]]\n",
            "\n",
            " [[ 0.02290972 -0.09478634 -0.16024638]\n",
            "  [ 0.02560695  0.17363427  0.29558864]\n",
            "  [ 0.06733089  0.08653142 -0.58576511]\n",
            "  [ 0.04238705  0.07640663  0.30815549]\n",
            "  [ 0.027527    0.11416233 -0.24707388]\n",
            "  [ 0.04120535  0.08939601 -0.03509919]\n",
            "  [-0.02882536 -0.01840046 -0.48153282]\n",
            "  [ 0.06000159  0.02491497  0.31202162]]\n",
            "\n",
            " [[-0.01385662  0.10207034 -0.7266372 ]\n",
            "  [-0.015488   -0.05501263 -0.09195798]\n",
            "  [-0.04072413  0.07915258  0.07191684]\n",
            "  [-0.0256372   0.03656381 -0.26863028]\n",
            "  [-0.01664931 -0.01529224  0.05917413]\n",
            "  [-0.02492247  0.02639964  0.6712396 ]\n",
            "  [ 0.01743461 -0.04516352  0.26437261]\n",
            "  [-0.03629111  0.10210709  0.18888053]]\n",
            "\n",
            " [[ 0.00516088 -0.03460136  0.83886093]\n",
            "  [ 0.00576849  0.02430603  0.02683377]\n",
            "  [ 0.01516766 -0.01944481 -0.27183868]\n",
            "  [ 0.00954855 -0.00730048 -0.5218921 ]\n",
            "  [ 0.00620102  0.0097984   0.70009565]\n",
            "  [ 0.00928234 -0.00369098 -0.56872174]\n",
            "  [-0.0064935   0.01252477 -0.23162331]\n",
            "  [ 0.01351658 -0.02908661 -0.05699441]]\n",
            "\n",
            " [[-0.00365026  0.05133576  0.48710663]\n",
            "  [-0.00408002  0.01283349  0.01473779]\n",
            "  [-0.010728    0.09270093 -0.2801552 ]\n",
            "  [-0.00675363  0.05486383 -1.06739547]\n",
            "  [-0.00438594  0.02534597  1.3212339 ]\n",
            "  [-0.00656535  0.05092526 -0.24373003]\n",
            "  [ 0.00459282 -0.04265739 -0.06042691]\n",
            "  [-0.0095602   0.09092667  0.29654758]]\n",
            "\n",
            " [[ 0.00386947 -0.00616447  0.6176198 ]\n",
            "  [ 0.00432503  0.04033105  0.70532182]\n",
            "  [ 0.01137224  0.04354938 -0.5071987 ]\n",
            "  [ 0.0071592   0.03112016  0.50186649]\n",
            "  [ 0.00464933  0.0311113  -0.0138038 ]\n",
            "  [ 0.00695961  0.03280626 -1.21862092]\n",
            "  [-0.00486862 -0.01549499 -0.70096356]\n",
            "  [ 0.01013431  0.02999269  0.43593738]]\n",
            "\n",
            " [[ 0.0024673  -0.03839636 -0.35437994]\n",
            "  [ 0.00275778 -0.01280706 -0.23998   ]\n",
            "  [ 0.00725131 -0.07352502 -0.07100988]\n",
            "  [ 0.00456494 -0.04392444  0.08191717]\n",
            "  [ 0.00296456 -0.02157441 -0.69831334]\n",
            "  [ 0.00443768 -0.04107155  1.44566338]\n",
            "  [-0.00310439  0.03348515 -0.27668244]\n",
            "  [ 0.00646197 -0.07114291 -0.26243486]]\n",
            "\n",
            " [[-0.02412465  0.10539597 -0.21195366]\n",
            "  [-0.02696493 -0.17660205  0.11913615]\n",
            "  [-0.07090154 -0.0747121  -0.21053443]\n",
            "  [-0.04463489 -0.07012907  0.27180303]\n",
            "  [-0.02898679 -0.11350833 -0.7902721 ]\n",
            "  [-0.04339052 -0.08409526  0.35369761]\n",
            "  [ 0.03035401  0.01235166 -0.30216209]\n",
            "  [-0.06318356 -0.01161416 -0.04895072]]]\n",
            "[[[ 9.51087004e-06 -1.31036344e-03 -1.01518732e+00]\n",
            "  [ 9.14530376e-05 -1.37580359e-02 -5.30842232e-02]\n",
            "  [-2.49365989e-04  3.59069106e-02 -1.61966509e-01]\n",
            "  [-1.38352603e-05  2.08834349e-03  8.61350551e-02]\n",
            "  [-6.66505797e-05  8.94257153e-03 -5.16494492e-01]\n",
            "  [-2.68587915e-04  3.76394382e-02  7.33663679e-01]\n",
            "  [-8.47125781e-05  1.22514960e-02  1.36686779e-01]\n",
            "  [ 6.18858515e-06  2.29493121e-04  1.38336548e-01]]\n",
            "\n",
            " [[-1.03668522e-03 -9.54707043e-03 -1.45294459e-01]\n",
            "  [-9.96838482e-03  3.44276423e-02  3.66936073e-01]\n",
            "  [ 2.71809030e-02  8.13188116e-02 -4.77686119e-01]\n",
            "  [ 1.50804393e-03 -5.97032573e-03  2.40510068e-01]\n",
            "  [ 7.26491590e-03  9.30899305e-02 -2.21986374e-01]\n",
            "  [ 2.92760937e-02  2.00433963e-01  3.10775991e-02]\n",
            "  [ 9.23367446e-03  2.17941774e-02 -5.53698858e-01]\n",
            "  [-6.74556034e-04 -1.24164093e-01  2.76846125e-01]]\n",
            "\n",
            " [[ 3.41358109e-04  2.08996932e-04 -7.57564790e-01]\n",
            "  [ 3.28237436e-03 -3.95547765e-02 -1.57821105e-01]\n",
            "  [-8.95008577e-03  5.01671453e-02  1.89284610e-02]\n",
            "  [-4.96566378e-04  6.23486917e-03 -2.68857843e-01]\n",
            "  [-2.39218029e-03 -1.00869906e-02  6.29570096e-02]\n",
            "  [-9.63998694e-03  1.68761565e-02  6.87052367e-01]\n",
            "  [-3.04045007e-03  1.89623251e-02  3.04698084e-01]\n",
            "  [ 2.22116769e-04  3.89750281e-02  2.22496442e-01]]\n",
            "\n",
            " [[ 2.72575925e-04 -4.49897496e-04  8.56258477e-01]\n",
            "  [ 2.62099011e-03 -3.75154138e-02  9.07680689e-02]\n",
            "  [-7.14668217e-03  5.62301330e-02 -2.87711542e-01]\n",
            "  [-3.96510399e-04  5.87579029e-03 -5.10385807e-01]\n",
            "  [-1.91016630e-03 -3.73219775e-03  7.49278005e-01]\n",
            "  [-7.69757123e-03  3.08936816e-02 -5.51366995e-01]\n",
            "  [-2.42781252e-03  2.06351317e-02 -2.09657983e-01]\n",
            "  [ 1.77361200e-04  3.07203970e-02 -6.20579857e-02]]\n",
            "\n",
            " [[ 4.64144848e-04 -2.42666190e-03  5.47278618e-01]\n",
            "  [ 4.46304660e-03 -7.98490526e-02  3.16319108e-02]\n",
            "  [-1.21694376e-02  1.39287827e-01 -3.13462025e-01]\n",
            "  [-6.75181634e-04  1.24209500e-02 -1.01518890e+00]\n",
            "  [-3.25264913e-03  5.28178979e-03  1.35690806e+00]\n",
            "  [-1.31074966e-02  9.95007759e-02 -1.85089632e-01]\n",
            "  [-4.13410198e-03  4.99282836e-02 -2.87847727e-02]\n",
            "  [ 3.02012319e-04  5.12304705e-02  2.89897294e-01]]\n",
            "\n",
            " [[-9.08178853e-04 -4.93613793e-03  6.69459272e-01]\n",
            "  [-8.73271473e-03  6.31174975e-02  5.82303465e-01]\n",
            "  [ 2.38115879e-02 -1.86268652e-02 -4.96962180e-01]\n",
            "  [ 1.32110845e-03 -1.02161447e-02  4.72026512e-01]\n",
            "  [ 6.36436486e-03  5.75313436e-02 -4.37086402e-02]\n",
            "  [ 2.56470611e-02  7.87957834e-02 -1.19537326e+00]\n",
            "  [ 8.08907826e-03 -1.14357743e-02 -7.46277888e-01]\n",
            "  [-5.90938804e-04 -1.06542631e-01  4.37699575e-01]]\n",
            "\n",
            " [[ 9.50293459e-04  1.87869856e-03 -3.10547827e-01]\n",
            "  [ 9.13767332e-03 -9.76446676e-02 -1.63348186e-01]\n",
            "  [-2.49157929e-02  1.05655381e-01 -1.23176273e-01]\n",
            "  [-1.38237167e-03  1.54704639e-02  1.14085300e-01]\n",
            "  [-6.65949694e-03 -3.71690962e-02 -6.02780639e-01]\n",
            "  [-2.68363818e-02  1.03568447e-02  1.47744155e+00]\n",
            "  [-8.46418977e-03  4.12372626e-02 -2.20103291e-01]\n",
            "  [ 6.18342167e-04  1.09344914e-01 -2.49936341e-01]]\n",
            "\n",
            " [[ 1.12616855e-03  7.60589654e-03 -2.05518251e-01]\n",
            "  [ 1.08288237e-02 -6.39889196e-02  8.42248488e-03]\n",
            "  [-2.95270711e-02 -1.58358554e-02 -3.28817991e-01]\n",
            "  [-1.63821343e-03  1.05082100e-02  3.71164632e-01]\n",
            "  [-7.89200006e-03 -8.17467721e-02 -8.02522188e-01]\n",
            "  [-3.18031119e-02 -1.39643947e-01  3.21769874e-01]\n",
            "  [-1.00306955e-02  9.54452567e-04 -2.15046318e-01]\n",
            "  [ 7.32781539e-04  1.33082232e-01  2.87267961e-02]]]\n",
            "Matrix is not positive definite\n",
            "found stable Phi for ii= 9\n",
            "failed for ii=9\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6MRP7qSHGpI9",
        "colab_type": "text"
      },
      "source": [
        "## fitted llk is usually better than original llk in this case\n",
        "This is probably because there is some unintended autoregression in the randomly generated data. However, the fitted likelihood for the minimal state-space model is almost the same as the full regression likelihood."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5WJhIznbpWjb",
        "colab_type": "code",
        "outputId": "26db66a9-2a3a-4b2f-d0bd-4970d4bc8663",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        }
      },
      "source": [
        "print(fitted_k8p3)\n",
        "print(fitted_k8p3.to_latex())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "     org_llk  fitted_llk   full_llk  success\n",
            "0  -6.778974   -7.333462  -7.397742      1.0\n",
            "1  -7.664920   -8.280117  -8.329034      1.0\n",
            "2  -7.909143   -9.150681  -9.203443      1.0\n",
            "3 -14.679623  -15.425846 -15.491684      1.0\n",
            "4  -9.291283  -10.052678 -10.098918      1.0\n",
            "5 -12.626511  -13.004966 -13.049997      1.0\n",
            "6 -11.045051  -12.250215 -12.296307      1.0\n",
            "7  -6.679380   -7.898204  -7.974920      1.0\n",
            "8 -10.012286  -10.811005 -11.115286      1.0\n",
            "9 -64.521764  -65.580908 -65.678105      0.0\n",
            "\\begin{tabular}{lrrrr}\n",
            "\\toprule\n",
            "{} &    org\\_llk &  fitted\\_llk &   full\\_llk &  success \\\\\n",
            "\\midrule\n",
            "0 &  -6.778974 &   -7.333462 &  -7.397742 &      1.0 \\\\\n",
            "1 &  -7.664920 &   -8.280117 &  -8.329034 &      1.0 \\\\\n",
            "2 &  -7.909143 &   -9.150681 &  -9.203443 &      1.0 \\\\\n",
            "3 & -14.679623 &  -15.425846 & -15.491684 &      1.0 \\\\\n",
            "4 &  -9.291283 &  -10.052678 & -10.098918 &      1.0 \\\\\n",
            "5 & -12.626511 &  -13.004966 & -13.049997 &      1.0 \\\\\n",
            "6 & -11.045051 &  -12.250215 & -12.296307 &      1.0 \\\\\n",
            "7 &  -6.679380 &   -7.898204 &  -7.974920 &      1.0 \\\\\n",
            "8 & -10.012286 &  -10.811005 & -11.115286 &      1.0 \\\\\n",
            "9 & -64.521764 &  -65.580908 & -65.678105 &      0.0 \\\\\n",
            "\\bottomrule\n",
            "\\end{tabular}\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FWwx_qEBScbP",
        "colab_type": "text"
      },
      "source": [
        "## Using pymanopt\n",
        "We also use manifold optimization to fit. As there is yet a package for the type of manifold we deal with here - vector bundle on flag manifolds, we work on flag manifolds only, which is the case when $\\mathfrak{l} = h$. We will not take advantage of the invariant property to reduce dimension further than $O(m)$. We install the package from the github page\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "42wCQa2hSZvC",
        "colab_type": "code",
        "outputId": "e67f815d-5e6d-4cb9-bb99-079aa0d3c24b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        }
      },
      "source": [
        "pip install git+https://github.com/pymanopt/pymanopt.git"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting git+https://github.com/pymanopt/pymanopt.git\n",
            "  Cloning https://github.com/pymanopt/pymanopt.git to /tmp/pip-req-build-yx13fli8\n",
            "  Running command git clone -q https://github.com/pymanopt/pymanopt.git /tmp/pip-req-build-yx13fli8\n",
            "Requirement already satisfied: numpy>=1.10 in /usr/local/lib/python3.6/dist-packages (from pymanopt==0.2.4) (1.16.5)\n",
            "Requirement already satisfied: scipy>=0.17 in /usr/local/lib/python3.6/dist-packages (from pymanopt==0.2.4) (1.3.1)\n",
            "Building wheels for collected packages: pymanopt\n",
            "  Building wheel for pymanopt (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pymanopt: filename=pymanopt-0.2.4-cp36-none-any.whl size=59256 sha256=210a778c1c50b946e783aa8c3d058fe5a7de60206b3b6ceab69c0a5f3b0dd6fc\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-qznju2v8/wheels/3a/04/c1/2fa89da3831851276030dfcd8fccb26cd9524593f891dbe62b\n",
            "Successfully built pymanopt\n",
            "Installing collected packages: pymanopt\n",
            "Successfully installed pymanopt-0.2.4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BWdiCoOAbs5X",
        "colab_type": "code",
        "outputId": "78c0baaf-1569-4bcb-fd1d-6f0b55602043",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "def test_manifold_fit():\n",
        "    ### We only implemt this for the case where sum(d_i) = h\n",
        "    ###\n",
        "    from numpy.linalg import solve\n",
        "    Psi = [(2, 3), (1, 1)]\n",
        "    k_zero = 0\n",
        "    k = sum([a[1] for a in Psi]) + k_zero\n",
        "    p = Psi[0][0]\n",
        "    T = 1000\n",
        "    n = T + p\n",
        "\n",
        "    for ii in range(1):\n",
        "        D = np.arange(k) * 0.2 + 1\n",
        "        OO = random_orthogonal(k)\n",
        "        success = False\n",
        "        while not success:\n",
        "          try:\n",
        "              es = varx_minimal_estimator(Psi, m=k)\n",
        "              stable, H, F, G, Phi = gen_random_stable(es, k)\n",
        "              Y, e = VAR_sim(Phi, n, D, OO)\n",
        "              Y = Y.T\n",
        "              e = e.T\n",
        "              X = Y.copy()\n",
        "              cov_res, cov_xlag, cov_y_xlag = calc_extended_covariance(Y, X, p)\n",
        "              es_G = varx_minimal_estimator(Psi, m=k)\n",
        "              es_G.set_covs(cov_res, cov_xlag)\n",
        "              es_G.calc_states(G)\n",
        "              if ~np.isnan(es_G.neg_log_llk):\n",
        "                success = True\n",
        "          except Exception as ex:\n",
        "            print(ex)\n",
        "            print(\"try again - problem finding random stable matrix\")\n",
        "            continue\n",
        "\n",
        "        es1 = varx_minimal_estimator(Psi, m=k)\n",
        "        es1.set_covs(cov_res, cov_xlag)\n",
        "\n",
        "        es2 = varx_minimal_estimator(Psi, m=k)\n",
        "        es2.set_covs(cov_res, cov_xlag)\n",
        "        # h_opt = es2.hessian_fit(Y, X)\n",
        "        # print(h_opt)\n",
        "        g_opt = es2.gradient_fit(Y, X)\n",
        "        # print(g_opt)\n",
        "        # print(1)\n",
        "        # self = es1\n",
        "        opt = es1.manifold_fit( Y, X)\n",
        "        print(opt)\n",
        "        # print(es1.Phi)\n",
        "        \n",
        "        print(\"original_llk=%f gradient_fit=%f manifold_fit=%f\" % (es_G.neg_log_llk, g_opt['fun'], es1.neg_log_llk))\n",
        "        print(\"original Phi\")\n",
        "        print(Phi.PolynomialMatrix_to_3darray())\n",
        "        print(\"gradient fitted Phi\")\n",
        "        print(es2.Phi)\n",
        "        print(\"manifold fitted Phi\")\n",
        "        print(es1.Phi)\n",
        "test_manifold_fit()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Compiling cost function...\n",
            "Optimizing...\n",
            "                                            f: -8.523332e+00   |grad|: 4.397016e-01\n",
            "REJ TR-   k:     1     num_inner:     0     f: -8.523332e+00   |grad|: 4.397016e-01   negative curvature\n",
            "acc       k:     2     num_inner:     0     f: -8.568086e+00   |grad|: 7.918425e-02   exceeded trust region\n",
            "acc       k:     3     num_inner:     0     f: -8.575196e+00   |grad|: 1.004817e-01   negative curvature\n",
            "REJ TR-   k:     4     num_inner:     0     f: -8.575196e+00   |grad|: 1.004817e-01   negative curvature\n",
            "acc       k:     5     num_inner:     0     f: -8.578437e+00   |grad|: 3.721036e-02   negative curvature\n",
            "acc       k:     6     num_inner:     0     f: -8.579408e+00   |grad|: 3.559442e-02   exceeded trust region\n",
            "acc TR-   k:     7     num_inner:     0     f: -8.579720e+00   |grad|: 4.263980e-02   negative curvature\n",
            "acc       k:     8     num_inner:     0     f: -8.580132e+00   |grad|: 2.516946e-02   negative curvature\n",
            "acc       k:     9     num_inner:     0     f: -8.580350e+00   |grad|: 1.364232e-02   negative curvature\n",
            "acc TR+   k:    10     num_inner:     0     f: -8.580497e+00   |grad|: 1.118137e-02   exceeded trust region\n",
            "acc       k:    11     num_inner:     0     f: -8.580704e+00   |grad|: 8.649773e-03   negative curvature\n",
            "REJ TR-   k:    12     num_inner:     0     f: -8.580704e+00   |grad|: 8.649773e-03   exceeded trust region\n",
            "acc       k:    13     num_inner:     0     f: -8.580743e+00   |grad|: 6.268255e-03   negative curvature\n",
            "acc TR+   k:    14     num_inner:     0     f: -8.580778e+00   |grad|: 5.324339e-03   negative curvature\n",
            "acc TR+   k:    15     num_inner:     0     f: -8.580829e+00   |grad|: 4.380166e-03   exceeded trust region\n",
            "REJ TR-   k:    16     num_inner:     0     f: -8.580829e+00   |grad|: 4.380166e-03   negative curvature\n",
            "acc       k:    17     num_inner:     0     f: -8.580843e+00   |grad|: 4.641305e-03   negative curvature\n",
            "acc TR-   k:    18     num_inner:     0     f: -8.580850e+00   |grad|: 5.218426e-03   negative curvature\n",
            "acc       k:    19     num_inner:     0     f: -8.580857e+00   |grad|: 3.208156e-03   negative curvature\n",
            "acc       k:    20     num_inner:     0     f: -8.580860e+00   |grad|: 2.129690e-03   negative curvature\n",
            "acc TR+   k:    21     num_inner:     0     f: -8.580863e+00   |grad|: 1.888973e-03   negative curvature\n",
            "acc TR+   k:    22     num_inner:     0     f: -8.580869e+00   |grad|: 1.485084e-03   exceeded trust region\n",
            "acc       k:    23     num_inner:     0     f: -8.580875e+00   |grad|: 1.225545e-03   negative curvature\n",
            "REJ TR-   k:    24     num_inner:     0     f: -8.580875e+00   |grad|: 1.225545e-03   negative curvature\n",
            "acc TR-   k:    25     num_inner:     0     f: -8.580875e+00   |grad|: 1.287006e-03   negative curvature\n",
            "acc       k:    26     num_inner:     0     f: -8.580876e+00   |grad|: 7.826600e-04   negative curvature\n",
            "acc       k:    27     num_inner:     0     f: -8.580876e+00   |grad|: 5.087166e-04   negative curvature\n",
            "acc TR+   k:    28     num_inner:     0     f: -8.580876e+00   |grad|: 4.509452e-04   negative curvature\n",
            "acc TR+   k:    29     num_inner:     0     f: -8.580876e+00   |grad|: 3.532572e-04   exceeded trust region\n",
            "acc       k:    30     num_inner:     0     f: -8.580877e+00   |grad|: 3.555653e-04   negative curvature\n",
            "REJ TR-   k:    31     num_inner:     0     f: -8.580877e+00   |grad|: 3.555653e-04   negative curvature\n",
            "acc TR-   k:    32     num_inner:     0     f: -8.580877e+00   |grad|: 2.966252e-04   negative curvature\n",
            "acc       k:    33     num_inner:     0     f: -8.580877e+00   |grad|: 1.729730e-04   negative curvature\n",
            "acc       k:    34     num_inner:     0     f: -8.580877e+00   |grad|: 1.152649e-04   negative curvature\n",
            "acc TR+   k:    35     num_inner:     0     f: -8.580877e+00   |grad|: 1.025756e-04   negative curvature\n",
            "acc TR+   k:    36     num_inner:     0     f: -8.580877e+00   |grad|: 7.776228e-05   exceeded trust region\n",
            "acc       k:    37     num_inner:     0     f: -8.580877e+00   |grad|: 5.491581e-05   negative curvature\n",
            "REJ TR-   k:    38     num_inner:     0     f: -8.580877e+00   |grad|: 5.491581e-05   negative curvature\n",
            "REJ TR-   k:    39     num_inner:     0     f: -8.580877e+00   |grad|: 5.491581e-05   negative curvature\n",
            "acc       k:    40     num_inner:     0     f: -8.580877e+00   |grad|: 2.881592e-05   negative curvature\n",
            "acc TR+   k:    41     num_inner:     0     f: -8.580877e+00   |grad|: 2.374900e-05   exceeded trust region\n",
            "acc       k:    42     num_inner:     0     f: -8.580877e+00   |grad|: 2.102981e-05   negative curvature\n",
            "acc TR-   k:    43     num_inner:     0     f: -8.580877e+00   |grad|: 3.706978e-05   negative curvature\n",
            "acc       k:    44     num_inner:     0     f: -8.580877e+00   |grad|: 1.959122e-05   negative curvature\n",
            "acc       k:    45     num_inner:     0     f: -8.580877e+00   |grad|: 1.060006e-05   negative curvature\n",
            "acc TR+   k:    46     num_inner:     0     f: -8.580877e+00   |grad|: 9.038668e-06   exceeded trust region\n",
            "acc TR+   k:    47     num_inner:     0     f: -8.580877e+00   |grad|: 6.184971e-06   exceeded trust region\n",
            "REJ TR-   k:    48     num_inner:     0     f: -8.580877e+00   |grad|: 6.184971e-06   exceeded trust region\n",
            "acc TR+   k:    49     num_inner:     0     f: -8.580877e+00   |grad|: 6.106725e-06   exceeded trust region\n",
            "REJ TR-   k:    50     num_inner:     0     f: -8.580877e+00   |grad|: 6.106725e-06   negative curvature\n",
            "acc       k:    51     num_inner:     0     f: -8.580877e+00   |grad|: 4.756032e-06   negative curvature\n",
            "acc       k:    52     num_inner:     0     f: -8.580877e+00   |grad|: 4.517687e-06   negative curvature\n",
            "acc       k:    53     num_inner:     0     f: -8.580877e+00   |grad|: 4.769448e-06   negative curvature\n",
            "acc TR-   k:    54     num_inner:     0     f: -8.580877e+00   |grad|: 4.991684e-06   negative curvature\n",
            "acc TR+   k:    55     num_inner:     0     f: -8.580877e+00   |grad|: 3.063565e-06   negative curvature\n",
            "acc       k:    56     num_inner:     0     f: -8.580877e+00   |grad|: 2.356424e-06   negative curvature\n",
            "acc       k:    57     num_inner:     0     f: -8.580877e+00   |grad|: 2.277998e-06   negative curvature\n",
            "acc       k:    58     num_inner:     0     f: -8.580877e+00   |grad|: 2.417452e-06   negative curvature\n",
            "acc       k:    59     num_inner:     0     f: -8.580877e+00   |grad|: 2.495809e-06   negative curvature\n",
            "acc TR-   k:    60     num_inner:     0     f: -8.580877e+00   |grad|: 2.498348e-06   negative curvature\n",
            "acc TR+   k:    61     num_inner:     0     f: -8.580877e+00   |grad|: 1.440647e-06   negative curvature\n",
            "acc       k:    62     num_inner:     0     f: -8.580877e+00   |grad|: 1.154093e-06   negative curvature\n",
            "acc       k:    63     num_inner:     0     f: -8.580877e+00   |grad|: 1.219823e-06   negative curvature\n",
            "acc       k:    64     num_inner:     0     f: -8.580877e+00   |grad|: 1.247140e-06   negative curvature\n",
            "acc       k:    65     num_inner:     0     f: -8.580877e+00   |grad|: 1.251515e-06   negative curvature\n",
            "acc       k:    66     num_inner:     0     f: -8.580877e+00   |grad|: 1.259773e-06   negative curvature\n",
            "acc       k:    67     num_inner:     0     f: -8.580877e+00   |grad|: 1.260768e-06   negative curvature\n",
            "acc       k:    68     num_inner:     0     f: -8.580877e+00   |grad|: 1.264936e-06   negative curvature\n",
            "acc       k:    69     num_inner:     0     f: -8.580877e+00   |grad|: 1.264687e-06   negative curvature\n",
            "acc       k:    70     num_inner:     0     f: -8.580877e+00   |grad|: 1.267328e-06   negative curvature\n",
            "acc       k:    71     num_inner:     0     f: -8.580877e+00   |grad|: 1.266531e-06   negative curvature\n",
            "acc       k:    72     num_inner:     0     f: -8.580877e+00   |grad|: 1.268497e-06   negative curvature\n",
            "acc       k:    73     num_inner:     0     f: -8.580877e+00   |grad|: 1.267439e-06   negative curvature\n",
            "acc       k:    74     num_inner:     0     f: -8.580877e+00   |grad|: 1.269081e-06   negative curvature\n",
            "acc       k:    75     num_inner:     0     f: -8.580877e+00   |grad|: 1.267894e-06   negative curvature\n",
            "acc       k:    76     num_inner:     0     f: -8.580877e+00   |grad|: 1.269377e-06   negative curvature\n",
            "acc       k:    77     num_inner:     0     f: -8.580877e+00   |grad|: 1.268125e-06   negative curvature\n",
            "acc       k:    78     num_inner:     0     f: -8.580877e+00   |grad|: 1.269527e-06   negative curvature\n",
            "acc       k:    79     num_inner:     0     f: -8.580877e+00   |grad|: 1.268243e-06   negative curvature\n",
            "acc       k:    80     num_inner:     0     f: -8.580877e+00   |grad|: 1.269604e-06   negative curvature\n",
            "acc       k:    81     num_inner:     0     f: -8.580877e+00   |grad|: 1.268303e-06   negative curvature\n",
            "acc       k:    82     num_inner:     0     f: -8.580877e+00   |grad|: 1.269643e-06   negative curvature\n",
            "acc       k:    83     num_inner:     0     f: -8.580877e+00   |grad|: 1.268333e-06   negative curvature\n",
            "acc       k:    84     num_inner:     0     f: -8.580877e+00   |grad|: 1.269663e-06   negative curvature\n",
            "acc       k:    85     num_inner:     0     f: -8.580877e+00   |grad|: 1.268349e-06   negative curvature\n",
            "acc       k:    86     num_inner:     0     f: -8.580877e+00   |grad|: 1.269674e-06   negative curvature\n",
            "acc       k:    87     num_inner:     0     f: -8.580877e+00   |grad|: 1.268357e-06   negative curvature\n",
            "acc       k:    88     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:    89     num_inner:     0     f: -8.580877e+00   |grad|: 1.268361e-06   negative curvature\n",
            "acc       k:    90     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:    91     num_inner:     0     f: -8.580877e+00   |grad|: 1.268363e-06   negative curvature\n",
            "acc       k:    92     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:    93     num_inner:     0     f: -8.580877e+00   |grad|: 1.268365e-06   negative curvature\n",
            "acc       k:    94     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:    95     num_inner:     0     f: -8.580877e+00   |grad|: 1.268365e-06   negative curvature\n",
            "acc       k:    96     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:    97     num_inner:     0     f: -8.580877e+00   |grad|: 1.268365e-06   negative curvature\n",
            "acc       k:    98     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:    99     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   100     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   101     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   102     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   103     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   104     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   105     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   106     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   107     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   108     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   109     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   110     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   111     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   112     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   113     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   114     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   115     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   116     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   117     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   118     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   119     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   120     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   121     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   122     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   123     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   124     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   125     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   126     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   127     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   128     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   129     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   130     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   131     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   132     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   133     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   134     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   135     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   136     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   137     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   138     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   139     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   140     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   141     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   142     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   143     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   144     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   145     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   146     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   147     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   148     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   149     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   150     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   151     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   152     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   153     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   154     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   155     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   156     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   157     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   158     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   159     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   160     num_inner:     0     f: -8.580877e+00   |grad|: 1.269684e-06   negative curvature\n",
            "acc       k:   161     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   162     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   163     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   164     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   165     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   166     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   167     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   168     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   169     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   170     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   171     num_inner:     0     f: -8.580877e+00   |grad|: 1.268366e-06   negative curvature\n",
            "acc       k:   172     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   173     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   174     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   175     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   176     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   177     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   178     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   179     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   180     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   181     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   182     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   183     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   184     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   185     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   186     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   187     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   188     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   189     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   190     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   191     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   192     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   193     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   194     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   195     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   196     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   197     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   198     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   199     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   200     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   201     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   202     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   203     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   204     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   205     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   206     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   207     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   208     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   209     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   210     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   211     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   212     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   213     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   214     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   215     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   216     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   217     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   218     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   219     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   220     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   221     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   222     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   223     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   224     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   225     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   226     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   227     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   228     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   229     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   230     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   231     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   232     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   233     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   234     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   235     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   236     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   237     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   238     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   239     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   240     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   241     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   242     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   243     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   244     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   245     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   246     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   247     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   248     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   249     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   250     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   251     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   252     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   253     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   254     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   255     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   256     num_inner:     0     f: -8.580877e+00   |grad|: 1.269683e-06   negative curvature\n",
            "acc       k:   257     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   258     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   259     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   260     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   261     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   262     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   263     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   264     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   265     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   266     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   267     num_inner:     0     f: -8.580877e+00   |grad|: 1.268367e-06   negative curvature\n",
            "acc       k:   268     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   269     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   270     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   271     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   272     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   273     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   274     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   275     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   276     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   277     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   278     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   279     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   280     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   281     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   282     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   283     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   284     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   285     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   286     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   287     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   288     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   289     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   290     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   291     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   292     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   293     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   294     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   295     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   296     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   297     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   298     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   299     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   300     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   301     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   302     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   303     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   304     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   305     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   306     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   307     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   308     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   309     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   310     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   311     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   312     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   313     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   314     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   315     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   316     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   317     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   318     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   319     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   320     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   321     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   322     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   323     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   324     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   325     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   326     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   327     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   328     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   329     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   330     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   331     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   332     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   333     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   334     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   335     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   336     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   337     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   338     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   339     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   340     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   341     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   342     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   343     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   344     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   345     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   346     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   347     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   348     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   349     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   350     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   351     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   352     num_inner:     0     f: -8.580877e+00   |grad|: 1.269682e-06   negative curvature\n",
            "acc       k:   353     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   354     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   355     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   356     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   357     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   358     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   359     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   360     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   361     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   362     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   363     num_inner:     0     f: -8.580877e+00   |grad|: 1.268368e-06   negative curvature\n",
            "acc       k:   364     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   365     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   366     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   367     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   368     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   369     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   370     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   371     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   372     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   373     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   374     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   375     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   376     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   377     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   378     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   379     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   380     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   381     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   382     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   383     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   384     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   385     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   386     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   387     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   388     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   389     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   390     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   391     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   392     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   393     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   394     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   395     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   396     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   397     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   398     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   399     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   400     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   401     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   402     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   403     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   404     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   405     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   406     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   407     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   408     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   409     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   410     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   411     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   412     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   413     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   414     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   415     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   416     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   417     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   418     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   419     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   420     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   421     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   422     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   423     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   424     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   425     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   426     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   427     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   428     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   429     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   430     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   431     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   432     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   433     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   434     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   435     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   436     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   437     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   438     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   439     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   440     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   441     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   442     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   443     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   444     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   445     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   446     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   447     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   448     num_inner:     0     f: -8.580877e+00   |grad|: 1.269681e-06   negative curvature\n",
            "acc       k:   449     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   450     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   451     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   452     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   453     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   454     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   455     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   456     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   457     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   458     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   459     num_inner:     0     f: -8.580877e+00   |grad|: 1.268369e-06   negative curvature\n",
            "acc       k:   460     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   461     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   462     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   463     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   464     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   465     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   466     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   467     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   468     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   469     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   470     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   471     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   472     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   473     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   474     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   475     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   476     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   477     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   478     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   479     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   480     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   481     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   482     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   483     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   484     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   485     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   486     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   487     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   488     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   489     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   490     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   491     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   492     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   493     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   494     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   495     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   496     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   497     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   498     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   499     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   500     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   501     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   502     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   503     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   504     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   505     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   506     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   507     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   508     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   509     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   510     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   511     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   512     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   513     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   514     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   515     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   516     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   517     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   518     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   519     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   520     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   521     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   522     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   523     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   524     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   525     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   526     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   527     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   528     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   529     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   530     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   531     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   532     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   533     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   534     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   535     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   536     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   537     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   538     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   539     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   540     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   541     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   542     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   543     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   544     num_inner:     0     f: -8.580877e+00   |grad|: 1.269680e-06   negative curvature\n",
            "acc       k:   545     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   546     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   547     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   548     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   549     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   550     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   551     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   552     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   553     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   554     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   555     num_inner:     0     f: -8.580877e+00   |grad|: 1.268370e-06   negative curvature\n",
            "acc       k:   556     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   557     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   558     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   559     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   560     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   561     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   562     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   563     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   564     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   565     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   566     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   567     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   568     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   569     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   570     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   571     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   572     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   573     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   574     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   575     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   576     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   577     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   578     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   579     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   580     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   581     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   582     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   583     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   584     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   585     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   586     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   587     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   588     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   589     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   590     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   591     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   592     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   593     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   594     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   595     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   596     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   597     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   598     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   599     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   600     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   601     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   602     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   603     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   604     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   605     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   606     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   607     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   608     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   609     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   610     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   611     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   612     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   613     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   614     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   615     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   616     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   617     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   618     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   619     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   620     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   621     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   622     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   623     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   624     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   625     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   626     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   627     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   628     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   629     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   630     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   631     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   632     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   633     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   634     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   635     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   636     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   637     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   638     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   639     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   640     num_inner:     0     f: -8.580877e+00   |grad|: 1.269679e-06   negative curvature\n",
            "acc       k:   641     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   642     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   643     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   644     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   645     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   646     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   647     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   648     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   649     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   650     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   651     num_inner:     0     f: -8.580877e+00   |grad|: 1.268371e-06   negative curvature\n",
            "acc       k:   652     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   653     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   654     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   655     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   656     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   657     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   658     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   659     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   660     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   661     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   662     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   663     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   664     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   665     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   666     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   667     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   668     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   669     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   670     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   671     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   672     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   673     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   674     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   675     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   676     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   677     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   678     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   679     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   680     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   681     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   682     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   683     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   684     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   685     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   686     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   687     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   688     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   689     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   690     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   691     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   692     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   693     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   694     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   695     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   696     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   697     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   698     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   699     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   700     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   701     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   702     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   703     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   704     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   705     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   706     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   707     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   708     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   709     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   710     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   711     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   712     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   713     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   714     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   715     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   716     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   717     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   718     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   719     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   720     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   721     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   722     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   723     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   724     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   725     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   726     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   727     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   728     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   729     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   730     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   731     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   732     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   733     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   734     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   735     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   736     num_inner:     0     f: -8.580877e+00   |grad|: 1.269678e-06   negative curvature\n",
            "acc       k:   737     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   738     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   739     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   740     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   741     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   742     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   743     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   744     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   745     num_inner:     0     f: -8.580877e+00   |grad|: 1.268372e-06   negative curvature\n",
            "acc       k:   746     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   747     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   748     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   749     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   750     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   751     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   752     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   753     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   754     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   755     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   756     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   757     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   758     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   759     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   760     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   761     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   762     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   763     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   764     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   765     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   766     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   767     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   768     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   769     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   770     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   771     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   772     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   773     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   774     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   775     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   776     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   777     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   778     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   779     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   780     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   781     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   782     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   783     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   784     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   785     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   786     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   787     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   788     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   789     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   790     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   791     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   792     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   793     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   794     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   795     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   796     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   797     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   798     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   799     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   800     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   801     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   802     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   803     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   804     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   805     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   806     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   807     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   808     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   809     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   810     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   811     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   812     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   813     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   814     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   815     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   816     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   817     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   818     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   819     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   820     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   821     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   822     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   823     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   824     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   825     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   826     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   827     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   828     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   829     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   830     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   831     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   832     num_inner:     0     f: -8.580877e+00   |grad|: 1.269677e-06   negative curvature\n",
            "acc       k:   833     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   834     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   835     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   836     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   837     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   838     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   839     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   840     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   841     num_inner:     0     f: -8.580877e+00   |grad|: 1.268373e-06   negative curvature\n",
            "acc       k:   842     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   843     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   844     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   845     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   846     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   847     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   848     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   849     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   850     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   851     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   852     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   853     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   854     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   855     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   856     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   857     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   858     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   859     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   860     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   861     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   862     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   863     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   864     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   865     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   866     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   867     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   868     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   869     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   870     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   871     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   872     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   873     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   874     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   875     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   876     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   877     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   878     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   879     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   880     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   881     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   882     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   883     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   884     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   885     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   886     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   887     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   888     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   889     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   890     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   891     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   892     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   893     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   894     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   895     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   896     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   897     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   898     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   899     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   900     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   901     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   902     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   903     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   904     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   905     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   906     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   907     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   908     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   909     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   910     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   911     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   912     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   913     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   914     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   915     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   916     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   917     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   918     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   919     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   920     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   921     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   922     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   923     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   924     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   925     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   926     num_inner:     0     f: -8.580877e+00   |grad|: 1.269676e-06   negative curvature\n",
            "acc       k:   927     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   928     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   929     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   930     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   931     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   932     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   933     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   934     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   935     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   936     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   937     num_inner:     0     f: -8.580877e+00   |grad|: 1.268374e-06   negative curvature\n",
            "acc       k:   938     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   939     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   940     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   941     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   942     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   943     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   944     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   945     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   946     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   947     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   948     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   949     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   950     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   951     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   952     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   953     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   954     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   955     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   956     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   957     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   958     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   959     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   960     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   961     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   962     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   963     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   964     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   965     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   966     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   967     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   968     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   969     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   970     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   971     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   972     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   973     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   974     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   975     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   976     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   977     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   978     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   979     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   980     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   981     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   982     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   983     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   984     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   985     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   986     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   987     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   988     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   989     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   990     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   991     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   992     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   993     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   994     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   995     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   996     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   997     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:   998     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "acc       k:   999     num_inner:     0     f: -8.580877e+00   |grad|: 1.268375e-06   negative curvature\n",
            "acc       k:  1000     num_inner:     0     f: -8.580877e+00   |grad|: 1.269675e-06   negative curvature\n",
            "Terminated - max iterations reached after 10.38 seconds.\n",
            "\n",
            "[[-0.50149316 -0.19111721  0.00108873 -0.84378767]\n",
            " [ 0.67507188  0.02405477  0.61560222 -0.40587341]\n",
            " [ 0.14063272  0.87236114 -0.37400415 -0.2816547 ]\n",
            " [-0.52249881  0.44931238  0.69365237  0.20966584]]\n",
            "original_llk=-8.578546 gradient_fit=-8.580877 manifold_fit=-8.580877\n",
            "original Phi\n",
            "[[[ 0.13193888 -0.21927422]\n",
            "  [ 0.46330974  0.40756997]\n",
            "  [-0.16771385 -0.4921311 ]\n",
            "  [-0.03414797 -0.02014281]]\n",
            "\n",
            " [[ 0.00837191 -0.09103331]\n",
            "  [ 0.63177753  0.44591095]\n",
            "  [-0.47056485 -1.18247158]\n",
            "  [ 0.27719012 -0.29644986]]\n",
            "\n",
            " [[-0.4639859   0.54607493]\n",
            "  [-0.0844373   0.38459476]\n",
            "  [-0.28132253 -0.79837933]\n",
            "  [-0.20787942  0.32759414]]\n",
            "\n",
            " [[-0.2432056  -0.90486695]\n",
            "  [-0.79173487  0.65092753]\n",
            "  [ 0.24652816  0.26709207]\n",
            "  [ 0.14283634 -0.50855748]]]\n",
            "gradient fitted Phi\n",
            "[[[ 0.14063387 -0.23222932]\n",
            "  [ 0.49350794  0.38280812]\n",
            "  [-0.20112106 -0.49448887]\n",
            "  [-0.04173245 -0.02570015]]\n",
            "\n",
            " [[ 0.03240514 -0.05548998]\n",
            "  [ 0.62738175  0.46931166]\n",
            "  [-0.46899078 -1.18658144]\n",
            "  [ 0.28784078 -0.27978872]]\n",
            "\n",
            " [[-0.50037651  0.58754522]\n",
            "  [-0.12480103  0.39623359]\n",
            "  [-0.2274299  -0.77085316]\n",
            "  [-0.22704937  0.32237522]]\n",
            "\n",
            " [[-0.26519308 -0.92105951]\n",
            "  [-0.79625593  0.68559323]\n",
            "  [ 0.26830833  0.25339215]\n",
            "  [ 0.1578199  -0.50923733]]]\n",
            "manifold fitted Phi\n",
            "[[[ 0.14063409 -0.2322293 ]\n",
            "  [ 0.49350796  0.38280797]\n",
            "  [-0.20112124 -0.49448892]\n",
            "  [-0.04173244 -0.0257001 ]]\n",
            "\n",
            " [[ 0.03239601 -0.05549099]\n",
            "  [ 0.62738188  0.46931378]\n",
            "  [-0.46898595 -1.18657837]\n",
            "  [ 0.28783731 -0.27979213]]\n",
            "\n",
            " [[-0.5003646   0.58754653]\n",
            "  [-0.12480121  0.39623087]\n",
            "  [-0.22743617 -0.77085717]\n",
            "  [-0.22704481  0.32237969]]\n",
            "\n",
            " [[-0.26519608 -0.92105985]\n",
            "  [-0.79625588  0.68559388]\n",
            "  [ 0.26830989  0.25339317]\n",
            "  [ 0.15781873 -0.50923846]]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vf8TpLvFWU-4",
        "colab_type": "text"
      },
      "source": [
        "## Conclusion:\n",
        "We will focus our efforts on improving numerical methods, as well as extending the model to VARMA. We look forward to testing with real data.\n"
      ]
    }
  ]
}