tensorCalc_Graphics_Murnaghan_sklearn.ipynb

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    "import os\n",
    "import importlib.util\n",
    "from IPython.display import display\n",
    "import sympy as sym\n",
    "from sympy.assumptions.assume import global_assumptions\n",
    "import pandas as pd\n",
    "from scipy.integrate import solve_bvp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import simpson\n",
    "from scipy.optimize import root\n",
    "from scipy.signal import argrelextrema\n",
    "seed = 73\n",
    "CARTESIAN = 0\n",
    "CYLINDRICAL = 1\n",
    "SPHERICAL = 2\n",
    "np.random.seed(seed)\n",
    "#Начальная система\n",
    "r = sym.Symbol('r', real=True, positive=True)\n",
    "phi = sym.Symbol('phi', real=True, nonnegative=True)\n",
    "theta = sym.Symbol('theta', real=True)\n",
    "x = sym.Symbol('x', real=True)\n",
    "y = sym.Symbol('y', real=True)\n",
    "z = sym.Symbol('z', real=True)\n",
    "global_assumptions.add(sym.Q.positive(sym.cos(theta)), sym.Q.positive(r))\n",
    "#Конечная система\n",
    "R = sym.Symbol('R', real=True, positive=True)\n",
    "Phi = sym.Symbol('Phi', real=True)\n",
    "Theta = sym.Symbol('Theta', real=True)\n",
    "X = sym.Symbol('X', real=True)\n",
    "Y = sym.Symbol('Y', real=True)\n",
    "Z = sym.Symbol('Z', real=True)\n",
    "global_assumptions.add(sym.Q.positive(sym.cos(Theta)), sym.Q.positive(R))\n",
    "I1 = sym.Symbol('I1', real=True)\n",
    "I2 = sym.Symbol('I2', real=True)\n",
    "I3 = sym.Symbol('I3', real=True)\n",
    "mu = sym.Symbol('mu', real=True, positive=True)\n",
    "global_assumptions.add(sym.Q.positive(mu))\n",
    "P = sym.Function('P', real=True, positive=True)(r)\n",
    "Psi = sym.Symbol('psi', real=True)\n",
    "k = sym.Symbol('k', real=True, positive=True)\n",
    "alpha = sym.Symbol('alpha', real=True)\n",
    "beta = sym.Symbol('beta', real=True)\n",
    "lambdas = sym.Symbol('lambda', real=True)\n",
    "ms = sym.Symbol('m', real=True)\n",
    "ls = sym.Symbol('l', real=True)\n",
    "ns = sym.Symbol('n', real=True)\n",
    "global_assumptions.add(sym.Q.positive(P), sym.Q.positive(sym.diff(P, r)), sym.Q.positive(k))"
   ]
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   "source": [
    "def MurnaghanMaterial():\n",
    "    '''\n",
    "    Возвращает выражение энергии материала Мурнагана.\n",
    "    '''\n",
    "    W = (-3 * lambdas - 2 * mu + sym.Rational(9, 2) * ls + ns / 2) * I1\n",
    "    W = W + sym.Rational(1, 2) * (lambdas + 2 * mu - 3 * ls - 2 * ms) * sym.Pow(I1, 2)\n",
    "    W = W + (-2 * mu + 3 * ms - ns / 2) * I2\n",
    "    W = W - ms * I1 * I2\n",
    "    W = W + sym.Rational(1, 6) * (ls + 2*ms) * sym.Pow(I1, 3)\n",
    "    W = W + ns / 2*(I3 - 1)\n",
    "    return sym.Rational(1, 4) * W"
   ]
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   "execution_count": 3,
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   "source": [
    "def GetI1(G):\n",
    "    '''\n",
    "    Возвращает выражение инварианта I_1 тензора второго ранга G.\n",
    "    '''\n",
    "    return sym.simplify(sym.Trace(G))"
   ]
  },
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   "execution_count": 4,
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   "source": [
    "def GetI2(G):\n",
    "    '''\n",
    "    Возвращает выражение инварианта I_2 тензора второго ранга G.\n",
    "    '''\n",
    "    return sym.simplify(sym.Rational(1, 2) * (sym.Pow(sym.Trace(G), 2) - sym.Trace(G * G)))"
   ]
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   "execution_count": 5,
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   "source": [
    "def GetI3(G):\n",
    "    '''\n",
    "    Возвращает выражение инварианта I_3 тензора второго ранга G.\n",
    "    '''\n",
    "    return sym.simplify(sym.det(G))"
   ]
  },
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   "source": [
    "def MySimplifyMatrix(A):\n",
    "    '''\n",
    "    Упрощение элементов матрицы или вектора с использованием функции MySimplify.\n",
    "    '''\n",
    "    for i in range(A.shape[0]):\n",
    "        for j in range(A.shape[1]):\n",
    "            A[i, j] = MySimplify(A[i, j])\n",
    "    return A"
   ]
  },
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   "execution_count": 7,
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   "source": [
    "def MySimplify(A):\n",
    "    '''\n",
    "    Упрощение символьных выражений с учётом глобальных условий и правила перемножения степеней.\n",
    "    '''\n",
    "    return sym.simplify(sym.refine(sym.powdenest(A, force=True)), rational=True)"
   ]
  },
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   "execution_count": 8,
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   "source": [
    "def dW(W, G):\n",
    "    '''\n",
    "    Выражение производной выражения W по тензору второго ранга G.\n",
    "    '''\n",
    "    E = sym.eye(3)\n",
    "    I1G = E\n",
    "    I2G = I1 * E - G\n",
    "    I3G = I3 * G.inv()\n",
    "    dWdG = sym.diff(W, I1) * I1G + sym.diff(W, I2) * I2G + sym.diff(W, I3) * I3G\n",
    "    dWdG = MySimplifyMatrix(dWdG.subs([(I1, GetI1(G)), (I2, GetI2(G)), (I3, GetI3(G))]))\n",
    "    return dWdG"
   ]
  },
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   "execution_count": 9,
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   "source": [
    "def VectorGradient(B, Q, Gamma, H):\n",
    "    '''\n",
    "    Выражение градиента вектора B, приведённое к ортонормированному базису.\n",
    "    Q - символы криволинейных координат.\n",
    "    Gamma - символы Кристоффеля второго рода.\n",
    "    H - коэффициенты Ламе.\n",
    "    '''\n",
    "    #Приведено к ортонормированному базису.\n",
    "    NablaA = sym.zeros(3, 3)\n",
    "    if len(B.shape) == 2:\n",
    "        A = B[0, :]\n",
    "    else:\n",
    "        A = B\n",
    "    for N in range(0, 3):\n",
    "        for K in range(0, 3):\n",
    "            NablaA[K, N] = sym.simplify((sym.diff(A[N], Q[K]) + sum(A[M] * Gamma[N, M, K] for M in range(3))) / H[K] * H[N])\n",
    "    return NablaA"
   ]
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   "source": [
    "def TensorSecondRankCov(P, Q, Gamma, M, N, S):\n",
    "    '''\n",
    "    Выражение ковариантной производной компоненты тензора второго ранга P.\n",
    "    Q - символы криволинейных координат.\n",
    "    Gamma - символы Кристоффеля второго рода.\n",
    "    M, N, S - индексы.\n",
    "    '''\n",
    "    #Формула 38.6.\n",
    "    sm = sym.diff(P[M, N], Q[S])\n",
    "    sm += sum(Gamma[M, T, S] * P[T, N] for T in range(3))\n",
    "    sm += sum(Gamma[N, T, S] * P[M, T] for T in range(3))\n",
    "    return MySimplify(sm)"
   ]
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   "source": [
    "def TensorSecondRankDiv(P, Q, Gamma, H):\n",
    "    '''\n",
    "    Выражение дивергенции тензора второго ранга P, приведённое к ортонормированному базису.\n",
    "    Q - символы криволинейных координат.\n",
    "    Gamma - символы Кристоффеля второго рода.\n",
    "    H - коэффициенты Ламе.\n",
    "    '''\n",
    "    #Приведено к ортонормированному базису.\n",
    "    DivP = sym.zeros(1, 3)\n",
    "    for N in range(3):\n",
    "        DivP[N] = MySimplify(sum(TensorSecondRankCov(P, Q, Gamma, M, N, M) for M in range(3)) * H[N])\n",
    "    return DivP"
   ]
  },
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   "execution_count": 12,
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   "source": [
    "def dotprod(a, b):\n",
    "    '''\n",
    "    Скалярное произведение векторов a и b.\n",
    "    '''\n",
    "    return sym.simplify(sum(a[i] * b[i] for i in range(3)))"
   ]
  },
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   "execution_count": 13,
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   "source": [
    "def Reference_configuration(coordType):\n",
    "    '''\n",
    "    Вычисление характеристик отсчётной конфигурации.\n",
    "    coordType - тип системы координат (0 - прямоугольная, 1 - цилиндрическая, 2 - сферическая).\n",
    "    '''\n",
    "    x_ = sym.zeros(1, 3) #Уравнения отсчётной конфигурации.\n",
    "    rt = sym.zeros(1, 3) #Радиус-вектор отсчётной конфигурации.\n",
    "    q = sym.zeros(1, 3)\n",
    "    if coordType == CARTESIAN:\n",
    "            q[0] = x\n",
    "            q[1] = y\n",
    "            q[2] = z\n",
    "            rt[0] = x\n",
    "            rt[1] = y\n",
    "            rt[2] = z\n",
    "            x_[0] = x\n",
    "            x_[1] = y\n",
    "            x_[2] = z\n",
    "            #print(\"Начальная система координат: прямоугольная.\")\n",
    "    elif coordType == CYLINDRICAL:\n",
    "            x_[0] = r * sym.cos(phi)\n",
    "            x_[1] = r * sym.sin(phi)\n",
    "            x_[2] = z\n",
    "            rt[0] = r\n",
    "            rt[1] = 0\n",
    "            rt[2] = z\n",
    "            q[0] = r\n",
    "            q[1] = phi\n",
    "            q[2] = z\n",
    "            #print(\"Начальная система координат: цилиндрическая.\")\n",
    "    else:\n",
    "            x_[0] = r * sym.cos(theta) * sym.cos(phi)\n",
    "            x_[1] = r * sym.cos(theta) * sym.sin(phi)\n",
    "            x_[2] = r * sym.sin(theta)\n",
    "            rt[0] = r\n",
    "            rt[1] = 0\n",
    "            rt[2] = 0\n",
    "            q[0] = r\n",
    "            q[1] = phi\n",
    "            q[2] = theta\n",
    "            #print(\"Начальная система координат: сферическая.\")\n",
    "    r_ = sym.zeros(3, 3)\n",
    "    for n in range(0, 3):\n",
    "        for s in range(0, 3):\n",
    "            r_[n, s] = sym.diff(x_[s], q[n])\n",
    "    #print(\"Основной базис:\")\n",
    "    #sym.pprint(r_)\n",
    "    g_ = sym.zeros(3, 3)\n",
    "    for m in range(0, 3):\n",
    "        for n in range(0, 3):\n",
    "            for i in range(0, 3):\n",
    "                g_[m, n] = sym.simplify(g_[m, n]+r_[m, i]*r_[n, i])\n",
    "    #print(\"Метрические коэффициенты:\")\n",
    "    #sym.pprint(g_)\n",
    "    g = sym.Inverse(g_)\n",
    "    #print(\"Обратная матрица метрических коэффициентов: \")\n",
    "    #sym.pprint(g)\n",
    "    h = sym.zeros(1, 3)\n",
    "    for m in range(0, 3):\n",
    "        #refine - упрощение выражений с использованием предположений. Предположения могут быть или в global_assumptions, или могут быть переданы напрямую при вызове функции.\n",
    "        #powdenest - упрощение выражения со степенями, используя правило перемножения степеней при возведении степени в степень.\n",
    "        h[m] = MySimplify(sym.sqrt(g_[m, m]))\n",
    "    #print(\"Коэффициенты Ламе:\")\n",
    "    #sym.pprint(h)\n",
    "    gamma = sym.MutableDenseNDimArray.zeros(3, 3, 3)\n",
    "    for n in range(0, 3):\n",
    "        for k in range(0, 3):\n",
    "            for m in range(0, 3):\n",
    "                gamma[m, n, k] = sym.simplify(1/2*sum(g[m, s]*(sym.diff(g_[n, s], q[k])+sym.diff(g_[k, s], q[n])-sym.diff(g_[n, k], q[s]))\n",
    "                for s in range(3)))\n",
    "    #print(\"Символы Кристоффеля второго рода:\")\n",
    "    #sym.pprint(gamma)\n",
    "    return q, rt, r_, h, gamma"
   ]
  },
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   "source": [
    "def Actual_configuration(coordType):\n",
    "    '''\n",
    "    Вычисление характеристик текущей конфигурации.\n",
    "    coordType - тип системы координат (0 - прямоугольная, 1 - цилиндрическая, 2 - сферическая).\n",
    "    '''\n",
    "    X_ = sym.zeros(1, 3) #Уравнения конечной системы.\n",
    "    Rt = sym.zeros(1, 3) #Радиус-вектор конечной системы.\n",
    "    Q = sym.zeros(1, 3)\n",
    "    if coordType == CARTESIAN:\n",
    "            Q[0] = X\n",
    "            Q[1] = Y\n",
    "            Q[2] = Z\n",
    "            Rt[0] = X\n",
    "            Rt[1] = Y\n",
    "            Rt[2] = Z\n",
    "            X_[0] = X\n",
    "            X_[1] = Y\n",
    "            X_[2] = Z\n",
    "            #print(\"Конечная система координат: прямоугольная.\")\n",
    "    elif coordType == CYLINDRICAL:\n",
    "            X_[0] = R * sym.cos(Phi)\n",
    "            X_[1] = R * sym.sin(Phi)\n",
    "            X_[2] = Z\n",
    "            Rt[0] = R\n",
    "            Rt[1] = 0\n",
    "            Rt[2] = Z\n",
    "            Q[0] = R\n",
    "            Q[1] = Phi\n",
    "            Q[2] = Z\n",
    "            #print(\"Конечная система координат: цилиндрическая.\")\n",
    "    else:\n",
    "            X_[0] = R * sym.cos(Theta) * sym.cos(Phi)\n",
    "            X_[1] = R * sym.cos(Theta) * sym.sin(Phi)\n",
    "            X_[2] = R * sym.sin(Theta)\n",
    "            Rt[0] = R\n",
    "            Rt[1] = 0\n",
    "            Rt[2] = 0\n",
    "            Q[0] = R\n",
    "            Q[1] = Phi\n",
    "            Q[2] = Theta\n",
    "            #print(\"Конечная система координат: сферическая.\")\n",
    "    R_ = sym.zeros(3, 3)\n",
    "    for n in range(0, 3):\n",
    "        for s in range(0, 3):\n",
    "            R_[n, s] = sym.diff(X_[s], Q[n])\n",
    "    #print(\"Основной базис:\")\n",
    "    #sym.pprint(R_)\n",
    "    G_ = sym.zeros(3, 3)\n",
    "    for M in range(0, 3):\n",
    "        for N in range(0, 3):\n",
    "            for I in range(0, 3):\n",
    "                G_[M, N] = sym.simplify(G_[M, N] + R_[M, I] * R_[N, I])\n",
    "    #print(\"Метрические коэффициенты:\")\n",
    "    #sym.pprint(G_)\n",
    "    G = sym.Inverse(G_)\n",
    "    #print(\"Обратная матрица метрических коэффициентов: \")\n",
    "    #sym.pprint(G)\n",
    "    H = sym.zeros(1, 3)\n",
    "    for M in range(0, 3):\n",
    "        #refine - упрощение выражений с использованием предположений. Предположения могут быть или в global_assumptions, или могут быть переданы напрямую при вызове функции.\n",
    "        #powdenest - упрощение выражения со степенями, используя правило перемножения степеней при возведении степени в степень.\n",
    "        H[M] = MySimplify(sym.sqrt(G_[M, M]))\n",
    "    #print(\"Коэффициенты Ламе: \")\n",
    "    #sym.pprint(H)\n",
    "    Gamma = sym.MutableDenseNDimArray.zeros(3, 3, 3)\n",
    "    for N in range(0, 3):\n",
    "        for K in range(0, 3):\n",
    "            for M in range(0, 3):\n",
    "                Gamma[M, N, K] = sym.simplify(1/2*sum(G[M, S]*(sym.diff(G_[N, S], Q[K])+sym.diff(G_[K, S], Q[N])-sym.diff(G_[N, K], Q[S]))\n",
    "                for S in range(3)))\n",
    "    #print(\"Символы Кристоффеля второго рода:\")\n",
    "    #sym.pprint(Gamma)\n",
    "    return Q, Rt, R_, H, Gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:15:17.445956Z",
     "start_time": "2024-05-29T00:15:14.692434Z"
    },
    "collapsed": false,
    "id": "E4xwur-QUE_Y",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "3da65602-a1a4-4d34-feeb-263d2e5c9104",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Градиент деформации:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{d}{d r} P{\\left(r \\right)} & 0 & 0\\\\0 & \\frac{P{\\left(r \\right)}}{r} & 0\\\\0 & \\psi P{\\left(r \\right)} & k\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[Derivative(P(r), r),        0, 0],\n",
       "[                  0,   P(r)/r, 0],\n",
       "[                  0, psi*P(r), k]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q, rt, r_, h, gamma = Reference_configuration(CYLINDRICAL)\n",
    "e = sym.zeros(3, 3)\n",
    "for m in range(3):\n",
    "    for i in range(3):\n",
    "        e[m, i] = 1/h[m]*r_[m, i]\n",
    "Q, Rt, R_, H, Gamma = Actual_configuration(CYLINDRICAL)\n",
    "E = sym.zeros(3, 3)\n",
    "for M in range(3):\n",
    "    for I in range(3):\n",
    "        E[M, I] = 1/H[M]*R_[M, I]\n",
    "A = sym.zeros(3, 3)\n",
    "for M in range(3):\n",
    "    for K in range(3):\n",
    "        A[M, K] = dotprod(E[M, :], e[K, :])\n",
    "A = A.subs([(R, P), (Phi, phi+Psi*z), (Z, k*z)])\n",
    "Rt = Rt.subs([(R, P), (Phi, phi+Psi*z), (Z, k*z)])\n",
    "C = Rt*A\n",
    "for i in range(3):\n",
    "    C[i] = C[i]/h[i]\n",
    "C = MySimplifyMatrix(VectorGradient(C, q, gamma, h)*A.T)\n",
    "print(\"Градиент деформации:\")\n",
    "display(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:15:17.540322Z",
     "start_time": "2024-05-29T00:15:17.447339Z"
    },
    "collapsed": false,
    "id": "OQYRQ1MCUE_Z",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "7448abc1-2599-4dcb-da40-ab6f67bd6b30",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Мера деформации Коши:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} & 0 & 0\\\\0 & \\frac{P^{2}{\\left(r \\right)}}{r^{2}} & \\frac{\\psi P^{2}{\\left(r \\right)}}{r}\\\\0 & \\frac{\\psi P^{2}{\\left(r \\right)}}{r} & k^{2} + \\psi^{2} P^{2}{\\left(r \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[Derivative(P(r), r)**2,             0,                     0],\n",
       "[                     0,  P(r)**2/r**2,         psi*P(r)**2/r],\n",
       "[                     0, psi*P(r)**2/r, k**2 + psi**2*P(r)**2]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = MySimplifyMatrix(C*C.T)\n",
    "print(\"Мера деформации Коши:\")\n",
    "display(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:15:17.560156Z",
     "start_time": "2024-05-29T00:15:17.542332Z"
    },
    "id": "ehr-KafyUE_b",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def surface_simpson(rho_0_val, rho_1_val, val_k, val_Psitilde, sec_p_lmbd, cond_lmbd, f_inner_lmbd, list_len = 400):\n",
    "    '''\n",
    "    Функция для вычисления численного решения краевой задачи равновесия и значения определённого интеграла для найденного решения.\n",
    "    rho_0_val - нижний предел интеграла/левое краевое условие.\n",
    "    rho_1_val - верхнил предел интеграла/правое краевое условие.\n",
    "    val_k - значение параметра k.\n",
    "    val_Psitilde - значения параметра Psitilde.\n",
    "    sec_p_lmbd - лямба-функция второй производной краевой задачи.\n",
    "    cond_lmbd - лямба-функция краевого условия краевой задачи.\n",
    "    f_inner_lmbd - лямба-функция подынтегрального выражения.\n",
    "    list_len - размер массива для аппроксимации интегралом Симпсона.\n",
    "    '''\n",
    "    max_nodes = 2000\n",
    "    tol = 0.0001\n",
    "    def fun(x, y):\n",
    "        temp = np.array([y[1], sec_p_lmbd(val_k, val_Psitilde, x, y[0], y[1])])\n",
    "        return temp\n",
    "    def bc(y0, y1):\n",
    "        temp = np.array([cond_lmbd(val_k, val_Psitilde, rho_0_val, y0[0], y0[1]), cond_lmbd(val_k, val_Psitilde, rho_1_val, y1[0], y1[1])]).reshape([2, ])\n",
    "        return temp\n",
    "    x = np.linspace(rho_0_val, rho_1_val, list_len)\n",
    "    y_zero = x\n",
    "    y1_zero = np.ones(x.size)\n",
    "    y_appr = np.vstack([y_zero, y1_zero])\n",
    "    res_a = solve_bvp(fun, bc, x, y_appr, max_nodes = max_nodes, tol = tol)\n",
    "    q = 2*np.pi*simpson(f_inner_lmbd(val_k, val_Psitilde, res_a.x, res_a.y[0], res_a.y[1]), x = res_a.x)\n",
    "    return q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:15:17.572548Z",
     "start_time": "2024-05-29T00:15:17.565167Z"
    },
    "id": "KFqP-1t6UE_c",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def Solve_Q_Psi(rho_0_val, rho_1_val, val_Psitilde, sec_p_lmbd, cond_lmbd, Q_inner_lmbd, res_k_approx = 1.0):\n",
    "    '''\n",
    "    Функция для решения уравнения Q(k, Psitilde) = 0 относительно k.\n",
    "    rho_0_val - нижний предел интеграла.\n",
    "    rho_1_val - верхнил предел интеграла.\n",
    "    val_Psitilde - значение параметра Pstilde.\n",
    "    sec_p_lmbd - лямба-функция выражения второй производной краевой задачи.\n",
    "    cond_lmbd - лямба-функция выражения краевого условия краевой задачи.\n",
    "    Q_inner_lmbd - лямба-функция подынтегрального выражения растягивающей/сжимающей силы.\n",
    "    res_k_approx - начальное приближение для параметра k.\n",
    "    '''\n",
    "    factor = 0.1\n",
    "    maxfev = 400\n",
    "    tol = 0.0001\n",
    "    sol = root(lambda x: surface_simpson(rho_0_val, rho_1_val, x, val_Psitilde, sec_p_lmbd, cond_lmbd, Q_inner_lmbd), res_k_approx, tol = tol, options = {\"maxfev\": maxfev, \"factor\": factor})\n",
    "    return sol.x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:15:17.644097Z",
     "start_time": "2024-05-29T00:15:17.575547Z"
    },
    "collapsed": false,
    "id": "gn2zioAWUE_c",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "d76be483-1bdf-4c05-fb16-d6653e9da1f1"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W = \\frac{I_{1}^{3} \\left(\\frac{l}{6} + \\frac{m}{3}\\right)}{4} + \\frac{I_{1}^{2} \\left(- \\frac{3 l}{2} + \\frac{\\lambda}{2} - m + \\mu\\right)}{4} - \\frac{I_{1} I_{2} m}{4} + \\frac{I_{1} \\cdot \\left(\\frac{9 l}{2} - 3 \\lambda - 2 \\mu + \\frac{n}{2}\\right)}{4} + \\frac{I_{2} \\cdot \\left(3 m - 2 \\mu - \\frac{n}{2}\\right)}{4} + \\frac{n \\left(I_{3} - 1\\right)}{8}$"
      ],
      "text/plain": [
       "Eq(W, I1**3*(l/6 + m/3)/4 + I1**2*(-3*l/2 + lambda/2 - m + mu)/4 - I1*I2*m/4 + I1*(9*l/2 - 3*lambda - 2*mu + n/2)/4 + I2*(3*m - 2*mu - n/2)/4 + n*(I3 - 1)/8)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "W5 = MurnaghanMaterial()\n",
    "display(sym.Eq(sym.Symbol('W'), W5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.060248Z",
     "start_time": "2024-05-29T00:15:17.645104Z"
    },
    "collapsed": false,
    "id": "wxWKNEWxUE_c",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "0ac62c4b-d66a-4457-be64-74fb97dae956"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Уравнение равновесия и граничное условие:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d r^{2}} P{\\left(r \\right)} = \\frac{k^{4} l \\psi^{2} r^{6} P{\\left(r \\right)} - k^{4} l r^{5} \\frac{d}{d r} P{\\left(r \\right)} + k^{4} l r^{4} P{\\left(r \\right)} + 2 k^{4} m \\psi^{2} r^{6} P{\\left(r \\right)} + 2 k^{2} l \\psi^{4} r^{6} P^{3}{\\left(r \\right)} - 2 k^{2} l \\psi^{2} r^{6} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 k^{2} l \\psi^{2} r^{6} P{\\left(r \\right)} - 2 k^{2} l \\psi^{2} r^{5} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 4 k^{2} l \\psi^{2} r^{4} P^{3}{\\left(r \\right)} - 2 k^{2} l r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} + 6 k^{2} l r^{5} \\frac{d}{d r} P{\\left(r \\right)} - 2 k^{2} l r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 k^{2} l r^{4} P{\\left(r \\right)} + 2 k^{2} l r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 2 k^{2} l r^{2} P^{3}{\\left(r \\right)} + 2 k^{2} \\lambda \\psi^{2} r^{6} P{\\left(r \\right)} - 2 k^{2} \\lambda r^{5} \\frac{d}{d r} P{\\left(r \\right)} + 2 k^{2} \\lambda r^{4} P{\\left(r \\right)} + 4 k^{2} m \\psi^{4} r^{6} P^{3}{\\left(r \\right)} - 4 k^{2} m \\psi^{2} r^{6} P{\\left(r \\right)} + 4 k^{2} m \\psi^{2} r^{4} P^{3}{\\left(r \\right)} - 2 k^{2} m r^{5} \\frac{d}{d r} P{\\left(r \\right)} + 2 k^{2} m r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + 2 k^{2} m r^{4} P{\\left(r \\right)} - 2 k^{2} m r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 4 k^{2} \\mu \\psi^{2} r^{6} P{\\left(r \\right)} + k^{2} n r^{5} \\frac{d}{d r} P{\\left(r \\right)} - k^{2} n r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - k^{2} n r^{4} P{\\left(r \\right)} + k^{2} n r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + l \\psi^{6} r^{6} P^{5}{\\left(r \\right)} - 2 l \\psi^{4} r^{6} P^{3}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 l \\psi^{4} r^{6} P^{3}{\\left(r \\right)} - l \\psi^{4} r^{5} P^{4}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 3 l \\psi^{4} r^{4} P^{5}{\\left(r \\right)} - 3 l \\psi^{2} r^{6} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} + 6 l \\psi^{2} r^{6} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + 9 l \\psi^{2} r^{6} P{\\left(r \\right)} - 2 l \\psi^{2} r^{5} P^{2}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} + 6 l \\psi^{2} r^{5} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} - 4 l \\psi^{2} r^{4} P^{3}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 12 l \\psi^{2} r^{4} P^{3}{\\left(r \\right)} + 2 l \\psi^{2} r^{3} P^{4}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 3 l \\psi^{2} r^{2} P^{5}{\\left(r \\right)} - l r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{5} + 6 l r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} - 9 l r^{5} \\frac{d}{d r} P{\\left(r \\right)} - 3 l r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} + 6 l r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + 9 l r^{4} P{\\left(r \\right)} + 2 l r^{3} P^{2}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} - 6 l r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} - 2 l r^{2} P^{3}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 l r^{2} P^{3}{\\left(r \\right)} + 3 l r P^{4}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + l P^{5}{\\left(r \\right)} + 2 \\lambda \\psi^{4} r^{6} P^{3}{\\left(r \\right)} - 2 \\lambda \\psi^{2} r^{6} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 \\lambda \\psi^{2} r^{6} P{\\left(r \\right)} - 2 \\lambda \\psi^{2} r^{5} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 4 \\lambda \\psi^{2} r^{4} P^{3}{\\left(r \\right)} - 2 \\lambda r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} + 6 \\lambda r^{5} \\frac{d}{d r} P{\\left(r \\right)} - 2 \\lambda r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 \\lambda r^{4} P{\\left(r \\right)} + 2 \\lambda r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} + 2 \\lambda r^{2} P^{3}{\\left(r \\right)} + 2 m \\psi^{6} r^{6} P^{5}{\\left(r \\right)} - 4 m \\psi^{4} r^{6} P^{3}{\\left(r \\right)} + 6 m \\psi^{4} r^{4} P^{5}{\\left(r \\right)} - 2 m \\psi^{2} r^{6} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 2 m \\psi^{2} r^{5} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} - 8 m \\psi^{2} r^{4} P^{3}{\\left(r \\right)} + 6 m \\psi^{2} r^{2} P^{5}{\\left(r \\right)} - 2 m r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{5} + 4 m r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} - 2 m r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + 2 m r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} - 4 m r^{2} P^{3}{\\left(r \\right)} + 2 m P^{5}{\\left(r \\right)} + 4 \\mu \\psi^{4} r^{6} P^{3}{\\left(r \\right)} - 4 \\mu \\psi^{2} r^{6} P{\\left(r \\right)} + 8 \\mu \\psi^{2} r^{4} P^{3}{\\left(r \\right)} - 4 \\mu r^{5} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{3} + 4 \\mu r^{5} \\frac{d}{d r} P{\\left(r \\right)} - 4 \\mu r^{4} P{\\left(r \\right)} + 4 \\mu r^{2} P^{3}{\\left(r \\right)} + n \\psi^{2} r^{6} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + n \\psi^{2} r^{6} P{\\left(r \\right)} + n \\psi^{2} r^{5} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)} - n r^{5} \\frac{d}{d r} P{\\left(r \\right)} + n r^{4} P{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + n r^{4} P{\\left(r \\right)} - n r^{3} P^{2}{\\left(r \\right)} \\frac{d}{d r} P{\\left(r \\right)}}{r^{2} \\left(k^{4} l r^{4} + 2 k^{2} l \\psi^{2} r^{4} P^{2}{\\left(r \\right)} + 6 k^{2} l r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 k^{2} l r^{4} + 2 k^{2} l r^{2} P^{2}{\\left(r \\right)} + 2 k^{2} \\lambda r^{4} + 2 k^{2} m r^{4} - 2 k^{2} m r^{2} P^{2}{\\left(r \\right)} - k^{2} n r^{4} + k^{2} n r^{2} P^{2}{\\left(r \\right)} + l \\psi^{4} r^{4} P^{4}{\\left(r \\right)} + 6 l \\psi^{2} r^{4} P^{2}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 l \\psi^{2} r^{4} P^{2}{\\left(r \\right)} + 2 l \\psi^{2} r^{2} P^{4}{\\left(r \\right)} + 5 l r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} - 18 l r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + 9 l r^{4} + 6 l r^{2} P^{2}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 l r^{2} P^{2}{\\left(r \\right)} + l P^{4}{\\left(r \\right)} + 2 \\lambda \\psi^{2} r^{4} P^{2}{\\left(r \\right)} + 6 \\lambda r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 6 \\lambda r^{4} + 2 \\lambda r^{2} P^{2}{\\left(r \\right)} + 2 m \\psi^{2} r^{4} P^{2}{\\left(r \\right)} + 10 m r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} - 12 m r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + 2 m r^{2} P^{2}{\\left(r \\right)} + 12 \\mu r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 4 \\mu r^{4} - n \\psi^{2} r^{4} P^{2}{\\left(r \\right)} + n r^{4} - n r^{2} P^{2}{\\left(r \\right)}\\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(P(r), (r, 2)), (k**4*l*psi**2*r**6*P(r) - k**4*l*r**5*Derivative(P(r), r) + k**4*l*r**4*P(r) + 2*k**4*m*psi**2*r**6*P(r) + 2*k**2*l*psi**4*r**6*P(r)**3 - 2*k**2*l*psi**2*r**6*P(r)*Derivative(P(r), r)**2 - 6*k**2*l*psi**2*r**6*P(r) - 2*k**2*l*psi**2*r**5*P(r)**2*Derivative(P(r), r) + 4*k**2*l*psi**2*r**4*P(r)**3 - 2*k**2*l*r**5*Derivative(P(r), r)**3 + 6*k**2*l*r**5*Derivative(P(r), r) - 2*k**2*l*r**4*P(r)*Derivative(P(r), r)**2 - 6*k**2*l*r**4*P(r) + 2*k**2*l*r**3*P(r)**2*Derivative(P(r), r) + 2*k**2*l*r**2*P(r)**3 + 2*k**2*lambda*psi**2*r**6*P(r) - 2*k**2*lambda*r**5*Derivative(P(r), r) + 2*k**2*lambda*r**4*P(r) + 4*k**2*m*psi**4*r**6*P(r)**3 - 4*k**2*m*psi**2*r**6*P(r) + 4*k**2*m*psi**2*r**4*P(r)**3 - 2*k**2*m*r**5*Derivative(P(r), r) + 2*k**2*m*r**4*P(r)*Derivative(P(r), r)**2 + 2*k**2*m*r**4*P(r) - 2*k**2*m*r**3*P(r)**2*Derivative(P(r), r) + 4*k**2*mu*psi**2*r**6*P(r) + k**2*n*r**5*Derivative(P(r), r) - k**2*n*r**4*P(r)*Derivative(P(r), r)**2 - k**2*n*r**4*P(r) + k**2*n*r**3*P(r)**2*Derivative(P(r), r) + l*psi**6*r**6*P(r)**5 - 2*l*psi**4*r**6*P(r)**3*Derivative(P(r), r)**2 - 6*l*psi**4*r**6*P(r)**3 - l*psi**4*r**5*P(r)**4*Derivative(P(r), r) + 3*l*psi**4*r**4*P(r)**5 - 3*l*psi**2*r**6*P(r)*Derivative(P(r), r)**4 + 6*l*psi**2*r**6*P(r)*Derivative(P(r), r)**2 + 9*l*psi**2*r**6*P(r) - 2*l*psi**2*r**5*P(r)**2*Derivative(P(r), r)**3 + 6*l*psi**2*r**5*P(r)**2*Derivative(P(r), r) - 4*l*psi**2*r**4*P(r)**3*Derivative(P(r), r)**2 - 12*l*psi**2*r**4*P(r)**3 + 2*l*psi**2*r**3*P(r)**4*Derivative(P(r), r) + 3*l*psi**2*r**2*P(r)**5 - l*r**5*Derivative(P(r), r)**5 + 6*l*r**5*Derivative(P(r), r)**3 - 9*l*r**5*Derivative(P(r), r) - 3*l*r**4*P(r)*Derivative(P(r), r)**4 + 6*l*r**4*P(r)*Derivative(P(r), r)**2 + 9*l*r**4*P(r) + 2*l*r**3*P(r)**2*Derivative(P(r), r)**3 - 6*l*r**3*P(r)**2*Derivative(P(r), r) - 2*l*r**2*P(r)**3*Derivative(P(r), r)**2 - 6*l*r**2*P(r)**3 + 3*l*r*P(r)**4*Derivative(P(r), r) + l*P(r)**5 + 2*lambda*psi**4*r**6*P(r)**3 - 2*lambda*psi**2*r**6*P(r)*Derivative(P(r), r)**2 - 6*lambda*psi**2*r**6*P(r) - 2*lambda*psi**2*r**5*P(r)**2*Derivative(P(r), r) + 4*lambda*psi**2*r**4*P(r)**3 - 2*lambda*r**5*Derivative(P(r), r)**3 + 6*lambda*r**5*Derivative(P(r), r) - 2*lambda*r**4*P(r)*Derivative(P(r), r)**2 - 6*lambda*r**4*P(r) + 2*lambda*r**3*P(r)**2*Derivative(P(r), r) + 2*lambda*r**2*P(r)**3 + 2*m*psi**6*r**6*P(r)**5 - 4*m*psi**4*r**6*P(r)**3 + 6*m*psi**4*r**4*P(r)**5 - 2*m*psi**2*r**6*P(r)*Derivative(P(r), r)**2 - 2*m*psi**2*r**5*P(r)**2*Derivative(P(r), r) - 8*m*psi**2*r**4*P(r)**3 + 6*m*psi**2*r**2*P(r)**5 - 2*m*r**5*Derivative(P(r), r)**5 + 4*m*r**5*Derivative(P(r), r)**3 - 2*m*r**4*P(r)*Derivative(P(r), r)**2 + 2*m*r**3*P(r)**2*Derivative(P(r), r) - 4*m*r**2*P(r)**3 + 2*m*P(r)**5 + 4*mu*psi**4*r**6*P(r)**3 - 4*mu*psi**2*r**6*P(r) + 8*mu*psi**2*r**4*P(r)**3 - 4*mu*r**5*Derivative(P(r), r)**3 + 4*mu*r**5*Derivative(P(r), r) - 4*mu*r**4*P(r) + 4*mu*r**2*P(r)**3 + n*psi**2*r**6*P(r)*Derivative(P(r), r)**2 + n*psi**2*r**6*P(r) + n*psi**2*r**5*P(r)**2*Derivative(P(r), r) - n*r**5*Derivative(P(r), r) + n*r**4*P(r)*Derivative(P(r), r)**2 + n*r**4*P(r) - n*r**3*P(r)**2*Derivative(P(r), r))/(r**2*(k**4*l*r**4 + 2*k**2*l*psi**2*r**4*P(r)**2 + 6*k**2*l*r**4*Derivative(P(r), r)**2 - 6*k**2*l*r**4 + 2*k**2*l*r**2*P(r)**2 + 2*k**2*lambda*r**4 + 2*k**2*m*r**4 - 2*k**2*m*r**2*P(r)**2 - k**2*n*r**4 + k**2*n*r**2*P(r)**2 + l*psi**4*r**4*P(r)**4 + 6*l*psi**2*r**4*P(r)**2*Derivative(P(r), r)**2 - 6*l*psi**2*r**4*P(r)**2 + 2*l*psi**2*r**2*P(r)**4 + 5*l*r**4*Derivative(P(r), r)**4 - 18*l*r**4*Derivative(P(r), r)**2 + 9*l*r**4 + 6*l*r**2*P(r)**2*Derivative(P(r), r)**2 - 6*l*r**2*P(r)**2 + l*P(r)**4 + 2*lambda*psi**2*r**4*P(r)**2 + 6*lambda*r**4*Derivative(P(r), r)**2 - 6*lambda*r**4 + 2*lambda*r**2*P(r)**2 + 2*m*psi**2*r**4*P(r)**2 + 10*m*r**4*Derivative(P(r), r)**4 - 12*m*r**4*Derivative(P(r), r)**2 + 2*m*r**2*P(r)**2 + 12*mu*r**4*Derivative(P(r), r)**2 - 4*mu*r**4 - n*psi**2*r**4*P(r)**2 + n*r**4 - n*r**2*P(r)**2)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\left(m \\left(r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} + r^{2} \\left(\\psi^{2} P^{4}{\\left(r \\right)} + r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)}\\right)^{2}\\right) + \\left(\\psi^{2} r^{2} + 1\\right) P^{4}{\\left(r \\right)} - \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right)^{2}\\right) + r^{4} \\cdot \\left(9 l - 6 \\lambda - 4 \\mu + n\\right) + r^{2} \\left(k^{2} n P^{2}{\\left(r \\right)} - 2 \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) \\left(3 l - \\lambda + 2 m - 2 \\mu\\right)\\right) + \\left(l + 2 m\\right) \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right)^{2} - \\left(2 m \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) + r^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)}\\right) + P^{2}{\\left(r \\right)}\\right)\\right) \\frac{d}{d r} P{\\left(r \\right)}}{4 r^{4}} = 0$"
      ],
      "text/plain": [
       "Eq((m*(r**4*Derivative(P(r), r)**4 + r**2*(psi**2*P(r)**4 + r**2*(k**2 + psi**2*P(r)**2)**2) + (psi**2*r**2 + 1)*P(r)**4 - (r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)**2) + r**4*(9*l - 6*lambda - 4*mu + n) + r**2*(k**2*n*P(r)**2 - 2*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)*(3*l - lambda + 2*m - 2*mu)) + (l + 2*m)*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)**2 - (2*m*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2) + r**2*(-6*m + 4*mu + n))*(r**2*(k**2 + psi**2*P(r)**2) + P(r)**2))*Derivative(P(r), r)/(4*r**4), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import Math\n",
    "D_W5 = MySimplifyMatrix(2*dW(W5, G)*C)\n",
    "DA = D_W5*A\n",
    "for m in range(3):\n",
    "    for n in range(3):\n",
    "        DA[m, n] = DA[m, n]/h[m]/h[n]\n",
    "divD_W5 = TensorSecondRankDiv(DA, q, gamma, h)\n",
    "divD_W5 = MySimplifyMatrix(divD_W5*(A.T))\n",
    "sec_p = sym.solve(divD_W5[0], sym.diff(P, r, 2))[0]\n",
    "cond = D_W5[0, 0]\n",
    "print(\"Уравнение равновесия и граничное условие:\")\n",
    "display(sym.Eq(sym.diff(P, r, 2), sec_p))\n",
    "display(sym.Eq(cond, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.098427Z",
     "start_time": "2024-05-29T00:16:04.060248Z"
    },
    "collapsed": false,
    "id": "fSzVqVGbUE_d",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "787aa8b0-7544-45bb-9350-27e783b91473"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введём следующие соотношения для обезразмеривания уравнений:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle r = r_{1} \\rho$"
      ],
      "text/plain": [
       "Eq(r, r_1*rho)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P{\\left(r \\right)} = r_{1} \\tilde{P}{\\left(\\rho \\right)}$"
      ],
      "text/plain": [
       "Eq(P(r), r_1*Ptilde(rho))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d r} P{\\left(r \\right)} = \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(P(r), r), Derivative(Ptilde(rho), rho))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d r^{2}} P{\\left(r \\right)} = \\frac{\\frac{d^{2}}{d \\rho^{2}} \\tilde{P}{\\left(\\rho \\right)}}{r_{1}}$"
      ],
      "text/plain": [
       "Eq(Derivative(P(r), (r, 2)), Derivative(Ptilde(rho), (rho, 2))/r_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\psi = \\frac{\\tilde{\\Psi}}{r_{1}}$"
      ],
      "text/plain": [
       "Eq(psi, Psitilde/r_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho = sym.Symbol('rho', real = True, positive = True)\n",
    "Psitilde = sym.Symbol('Psitilde', real = True)\n",
    "global_assumptions.add(sym.Q.positive(rho))\n",
    "Ptilde = sym.Function('Ptilde', real = True, positive = True)(rho)\n",
    "global_assumptions.add(sym.Q.positive(Ptilde), sym.Q.positive(sym.diff(Ptilde, rho)))\n",
    "print(\"Введём следующие соотношения для обезразмеривания уравнений:\")\n",
    "r_0 = sym.Symbol(\"r_0\", real = True, positive = True)\n",
    "r_1 = sym.Symbol(\"r_1\", real = True, positive = True)\n",
    "global_assumptions.add(sym.Q.positive(r_0), sym.Q.positive(r_1))\n",
    "rho_0 = sym.Symbol(\"rho_0\", real = True, positive = True)\n",
    "rho_1 = sym.Symbol(\"rho_1\", real = True, positive = True)\n",
    "global_assumptions.add(sym.Q.positive(rho_0), sym.Q.positive(rho_1))\n",
    "P_new = Ptilde*r_1\n",
    "r_new = rho*r_1\n",
    "Psi_new = Psitilde/r_1\n",
    "diff_P_new = sym.diff(Ptilde, rho)\n",
    "diff_P_2_new = sym.diff(Ptilde, rho, 2)/r_1\n",
    "display(sym.Eq(r, r_new))\n",
    "display(sym.Eq(P, P_new))\n",
    "display(sym.Eq(sym.diff(P, r), diff_P_new))\n",
    "display(sym.Eq(sym.diff(P, r, 2), diff_P_2_new))\n",
    "display(sym.Eq(Psi, Psi_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.773986Z",
     "start_time": "2024-05-29T00:16:04.098427Z"
    },
    "collapsed": false,
    "id": "ixxwfCM_UE_d",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "215b5d0b-aaf5-4483-954b-3681edfea630"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Обезразмеренные уравнение равновесия и граничное условие:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d r^{2}} P{\\left(r \\right)} = \\frac{\\tilde{\\Psi}^{6} l r_{1}^{5} \\rho^{6} \\tilde{P}^{5}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{6} m r_{1}^{5} \\rho^{6} \\tilde{P}^{5}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{4} k^{2} l r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} + 4 \\tilde{\\Psi}^{4} k^{2} m r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{4} l r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 \\tilde{\\Psi}^{4} l r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} - \\tilde{\\Psi}^{4} l r_{1}^{5} \\rho^{5} \\tilde{P}^{4}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 3 \\tilde{\\Psi}^{4} l r_{1}^{5} \\rho^{4} \\tilde{P}^{5}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{4} \\lambda r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} - 4 \\tilde{\\Psi}^{4} m r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} + 6 \\tilde{\\Psi}^{4} m r_{1}^{5} \\rho^{4} \\tilde{P}^{5}{\\left(\\rho \\right)} + 4 \\tilde{\\Psi}^{4} \\mu r_{1}^{5} \\rho^{6} \\tilde{P}^{3}{\\left(\\rho \\right)} + \\tilde{\\Psi}^{2} k^{4} l r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} k^{4} m r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{2} k^{2} l r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 \\tilde{\\Psi}^{2} k^{2} l r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{2} k^{2} l r_{1}^{5} \\rho^{5} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 4 \\tilde{\\Psi}^{2} k^{2} l r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} k^{2} \\lambda r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} - 4 \\tilde{\\Psi}^{2} k^{2} m r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} + 4 \\tilde{\\Psi}^{2} k^{2} m r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} + 4 \\tilde{\\Psi}^{2} k^{2} \\mu r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} - 3 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} + 6 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + 9 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{5} \\tilde{P}^{2}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} + 6 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{5} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 4 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 12 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{3} \\tilde{P}^{4}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 3 \\tilde{\\Psi}^{2} l r_{1}^{5} \\rho^{2} \\tilde{P}^{5}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{2} \\lambda r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 \\tilde{\\Psi}^{2} \\lambda r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{2} \\lambda r_{1}^{5} \\rho^{5} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 4 \\tilde{\\Psi}^{2} \\lambda r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} - 2 \\tilde{\\Psi}^{2} m r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 2 \\tilde{\\Psi}^{2} m r_{1}^{5} \\rho^{5} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 8 \\tilde{\\Psi}^{2} m r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} + 6 \\tilde{\\Psi}^{2} m r_{1}^{5} \\rho^{2} \\tilde{P}^{5}{\\left(\\rho \\right)} - 4 \\tilde{\\Psi}^{2} \\mu r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} + 8 \\tilde{\\Psi}^{2} \\mu r_{1}^{5} \\rho^{4} \\tilde{P}^{3}{\\left(\\rho \\right)} + \\tilde{\\Psi}^{2} n r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + \\tilde{\\Psi}^{2} n r_{1}^{5} \\rho^{6} \\tilde{P}{\\left(\\rho \\right)} + \\tilde{\\Psi}^{2} n r_{1}^{5} \\rho^{5} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - k^{4} l r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + k^{4} l r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} - 2 k^{2} l r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} + 6 k^{2} l r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 2 k^{2} l r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 k^{2} l r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} + 2 k^{2} l r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 2 k^{2} l r_{1}^{5} \\rho^{2} \\tilde{P}^{3}{\\left(\\rho \\right)} - 2 k^{2} \\lambda r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 2 k^{2} \\lambda r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} - 2 k^{2} m r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 2 k^{2} m r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + 2 k^{2} m r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} - 2 k^{2} m r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + k^{2} n r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - k^{2} n r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - k^{2} n r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} + k^{2} n r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - l r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{5} + 6 l r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} - 9 l r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 3 l r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} + 6 l r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + 9 l r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} + 2 l r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} - 6 l r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 2 l r_{1}^{5} \\rho^{2} \\tilde{P}^{3}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 l r_{1}^{5} \\rho^{2} \\tilde{P}^{3}{\\left(\\rho \\right)} + 3 l r_{1}^{5} \\rho \\tilde{P}^{4}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + l r_{1}^{5} \\tilde{P}^{5}{\\left(\\rho \\right)} - 2 \\lambda r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} + 6 \\lambda r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 2 \\lambda r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 \\lambda r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} + 2 \\lambda r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + 2 \\lambda r_{1}^{5} \\rho^{2} \\tilde{P}^{3}{\\left(\\rho \\right)} - 2 m r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{5} + 4 m r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} - 2 m r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + 2 m r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 4 m r_{1}^{5} \\rho^{2} \\tilde{P}^{3}{\\left(\\rho \\right)} + 2 m r_{1}^{5} \\tilde{P}^{5}{\\left(\\rho \\right)} - 4 \\mu r_{1}^{5} \\rho^{5} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{3} + 4 \\mu r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} - 4 \\mu r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} + 4 \\mu r_{1}^{5} \\rho^{2} \\tilde{P}^{3}{\\left(\\rho \\right)} - n r_{1}^{5} \\rho^{5} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)} + n r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + n r_{1}^{5} \\rho^{4} \\tilde{P}{\\left(\\rho \\right)} - n r_{1}^{5} \\rho^{3} \\tilde{P}^{2}{\\left(\\rho \\right)} \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}}{r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{4} l r_{1}^{4} \\rho^{4} \\tilde{P}^{4}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} k^{2} l r_{1}^{4} \\rho^{4} \\tilde{P}^{2}{\\left(\\rho \\right)} + 6 \\tilde{\\Psi}^{2} l r_{1}^{4} \\rho^{4} \\tilde{P}^{2}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 \\tilde{\\Psi}^{2} l r_{1}^{4} \\rho^{4} \\tilde{P}^{2}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} l r_{1}^{4} \\rho^{2} \\tilde{P}^{4}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} \\lambda r_{1}^{4} \\rho^{4} \\tilde{P}^{2}{\\left(\\rho \\right)} + 2 \\tilde{\\Psi}^{2} m r_{1}^{4} \\rho^{4} \\tilde{P}^{2}{\\left(\\rho \\right)} - \\tilde{\\Psi}^{2} n r_{1}^{4} \\rho^{4} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{4} l r_{1}^{4} \\rho^{4} + 6 k^{2} l r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 k^{2} l r_{1}^{4} \\rho^{4} + 2 k^{2} l r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + 2 k^{2} \\lambda r_{1}^{4} \\rho^{4} + 2 k^{2} m r_{1}^{4} \\rho^{4} - 2 k^{2} m r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} - k^{2} n r_{1}^{4} \\rho^{4} + k^{2} n r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + 5 l r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} - 18 l r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + 9 l r_{1}^{4} \\rho^{4} + 6 l r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 l r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + l r_{1}^{4} \\tilde{P}^{4}{\\left(\\rho \\right)} + 6 \\lambda r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 6 \\lambda r_{1}^{4} \\rho^{4} + 2 \\lambda r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + 10 m r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} - 12 m r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + 2 m r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + 12 \\mu r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 4 \\mu r_{1}^{4} \\rho^{4} + n r_{1}^{4} \\rho^{4} - n r_{1}^{4} \\rho^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(P(r), (r, 2)), (Psitilde**6*l*r_1**5*rho**6*Ptilde(rho)**5 + 2*Psitilde**6*m*r_1**5*rho**6*Ptilde(rho)**5 + 2*Psitilde**4*k**2*l*r_1**5*rho**6*Ptilde(rho)**3 + 4*Psitilde**4*k**2*m*r_1**5*rho**6*Ptilde(rho)**3 - 2*Psitilde**4*l*r_1**5*rho**6*Ptilde(rho)**3*Derivative(Ptilde(rho), rho)**2 - 6*Psitilde**4*l*r_1**5*rho**6*Ptilde(rho)**3 - Psitilde**4*l*r_1**5*rho**5*Ptilde(rho)**4*Derivative(Ptilde(rho), rho) + 3*Psitilde**4*l*r_1**5*rho**4*Ptilde(rho)**5 + 2*Psitilde**4*lambda*r_1**5*rho**6*Ptilde(rho)**3 - 4*Psitilde**4*m*r_1**5*rho**6*Ptilde(rho)**3 + 6*Psitilde**4*m*r_1**5*rho**4*Ptilde(rho)**5 + 4*Psitilde**4*mu*r_1**5*rho**6*Ptilde(rho)**3 + Psitilde**2*k**4*l*r_1**5*rho**6*Ptilde(rho) + 2*Psitilde**2*k**4*m*r_1**5*rho**6*Ptilde(rho) - 2*Psitilde**2*k**2*l*r_1**5*rho**6*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 - 6*Psitilde**2*k**2*l*r_1**5*rho**6*Ptilde(rho) - 2*Psitilde**2*k**2*l*r_1**5*rho**5*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) + 4*Psitilde**2*k**2*l*r_1**5*rho**4*Ptilde(rho)**3 + 2*Psitilde**2*k**2*lambda*r_1**5*rho**6*Ptilde(rho) - 4*Psitilde**2*k**2*m*r_1**5*rho**6*Ptilde(rho) + 4*Psitilde**2*k**2*m*r_1**5*rho**4*Ptilde(rho)**3 + 4*Psitilde**2*k**2*mu*r_1**5*rho**6*Ptilde(rho) - 3*Psitilde**2*l*r_1**5*rho**6*Ptilde(rho)*Derivative(Ptilde(rho), rho)**4 + 6*Psitilde**2*l*r_1**5*rho**6*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 + 9*Psitilde**2*l*r_1**5*rho**6*Ptilde(rho) - 2*Psitilde**2*l*r_1**5*rho**5*Ptilde(rho)**2*Derivative(Ptilde(rho), rho)**3 + 6*Psitilde**2*l*r_1**5*rho**5*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) - 4*Psitilde**2*l*r_1**5*rho**4*Ptilde(rho)**3*Derivative(Ptilde(rho), rho)**2 - 12*Psitilde**2*l*r_1**5*rho**4*Ptilde(rho)**3 + 2*Psitilde**2*l*r_1**5*rho**3*Ptilde(rho)**4*Derivative(Ptilde(rho), rho) + 3*Psitilde**2*l*r_1**5*rho**2*Ptilde(rho)**5 - 2*Psitilde**2*lambda*r_1**5*rho**6*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 - 6*Psitilde**2*lambda*r_1**5*rho**6*Ptilde(rho) - 2*Psitilde**2*lambda*r_1**5*rho**5*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) + 4*Psitilde**2*lambda*r_1**5*rho**4*Ptilde(rho)**3 - 2*Psitilde**2*m*r_1**5*rho**6*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 - 2*Psitilde**2*m*r_1**5*rho**5*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) - 8*Psitilde**2*m*r_1**5*rho**4*Ptilde(rho)**3 + 6*Psitilde**2*m*r_1**5*rho**2*Ptilde(rho)**5 - 4*Psitilde**2*mu*r_1**5*rho**6*Ptilde(rho) + 8*Psitilde**2*mu*r_1**5*rho**4*Ptilde(rho)**3 + Psitilde**2*n*r_1**5*rho**6*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 + Psitilde**2*n*r_1**5*rho**6*Ptilde(rho) + Psitilde**2*n*r_1**5*rho**5*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) - k**4*l*r_1**5*rho**5*Derivative(Ptilde(rho), rho) + k**4*l*r_1**5*rho**4*Ptilde(rho) - 2*k**2*l*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**3 + 6*k**2*l*r_1**5*rho**5*Derivative(Ptilde(rho), rho) - 2*k**2*l*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 - 6*k**2*l*r_1**5*rho**4*Ptilde(rho) + 2*k**2*l*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) + 2*k**2*l*r_1**5*rho**2*Ptilde(rho)**3 - 2*k**2*lambda*r_1**5*rho**5*Derivative(Ptilde(rho), rho) + 2*k**2*lambda*r_1**5*rho**4*Ptilde(rho) - 2*k**2*m*r_1**5*rho**5*Derivative(Ptilde(rho), rho) + 2*k**2*m*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 + 2*k**2*m*r_1**5*rho**4*Ptilde(rho) - 2*k**2*m*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) + k**2*n*r_1**5*rho**5*Derivative(Ptilde(rho), rho) - k**2*n*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 - k**2*n*r_1**5*rho**4*Ptilde(rho) + k**2*n*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) - l*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**5 + 6*l*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**3 - 9*l*r_1**5*rho**5*Derivative(Ptilde(rho), rho) - 3*l*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**4 + 6*l*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 + 9*l*r_1**5*rho**4*Ptilde(rho) + 2*l*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho)**3 - 6*l*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) - 2*l*r_1**5*rho**2*Ptilde(rho)**3*Derivative(Ptilde(rho), rho)**2 - 6*l*r_1**5*rho**2*Ptilde(rho)**3 + 3*l*r_1**5*rho*Ptilde(rho)**4*Derivative(Ptilde(rho), rho) + l*r_1**5*Ptilde(rho)**5 - 2*lambda*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**3 + 6*lambda*r_1**5*rho**5*Derivative(Ptilde(rho), rho) - 2*lambda*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 - 6*lambda*r_1**5*rho**4*Ptilde(rho) + 2*lambda*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) + 2*lambda*r_1**5*rho**2*Ptilde(rho)**3 - 2*m*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**5 + 4*m*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**3 - 2*m*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 + 2*m*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho) - 4*m*r_1**5*rho**2*Ptilde(rho)**3 + 2*m*r_1**5*Ptilde(rho)**5 - 4*mu*r_1**5*rho**5*Derivative(Ptilde(rho), rho)**3 + 4*mu*r_1**5*rho**5*Derivative(Ptilde(rho), rho) - 4*mu*r_1**5*rho**4*Ptilde(rho) + 4*mu*r_1**5*rho**2*Ptilde(rho)**3 - n*r_1**5*rho**5*Derivative(Ptilde(rho), rho) + n*r_1**5*rho**4*Ptilde(rho)*Derivative(Ptilde(rho), rho)**2 + n*r_1**5*rho**4*Ptilde(rho) - n*r_1**5*rho**3*Ptilde(rho)**2*Derivative(Ptilde(rho), rho))/(r_1**2*rho**2*(Psitilde**4*l*r_1**4*rho**4*Ptilde(rho)**4 + 2*Psitilde**2*k**2*l*r_1**4*rho**4*Ptilde(rho)**2 + 6*Psitilde**2*l*r_1**4*rho**4*Ptilde(rho)**2*Derivative(Ptilde(rho), rho)**2 - 6*Psitilde**2*l*r_1**4*rho**4*Ptilde(rho)**2 + 2*Psitilde**2*l*r_1**4*rho**2*Ptilde(rho)**4 + 2*Psitilde**2*lambda*r_1**4*rho**4*Ptilde(rho)**2 + 2*Psitilde**2*m*r_1**4*rho**4*Ptilde(rho)**2 - Psitilde**2*n*r_1**4*rho**4*Ptilde(rho)**2 + k**4*l*r_1**4*rho**4 + 6*k**2*l*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**2 - 6*k**2*l*r_1**4*rho**4 + 2*k**2*l*r_1**4*rho**2*Ptilde(rho)**2 + 2*k**2*lambda*r_1**4*rho**4 + 2*k**2*m*r_1**4*rho**4 - 2*k**2*m*r_1**4*rho**2*Ptilde(rho)**2 - k**2*n*r_1**4*rho**4 + k**2*n*r_1**4*rho**2*Ptilde(rho)**2 + 5*l*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**4 - 18*l*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**2 + 9*l*r_1**4*rho**4 + 6*l*r_1**4*rho**2*Ptilde(rho)**2*Derivative(Ptilde(rho), rho)**2 - 6*l*r_1**4*rho**2*Ptilde(rho)**2 + l*r_1**4*Ptilde(rho)**4 + 6*lambda*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**2 - 6*lambda*r_1**4*rho**4 + 2*lambda*r_1**4*rho**2*Ptilde(rho)**2 + 10*m*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**4 - 12*m*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**2 + 2*m*r_1**4*rho**2*Ptilde(rho)**2 + 12*mu*r_1**4*rho**4*Derivative(Ptilde(rho), rho)**2 - 4*mu*r_1**4*rho**4 + n*r_1**4*rho**4 - n*r_1**4*rho**2*Ptilde(rho)**2)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\left(m \\left(r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} + r_{1}^{4} \\left(\\tilde{\\Psi}^{2} \\rho^{2} + 1\\right) \\tilde{P}^{4}{\\left(\\rho \\right)} + r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} r_{1}^{2} \\tilde{P}^{4}{\\left(\\rho \\right)} + r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2}\\right)^{2}\\right) - \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{4} \\rho^{4} \\cdot \\left(9 l - 6 \\lambda - 4 \\mu + n\\right) + r_{1}^{2} \\rho^{2} \\left(k^{2} n r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} - 2 \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) \\left(3 l - \\lambda + 2 m - 2 \\mu\\right)\\right) + \\left(l + 2 m\\right) \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)^{2} - \\left(2 m \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) + r_{1}^{2} \\rho^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)\\right) \\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}}{4 r_{1}^{4} \\rho^{4}} = 0$"
      ],
      "text/plain": [
       "Eq((m*(r_1**4*rho**4*Derivative(Ptilde(rho), rho)**4 + r_1**4*(Psitilde**2*rho**2 + 1)*Ptilde(rho)**4 + r_1**2*rho**2*(Psitilde**2*r_1**2*Ptilde(rho)**4 + r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2)**2) - (r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)**2) + r_1**4*rho**4*(9*l - 6*lambda - 4*mu + n) + r_1**2*rho**2*(k**2*n*r_1**2*Ptilde(rho)**2 - 2*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)*(3*l - lambda + 2*m - 2*mu)) + (l + 2*m)*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)**2 - (2*m*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2) + r_1**2*rho**2*(-6*m + 4*mu + n))*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2) + r_1**2*Ptilde(rho)**2))*Derivative(Ptilde(rho), rho)/(4*r_1**4*rho**4), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D_W5_subs = D_W5.subs(sym.diff(P, r, 2), diff_P_2_new)\n",
    "D_W5_subs = D_W5_subs.subs(sym.diff(P, r), diff_P_new)\n",
    "D_W5_subs = D_W5_subs.subs(P, P_new).subs(r, r_new).subs(Psi, Psi_new)\n",
    "sec_p_subs = sec_p.subs(sym.diff(P, r, 2), diff_P_2_new)\n",
    "sec_p_subs = sec_p_subs.subs(sym.diff(P, r), diff_P_new)\n",
    "sec_p_subs = sec_p_subs.subs(P, P_new).subs(r, r_new).subs(Psi, Psi_new)\n",
    "cond_subs = D_W5_subs[0, 0]\n",
    "print(\"Обезразмеренные уравнение равновесия и граничное условие:\")\n",
    "display(sym.Eq(sym.diff(P, r, 2), sec_p_subs))\n",
    "display(sym.Eq(cond_subs, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.800778Z",
     "start_time": "2024-05-29T00:16:04.774467Z"
    },
    "collapsed": false,
    "id": "OihjPxYlUE_e",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "9bb54d59-f96e-4a32-adbc-5f3dc14a80dd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Положим следующее:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\rho_{0} = 0.5$"
      ],
      "text/plain": [
       "Eq(rho_0, 0.5)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\rho_{1} = 1.0$"
      ],
      "text/plain": [
       "Eq(rho_1, 1.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_r_0 = 5\n",
    "val_r_1 = 10\n",
    "def get_rho(val_r):\n",
    "    return val_r/val_r_1\n",
    "print(\"Положим следующее:\")\n",
    "display(sym.Eq(rho_0, get_rho(val_r_0)))\n",
    "display(sym.Eq(rho_1, get_rho(val_r_1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.941200Z",
     "start_time": "2024-05-29T00:16:04.800778Z"
    },
    "collapsed": false,
    "id": "2QvteRd6UE_e",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "26760c4c-4788-44aa-a2e3-83b25ac54a17"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Выражения для растягивающей силы и момента кручения:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q = 2 \\pi \\int\\limits_{r_{0}}^{r_{1}} \\frac{k \\left(m \\left(r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} + r^{2} \\left(\\psi^{2} P^{4}{\\left(r \\right)} + r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)}\\right)^{2}\\right) + \\left(\\psi^{2} r^{2} + 1\\right) P^{4}{\\left(r \\right)} - \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right)^{2}\\right) + r^{4} \\cdot \\left(9 l - 6 \\lambda - 4 \\mu + n\\right) + r^{2} \\left(n P^{2}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 2 \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) \\left(3 l - \\lambda + 2 m - 2 \\mu\\right)\\right) + \\left(l + 2 m\\right) \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right)^{2} - \\left(2 m \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) + r^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\left(r^{2} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + P^{2}{\\left(r \\right)}\\right)\\right)}{4 r^{3}}\\, dr$"
      ],
      "text/plain": [
       "Eq(Q, 2*pi*Integral(k*(m*(r**4*Derivative(P(r), r)**4 + r**2*(psi**2*P(r)**4 + r**2*(k**2 + psi**2*P(r)**2)**2) + (psi**2*r**2 + 1)*P(r)**4 - (r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)**2) + r**4*(9*l - 6*lambda - 4*mu + n) + r**2*(n*P(r)**2*Derivative(P(r), r)**2 - 2*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)*(3*l - lambda + 2*m - 2*mu)) + (l + 2*m)*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)**2 - (2*m*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2) + r**2*(-6*m + 4*mu + n))*(r**2*Derivative(P(r), r)**2 + P(r)**2))/(4*r**3), (r, r_0, r_1)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle M = 2 \\pi \\int\\limits_{r_{0}}^{r_{1}} \\frac{\\psi \\left(m \\left(r^{4} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{4} + r^{2} \\left(\\psi^{2} P^{4}{\\left(r \\right)} + r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)}\\right)^{2}\\right) + \\left(\\psi^{2} r^{2} + 1\\right) P^{4}{\\left(r \\right)} - \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right)^{2}\\right) + r^{4} \\cdot \\left(9 l - 6 \\lambda - 4 \\mu + n\\right) + r^{2} \\left(n P^{2}{\\left(r \\right)} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} - 2 \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) \\left(3 l - \\lambda + 2 m - 2 \\mu\\right)\\right) + \\left(l + 2 m\\right) \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right)^{2} - \\left(2 m \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) + r^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\left(r^{2} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + P^{2}{\\left(r \\right)}\\right) + \\left(2 m \\left(r^{2} \\left(k^{2} + \\psi^{2} P^{2}{\\left(r \\right)} + \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2}\\right) + P^{2}{\\left(r \\right)}\\right) - n r^{2} \\left(\\frac{d}{d r} P{\\left(r \\right)}\\right)^{2} + r^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) P^{2}{\\left(r \\right)}\\right) P^{2}{\\left(r \\right)}}{4 r^{3}}\\, dr$"
      ],
      "text/plain": [
       "Eq(M, 2*pi*Integral(psi*(m*(r**4*Derivative(P(r), r)**4 + r**2*(psi**2*P(r)**4 + r**2*(k**2 + psi**2*P(r)**2)**2) + (psi**2*r**2 + 1)*P(r)**4 - (r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)**2) + r**4*(9*l - 6*lambda - 4*mu + n) + r**2*(n*P(r)**2*Derivative(P(r), r)**2 - 2*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)*(3*l - lambda + 2*m - 2*mu)) + (l + 2*m)*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2)**2 - (2*m*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2) + r**2*(-6*m + 4*mu + n))*(r**2*Derivative(P(r), r)**2 + P(r)**2) + (2*m*(r**2*(k**2 + psi**2*P(r)**2 + Derivative(P(r), r)**2) + P(r)**2) - n*r**2*Derivative(P(r), r)**2 + r**2*(-6*m + 4*mu + n))*P(r)**2)*P(r)**2/(4*r**3), (r, r_0, r_1)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Обезразмеренные выражения для растягивающей силы и момента кручения:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q = 2 \\pi \\int\\limits_{\\rho_{0}}^{\\rho_{1}} \\frac{k \\left(m \\left(r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} + r_{1}^{4} \\left(\\tilde{\\Psi}^{2} \\rho^{2} + 1\\right) \\tilde{P}^{4}{\\left(\\rho \\right)} + r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} r_{1}^{2} \\tilde{P}^{4}{\\left(\\rho \\right)} + r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2}\\right)^{2}\\right) - \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{4} \\rho^{4} \\cdot \\left(9 l - 6 \\lambda - 4 \\mu + n\\right) + r_{1}^{2} \\rho^{2} \\left(n r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 2 \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) \\left(3 l - \\lambda + 2 m - 2 \\mu\\right)\\right) + \\left(l + 2 m\\right) \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)^{2} - \\left(2 m \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) + r_{1}^{2} \\rho^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\left(r_{1}^{2} \\rho^{2} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)\\right)}{4 r_{1}^{2} \\rho^{3}}\\, d\\rho$"
      ],
      "text/plain": [
       "Eq(Q, 2*pi*Integral(k*(m*(r_1**4*rho**4*Derivative(Ptilde(rho), rho)**4 + r_1**4*(Psitilde**2*rho**2 + 1)*Ptilde(rho)**4 + r_1**2*rho**2*(Psitilde**2*r_1**2*Ptilde(rho)**4 + r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2)**2) - (r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)**2) + r_1**4*rho**4*(9*l - 6*lambda - 4*mu + n) + r_1**2*rho**2*(n*r_1**2*Ptilde(rho)**2*Derivative(Ptilde(rho), rho)**2 - 2*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)*(3*l - lambda + 2*m - 2*mu)) + (l + 2*m)*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)**2 - (2*m*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2) + r_1**2*rho**2*(-6*m + 4*mu + n))*(r_1**2*rho**2*Derivative(Ptilde(rho), rho)**2 + r_1**2*Ptilde(rho)**2))/(4*r_1**2*rho**3), (rho, rho_0, rho_1)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle M = 2 \\pi \\int\\limits_{\\rho_{0}}^{\\rho_{1}} \\frac{\\tilde{\\Psi} \\left(m \\left(r_{1}^{4} \\rho^{4} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{4} + r_{1}^{4} \\left(\\tilde{\\Psi}^{2} \\rho^{2} + 1\\right) \\tilde{P}^{4}{\\left(\\rho \\right)} + r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} r_{1}^{2} \\tilde{P}^{4}{\\left(\\rho \\right)} + r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2}\\right)^{2}\\right) - \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{4} \\rho^{4} \\cdot \\left(9 l - 6 \\lambda - 4 \\mu + n\\right) + r_{1}^{2} \\rho^{2} \\left(n r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} - 2 \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) \\left(3 l - \\lambda + 2 m - 2 \\mu\\right)\\right) + r_{1}^{2} \\cdot \\left(2 m \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) - n r_{1}^{2} \\rho^{2} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + r_{1}^{2} \\rho^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\tilde{P}^{2}{\\left(\\rho \\right)} + \\left(l + 2 m\\right) \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)^{2} - \\left(2 m \\left(r_{1}^{2} \\rho^{2} \\left(\\tilde{\\Psi}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)} + k^{2} + \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2}\\right) + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right) + r_{1}^{2} \\rho^{2} \\left(- 6 m + 4 \\mu + n\\right)\\right) \\left(r_{1}^{2} \\rho^{2} \\left(\\frac{d}{d \\rho} \\tilde{P}{\\left(\\rho \\right)}\\right)^{2} + r_{1}^{2} \\tilde{P}^{2}{\\left(\\rho \\right)}\\right)\\right) \\tilde{P}^{2}{\\left(\\rho \\right)}}{4 r_{1} \\rho^{3}}\\, d\\rho$"
      ],
      "text/plain": [
       "Eq(M, 2*pi*Integral(Psitilde*(m*(r_1**4*rho**4*Derivative(Ptilde(rho), rho)**4 + r_1**4*(Psitilde**2*rho**2 + 1)*Ptilde(rho)**4 + r_1**2*rho**2*(Psitilde**2*r_1**2*Ptilde(rho)**4 + r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2)**2) - (r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)**2) + r_1**4*rho**4*(9*l - 6*lambda - 4*mu + n) + r_1**2*rho**2*(n*r_1**2*Ptilde(rho)**2*Derivative(Ptilde(rho), rho)**2 - 2*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)*(3*l - lambda + 2*m - 2*mu)) + r_1**2*(2*m*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2) - n*r_1**2*rho**2*Derivative(Ptilde(rho), rho)**2 + r_1**2*rho**2*(-6*m + 4*mu + n))*Ptilde(rho)**2 + (l + 2*m)*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2)**2 - (2*m*(r_1**2*rho**2*(Psitilde**2*Ptilde(rho)**2 + k**2 + Derivative(Ptilde(rho), rho)**2) + r_1**2*Ptilde(rho)**2) + r_1**2*rho**2*(-6*m + 4*mu + n))*(r_1**2*rho**2*Derivative(Ptilde(rho), rho)**2 + r_1**2*Ptilde(rho)**2))*Ptilde(rho)**2/(4*r_1*rho**3), (rho, rho_0, rho_1)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Выражения для растягивающей силы и момента кручения:\")\n",
    "display(sym.Eq(sym.Symbol(\"Q\"), 2*sym.pi*sym.Integral(r*D_W5[2, 2], (r, r_0, r_1)), evaluate = False))\n",
    "display(sym.Eq(sym.Symbol(\"M\"), 2*sym.pi*sym.Integral(P*r*D_W5[2, 1], (r, r_0, r_1)), evaluate = False))\n",
    "Q_inner = r_new*D_W5_subs[2, 2]*sym.diff(r_new, rho)\n",
    "M_inner = P_new*r_new*D_W5_subs[2, 1]*sym.diff(r_new, rho)\n",
    "print(\"Обезразмеренные выражения для растягивающей силы и момента кручения:\")\n",
    "display(sym.Eq(sym.Symbol(\"Q\"), 2*sym.pi*sym.Integral(Q_inner, (rho, rho_0, rho_1)), evaluate = False))\n",
    "display(sym.Eq(sym.Symbol(\"M\"), 2*sym.pi*sym.Integral(M_inner, (rho, rho_0, rho_1)), evaluate = False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.956956Z",
     "start_time": "2024-05-29T00:16:04.942207Z"
    },
    "id": "GrTLRiT_UE_e"
   },
   "outputs": [],
   "source": [
    "material_infos = []\n",
    "material_infos.append({'Название': 'Сталь Rex 535 Никелесодержащая', '$\\lambda$': 0.909, '$\\mu$': 0.78, '$\\nu_1$': 3.58, '$\\nu_2$': -2.65, '$\\nu_3$': -1.82})\n",
    "material_infos.append({'Название': 'Сталь Rex 535', '$\\lambda$': 1.09, '$\\mu$': 0.818, '$\\nu_1$': -1.75, '$\\nu_2$': -2.4, '$\\nu_3$': -1.69})\n",
    "material_infos.append({'Название': 'Сталь Hecla 37', '$\\lambda$': 1.11, '$\\mu$': 0.821, '$\\nu_1$': -3.58, '$\\nu_2$': -2.82, '$\\nu_3$': -1.77})\n",
    "material_infos.append({'Название': 'Сталь Hecla 17', '$\\lambda$': 1.1, '$\\mu$': 0.82, '$\\nu_1$': -1.34, '$\\nu_2$': -2.61, '$\\nu_3$': -1.67})\n",
    "material_infos.append({'Название': 'Сталь Hecla 138A', '$\\lambda$': 1.09, '$\\mu$': 0.819, '$\\nu_1$': -3.23, '$\\nu_2$': -2.65, '$\\nu_3$': -1.77})\n",
    "material_infos.append({'Название': 'Сталь Hecla ATV', '$\\lambda$': 0.87, '$\\mu$': 0.716, '$\\nu_1$': 0.34, '$\\nu_2$': -5.52, '$\\nu_3$': -1.0})\n",
    "material_infos.append({'Название': 'Сталь 35ХГСА', '$\\lambda$': 1.1, '$\\mu$': 0.804, '$\\nu_1$': -1.9, '$\\nu_2$': -2.3, '$\\nu_3$': -2.01})\n",
    "material_infos.append({'Название': 'Сталь 50ХГСМ2Ф', '$\\lambda$': 1.129, '$\\mu$': 0.803, '$\\nu_1$': -2.8, '$\\nu_2$': -2.7, '$\\nu_3$': -1.87})\n",
    "material_infos.append({'Название': 'B 53 S', '$\\lambda$': 0.58, '$\\mu$': 0.26, '$\\nu_1$': -2.49, '$\\nu_2$': -0.99, '$\\nu_3$': -0.6})\n",
    "material_infos.append({'Название': 'D 54 S', '$\\lambda$': 0.491, '$\\mu$': 0.26, '$\\nu_1$': -3.79, '$\\nu_2$': -1.98, '$\\nu_3$': -0.8})\n",
    "material_infos.append({'Название': 'БрОФ 65-0,15', '$\\lambda$': 1.133, '$\\mu$': 0.417, '$\\nu_1$': -4.9, '$\\nu_2$': -1.67, '$\\nu_3$': -0.5})\n",
    "material_infos.append({'Название': 'Бронза бериллиевая', '$\\lambda$': 1.042, '$\\mu$': 0.49, '$\\nu_1$': -4.0, '$\\nu_2$': -1.7, '$\\nu_3$': -0.6})\n",
    "material_infos.append({'Название': 'Медь', '$\\lambda$': 1.07, '$\\mu$': 0.477, '$\\nu_1$': -5.6, '$\\nu_2$': 1.72, '$\\nu_3$': -3.98})\n",
    "material_infos.append({'Название': 'Магний', '$\\lambda$': 0.259, '$\\mu$': 0.166, '$\\nu_1$': -0.654, '$\\nu_2$': -0.574, '$\\nu_3$': -0.421})\n",
    "material_infos.append({'Название': 'Железо Армко', '$\\lambda$': 1.1, '$\\mu$': 0.82, '$\\nu_1$': 2.6, '$\\nu_2$': -4.8, '$\\nu_3$': -2.8})\n",
    "material_infos.append({'Название': 'Молибден спечённый из порошка 99.9% чистоты', '$\\lambda$': 1.57, '$\\mu$': 1.1, '$\\nu_1$': -0.51, '$\\nu_2$': -2.83, '$\\nu_3$': -0.93})\n",
    "material_infos.append({'Название': 'Молибден рекристаллизованный', '$\\lambda$': 1.78, '$\\mu$': 1.24, '$\\nu_1$': 1.94, '$\\nu_2$': -3.98, '$\\nu_3$': -2.27})\n",
    "material_infos.append({'Название': 'Вольфрам спечённый из порошка 99.9% чистоты', '$\\lambda$': 0.75, '$\\mu$': 0.73, '$\\nu_1$': -2.15, '$\\nu_2$': -1.43, '$\\nu_3$': -1.24})\n",
    "material_infos.append({'Название': 'Вольфрам рекристаллизованный', '$\\lambda$': 1.63, '$\\mu$': 1.37, '$\\nu_1$': -4.29, '$\\nu_2$': -2.58, '$\\nu_3$': -2.67})\n",
    "material_infos.append({'Название': 'Оргстекло', '$\\lambda$': 0.39, '$\\mu$': 0.186, '$\\nu_1$': -0.078, '$\\nu_2$': -0.07, '$\\nu_3$': 0.047})\n",
    "material_infos.append({'Название': 'Плавленный кварц', '$\\lambda$': 0.15872, '$\\mu$': 0.31261, '$\\nu_1$': 0.54, '$\\nu_2$': 0.93, '$\\nu_3$': -0.11})\n",
    "material_infos.append({'Название': 'Стекло (пирекс)', '$\\lambda$': 0.1353, '$\\mu$': 0.275, '$\\nu_1$': 2.6, '$\\nu_2$': -1.68, '$\\nu_3$': 1.05})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.974770Z",
     "start_time": "2024-05-29T00:16:04.959957Z"
    },
    "id": "tnNvAzdfUE_f"
   },
   "outputs": [],
   "source": [
    "def getFirstExtremaIndex(arr):\n",
    "    '''\n",
    "    Функция, возвращающая индекс самого первого экстремума в массиве или None, если экстремума нет.\n",
    "    Работает только для массивов из Numpy.\n",
    "    '''\n",
    "    if not isinstance(arr, np.ndarray):\n",
    "        return None\n",
    "    if arr.size < 1 or np.isnan(arr).all():\n",
    "        return None\n",
    "    min_indexes = argrelextrema(arr, np.less)[0]\n",
    "    max_indexes = argrelextrema(arr, np.greater)[0]\n",
    "    extrema_indexes = np.hstack([min_indexes, max_indexes])\n",
    "    if extrema_indexes.size > 0:\n",
    "        return np.min(extrema_indexes)\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:04.995273Z",
     "start_time": "2024-05-29T00:16:04.975776Z"
    }
   },
   "outputs": [],
   "source": [
    "def display_material_plots(val_r_0, val_r_1, val_mu, val_lambda, val_l, val_m, val_n, file_prefix = \"\", val_Psitilde_step = 0.0001, val_k_step = 0.001):\n",
    "    val_rho_0 = get_rho(val_r_0)\n",
    "    val_rho_1 = get_rho(val_r_1)\n",
    "    lmbd_sec_p = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], sec_p_subs.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    lmbd_cond = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], cond_subs.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    lmbd_Q_inner = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], Q_inner.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    lmbd_M_inner = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], M_inner.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    val_k_range = np.array([])\n",
    "    res_Q_range = np.array([])\n",
    "    val_k = 1.0\n",
    "    i = None\n",
    "    while i is None:\n",
    "        val_k_range = np.append(val_k_range, val_k)\n",
    "        res_Q_range = np.append(res_Q_range, surface_simpson(val_rho_0, val_rho_1, val_k, 0.0, lmbd_sec_p, lmbd_cond, lmbd_Q_inner))\n",
    "        i = getFirstExtremaIndex(res_Q_range)\n",
    "        val_k += val_k_step\n",
    "    plt.figure() #График Q(k, 0).\n",
    "    plt.plot(val_k_range[:i+1], res_Q_range[:i+1])\n",
    "    plt.scatter(val_k_range[i], res_Q_range[i])\n",
    "    #if res_Q_range[i+1] > res_Q_range[i]: #Локальный минимум.\n",
    "        #plt.annotate(f\"({val_k_range[i]}, {res_Q_range[i]})\", (val_k_range[i], res_Q_range[i]), textcoords = \"offset points\", xytext = (0.0, -10.0), ha = \"center\")\n",
    "    #else: #Локальный максимум.\n",
    "        #plt.annotate(f\"({val_k_range[i]}, {res_Q_range[i]})\", (val_k_range[i], res_Q_range[i]), textcoords = \"offset points\", xytext = (0.0, 10.0), ha = \"center\")\n",
    "    plt.xlabel(\"$\"+sym.printing.latex(k)+\"$\")\n",
    "    plt.ylabel(\"$Q$\")\n",
    "    plt.title(\"$Q(\"+sym.printing.latex(k)+\",0)$\")\n",
    "    plt.grid(True)\n",
    "    if file_prefix != \"\":\n",
    "        plt.savefig(file_prefix+\"_plot_Q_k_0.svg\")\n",
    "    plt.show()\n",
    "    val_Psitilde_range = np.array([])\n",
    "    res_Q_range = np.array([])\n",
    "    val_Psitilde = 0.0\n",
    "    i = None\n",
    "    while i is None:\n",
    "        val_Psitilde_range = np.append(val_Psitilde_range, val_Psitilde)\n",
    "        res_Q_range = np.append(res_Q_range, surface_simpson(val_rho_0, val_rho_1, 1.0, val_Psitilde, lmbd_sec_p, lmbd_cond, lmbd_Q_inner))\n",
    "        i = getFirstExtremaIndex(res_Q_range)\n",
    "        val_Psitilde += val_Psitilde_step\n",
    "    plt.figure() #График Q(1, Psitilde).\n",
    "    plt.plot(val_Psitilde_range[:i+1], res_Q_range[:i+1])\n",
    "    plt.scatter(val_Psitilde_range[i], res_Q_range[i])\n",
    "    #if res_Q_range[i+1] > res_Q_range[i]: #Локальный минимум.\n",
    "        #plt.annotate(f\"({val_Psitilde_range[i]}, {res_Q_range[i]})\", (val_Psitilde_range[i], res_Q_range[i]), textcoords = \"offset points\", xytext = (0.0, -10.0), ha = \"center\")\n",
    "    #else: #Локальный максимум.\n",
    "        #plt.annotate(f\"({val_Psitilde_range[i]}, {res_Q_range[i]})\", (val_Psitilde_range[i], res_Q_range[i]), textcoords = \"offset points\", xytext = (0.0, 10.0), ha = \"center\")\n",
    "    plt.xlabel(\"$\"+sym.printing.latex(Psitilde)+\"$\")\n",
    "    plt.ylabel(\"$Q$\")\n",
    "    plt.title(\"$Q(1,\"+sym.printing.latex(Psitilde)+\")$\")\n",
    "    plt.grid(True)\n",
    "    if file_prefix != \"\":\n",
    "        plt.savefig(file_prefix+\"_plot_Q_1_Psitilde.svg\")\n",
    "    plt.show()\n",
    "    val_Psitilde_range = np.array([])\n",
    "    res_M_range = np.array([])\n",
    "    root_k_range = np.array([])\n",
    "    val_Psitilde = 0.0\n",
    "    i = None\n",
    "    while i is None:\n",
    "        val_Psitilde_range = np.append(val_Psitilde_range, val_Psitilde)\n",
    "        root_k = Solve_Q_Psi(val_rho_0, val_rho_1, val_Psitilde, lmbd_sec_p, lmbd_cond, lmbd_Q_inner, 1.0)\n",
    "        root_k_range = np.append(root_k_range, root_k)\n",
    "        res_M_range = np.append(res_M_range, surface_simpson(val_rho_0, val_rho_1, root_k, val_Psitilde, lmbd_sec_p, lmbd_cond, lmbd_M_inner))\n",
    "        i = getFirstExtremaIndex(res_M_range)\n",
    "        val_Psitilde += val_Psitilde_step\n",
    "    plt.figure() #График k(Psitilde).\n",
    "    plt.plot(val_Psitilde_range[:i+1], root_k_range[:i+1])\n",
    "    plt.scatter(val_Psitilde_range[i], root_k_range[i])\n",
    "    #if res_M_range[i+1] > res_M_range[i]: #Локальный минимум.\n",
    "        #plt.annotate(f\"({val_Psitilde_range[i]}, {root_k_range[i]})\", (val_Psitilde_range[i], root_k_range[i]), textcoords = \"offset points\", xytext = (0.0, -10.0), ha = \"center\")\n",
    "    #else: #Локальный максимум.\n",
    "        #plt.annotate(f\"({val_Psitilde_range[i]}, {root_k_range[i]})\", (val_Psitilde_range[i], root_k_range[i]), textcoords = \"offset points\", xytext = (0.0, 10.0), ha = \"center\")\n",
    "    plt.xlabel(\"$\"+sym.printing.latex(Psitilde)+\"$\")\n",
    "    plt.ylabel(\"k\")\n",
    "    plt.title(\"$Q(k,\"+sym.printing.latex(Psitilde)+\")=0$\")\n",
    "    plt.grid(True)\n",
    "    if file_prefix != \"\":\n",
    "        plt.savefig(file_prefix+\"_plot_k_Psitilde.svg\")\n",
    "    plt.figure() #График M(Psitilde).\n",
    "    plt.plot(val_Psitilde_range[:i+1], res_M_range[:i+1])\n",
    "    plt.scatter(val_Psitilde_range[i], res_M_range[i])\n",
    "    #if res_M_range[i+1] > res_M_range[i]: #Локальный минимум.\n",
    "        #plt.annotate(f\"({val_Psitilde_range[i]}, {res_M_range[i]})\", (val_Psitilde_range[i], res_M_range[i]), textcoords = \"offset points\", xytext = (0.0, -10.0), ha = \"center\")\n",
    "    #else: #Локальный максимум.\n",
    "        #plt.annotate(f\"({val_Psitilde_range[i]}, {res_M_range[i]})\", (val_Psitilde_range[i], res_M_range[i]), textcoords = \"offset points\", xytext = (0.0, 10.0), ha = \"center\")\n",
    "    plt.xlabel(\"$\"+sym.printing.latex(Psitilde)+\"$\")\n",
    "    plt.ylabel(\"$M$\")\n",
    "    plt.title(\"$M(\"+sym.printing.latex(Psitilde)+\")$\")\n",
    "    plt.grid(True)\n",
    "    if file_prefix != \"\":\n",
    "        plt.savefig(file_prefix+\"_plot_M_Psitilde.svg\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:05.004564Z",
     "start_time": "2024-05-29T00:16:04.995273Z"
    }
   },
   "outputs": [],
   "source": [
    "def display_materials_plots(material_infos, val_r_0, val_r_1):\n",
    "    for i, material_info in enumerate(material_infos):\n",
    "        val_mu = material_info[\"$\\mu$\"]\n",
    "        val_lambda = material_info[\"$\\lambda$\"]\n",
    "        val_nu_1 = material_info[\"$\\nu_1$\"]\n",
    "        val_nu_2 = material_info[\"$\\nu_2$\"]\n",
    "        val_nu_3 = material_info[\"$\\nu_3$\"]\n",
    "        val_l = 0.5*val_nu_1+val_nu_2\n",
    "        val_m = val_nu_2+2*val_nu_3\n",
    "        val_n = 4*val_nu_3\n",
    "        display(pd.DataFrame([material_info]))\n",
    "        display_material_plots(val_r_0, val_r_1, val_mu, val_lambda, val_l, val_m, val_n, \"material\"+str(i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Сталь Rex 535 Никелесодержащая</td>\n",
       "      <td>0.909</td>\n",
       "      <td>0.78</td>\n",
       "      <td>3.58</td>\n",
       "      <td>-2.65</td>\n",
       "      <td>-1.82</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Название  $\\lambda$  $\\mu$  $\\nu_1$  $\\nu_2$  $\\nu_3$\n",
       "0  Сталь Rex 535 Никелесодержащая      0.909   0.78     3.58    -2.65    -1.82"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_materials_plots(material_infos[:1], val_r_0, val_r_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:05.019512Z",
     "start_time": "2024-05-29T00:16:05.004564Z"
    },
    "id": "0VlLjgu6UE_g"
   },
   "outputs": [],
   "source": [
    "def get_material_M_data(val_r_0, val_r_1, val_Psitilde_min, val_Psitilde_max, val_mu, val_lambda, val_l, val_m, val_n, list_len = 100):\n",
    "    val_rho_0 = get_rho(val_r_0)\n",
    "    val_rho_1 = get_rho(val_r_1)\n",
    "    lmbd_sec_p = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], sec_p_subs.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    lmbd_cond = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], cond_subs.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    lmbd_Q_inner = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], Q_inner.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    lmbd_M_inner = sym.lambdify([k, Psitilde, rho, Ptilde, sym.diff(Ptilde, rho)], M_inner.subs(mu, val_mu).subs(lambdas, val_lambda).subs(ls, val_l).subs(ms, val_m).subs(ns, val_n).subs(r_1, val_r_1), \"numpy\")\n",
    "    val_Psitilde_range = np.array([])\n",
    "    root_k_range = np.array([])\n",
    "    res_M_range = np.array([])\n",
    "    root_k = 1.0 #Начальное приближение параметра k.\n",
    "    for val_Psitilde in np.linspace(val_Psitilde_min, val_Psitilde_max, list_len):\n",
    "        root_k = Solve_Q_Psi(val_rho_0, val_rho_1, val_Psitilde, lmbd_sec_p, lmbd_cond, lmbd_Q_inner, root_k) #Для каждого следующего вызова функции подставляем предыдущее найденное значение k.\n",
    "        res_M = surface_simpson(val_rho_0, val_rho_1, root_k, val_Psitilde, lmbd_sec_p, lmbd_cond, lmbd_M_inner, list_len)\n",
    "        val_Psitilde_range = np.append(val_Psitilde_range, val_Psitilde)\n",
    "        root_k_range = np.append(root_k_range, root_k)\n",
    "        res_M_range = np.append(res_M_range, res_M)\n",
    "    return val_Psitilde_range, root_k_range, res_M_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:05.046893Z",
     "start_time": "2024-05-29T00:16:05.020533Z"
    },
    "id": "z2euC2UzUE_g"
   },
   "outputs": [],
   "source": [
    "def get_materials_M_data(material_infos, val_r_0, val_r_1, val_Psitilde_min, val_Psitilde_max, list_len = 100, display_data = False):\n",
    "    for material_info in material_infos:\n",
    "        val_mu = material_info[\"$\\mu$\"]\n",
    "        val_lambda = material_info[\"$\\lambda$\"]\n",
    "        val_nu_1 = material_info[\"$\\nu_1$\"]\n",
    "        val_nu_2 = material_info[\"$\\nu_2$\"]\n",
    "        val_nu_3 = material_info[\"$\\nu_3$\"]\n",
    "        val_l = 0.5*val_nu_1+val_nu_2\n",
    "        val_m = val_nu_2+2*val_nu_3\n",
    "        val_n = 4*val_nu_3\n",
    "        val_Psitilde_range, root_k_range, res_M_range = get_material_M_data(val_r_0, val_r_1, val_Psitilde_min, val_Psitilde_max, val_mu, val_lambda, val_l, val_m, val_n, list_len)\n",
    "        if display_data:\n",
    "            if \"Название\" in material_info:\n",
    "                print(\"Название материала: \"+material_info[\"Название\"]+\".\")\n",
    "            display(sym.Eq(mu, val_mu, evaluate = False))\n",
    "            display(sym.Eq(lambdas, val_lambda, evaluate = False))\n",
    "            display(sym.Eq(sym.Symbol(\"l\"), val_l, evaluate = False))\n",
    "            display(sym.Eq(sym.Symbol(\"m\"), val_m, evaluate = False))\n",
    "            display(sym.Eq(sym.Symbol(\"n\"), val_n, evaluate = False))\n",
    "            plt.figure()\n",
    "            plt.plot(val_Psitilde_range, root_k_range)\n",
    "            plt.xlabel(\"$\"+sym.printing.latex(Psitilde)+\"$\")\n",
    "            plt.ylabel(\"$\"+sym.printing.latex(k)+\"$\")\n",
    "            plt.title(\"$Q(\"+sym.printing.latex(k)+\",\"+sym.printing.latex(Psitilde)+\")=0$\")\n",
    "            plt.grid(True)\n",
    "            plt.show()\n",
    "            plt.figure()\n",
    "            plt.plot(val_Psitilde_range, res_M_range)\n",
    "            plt.xlabel(\"$\"+sym.printing.latex(Psitilde)+\"$\")\n",
    "            plt.ylabel(\"$M$\")\n",
    "            plt.title(\"$M(\"+sym.printing.latex(Psitilde)+\")$\")\n",
    "            plt.grid(True)\n",
    "            plt.show()\n",
    "        material_info.update({\"$k$\": root_k_range})\n",
    "        material_info.update({\"$M$\": res_M_range})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:05.076404Z",
     "start_time": "2024-05-29T00:16:05.048048Z"
    },
    "collapsed": false,
    "id": "e8mOO-PUUE_h",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "158d4325-ae75-458f-f491-510b6f8b7e97"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.0 \\leq \\tilde{\\Psi} \\leq 0.15707963267949$"
      ],
      "text/plain": [
       "0.0 <= (Psitilde <= 0.15707963267949)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_Psitilde_min = 0.0\n",
    "val_Psitilde_max = 0.05*float(sym.pi)\n",
    "display(sym.Le(val_Psitilde_min, sym.Le(Psitilde, val_Psitilde_max, evaluate = False), evaluate = False))\n",
    "list_len = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:05.124696Z",
     "start_time": "2024-05-29T00:16:05.076404Z"
    },
    "collapsed": false,
    "id": "7DfxXEoiUE_i",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "9b61b14c-e51e-4e74-f601-e17789086393"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$k$</th>\n",
       "      <th>$M$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.78000</td>\n",
       "      <td>0.90900</td>\n",
       "      <td>3.580</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-1.820</td>\n",
       "      <td>[1.0, 1.0000465707803576, 1.0001864209507842, ...</td>\n",
       "      <td>[0.0, 9.492151199410573, 18.959675285731205, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.81800</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>-1.750</td>\n",
       "      <td>-2.400</td>\n",
       "      <td>-1.690</td>\n",
       "      <td>[1.0, 1.0000329574705091, 1.0001320427859057, ...</td>\n",
       "      <td>[0.0, 9.955446066092604, 19.890213939644912, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.82100</td>\n",
       "      <td>1.11000</td>\n",
       "      <td>-3.580</td>\n",
       "      <td>-2.820</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>[1.0000000000000007, 1.0000387834110345, 1.000...</td>\n",
       "      <td>[0.0, 9.991409453127538, 19.958767881098407, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>-1.340</td>\n",
       "      <td>-2.610</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>[1.0000000000000004, 1.0000346144909171, 1.000...</td>\n",
       "      <td>[0.0, 9.979620350385224, 19.937511537266836, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.81900</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>-3.230</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>[0.9999999999999984, 1.000037498155892, 1.0001...</td>\n",
       "      <td>[0.0, 9.96722163572521, 19.911365229868075, 29...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.71600</td>\n",
       "      <td>0.87000</td>\n",
       "      <td>0.340</td>\n",
       "      <td>-5.520</td>\n",
       "      <td>-1.000</td>\n",
       "      <td>[1.0, 1.000073251822272, 1.0002939934037645, 1...</td>\n",
       "      <td>[0.0, 8.710288433946381, 17.379706947443864, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.80400</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>-1.900</td>\n",
       "      <td>-2.300</td>\n",
       "      <td>-2.010</td>\n",
       "      <td>[0.9999999999999988, 1.0000389954627618, 1.000...</td>\n",
       "      <td>[0.0, 9.784495213902536, 19.545271661747005, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.80300</td>\n",
       "      <td>1.12900</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>-2.700</td>\n",
       "      <td>-1.870</td>\n",
       "      <td>[1.0, 1.000039875603291, 1.0001597369185058, 1...</td>\n",
       "      <td>[0.0, 9.772199326175482, 19.519958774911977, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.58000</td>\n",
       "      <td>-2.490</td>\n",
       "      <td>-0.990</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>[1.0, 1.0000300322099496, 1.0001203483993826, ...</td>\n",
       "      <td>[0.0, 3.164178317714649, 6.320916031284339, 9....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.49100</td>\n",
       "      <td>-3.790</td>\n",
       "      <td>-1.980</td>\n",
       "      <td>-0.800</td>\n",
       "      <td>[0.9999999999999991, 1.0000732378652395, 1.000...</td>\n",
       "      <td>[0.0, 3.1623908592296455, 6.306577550839029, 9...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.41700</td>\n",
       "      <td>1.13300</td>\n",
       "      <td>-4.900</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>-0.500</td>\n",
       "      <td>[0.9999999999999996, 1.0000089885821861, 1.000...</td>\n",
       "      <td>[0.0, 5.075724016896612, 10.144732216471288, 1...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.49000</td>\n",
       "      <td>1.04200</td>\n",
       "      <td>-4.000</td>\n",
       "      <td>-1.700</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>[0.9999999999999988, 1.0000114885827023, 1.000...</td>\n",
       "      <td>[0.0, 5.964283613780426, 11.92069721384328, 17...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.47700</td>\n",
       "      <td>1.07000</td>\n",
       "      <td>-5.600</td>\n",
       "      <td>1.720</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>[1.0000000000000002, 1.0000849928585882, 1.000...</td>\n",
       "      <td>[0.0, 5.797147375364796, 11.533050500294019, 1...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.16600</td>\n",
       "      <td>0.25900</td>\n",
       "      <td>-0.654</td>\n",
       "      <td>-0.574</td>\n",
       "      <td>-0.421</td>\n",
       "      <td>[1.0, 1.0000410410713385, 1.0001644625472323, ...</td>\n",
       "      <td>[0.0, 2.0200931201265457, 4.034756632934332, 6...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-4.800</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>[1.0, 1.0000836174928014, 1.0003353095594008, ...</td>\n",
       "      <td>[0.0, 9.975033599399309, 19.900631191855485, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.57000</td>\n",
       "      <td>-0.510</td>\n",
       "      <td>-2.830</td>\n",
       "      <td>-0.930</td>\n",
       "      <td>[1.0000000000000004, 1.000006999609711, 1.0000...</td>\n",
       "      <td>[0.0, 13.390022805052995, 26.767273293221844, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.24000</td>\n",
       "      <td>1.78000</td>\n",
       "      <td>1.940</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>-2.270</td>\n",
       "      <td>[0.9999999999999994, 1.0000293501141375, 1.000...</td>\n",
       "      <td>[0.0, 15.091633478559242, 30.153416019909546, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.73000</td>\n",
       "      <td>0.75000</td>\n",
       "      <td>-2.150</td>\n",
       "      <td>-1.430</td>\n",
       "      <td>-1.240</td>\n",
       "      <td>[1.0, 1.0000227829944643, 1.0000912416662069, ...</td>\n",
       "      <td>[0.0, 8.885409930932605, 17.75816497345162, 26...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.37000</td>\n",
       "      <td>1.63000</td>\n",
       "      <td>-4.290</td>\n",
       "      <td>-2.580</td>\n",
       "      <td>-2.670</td>\n",
       "      <td>[1.0, 1.000023187390938, 1.000092880539445, 1....</td>\n",
       "      <td>[0.0, 16.675104682855505, 33.32493354713604, 4...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.18600</td>\n",
       "      <td>0.39000</td>\n",
       "      <td>-0.078</td>\n",
       "      <td>-0.070</td>\n",
       "      <td>0.047</td>\n",
       "      <td>[1.0, 0.9999685575547786, 0.9998741953309627, ...</td>\n",
       "      <td>[0.0, 2.2647406237665675, 4.530979416872862, 6...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.31261</td>\n",
       "      <td>0.15872</td>\n",
       "      <td>0.540</td>\n",
       "      <td>0.930</td>\n",
       "      <td>-0.110</td>\n",
       "      <td>[1.0000000000000002, 0.9999061272259595, 0.999...</td>\n",
       "      <td>[0.0, 3.8119962202893896, 7.658616614144974, 1...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.27500</td>\n",
       "      <td>0.13530</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-1.680</td>\n",
       "      <td>1.050</td>\n",
       "      <td>[0.9999999999999991, 1.0000322578450158, 1.000...</td>\n",
       "      <td>[0.0, 3.337415054600703, 6.613263863309272, 9....</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$  $\\nu_1$  $\\nu_2$  $\\nu_3$  \\\n",
       "0   0.78000    0.90900    3.580   -2.650   -1.820   \n",
       "1   0.81800    1.09000   -1.750   -2.400   -1.690   \n",
       "2   0.82100    1.11000   -3.580   -2.820   -1.770   \n",
       "3   0.82000    1.10000   -1.340   -2.610   -1.670   \n",
       "4   0.81900    1.09000   -3.230   -2.650   -1.770   \n",
       "5   0.71600    0.87000    0.340   -5.520   -1.000   \n",
       "6   0.80400    1.10000   -1.900   -2.300   -2.010   \n",
       "7   0.80300    1.12900   -2.800   -2.700   -1.870   \n",
       "8   0.26000    0.58000   -2.490   -0.990   -0.600   \n",
       "9   0.26000    0.49100   -3.790   -1.980   -0.800   \n",
       "10  0.41700    1.13300   -4.900   -1.670   -0.500   \n",
       "11  0.49000    1.04200   -4.000   -1.700   -0.600   \n",
       "12  0.47700    1.07000   -5.600    1.720   -3.980   \n",
       "13  0.16600    0.25900   -0.654   -0.574   -0.421   \n",
       "14  0.82000    1.10000    2.600   -4.800   -2.800   \n",
       "15  1.10000    1.57000   -0.510   -2.830   -0.930   \n",
       "16  1.24000    1.78000    1.940   -3.980   -2.270   \n",
       "17  0.73000    0.75000   -2.150   -1.430   -1.240   \n",
       "18  1.37000    1.63000   -4.290   -2.580   -2.670   \n",
       "19  0.18600    0.39000   -0.078   -0.070    0.047   \n",
       "20  0.31261    0.15872    0.540    0.930   -0.110   \n",
       "21  0.27500    0.13530    2.600   -1.680    1.050   \n",
       "\n",
       "                                                  $k$  \\\n",
       "0   [1.0, 1.0000465707803576, 1.0001864209507842, ...   \n",
       "1   [1.0, 1.0000329574705091, 1.0001320427859057, ...   \n",
       "2   [1.0000000000000007, 1.0000387834110345, 1.000...   \n",
       "3   [1.0000000000000004, 1.0000346144909171, 1.000...   \n",
       "4   [0.9999999999999984, 1.000037498155892, 1.0001...   \n",
       "5   [1.0, 1.000073251822272, 1.0002939934037645, 1...   \n",
       "6   [0.9999999999999988, 1.0000389954627618, 1.000...   \n",
       "7   [1.0, 1.000039875603291, 1.0001597369185058, 1...   \n",
       "8   [1.0, 1.0000300322099496, 1.0001203483993826, ...   \n",
       "9   [0.9999999999999991, 1.0000732378652395, 1.000...   \n",
       "10  [0.9999999999999996, 1.0000089885821861, 1.000...   \n",
       "11  [0.9999999999999988, 1.0000114885827023, 1.000...   \n",
       "12  [1.0000000000000002, 1.0000849928585882, 1.000...   \n",
       "13  [1.0, 1.0000410410713385, 1.0001644625472323, ...   \n",
       "14  [1.0, 1.0000836174928014, 1.0003353095594008, ...   \n",
       "15  [1.0000000000000004, 1.000006999609711, 1.0000...   \n",
       "16  [0.9999999999999994, 1.0000293501141375, 1.000...   \n",
       "17  [1.0, 1.0000227829944643, 1.0000912416662069, ...   \n",
       "18  [1.0, 1.000023187390938, 1.000092880539445, 1....   \n",
       "19  [1.0, 0.9999685575547786, 0.9998741953309627, ...   \n",
       "20  [1.0000000000000002, 0.9999061272259595, 0.999...   \n",
       "21  [0.9999999999999991, 1.0000322578450158, 1.000...   \n",
       "\n",
       "                                                  $M$  \n",
       "0   [0.0, 9.492151199410573, 18.959675285731205, 2...  \n",
       "1   [0.0, 9.955446066092604, 19.890213939644912, 2...  \n",
       "2   [0.0, 9.991409453127538, 19.958767881098407, 2...  \n",
       "3   [0.0, 9.979620350385224, 19.937511537266836, 2...  \n",
       "4   [0.0, 9.96722163572521, 19.911365229868075, 29...  \n",
       "5   [0.0, 8.710288433946381, 17.379706947443864, 2...  \n",
       "6   [0.0, 9.784495213902536, 19.545271661747005, 2...  \n",
       "7   [0.0, 9.772199326175482, 19.519958774911977, 2...  \n",
       "8   [0.0, 3.164178317714649, 6.320916031284339, 9....  \n",
       "9   [0.0, 3.1623908592296455, 6.306577550839029, 9...  \n",
       "10  [0.0, 5.075724016896612, 10.144732216471288, 1...  \n",
       "11  [0.0, 5.964283613780426, 11.92069721384328, 17...  \n",
       "12  [0.0, 5.797147375364796, 11.533050500294019, 1...  \n",
       "13  [0.0, 2.0200931201265457, 4.034756632934332, 6...  \n",
       "14  [0.0, 9.975033599399309, 19.900631191855485, 2...  \n",
       "15  [0.0, 13.390022805052995, 26.767273293221844, ...  \n",
       "16  [0.0, 15.091633478559242, 30.153416019909546, ...  \n",
       "17  [0.0, 8.885409930932605, 17.75816497345162, 26...  \n",
       "18  [0.0, 16.675104682855505, 33.32493354713604, 4...  \n",
       "19  [0.0, 2.2647406237665675, 4.530979416872862, 6...  \n",
       "20  [0.0, 3.8119962202893896, 7.658616614144974, 1...  \n",
       "21  [0.0, 3.337415054600703, 6.613263863309272, 9....  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_data_file_name = \"Datasets/material_results_M_test_0.05Pi\"\n",
    "if os.path.isfile(test_data_file_name+\".pickle\"):\n",
    "    df_test = pd.read_pickle(test_data_file_name+\".pickle\")\n",
    "elif os.path.isfile(test_data_file_name+\".feather\"):\n",
    "    df_test = pd.read_feather(test_data_file_name+\".feather\")\n",
    "elif os.path.isfile(test_data_file_name+\".csv\"):\n",
    "    df_test = pd.read_csv(test_data_file_name+\".csv\", encoding = \"utf-8-sig\")\n",
    "    if \"Unnamed: 0\" in df_test.columns:\n",
    "        df_test = df_test.drop(columns = \"Unnamed: 0\")\n",
    "    df_test[df_test.columns[5]] = df_test[df_test.columns[5]].apply(lambda s: np.fromstring(s[1:-1], dtype = np.float64, sep = \" \"))\n",
    "    df_test[df_test.columns[6]] = df_test[df_test.columns[6]].apply(lambda s: np.fromstring(s[1:-1], dtype = np.float64, sep = \" \"))\n",
    "else:\n",
    "    from tqdm import tqdm\n",
    "    test_data = []\n",
    "    for material_info in material_infos:\n",
    "        material_data = {}\n",
    "        material_data.update({\"$\\mu$\": material_info[\"$\\mu$\"]})\n",
    "        material_data.update({\"$\\lambda$\": material_info[\"$\\lambda$\"]})\n",
    "        material_data.update({\"$\\nu_1$\": material_info[\"$\\nu_1$\"]})\n",
    "        material_data.update({\"$\\nu_2$\": material_info[\"$\\nu_2$\"]})\n",
    "        material_data.update({\"$\\nu_3$\": material_info[\"$\\nu_3$\"]})\n",
    "        test_data.append(material_data)\n",
    "    get_materials_M_data(tqdm(test_data), val_r_0, val_r_1, val_Psitilde_min, val_Psitilde_max, list_len, False)\n",
    "    df_test = pd.DataFrame.from_dict(test_data)\n",
    "display(df_test)\n",
    "if not os.path.isfile(test_data_file_name+\".pickle\"):\n",
    "    df_test.to_pickle(test_data_file_name+\".pickle\")\n",
    "if not os.path.isfile(test_data_file_name+\".feather\"):\n",
    "    df_test.to_feather(test_data_file_name+\".feather\")\n",
    "if not os.path.isfile(test_data_file_name+\".csv\"):\n",
    "    df_test.to_csv(test_data_file_name+\".csv\", encoding = \"utf-8-sig\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:05.154519Z",
     "start_time": "2024-05-29T00:16:05.124696Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$k_{1}$</th>\n",
       "      <th>$k_{2}$</th>\n",
       "      <th>$k_{3}$</th>\n",
       "      <th>$k_{4}$</th>\n",
       "      <th>$k_{5}$</th>\n",
       "      <th>...</th>\n",
       "      <th>$M_{10}$</th>\n",
       "      <th>$M_{11}$</th>\n",
       "      <th>$M_{12}$</th>\n",
       "      <th>$M_{13}$</th>\n",
       "      <th>$M_{14}$</th>\n",
       "      <th>$M_{15}$</th>\n",
       "      <th>$M_{16}$</th>\n",
       "      <th>$M_{17}$</th>\n",
       "      <th>$M_{18}$</th>\n",
       "      <th>$M_{19}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.78000</td>\n",
       "      <td>0.90900</td>\n",
       "      <td>3.580</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-1.820</td>\n",
       "      <td>1.000047</td>\n",
       "      <td>1.000186</td>\n",
       "      <td>1.000420</td>\n",
       "      <td>1.000748</td>\n",
       "      <td>1.001172</td>\n",
       "      <td>...</td>\n",
       "      <td>90.769905</td>\n",
       "      <td>98.850332</td>\n",
       "      <td>106.632434</td>\n",
       "      <td>114.081220</td>\n",
       "      <td>121.160588</td>\n",
       "      <td>127.829648</td>\n",
       "      <td>134.043500</td>\n",
       "      <td>139.751464</td>\n",
       "      <td>144.895071</td>\n",
       "      <td>149.404932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.81800</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>-1.750</td>\n",
       "      <td>-2.400</td>\n",
       "      <td>-1.690</td>\n",
       "      <td>1.000033</td>\n",
       "      <td>1.000132</td>\n",
       "      <td>1.000298</td>\n",
       "      <td>1.000531</td>\n",
       "      <td>1.000833</td>\n",
       "      <td>...</td>\n",
       "      <td>96.101936</td>\n",
       "      <td>104.893688</td>\n",
       "      <td>113.445380</td>\n",
       "      <td>121.732244</td>\n",
       "      <td>129.727715</td>\n",
       "      <td>137.404392</td>\n",
       "      <td>144.733016</td>\n",
       "      <td>151.682188</td>\n",
       "      <td>158.217369</td>\n",
       "      <td>164.301639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.82100</td>\n",
       "      <td>1.11000</td>\n",
       "      <td>-3.580</td>\n",
       "      <td>-2.820</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>1.000039</td>\n",
       "      <td>1.000155</td>\n",
       "      <td>1.000351</td>\n",
       "      <td>1.000626</td>\n",
       "      <td>1.000979</td>\n",
       "      <td>...</td>\n",
       "      <td>95.875868</td>\n",
       "      <td>104.501768</td>\n",
       "      <td>112.839721</td>\n",
       "      <td>120.859732</td>\n",
       "      <td>128.527034</td>\n",
       "      <td>135.805721</td>\n",
       "      <td>142.654929</td>\n",
       "      <td>149.030449</td>\n",
       "      <td>154.879841</td>\n",
       "      <td>160.146890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>-1.340</td>\n",
       "      <td>-2.610</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>1.000035</td>\n",
       "      <td>1.000139</td>\n",
       "      <td>1.000313</td>\n",
       "      <td>1.000558</td>\n",
       "      <td>1.000875</td>\n",
       "      <td>...</td>\n",
       "      <td>96.165802</td>\n",
       "      <td>104.920929</td>\n",
       "      <td>113.423168</td>\n",
       "      <td>121.645521</td>\n",
       "      <td>129.560138</td>\n",
       "      <td>137.137415</td>\n",
       "      <td>144.345735</td>\n",
       "      <td>151.150555</td>\n",
       "      <td>157.514993</td>\n",
       "      <td>163.397266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.81900</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>-3.230</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>1.000037</td>\n",
       "      <td>1.000150</td>\n",
       "      <td>1.000339</td>\n",
       "      <td>1.000605</td>\n",
       "      <td>1.000946</td>\n",
       "      <td>...</td>\n",
       "      <td>95.804295</td>\n",
       "      <td>104.463525</td>\n",
       "      <td>112.849740</td>\n",
       "      <td>120.933462</td>\n",
       "      <td>128.683038</td>\n",
       "      <td>136.063636</td>\n",
       "      <td>143.039340</td>\n",
       "      <td>149.568756</td>\n",
       "      <td>155.606956</td>\n",
       "      <td>161.100066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.71600</td>\n",
       "      <td>0.87000</td>\n",
       "      <td>0.340</td>\n",
       "      <td>-5.520</td>\n",
       "      <td>-1.000</td>\n",
       "      <td>1.000073</td>\n",
       "      <td>1.000294</td>\n",
       "      <td>1.000658</td>\n",
       "      <td>1.001170</td>\n",
       "      <td>1.001831</td>\n",
       "      <td>...</td>\n",
       "      <td>79.355797</td>\n",
       "      <td>85.180428</td>\n",
       "      <td>90.244604</td>\n",
       "      <td>94.369032</td>\n",
       "      <td>97.306739</td>\n",
       "      <td>98.675294</td>\n",
       "      <td>97.790774</td>\n",
       "      <td>93.085077</td>\n",
       "      <td>76.678420</td>\n",
       "      <td>73.826581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.80400</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>-1.900</td>\n",
       "      <td>-2.300</td>\n",
       "      <td>-2.010</td>\n",
       "      <td>1.000039</td>\n",
       "      <td>1.000156</td>\n",
       "      <td>1.000353</td>\n",
       "      <td>1.000629</td>\n",
       "      <td>1.000987</td>\n",
       "      <td>...</td>\n",
       "      <td>93.863362</td>\n",
       "      <td>102.298781</td>\n",
       "      <td>110.451658</td>\n",
       "      <td>118.291407</td>\n",
       "      <td>125.783184</td>\n",
       "      <td>132.891134</td>\n",
       "      <td>139.575376</td>\n",
       "      <td>145.791544</td>\n",
       "      <td>151.487910</td>\n",
       "      <td>156.607321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.80300</td>\n",
       "      <td>1.12900</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>-2.700</td>\n",
       "      <td>-1.870</td>\n",
       "      <td>1.000040</td>\n",
       "      <td>1.000160</td>\n",
       "      <td>1.000360</td>\n",
       "      <td>1.000643</td>\n",
       "      <td>1.001007</td>\n",
       "      <td>...</td>\n",
       "      <td>93.615691</td>\n",
       "      <td>101.995999</td>\n",
       "      <td>110.083816</td>\n",
       "      <td>117.846589</td>\n",
       "      <td>125.249064</td>\n",
       "      <td>132.252102</td>\n",
       "      <td>138.814343</td>\n",
       "      <td>144.887696</td>\n",
       "      <td>150.417501</td>\n",
       "      <td>155.340845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.58000</td>\n",
       "      <td>-2.490</td>\n",
       "      <td>-0.990</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>1.000030</td>\n",
       "      <td>1.000120</td>\n",
       "      <td>1.000272</td>\n",
       "      <td>1.000485</td>\n",
       "      <td>1.000761</td>\n",
       "      <td>...</td>\n",
       "      <td>30.392541</td>\n",
       "      <td>33.133612</td>\n",
       "      <td>35.786312</td>\n",
       "      <td>38.340978</td>\n",
       "      <td>40.787405</td>\n",
       "      <td>43.114723</td>\n",
       "      <td>45.311178</td>\n",
       "      <td>47.364005</td>\n",
       "      <td>49.259094</td>\n",
       "      <td>50.980637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.49100</td>\n",
       "      <td>-3.790</td>\n",
       "      <td>-1.980</td>\n",
       "      <td>-0.800</td>\n",
       "      <td>1.000073</td>\n",
       "      <td>1.000294</td>\n",
       "      <td>1.000667</td>\n",
       "      <td>1.001186</td>\n",
       "      <td>1.001869</td>\n",
       "      <td>...</td>\n",
       "      <td>28.317371</td>\n",
       "      <td>30.262320</td>\n",
       "      <td>31.880243</td>\n",
       "      <td>33.078765</td>\n",
       "      <td>33.709435</td>\n",
       "      <td>33.478455</td>\n",
       "      <td>31.449531</td>\n",
       "      <td>26.707736</td>\n",
       "      <td>27.484370</td>\n",
       "      <td>25.359055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.41700</td>\n",
       "      <td>1.13300</td>\n",
       "      <td>-4.900</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>-0.500</td>\n",
       "      <td>1.000009</td>\n",
       "      <td>1.000036</td>\n",
       "      <td>1.000081</td>\n",
       "      <td>1.000145</td>\n",
       "      <td>1.000228</td>\n",
       "      <td>...</td>\n",
       "      <td>49.633613</td>\n",
       "      <td>54.330226</td>\n",
       "      <td>58.949458</td>\n",
       "      <td>63.481988</td>\n",
       "      <td>67.920098</td>\n",
       "      <td>72.255248</td>\n",
       "      <td>76.478598</td>\n",
       "      <td>80.580976</td>\n",
       "      <td>84.552844</td>\n",
       "      <td>88.384265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.49000</td>\n",
       "      <td>1.04200</td>\n",
       "      <td>-4.000</td>\n",
       "      <td>-1.700</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>1.000011</td>\n",
       "      <td>1.000046</td>\n",
       "      <td>1.000104</td>\n",
       "      <td>1.000185</td>\n",
       "      <td>1.000291</td>\n",
       "      <td>...</td>\n",
       "      <td>58.328637</td>\n",
       "      <td>63.850237</td>\n",
       "      <td>69.280867</td>\n",
       "      <td>74.611319</td>\n",
       "      <td>79.832130</td>\n",
       "      <td>84.933560</td>\n",
       "      <td>89.905561</td>\n",
       "      <td>94.737744</td>\n",
       "      <td>99.419351</td>\n",
       "      <td>103.939205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.47700</td>\n",
       "      <td>1.07000</td>\n",
       "      <td>-5.600</td>\n",
       "      <td>1.720</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>1.000085</td>\n",
       "      <td>1.000341</td>\n",
       "      <td>1.000771</td>\n",
       "      <td>1.001372</td>\n",
       "      <td>1.002157</td>\n",
       "      <td>...</td>\n",
       "      <td>47.236654</td>\n",
       "      <td>49.218924</td>\n",
       "      <td>50.275885</td>\n",
       "      <td>50.224767</td>\n",
       "      <td>48.812883</td>\n",
       "      <td>45.743292</td>\n",
       "      <td>40.318568</td>\n",
       "      <td>31.165423</td>\n",
       "      <td>12.469530</td>\n",
       "      <td>-4.002243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.16600</td>\n",
       "      <td>0.25900</td>\n",
       "      <td>-0.654</td>\n",
       "      <td>-0.574</td>\n",
       "      <td>-0.421</td>\n",
       "      <td>1.000041</td>\n",
       "      <td>1.000164</td>\n",
       "      <td>1.000371</td>\n",
       "      <td>1.000662</td>\n",
       "      <td>1.001040</td>\n",
       "      <td>...</td>\n",
       "      <td>19.286569</td>\n",
       "      <td>20.995885</td>\n",
       "      <td>22.639727</td>\n",
       "      <td>24.210246</td>\n",
       "      <td>25.699323</td>\n",
       "      <td>27.097920</td>\n",
       "      <td>28.395742</td>\n",
       "      <td>29.581469</td>\n",
       "      <td>30.641463</td>\n",
       "      <td>31.559406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-4.800</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>1.000084</td>\n",
       "      <td>1.000335</td>\n",
       "      <td>1.000756</td>\n",
       "      <td>1.001349</td>\n",
       "      <td>1.002120</td>\n",
       "      <td>...</td>\n",
       "      <td>90.560832</td>\n",
       "      <td>97.121590</td>\n",
       "      <td>102.767115</td>\n",
       "      <td>107.273220</td>\n",
       "      <td>110.304710</td>\n",
       "      <td>111.300510</td>\n",
       "      <td>109.073120</td>\n",
       "      <td>99.003646</td>\n",
       "      <td>87.700573</td>\n",
       "      <td>90.571731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.57000</td>\n",
       "      <td>-0.510</td>\n",
       "      <td>-2.830</td>\n",
       "      <td>-0.930</td>\n",
       "      <td>1.000007</td>\n",
       "      <td>1.000028</td>\n",
       "      <td>1.000063</td>\n",
       "      <td>1.000113</td>\n",
       "      <td>1.000177</td>\n",
       "      <td>...</td>\n",
       "      <td>131.781248</td>\n",
       "      <td>144.461613</td>\n",
       "      <td>156.998330</td>\n",
       "      <td>169.377706</td>\n",
       "      <td>181.585894</td>\n",
       "      <td>193.608880</td>\n",
       "      <td>205.432477</td>\n",
       "      <td>217.042318</td>\n",
       "      <td>228.423842</td>\n",
       "      <td>239.562295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.24000</td>\n",
       "      <td>1.78000</td>\n",
       "      <td>1.940</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>-2.270</td>\n",
       "      <td>1.000029</td>\n",
       "      <td>1.000118</td>\n",
       "      <td>1.000265</td>\n",
       "      <td>1.000472</td>\n",
       "      <td>1.000740</td>\n",
       "      <td>...</td>\n",
       "      <td>145.950373</td>\n",
       "      <td>159.373877</td>\n",
       "      <td>172.456494</td>\n",
       "      <td>185.164060</td>\n",
       "      <td>197.461308</td>\n",
       "      <td>209.311664</td>\n",
       "      <td>220.676913</td>\n",
       "      <td>231.516948</td>\n",
       "      <td>241.789212</td>\n",
       "      <td>251.448171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.73000</td>\n",
       "      <td>0.75000</td>\n",
       "      <td>-2.150</td>\n",
       "      <td>-1.430</td>\n",
       "      <td>-1.240</td>\n",
       "      <td>1.000023</td>\n",
       "      <td>1.000091</td>\n",
       "      <td>1.000206</td>\n",
       "      <td>1.000367</td>\n",
       "      <td>1.000575</td>\n",
       "      <td>...</td>\n",
       "      <td>86.752538</td>\n",
       "      <td>94.933369</td>\n",
       "      <td>102.971104</td>\n",
       "      <td>110.851857</td>\n",
       "      <td>118.560730</td>\n",
       "      <td>126.084339</td>\n",
       "      <td>133.407382</td>\n",
       "      <td>140.514591</td>\n",
       "      <td>147.390217</td>\n",
       "      <td>154.018668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.37000</td>\n",
       "      <td>1.63000</td>\n",
       "      <td>-4.290</td>\n",
       "      <td>-2.580</td>\n",
       "      <td>-2.670</td>\n",
       "      <td>1.000023</td>\n",
       "      <td>1.000093</td>\n",
       "      <td>1.000209</td>\n",
       "      <td>1.000373</td>\n",
       "      <td>1.000585</td>\n",
       "      <td>...</td>\n",
       "      <td>162.539540</td>\n",
       "      <td>177.798510</td>\n",
       "      <td>192.767627</td>\n",
       "      <td>207.417870</td>\n",
       "      <td>221.719434</td>\n",
       "      <td>235.641582</td>\n",
       "      <td>249.152568</td>\n",
       "      <td>262.218702</td>\n",
       "      <td>274.806648</td>\n",
       "      <td>286.879828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.18600</td>\n",
       "      <td>0.39000</td>\n",
       "      <td>-0.078</td>\n",
       "      <td>-0.070</td>\n",
       "      <td>0.047</td>\n",
       "      <td>0.999969</td>\n",
       "      <td>0.999874</td>\n",
       "      <td>0.999717</td>\n",
       "      <td>0.999496</td>\n",
       "      <td>0.999213</td>\n",
       "      <td>...</td>\n",
       "      <td>22.895935</td>\n",
       "      <td>25.243913</td>\n",
       "      <td>27.608747</td>\n",
       "      <td>29.992049</td>\n",
       "      <td>32.395454</td>\n",
       "      <td>34.820621</td>\n",
       "      <td>37.269234</td>\n",
       "      <td>39.743007</td>\n",
       "      <td>42.243681</td>\n",
       "      <td>44.773035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.31261</td>\n",
       "      <td>0.15872</td>\n",
       "      <td>0.540</td>\n",
       "      <td>0.930</td>\n",
       "      <td>-0.110</td>\n",
       "      <td>0.999906</td>\n",
       "      <td>0.999631</td>\n",
       "      <td>0.999179</td>\n",
       "      <td>0.998570</td>\n",
       "      <td>0.997806</td>\n",
       "      <td>...</td>\n",
       "      <td>41.806893</td>\n",
       "      <td>46.550325</td>\n",
       "      <td>51.393256</td>\n",
       "      <td>56.320180</td>\n",
       "      <td>61.323199</td>\n",
       "      <td>66.396765</td>\n",
       "      <td>71.539163</td>\n",
       "      <td>76.686651</td>\n",
       "      <td>81.865686</td>\n",
       "      <td>87.052084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.27500</td>\n",
       "      <td>0.13530</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-1.680</td>\n",
       "      <td>1.050</td>\n",
       "      <td>1.000032</td>\n",
       "      <td>1.000126</td>\n",
       "      <td>1.000279</td>\n",
       "      <td>1.000498</td>\n",
       "      <td>1.000766</td>\n",
       "      <td>...</td>\n",
       "      <td>26.524917</td>\n",
       "      <td>28.117946</td>\n",
       "      <td>29.418559</td>\n",
       "      <td>30.585172</td>\n",
       "      <td>31.571458</td>\n",
       "      <td>32.387147</td>\n",
       "      <td>33.039514</td>\n",
       "      <td>33.537683</td>\n",
       "      <td>33.889957</td>\n",
       "      <td>34.104190</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>22 rows × 43 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$  $\\nu_1$  $\\nu_2$  $\\nu_3$   $k_{1}$   $k_{2}$  \\\n",
       "0   0.78000    0.90900    3.580   -2.650   -1.820  1.000047  1.000186   \n",
       "1   0.81800    1.09000   -1.750   -2.400   -1.690  1.000033  1.000132   \n",
       "2   0.82100    1.11000   -3.580   -2.820   -1.770  1.000039  1.000155   \n",
       "3   0.82000    1.10000   -1.340   -2.610   -1.670  1.000035  1.000139   \n",
       "4   0.81900    1.09000   -3.230   -2.650   -1.770  1.000037  1.000150   \n",
       "5   0.71600    0.87000    0.340   -5.520   -1.000  1.000073  1.000294   \n",
       "6   0.80400    1.10000   -1.900   -2.300   -2.010  1.000039  1.000156   \n",
       "7   0.80300    1.12900   -2.800   -2.700   -1.870  1.000040  1.000160   \n",
       "8   0.26000    0.58000   -2.490   -0.990   -0.600  1.000030  1.000120   \n",
       "9   0.26000    0.49100   -3.790   -1.980   -0.800  1.000073  1.000294   \n",
       "10  0.41700    1.13300   -4.900   -1.670   -0.500  1.000009  1.000036   \n",
       "11  0.49000    1.04200   -4.000   -1.700   -0.600  1.000011  1.000046   \n",
       "12  0.47700    1.07000   -5.600    1.720   -3.980  1.000085  1.000341   \n",
       "13  0.16600    0.25900   -0.654   -0.574   -0.421  1.000041  1.000164   \n",
       "14  0.82000    1.10000    2.600   -4.800   -2.800  1.000084  1.000335   \n",
       "15  1.10000    1.57000   -0.510   -2.830   -0.930  1.000007  1.000028   \n",
       "16  1.24000    1.78000    1.940   -3.980   -2.270  1.000029  1.000118   \n",
       "17  0.73000    0.75000   -2.150   -1.430   -1.240  1.000023  1.000091   \n",
       "18  1.37000    1.63000   -4.290   -2.580   -2.670  1.000023  1.000093   \n",
       "19  0.18600    0.39000   -0.078   -0.070    0.047  0.999969  0.999874   \n",
       "20  0.31261    0.15872    0.540    0.930   -0.110  0.999906  0.999631   \n",
       "21  0.27500    0.13530    2.600   -1.680    1.050  1.000032  1.000126   \n",
       "\n",
       "     $k_{3}$   $k_{4}$   $k_{5}$  ...    $M_{10}$    $M_{11}$    $M_{12}$  \\\n",
       "0   1.000420  1.000748  1.001172  ...   90.769905   98.850332  106.632434   \n",
       "1   1.000298  1.000531  1.000833  ...   96.101936  104.893688  113.445380   \n",
       "2   1.000351  1.000626  1.000979  ...   95.875868  104.501768  112.839721   \n",
       "3   1.000313  1.000558  1.000875  ...   96.165802  104.920929  113.423168   \n",
       "4   1.000339  1.000605  1.000946  ...   95.804295  104.463525  112.849740   \n",
       "5   1.000658  1.001170  1.001831  ...   79.355797   85.180428   90.244604   \n",
       "6   1.000353  1.000629  1.000987  ...   93.863362  102.298781  110.451658   \n",
       "7   1.000360  1.000643  1.001007  ...   93.615691  101.995999  110.083816   \n",
       "8   1.000272  1.000485  1.000761  ...   30.392541   33.133612   35.786312   \n",
       "9   1.000667  1.001186  1.001869  ...   28.317371   30.262320   31.880243   \n",
       "10  1.000081  1.000145  1.000228  ...   49.633613   54.330226   58.949458   \n",
       "11  1.000104  1.000185  1.000291  ...   58.328637   63.850237   69.280867   \n",
       "12  1.000771  1.001372  1.002157  ...   47.236654   49.218924   50.275885   \n",
       "13  1.000371  1.000662  1.001040  ...   19.286569   20.995885   22.639727   \n",
       "14  1.000756  1.001349  1.002120  ...   90.560832   97.121590  102.767115   \n",
       "15  1.000063  1.000113  1.000177  ...  131.781248  144.461613  156.998330   \n",
       "16  1.000265  1.000472  1.000740  ...  145.950373  159.373877  172.456494   \n",
       "17  1.000206  1.000367  1.000575  ...   86.752538   94.933369  102.971104   \n",
       "18  1.000209  1.000373  1.000585  ...  162.539540  177.798510  192.767627   \n",
       "19  0.999717  0.999496  0.999213  ...   22.895935   25.243913   27.608747   \n",
       "20  0.999179  0.998570  0.997806  ...   41.806893   46.550325   51.393256   \n",
       "21  1.000279  1.000498  1.000766  ...   26.524917   28.117946   29.418559   \n",
       "\n",
       "      $M_{13}$    $M_{14}$    $M_{15}$    $M_{16}$    $M_{17}$    $M_{18}$  \\\n",
       "0   114.081220  121.160588  127.829648  134.043500  139.751464  144.895071   \n",
       "1   121.732244  129.727715  137.404392  144.733016  151.682188  158.217369   \n",
       "2   120.859732  128.527034  135.805721  142.654929  149.030449  154.879841   \n",
       "3   121.645521  129.560138  137.137415  144.345735  151.150555  157.514993   \n",
       "4   120.933462  128.683038  136.063636  143.039340  149.568756  155.606956   \n",
       "5    94.369032   97.306739   98.675294   97.790774   93.085077   76.678420   \n",
       "6   118.291407  125.783184  132.891134  139.575376  145.791544  151.487910   \n",
       "7   117.846589  125.249064  132.252102  138.814343  144.887696  150.417501   \n",
       "8    38.340978   40.787405   43.114723   45.311178   47.364005   49.259094   \n",
       "9    33.078765   33.709435   33.478455   31.449531   26.707736   27.484370   \n",
       "10   63.481988   67.920098   72.255248   76.478598   80.580976   84.552844   \n",
       "11   74.611319   79.832130   84.933560   89.905561   94.737744   99.419351   \n",
       "12   50.224767   48.812883   45.743292   40.318568   31.165423   12.469530   \n",
       "13   24.210246   25.699323   27.097920   28.395742   29.581469   30.641463   \n",
       "14  107.273220  110.304710  111.300510  109.073120   99.003646   87.700573   \n",
       "15  169.377706  181.585894  193.608880  205.432477  217.042318  228.423842   \n",
       "16  185.164060  197.461308  209.311664  220.676913  231.516948  241.789212   \n",
       "17  110.851857  118.560730  126.084339  133.407382  140.514591  147.390217   \n",
       "18  207.417870  221.719434  235.641582  249.152568  262.218702  274.806648   \n",
       "19   29.992049   32.395454   34.820621   37.269234   39.743007   42.243681   \n",
       "20   56.320180   61.323199   66.396765   71.539163   76.686651   81.865686   \n",
       "21   30.585172   31.571458   32.387147   33.039514   33.537683   33.889957   \n",
       "\n",
       "      $M_{19}$  \n",
       "0   149.404932  \n",
       "1   164.301639  \n",
       "2   160.146890  \n",
       "3   163.397266  \n",
       "4   161.100066  \n",
       "5    73.826581  \n",
       "6   156.607321  \n",
       "7   155.340845  \n",
       "8    50.980637  \n",
       "9    25.359055  \n",
       "10   88.384265  \n",
       "11  103.939205  \n",
       "12   -4.002243  \n",
       "13   31.559406  \n",
       "14   90.571731  \n",
       "15  239.562295  \n",
       "16  251.448171  \n",
       "17  154.018668  \n",
       "18  286.879828  \n",
       "19   44.773035  \n",
       "20   87.052084  \n",
       "21   34.104190  \n",
       "\n",
       "[22 rows x 43 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_test_k = pd.DataFrame(df_test[\"$k$\"].to_list(), columns = [\"$k_{\"+str(i)+\"}$\" for i in range(list_len)])\n",
    "df_test_k = df_test_k.drop(df_test_k.columns[0], axis = 1)\n",
    "df_test_M = pd.DataFrame(df_test[\"$M$\"].to_list(), columns = [\"$M_{\"+str(i)+\"}$\" for i in range(list_len)])\n",
    "df_test_M = df_test_M.drop(df_test_M.columns[0], axis = 1)\n",
    "df_test = pd.concat([df_test.drop(columns = [\"$k$\", \"$M$\"]), df_test_k, df_test_M], axis = 1)\n",
    "list_len -= 1\n",
    "display(df_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:10.527412Z",
     "start_time": "2024-05-29T00:16:05.154519Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "df_test_corr_k = df_test.iloc[:, :5+list_len].corr()\n",
    "df_test_corr_M = df_test.iloc[:, [0, 1, 2, 3, 4]+[list_len+i+5 for i in range(list_len)]].corr()\n",
    "plt.figure()\n",
    "sns.heatmap(df_test_corr_k)\n",
    "plt.savefig(\"material_results_k_heatmap.svg\")\n",
    "plt.figure()\n",
    "sns.heatmap(df_test_corr_M)\n",
    "plt.savefig(\"material_results_M_heatmap.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:10.533584Z",
     "start_time": "2024-05-29T00:16:10.528410Z"
    },
    "id": "x7_g3J0vUE_j"
   },
   "outputs": [],
   "source": [
    "X_test = np.array(df_test.iloc[:, 5:].values.tolist())\n",
    "y_test = np.array(df_test.iloc[:, :5].values.tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:11.396941Z",
     "start_time": "2024-05-29T00:16:10.542156Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Intel(R) Extension for Scikit-learn* enabled (https://github.com/intel/scikit-learn-intelex)\n"
     ]
    }
   ],
   "source": [
    "if importlib.util.find_spec(\"sklearnex\") is not None: #Intel(R) Extension for Scikit-learn\n",
    "    from sklearnex import patch_sklearn\n",
    "    patch_sklearn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:11.404255Z",
     "start_time": "2024-05-29T00:16:11.398947Z"
    },
    "collapsed": false,
    "id": "zj1c_j7QUE_k",
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "X_scaler = StandardScaler()\n",
    "X_test = X_scaler.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:11.412727Z",
     "start_time": "2024-05-29T00:16:11.407335Z"
    },
    "id": "vqCLJXGkUE_k"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import LeaveOneOut, cross_val_predict\n",
    "from sklearn.ensemble import ExtraTreesRegressor\n",
    "from sklearn.linear_model import Ridge, RidgeCV\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.metrics import root_mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:11.419210Z",
     "start_time": "2024-05-29T00:16:11.414735Z"
    }
   },
   "outputs": [],
   "source": [
    "def CreateExtraTreesRegressor():\n",
    "    return ExtraTreesRegressor(n_estimators = 1000, criterion = \"absolute_error\", random_state = seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:29.568259Z",
     "start_time": "2024-05-29T00:16:11.420285Z"
    },
    "collapsed": false,
    "id": "v9hy-QdUUE_l",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "1c74c708-efe7-48bf-e269-e0a5f6d0d2d0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qClVVvWJZBF/EUENERORBdQKMIDj1KqeWhuNaRERE5BcYaoiIiMgvMNQQERGRX2CoISIiIr/AUENERER+gVc/EREReZBstUIQBAiiCFVRoKoqJA0/npuDPzUiIiIPUCxWKLKM4qxcXDxyCnKNGVKADhGpCYju0wWiJEHU8mPaETz9RERE5GaKtTbM7H1rBU5vyUZVySWYyipQVXIJp7dkY+9bK1CclQvFKnu6VEyYMAHx8fEICAhATEwMHnzwQRQVFTXap6amBjNnzkRERARCQkJw9913o6SkxOW1MtQQERG5kWKxonjvYRRs2gNVUeptoyoKCjbtqQ02FqubK6xrxIgR+Pzzz5GXl4eVK1fixIkTuOeeexrtM3v2bHz99df44osvsGXLFhQVFeGuu+5yea1eE2q2bt2K8ePHIzY2FoIgYM2aNQ22/dWvfgVBEPDWW2+5rT4iIiJnUKwyCjOz7GpbuHkvFNmzozWzZ8/GwIED0aFDBwwePBjz5s3Dzp07YbFY6m1fVlaGf/7zn3jzzTcxcuRI9OnTBx988AG+//577Ny506W1ek2oqaysRI8ePbBkyZJG261evRo7d+5EbGysmyojIiJyDtlqRXFWboMjNNdTFQXFWbmQrZ4drbnq0qVLWL58OQYPHgytVltvm6ysLFgsFowePdq2LTU1FfHx8dixY4dL6/OaUDN27FgsWLAAkydPbrDN2bNn8Zvf/AbLly9v8IdJRETkrQRBwMW8Uw71uXSkAJ5eEerZZ59FcHAwIiIiUFhYiC+//LLBtsXFxdDpdAgPD6+zvW3btiguLnZpnV4TapqiKAoefPBBzJ07F127dm2yvclkgtForPMgIiLyJEEUIdeYHepjNZkhSM79uJ43b17tZeSNPI4cOWJrP3fuXOzbtw/r16+HJEl46KGHoKqqU2tyBp+5VmzRokXQaDR44okn7Gq/cOFCvPzyyy6uioiIyH6qokAK0AFl9vfR6HVQZQWCRmq6sZ2efvppTJ8+vdE2SUlJtv9v06YN2rRpg06dOqFLly6Ii4vDzp07MWjQoBv6RUdHw2w248qVK3VGa0pKShAdHe2sb6FePhFqsrKy8PbbbyM7OxuCYN8Q3Pz58zFnzhzbc6PRiLi4OFeVSERE1CRVVRGRmoCqkkt292md2gEqnDsqEhkZicjIyGb1VX6cD2Qymerd36dPH2i1WmzcuBF33303ACAvLw+FhYX1hiBn8onTT9u2bUNpaSni4+Oh0Wig0WhQUFCAp59+GgkJCfX20ev1CAsLq/MgIiLyJEmjQXTvLhBE+z5+BVFEdJ8uHrvD8K5du7B48WLk5OSgoKAAmzZtwgMPPIDk5GRbQDl79ixSU1Oxe/duAIDBYMAjjzyCOXPmYPPmzcjKysKMGTMwaNAgDBw40KX1+sRIzYMPPlhnFjUAZGRk4MEHH8SMGTM8VBUREZHjRI2E+OF9ULBpT5Nt40f0hSg577STo4KCgrBq1Sq8+OKLqKysRExMDMaMGYPnnnsOer0eAGCxWJCXl4eqqipbvz//+c8QRRF33303TCYTMjIy8Le//c3l9XpNqKmoqMDx48dtz/Pz85GTk4PWrVsjPj4eERERddprtVpER0ejc+fO7i6ViIio2UStBtF90wBBQOHmvfVe3i2IIuJH9K1dLsGJc2kc1a1bN2zatKnRNgkJCTdMGg4ICMCSJUuavE2Ls3lNqNm7dy9GjBhhe351Psy0adOwdOlSD1VFRETkfKJGQnTvVET1SEFxVi4uHSmA1WSGRq9D69QOP6395MFA44u8JtQMHz7cocvDTp065bpiiPyAqqpQ5dq/AAVJtHuSPRG5h6jVQNRqEDMgHbEDukGQRKiyAhVcpbu5+FMj8jOyxQpBFHHpSAEqSi4CAEJi2yCiUzwUWYHEVX+JvMq1AcaZl223RHx3I/IjiizjzHcHcG73D7BU1dTZpw0OROzAdLQf3M2jEw+JiFyFoYbITyiyjLxVmbjww8l691sqq1GwcQ+qL1xByoRbGWyIyO/4xH1qiKhxstWKc3tzGww01yrdfwyl+49DsXp25V8iImdjqCHyA6IoomjnIbvbn915EILIicNE5F8Yaoj8QEXRBdRcLre7fVXpZVSdv+K6goiIPIChhsgPVF9yfBX6mstcuZ7IG1jNVshWGaqqQrbKsJqtni7JZ3GiMJEfECTH/z4ROFGYyKOsZgtki4zcb/fh1N48mCtN0AXrkdC3M7qM7gVJK0Gj03q6TJ/CkRoiPxDWPsqxDoKAkNg2rimGiJokW6zI3bgPK2YtRvbKbbhUUIqKC2W4VFCK7JXbsGLWYuRu3AfZ4vlRm1dffRWDBw9GUFAQwsPD7eozffp0CIJQ5zFmzBjXFgqGGiK/oA0ORHhirN3tW6fEQeJfgEQeYTVbcPjbbOxZkQlFvnHdJwBQZAV7VmQi99t9sJotbq6wLrPZjClTpuDxxx93qN+YMWNw7tw522PFihUuqvAnPP1E5AcEUUSHkX1x5YOvAaXx5UYESUSHEX14nxoiD5EtMrI+32pX272fb0HK0G4ePQ318ssvA4DD6zDq9XpER0e7oKKGcaSGyA8IooDg6Ah0njy80Uu1BUlE6j2jENgmnJd0E3mA1WxF7rfZDY7QXE+RFeRu3OeTk4czMzMRFRWFzp074/HHH8fFixdd/jUZaoj8hKTVICI1Ab0fvxtRPVLqrCEjaiW07dUZfX59D1p1bM/1n4g8RBAFnNp71KE+BXuO+tyCtGPGjMGHH36IjRs3YtGiRdiyZQvGjh0LWXbtTT/5zkbkRyStBkGRrdBx3C3oeOcQmI2VgADoQoMBFZB0/CdP5EmiJMJcaXKoj7mqBmIzrnBszLx587Bo0aJG2+Tm5iI1NbVZr3///ffb/r9bt27o3r07kpOTkZmZiVGjRjXrNe3BdzgiP3R1EnBghMHDlRDRtRRZgS5YD1ywv48uKACKrEASnTcP7umnn8b06dMbbZOUlOS0r5eUlIQ2bdrg+PHjDDVERET+QFVUJPTtjEsFpXb36dCvE1S18QsAHBUZGYnIyEinvmZjzpw5g4sXLyImJsalX4dzaoiIiNxEo9Ogy+hedp9OEiURXUb1gsaDp44LCwuRk5ODwsJCyLKMnJwc5OTkoKKiwtYmNTUVq1evBgBUVFRg7ty52LlzJ06dOoWNGzdi4sSJ6NixIzIyMlxaK0MNERGRG0laCX3uHWpX2773DoOk9eztF1544QX06tULL774IioqKtCrVy/06tULe/futbXJy8tDWVkZAECSJBw4cAATJkxAp06d8Mgjj6BPnz7Ytm0b9Hq9S2vl6SciIiI30ui0SBvdGwIE7P18S72Xd4uSiL73DvtxuQTPflQvXbq0yXvUXHt6LDAwEN98842Lq6ofQw0REZGbSVoNUkf1RMrQbsjduA8Fe47CXFUDXVAAOvTrhC6jatd+8nSg8TX8aREREXmARqeFRqdF+ph+6Da2P0RJhCIrUFXVo3NofBl/akRERB50bYBx5mXbLREnChMREZFfYKghIiIiv8BQQ0RERH6BoYaIiIj8AicKExEReZDFZIEgCpA0EmSrDFVRodVrPV2WT2KoISIi8gCzyQKr2YItq7dj35b9qK6oRmBIIHoN64Fhk4dAo9NCx3DjEIYaIiIiN7Oardi6eju+fG8tZKtcZ9+ZY2fx36XfYOJjd2L43bdCwxvw2Y1zaoiIiNzIbLIgc9U2rPrblzcEmqtkq4xVf/sSmau2wWyyuKSOJUuWICEhAQEBARgwYAB2797daPsvvvgCqampCAgIQLdu3fDf//7XJXXdDIYaIiIiN7KYLfjyvbV2tf3y3bWwmp0faj777DPMmTMHL774IrKzs9GjRw9kZGSgtLS03vbff/89HnjgATzyyCPYt28fJk2ahEmTJuHQoUNOr+1mMNQQERG5icVkwdbV2xscobmebJWxZfV2WJw8WvPmm2/i0UcfxYwZM5CWloZ33nkHQUFB+Ne//lVv+7fffhtjxozB3Llz0aVLF7zyyivo3bs3Fi9e7NS6bhZDDRERkZsIooB9W/Y71Cdn6wEIouC0GsxmM7KysjB69GjbNlEUMXr0aOzYsaPePjt27KjTHgAyMjIabO8pDDVERERuImkkVFdUO9SnqrwaouS8NaEuXLgAWZbRtm3bOtvbtm2L4uLievsUFxc71N5TvCbUbN26FePHj0dsbCwEQcCaNWts+ywWC5599ll069YNwcHBiI2NxUMPPYSioiLPFUxEROQg2SojMCTQoT5BoYFQZPtOV7V0XhNqKisr0aNHDyxZsuSGfVVVVcjOzsbzzz+P7OxsrFq1Cnl5eZgwYYIHKiUiImoeVVHRa1gPh/r0HNodqqI6rYY2bdpAkiSUlJTU2V5SUoLo6Oh6+0RHRzvU3lO8JtSMHTsWCxYswOTJk2/YZzAYsGHDBtx7773o3LkzBg4ciMWLFyMrKwuFhYUeqJaIiMhxWr0WQycPgaSx73SSpJEwbPIQp95hWKfToU+fPti4caNtm6Io2LhxIwYNGlRvn0GDBtVpDwAbNmxosL2neE2ocVRZWRkEQUB4eLinSyEiIrKbVqfFxMfutKvtpF+Oh0bn/LsKz5kzB++//z6WLVuG3NxcPP7446isrMSMGTMAAA899BDmz59va//kk09i3bp1eOONN3DkyBG89NJL2Lt3L2bNmuX02m6GT96msKamBs8++yweeOABhIWF1dvGZDLBZDLZnhuNRneVR0RE1CCdXovhd98KCLX3oanv8m5JI2HiL+/EsLuGuOSOwvfddx/Onz+PF154AcXFxejZsyfWrVtnmwxcWFgIUfxp3GPw4MH45JNP8Nxzz+H//u//kJKSgjVr1iA9Pd3ptd0MQVVV552ocxJBELB69WpMmjTphn0WiwV33303zpw5g8zMzAZDzUsvvYSXX375hu1lZWUN9iEiIrJXTU0N8vPzkZiYiICAAIf7X7v2U87WA6gqr0ZQaCB6Du3e4tZ+auxnaTQaYTAY7Pr89qmRGovFgnvvvRcFBQXYtGlTo9/c/PnzMWfOHNtzo9GIuLg4d5RJRETUJJ2+NrSMvm8EbntgJERJgiJzle6b4TOh5mqgOXbsGDZv3oyIiIhG2+v1euj1ejdVR0RE1DzXBhhR9JmPZa/kNT+9iooKHD9+3PY8Pz8fOTk5aN26NWJiYnDPPfcgOzsba9euhSzLthv+tG7dGjqdzlNlExERkZfwmlCzd+9ejBgxwvb86qmjadOm4aWXXsJXX30FAOjZs2edfps3b8bw4cPdVSYRERF5Ka8JNcOHD0djc5a9cD4zEREReRGfvU8NERER0bUYaoiIiMgveM3pJyIiopbIVGOCKIqQNBrIVisURYE+gFfvNgdDDRERkQeYakwwmyz4/OOvsGndNlQYKxESFoyRY27FvT+fAJ1ey3DjIIYaIiIiNzObLfji46+x5PV/wWqx1tl39PAJ/OOvH2Pmbx/GvQ9NhM4Faz/5K86pISIiciNTjQmff/gl3l743g2B5iqrxYq3F76HLz76EqYaU71tbsbWrVsxfvx4xMbGQhAErFmzptH2mZmZEAThhsfVe8Z5C4YaIiIiNzKZzFjy+r/sarv4T/+C2WRxeg2VlZXo0aMHlixZ4lC/vLw8nDt3zvaIiopyem03g6efiIiI3MRUY8IXH33V4AjN9awWK75Y/hWmPny3U+fXjB07FmPHjnW4X1RUFMLDw51Wh7NxpIaIiMhNRFHEpm+2O9Rn07rtEETv+Lju2bMnYmJicNttt+G7777zdDk38I6fEhERUQsgaTSoMFY61KfCWAGNRnJRRfaJiYnBO++8g5UrV2LlypWIi4vD8OHDkZ2d7dG6rsfTT0RERG4iW60ICQt2qE9IWAisVhk6nefGITp37ozOnTvbng8ePBgnTpzAn//8Z3z00Uceq+t6HKkhIiJyE0VRMHLMrQ71GTlmCFRFcVFFzde/f38cP37c02XUwVBDRETkJvoAPab8fDw0WvtOlGi0GkyZOsErb8KXk5ODmJgYT5dRB08/ERERuZFer8PM3z6Mtxe+12TbWXMfgU7v/JvvVVRU1Bllyc/PR05ODlq3bo34+HjMnz8fZ8+exYcffggAeOutt5CYmIiuXbuipqYG//jHP7Bp0yasX7/e6bXdDIYaIiIiN9IH6HHvQxMhCLX3oanv8m6NVoNZcx/GlAcnuOSOwnv37sWIESNsz+fMmQMAmDZtGpYuXYpz586hsLDQtt9sNuPpp5/G2bNnERQUhO7du+Pbb7+t8xreQFBVVfV0Ee5gNBphMBhQVlaGsLAwT5dDREQ+rqamBvn5+UhMTERAQIDD/a+u/fTF8q+wad12VBgrEBIWgpFjhmDK1Ja19lNjP0tHPr85UkNEROQB+gA99AF6TH34bvz8F1Og0UiwWmWoXKW72RhqiIiIPOjaAOPJy7b9AX96RERE5BcYaoiIiMgvMNQQERHdhBZyvY1LOetnyFBDRETUDFpt7aXWVVVVHq7E95nNZgCAJN3cGlecKExERNQMkiQhPDwcpaWlAICgoCAIguDhqnyPoig4f/48goKCoNHcXCxhqCEiImqm6OhoALAFG2oeURQRHx9/06GQoYaIiKiZBEFATEwMoqKiYLFYPF2Oz9LpdBDFm58Rw1BDRER0kyRJuun5IHTzOFGYiIiI/AJDDREREfkFhhoiIiLyCww1RERE5BcYaoiIiMgvMNQQERGRX+Al3UTU4qmKAsUqAwAEUYSo4aW5RL6IoYaIfJ5ssUJVVQiiCKgqLFU1qCy5BFUFgqPCoQ8NBgQBolQ7OC2bLZB0WsgWK0RJgmyxoqywGMZT5yDpdYjukwpJp4WokXjbe3IrRZYhCAKs1dWAqkLS62t/r0WRv4t2YKghIp8lW6xQFQXnco4jsnM8Ks9fQeHWHFw+ebZOO0N8WyRnDEBY+0hUXShD4fb9OH/oZO3ojAC0Tm6P2AFdET+sD459vRW73liOiM4d0GniMEg6Te2HCpELqbIMxWJB+alTqC4+B1WWbfv0EREI6ZAAncHA38UmeM1PZ+vWrRg/fjxiY2MhCALWrFlTZ7+qqnjhhRcQExODwMBAjB49GseOHfNMsUTkcYpVxqlt+7HtjysQ0bEdzh/Ox/5l/7kh0AC14SckujVOrN+NPYv/jZKcY7bTTVCBS8fP4NDyb3Dok2/Q8c4hiExLxMXcU8h5f41tFIjIVVRZhqW8HKU7d6Dq7Jk6gQYATBcv4mJ2FspPnYKqKB6q0jd4TaiprKxEjx49sGTJknr3//GPf8Rf/vIXvPPOO9i1axeCg4ORkZGBmpoaN1dKRJ4mW6w4/u1eHPvfLnS4pRuqLxpx7L/fAw1kj7QpI1H43UGc+f5go6976fgZ/PDpt0iZMAyaID2qL5bh+NfbfgpARC6gWCy4mLPvhjBzvYr8k6guLobSRLuWzGtOP40dOxZjx46td5+qqnjrrbfw3HPPYeLEiQCADz/8EG3btsWaNWtw//33u7NUIvIwk7ESJzdmQZBEtO/fBT98vrHBQBOeGAtdSCBOb8tp8PUMHaLRrn8aWnVsD02ADqqioM+vp6DqwhVcyS+CYpUhab3m7ZL8iCLLKC841WSguar8VD4CY2JcXJXv8ol/pfn5+SguLsbo0aNt2wwGAwYMGIAdO3Yw1BC1ILLZgvwtOQCAyNQOsJrM9Z5yuqpd/zScy8qrd7RFFxqE9AduR1AbA8rOnIeqqDAZq1B64DjM5ZUQtRq0TomzTSpmsCFnEwQB1efO2d1erq6G+cpl6Fu1dmFVvssn/oUWFxcDANq2bVtne9u2bW37rmcymWAymWzPjUaj6wokIreRdFoU7z8BAAhsFYqK4ksNjtIAQEhMa5zLPnLDdl1oEHo/NgkXjp5G2dkLiOrSAUe/3IpLx04D18yhOfPdAQS0CkVSxsDagMNgQ04k11TbPUpzlfnKFegM4Zw0XA+//YksXLgQBoPB9oiLi/N0SUTkJJYq++fSSRoNFIv1hu1pU0bh4vEzqCi9gqgu8cj5x5e4dLSwTqC5quZyOQ5/ugGlB45Brue1iJqrOZPQOXG9YT4RaqKjowEAJSUldbaXlJTY9l1v/vz5KCsrsz1Onz7t8jqJyD0kvRYAUFNWgeDI8EbbWmpM0IUE1dkWEhOB0PaROLJ2BzqO6o281ZkwGSub/LpHv9oOS2V1s+smup6k0wMO3n9GExTkcJ+WwidCTWJiIqKjo7Fx40bbNqPRiF27dmHQoEH19tHr9QgLC6vzICLfJ5utiEztAAA4f6QQupBAGDrU/8cNAFw8Uoi2PVPqbIvtn4airKOI7NIBJmMlruTbOadBVXH6uwOQzZZm1090LUEUERDRxv72Gg0Co9ryRnwN8JpQU1FRgZycHOTk5AConRyck5ODwsJCCIKAp556CgsWLMBXX32FgwcP4qGHHkJsbCwmTZrk0bqJyL0knQaJw3oAABSLFWf2HEH8kO4Ntj+7JxcRKXHQh4fYtoV3iEHxwZOI6Z6MkpyjDn39kpyjEDmvhpxFFBHSoYPdzYNiY3n6qRFeE2r27t2LXr16oVevXgCAOXPmoFevXnjhhRcAAM888wx+85vf4LHHHkO/fv1QUVGBdevWISAgwJNlE5EHhMZGIrp7MgDg1JYchMZGInFUn3rbmsoqUHLgONKmjLKFEUmvhbXaBF1wAExlTZ92upZsskCxWCFba+9mbK6oRs2VCshmy493OOYHDtlPEARoQ0MRmpzcZFtdq1YIS+4IUeLaZA0R1BYS+YxGIwwGA8rKyngqisgPKLKMAys2onj/cYS0bY2+j96JssISFG7NQXnRhTptQ2LaoPuDGbBU1uDw5xuRPjUDP6zeho6j+6Ak+whKDxx36Gvf+sIjKD5wDAWZ+1Bz6ccrKwUBEZ3iET+kO8Li2nJRTHKIKsuoPn8e5SdPQq6uqrNP0GgQFBuLsOSOgCC0uFNPjnx+M9QQkc9SZBmVpVeQv6U2yMTfko6Ynp1QfanMtqBlSHQEgqNa2a5qEkQBpvIqlOYWACogScDxtd/Z/TVDoiPQ8xcT8N1rH0I2138lVLtB6eiYMZDBhhyiKjIgiDCXlcF85TKgqJCCghAYFQVVVVvsCI0jn98uOTG8a9cuDBgwwBUvTURkI0oSQmMi0PWuoZB0tVdEqaqK4MhWCI1pePKlPiwY7fp0xu73vka/X4xD/obdkE32Tf6N7Z+G4v3HGgw0AHB2xyHoQ4LQflA3SDrOvyH7CGJtaNGHh0N39cP7x5GZljU203wumVMzZcoUV7wsEVG9rgYaoHaOQlMjJFeH7+MHpqGi5DLa39LwRONrBUYYENW9I4p2HW6ybcHWHAgiP4qoeQRRrH20sFNNN6vZf0Lce++99W5XVRWXLl1qdkFERO4gaTWI7p6MC3mFaDcwHZaKahTtbjisBEYY0H3aHTiz4xAqii82+fqyyYyS/cfQtmdKiz1tQORuzQ413377LT766COEhITU2a6qKrZu3XrThRERuZqk1aBNp3ioUJF4W39EpCagaNcPuHjNnYUDIwyIHdAVMX1ScWbHQZz8drfdr3/l1DlEpicx1BC5SbNDzfDhwxEaGoqhQ4fesK97d/uGcomIPO3qnBfZYkV4YkztjfxUFdZqEwSNBG2gHqqiQlVVnFxvf6ABUO8imkTkOnaHmgULFqB3797o06cP2rZti1WrVjXYdsOGDU4pjojIXWwLVf44qFJnno5YOwot6XWQTWa7XzPAEMJ5NURuZHeoeeGFF2wTlqKjo20B5+p/27Vr57IiiYg8TbFYEd0zBWd3/WB3n3YDukLSaptuSEROYXeo6devH86dO4cZM2agTZs2yM7OxqpVq/CHP/wBsiwjMjISvXv3xn//+19X1ktE5BGSTov4IT1QtOewXXcNbpXcDrrQoCbbEZHz2B1qdu3ahaVLl+L//u//0K9fP7z55ptITk6GyWRCTk4OsrOzsW/fPlfWSkTkUdqQQHQafyvyvmz8Ygi9IQRp944CeOqJyK0cvqNwRUUFfv/73+Pdd9/Fr3/9azz//PMICvL+v0Z4R2EicgbZYsWlY6dxfN3On5ZIuEoQENE5Hl3uGg5Jr+VVT0RO4JZlEo4dO4Y5c+YgKysLr732Gh566KFmFesuDDVE5Cyy1QpRFFFWUIyLeYWQrVbow4IR0zvVFmY4QZjIOVy+TILVaoXJZMIDDzyAkpISzJgxA3feeSdat27drIKJyD9ZzVaIGhHGkiuw1JihD9IjpI0BqqL8dLWRD5I0tbUbOsQgtH0UoKoQRJFrPRF5mN3vKq+99hoOHjyIgwcP4siRIwgICED37t3Rv39//PKXv4TBYHBlnUTkQxRZgSLL+OGbLORuzEHFxZ9O0xiiWyPttl5IHdETosa3bwMviAIk0XfDGZG/sfv0kyiKSEhIwLRp0/DAAw+gU6dOrq7NqXj6icg9FEWBpdqMtQs+weUzFxpsF5USizvm3QeNjpc8E1HDXDKnZtiwYcjJyUF5eTmCg4PRvXt39O7d2/ZIT0+H5MWT4hhqiNxDkRV8/fuPcf5kcZNt43okYfRTkyHxtA0RNcAlc2q2bNkCoHaCcFZWFrKzs5GdnY3ly5fjypUr0Ov16NatG3bvduw24kTkP1RFRcmxs3YFGgA4vf8kKs6XwRDD+Xh081RVBVQVqiJDsVhqV2zX6QGoEEQG55bA4ZPBKSkpSElJwf3332/blp+fj7179/I+NUQtnGy14tC6PQ71OfC/PRg4dQS0ep2LqqKWQFUUWCqMqDlfAmtluW27IEnQtYpAYGQMBEmCIIoerJJczSkz3BITE5GYmIgpU6Y44+WIyEdpdFq7R2muupBfDJEfNHQTVEVB1bnTMF08f+M+WYbpQinMly8iNKkzJH0Ag40f45ElIqeyZwmBuu0VAL57BRR5lqrIqLlYWm+gqdNOllF+8uiPv2/krxhqiMhpZKuMsLbhDvUJiwqHwg8aai5BRE2pfaODqmxFzYUSqIrs4qLIUxhqiMhpBAHoMqqXQ33SbusDjQ/fiI88R1VVmMsuQ5WtdvcxXboACPzo81c8skTkNKIkIal/ZwQagu1qb4hpjejO7bmkADWPqsBaVeFYF6vFoRBEvoWhhoicSlVVjHlmCrSBjV/NFBgWhDFzpwDNW36OCFDRvN8f/s75LYYaInIqSauBIaY1Jv1+Gtr3SLphGQRBEpHQtxMmLZiOoFYhXC+Jmk8QIOkDHOwjQpB4utNf8cgSkdNptBqERhkw+olJMFfVIH93HsxVJuhDA5E0IBUanQaSVuPT6z6R5wmiCH2rNqg6d8bu0RddeCvUDvGQP2KoISKXEEURok6ERheCtNt6Q5UVCJJvL2BJXkgAdOGtYb580a7mgZHRvLuwH+PpJyJyOUEQIGokBhpyOkGUENyuA6TAoCbbBrXr8OOyCeSvGGqIiMi3CQLCklOhj4gE6rlbsBQQiJCEjtC3iuDdhP0cTz8REZFPEwQBEAQExbRHUEwczFcuQbGYAUGANiSsdhRHVRloWgCGGiIi8gtX58roWkXUThwWhJ9OefLUZ4vAUENERH7l6sgNtTwciyMiIiK/wFBDREREfoGhhoiIiPyCz4QaWZbx/PPPIzExEYGBgUhOTsYrr7wClWt4EBEREXxoovCiRYvw97//HcuWLUPXrl2xd+9ezJgxAwaDAU888YSnyyMiIiIP85lQ8/3332PixIkYN24cACAhIQErVqzA7t27PVwZEREReQOfOf00ePBgbNy4EUePHgUA7N+/H9u3b8fYsWPrbW8ymWA0Gus8iIiIyH/5zEjNvHnzYDQakZqaCkmSIMsyXn31VUydOrXe9gsXLsTLL7/s5iqJiIjIU3xmpObzzz/H8uXL8cknnyA7OxvLli3D66+/jmXLltXbfv78+SgrK7M9Tp8+7eaKiYiIyJ0E1UcuH4qLi8O8efMwc+ZM27YFCxbg448/xpEjR5rsbzQaYTAYUFZWhrCwMFeWSkRERE7iyOe3z4zUVFVVQbxuMTJJkqAoiocqIiIiIm/iM3Nqxo8fj1dffRXx8fHo2rUr9u3bhzfffBMPP/ywp0sjIiIiL+Azp5/Ky8vx/PPPY/Xq1SgtLUVsbCweeOABvPDCC9DpdE325+knIiIi3+PI57fPhJqbxVBDRETke/xyTg0RERFRYxhqiIiIyC8w1BAREZFfYKghIiIiv8BQQ0RERH6BoYaIiIj8AkMNERER+QWGGiIiIvILDDVERETkFxhqiIiIyC8w1BAREZFfYKghIiIiv8BQQ0RERH6BoYaIiIj8AkMNERER+QWGGiIiIvILDDVERETkFxhqiIiIyC8w1BAREZFfYKghIiIiv8BQQ0RERH6BoYaIiIj8AkMNERER+QWGGiIiIvILDDVERETkFxhqiIiIyC8w1BAREZFfYKghIiIiv8BQQ0RERH6BoYaIiIj8AkMNERER+QWGGiIiIvILDDVERETkFzSeLoCIPMtqtkCUJFw5ewFWkwUBoUEIiTRAVVVIGsnT5RER2Y2hhqiFkq0yZLMFh/67Gye2HYKpotq2LyymNTqP6oWUW7tBZLAhIh/hU6efzp49i5///OeIiIhAYGAgunXrhr1793q6LCKfo8gyaoyVWPvihzj8vz11Ag0AGM9dwp6PN2LTW6sgW2QPVUlE5BifCTWXL1/GLbfcAq1Wi//97384fPgw3njjDbRq1crTpRH5HhXY8MfPUXWpvNFmxbmF2Ln0G8gWq5sKIyJfpaqqp0vwndNPixYtQlxcHD744APbtsTERA9WROSbFFlGQdZRVJwvs6v9qV1H0PveYQg0+MzbBRG5SU2NCVqtBnt25uBEXj40Wg169e2GpI4doALQat37vuEz71JfffUVMjIyMGXKFGzZsgXt2rXDr3/9azz66KP1tjeZTDCZTLbnRqPRXaUSeTcVyPt2n/3NVRVHvs1Gt/EDodFpXVgYEfkSi8WCTz5YiRVLV6Gk+HydfaldU/D4U9MxeGh/6AN0bqvJZ04/nTx5En//+9+RkpKCb775Bo8//jieeOIJLFu2rN72CxcuhMFgsD3i4uLcXDGRdxI1Ei4VljrU51JhKVTF80PLROQdLBYLnpn1Mt567d0bAg0AHPnhGJ589Hf47OM1MNWY6nkF1/CZUKMoCnr37o0//OEP6NWrFx577DE8+uijeOedd+ptP3/+fJSVldkep0+fdnPFRN7L0XPfqqICgouKISKfUlNtwr/+vgIb121rsu0bC/6G3B+OQVEUN1TmQ6EmJiYGaWlpdbZ16dIFhYWF9bbX6/UICwur8yAiQFUUhEaFO9QnNCocAlMNEQHQaCWsWLbKrraqquJff1sOs9ni4qpq+UyoueWWW5CXl1dn29GjR9GhQwcPVUTkmxRZQcqw7g71Sb2tNzR6zqchIuC7zN24dOGy3e23btrptlNQPhNqZs+ejZ07d+IPf/gDjh8/jk8++QTvvfceZs6c6enSiHyKpNWg463doA3U29U+qlN7hLQxuLgqIvIFslXGsSMnHeqjKArOnS1xUUV1+Uyo6devH1avXo0VK1YgPT0dr7zyCt566y1MnTrV06UR+RxREjHyqbsg6Rq/ADIkKhzDZk2EIPLUExEBEGrfPxzVnD7N4TOXdAPAnXfeiTvvvNPTZRD5PEmrQesOURj73FRkfb4F5344BVwzd1jSaZDQPxV97h8OjU4DUfSZv3+IyIUkSUL33mlNN7yGTq9D+7hYF1VUl0+FGiJyHkmrgSEmAsNnTYSpogZnco7DUmNBYHgw4nunAADn0RDRDXr17Yb28bE4U1hkV/uMcSPcNtrLP7+IWjBBFCBpNQhqFYJOI3oiLaMvkgalQaPXMtAQUb2sVhm/mPlzu9pqdVo8OuvnCAwMcHFVtRhqiMiGc2eIqCl6vQ53Tr4NDz/+s0bbaXVavPG3lxHdrq2bKmOoISIiIgfp9Dr8evYMLP7gNfTpX/cWERqtBmPGj8Tn//kHBt3aFwEB9l1p6QycU0NEREQO0+l1uGVofwwc0geXLl7B2cJz0GglJHVMgFarQYCbTjldi6GGiIiImkXSSJAgITomCtExUZ4uh6efiIiIyD8w1BC1MFaTxbbitmKVIVtlD1dEROQcPP1E1EIosoyyc5eQ+81elBw9A8UiIzA8BB1vTUfSLekQgCbvMExE5M34DkbUAsgWK7a9+x+c2Xe8zvbqskrsLijBvn9vw62/Ho+olPbQMNgQkY/i6SciP6fICjL/uuaGQHMtS40Zm99ejYuniiFbrG6sjojIeRhqiPyYoig4e/Akzv1Q0GRbVVawa9kGCFzniYh8FN+9iPyYKis4sj7L7vbG4ku4mF8MVVWbbkxE5GUYaoj8mKqqKMk741CfU7uPQDbzFBQR+R6GGiI/1pxwYqkxc6SGiHwSQw2RH9PotYCDa1TqgvQQBC5sSUS+h6GGyM/FpHVwqH3SoLTaMERE5GMYaoj8mKiR0OX2vna3bxUXifD2kS6siIjIdRhqiPyYIAiITo1DfN9OTbaVtBoMengM59MQkc9iqCHyc6JGwpBH70DykPQG59cEhAXhtmfuRVhMa0gayb0FEhE5iaC2kD/LjEYjDAYDysrKEBYW5ulyiNxOtlhhqqhG7voslOSdgWy1Iig8BCnDuqN9z45QFQWSlkskEJF3ceTzm+9gRC2EpNUgqFUoeky6BYIoQBAEKLICUSNBlERA4sAtEfk2hhqiFubaK5tEnmoiIj/CP82IiIjILzDUEBERkV9gqCEiIiK/wFBDREREfoGhhoiIiPwCQw0RERH5BYYaIiIi8gsMNUREROQXGGqIiIjILzDUEBERkV9gqCEiIiK/wFBDREREfsFnQ81rr70GQRDw1FNPeboUIiIi8gI+GWr27NmDd999F927d/doHbJVhsVssT03my2QZcWDFREREbVcGk8X4KiKigpMnToV77//PhYsWOCRGqwWKyAI2LFxD75asQ6nT54FBAEJHeMw6edj0W9oL0AFJI3kkfqIiIhaIp8LNTNnzsS4ceMwevToRkONyWSCyWSyPTcajU75+hazBeeLL2L+Lxag9NyFOvv27/4B+3f/gHYdYrDwH8+hVYQBGq3P/YiJiIh8kk+dfvr000+RnZ2NhQsXNtl24cKFMBgMtkdcXJxTaigvq8CcB1+4IdBc62zBOcz5+QuorqpxytckIiKipvlMqDl9+jSefPJJLF++HAEBAU22nz9/PsrKymyP06dP33QNNdUmfPDWCpRdanrU50LJRXz8ty9QU21qsi0RERHdPEFVVdXTRdhjzZo1mDx5MiTpp3kqsixDEASIogiTyVRn3/WMRiMMBgPKysoQFhbWrBqqK6tx39DH6kwObkxQSCA+3fIetDpts74eERFRS+fI57fPTPgYNWoUDh48WGfbjBkzkJqaimeffbbRQOMsObsO2R1oAKCqohpHDhxDt75pLqyKiIiIAB8KNaGhoUhPT6+zLTg4GBERETdsd5UKY6XDfSrLq1xQCREREV3PZ+bUeANDa4PDfcJahbqgEiIiIrqez4zU1CczM9OtX6/nwHQEBQeiqrLarvbhEQZ0Tu/o4qqIiIgI4EiNQxRZwagJQ+1uP+auEbBarS6siIiIiK5iqHFAQKAe05+8H7Hx0U22TUiJw/2PTYY+QO+Gyoj8j6qqsJotUFUVssVa5zkRUX18+vSTJ+j1Ovx5+St4ceYiHDlwvN423fqm4cW//hZaLS/lJmoOxSrj4qkSHF6/F2dyTkCVFYiSiPa9OqLL7X0Q0aEtRC5DQkTX8Zn71NwsZ9yn5ipFVqCqKvKPFWLNR//9ae2nlHhMfugOtO8QA1ESIYocCCNylGKV8f2/1uHUriMNtkkc1AWDpmcw2BC1AI58fjPU3KSaqhqIUm14UWQFAUFN3+2YiOonW2Ts/vhbnNh+qMm2KcO6o+8DIyBxfTUiv+bI5zeHEm5SQFAAdHoddHodAw3RTaouq7Ar0ADAsa0HYKqohtVshcVkgaIosFo4Mb+lki1WqIpaO5KuKFAUBbJV9nRZ5Gb8E4eIvILVZEHuN1n2d1CB3PVZaNstEZ8//yEMbcPRI6Mvut/eG6JGgoYjOC2CbLFCkRWc3HYQJ7ceQOXF2rX5Qtu2QvKw7kgY3BWCKELiqcoWgSM1ROQVRI2Ec7kFDvU5d7gAkR3aAgDKSq5g64ff4p+/XozLRRc5atMCyBYrrpy5gP/+7l84uHq7LdAAQHnJZeR8vgX/e34pKkqvQObvQ4vAUENEXkEQBchmxz54ZLMVGn3dqwyrjVX44oWPUFNh300yyTepqoqqS+XY+pdVsFSbGmxnKq/Clj//G+bKGjdWR57CUENEXkGxygg0BDvUJyAsGKZ6wktNRTV2fr4VFpP9C9CSb5EtMg6u+Q6yHcfYXFmDH9buhNWBBYnJNzHUEJF3EAQkDXZsRfuEgak4sfdYvftytx6CIDijMPJGstmCcwdP2t3+9N48F1ZD3oKhhoi8gqSRkHRLOjQB9t20UhuoQ9KgNOxft7fe/ZYaM86fKnVmieRFSvNOQ1XsvyOJbLbi0qkSF1ZE3oChhoi8ypDHxkEQGx9iEUQBgx4Zi6Ijp1GaX9xgO55+8l/WGsePrczTT36PoYaIvIZGp0F0lw4Y8dRdCGodWm+b4IhQDJs1EUGtQ7H2zVWNvl5IA69Bvi+wVYjDfQIcnLNFvoc3ciAir6LRaRCV0h6TFv0CxYcLcGrXEZirzdAF6RHXqyNiuyXi+K4j+PL1lTBVNXzVS0RcJMKjW7mxcnKnqM5x0AUH2H1VU1BEGMLbtXFxVeRpDDVE5HU0utq3ppi0BER2bAeg9hLeorwz+OevF6PimvuRNKTXHf1q51zwnmt+SZFlJAxOw9EN2Xa1Tx7aHYqsQOKafH6NR5eIvJYgCtAG6KAN0EEXqEf7tHgEGYKa7JfUtxO6juwJSctE4680Oi263jkI4XFRTbaNTGmHlBE9uU5YC8BQQ0Q+Q9RIuG/BdHQanFbvZGKNToOeY/th/Nx7eFv8FkCURAx/+h7E9kwG6plbLogC4vunYsisyRAkfty1BFylm4h8jtVsgbnajP3fZOHy2YsQJAFRidHoNrp37eiO3r7Lwsk/yBYrzFU1OJ65H+XFlwEBMMS2QcfhPaDRaSHpOELjyxz5/GaoISKfZTVboMgKAHARS4JstkD58d41oigyzPgJRz6/ecSJyGdpdByRoZ9IOi3nhbdwPMlIREREfoGhhoiIiPwCQw0RERH5BYYaIiIi8gsMNeTVVFVFC7lAj4iIbhKvfiKvYzFbIEkS8n84hcKjpwEAcZ3aI6lrImRZhpZXvBARUT0YasirWC1W7Fq3Bxs/3YQLRRfr7GsTG4FR94/EwLH9eT8SIiK6AT8ZyGtYLVas/tuX2Lp6e737LxRdxGdvfoGiE0W4a9YkBhsiIqqDc2rIK1itVuzL3N9goLnWti+/Q/amfbBarG6ojIiIfAVDDXkFAQI2frbJ7vYbP9sMQahnBTsiImqxGGrIK5SePo+zx4vsbl908hxKCktcWBHRTxRFgbnGDNkqQ7bKMNeYPV0SEdWDkxLIKzQnoJQUlCI2KdYF1RDVkmUZAgQUHDqFXV/twMUzFyCIAtomxmDQ5MFomxQNQRAgivz7kMgbMNSQVxAlxz8UmtOHyF6yVUbF5Qp8/NxSnD99vs6+0oJSHMzcj7i0eEx9+SHoAnT8fSTyAvxXSF6hfUp7h/vEdXK8D5G9aipr8I8579wQaK51+nAh/vXb9yBbZTdWRkQN8ZlQs3DhQvTr1w+hoaGIiorCpEmTkJeX5+myyElCW4UgpWdHu9t37JmMsNZhLqyIWjJzjRnr/7EO5RfLm2xbWlCK7/69DRaTxQ2VEVFjfCbUbNmyBTNnzsTOnTuxYcMGWCwW3H777aisrPR0aeQEkiRh7PQMu65oEgQBYx/K4HA/uYyqqvhh20G722f9bw8kjeTCiojIHj4zp2bdunV1ni9duhRRUVHIysrC0KFDPVQVOYsoiUjo0gH3zZmCz/78BVSl/vWeBEHAvbPvRmLXBIYacplje47Carb/Pkjll8pRfPIcYlPaubAqImqKz4Sa65WVlQEAWrduXe9+k8kEk8lke240Gt1SFzWfVq9F/9v7ol3HWHzz0Qb8sPOwLdwIooCuA9Nw+89Ho31yO2j1XP+JXKfySoXDfaorql1QCRE5widDjaIoeOqpp3DLLbcgPT293jYLFy7Eyy+/7ObK6GZp9VrEd47Dwy9Og6nGjPNnzwMqENmuDfSBekhaiZfPkssFhQU73CcgONAFlRCRI3wy1MycOROHDh3C9u0N31J//vz5mDNnju250WhEXFycO8qjmySKIkS9CK1eixCD4x8uRDcrpV8nSBrJ7quagsODEZ0U7eKqiKgpPvcn76xZs7B27Vps3rwZ7ds3fEmvXq9HWFhYnQcRkT1EjYi0IV3tbt87oy8UWXFhRURkD58JNaqqYtasWVi9ejU2bdqExMRET5dERH5Kp9fh9kfGIDi86ZHCiHZtcOu9wzjPi8gL+EyomTlzJj7++GN88sknCA0NRXFxMYqLi1Fdzcl5ROR8gWFB+MWbv0Sr6PovRgCAmOQYPPz6o9DofPJMPpHfEVRVrf/aWS/T0P1LPvjgA0yfPr3J/kajEQaDAWVlZTwVRUR2ka0yBEHAsb1Ha9d+OnsRgiAgOikaAycNRnxaB0AAJ68TuZAjn98+8+eFj2QvIvIjV2+ol9K3E5J6JteOyKiA1WKBpNUwzBB5GZ8JNUREniJK4k83exQArV7n2YKIqF78M4OIiIj8AkMNERER+QWGGiIiIvILDDVERETkFxhqiIiIyC8w1BAREZFfYKghIiIiv9Bi7lNz9eZ9RqPRw5UQERGRva5+bttzE94WE2rKy8sBAHFxcR6uhIiIiBxVXl4Og8HQaBufWfvpZimKgqKiIoSGhja4jpQ/MxqNiIuLw+nTp7n2lQ/hcfNNPG6+icfNO6mqivLycsTGxja5NEmLGakRRRHt27f3dBkeFxYWxn+sPojHzTfxuPkmHjfv09QIzVWcKExERER+gaGGiIiI/AJDTQuh1+vx4osvQq/Xe7oUcgCPm2/icfNNPG6+r8VMFCYiIiL/xpEaIiIi8gsMNUREROQXGGqIiIjILzDUEBERkV9gqPFRS5YsQUJCAgICAjBgwADs3r27wbYWiwW///3vkZycjICAAPTo0QPr1q2r00aWZTz//PNITExEYGAgkpOT8corr9i11gbZZ+vWrRg/fjxiY2MhCALWrFnTZJ/MzEz07t0ber0eHTt2xNKlS29o48jvAjnOFcdt4cKF6NevH0JDQxEVFYVJkyYhLy/PNd9AC+Wqf29XvfbaaxAEAU899ZTTaqabx1Djgz777DPMmTMHL774IrKzs9GjRw9kZGSgtLS03vbPPfcc3n33Xfz1r3/F4cOH8atf/QqTJ0/Gvn37bG0WLVqEv//971i8eDFyc3OxaNEi/PGPf8Rf//pXd31bfq+yshI9evTAkiVL7Gqfn5+PcePGYcSIEcjJycFTTz2FX/ziF/jmm29sbRz9XSDHueK4bdmyBTNnzsTOnTuxYcMGWCwW3H777aisrHTVt9HiuOK4XbVnzx68++676N69u7PLppulks/p37+/OnPmTNtzWZbV2NhYdeHChfW2j4mJURcvXlxn21133aVOnTrV9nzcuHHqww8/3Ggbch4A6urVqxtt88wzz6hdu3ats+2+++5TMzIybM8d/V2gm+Os43a90tJSFYC6ZcsWZ5RJ13HmcSsvL1dTUlLUDRs2qMOGDVOffPJJJ1dLN4MjNT7GbDYjKysLo0ePtm0TRRGjR4/Gjh076u1jMpkQEBBQZ1tgYCC2b99uez548GBs3LgRR48eBQDs378f27dvx9ixY13wXZA9duzYUec4A0BGRobtODfnd4Fcr6njVp+ysjIAQOvWrV1aGzXM3uM2c+ZMjBs37oa25B1azIKW/uLChQuQZRlt27ats71t27Y4cuRIvX0yMjLw5ptvYujQoUhOTsbGjRuxatUqyLJsazNv3jwYjUakpqZCkiTIsoxXX30VU6dOden3Qw0rLi6u9zgbjUZUV1fj8uXLDv8ukOs1ddwCAwPr7FMUBU899RRuueUWpKenu7NUuoY9x+3TTz9FdnY29uzZ46EqqSkcqWkB3n77baSkpCA1NRU6nQ6zZs3CjBkz6izh/vnnn2P58uX45JNPkJ2djWXLluH111/HsmXLPFg5kf+bOXMmDh06hE8//dTTpVAjTp8+jSeffBLLly+/YeSbvAdHanxMmzZtIEkSSkpK6mwvKSlBdHR0vX0iIyOxZs0a1NTU4OLFi4iNjcW8efOQlJRkazN37lzMmzcP999/PwCgW7duKCgowMKFCzFt2jTXfUPUoOjo6HqPc1hYGAIDAyFJksO/C+R6TR23a82aNQtr167F1q1b0b59e3eWSddp6rhlZWWhtLQUvXv3tu2XZRlbt27F4sWLYTKZIEmSu8um63CkxsfodDr06dMHGzdutG1TFAUbN27EoEGDGu0bEBCAdu3awWq1YuXKlZg4caJtX1VVVZ2RGwCQJAmKojj3GyC7DRo0qM5xBoANGzbYjvPN/C6Q6zR13ABAVVXMmjULq1evxqZNm5CYmOjuMuk6TR23UaNG4eDBg8jJybE9+vbti6lTpyInJ4eBxlt4eqYyOe7TTz9V9Xq9unTpUvXw4cPqY489poaHh6vFxcWqqqrqgw8+qM6bN8/WfufOnerKlSvVEydOqFu3blVHjhypJiYmqpcvX7a1mTZtmtquXTt17dq1an5+vrpq1Sq1TZs26jPPPOPub89vlZeXq/v27VP37dunAlDffPNNdd++fWpBQYGqqqo6b9489cEHH7S1P3nypBoUFKTOnTtXzc3NVZcsWaJKkqSuW7fO1qap3wW6ea44bo8//rhqMBjUzMxM9dy5c7ZHVVWV278/f+WK43Y9Xv3kfRhqfNRf//pXNT4+XtXpdGr//v3VnTt32vYNGzZMnTZtmu15Zmam2qVLF1Wv16sRERHqgw8+qJ49e7bO6xmNRvXJJ59U4+Pj1YCAADUpKUn93e9+p5pMJnd9S35v8+bNKoAbHleP1bRp09Rhw4bd0Kdnz56qTqdTk5KS1A8++OCG123sd4FuniuOW32vB6De40vN46p/b9diqPE+gqrylrFERETk+zinhoiIiPwCQw0RERH5BYYaIiIi8gsMNUREROQXGGqIiIjILzDUEBERkV9gqCEiIiK/wFBDREREfoGhhoiIiPwCQw0R+Yzf/va3mDRpkqfLICIvxVBDRD4jJycHPXv29HQZROSlGGqIyGfs37+foYaIGsRQQ0Q+4cyZM7hw4YIt1Fy5cgXjx4/HkCFDUFxc7NniiMgrMNQQkU/IyclBeHg4EhIScPDgQfTr1w/t2rXD5s2bER0d7enyiMgLMNQQkU/IyclBjx498Mknn2DYsGF45pln8M4770Cr1QIAJk+ejFatWuGee+6p0+/1119H165dkZ6ejo8//tgTpRORmwiqqqqeLoKIqCn33HMPNm3aBAD4z3/+g0GDBtXZn5mZifLycixbtgz//ve/AQAHDx7EtGnT8P3330NVVYwYMQLr1q1DeHi4u8snIjfgSA0R+YScnBzcddddqKmpwZUrV27YP3z4cISGhtbZlpubi0GDBiEgIACBgYHo0aMH1q1b56aKicjdGGqIyOuVl5fj5MmTmDlzJhYvXoz7778fP/zwQ5P90tPTkZmZiStXruDy5cvIzMzE2bNn3VAxEXmCxtMFEBE1Zf/+/ZAkCWlpaejVqxcOHTqE8ePHY/fu3WjTpk2D/dLS0vDEE09g5MiRMBgMGDhwICRJcmPlROROHKkhIq+Xk5OD1NRU6PV6AMCf/vQndO7cGXfddRfMZnOjfX/5y18iOzsbmzdvhlarRUpKijtKJiIP4ERhIvIbmZmZWLx4sW2iMACUlpYiKioKeXl5mDJlCrKzs6HRcJCayB/xXzYR+YXRo0dj//79qKysRPv27fHFF19g0KBBmDhxIsrKyhAcHIwPPviAgYbIj3GkhoiIiPwC59QQERGRX2CoISIiIr/AUENERER+gaGGiIiI/AJDDREREfkFhhoiIiLyCww1RERE5BcYaoiIiMgvMNQQERGRX2CoISIiIr/AUENERER+gaGGiIiI/ML/A748u/TYOuE7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(y_test.shape[1]):\n",
    "    estimator = CreateExtraTreesRegressor()\n",
    "    estimator.fit(X_test, y_test[:, i])\n",
    "    plt.figure()\n",
    "    plt.bar([df_test.columns[j+5] for j in range(list_len*2)], estimator.feature_importances_)\n",
    "    plt.ylabel(\"Важность\")\n",
    "    plt.xticks(rotation = 90)\n",
    "    plt.savefig(\"material_results_M_feature_importance_\"+str(i)+\"_sklearn_ETR.svg\")\n",
    "    ind_k = np.argpartition(estimator.feature_importances_[:list_len], -1)[-1:][0]\n",
    "    ind_M = np.argpartition(estimator.feature_importances_[list_len:], -1)[-1:][0]\n",
    "    plt.figure()\n",
    "    ax = sns.scatterplot(data = df_test, x = df_test.columns[ind_k+5], y = df_test.columns[ind_M+5+list_len], hue = df_test.columns[i], s = 100)\n",
    "    plt.savefig(\"material_results_M_feature_importance_\"+str(i)+\"_most_important_features_sklearn_ETR.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:32.970859Z",
     "start_time": "2024-05-29T00:16:29.569266Z"
    },
    "collapsed": false,
    "id": "v9hy-QdUUE_l",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "1c74c708-efe7-48bf-e269-e0a5f6d0d2d0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "estimator = CreateExtraTreesRegressor()\n",
    "estimator.fit(X_test, y_test)\n",
    "fig = plt.figure()\n",
    "plt.bar([df_test.columns[j+5] for j in range(list_len*2)], estimator.feature_importances_)\n",
    "plt.ylabel(\"Важность\")\n",
    "plt.xticks(rotation = 90)\n",
    "plt.savefig(\"material_results_M_feature_importance_sklearn_ETR.svg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:48.756212Z",
     "start_time": "2024-05-29T00:16:32.971865Z"
    },
    "collapsed": false,
    "id": "v9hy-QdUUE_l",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "1c74c708-efe7-48bf-e269-e0a5f6d0d2d0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Коэффициент детерминации:\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
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       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
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       "      <th>0</th>\n",
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       "      <td>0.607873</td>\n",
       "      <td>-0.431295</td>\n",
       "      <td>0.122147</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
       "0  0.960283   0.607873 -0.431295  0.122147  0.112094"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя абсолютная ошибка:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "      <td>1.024837</td>\n",
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      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Корень среднеквадратической ошибки:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
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       "      <th>$\\mu$</th>\n",
       "      <th>$\\mu^*$</th>\n",
       "      <th>$\\mu_{APE}$</th>\n",
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       "      <th>$\\nu_2^*$</th>\n",
       "      <th>${\\nu_2}_{APE}$</th>\n",
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       "      <td>-1.820</td>\n",
       "      <td>-1.850100</td>\n",
       "      <td>1.653846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.81800</td>\n",
       "      <td>0.815915</td>\n",
       "      <td>0.254890</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>1.080320</td>\n",
       "      <td>0.888073</td>\n",
       "      <td>-1.750</td>\n",
       "      <td>-1.404630</td>\n",
       "      <td>19.735429</td>\n",
       "      <td>-2.400</td>\n",
       "      <td>-2.538830</td>\n",
       "      <td>5.784583</td>\n",
       "      <td>-1.690</td>\n",
       "      <td>-1.642560</td>\n",
       "      <td>2.807101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.82100</td>\n",
       "      <td>0.814498</td>\n",
       "      <td>0.791961</td>\n",
       "      <td>1.11000</td>\n",
       "      <td>1.095790</td>\n",
       "      <td>1.280180</td>\n",
       "      <td>-3.580</td>\n",
       "      <td>-2.681770</td>\n",
       "      <td>25.090223</td>\n",
       "      <td>-2.820</td>\n",
       "      <td>-2.520060</td>\n",
       "      <td>10.636170</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>-1.858540</td>\n",
       "      <td>5.002260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>0.818647</td>\n",
       "      <td>0.165000</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.092140</td>\n",
       "      <td>0.714545</td>\n",
       "      <td>-1.340</td>\n",
       "      <td>-2.428290</td>\n",
       "      <td>81.215672</td>\n",
       "      <td>-2.610</td>\n",
       "      <td>-2.526440</td>\n",
       "      <td>3.201533</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>-1.724640</td>\n",
       "      <td>3.271856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.81900</td>\n",
       "      <td>0.819087</td>\n",
       "      <td>0.010623</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>1.104920</td>\n",
       "      <td>1.368807</td>\n",
       "      <td>-3.230</td>\n",
       "      <td>-2.734450</td>\n",
       "      <td>15.342105</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-2.687900</td>\n",
       "      <td>1.430189</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>-1.758240</td>\n",
       "      <td>0.664407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.71600</td>\n",
       "      <td>0.673583</td>\n",
       "      <td>5.924162</td>\n",
       "      <td>0.87000</td>\n",
       "      <td>0.960728</td>\n",
       "      <td>10.428460</td>\n",
       "      <td>0.340</td>\n",
       "      <td>0.545730</td>\n",
       "      <td>60.508824</td>\n",
       "      <td>-5.520</td>\n",
       "      <td>-2.995420</td>\n",
       "      <td>45.735145</td>\n",
       "      <td>-1.000</td>\n",
       "      <td>-2.045700</td>\n",
       "      <td>104.570000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.80400</td>\n",
       "      <td>0.808556</td>\n",
       "      <td>0.566667</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.121278</td>\n",
       "      <td>1.934364</td>\n",
       "      <td>-1.900</td>\n",
       "      <td>-3.018640</td>\n",
       "      <td>58.875789</td>\n",
       "      <td>-2.300</td>\n",
       "      <td>-2.723880</td>\n",
       "      <td>18.429565</td>\n",
       "      <td>-2.010</td>\n",
       "      <td>-1.838200</td>\n",
       "      <td>8.547264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.80300</td>\n",
       "      <td>0.799750</td>\n",
       "      <td>0.404732</td>\n",
       "      <td>1.12900</td>\n",
       "      <td>1.070559</td>\n",
       "      <td>5.176351</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>-1.263770</td>\n",
       "      <td>54.865357</td>\n",
       "      <td>-2.700</td>\n",
       "      <td>-2.360120</td>\n",
       "      <td>12.588148</td>\n",
       "      <td>-1.870</td>\n",
       "      <td>-1.984280</td>\n",
       "      <td>6.111230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.275813</td>\n",
       "      <td>6.081746</td>\n",
       "      <td>0.58000</td>\n",
       "      <td>0.144526</td>\n",
       "      <td>75.081659</td>\n",
       "      <td>-2.490</td>\n",
       "      <td>2.261062</td>\n",
       "      <td>190.805703</td>\n",
       "      <td>-0.990</td>\n",
       "      <td>-1.335182</td>\n",
       "      <td>34.866869</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>0.874231</td>\n",
       "      <td>245.705167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.244184</td>\n",
       "      <td>6.083077</td>\n",
       "      <td>0.49100</td>\n",
       "      <td>0.480600</td>\n",
       "      <td>2.118126</td>\n",
       "      <td>-3.790</td>\n",
       "      <td>-1.879218</td>\n",
       "      <td>50.416412</td>\n",
       "      <td>-1.980</td>\n",
       "      <td>-0.400174</td>\n",
       "      <td>79.789192</td>\n",
       "      <td>-0.800</td>\n",
       "      <td>-0.945485</td>\n",
       "      <td>18.185625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.41700</td>\n",
       "      <td>0.420564</td>\n",
       "      <td>0.854616</td>\n",
       "      <td>1.13300</td>\n",
       "      <td>0.798300</td>\n",
       "      <td>29.541050</td>\n",
       "      <td>-4.900</td>\n",
       "      <td>-2.811940</td>\n",
       "      <td>42.613469</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>-0.494090</td>\n",
       "      <td>70.413772</td>\n",
       "      <td>-0.500</td>\n",
       "      <td>-1.174405</td>\n",
       "      <td>134.881000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.49000</td>\n",
       "      <td>0.517023</td>\n",
       "      <td>5.514898</td>\n",
       "      <td>1.04200</td>\n",
       "      <td>1.007982</td>\n",
       "      <td>3.264664</td>\n",
       "      <td>-4.000</td>\n",
       "      <td>-4.151610</td>\n",
       "      <td>3.790250</td>\n",
       "      <td>-1.700</td>\n",
       "      <td>-1.102440</td>\n",
       "      <td>35.150588</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>-1.252740</td>\n",
       "      <td>108.790000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.47700</td>\n",
       "      <td>0.504617</td>\n",
       "      <td>5.789727</td>\n",
       "      <td>1.07000</td>\n",
       "      <td>0.826208</td>\n",
       "      <td>22.784336</td>\n",
       "      <td>-5.600</td>\n",
       "      <td>-2.058198</td>\n",
       "      <td>63.246464</td>\n",
       "      <td>1.720</td>\n",
       "      <td>-3.291948</td>\n",
       "      <td>291.392326</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>-0.771042</td>\n",
       "      <td>80.627085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.16600</td>\n",
       "      <td>0.271160</td>\n",
       "      <td>63.349398</td>\n",
       "      <td>0.25900</td>\n",
       "      <td>0.236505</td>\n",
       "      <td>8.685251</td>\n",
       "      <td>-0.654</td>\n",
       "      <td>1.112360</td>\n",
       "      <td>270.085627</td>\n",
       "      <td>-0.574</td>\n",
       "      <td>-1.643940</td>\n",
       "      <td>186.400697</td>\n",
       "      <td>-0.421</td>\n",
       "      <td>0.599200</td>\n",
       "      <td>242.327791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>0.720756</td>\n",
       "      <td>12.102927</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>0.879811</td>\n",
       "      <td>20.017182</td>\n",
       "      <td>2.600</td>\n",
       "      <td>0.703960</td>\n",
       "      <td>72.924615</td>\n",
       "      <td>-4.800</td>\n",
       "      <td>-4.947570</td>\n",
       "      <td>3.074375</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>-1.181780</td>\n",
       "      <td>57.793571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.097440</td>\n",
       "      <td>0.232727</td>\n",
       "      <td>1.57000</td>\n",
       "      <td>1.537704</td>\n",
       "      <td>2.057070</td>\n",
       "      <td>-0.510</td>\n",
       "      <td>0.709160</td>\n",
       "      <td>239.050980</td>\n",
       "      <td>-2.830</td>\n",
       "      <td>-3.385460</td>\n",
       "      <td>19.627562</td>\n",
       "      <td>-0.930</td>\n",
       "      <td>-2.020040</td>\n",
       "      <td>117.208602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.24000</td>\n",
       "      <td>1.077382</td>\n",
       "      <td>13.114355</td>\n",
       "      <td>1.78000</td>\n",
       "      <td>1.349880</td>\n",
       "      <td>24.164045</td>\n",
       "      <td>1.940</td>\n",
       "      <td>-2.618780</td>\n",
       "      <td>234.988660</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>-2.468520</td>\n",
       "      <td>37.976884</td>\n",
       "      <td>-2.270</td>\n",
       "      <td>-1.945990</td>\n",
       "      <td>14.273568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.73000</td>\n",
       "      <td>0.856648</td>\n",
       "      <td>17.349041</td>\n",
       "      <td>0.75000</td>\n",
       "      <td>1.147530</td>\n",
       "      <td>53.004000</td>\n",
       "      <td>-2.150</td>\n",
       "      <td>-0.703810</td>\n",
       "      <td>67.264651</td>\n",
       "      <td>-1.430</td>\n",
       "      <td>-2.793450</td>\n",
       "      <td>95.346154</td>\n",
       "      <td>-1.240</td>\n",
       "      <td>-1.652420</td>\n",
       "      <td>33.259677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.37000</td>\n",
       "      <td>1.240000</td>\n",
       "      <td>9.489051</td>\n",
       "      <td>1.63000</td>\n",
       "      <td>1.780000</td>\n",
       "      <td>9.202454</td>\n",
       "      <td>-4.290</td>\n",
       "      <td>1.940000</td>\n",
       "      <td>145.221445</td>\n",
       "      <td>-2.580</td>\n",
       "      <td>-3.980000</td>\n",
       "      <td>54.263566</td>\n",
       "      <td>-2.670</td>\n",
       "      <td>-2.270000</td>\n",
       "      <td>14.981273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.18600</td>\n",
       "      <td>0.263762</td>\n",
       "      <td>41.807758</td>\n",
       "      <td>0.39000</td>\n",
       "      <td>0.241255</td>\n",
       "      <td>38.139677</td>\n",
       "      <td>-0.078</td>\n",
       "      <td>0.517970</td>\n",
       "      <td>764.064103</td>\n",
       "      <td>-0.070</td>\n",
       "      <td>-0.721680</td>\n",
       "      <td>930.971429</td>\n",
       "      <td>0.047</td>\n",
       "      <td>0.187530</td>\n",
       "      <td>299.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.31261</td>\n",
       "      <td>0.378878</td>\n",
       "      <td>21.198298</td>\n",
       "      <td>0.15872</td>\n",
       "      <td>0.971315</td>\n",
       "      <td>511.967616</td>\n",
       "      <td>0.540</td>\n",
       "      <td>-4.042764</td>\n",
       "      <td>848.660000</td>\n",
       "      <td>0.930</td>\n",
       "      <td>-1.497840</td>\n",
       "      <td>261.058065</td>\n",
       "      <td>-0.110</td>\n",
       "      <td>-0.475359</td>\n",
       "      <td>332.144545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.27500</td>\n",
       "      <td>0.250326</td>\n",
       "      <td>8.972284</td>\n",
       "      <td>0.13530</td>\n",
       "      <td>0.517745</td>\n",
       "      <td>282.664775</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-2.685550</td>\n",
       "      <td>203.290385</td>\n",
       "      <td>-1.680</td>\n",
       "      <td>-1.248582</td>\n",
       "      <td>25.679643</td>\n",
       "      <td>1.050</td>\n",
       "      <td>-0.634826</td>\n",
       "      <td>160.459619</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$   $\\mu^*$  $\\mu_{APE}$  $\\lambda$  $\\lambda^*$  $\\lambda_{APE}$  \\\n",
       "0   0.78000  0.795844     2.031282    0.90900     1.102720        21.311331   \n",
       "1   0.81800  0.815915     0.254890    1.09000     1.080320         0.888073   \n",
       "2   0.82100  0.814498     0.791961    1.11000     1.095790         1.280180   \n",
       "3   0.82000  0.818647     0.165000    1.10000     1.092140         0.714545   \n",
       "4   0.81900  0.819087     0.010623    1.09000     1.104920         1.368807   \n",
       "5   0.71600  0.673583     5.924162    0.87000     0.960728        10.428460   \n",
       "6   0.80400  0.808556     0.566667    1.10000     1.121278         1.934364   \n",
       "7   0.80300  0.799750     0.404732    1.12900     1.070559         5.176351   \n",
       "8   0.26000  0.275813     6.081746    0.58000     0.144526        75.081659   \n",
       "9   0.26000  0.244184     6.083077    0.49100     0.480600         2.118126   \n",
       "10  0.41700  0.420564     0.854616    1.13300     0.798300        29.541050   \n",
       "11  0.49000  0.517023     5.514898    1.04200     1.007982         3.264664   \n",
       "12  0.47700  0.504617     5.789727    1.07000     0.826208        22.784336   \n",
       "13  0.16600  0.271160    63.349398    0.25900     0.236505         8.685251   \n",
       "14  0.82000  0.720756    12.102927    1.10000     0.879811        20.017182   \n",
       "15  1.10000  1.097440     0.232727    1.57000     1.537704         2.057070   \n",
       "16  1.24000  1.077382    13.114355    1.78000     1.349880        24.164045   \n",
       "17  0.73000  0.856648    17.349041    0.75000     1.147530        53.004000   \n",
       "18  1.37000  1.240000     9.489051    1.63000     1.780000         9.202454   \n",
       "19  0.18600  0.263762    41.807758    0.39000     0.241255        38.139677   \n",
       "20  0.31261  0.378878    21.198298    0.15872     0.971315       511.967616   \n",
       "21  0.27500  0.250326     8.972284    0.13530     0.517745       282.664775   \n",
       "\n",
       "    $\\nu_1$  $\\nu_1^*$  ${\\nu_1}_{APE}$  $\\nu_2$  $\\nu_2^*$  ${\\nu_2}_{APE}$  \\\n",
       "0     3.580  -2.171280       160.650279   -2.650  -3.078580        16.172830   \n",
       "1    -1.750  -1.404630        19.735429   -2.400  -2.538830         5.784583   \n",
       "2    -3.580  -2.681770        25.090223   -2.820  -2.520060        10.636170   \n",
       "3    -1.340  -2.428290        81.215672   -2.610  -2.526440         3.201533   \n",
       "4    -3.230  -2.734450        15.342105   -2.650  -2.687900         1.430189   \n",
       "5     0.340   0.545730        60.508824   -5.520  -2.995420        45.735145   \n",
       "6    -1.900  -3.018640        58.875789   -2.300  -2.723880        18.429565   \n",
       "7    -2.800  -1.263770        54.865357   -2.700  -2.360120        12.588148   \n",
       "8    -2.490   2.261062       190.805703   -0.990  -1.335182        34.866869   \n",
       "9    -3.790  -1.879218        50.416412   -1.980  -0.400174        79.789192   \n",
       "10   -4.900  -2.811940        42.613469   -1.670  -0.494090        70.413772   \n",
       "11   -4.000  -4.151610         3.790250   -1.700  -1.102440        35.150588   \n",
       "12   -5.600  -2.058198        63.246464    1.720  -3.291948       291.392326   \n",
       "13   -0.654   1.112360       270.085627   -0.574  -1.643940       186.400697   \n",
       "14    2.600   0.703960        72.924615   -4.800  -4.947570         3.074375   \n",
       "15   -0.510   0.709160       239.050980   -2.830  -3.385460        19.627562   \n",
       "16    1.940  -2.618780       234.988660   -3.980  -2.468520        37.976884   \n",
       "17   -2.150  -0.703810        67.264651   -1.430  -2.793450        95.346154   \n",
       "18   -4.290   1.940000       145.221445   -2.580  -3.980000        54.263566   \n",
       "19   -0.078   0.517970       764.064103   -0.070  -0.721680       930.971429   \n",
       "20    0.540  -4.042764       848.660000    0.930  -1.497840       261.058065   \n",
       "21    2.600  -2.685550       203.290385   -1.680  -1.248582        25.679643   \n",
       "\n",
       "    $\\nu_3$  $\\nu_3^*$  ${\\nu_3}_{APE}$  \n",
       "0    -1.820  -1.850100         1.653846  \n",
       "1    -1.690  -1.642560         2.807101  \n",
       "2    -1.770  -1.858540         5.002260  \n",
       "3    -1.670  -1.724640         3.271856  \n",
       "4    -1.770  -1.758240         0.664407  \n",
       "5    -1.000  -2.045700       104.570000  \n",
       "6    -2.010  -1.838200         8.547264  \n",
       "7    -1.870  -1.984280         6.111230  \n",
       "8    -0.600   0.874231       245.705167  \n",
       "9    -0.800  -0.945485        18.185625  \n",
       "10   -0.500  -1.174405       134.881000  \n",
       "11   -0.600  -1.252740       108.790000  \n",
       "12   -3.980  -0.771042        80.627085  \n",
       "13   -0.421   0.599200       242.327791  \n",
       "14   -2.800  -1.181780        57.793571  \n",
       "15   -0.930  -2.020040       117.208602  \n",
       "16   -2.270  -1.945990        14.273568  \n",
       "17   -1.240  -1.652420        33.259677  \n",
       "18   -2.670  -2.270000        14.981273  \n",
       "19    0.047   0.187530       299.000000  \n",
       "20   -0.110  -0.475359       332.144545  \n",
       "21    1.050  -0.634826       160.459619  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = cross_val_predict(CreateExtraTreesRegressor(), X_test, y_test, cv = LeaveOneOut(), n_jobs = -1)\n",
    "prediction_data = []\n",
    "for i in range(df_test.shape[0]):\n",
    "    material_data = {}\n",
    "    material_data.update({\"$\\mu$\": y_test[i][0]})\n",
    "    material_data.update({\"$\\mu^*$\": y_pred[i][0]})\n",
    "    material_data.update({\"$\\mu_{APE}$\": np.abs((y_pred[i][0]-y_test[i][0])/y_test[i][0])*100.0})\n",
    "    material_data.update({\"$\\lambda$\": y_test[i][1]})\n",
    "    material_data.update({\"$\\lambda^*$\": y_pred[i][1]})\n",
    "    material_data.update({\"$\\lambda_{APE}$\": np.abs((y_pred[i][1]-y_test[i][1])/y_test[i][1])*100.0})\n",
    "    material_data.update({\"$\\nu_1$\": y_test[i][2]})\n",
    "    material_data.update({\"$\\nu_1^*$\": y_pred[i][2]})\n",
    "    material_data.update({\"${\\nu_1}_{APE}$\": np.abs((y_pred[i][2]-y_test[i][2])/y_test[i][2])*100.0})\n",
    "    material_data.update({\"$\\nu_2$\": y_test[i][3]})\n",
    "    material_data.update({\"$\\nu_2^*$\": y_pred[i][3]})\n",
    "    material_data.update({\"${\\nu_2}_{APE}$\": np.abs((y_pred[i][3]-y_test[i][3])/y_test[i][3])*100.0})\n",
    "    material_data.update({\"$\\nu_3$\": y_test[i][4]})\n",
    "    material_data.update({\"$\\nu_3^*$\": y_pred[i][4]})\n",
    "    material_data.update({\"${\\nu_3}_{APE}$\": np.abs((y_pred[i][4]-y_test[i][4])/y_test[i][4])*100.0})\n",
    "    prediction_data.append(material_data)\n",
    "score = r2_score(y_test, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Коэффициент детерминации:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = mean_absolute_error(y_test, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Средняя абсолютная ошибка:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = root_mean_squared_error(y_test, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Корень среднеквадратической ошибки:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "display(pd.DataFrame.from_dict(prediction_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:48.761447Z",
     "start_time": "2024-05-29T00:16:48.757219Z"
    }
   },
   "outputs": [],
   "source": [
    "def CreateRidgeCV():\n",
    "    return RidgeCV()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:57.511208Z",
     "start_time": "2024-05-29T00:16:48.762452Z"
    },
    "collapsed": false,
    "id": "g6H11rEtUE_l",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "7d6954a3-4270-48a8-892e-c130ae9e3f31"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QUdAyWy7M34lJ7Oy+zcBPNSJqAQ9nJyIiIt1g8CEiIiLd4KAwkQ457U5IEnBy+xHUV9fCZDEjuV8mjBYjFIMBkpdPXEhEFCgYfIh0RFNVuBwubPnbWhwt2AfXJWdzlmQJyTkZGPzASIR3ioDBxI8HomCmOl0XzoiuyBCqBiEEFJ7ChcGHSC80TYOzwYF/vfBX1FRUXbFdaAIntx9B2b6TGDd/CqK6dOaHJFEQUp0uaC4VJZv2oHJvMVwNDhjCTIjNTkfSkF6QDYqu39uc40OkF5rAqt8tazb0XMrZ6MCXv/mofWoiIq/SXCpOb96Lb1/+C4pXbUVt6Vk0VtWgtvQsildtxbcv/wWnN++F5lL9WuexY8cwY8YMpKenIywsDJmZmXj++efhcDh8/tj6jXxEOlNddh7lB0971NZe24DDG/Yg65beUAxc6ZUoGKhOF05v3oujKzZetY1QNRxdsRESgKTB2X4b+dm/fz80TcM777yDrKws7N69GzNnzkRdXR1effVVnz42gw+RDjgbHdj7VWGb+uxfXYRuw/v4qCIi8jbNpaJ45WaP2h5duRkJ/W/wW/AZO3Ysxo4d676ekZGBAwcO4O233/Z58OGuLiIdkCQJtvLzbepTXXoOssKPCKJgoDpdOL1pD8RVzl93OaFqKNm8B6rT5ePKPFddXY3o6GifPw4/1Yh0QEBAktp2iDoPaScKHpIk4cze4jb1qdxT3ObPBV85fPgw3nzzTTz22GM+fywGHyIdkCChU2psm/pEp8ZB9fMESCLyjKTIcDW0bWKwq9EBycujuvPmzbtwCH0Ll/379zfpc/r0aYwdOxb33XcfZs6c6dV6msM5PkQ6YDAb0Stv4IV5PsKzPtlj+gfMX4NE1DKhajCEmYAqz/sYLCYIVYPkxQMYfvKTn+Dhhx9usU1GRob7/yUlJRg5ciRuuukmvPvuu16royUMPkQ6EWYNR9cB3XF868FW20bERaHrgO6c40MUJIQQiM1OR23pWY/7xPZKhxAe/iXk6X3GxiI21rPR5dOnT2PkyJEYMGAA3nvvPchy+3ze8FONSCcUowHDHxuPuG5dWmzXIToC4+bdD4+HhojI7xSjAUlDenm860pSZCQN7uW3o7pOnz6NESNGIDU1Fa+++ioqKytRVlaGsrIynz82R3yIdEQxKhg7737s+3o79n29DbWV1e5t5g4WdBveB30nDIXBbISscP0eomAiGxSk3z64xXV8Lsq4fTBkP67RtXLlShw+fBiHDx9GcnJyk23eHoW6nCR8/QhBxGazITIyEtXV1bBarf4uh8hnXE4XZFlGdelZNNY0wGgxITolFpqqwWA2+rs8Il1rbGxEcXEx0tPTYbFY2tRXc6k4vWkPjq7c3Oyh7ZIiI+P2wejy3akrgklLP5e2fH9zxIdIhwzfDW93Sm66Lz7YPgiJqCnZoCBpcDYS+t+Aks17ULmnGK5GBwwWE2J7pSNp8IXAo+f3OoMPERFRCFGMBihGA5Jv6ouUYTk8O/tl+BMgIiIKQZeGHG8esh7seFQXERER6QaDDxEREekGgw8RERHpBoMPERER6QaDDxEREekGj+oiIiIKQS6HE5IkQzbI0FwahNBgMHGBUgYfIiKiEOJyOOFyqti5YisOb9wHe70d5nAzsob2RN+xA2EwKroOQNzVRUREFCJUpws7VmzFH374Ggo+WIvKY+WwVVSh8lg5Cj5Yiz/88DXsWLEVqtPlsxoWLlyItLQ0WCwWDBkyBJs3b/bZY10LBh8iIqIQ4HI4UfTFFmz4yyporivP0wUAmkvDhr+swo4VW+FyOL1ew4cffoi5c+fi+eefx7Zt25CTk4O8vDxUVFR4/bGuFYMPERFRCHA5XPj2b2s8avvN0tVwOVWv1/Daa69h5syZmD59OrKzs7Fo0SKEh4fjT3/6k9cf61ox+BAREQU5l8OJHSu2XnWk53KaS8POL7076uNwOFBYWIjRo0e7b5NlGaNHj0ZBQYHXHud6MfgQEREFOUmScWTT/jb1ObxxPyRJ8loNZ86cgaqqiI+Pb3J7fHw8ysrKvPY414vBh4iIKMjJBhn2enub+tjrGiEr+jt5KYMPERFRkNNcGszh5jb1MXewQFO9N88nJiYGiqKgvLy8ye3l5eVISEjw2uNcLwYfIiKiICeEhqyhPdvUJ2toDwghvFaDyWTCgAEDsGrVKvdtmqZh1apVyM3N9drjXC8GHyIioiBnMBnRN28AZINnX+uyQUbfvIFeX8hw7ty5+MMf/oD3338f+/btw+OPP466ujpMnz7dq49zPbhyMxERUQgwmAy46YGR2PCXVa22HfbgKBiM3p/fc//996OyshLPPfccysrK0K9fP6xYseKKCc/+xOBDREQUAgwmI/qNGwRJkvDN0tXNHtouG2QMe3AUcsYOhGL0TQSYNWsWZs2a5ZP79gYGHyIiohChGA3omzcA2aP6YeeXW3F4437Y6xph7mBB1tAeF3ZvGRWfhZ5goN9nTkREFIIMJiMMJiP63zkEAyYMhawo0FQVQghdn5z0IgYfIiKiEHRpyFFkft1fxKO6iIiISDcCIvgsWLAAgwYNQkREBOLi4jBx4kQcOHCgSZvGxkbk5+ejc+fO6NixIyZPnnzFIkknTpzA+PHjER4ejri4ODz11FNwuVzt+VSIiIgogAVE8Fm3bh3y8/OxceNGrFy5Ek6nE2PGjEFdXZ27zZw5c/Cvf/0LH330EdatW4eSkhJMmjTJvV1VVYwfPx4OhwPffvst3n//fSxevBjPPfecP54SERERBSBJeHPZRi+prKxEXFwc1q1bh+HDh6O6uhqxsbFYunQp7r33XgDA/v370bNnTxQUFGDo0KH44osvcOedd6KkpMS9XsCiRYvws5/9DJWVlTCZTK0+rs1mQ2RkJKqrq2G1Wn36HImIiJrT2NiI4uJipKenw2Kx+LucgNHSz6Ut398BMeJzuerqagBAdHQ0AKCwsBBOp7PJqe579OiB1NRU96nuCwoK0KdPnyaLJOXl5cFms2HPnj3NPo7dbofNZmtyISIiCgUOuwMupwtCE3A5XXDYHf4uKSAE3DRvTdMwe/ZsDBs2DL179wYAlJWVwWQyISoqqknbS091X1ZWdsXKkBevX2xzuQULFuCFF17w8jMgIiLyH4fdAafDha8+WoPNqwtRX9uA8I5hGDxqAMbcNxJGkwEmc+t7QUJVwAWf/Px87N69Gxs2bPD5Y82fPx9z5851X7fZbEhJSfH54xIREfmC0+HEyo/X4IOFy6C6mp55/fjBk/j0//6FKfn3YMx9o2DU6Zo+AbWra9asWVi+fDnWrFmD5ORk9+0JCQlwOByoqqpq0v7SU90nJCRccZTXxesX21zObDbDarU2uRAREQUjh92Brz5ajSW/+/iK0HOR6lKx5Hcf46uP1nh915cnR2gHgoAIPkIIzJo1C8uWLcPq1auRnp7eZPuAAQNgNBqbnOr+wIEDOHHihPtU97m5udi1axcqKircbVauXAmr1Yrs7Oz2eSJERER+4rQ78cHCZR61/WDhp3A6vLvciydHaAeCgNjVlZ+fj6VLl+If//gHIiIi3HNyIiMjERYWhsjISMyYMQNz585FdHQ0rFYrnnjiCeTm5mLo0KEAgDFjxiA7OxsPPfQQXnnlFZSVleHZZ59Ffn4+zGazP58eERGRTznsDnz18ZqrjvRcTnWpWPnxGtzx4O1em++zYsWKJtcXL16MuLg4FBYWYvjw4V55DG8IiBGft99+G9XV1RgxYgQSExPdlw8//NDd5vXXX8edd96JyZMnY/jw4UhISMCnn37q3q4oCpYvXw5FUZCbm4vvf//7+MEPfoAXX3zRH0+JiIio3ciyjM2rt7Wpz+bV2yBJvosBlx+hHSgCYsTHk6WELBYLFi5ciIULF161TdeuXfH55597szQiIqKApygK6msb2tSnvqYeisE3wae5I7QDRUAEHyIiIrp2qqoivGNYm/qER4RDdWmQTd4PP+15hHZbBcSuLiIiIrp2mqZh8KgBbeozeFR/CKF5vZarHaEdKBh8iIiIgpzJbMKYe0dAMSgetVcMCm6/d6RXFzJs7QjtQMHgQ0REFAKMZiOm5N/jUdspsybDaPLubJf8/Hz89a9/xdKlS91HaJeVlaGhoW1zj3yNwYeIiCgEmMwmjLlvFKY+ed9VR34Ug4KpT96HMfeO8PppKzw5QjsQcHIzERFRiDCajLj93hEYcdfNWPnxGmxevQ31NfUIjwjH4FH9cfu9F87V5YvTVXhyhHYgYPAhIiIKISazCSazCXc8eDvGT82DYpChujQIoen65KQXMfgQERGFoEtDji8OWQ9W/EkQERGRbjD4EBERkW4w+BAREQWgYJks3F689fNg8CEiIgogRuOFI67q6+v9XElgufjzuPjzuVac3ExERBRAFEVBVFQUKioqAADh4eGQJMnPVfmPEAL19fWoqKhAVFQUFMWz1amvhsGHiIgowCQkJACAO/wQEBUV5f65XA8GHyIiogAjSRISExMRFxcHp9Pp73L8zmg0XvdIz0UMPkRERAFKURSvfeHTBZzcTERERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6YfB3AURE7UEIAaFqAABJkSFJkp8rIiJ/YPAhopCmOl2QZBln9h1DTckZSLKMmJ5dER4bBaFpkCQZitEASWYQItIDBh8iClmaquLEhp04sWEnHHUNSB81AKk39UZDVS0OfrkF9pp6KEYDEnqnI/aGFGiqBsXIj0WiUMZ3OBGFJM2lYs9Ha1BWdAiQJPSeMhoRSTHY9H//xrkjJU3aHtuwC2GdOqLXxFsQ3yuN4YcohHFyMxGFHNWl4vTW/RdCD4DMMYMQkRiDDb/9+IrQc1HD+Vpsfe8LnDl8GqrDCaFpcNbVw2Grhep0QnO5IIRoz6dBRD7AP2uIKOTIsoQT/9kJADBYTEgd1hffvPEJHHWNV+0jyTJypoxEdGoczu46gHN7D8NV1/DdRgkRXZMQk9MTYTGdAFkChIBs4EcoUbDhu5aIQk5N6VnUn6kCACT2vwG2kjOoPlXZYp+c+0ciNjMJRz798r+B5yIhUHPsNGqOnUbMjdmIzemB8/sPIbJbBhSLGbKi+OiZEJG3cVcXEYWc+jPV7v/H9UrHyS37W2wf0z0FiX0zcPyLtVeGnsuc2b4X5w8dgyU2Bsf+8SXs56qgqapX6iYi32PwIaKQIyn//WgzhpvRWFXbYvuMW/rg/P4jrYaei85s34fwhFgoFgtOrVwPzeG8rnqJqP1wVxcRhZzIlDhAAiAATdUgG66+K8ocEY64Xmk49MG/r9pGNhkR1T0dnXpkwhJthSTLUJ0uJA4fgvKCQpzbvR8xN/bmnB+iIMB3KRGFHGO4BdFZyTh36BRqy8+hc2YSSnccabZteGcrnPWNcNbUNbs9sltXJN0yCLVlZ3F09TbUlp9FTI+usCbHITwmEinjRsJ+vhqSzAF0omDAdyoRhRxZUZB5+yBIsoTTm/YiZXBPKKbm/86TDYr7VBaX69QjA4nDBmLX0pXY8f4XiEpLwMDHJiIuOw3O6mpU7S/GmR0HYerYAZqq8nB3oiDAER8iCjmSLCEiKQa9vncb9vx9NRrO2pA1qj8OrNh8RVtHbQOM4RZIitwkAJk7WZEwbAB2LP4cdZXn0f/Ru6HWN+DAh1+iofJck/s49Z9CdMpKRerooZCNBh7lRRTAGHyIKCQpRgPieqcjosv3ULb9IDJG9IOjvhHF63c2aVdTdg4NVbWIzExF1cFj7tujs7uhYtcRVJ8ow4BHJ8J+vhrHvtgANDeqowmcP3gcdWVn0HPqeEhmibu+iAJUwLwz169fjwkTJiApKQmSJOGzzz5rsv3hhx+GJElNLmPHjm3S5ty5c5g6dSqsViuioqIwY8YM1Na2fDQHEfmf5lKh2p1w2R1QnS6v3a9iNKBjXCekj+wP2aAg+65huHn2vUjMyWwSTEp3HkXnvj3c12WDAVHd03Bq0x507tEVZms4jn/5TfOh5xIOWx2OLF/HXV5EASxgRnzq6uqQk5ODRx55BJMmTWq2zdixY/Hee++5r5vN5ibbp06ditLSUqxcuRJOpxPTp0/Ho48+iqVLl/q0diK6NqrTBQiBsm0HUFt6BkLTEBYThaSBPSGbjF47Z5ZiMrr/3yktAf2/PwaQJbgaHVAMCmSjAgiBhNwbUVawHebOkVAdLtScqkTm9MGo3HngqvOALld7shyOmnpYoiK8UjsRedd1faps2rQJcXFxSE9Px4YNG7Bx40bccMMNmDBhQpvva9y4cRg3blyLbcxmMxISEprdtm/fPqxYsQJbtmzBwIEDAQBvvvkm7rjjDrz66qtISkpqc01E5DuaquLYqi0oK9wHzdl0AcAT67Yhpmc6uk+8FbIie3W3kSRJ7onOSsewJtuie3WDIdyCmhOlcNkdMISZEZ2VjJNff9umx6jcvh9JN9/Ik50SBaBrflfOnj0bW7duhcvlwujRo/HNN99g/PjxeOedd7B69Wq8/vrr3qwTALB27VrExcWhU6dOGDVqFF566SV07twZAFBQUICoqCh36AGA0aNHQ5ZlbNq0Cffcc88V92e322G3293XbTab12smoitpqor9H6/G2X3HrtJA4Myeo2g4V42cR+6C0k7zZWSDAmt6CiIzU+GyO2HqYIHqdMFVf/VzfDXHbqttslvs4q4vSZK8Wi8Rtd01B5+vv/4au3btgt1uR3JyMk6fPg2z2Yw5c+agX79+XizxgrFjx2LSpElIT0/HkSNH8Mwzz2DcuHEoKCiAoigoKytDXFxckz4GgwHR0dEoKytr9j4XLFiAF154weu1EtHVaS4VFbsOXz30XKKu9CyOrdqCtFEDm+yu8qWLix0qRgM6JHS+ptEmSZYhhICqqtiysQiH9h2BrCjI6d8LPXplQdMETO30fIioqesah3W5XLDb7XA6nWhsbITZbIaqqlB9cN6aKVOmuP/fp08f9O3bF5mZmVi7di1uu+22a7rP+fPnY+7cue7rNpsNKSkp110rEbVAklCycbfHzcuLDiJ99GAfFtQ8SZYQn9MNQlURFheNhopzrXf6TsfEWJw4fhqPPfQUysuanhw1s1saHv3xD3Bb3i0wmU3eLpuIWnHN48czZsxAz5490a9fP/zqV7/C/fffjyeeeAK5ubmYPHmyN2tsVkZGBmJiYnD48GEAQEJCAioqKpq0cblcOHfu3FXnBZnNZlit1iYXIvIte3UN6so9DxFqowPnDp7wYUXNk2QZMTek4nxxKWL7dve8n0FBVHYGfvk/r10RegDgyKFj+NkTL+JPby+F3e7wZslE5IFrHvGZM2cOHnroIQBATEwMvv/97+Prr7/G97//fQwZMsRrBV7NqVOncPbsWSQmJgIAcnNzUVVVhcLCQgwYMAAAsHr1amia1i71EJFnHDX1be7TWF0LIUS7z5GRFRnRmV0ghED51j2wV9W02ic25waUlVagcPPOFtv9/vX3kDOgNwbf1B+KEjArixCFvOva1RUTE+P+f1RUFO69995rvq/a2lr36A0AFBcXo6ioCNHR0YiOjsYLL7yAyZMnIyEhAUeOHMHTTz+NrKws5OXlAQB69uyJsWPHYubMmVi0aBGcTidmzZqFKVOm8IguogDS0glDr0YxGvw2MVg2KNBcKrrfNwYH/v4lHNVXXxssukc64of0wYwH53h03396eyn6D+4LReEuL6L24pM/MzZt2tTmPlu3bsWNN96IG2+8EQAwd+5c3HjjjXjuueegKAp27tyJu+66C927d8eMGTMwYMAA/Oc//2myls+SJUvQo0cP3Hbbbbjjjjtw880349133/Xa8yKi69chPhqKuW0TeztlJfuoGs/IBgXG8DBkPzQBScNuhLFjeJPtHbvEIfOuEUi5PRdP/PAZ7Cjc49H9bvqmEDYPRpGIyHsk4YMlRlNTU3HiRPvvk79eNpsNkZGRqK6u5nwfIh9RHS4Ur9yI0i37PGofmZaI3t8fd00jRb6gOV2QFBmO2noIlwrFYv4uyEn4x8df4PmnX2nT/f35k4XoN7C3b4ol0om2fH9f866u733ve83eLoTAuXOeT1wkIn1RTAakDu+Pyj1H4aq3t9hWUmSk3z4Ykhw469/I3y1KaLZ2vGJbY2PLz6fZ++P8HqJ2dV3r+PzlL39Bx45N3/xCCKxfv/66CyOi0GUIM6PvtDux68//hrOu+cUBZYOCnt8bjfC46KA54WdO/15tam8wGpCWwSU0iNrTNQefESNGICIiAsOHD79iW9++fa+rKCIKbbJBQVjnSAz88f0oK9yP0i170Xj+wlwXYwcL4m+8AV2G9oZiNgXVaR+698xCVvd0HD5Y7FH7UWNu4UKGRO3M4zk+L730Evr3748BAwYgPj7e13X5Bef4ELU/zeWCJCvQVBUQArLRAM2lBlXgucjpcGL1VxvwVP4vWm1rMBrwwfJ30e2GDJ7Kgug6teX72+PgI8uy+82ZkJDgDkEX/+3Spcv1V+5nDD5EdL3sdgfef/cDvPXqH6/axmA04OU3nsMto4bCYjFftR0RecYnwWfIkCEoLS3F9OnTERMTg23btqGwsBD79++HqqqIjY1F//798fnnn3vlSfgDgw8ReYPd7kDR1t344++XYNM3he6TlBqMBtyWdwse/fEPkNK1C0MPkZf45KiuTZs2YfHixXjmmWcwaNAgvPbaa8jMzITdbkdRURG2bduG7du3X3fxRETBzmw2YVBuP/Qb2Bs1tlqcPlkCRVbQNSMFRqMBljCLv0sk0q02r+NTW1uLF198Ee+88w7+3//7f/j5z3+O8PDw1jsGAY74EBERBZ+2fH+3+RjRjh074pVXXsHWrVuxe/duZGVl4c9//vM1F0tERETUXq5pcQyXywW73Y4HHngAycnJmD59OhctJCIiooDn8RyfX//619i1axd27dqF/fv3w2KxoG/fvhg8eDAee+wxREZG+rJOIiIiouvWpsPZ09LSMG3aNDzwwAPo3r27r2trd5zjQ0REFHx8cjj7rbfeiqKiItTU1KBDhw7o27cv+vfv77707t0bihIYJxG8Vgw+REREwccnh7OvW7cOAHDo0CEUFhZi27Zt2LZtG5YsWYKqqiqYzWb06dMHmzdvvr7qiYiIiHykzWvCd+vWDd26dcOUKVPctxUXF2Pr1q1cx4eIiIgCWpvX8Qll3NVFREQUfHy6jg8RERFRsGLwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt1g8CEiIiLdYPAhIiIi3WDwISIiIt0w+LsAIgp8mssFAHA1NAIADGEWAIBs4EcIEQUXfmoR0VVpqgpXXT2q9h9C3cnTEJoGAJBkGR1SuiCqRzcYOoRDVhQ/V0pE5JmA2dW1fv16TJgwAUlJSZAkCZ999lmT7UIIPPfcc0hMTERYWBhGjx6NQ4cONWlz7tw5TJ06FVarFVFRUZgxYwZqa2vb8VkQhQ5NVVFfUoZTX61B7fGT7tADAELTUHv8JE59tQb1JWXQVNWPlRIReS5ggk9dXR1ycnKwcOHCZre/8soreOONN7Bo0SJs2rQJHTp0QF5eHhobG91tpk6dij179mDlypVYvnw51q9fj0cffbS9ngJRyBBCwFFlQ8WmQkCIlhqiYlMhHFU2iJbaEREFCEkE4KeVJElYtmwZJk6cCODCh3BSUhJ+8pOf4Kc//SkAoLq6GvHx8Vi8eDGmTJmCffv2ITs7G1u2bMHAgQMBACtWrMAdd9yBU6dOISkpqdXHtdlsiIyMRHV1NaxWq8+eH1Gg01QV5d9sQkN5pUftwxLiEH/TYO7yIiK/aMv3d8CM+LSkuLgYZWVlGD16tPu2yMhIDBkyBAUFBQCAgoICREVFuUMPAIwePRqyLGPTpk3N3q/dbofNZmtyISJAczg9Dj0A0FBWAc3h9GFFRETeERTBp6ysDAAQHx/f5Pb4+Hj3trKyMsTFxTXZbjAYEB0d7W5zuQULFiAyMtJ9SUlJ8UH1RMHHfu58u/QhImpvQRF8fGX+/Pmorq52X06ePOnvkogCwqUTmX3Zh4iovQVF8ElISAAAlJeXN7m9vLzcvS0hIQEVFRVNtrtcLpw7d87d5nJmsxlWq7XJhYgAY8cO7dKHiKi9BUXwSU9PR0JCAlatWuW+zWazYdOmTcjNzQUA5ObmoqqqCoWFhe42q1evhqZpGDJkSLvXTBTMTJFWGCM6etzeGNERpkj+4UBEgS9gFjCsra3F4cOH3deLi4tRVFSE6OhopKamYvbs2XjppZfQrVs3pKen4+c//zmSkpLcR3717NkTY8eOxcyZM7Fo0SI4nU7MmjULU6ZM8eiILiL6LyEEIrtl4My2nR61j+yeCSEEJB/XRUR0vQIm+GzduhUjR450X587dy4AYNq0aVi8eDGefvpp1NXV4dFHH0VVVRVuvvlmrFixAhaLxd1nyZIlmDVrFm677TbIsozJkyfjjTfeaPfnQhTsZEVBRHpXNFSeRd3J0y227ZiajIi0VEhyUAwgE5HOBeQ6Pv7CdXyImhKahqr9h1B9+Cg0u6PJNsVshjUrHVE9ujH0EJFfteX7O2BGfIgo8EiyjMjuWYjq0Q31JWWwV1UDAMydohCeGA+hCYYeIgoqDD5E1CLZcGE15vAuiQhLvLCWliTLkCQJEjMPEQUZBh8i8ogkSZB4Sgoiv9I0AZfTCYfdiapz1TAaDYiJ7wyXywWzxezv8oICgw8REVEQcDqc2Ft0EJ8s/hcKv9kBTbswRTeqcyTGThqJSdPuhCXMAqOJX+0t4eTmS3ByMxERBSKn04XFv/sbPn3/31dtE9U5Eq/86TkkJMfBaDK2Y3X+F3InKSUiItIre6Md//5wZYuhBwCqzlbjZ4+8CAdPGNwiBh8iakKoKoSqQm1shGq3QwgBTVX9XRaRbikGAz74wzKP2p4/W41//e0r2BsdrTfWKe4IJCIAFwKPq7EBdSdPoLGyEhAXTjoqGY0Ij09EeHIKZIOBh68TtSNV1bBxzVZUn7N53Ofzv6/EfY/c5cOqghuDDxFBaCoaystgO3zwym1OJ+pOnUB9aQmi++bAEN6BR3cRtROnw4ldW/e1qU9l2VnU2epg7RTho6qCG/908zGhaXA02OFodMDeYIfq4i4DCixC02A/f77Z0NOknerCuZ07oLlc7VQZEQkhrul7Q+Xu6aviiI+PuBwuyIqM4qIj2Lm6CPW2OhgtJtwwpCd639oXmqbBaNbXrHsKXLXHjnrUTqgu1J04jo4ZmZA56kPkcwajAQnJsW3qYzIb0dHawUcVBT8GHx9w2p0oPVyCZa9+BFtldZNtBwr24as/fI7RM8aiz4gcGLjeAvmZq64Orro6j9s3VJQhIjPLhxUR0UVGowF5k0Zh8RsfejzyM3zsTVBVDfzTunnc1eVlTseF0POX/3nvitBzUWNdI5a/8Rm2f7UVTh52SH4khICj6nzb+qgqXA31PqqIiC5nMhtxy5ihHrWVJAn3Tp8ASxhXcb4aBh8vUxQFn7z8ITQPkvmX734Oe529HaoiugohIL47eqtNNK57StRezBYznvzFTKR1T2217ePzH0ZCl7h2qCp4Mfh4kaZqOLT1AGrP1XjUXmgCm/5ZAKedoz7kH5IsQ7GEtbmfbOZfk0TtyWgy4vW//hJjJo6AqZn5oV3SEvHs63OQN2kkzBaTHyoMHpxg4kUuhws7Vm5vU589a3fgtmm3+6giotZZYmJhUxQID48CMUVGQTbwo4OoPSmKAiVMwePPTMeP5k3D6n9vQHlJJYxGI/rn9kGPvt0uHDSjs1NVXAt+enmRJEuoq/Z8kiiANrcn8jYhBMISElF/+pRH7cOTUwFJ8nFVRL6hqRo0TYMEwOV0wWg2QnVpMJgMkILg9/ri3J2xk2+D6nJBkmUYjRe+yhXwSEtPMPh4kdAETJa2pW0jhyTJz2RFQUR6Jpw1NXDamp+Qf1F4UheYO3UKii8IosupLhVHtx3Cln9uxMndxwAAsiKj25AeGDzxJsSnJ0AxBsfXoqLIUBR+f1yL4HiFg4SsyMgc0B1Htx/xuE9m/yw47Q4YzfwFJj+SJET37QfbkUNoKC8DtKYTnmWjCR1SUhGe1IWnrKCg5LQ78fFLS3FiV3GT2zVVw4Fv9+LAt3uRM2YAbn/0DigGjpyEMgYfLzKYDOifNxBr/rwSLodnq9vm3jOMoYf8TpIkQJIQkZGFiIwsNJSXQW2oByQJJmskzJ1jIDSNoYeCkqZq+HTBB1eEnsvt+KoQlo4WDLt/BBeYDWH8FPMySZYw/IGRHrXtcVM2YrvG+7giIs/JigJZURCekIiItAx07JoOc+cYSJLElZopKAkhUHroNI4VeTYSv+WfG3lqoRDH4ONlRrMRQyfehFumjGixXY/cbEx66nscUqWAJMkypO9CEOfzUDBzOVzY/I9vPW6vuVRs/2ILF5cNYdzV5QOK0YCbv3cr+t52IzZ+ugF7/rMbjbUNMJiN6DawO4ZOGobEzCSGHiIiHzOajTix61ib+hzfeRQD7hzim4LI7xh8fMRgMiA6MRqjZ4zFHfl3QQgBSZLgtDuD5rBJIqJQ4Omcy0vb8zM6dHFXl4+Zvjtc/eKbyGg28g1FRNROhBDoGB3Rpj4dO0VA8LQsIYvBh4iIQpbL6ULvkTlt6pOTN4BHdYUwBh8iIgpZRpMRA8YP9nhOpTUuCl37pEOSOTIfqhh8iIgopCkmA+748cRWT7ViNBsxaf4UaJct4EmhhcGHiIhCmtFkRPehPTBp/v2IiIlstk1s13g89MoP0blLZxiC5LQVdG0kIQRncH3HZrMhMjIS1dXVsFqt/i6HiIi8yOVwQlYUHNtxFAcL9sLR6ECYNRx9RvVDXFo8hBBQDAw9wagt3998hYmISBcMpgsTltP7ZSC5Z8qFGyXJffQt6QODDxER6YokyzCFmf1dBvkJ5/gQERGRbjD4EBERkW4w+BAREZFuMPgQERGRbjD4EBERkW4w+BAREZFuMPgQERGRbjD4EBERkW4w+BAREZFuMPgQERGRbjD4EBERkW4w+BAREZFuMPgQERGRbjD4EBERkW4w+BAREZFuMPgQERGRbjD4EBERkW4w+BAREZFuMPgQERGRbjD4EFHIUp2uFq8Tkf4Y/F0AEZG3aS4VzvoGlG7eg3P7j8HVaIdiMqJTVgoSh/SGOSoCsqL4u0wi8oOgGfH5xS9+AUmSmlx69Ojh3t7Y2Ij8/Hx07twZHTt2xOTJk1FeXu7HionIHzRVRUnBDhT9/iOUb90LZ209hEuFq74RlTsPYecfluHYlwXQVNXfpRKRHwRN8AGAXr16obS01H3ZsGGDe9ucOXPwr3/9Cx999BHWrVuHkpISTJo0yY/VElF705wulG7ajdPf7GixXeXOQzj21UaGHyIdCqpdXQaDAQkJCVfcXl1djT/+8Y9YunQpRo0aBQB477330LNnT2zcuBFDhw5t71KJyA80TcPpb4o8alu54yCScvvAEmX1bVFEFFCCasTn0KFDSEpKQkZGBqZOnYoTJ04AAAoLC+F0OjF69Gh32x49eiA1NRUFBQVXvT+73Q6bzdbkQkTBSXO5ULFtP4SqedyndNMeTngm0pmgCT5DhgzB4sWLsWLFCrz99tsoLi7GLbfcgpqaGpSVlcFkMiEqKqpJn/j4eJSVlV31PhcsWIDIyEj3JSUlxcfPgoh8RQjg/JGTbepTdfQUZAMnORPpSdDs6ho3bpz7/3379sWQIUPQtWtX/P3vf0dYWNg13ef8+fMxd+5c93WbzcbwQxSkJEmC5mjb6I3mcEKSJB9VRESBKGhGfC4XFRWF7t274/Dhw0hISIDD4UBVVVWTNuXl5c3OCbrIbDbDarU2uRBRcBJCwBBmblMfQ5gFQggfVUREgShog09tbS2OHDmCxMREDBgwAEajEatWrXJvP3DgAE6cOIHc3Fw/Vkm+5LQ7m1x3XXad9EWSZXTuldmmPp2z06G5eGQXkZ4Eza6un/70p5gwYQK6du2KkpISPP/881AUBQ888AAiIyMxY8YMzJ07F9HR0bBarXjiiSeQm5vLI7pCkMvhQmNtA3b8exMOfrsXjbZ6GMxGpOZk4MY7hyImLY6L0+mQrMiIyc7AiVWbododrbaXZAnxA3pCMQbNxyAReUHQvONPnTqFBx54AGfPnkVsbCxuvvlmbNy4EbGxsQCA119/HbIsY/LkybDb7cjLy8Pvf/97P1dN3qY6Xdj11VZ8u2Q1cMkeCke9HYcL9uFwwT6kD+qOvB9P5BeaHgmBzDtvwcFPV1+Y7dyC1NuGQDHwd4RIbyTBHdxuNpsNkZGRqK6u5nyfAOS0O3Fg/U6s++OXrbZNH9QdY2ffw5EfHdJcLlQXl+Do5xvgarBfsV0xGZE6ahBiemfxiC6iENGW72/+uUNBQ5IlfLt0jUdti7ccRGVxOeIyE3nUjs7IBgOsaUnoP2sKzh44hrN7j8LVcOFcXdE3dEVM7ywIIRh6iHSKwYeCgupSceA/u+FsaH3uxkVFyzfhtsfvhMFs9GFlFIgu7ubsfEMaOmWlAJIECAFJlhl4iHSOwYeCgupScazwUJv6HN9+mKFH5yRFhqIE7cGrROQD/ESgoCCh7YerOx08vJ2IiJpi8KGgIABYItq2QrelY7hviiEioqDF4ENBwWgyosetfdvUp9tN2VcsckhERPrG4ENBQZIlpPRNR8fOni8z0O/OITByjg8REV2CwYeChqZqGPPjuyF7MFl18PeGIzyyQztURf7U2GBHXW099u88hL1FB3C24jycDidUVfN3aUQUoHhUFwUNg9GA2PQETHxuKr787TLUna+9oo3RbMTg7w1HnzEDuHJzCHM0OlBWUomliz7Bt19vhtP537Oy9x2UjfseuQt9B/eCycQRPyJqiis3X4IrNwcHl8MFWZFxYsdR7F+3Ew22ehjNRnTtn4We380D4mHsoctud2DHpt14afZrTQLP5e6fOREP/mgyww+RDnDlZgppBtOFX9vUfhnokp0KSBKEEFAUmaM8OlBZehYvzXm9xdADAB/+4TMkpyVi+NibGH6IyI1zfChoybIMo8UEo9kIk8XE0KMDjQ12fPDupx6v0fS3d5a1ywKGQgioThdcDicaa+rhbHRAdanQONeIKODwm4KIgoYQAuu/3Ohx+5ITZdi34xB69+/hs5o0l4qyAyex78tClOw5dmHRKQCxmUnoOaY/Uvpn8WS5RAGEwYeIgkbpyfI2r8i9r+ggsnO6e3Q0YFtpLhXf/N8XOLb5wBXbKo+UoPLtEsTfkIxRcybBwN1tRAGBu7qIKGhoWtt3HWmaBgHvH8OhOl3YvGRVs6HnUuUHTmHtm//gbi+iAMHgQ0RBIy4xBrIstalPWlYKFB/sanLU23F4/W6P2pbuOY5zJ8q9XgN5TggBzaVCaAKa0wmhadBUFTywWX+4q4uIgoYlzIyBN9+Izeu3edS+U+dIDLy5n9frcNmd2LdyW5u+NPeuKMRNj+RxqQU/EKoGe1UVqvYdQu2pEkC78LqFxcciqkcWwhPjIckcB9ALBh8iChoGowHf++HdHgefCQ+MgcvlgmLw8oiPBFQcPNWmLhWHTjH0+IHQNFQW7oDtcPEV2xrKK9FQXomw+FgkjriJk9B1ghGXiIKGLMvolp2OGXOntto2d9RA3PfI3TBbzF6vQ5IkqK2sI3Q51al6vQ5qmeZScXbHnmZDz6UayitRtn4jxDXMIaPgwxEfIgoqJrMJdz2Yh8SUePz17Y9x7OCJJtujYzvhrgfzMHnanTD4aG0nTRMI7xSBc8crPO4THtURmqZB5i6VdiM0FVUHDnvUtr60HPZzVTB37gRJats8MgouDD5EFHRMZhMG39ofQ0YMwPFDJ7Fn+36oLhWpmcnoN7Q3XE7VZ6EHAAxGBd1u7YtTRUc87pN1S28IVQMYfNqF5lJRffCoez6PJ6r2H0Lc0IGQvL1rlAIKgw8RBSXjd8Ems2caMnp0BQD3X+q+OIrrUpIsI6lPGsKjI1B/rqbV9gaTAVnD+3B18XYl0FDm+YgcANSXV0Jm6Al5/NODiIKeJEntvntCqBpG/nhiqxOWJVnCLY9P4FFD7U5q85wd4eI8LD3gO5GI6BooRgMiE6Mx7tkHEZ0W32wba0I0Rv/0PiT0THWfXJfaiRBQLJY2dTGEW7iujw7wnUhEdI0UowHW+E4Y98wDsJWdx5Fv98Be2whjmAlpg25A5/QECE1AMXL3SXuTDAqsWWmoO1XicZ+I9K4QqsY5PiGOwYeI6DpcnBMSlRyDnIk3QWgCkiRBMRku7H7jd6hfSJKE8IQ4GMLD4KpvaL2DLCOyWwbn+OgAd3UREXmJwWSE0WKCwWzkIdEBQAiBhOFDIXkw2T1+6ACP2lHwY/AhIqKQJCsKTFYrkseMgCnS2mwbQ3gYEoYPRYeUJI726AR3dRERUciSDQpM1o5IGTcK9vPVsB09Ds1uh2QwoGNqF4QnxEMIjaer0BEGHyIiCmkXd2FZOneCKTIC+O7ILclwYR6WxIlYusLgQ0REuiEb+LWnd5zjQ0RERLrB4ENERES6weBDREREusGdnURERORT7vOmSdJ/J5f76fx1DD5ERETkE0LTACHQeLYSjurzEKoLkmKAKTIKls5xgCS1ewBi8CEiIiKvE5oG+7kzqC896R7lucCOhoY6NJSXICwhGZbOse0afhh8iIiIyKsuhJ5K1JecbKGRQEPpSQACls5x7RZ+OLmZiIiIvEoIgfrSUx61bSg7DSE0H1f0Xww+RERE5DVC02A/W3HZ7q2WOgjYz1T+dwK0jzH4EBERkVc5qs+3sf05H1VyJQYfIiIi8h5JglDVNnURqnrhUPd2wOBDRERE3iOE+8SwnrrQ3sNdY9eJwYeIiIi8ymSNalN7ozXK8zlB14nBh4iIiLxGkmWYO8cB8HTXlQRLTDwkuW2jRNeKwYeIiIi8SpJlhCUkedQ2LCGpXRcwZPAhIiIir5JkGZaYeIQldGmxXVh80nejPVy5mYiIiILYxfBjjo5B45kKOKvPQ9NUyLICY2QnWGLiIMkKz9VFREREoUGS5Qu7veISEBafBEmSIIS4cOQXz85OREREoejSicuSJLXbmj3N4RwfIiIi0g0GHyIiItINBh8iIiLSjZALPgsXLkRaWhosFguGDBmCzZs3+7skIiIiChAhFXw+/PBDzJ07F88//zy2bduGnJwc5OXloaKiwt+lERERUQAIqeDz2muvYebMmZg+fTqys7OxaNEihIeH409/+pO/SyMiIqIAEDLBx+FwoLCwEKNHj3bfJssyRo8ejYKCgmb72O122Gy2JhciIiIKXSGzjs+ZM2egqiri4+Ob3B4fH4/9+/c322fBggV44YUXrridAYiIiCh4XPzeFh6c4T1kgs+1mD9/PubOneu+fvr0aWRnZyMlJcWPVREREdG1qKmpQWRkZIttQib4xMTEQFEUlJeXN7m9vLwcCQkJzfYxm80wm83u6x07dsTJkycRERFxYWVJnbHZbEhJScHJkydhtVr9XQ55iK9b8OFrFpz4ugUuIQRqamqQlNT6GeFDJviYTCYMGDAAq1atwsSJEwEAmqZh1apVmDVrlkf3IcsykpOTfVhlcLBarXxTByG+bsGHr1lw4usWmFob6bkoZIIPAMydOxfTpk3DwIEDMXjwYPz2t79FXV0dpk+f7u/SiIiIKACEVPC5//77UVlZieeeew5lZWXo168fVqxYccWEZyIiItKnkAo+ADBr1iyPd21RU2azGc8//3yTeU8U+Pi6BR++ZsGJr1tokIQnx34RERERhYCQWcCQiIiIqDUMPkRERKQbDD5ERESkGww+REREpBsMPiFs4cKFSEtLg8ViwZAhQ7B58+artnU6nXjxxReRmZkJi8WCnJwcrFixokkbVVXx85//HOnp6QgLC0NmZiZ++ctfenRuFPLM+vXrMWHCBCQlJUGSJHz22Wet9lm7di369+8Ps9mMrKwsLF68+Io2bfldoLbzxeu2YMECDBo0CBEREYiLi8PEiRNx4MAB3zwBnfLV++2iX//615AkCbNnz/ZazXT9GHxC1Icffoi5c+fi+eefx7Zt25CTk4O8vDxUVFQ02/7ZZ5/FO++8gzfffBN79+7Fj370I9xzzz3Yvn27u83LL7+Mt99+G2+99Rb27duHl19+Ga+88grefPPN9npaIa+urg45OTlYuHChR+2Li4sxfvx4jBw5EkVFRZg9ezZ++MMf4ssvv3S3aevvArWdL163devWIT8/Hxs3bsTKlSvhdDoxZswY1NXV+epp6I4vXreLtmzZgnfeeQd9+/b1dtl0vQSFpMGDB4v8/Hz3dVVVRVJSkliwYEGz7RMTE8Vbb73V5LZJkyaJqVOnuq+PHz9ePPLIIy22Ie8BIJYtW9Zim6efflr06tWryW3333+/yMvLc19v6+8CXR9vvW6Xq6ioEADEunXrvFEmXcabr1tNTY3o1q2bWLlypbj11lvFk08+6eVq6XpwxCcEORwOFBYWYvTo0e7bZFnG6NGjUVBQ0Gwfu90Oi8XS5LawsDBs2LDBff2mm27CqlWrcPDgQQDAjh07sGHDBowbN84Hz4I8UVBQ0OR1BoC8vDz363wtvwvke629bs2prq4GAERHR/u0Nro6T1+3/Px8jB8//oq2FBhCbuVmAs6cOQNVVa84VUd8fDz279/fbJ+8vDy89tprGD58ODIzM7Fq1Sp8+umnUFXV3WbevHmw2Wzo0aMHFEWBqqr41a9+halTp/r0+dDVlZWVNfs622w2NDQ04Pz5823+XSDfa+11CwsLa7JN0zTMnj0bw4YNQ+/evduzVLqEJ6/bBx98gG3btmHLli1+qpJawxEfAgD87ne/Q7du3dCjRw+YTCbMmjUL06dPhyz/91fk73//O5YsWYKlS5di27ZteP/99/Hqq6/i/fff92PlRKEvPz8fu3fvxgcffODvUqgFJ0+exJNPPoklS5ZcMYJOgYMjPiEoJiYGiqKgvLy8ye3l5eVISEhotk9sbCw+++wzNDY24uzZs0hKSsK8efOQkZHhbvPUU09h3rx5mDJlCgCgT58+OH78OBYsWIBp06b57gnRVSUkJDT7OlutVoSFhUFRlDb/LpDvtfa6XWrWrFlYvnw51q9fj+Tk5PYsky7T2utWWFiIiooK9O/f371dVVWsX78eb731Fux2OxRFae+y6TIc8QlBJpMJAwYMwKpVq9y3aZqGVatWITc3t8W+FosFXbp0gcvlwieffIK7777bva2+vr7JCBAAKIoCTdO8+wTIY7m5uU1eZwBYuXKl+3W+nt8F8p3WXjcAEEJg1qxZWLZsGVavXo309PT2LpMu09rrdtttt2HXrl0oKipyXwYOHIipU6eiqKiIoSdQ+Ht2NfnGBx98IMxms1i8eLHYu3evePTRR0VUVJQoKysTQgjx0EMPiXnz5rnbb9y4UXzyySfiyJEjYv369WLUqFEiPT1dnD9/3t1m2rRpokuXLmL58uWiuLhYfPrppyImJkY8/fTT7f30QlZNTY3Yvn272L59uwAgXnvtNbF9+3Zx/PhxIYQQ8+bNEw899JC7/dGjR0V4eLh46qmnxL59+8TChQuFoihixYoV7jat/S7Q9fPF6/b444+LyMhIsXbtWlFaWuq+1NfXt/vzC1W+eN0ux6O6Ag+DTwh78803RWpqqjCZTGLw4MFi48aN7m233nqrmDZtmvv62rVrRc+ePYXZbBadO3cWDz30kDh9+nST+7PZbOLJJ58UqampwmKxiIyMDPE///M/wm63t9dTCnlr1qwRAK64XHytpk2bJm699dYr+vTr10+YTCaRkZEh3nvvvSvut6XfBbp+vnjdmrs/AM2+vnRtfPV+uxSDT+CRhOCyu0RERKQPnONDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDRCHjpz/9KSZOnOjvMogogDH4EFHIKCoqQr9+/fxdBhEFMAYfIgoZO3bsYPAhohYx+BBRSDh16hTOnDnjDj5VVVWYMGECbr75ZpSVlfm3OCIKGAw+RBQSioqKEBUVhbS0NOzatQuDBg1Cly5dsGbNGiQkJPi7PCIKEAw+RBQSioqKkJOTg6VLl+LWW2/F008/jUWLFsFoNAIA7rnnHnTq1An33ntvk36vvvoqevXqhd69e+Ovf/2rP0ononYkCSGEv4sgIrpe9957L1avXg0A+Pe//43c3Nwm29euXYuamhq8//77+PjjjwEAu3btwrRp0/Dtt99CCIGRI0dixYoViIqKau/yiaidcMSHiEJCUVERJk2ahMbGRlRVVV2xfcSIEYiIiGhy2759+5CbmwuLxYKwsDDk5ORgxYoV7VQxEfkDgw8RBb2amhocPXoU+fn5eOuttzBlyhTs2bOn1X69e/fG2rVrUVVVhfPnz2Pt2rU4ffp0O1RMRP5i8HcBRETXa8eOHVAUBdnZ2bjxxhuxe/duTJgwAZs3b0ZMTMxV+2VnZ+PHP/4xRo0ahcjISAwdOhSKorRj5UTU3jjiQ0RBr6ioCD169IDZbAYA/OY3v8ENN9yASZMmweFwtNj3sccew7Zt27BmzRoYjUZ069atPUomIj/h5GYi0o21a9firbfeck9uBoCKigrExcXhwIEDuO+++7Bt2zYYDBwMJwpVfHcTkS6MHj0aO3bsQF1dHZKTk/HRRx8hNzcXd999N6qrq9GhQwe89957DD1EIY4jPkRERKQbnONDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES6weBDREREusHgQ0RERLrB4ENERES68f8BxzH71CDgEvsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iIqLR/StWrMC//vUvxMXFYcKECXjqqacQGBgIACgoKECvXr0QGxtraz969GjMmjULBw4cQN++fa95HpPJBJPJZPvaaDS64nCIyAkEQYA20ODwfpoAvQuqIfIsqqoiKDEB5otVdu8TlNQeqgo482xXdHQ0oqOjb2hfRVEAoNHnsit4XPBRFAWPPfYYbr75ZvTs2dN2/y9+8Qt06NABCQkJ2Lt3L5544gkcOXIEq1evBgCUlpY2Cj0AbF+XlpY2+VyLFy/GokWLXHQkRORs7W5KhiCJUGXFrvb6sGAERIS6uCoi9xM1EsJuSsXFA4ftG+AsCgjrkuK2y9m3b9+OnTt34pZbbkG7du1w/PhxPPXUU+jUqZNLe3sADww+ubm52L9/P7777rtG9z/00EO2//fq1Qvx8fEYOXIkjh8/jk6dOt3Qcy1YsABz5861fW00GpGUlHRjhRORywmiiMi0jjh34IRd7WP7pUFVVAgeMZqRyLUEUUJk7x7Nz+Pzs8j0HhBE983hExgYiNWrV+Ppp59GbW0t4uPjMWbMGDz55JPQ613bS+tRwWf27NlYt24dtmzZgsTExGbbZmZmAgCOHTuGTp06IS4uDjt27GjUpqysDACuOy5Ir9e7/BtMRM4jaTXokJ0JY0kpzNXXn8cHAILioxDXv7tfT81P/uVyrw+Aa2dutjUSGmZu7uLemZt79eqFTZs2ueW5PeLvIFVVMXv2bKxZswabNm1CSkpKi/sUFRUBAOLjG6amz8rKwr59+1BeXm5rk5eXh9DQUHTv3t0ldRNR25P0WvTMuR0B0e2u2yYsJQHdfzGGl7KT3xEkCaFdUtHxrnFo17s7dO3CoAkKhK5dGNr17o6Od41DqJtDj7t5RI9Pbm4uVq5ciU8//RQhISG2MTlhYWEICAjA8ePHsXLlSowbNw6RkZHYu3cv5syZgyFDhqB3794AgFGjRqF79+6YPn06XnjhBZSWluLJJ59Ebm4ue3WIfIgoSdAGBaD3L+9A9ekKlBUewqULRgiigKCYCMRn9oA+PASiH7+xk39r6OWUEN61M9qldW64ZF1RoKpgDyg8JPi88cYbABomKbzSsmXLMGPGDOh0Onz99dd45ZVXUFtbi6SkJEyePBlPPvmkra0kSVi3bh1mzZqFrKwsBAUFIScnB88++2xbHgqRV1BkBaqiwFxvhqm2HhqdFoFhQVAUBRqtR7wtNOvy+lshiTEIio34+WsVqqJC0rl21lcib9Eo5EiSU6/e8mYe8Q7X0mRFSUlJyM/Pb/FxOnTogC+++MJZZRH5JNkq48SuH1D0+Q6cPXLKdn94fAR6j+6Pnrf1hSiJEL1gcU9BEBh0iMghHhF8iKhtyFYZ619egxM7j1yzrfLsBWxZ/hUObCrC5Gf+B7pAvVeEHyIiR/BdjchPWM1WbP7nhiZDz5XOl5RjzR9XAq6dNZ6IyC0YfIj8hPmSCQe/+d6uthXFpSjZewKqvSs9ExF5CQYfIj9gMVnw/YZdDgWZos93QLbKLqyKiKjtcYwPkT9Q1UYDme1RevQ0NDq+RRB5K9libVgR/edlXlRVheQFV226Gr8DRP5AABTZsd4b9vYQeSfZYoVilXFm+wFUHCyG9ZIZmgAdorunICGzB0SN5NcBiKe6iPyAqgKhUWEO7RMaHQ5VsW8xUCLyDIpVxukdB7H1+fdQvHEXas6eR31lNWrOnkfxxl3Y+vx7OL3jIBQ3/2Hz448/4oEHHkBKSgoCAgLQqVMnPP300zCbzS5/bv+NfER+RKvXoveY/jj8bcuLF17WY2QfyFYZGh3/PiLyBrLFitM7DuLEhm3XbaPKCk5s2AYBQMLA7m7r+Tl8+DAURcFbb72Fzp07Y//+/XjwwQdRW1uLF1980aXPzeBD5AcEQUBMajwik2NwvqS8xfYavRY9s/tCw8kBibyGYpVRnLej5YYATuTtQFy/rm4LPmPGjMGYMWNsX6empuLIkSN44403XB58+Kcckd9QMeGJexAQGthsK1EScfvvp3CtKyIvIlusOL39AFTZvtPTqqzgzI4DkC1WF1dmv6qqKkRERLj8eRh8iPyEKEkICg/CfS/8Ch37doYgXLtyT0xqPCYvmo6Ebkm8oovIiwiCgHMHix3ap+JAcZPvA+5w7NgxvPbaa3j44Ydd/lx8ZyPyI5JWg8DwIIz73WSYautxKH8vLlXXQWfQoXNmGsITIhvacQVnIq8iSCKslxwbGGytN0OQnNv/MX/+fDz//PPNtjl06BDS0tJsX58+fRpjxozB3XffjQcffNCp9TSFwYfIz4iiCFEnQqMLRr/bMyHLCkRR8OvLW4m8nSor0ATogEr799EYdFBlBYIT/9D53e9+hxkzZjTbJjU11fb/M2fOYPjw4Rg8eDD+/ve/O62O5vCdjsiPiRoJInt3iLyeqqqI7p6CmrPn7d4nukcKVNW5y9JER0cjOjrarranT5/G8OHDkZGRgWXLlrXZosgc40NEROTlJK0GCZk97D51JUgiEgb2cFtP7+nTpzFs2DAkJyfjxRdfREVFBUpLS1FaWury52aPDxERkQ8QNRJSbhvY7Dw+l6XeNtCtvb15eXk4duwYjh07hsTExEbbnN0LdTX2+BAREfkASatBYmYPdBoz6Lo9P4IkotOYQWif6b7eHgCYMWMGVFVt8uZq7PEhIiLyEaJGQsLA7ojr1xVndhxAxYFiWOvN0Bh0iO6RgoSBPfx+bB+DDxERkQ+RtJqG3p/BvZF0czpXZ78KvwNEREQ+6MqQ48xL1r0dx/gQERGR32DwISIiIr/B4ENERER+g8GHiIiI/AaDDxEREfkNXtVFRETkg6xmKwRRgCiJUGQFqqJCo+PHPr8DREREPsRqtkC2yNj3ZSFO7DgCU2099EEGpA7sil6jMyBpJWh0WneX6TYMPkRERD5Ctlix/6vd2Pb+ZiiyYru/uqIK534sw65PvsOg+4b9HIDcGwH+/Oc/4/PPP0dRURF0Oh0qKyvb5Hk5xoeIiMgHWM0W7PuyEFv/talR6LmSIivY+q9N2PdVIaxmSxtX2JjZbMbdd9+NWbNmtenzsseHiIjIB1jNVmx7f7Ndbbet3Ixuw9Ldespr0aJFAIDly5e36fOyx4eIiMjLWc0Np7iu19NzNUVWsP+r3bCarS6uzPMw+BAREXk5QRRwYscRh/Y5vv0wBMFFBXkwBh8iIiIvJ0oiTLX1Du1jrjNBlJy7eOn8+fMhCEKzt8OHDzv1OR3FMT5EREReTpEV6IMMqK6osnsfXaAeiixDEp0XBX73u99hxowZzbZJTU112vPdCAYfIiIiL6cqKlIHdsW5H8vs3qdTZhpU1bl1REdHIzo62rkP6mQ81UVEROTlNDoNeo7qB1Gy72NdlET0HNXPrTM5l5SUoKioCCUlJZBlGUVFRSgqKkJNTY1Ln5fBh4iIyAdodBoMum+YXW0H/WI4JK1zx/c4auHChejbty+efvpp1NTUoG/fvujbty927drl0udl8CEiIvIBGp0WvUZnYPD0Edft+RElEYOnj0CvUf3cvmzF8uXLoarqNbdhw4a59Hk5xoeIiMhHSFoNet7WD92GpWP/V7txfPthmOtM0AXq0SkzDT1H9YOkldy+XIU7+e+RExER+SCNTguNTov08QPR5/aBECUJiixDVcHV2cHgQ0RE5JOuDDnOvGTd23GMDxEREfkNBh8iIiLyGww+RERE5DcYfIiIiMhvcLQTERGRDzKbLBBFAZIkQZZlKIoKnd69c/d4AgYfIiIiH2I2mWE1W7Hpk3wUbi5CXfUlBIYEIGNYH4yYPBQanQY6vc7dZbqNR5zqWrx4MQYMGICQkBDExMRg4sSJOHLkSKM29fX1yM3NRWRkJIKDgzF58mSUlTVejK2kpATjx49HYGAgYmJiMG/ePFit1rY8FCIiIrexmK345pMteGz8fKz5+zqU/HAK586eR8kPp7Dm7+vw2Pj5+OaTLbCYXffZuHTpUnTs2BEGgwGZmZnYsWOHy57rRnhE8MnPz0dubi62bduGvLw8WCwWjBo1CrW1tbY2c+bMwWeffYaPPvoI+fn5OHPmDCZNmmTbLssyxo8fD7PZjK1bt+Kdd97B8uXLsXDhQnccEhERUZsym8zY9PFmfLhkDWSr3GQb2SrjwyVrsOmTfJhNZqfX8MEHH2Du3Ll4+umnsXv3bqSnp2P06NEoLy93+nPdKEFVnb0ofetVVFQgJiYG+fn5GDJkCKqqqhAdHY2VK1diypQpAIDDhw+jW7duKCgowKBBg7B+/XrcfvvtOHPmDGJjYwEAb775Jp544glUVFRAp2u5W89oNCIsLAxVVVUIDQ116TESERE1pb6+HsXFxUhJSYHBYLB7v1pjHebcPv+6oedKkkbCK58/h8CQwNaUeo3MzEwMGDAAS5YsAQAoioKkpCQ88sgjmD9/fqseu7nviyOf3x7R43O1qqoqAEBERAQAoLCwEBaLBdnZ2bY2aWlpSE5ORkFBAQCgoKAAvXr1soUeABg9ejSMRiMOHDjQ5POYTCYYjcZGNyIiIm9jNlmwaXW+XaEHaOj52fTJFphNFufVYDajsLCw0We1KIrIzs62fVZ7Ao8LPoqi4LHHHsPNN9+Mnj17AgBKS0uh0+kQHh7eqG1sbCxKS0ttba4MPZe3X97WlMWLFyMsLMx2S0pKcvLREBERuZ4oCti9ucihfQo3F0EUBafVcO7cOciy3ORn8fU+h93B44JPbm4u9u/fj1WrVrn8uRYsWICqqirb7eTJky5/TiIiImeTJAl11Zcc2qeupg6iJLmoIs/lUcFn9uzZWLduHb755hskJiba7o+Li4PZbEZlZWWj9mVlZYiLi7O1ufoqr8tfX25zNb1ej9DQ0EY3IiIibyPLMgJDAhzaJzA4EIps36kxe0RFRUGSpCY/i6/3OewOHhF8VFXF7NmzsWbNGmzatAkpKSmNtmdkZECr1WLjxo22+44cOYKSkhJkZWUBALKysrBv375GI8fz8vIQGhqK7t27t82BEBERuYGiqMgY1sehfTKG9YGiOO/6Jp1Oh4yMjEaf1YqiYOPGjbbPak/gERMY5ubmYuXKlfj0008REhJiOxcYFhaGgIAAhIWF4YEHHsDcuXMRERGB0NBQPPLII8jKysKgQYMAAKNGjUL37t0xffp0vPDCCygtLcWTTz6J3Nxc6PV6dx4eERGRS+n0WgyfNBT//n/r7b6qa8TkIU6fyXnu3LnIyclB//79MXDgQLzyyiuora3FzJkznfo8reERweeNN94AAAwbNqzR/cuWLcOMGTMAAC+//DJEUcTkyZNhMpkwevRovP7667a2kiRh3bp1mDVrFrKyshAUFIScnBw8++yzbXUYREREbqPVazD513fgwyVrWmw7Zdad0OicHwHuvfdeVFRUYOHChSgtLUWfPn2wYcOGawY8u5NHzuPjLpzHh4iI3O1G5/EBGmZu3vRJPj5549Mme34kjYTJs+7EiMlDoXVB8HElZ83j411HTURERNel1WkwfNKtuPX2LGz6ZEvDWl01dQgMDvx5ra4h0Og0Xhd6nMl/j5yIiMgH6fQ66PQ6jLpvJMZMy4YoSVC4OrsNgw8REZEPujLkiCI/7i/ziMvZiYiIiNoCgw8RERH5DQYfIiIi8hsMPkREROQ3GHyIiIjIb3CYNxERkQ8y1ZsgiiIkjQay1QpFUaA3cAknBh8iIiIfUl9vgtlkxgfvrsXXG/JRXVWDkLBgZI8ZinvvnwidXgeDHwcgnuoiIiLyEWazBR+8uxbD+9+FJf/3Txw+cAynT5Xi8IFjWPJ//8Tw/nfhg3fXwmy2uOT5t2zZggkTJiAhIQGCIGDt2rUueZ7WYPAhIiLyAfX1Jry/fDVe+ssbsFqsTbaxWqx46S9vYNU7q1Ffb3J6DbW1tUhPT8fSpUud/tjOwlNdREREPsBsMuPVv75tV9u/vfA2Jt4zzumnvMaOHYuxY8c69TGdjT0+REREXs5Ub8Kqd9dct6fnalaLFR++txYmF/T6eDoGHyIiIi8niiI2btji0D5567dAEP0vBvjfERMREfkYSaNBdVWNQ/tUG2ug0UguqshzMfgQERF5OdlqRUhYsEP7hIQGw2qVXVSR52LwISIi8nKKoiB7zFCH9rlt7BCoiuKiijwXgw8REZGX0xv0uPf+idBo7btYW6PV4J7pE50+k3NNTQ2KiopQVFQEACguLkZRURFKSkqc+jytweBDRETkA3R6HX4770G72j72xEPQ6XVOr2HXrl3o27cv+vbtCwCYO3cu+vbti4ULFzr9uW4U5/EhIiLyAQaDHvfNmARBaJinp6lL2zVaDR59/EHce/9d0Om0Tq9h2LBhUFXV6Y/rTAw+REREPkKn0+Ke6RMx8Z5x+PC9tchbvwXVxhqEhAbjtrFDcM/0hrW6XBF6vAWDDxERkQ8xGPQwGPSY/qt7cP9DU6HRSLBaZahcnR0Agw8REZFPujLk6HQc0nsZvxNERETkNxh8iIiIyG8w+BAREXkgT786qq056/vBMT5E5NNUVYVikaHIMurOVwEAAiPDIGo0EDUiBEFwc4VEjUlSw/pZZrMZAQEBbq7Gc9TV1QEAtNrWXZHG4ENEPku2WFFTdhHHvt6F0n3FCGgXjI639EZARCjMtZdguWSCRqdFQLtgKLICyc5Zb4lcSaPRIDAwEBUVFdBqtRD9cAX1K6mqirq6OpSXlyM8PNwWDG8Uf8uJyCfJFitO7/4Bez/4BlBVRKclo1/OGJQf/BE73l6Hi8WltraG8GB0GNwTqUPTIWokiJJ/f9CQewmCgPj4eBQXF+Onn35ydzkeIzw8HHFxca1+HAYfIvI5qqKgsqTMFnoiUuORMWMMvl+1CWf2HLumfX1lDY58sQ0ntx/Ezb+dDF1IAAQIUGQZUFUIkgixlX9lEjlCp9OhS5cuMJvN7i7FI2i12lb39FzG4ENEPkdRVPywYQfw82DI3veMwOHPtzUZehrtZ5VRdboC0WnJOH/iNM4fOQnFKsPQLgSJA9IgSiIkP57xltqWKIowGAzuLsPnMPgQkc8xV9fh/LHTAIDILonQBhnw03/2N7tPUHQ4snIn4vzRU8hfvAKXLhgbbT+8bivi0zujx6QhkM0W6IIbBp2yJ4jIu/BENhH5nMqT5bb/Jw/qjpJtB6HIynXba/RaZD48AWf3HMXeVRuvCT0AoMoKzuz+AQWvfQJRo8GxvF04f/QU5CYWgiQiz8XgQ0Q+58qQExQVjsqfypptnzggDZa6ehz+fGuLj11TdhH7P8lH4oBu2PnPz3G68AjDD5EX4akuIvI5wTHtbP8XJBGqcv3eHgDoeEsvnNi0G2hmfjRBFBDdNRlBse0gaTTQBuqQ0KcL9n+cj/AOcQiNj3RW+UTkQgw+RORzQuIjEBwXgZrSCzDX1CEwMvS6bYPjIhDQLgRnv2964LOo1SBlaDqSs3pCgIqqknKoioy68kr0njoSsT1ScHbPUQRFhnLgM5EX4KkuIvI9iorUYX0AAGf2HENSZrfrNtUHB8BcUwfFKl+zTRuox6DfTER8r1Qc+/w/2PHax6g8cQpB0e0QkhgDURIR2zMFnUZmACJngCbyBuzxISKfI2okJGZ0xcXisziz5wd0v/NmRKQm4MKJM9e0VawyhCauzBIkERm/HAdL7SUc/OBrhKckIOt396G+sgYnC/bjwrFTkC0ydMEBiO97ExIHdYesWjn7M5GH428oEbmNIitQFQV1lTU4/2MZVEVFWEIkwhMioaoqJM2NXyouaiT0mjIMIQlRKP5uL/pNvw3/eXU1Ll2sbtSu7rwR+uAABLQLabQtPr0zDCGB2PXuerTr1B497s3GwU/yUVp0tNH+5uo6HD1bgONf7UCPe0ciulsHhh8iD8bfTiJyC6vZivKjp1D06VaU/3C60bbwxCj0HDMAKYO6tTr8dMjqAVESUXexGrf+7h7s+zgfpXtP2AY8m6rrUHbgRyQN6oEf1m+z7dthcE+c3n4Akl6L7veMxP4PN6F834nrPpdilbFv5Vfoc/9YRHRJZPgh8lD8zSSiNmc1W3Hs233Y9q+vm7ySqvLUOXz3j/WoOHEWA38xolXh53IACYoMg6Io6PuLkZDvGYbTu46g3lgHSadBaPsoRHdNwk//2QeTsRaBkWEITYzGgZVfIn5AN1SVlDUbemxU4NDqfNz6h+k3XC8RuRYHNxNRm1IUBRd+Krtu6LnSkU1FOPbdfqfNkyOKDUtO6AIN6HhLL9w0egA6j8xAUFQYRI2EQbkToQ8NhCE8GCZjLawmCxIGdMfJggN2P4epug7nDpe0eAk9EbkHgw8RtSnFqmDvum0thp7L9n+xA4Lo/LcqQRQhaTW2ldhFjYSA8BAMeeIXSByYBgDQhwTCEBaMc4ccWyG7dO8xTmpI5KEYfIioTVnrzTi9t9ju9tXllaho4mosVxA1ErQGPeJ7d4YhPAS6kEAoVqvDvTdyvaXhX4sVqqpCscq2gdxNXTZPRG2HY3yIqE0Zyy5CVe3s7vnZ+R/LENO5PQShbebKkXQayGZLwyBlnbZh9udm1vq6miZAD1VR8dO3RTi1/SBMVbUAgKCYdkga3BPtB6RBEASIrRi7REQ3xmN6fLZs2YIJEyYgISEBgiBg7dq1jbbPmDEDgiA0uo0ZM6ZRmwsXLmDatGkIDQ1FeHg4HnjgAdTU1LThURBRi24gu7RV4LmSpNMivn831J2rQmzPVIf2jevbGScL9uP4VzttoQcAassv4vDab/Hd8ytx6WI1e3+I3MBjgk9tbS3S09OxdOnS67YZM2YMzp49a7u9//77jbZPmzYNBw4cQF5eHtatW4ctW7bgoYcecnXpROSA0Nh2DgeZyI6xbgk/2kADVEVBYlZPu/cxtAtBRGr7ZgdEm4y12PnGWljrzc4ok4gc4DGnusaOHYuxY8c220av1yMuLq7JbYcOHcKGDRuwc+dO9O/fHwDw2muvYdy4cXjxxReRkJDg9JqJyHEavQ7t01Nxqui4Xe1DY9shKiXexVU1TdJqYGgXAkO7ELQf0A2ndx5qtr0giug+aSjK9p1o1NPTFHPNJZzYWIguYzO5xhdRG2pVj4/RaMSHH36Il19+Ga+++irWr18PxYWXcG7evBkxMTHo2rUrZs2ahfPnz9u2FRQUIDw83BZ6ACA7OxuiKGL79u0uq4mIHCNpJKRPGGR3D07PcQPdeml4w5VfEtLuuhVJg3sB16lbG6hH31+OgzbIgIOr8+167DOFR1xyxRoRXd8N/8atWLECo0ePxqZNm/DWW29hz549WL16Nfr164eioiInlthgzJgxePfdd7Fx40Y8//zzyM/Px9ixYyHLDefIS0tLERMT02gfjUaDiIgIlJaWNvmYJpMJRqOx0Y2IXEsQBbRLisGgnNtaHO/TbVQ/dBrc3e2zIAuiAFGS0GXcIAx58n50HN4XoYnRCIqNQESn9uh570gM+d8cGNqFYtdb/4Zsstj1uNZ6M2pKL7i4eiK60g2/mzz//PPYsWMHDAYDLl68iClTpmDjxo04cuQI7r//fqf3skydOtX2/169eqF3797o1KkTNm/ejJEjR97QYy5evBiLFi1yVolEZCeNToNOg3sgLC4C33+6FWcPlTTaHtEhBj3HDkSH/je1atZmZ5O0GkhaDVJH9EfqyP4QRAGqrEKQBAiiiIqDxQ6P2+F8P0Rt64aDj6IokH5e0ViSJFRWVgIAunbtitra5s9tO0NqaiqioqJw7NgxjBw5EnFxcSgvL2/Uxmq14sKFC9cdF7RgwQLMnTvX9rXRaERSUpJL6yaiBhqdBrE3tUf23MmoN9bhQkk5FEVBWHwkQmPCoQIeFXquJOmueOu8okRDeIjDj6ULDnBCRURkrxsOPjNmzEBWVhaysrKwefNm/Pa3vwUAVFRUIDQ01GkFXs+pU6dw/vx5xMc3DHrMyspCZWUlCgsLkZGRAQDYtGkTFEVBZmZmk4+h1+uh1+tdXisRNU0QRUiiiKDIUARFuv59w9Wiu3WApNfafaorODYCARHef9xE3kRQHZ1J7Ar79+/HoUOH0LNnT3Tr1q1VhdTU1ODYsWMAgL59++Kll17C8OHDERERgYiICCxatAiTJ09GXFwcjh8/jscffxzV1dXYt2+fLbyMHTsWZWVlePPNN2GxWDBz5kz0798fK1eutKsGo9GIsLAwVFVVtUl4IyLfIpst+OHzArvX9uo2eSjaZ3TlRIZEreTI53ergo8zbd68GcOHD7/m/pycHLzxxhuYOHEi9uzZg8rKSiQkJGDUqFH44x//iNjYWFvbCxcuYPbs2fjss88giiImT56MV199FcHBwXbVwOBDRK0lmy3YvmR1i4OWo9KS0SdnDESJoYeotdwefLZv337d00uejMGHiFpLURQoFhn73v8aFYd+vGYxVkES0X5AGtLuuIU9PURO4vbgk5ycjJKSkpYbehgGHyJyhssLk1rqTCj5zz7UnauCIAoIbR+NxEHdIUpS4wHSRNQqjnx+3/Bv3j333NPk/aqq4sIFzktBRP5LEISGS9/DNOiU3R+q2jABoyCKbp+TiMjf3fBv4Ndff4333nvvmvEzqqpiy5YtrS6MiMgXsGeHyLPc8G/ksGHDEBISgiFDhlyzrXfv3q0qioiIiMgV7B7j86c//Qn9+vVDRkZGoyupfAnH+BAREXkflwxuFkXRtqhgXFycLQRd/rd9+/atr9zNGHyIiIi8j0sGNw8YMABnz57FzJkzERUVhd27d2P16tX4y1/+AlmWER0djX79+uGLL75o9QEQERERuYLdwWf79u1Yvnw5/vCHP2DAgAF46aWX0KlTJ5hMJhQVFWH37t3Ys2ePK2slIiIiahWH5/GpqanBs88+i7feegu/+c1v8NRTTyEwMNBV9bUpnuoiIiLyPo58fouOPnhwcDBeeOEF7Nq1C/v370fnzp3x7rvv3nCxRERERG3F4eADAFarFSaTCffddx8SExMxc+ZMTlpIREREHs/uMT7PPfcc9u3bh3379uHw4cMwGAzo3bs3Bg4ciIcffhhhYWGurJOIiIio1Ry6nL1jx47IycnBfffdh5tuusnVtbU5jvEhIiLyPi6Zx2fo0KEoKipCdXU1goKC0Lt3b/Tr189269mzJyTJu1caZvAhIiLyPi6Zxyc/Px8AcPToURQWFmL37t3YvXs3VqxYgcrKSuj1evTq1Qs7duxoXfVERERELuLwWl1dunRBly5dMHXqVNt9xcXF2LVrF+fxISIiIo/m8Dw+voynuoiIiLyPS+fxISIiIvJWDD5ERETkNxh8iIiIyG8w+BAREZHfYPAhIiIiv8HgQ0RERH6DwYeIiIj8BoMPERER+Q0GHyIiIvIbDD5ERETkNxh8iIiIyG8w+BAREZHfYPAhIiIiv8HgQ0RERH6DwYeIiIj8BoMPERER+Q0GHyIiIvIbDD5ERETkNxh8iIiIyG8w+BAREZHfYPAhIiIiv8HgQ0RERH5D4+4CiMg7qKoK2SIDACStBEEQ3FwREZHjGHyIqFkWkwWiJOKH7YdRevwsACCuUzxuykyDIivQ6rVurpCIyH4MPkR0XbJVRsGa/2DHpwWoM9Y12hYYGoiBd2bh5im3QtJIbqqQiMgxDD5E1CTZKmPt/32CA1v2Nbm9zliHze9tREVJOSbOnczwQ0RegYObiegaVosVe74qvG7oudKB/H0oytsNq8XaBpUREbUOgw8RXUMURWxfW2B3+21rt0IU+XZCRJ6P71REdI2y4lKcP33O7vbnT51D2Y+lLqyIiMg5GHyI6BoXzl5weJ+LN7APEVFb85jgs2XLFkyYMAEJCQkQBAFr165ttF1VVSxcuBDx8fEICAhAdnY2jh492qjNhQsXMG3aNISGhiI8PBwPPPAAampq2vAoiHyDpHH8rUHS8FoJIvJ8HhN8amtrkZ6ejqVLlza5/YUXXsCrr76KN998E9u3b0dQUBBGjx6N+vp6W5tp06bhwIEDyMvLw7p167BlyxY89NBDbXUIRD6jfddEwJEJCgUBCTe1d11BRERO4jF/oo0dOxZjx45tcpuqqnjllVfw5JNP4s477wQAvPvuu4iNjcXatWsxdepUHDp0CBs2bMDOnTvRv39/AMBrr72GcePG4cUXX0RCQkKbHQuRtwsIDkCnfp1wvPCYXe079+sMQ7DBxVUREbWex/T4NKe4uBilpaXIzs623RcWFobMzEwUFDRceVJQUIDw8HBb6AGA7OzshqtTtm9v8nFNJhOMRmOjGxE1nLYaNm0kRKnltwhREjH0f0ZAw1NdROQFvCL4lJY2XC0SGxvb6P7Y2FjbttLSUsTExDTartFoEBERYWtztcWLFyMsLMx2S0pKckH1RN5HEAXEdIzFpHl3Q2xmYkJRI2HS43cjpkMsBJFrdxGR5/OK4OMqCxYsQFVVle128uRJd5dE5DG0ei26DOyKWUtnIz27LzS6//boaPRapGf3xayls9FlQFeu10VEXsMr+qbj4uIAAGVlZYiPj7fdX1ZWhj59+tjalJeXN9rParXiwoULtv2vptfrodfrXVM0kQ/Q6rWITIzC2Fm3Y9xvbofxfDUAIDQyFKqqQmfQublCIiLHeEWPT0pKCuLi4rBx40bbfUajEdu3b0dWVhYAICsrC5WVlSgsLLS12bRpExRFQWZmZpvXTORLdAYdtHodIhMiEZkQCa1ey9BDRF7JY3p8ampqcOzYf68gKS4uRlFRESIiIpCcnIzHHnsMf/rTn9ClSxekpKTgqaeeQkJCAiZOnAgA6NatG8aMGYMHH3wQb775JiwWC2bPno2pU6fyii4iIvIZitUKQZR+/leAIIpQVRWixIWC7eExwWfXrl0YPny47eu5c+cCAHJycrB8+XI8/vjjqK2txUMPPYTKykrccsst2LBhAwyG/15Cu2LFCsyePRsjR46EKIqYPHkyXn311TY/FiIiImdTrDIstXW4sO8wqo6XQLU2LAysbxeGdt27IKxLRwhCQxCi6xNUVVXdXYSnMBqNCAsLQ1VVFUJDQ91dDpHbyLIMxaoAACStxAVIidxMscqoPHICZdt2X7eNLjQYHcaPgGTQ+134ceTz22N6fIjI/cz1ZgDA95v24NypcxBEEcndk5GW2Q2yVebVW0RuoFhlVP90qtnQAwBmYw1++nwTUu4aA8G/co9DGHxczFxvhs6ggywrkCQRZpMZGq2Gf0GTR1EUBYqsYMM/1qPo692wmCy2bf/5BAhuF4wh9wzFgPGZ0Gj5tkHUlgRRQPnOvXa1NRtrUPnDCYR3TeWYn+vgO5iLWMwWXCi9gLz3N6Hwmz2orzNB0kjoOag7sqcOR0r3jpCamRiOqC0psoJl8/+BkoMlTW6vuViDL976HBdKL2L0A2MYfojaiKqqqD1TBmttnd37XDx4FO3SOrmwKu/Gdy8XsFqs+HzZBny54utG98tWGd9/tw/ff7cPvW/uiQefnckPEHI7c70ZX7+Td93Qc6Vtn25Fl4wu6Nyvi13LWRBR66hWGTWnml594HrMVdVQLBZInKeuSXzncjKzyYy89zddE3qutvc/+/GPp5dDtsptVBlR00RJxJ68wpYb/uy7j7+FoigurIiILlOhQpUd/5xQZf6OXg+Dj5MpsoL1735lV9vvv9uHU8fPuLgiouYd2noQ9bX1drcv3nsC9TWXXFgREV0miCI0gQEO7iRA1HGC0eth8HEii9mC7z7bCovZ0nLjn329apPtShqitiZbZVw4e97h/YznjS6ohoiuJkoS2nVNdWifkA7tAXCmmuth8HEiRVZwYPthh/Y5tPMwp/4ntxFE4YYG2Usajk0jaiuiTofgpPiWG/4sslcaBF7RdV0MPk4kiILDvTfmevt7h4icTRRFpPZx7OoPfaAekQkRLqqIiK4miALih2RCExTYYtuI3mnQR4ZDEIQ2qMw7Mfg4kaqoCGkX4tA+IRGOtSdyttiOcYjtGGd3+/QRfaEo7EYnaiuCKELSapBy520ISohtso2o0yFmYB9E9+vJ+XtawP5qJ9LqtRg8LhPff2vfRFMAMPC2DNskh0TuoKoqsmfchpWL/oWWVrAxBBkw9N6h/HklamOCJEHSC0gcdSvkS/W4eOg4LLV1ECQRQfGxCE1NgqooDD12YPBxIlEU0WNQN4RFhaHqXFXL7SURw6fwQ4TcS6PVoFPfzrg99w6se/3fUK/Tm2MIMiDnzzMRGNpydzsROZ8gihAAiMFBiOrb3faHiihJDdu4IoBd+F1yMkVW8NCzM6HRtpy67310MgyBhhbbEbmaVqdF3+x+yF36CNJH9Gk0sWZgaCBuvXsIHv3HXMSlxEOj43pdRO4majSQtFpIWi0Dj4O4OvsVnLU6u9lkweljp/HPZ9/B+bMXrtkeFBqIKbPvQsaIvtDyQ4Q8jLneDEEQUFtVC1EUEBQeDEWWodWzZ5KIPJMjn98MPldwVvABGub0kSQJPxQdw7YNO1BTVQt9gA7pt/RGv+F9oMgydPwgISIiajVHPr85xsdFLvfk3NS3Mzp26/DzvSq0Om3DvClcoJSIiKjNMfi4mCiKMARyoTgiIk8hW2UoVhkQBEBVIek0EDlOxm8w+BARkV+wmiwQRAFHvt2P4l1HYak3wxASgK5DeqFDn05QZAUaHT8WfR1fYSIi8nmyxYoj3+7H1hWbYLnUeIb9E9uPIKhdMLJn34HYLgm8ctHHsW+PiIh8mtVsxf68Pcj/x4ZrQs9ltRdr8NlfVqHs6BlYzdY2rpDaEoMPERH5NHNdPba+t7HFdoqs4KtXP4Uo8aPRl/HVJSIin2U1WfD9FztbXI7lsktVtfhx91EosuLiyshdGHyIiMhnafRaHN160KF9Dm/eB9nC012+isGHiIh8Wr2xzrH21XUQBMFF1ZC7MfgQEZFP0+gdu0pLo9fafWqMvA+DDxER+SyLyYLkPp0c2qdjvy4c4OzD+MoSEZHP0uq16HP7QLvba3QadBveG5KW09z5KgYfIiLyae3aR6FzVje72g64+1YIIsf3+DJGWiIi8mmSRsLI3AkAgGMFh67bbsDdt6L32AENC0mTzxJUjuCycWRZeyIi8i6yVcaFkxUoWrcdP+0+3rBWV2gAOmd1R5/xAxEQFsS1uryUI5/ffIWJiMgvSBoJ0SlxGP7QuEZXellMFmgdvPKLvBfH+BARkV+5+vJ2hh7/wuBDREREfoPBh4iIiPwGgw8RERH5DQYfIiIi8hsMPkREROQ3GHyIiIjIbzD4EBERkd9g8CEiIiK/weBDREREfoPBh4iIiPwGgw8RERH5DS5SSkQ+yWIyQ5QknDxUgjpjHQyBBiT3SIaqqNAadO4uj4jchMGHiHyKIiuwWqzIX/ENivIKcan6km2bLkCHXsPTMXx6NvSBekgayY2VEpE7MPgQkc9QFAXmSyb8v9+/jXMnK67Zbr5kRuEXO/HD9iP45f89iOB2IQw/RH6GY3yIyGeoior3F/2rydBzperzRrz3h2UQBKGNKiMiT+E1weeZZ56BIAiNbmlpabbt9fX1yM3NRWRkJIKDgzF58mSUlZW5sWIiamsVJeU4ebDErrYXzlzA0V0/QJEVF1dFRJ7Ea4IPAPTo0QNnz5613b777jvbtjlz5uCzzz7DRx99hPz8fJw5cwaTJk1yY7VE1JbM9WZsW7vVoX12/LuAwYfIz3jVGB+NRoO4uLhr7q+qqsI///lPrFy5EiNGjAAALFu2DN26dcO2bdswaNCgti6ViNqYKAqo+KncoX0qfiqHRudVb4NE1Epe1eNz9OhRJCQkIDU1FdOmTUNJSUOXdmFhISwWC7Kzs21t09LSkJycjIKCgus+nslkgtFobHQj7yDLMqxmK2qqalF2qgIXKyohywosZou7SyMvorq7ACJqc17zp05mZiaWL1+Orl274uzZs1i0aBFuvfVW7N+/H6WlpdDpdAgPD2+0T2xsLEpLS6/7mIsXL8aiRYtcXDk5m9Vixd6CA/hq1Ub8UHTMdn9M+2iMmDIEwyYOgUYrQRS9KtdTKymKiqikaJw9dsbufaKTomG1WKHRes1bIRG1ktf8to8dO9b2/969eyMzMxMdOnTAhx9+iICAgBt6zAULFmDu3Lm2r41GI5KSklpdK7mO1WLF24uWY+em3ddsKz9dgVV/+wRb/r0V81+fg8DgQIgSw4+/0Bl0GDRxMPZ9873d+wy8YxADMpGf8drf+PDwcNx00004duwY4uLiYDabUVlZ2ahNWVlZk2OCLtPr9QgNDW10I89lNpmx6m8fNxl6rnSm+CxemP03qDyR4XdiUmKRmGbfHy/hce1w08A0hmMiP+O1v/E1NTU4fvw44uPjkZGRAa1Wi40bN9q2HzlyBCUlJcjKynJjleRMFpMF+Z9+13JDAKeOn8berQd4xY6fEQQBU5/+H0QkRDbbLrhdMO7/y0yoKsMxkb/xmuDz+9//Hvn5+fjxxx+xdetW3HXXXZAkCffddx/CwsLwwAMPYO7cufjmm29QWFiImTNnIisri1d0+QizyYxNq7dAdiDIfLVqo0PtyfuJoghDkB4PvjoLmXdmwRBsaLRdq9ei76gMPLwkFyERoZy1mcgPec0Yn1OnTuG+++7D+fPnER0djVtuuQXbtm1DdHQ0AODll1+GKIqYPHkyTCYTRo8ejddff93NVZOzKLKCY3uPO7TP8QPF0PJSZb8jShL0ARKG35+N7Jmj8eP+YtRV1sIQZEDH3ikAwEVKifyY13wqrFq1qtntBoMBS5cuxdKlS9uoImpLgiBAtsoO7eNoe/Itup/DTae+nd1cCRF5Eq851UX+TVWByLjmx21cLSouAqrCMRxERPRfDD7kFQyBeoyYMtShfW69fTAsFquLKiIiIm/E4ENeIzE1AR262nepslanxYjJQ6HTa11cFREReRMGH/Iqjzz/a4RGND/fkiSJ+M2ffwWNjqGHiIgaY/AhryFpJIS2C8GidxYgfXBPCKJwTZvkmxIx77VH0a1/V/b2+IlLdZdgtVohyzLqL9VzCgMiapagcgYvG6PRiLCwMFRVVXEWZw+mKAqsFhmXai9h6xfbYLxYA32ADv2G9kH7lHioqsq1l3ycqqqQZRlHD5/Au//4EAf2HoEiy0jq0B5Tc+7CLcMyoSgKtFqGXyJ/4MjnN4PPFRh8vI9slSHLMgRB5Jw9fkJRFFy6VI/fPvAH7CzY02Sb9klxePO9FxGfEAudnnP2EPk6Rz6/eaqLvJqkkaDT6xh6/IjVYsUv73n0uqEHAE6fLMX/TPwNzp+7CEVpm1NfFpPZ9lyqqsJcb26T5yUix/DTgoi8hslkxgfvrcWh/T+02Laq0ojnnnkVz7+2EAaD3mU1WUwWmC6Z8J81/8H+LftQV10HfaAeaZndcOuUWxHSLgQaBnMij8HfRiLyGhqNhFXvrLG7/ZaNBairveSy4GO1WLHtswJs+MeGRj1LdcY6FHy6FQWfbkXWnYMx/uHxXBeMyEPwVBcReY1TJWdwquSM3e1lWcZXn292ySrsFpMF2z/fji/+/kWzp9MKPt2KL976HFYzJ9Mk8gQMPkTkNaqNtQ7vY6wyQpadv26boijY8I/1drXd+ulWGC8YnV4DETmOwYeIvEZIaJDD+4SGhkCSnHuayWK2YNf6nQ714nz38bcc8EzkARh8iMhrJCYnoH1SvN3tRVHEqNuHQRCuneyyNVRFxYGtBx3a52DBQduK8UTkPgw+ROQ1rFYZU3Pusrv9kJFZCAwKdHodoijCVFfv0D6mS+ztcTdFVmC+ZIbFZIH5khlWLmLsl3hVFxF5Db1eh6n334Uv1ubh0P6jzbYNDQvB/EW/hc4Fa7YpioKAEMcCVWBIAFRVdXrvE7XMarZAlCQc23EEh/L34pKxDtoAPToP7Ioew3tDVQEtl7jxGww+RORVtFoN/t8Hr2L2zCdQuGNvk23i28fizfdeRGRUBETR+R3boiSiz/B0HN9zzO59eg3pDYvZwpmk25jFZMGZwyfxxd/WoK6y8eD4H/ccQ/47eRgyfSR6ZvflUjd+gq8yEXkVURQRGBSAt99/BT8cOoZ33/4QB/cdgdUqI6lDAqbmTMKtwwdBVRRoXdDbAwAarQZ9RvTFujfXwVRnarG9IAq4edLNDD1tzGK24PShEqz+00qoStNTGljqzdj49npYLVb0GdMfGhf9zJDn4FpdV+BaXUTe51JdPbQ6LURRgNlsgVarcfpVXE2xmCw4tO0QVv3l/RbnCRr9y9G4edItLgti1DRFlvHmr17Gpaq6FtsKooCH356DoHbBbVAZORvX6iIivxEQaIBGI0EURRgM+jYJPUDDmJBug7ph6h/ugz6w6ZmhNVoNxj00HrdMvpWhp40psoKj247YFXqAhiv1Ctdtg8VkcXFl5G481UVEdIO0ei3SBqXhyQ+fwp5Ne1C0qQiXjA1rdXUf3B0Dx2dCFEWOHXEDq8WKg/lNjwG7nsPfHcCQ6dkuqog8BX8biYha4fK4nb4j+yJ9WDpESYSqKIAgsJfHjURRwCWjfb09lznanrwTgw8RkRNotBqAOcdjqIoKrcGxF4QTTPoHjvEhIiKfI0giUvt3cWiflIzOHOPjBxh8iIjI52i0GvTK7geNzv4TG/3vyOJEhn6AwYeIiHySIAi4+b5hdrXtNqQX2iVEurYg8ggMPkRE5JO0ei36jhvYEH6aWSkkbUhPjJ59ByRN20yFQO7Fwc1EROSzJK0G/e8cjB7D07Hr39tw5D8HcKm6DjqDHqn9u6D/HVmISIxi6PEjnLn5Cpy5mYjId1lMlkZjeK7+mrwXZ24mIiK6ytUhh6HHPzH4EBERkd9g8CEiIiK/weBDREREfoPBh4iIiPwGgw8RERH5DQYfIiIi8hsMPkREROQ3GHyIiIjIbzD4EBERkd9g8CEiIiK/weBDREREfoPBh4iIiPwGgw8RERH5DQYfIiIi8hsMPkREROQ3GHyIiIjIbzD4EBERkd/wueCzdOlSdOzYEQaDAZmZmdixY4e7SyIiIiIP4VPB54MPPsDcuXPx9NNPY/fu3UhPT8fo0aNRXl7u7tKIiIj8lqooDTdVtf3fXQRVVVW3PbuTZWZmYsCAAViyZAkAQFEUJCUl4ZFHHsH8+fNb3N9oNCIsLAxVVVUIDQ11dblEREQ+TVUUQFVRf74C5qqLUGUrBEkDXVg4DJExgCBAEFvfB+PI57em1c/mIcxmMwoLC7FgwQLbfaIoIjs7GwUFBU3uYzKZYDKZbF8bjUaX10lEROQPVEWB6cI51J09CTTqYzHh0qVaXCo7g4C4RBgio50SfuzlM6e6zp07B1mWERsb2+j+2NhYlJaWNrnP4sWLERYWZrslJSW1RalEREQ+rSH0VKDuTMlVoefKRiounT2J+vPlbXrqy2eCz41YsGABqqqqbLeTJ0+6uyQiIiKvp6oq6s6esqvtpdLTUNW2Cz4+c6orKioKkiShrKys0f1lZWWIi4trch+9Xg+9Xt8W5REREfkFVVFgOl9+/Z6ea3ZQYTpXAUN0bJuc8vKZHh+dToeMjAxs3LjRdp+iKNi4cSOysrLcWBkREZF/MVdddLD9BRdVci2f6fEBgLlz5yInJwf9+/fHwIED8corr6C2thYzZ850d2lERET+QRCgyrJDu6iyDAiCiwpqzKeCz7333ouKigosXLgQpaWl6NOnDzZs2HDNgGciIiJyEVWFIEkO7dLQXgXg+vDjU/P4tBbn8SEiImodVVFQX1GKS2Vn7N7HEBOPgJg4CKJjgekyRz6/fWaMDxEREbmfIIrQR8bA/t4bAYao2BsOPY5i8CEiIiKnEkQRAXEJdrUNiEvgBIZERETkvQRRhCEqFgFx7ZttFxCb8HNvT9vFEZ8a3ExERESe4XL40UdEof5cOSxVF6EoMkRRgjasHQxRMRBEqU1DD8DgQ0RERC4iiGLDaa+YOATEJkAQBKiq2nDlVxsHnssYfIiIiMilrhy4LAhCm83Z0xSO8SEiIiK/weBDREREfoPBh4iIiPwGgw8RERH5DQYfIiIi8hsMPkREROQ3GHyIiIjIb3AenytcXqjeaDS6uRIiIiKy1+XP7cuf481h8LlCdXU1ACApKcnNlRAREZGjqqurERYW1mwbQbUnHvkJRVFw5swZhISENMws6WeMRiOSkpJw8uRJhIaGurscshNfN+/D18w78XXzXKqqorq6GgkJCRBbWAqDPT5XEEURiYmJ7i7D7UJDQ/lL7YX4unkfvmbeia+bZ2qpp+cyDm4mIiIiv8HgQ0RERH6DwYds9Ho9nn76aej1eneXQg7g6+Z9+Jp5J75uvoGDm4mIiMhvsMeHiIiI/AaDDxEREfkNBh8iIiLyGww+RERE5DcYfHzY0qVL0bFjRxgMBmRmZmLHjh3XbWuxWPDss8+iU6dOMBgMSE9Px4YNGxq1kWUZTz31FFJSUhAQEIBOnTrhj3/8o11ro5B9tmzZggkTJiAhIQGCIGDt2rUt7rN582b069cPer0enTt3xvLly69p48jPAjnOFa/b4sWLMWDAAISEhCAmJgYTJ07EkSNHXHMAfspVv2+XPffccxAEAY899pjTaqbWY/DxUR988AHmzp2Lp59+Grt370Z6ejpGjx6N8vLyJts/+eSTeOutt/Daa6/h4MGD+PWvf4277roLe/bssbV5/vnn8cYbb2DJkiU4dOgQnn/+ebzwwgt47bXX2uqwfF5tbS3S09OxdOlSu9oXFxdj/PjxGD58OIqKivDYY4/hV7/6Fb788ktbG0d/Fshxrnjd8vPzkZubi23btiEvLw8WiwWjRo1CbW2tqw7D77jidbts586deOutt9C7d29nl02tpZJPGjhwoJqbm2v7WpZlNSEhQV28eHGT7ePj49UlS5Y0um/SpEnqtGnTbF+PHz9e/eUvf9lsG3IeAOqaNWuabfP444+rPXr0aHTfvffeq44ePdr2taM/C9Q6znrdrlZeXq4CUPPz851RJl3Fma9bdXW12qVLFzUvL08dOnSo+uijjzq5WmoN9vj4ILPZjMLCQmRnZ9vuE0UR2dnZKCgoaHIfk8kEg8HQ6L6AgAB89913tq8HDx6MjRs34ocffgAAfP/99/juu+8wduxYFxwF2aOgoKDR6wwAo0ePtr3ON/KzQK7X0uvWlKqqKgBARESES2uj67P3dcvNzcX48eOvaUuegYuU+qBz585BlmXExsY2uj82NhaHDx9ucp/Ro0fjpZdewpAhQ9CpUyds3LgRq1evhizLtjbz58+H0WhEWloaJEmCLMv485//jGnTprn0eOj6SktLm3ydjUYjLl26hIsXLzr8s0Cu19LrFhAQ0Giboih47LHHcPPNN6Nnz55tWSpdwZ7XbdWqVdi9ezd27tzppiqpJezxIQDA3/72N3Tp0gVpaWnQ6XSYPXs2Zs6cCVH874/Ihx9+iBUrVmDlypXYvXs33nnnHbz44ot455133Fg5ke/Lzc3F/v37sWrVKneXQs04efIkHn30UaxYseKaHnTyHOzx8UFRUVGQJAllZWWN7i8rK0NcXFyT+0RHR2Pt2rWor6/H+fPnkZCQgPnz5yM1NdXWZt68eZg/fz6mTp0KAOjVqxd++uknLF68GDk5Oa47ILquuLi4Jl/n0NBQBAQEQJIkh38WyPVaet2uNHv2bKxbtw5btmxBYmJiW5ZJV2npdSssLER5eTn69etn2y7LMrZs2YIlS5bAZDJBkqS2Lpuuwh4fH6TT6ZCRkYGNGzfa7lMUBRs3bkRWVlaz+xoMBrRv3x5WqxWffPIJ7rzzTtu2urq6Rj1AACBJEhRFce4BkN2ysrIavc4AkJeXZ3udW/OzQK7T0usGAKqqYvbs2VizZg02bdqElJSUti6TrtLS6zZy5Ejs27cPRUVFtlv//v0xbdo0FBUVMfR4CnePribXWLVqlarX69Xly5erBw8eVB966CE1PDxcLS0tVVVVVadPn67Onz/f1n7btm3qJ598oh4/flzdsmWLOmLECDUlJUW9ePGirU1OTo7avn17dd26dWpxcbG6evVqNSoqSn388cfb+vB8VnV1tbpnzx51z549KgD1pZdeUvfs2aP+9NNPqqqq6vz589Xp06fb2p84cUINDAxU582bpx46dEhdunSpKkmSumHDBlubln4WqPVc8brNmjVLDQsLUzdv3qyePXvWdqurq2vz4/NVrnjdrsarujwPg48Pe+2119Tk5GRVp9OpAwcOVLdt22bbNnToUDUnJ8f29ebNm9Vu3bqper1ejYyMVKdPn66ePn260eMZjUb10UcfVZOTk1WDwaCmpqaq//u//6uaTKa2OiSf980336gArrldfq1ycnLUoUOHXrNPnz59VJ1Op6ampqrLli275nGb+1mg1nPF69bU4wFo8vWlG+Oq37crMfh4HkFVOe0uERER+QeO8SEiIiK/weBDREREfoPBh4iIiPwGgw8RERH5DQYfIiIi8hsMPkREROQ3GHyIiIjIbzD4EBERkd9g8CEiIiK/weBDRD7j97//PSZOnOjuMojIgzH4EJHPKCoqQp8+fdxdBhF5MAYfIvIZ33//PYMPETWLwYeIfMKpU6dw7tw5W/CprKzEhAkTcMstt6C0tNS9xRGRx2DwISKfUFRUhPDwcHTs2BH79u3DgAED0L59e3zzzTeIi4tzd3lE5CEYfIjIJxQVFSE9PR0rV67E0KFD8fjjj+PNN9+EVqsFANx1111o164dpkyZ0mi/F198ET169EDPnj3xr3/9yx2lE1EbElRVVd1dBBFRa02ZMgWbNm0CAHz++efIyspqtH3z5s2orq7GO++8g48//hgAsG/fPuTk5GDr1q1QVRXDhw/Hhg0bEB4e3tblE1EbYY8PEfmEoqIiTJo0CfX19aisrLxm+7BhwxASEtLovkOHDiErKwsGgwEBAQFIT0/Hhg0b2qhiInIHBh8i8nrV1dU4ceIEcnNzsWTJEkydOhUHDhxocb+ePXti8+bNqKysxMWLF7F582acPn26DSomInfRuLsAIqLW+v777yFJErp3746+ffti//79mDBhAnbs2IGoqKjr7te9e3f89re/xYgRIxAWFoZBgwZBkqQ2rJyI2hp7fIjI6xUVFSEtLQ16vR4A8Ne//hVdu3bFpEmTYDabm9334Ycfxu7du/HNN99Aq9WiS5cubVEyEbkJBzcTkd/YvHkzlixZYhvcDADl5eWIiYnBkSNHcPfdd2P37t3QaNgZTuSr+NtNRH4hOzsb33//PWpra5GYmIiPPvoIWVlZuPPOO1FVVYWgoCAsW7aMoYfIx7HHh4iIiPwGx/gQERGR32DwISIiIr/B4ENERER+g8GHiIiI/AaDDxEREfkNBh8iIiLyGww+RERE5DcYfIiIiMhvMPgQERGR32DwISIiIr/B4ENERER+g8GHiIiI/Mb/B0qkqtVmeZKRAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "estimator = CreateRidgeCV()\n",
    "estimator.fit(X_test, y_test)\n",
    "for i in range(estimator.coef_.shape[0]):\n",
    "    plt.figure()\n",
    "    plt.bar([df_test.columns[j+5] for j in range(list_len*2)], np.abs(estimator.coef_[i]))\n",
    "    plt.ylabel(\"Модуль веса\")\n",
    "    plt.xticks(rotation = 90)\n",
    "    plt.savefig(\"material_results_M_feature_importance_\"+str(i)+\"_sklearn_RCV.svg\")\n",
    "    ind_k = np.argpartition(np.abs(estimator.coef_[i])[:list_len], -1)[-1:][0]\n",
    "    ind_M = np.argpartition(np.abs(estimator.coef_[i])[list_len:], -1)[-1:][0]\n",
    "    plt.figure()\n",
    "    ax = sns.scatterplot(data = df_test, x = df_test.columns[ind_k+5], y = df_test.columns[ind_M+5+list_len], hue = df_test.columns[i], s = 100)\n",
    "    plt.savefig(\"material_results_M_feature_importance_\"+str(i)+\"_most_important_features_sklearn_RCV.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-29T00:16:57.511208Z",
     "start_time": "2024-05-29T00:16:48.762452Z"
    },
    "collapsed": false,
    "id": "g6H11rEtUE_l",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "7d6954a3-4270-48a8-892e-c130ae9e3f31"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Коэффициент детерминации:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.997014</td>\n",
       "      <td>0.79743</td>\n",
       "      <td>0.029633</td>\n",
       "      <td>0.49352</td>\n",
       "      <td>0.638738</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$  $\\nu_2$   $\\nu_3$\n",
       "0  0.997014    0.79743  0.029633  0.49352  0.638738"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя абсолютная ошибка:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.013408</td>\n",
       "      <td>0.151253</td>\n",
       "      <td>2.046988</td>\n",
       "      <td>0.652195</td>\n",
       "      <td>0.405219</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
       "0  0.013408   0.151253  2.046988  0.652195  0.405219"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Корень среднеквадратической ошибки:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.018064</td>\n",
       "      <td>0.197243</td>\n",
       "      <td>2.4914</td>\n",
       "      <td>1.151135</td>\n",
       "      <td>0.649323</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$  $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
       "0  0.018064   0.197243   2.4914  1.151135  0.649323"
      ]
     },
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    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\mu^*$</th>\n",
       "      <th>$\\mu_{APE}$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\lambda^*$</th>\n",
       "      <th>$\\lambda_{APE}$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_1^*$</th>\n",
       "      <th>${\\nu_1}_{APE}$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_2^*$</th>\n",
       "      <th>${\\nu_2}_{APE}$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$\\nu_3^*$</th>\n",
       "      <th>${\\nu_3}_{APE}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.78000</td>\n",
       "      <td>0.784644</td>\n",
       "      <td>0.595404</td>\n",
       "      <td>0.90900</td>\n",
       "      <td>1.095621</td>\n",
       "      <td>20.530387</td>\n",
       "      <td>3.580</td>\n",
       "      <td>-1.534792</td>\n",
       "      <td>142.871286</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-2.635697</td>\n",
       "      <td>0.539739</td>\n",
       "      <td>-1.820</td>\n",
       "      <td>-1.658158</td>\n",
       "      <td>8.892402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.81800</td>\n",
       "      <td>0.819949</td>\n",
       "      <td>0.238214</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>1.120118</td>\n",
       "      <td>2.763135</td>\n",
       "      <td>-1.750</td>\n",
       "      <td>-1.418989</td>\n",
       "      <td>18.914941</td>\n",
       "      <td>-2.400</td>\n",
       "      <td>-2.537593</td>\n",
       "      <td>5.733052</td>\n",
       "      <td>-1.690</td>\n",
       "      <td>-1.571313</td>\n",
       "      <td>7.022926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.82100</td>\n",
       "      <td>0.821591</td>\n",
       "      <td>0.071932</td>\n",
       "      <td>1.11000</td>\n",
       "      <td>1.129158</td>\n",
       "      <td>1.725922</td>\n",
       "      <td>-3.580</td>\n",
       "      <td>-1.457647</td>\n",
       "      <td>59.283603</td>\n",
       "      <td>-2.820</td>\n",
       "      <td>-2.623794</td>\n",
       "      <td>6.957668</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>-1.657178</td>\n",
       "      <td>6.374103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>0.821360</td>\n",
       "      <td>0.165904</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.123690</td>\n",
       "      <td>2.153651</td>\n",
       "      <td>-1.340</td>\n",
       "      <td>-1.428122</td>\n",
       "      <td>6.576306</td>\n",
       "      <td>-2.610</td>\n",
       "      <td>-2.564733</td>\n",
       "      <td>1.734358</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>-1.593733</td>\n",
       "      <td>4.566861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.81900</td>\n",
       "      <td>0.820301</td>\n",
       "      <td>0.158847</td>\n",
       "      <td>1.09000</td>\n",
       "      <td>1.126099</td>\n",
       "      <td>3.311874</td>\n",
       "      <td>-3.230</td>\n",
       "      <td>-1.451047</td>\n",
       "      <td>55.075939</td>\n",
       "      <td>-2.650</td>\n",
       "      <td>-2.602436</td>\n",
       "      <td>1.794859</td>\n",
       "      <td>-1.770</td>\n",
       "      <td>-1.635436</td>\n",
       "      <td>7.602512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.71600</td>\n",
       "      <td>0.695084</td>\n",
       "      <td>2.921280</td>\n",
       "      <td>0.87000</td>\n",
       "      <td>1.024971</td>\n",
       "      <td>17.812714</td>\n",
       "      <td>0.340</td>\n",
       "      <td>-1.545383</td>\n",
       "      <td>554.524525</td>\n",
       "      <td>-5.520</td>\n",
       "      <td>-2.713765</td>\n",
       "      <td>50.837588</td>\n",
       "      <td>-1.000</td>\n",
       "      <td>-2.103041</td>\n",
       "      <td>110.304132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.80400</td>\n",
       "      <td>0.805577</td>\n",
       "      <td>0.196192</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.111056</td>\n",
       "      <td>1.005129</td>\n",
       "      <td>-1.900</td>\n",
       "      <td>-1.468572</td>\n",
       "      <td>22.706747</td>\n",
       "      <td>-2.300</td>\n",
       "      <td>-2.583863</td>\n",
       "      <td>12.341888</td>\n",
       "      <td>-2.010</td>\n",
       "      <td>-1.633822</td>\n",
       "      <td>18.715323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.80300</td>\n",
       "      <td>0.803958</td>\n",
       "      <td>0.119278</td>\n",
       "      <td>1.12900</td>\n",
       "      <td>1.110192</td>\n",
       "      <td>1.665881</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>-1.472566</td>\n",
       "      <td>47.408358</td>\n",
       "      <td>-2.700</td>\n",
       "      <td>-2.591082</td>\n",
       "      <td>4.033998</td>\n",
       "      <td>-1.870</td>\n",
       "      <td>-1.642551</td>\n",
       "      <td>12.163055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.286791</td>\n",
       "      <td>10.304143</td>\n",
       "      <td>0.58000</td>\n",
       "      <td>0.502768</td>\n",
       "      <td>13.315781</td>\n",
       "      <td>-2.490</td>\n",
       "      <td>-1.640229</td>\n",
       "      <td>34.127352</td>\n",
       "      <td>-0.990</td>\n",
       "      <td>-1.061412</td>\n",
       "      <td>7.213288</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>-0.559563</td>\n",
       "      <td>6.739474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.26000</td>\n",
       "      <td>0.299857</td>\n",
       "      <td>15.329595</td>\n",
       "      <td>0.49100</td>\n",
       "      <td>0.567355</td>\n",
       "      <td>15.550858</td>\n",
       "      <td>-3.790</td>\n",
       "      <td>-2.024402</td>\n",
       "      <td>46.585701</td>\n",
       "      <td>-1.980</td>\n",
       "      <td>-1.812095</td>\n",
       "      <td>8.480030</td>\n",
       "      <td>-0.800</td>\n",
       "      <td>-1.382783</td>\n",
       "      <td>72.847914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.41700</td>\n",
       "      <td>0.427980</td>\n",
       "      <td>2.633059</td>\n",
       "      <td>1.13300</td>\n",
       "      <td>0.639513</td>\n",
       "      <td>43.555766</td>\n",
       "      <td>-4.900</td>\n",
       "      <td>-1.381269</td>\n",
       "      <td>71.810836</td>\n",
       "      <td>-1.670</td>\n",
       "      <td>-1.136184</td>\n",
       "      <td>31.965055</td>\n",
       "      <td>-0.500</td>\n",
       "      <td>-0.578023</td>\n",
       "      <td>15.604681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.49000</td>\n",
       "      <td>0.500199</td>\n",
       "      <td>2.081462</td>\n",
       "      <td>1.04200</td>\n",
       "      <td>0.725790</td>\n",
       "      <td>30.346445</td>\n",
       "      <td>-4.000</td>\n",
       "      <td>-1.377326</td>\n",
       "      <td>65.566845</td>\n",
       "      <td>-1.700</td>\n",
       "      <td>-1.367462</td>\n",
       "      <td>19.561070</td>\n",
       "      <td>-0.600</td>\n",
       "      <td>-0.735565</td>\n",
       "      <td>22.594109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.47700</td>\n",
       "      <td>0.448037</td>\n",
       "      <td>6.071989</td>\n",
       "      <td>1.07000</td>\n",
       "      <td>0.761079</td>\n",
       "      <td>28.871142</td>\n",
       "      <td>-5.600</td>\n",
       "      <td>-1.751781</td>\n",
       "      <td>68.718195</td>\n",
       "      <td>1.720</td>\n",
       "      <td>-2.145815</td>\n",
       "      <td>224.756690</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>-2.036898</td>\n",
       "      <td>48.821661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.16600</td>\n",
       "      <td>0.205027</td>\n",
       "      <td>23.509940</td>\n",
       "      <td>0.25900</td>\n",
       "      <td>0.422333</td>\n",
       "      <td>63.062987</td>\n",
       "      <td>-0.654</td>\n",
       "      <td>-1.793589</td>\n",
       "      <td>174.249157</td>\n",
       "      <td>-0.574</td>\n",
       "      <td>-1.000994</td>\n",
       "      <td>74.389136</td>\n",
       "      <td>-0.421</td>\n",
       "      <td>-0.530274</td>\n",
       "      <td>25.955769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.82000</td>\n",
       "      <td>0.794321</td>\n",
       "      <td>3.131592</td>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.151918</td>\n",
       "      <td>4.719835</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-1.596764</td>\n",
       "      <td>161.414002</td>\n",
       "      <td>-4.800</td>\n",
       "      <td>-3.172631</td>\n",
       "      <td>33.903511</td>\n",
       "      <td>-2.800</td>\n",
       "      <td>-2.584224</td>\n",
       "      <td>7.706286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.10000</td>\n",
       "      <td>1.093410</td>\n",
       "      <td>0.599077</td>\n",
       "      <td>1.57000</td>\n",
       "      <td>1.404285</td>\n",
       "      <td>10.555088</td>\n",
       "      <td>-0.510</td>\n",
       "      <td>-1.121714</td>\n",
       "      <td>119.943861</td>\n",
       "      <td>-2.830</td>\n",
       "      <td>-2.902348</td>\n",
       "      <td>2.556484</td>\n",
       "      <td>-0.930</td>\n",
       "      <td>-1.768076</td>\n",
       "      <td>90.115721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.24000</td>\n",
       "      <td>1.220807</td>\n",
       "      <td>1.547836</td>\n",
       "      <td>1.78000</td>\n",
       "      <td>1.577328</td>\n",
       "      <td>11.386046</td>\n",
       "      <td>1.940</td>\n",
       "      <td>-1.202146</td>\n",
       "      <td>161.966296</td>\n",
       "      <td>-3.980</td>\n",
       "      <td>-3.563049</td>\n",
       "      <td>10.476155</td>\n",
       "      <td>-2.270</td>\n",
       "      <td>-2.273339</td>\n",
       "      <td>0.147091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.73000</td>\n",
       "      <td>0.738254</td>\n",
       "      <td>1.130688</td>\n",
       "      <td>0.75000</td>\n",
       "      <td>1.013786</td>\n",
       "      <td>35.171427</td>\n",
       "      <td>-2.150</td>\n",
       "      <td>-1.388671</td>\n",
       "      <td>35.410640</td>\n",
       "      <td>-1.430</td>\n",
       "      <td>-2.173615</td>\n",
       "      <td>52.001034</td>\n",
       "      <td>-1.240</td>\n",
       "      <td>-1.286105</td>\n",
       "      <td>3.718161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.37000</td>\n",
       "      <td>1.352488</td>\n",
       "      <td>1.278241</td>\n",
       "      <td>1.63000</td>\n",
       "      <td>1.722195</td>\n",
       "      <td>5.656108</td>\n",
       "      <td>-4.290</td>\n",
       "      <td>-1.130637</td>\n",
       "      <td>73.644822</td>\n",
       "      <td>-2.580</td>\n",
       "      <td>-3.832127</td>\n",
       "      <td>48.532056</td>\n",
       "      <td>-2.670</td>\n",
       "      <td>-2.441065</td>\n",
       "      <td>8.574336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.18600</td>\n",
       "      <td>0.183945</td>\n",
       "      <td>1.104937</td>\n",
       "      <td>0.39000</td>\n",
       "      <td>0.309264</td>\n",
       "      <td>20.701504</td>\n",
       "      <td>-0.078</td>\n",
       "      <td>-1.099003</td>\n",
       "      <td>1308.978557</td>\n",
       "      <td>-0.070</td>\n",
       "      <td>0.111646</td>\n",
       "      <td>259.494439</td>\n",
       "      <td>0.047</td>\n",
       "      <td>0.288400</td>\n",
       "      <td>513.617693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.31261</td>\n",
       "      <td>0.301801</td>\n",
       "      <td>3.457778</td>\n",
       "      <td>0.15872</td>\n",
       "      <td>0.379082</td>\n",
       "      <td>138.837197</td>\n",
       "      <td>0.540</td>\n",
       "      <td>-0.652791</td>\n",
       "      <td>220.887233</td>\n",
       "      <td>0.930</td>\n",
       "      <td>0.609619</td>\n",
       "      <td>34.449614</td>\n",
       "      <td>-0.110</td>\n",
       "      <td>0.469953</td>\n",
       "      <td>527.229873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.27500</td>\n",
       "      <td>0.259231</td>\n",
       "      <td>5.734128</td>\n",
       "      <td>0.13530</td>\n",
       "      <td>0.469417</td>\n",
       "      <td>246.945495</td>\n",
       "      <td>2.600</td>\n",
       "      <td>-1.524558</td>\n",
       "      <td>158.636859</td>\n",
       "      <td>-1.680</td>\n",
       "      <td>-0.984569</td>\n",
       "      <td>41.394719</td>\n",
       "      <td>1.050</td>\n",
       "      <td>-0.511205</td>\n",
       "      <td>148.686192</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $\\mu$   $\\mu^*$  $\\mu_{APE}$  $\\lambda$  $\\lambda^*$  $\\lambda_{APE}$  \\\n",
       "0   0.78000  0.784644     0.595404    0.90900     1.095621        20.530387   \n",
       "1   0.81800  0.819949     0.238214    1.09000     1.120118         2.763135   \n",
       "2   0.82100  0.821591     0.071932    1.11000     1.129158         1.725922   \n",
       "3   0.82000  0.821360     0.165904    1.10000     1.123690         2.153651   \n",
       "4   0.81900  0.820301     0.158847    1.09000     1.126099         3.311874   \n",
       "5   0.71600  0.695084     2.921280    0.87000     1.024971        17.812714   \n",
       "6   0.80400  0.805577     0.196192    1.10000     1.111056         1.005129   \n",
       "7   0.80300  0.803958     0.119278    1.12900     1.110192         1.665881   \n",
       "8   0.26000  0.286791    10.304143    0.58000     0.502768        13.315781   \n",
       "9   0.26000  0.299857    15.329595    0.49100     0.567355        15.550858   \n",
       "10  0.41700  0.427980     2.633059    1.13300     0.639513        43.555766   \n",
       "11  0.49000  0.500199     2.081462    1.04200     0.725790        30.346445   \n",
       "12  0.47700  0.448037     6.071989    1.07000     0.761079        28.871142   \n",
       "13  0.16600  0.205027    23.509940    0.25900     0.422333        63.062987   \n",
       "14  0.82000  0.794321     3.131592    1.10000     1.151918         4.719835   \n",
       "15  1.10000  1.093410     0.599077    1.57000     1.404285        10.555088   \n",
       "16  1.24000  1.220807     1.547836    1.78000     1.577328        11.386046   \n",
       "17  0.73000  0.738254     1.130688    0.75000     1.013786        35.171427   \n",
       "18  1.37000  1.352488     1.278241    1.63000     1.722195         5.656108   \n",
       "19  0.18600  0.183945     1.104937    0.39000     0.309264        20.701504   \n",
       "20  0.31261  0.301801     3.457778    0.15872     0.379082       138.837197   \n",
       "21  0.27500  0.259231     5.734128    0.13530     0.469417       246.945495   \n",
       "\n",
       "    $\\nu_1$  $\\nu_1^*$  ${\\nu_1}_{APE}$  $\\nu_2$  $\\nu_2^*$  ${\\nu_2}_{APE}$  \\\n",
       "0     3.580  -1.534792       142.871286   -2.650  -2.635697         0.539739   \n",
       "1    -1.750  -1.418989        18.914941   -2.400  -2.537593         5.733052   \n",
       "2    -3.580  -1.457647        59.283603   -2.820  -2.623794         6.957668   \n",
       "3    -1.340  -1.428122         6.576306   -2.610  -2.564733         1.734358   \n",
       "4    -3.230  -1.451047        55.075939   -2.650  -2.602436         1.794859   \n",
       "5     0.340  -1.545383       554.524525   -5.520  -2.713765        50.837588   \n",
       "6    -1.900  -1.468572        22.706747   -2.300  -2.583863        12.341888   \n",
       "7    -2.800  -1.472566        47.408358   -2.700  -2.591082         4.033998   \n",
       "8    -2.490  -1.640229        34.127352   -0.990  -1.061412         7.213288   \n",
       "9    -3.790  -2.024402        46.585701   -1.980  -1.812095         8.480030   \n",
       "10   -4.900  -1.381269        71.810836   -1.670  -1.136184        31.965055   \n",
       "11   -4.000  -1.377326        65.566845   -1.700  -1.367462        19.561070   \n",
       "12   -5.600  -1.751781        68.718195    1.720  -2.145815       224.756690   \n",
       "13   -0.654  -1.793589       174.249157   -0.574  -1.000994        74.389136   \n",
       "14    2.600  -1.596764       161.414002   -4.800  -3.172631        33.903511   \n",
       "15   -0.510  -1.121714       119.943861   -2.830  -2.902348         2.556484   \n",
       "16    1.940  -1.202146       161.966296   -3.980  -3.563049        10.476155   \n",
       "17   -2.150  -1.388671        35.410640   -1.430  -2.173615        52.001034   \n",
       "18   -4.290  -1.130637        73.644822   -2.580  -3.832127        48.532056   \n",
       "19   -0.078  -1.099003      1308.978557   -0.070   0.111646       259.494439   \n",
       "20    0.540  -0.652791       220.887233    0.930   0.609619        34.449614   \n",
       "21    2.600  -1.524558       158.636859   -1.680  -0.984569        41.394719   \n",
       "\n",
       "    $\\nu_3$  $\\nu_3^*$  ${\\nu_3}_{APE}$  \n",
       "0    -1.820  -1.658158         8.892402  \n",
       "1    -1.690  -1.571313         7.022926  \n",
       "2    -1.770  -1.657178         6.374103  \n",
       "3    -1.670  -1.593733         4.566861  \n",
       "4    -1.770  -1.635436         7.602512  \n",
       "5    -1.000  -2.103041       110.304132  \n",
       "6    -2.010  -1.633822        18.715323  \n",
       "7    -1.870  -1.642551        12.163055  \n",
       "8    -0.600  -0.559563         6.739474  \n",
       "9    -0.800  -1.382783        72.847914  \n",
       "10   -0.500  -0.578023        15.604681  \n",
       "11   -0.600  -0.735565        22.594109  \n",
       "12   -3.980  -2.036898        48.821661  \n",
       "13   -0.421  -0.530274        25.955769  \n",
       "14   -2.800  -2.584224         7.706286  \n",
       "15   -0.930  -1.768076        90.115721  \n",
       "16   -2.270  -2.273339         0.147091  \n",
       "17   -1.240  -1.286105         3.718161  \n",
       "18   -2.670  -2.441065         8.574336  \n",
       "19    0.047   0.288400       513.617693  \n",
       "20   -0.110   0.469953       527.229873  \n",
       "21    1.050  -0.511205       148.686192  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = estimator.predict(X_test)\n",
    "prediction_data = []\n",
    "for i in range(df_test.shape[0]):\n",
    "    material_data = {}\n",
    "    material_data.update({\"$\\mu$\": y_test[i][0]})\n",
    "    material_data.update({\"$\\mu^*$\": y_pred[i][0]})\n",
    "    material_data.update({\"$\\mu_{APE}$\": np.abs((y_pred[i][0]-y_test[i][0])/y_test[i][0])*100.0})\n",
    "    material_data.update({\"$\\lambda$\": y_test[i][1]})\n",
    "    material_data.update({\"$\\lambda^*$\": y_pred[i][1]})\n",
    "    material_data.update({\"$\\lambda_{APE}$\": np.abs((y_pred[i][1]-y_test[i][1])/y_test[i][1])*100.0})\n",
    "    material_data.update({\"$\\nu_1$\": y_test[i][2]})\n",
    "    material_data.update({\"$\\nu_1^*$\": y_pred[i][2]})\n",
    "    material_data.update({\"${\\nu_1}_{APE}$\": np.abs((y_pred[i][2]-y_test[i][2])/y_test[i][2])*100.0})\n",
    "    material_data.update({\"$\\nu_2$\": y_test[i][3]})\n",
    "    material_data.update({\"$\\nu_2^*$\": y_pred[i][3]})\n",
    "    material_data.update({\"${\\nu_2}_{APE}$\": np.abs((y_pred[i][3]-y_test[i][3])/y_test[i][3])*100.0})\n",
    "    material_data.update({\"$\\nu_3$\": y_test[i][4]})\n",
    "    material_data.update({\"$\\nu_3^*$\": y_pred[i][4]})\n",
    "    material_data.update({\"${\\nu_3}_{APE}$\": np.abs((y_pred[i][4]-y_test[i][4])/y_test[i][4])*100.0})\n",
    "    prediction_data.append(material_data)\n",
    "score = r2_score(y_test, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Коэффициент детерминации:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = mean_absolute_error(y_test, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Средняя абсолютная ошибка:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = root_mean_squared_error(y_test, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Корень среднеквадратической ошибки:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "display(pd.DataFrame.from_dict(prediction_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "material_infos_new = []\n",
    "material_infos_new.append({'Название': 'Рельсовая сталь #1', '$\\lambda$': 1.158, '$\\mu$': 0.799, '$l$': -2.48, '$m$': -6.23, '$n$': -7.14, \"$\\nu_1$\": None, \"$\\nu_2$\": None, \"$\\nu_3$\": None})\n",
    "material_infos_new.append({'Название': 'Рельсовая сталь #4', '$\\lambda$': 1.107, '$\\mu$': 0.824, '$l$': -3.02, '$m$': -6.16, '$n$': -7.24, \"$\\nu_1$\": None, \"$\\nu_2$\": None, \"$\\nu_3$\": None})\n",
    "for material_info in material_infos_new:\n",
    "    material_info[\"$\\nu_3$\"] = 0.25*material_info[\"$n$\"]\n",
    "    material_info[\"$\\nu_2$\"] = material_info[\"$m$\"]-2.0*material_info[\"$\\nu_3$\"]\n",
    "    material_info[\"$\\nu_1$\"] = 2.0*(material_info[\"$l$\"]-material_info[\"$\\nu_2$\"])\n",
    "    material_info.pop(\"$l$\")\n",
    "    material_info.pop(\"$m$\")\n",
    "    material_info.pop(\"$n$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.0 \\leq \\tilde{\\Psi} \\leq 0.15707963267949$"
      ],
      "text/plain": [
       "0.0 <= (Psitilde <= 0.15707963267949)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_Psitilde_min = 0.0\n",
    "val_Psitilde_max = 0.05*float(sym.pi)\n",
    "display(sym.Le(val_Psitilde_min, sym.Le(Psitilde, val_Psitilde_max, evaluate = False), evaluate = False))\n",
    "list_len = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$k$</th>\n",
       "      <th>$M$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.799</td>\n",
       "      <td>1.158</td>\n",
       "      <td>0.36</td>\n",
       "      <td>-2.66</td>\n",
       "      <td>-1.785</td>\n",
       "      <td>[1.0, 1.0000370213927652, 1.0001482829553154, ...</td>\n",
       "      <td>[0.0, 9.723717098106626, 19.42429436954132, 29...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.824</td>\n",
       "      <td>1.107</td>\n",
       "      <td>-0.96</td>\n",
       "      <td>-2.54</td>\n",
       "      <td>-1.810</td>\n",
       "      <td>[0.9999999999999994, 1.000036375234913, 1.0001...</td>\n",
       "      <td>[0.0, 10.028160248369824, 20.033635337507715, ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\mu$  $\\lambda$  $\\nu_1$  $\\nu_2$  $\\nu_3$  \\\n",
       "0  0.799      1.158     0.36    -2.66   -1.785   \n",
       "1  0.824      1.107    -0.96    -2.54   -1.810   \n",
       "\n",
       "                                                 $k$  \\\n",
       "0  [1.0, 1.0000370213927652, 1.0001482829553154, ...   \n",
       "1  [0.9999999999999994, 1.000036375234913, 1.0001...   \n",
       "\n",
       "                                                 $M$  \n",
       "0  [0.0, 9.723717098106626, 19.42429436954132, 29...  \n",
       "1  [0.0, 10.028160248369824, 20.033635337507715, ...  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_data_file_name = \"Datasets/material_results_M_railsteel_0.05Pi\"\n",
    "if os.path.isfile(new_data_file_name+\".pickle\"):\n",
    "    df_new = pd.read_pickle(new_data_file_name+\".pickle\")\n",
    "elif os.path.isfile(new_data_file_name+\".feather\"):\n",
    "    df_new = pd.read_feather(new_data_file_name+\".feather\")\n",
    "elif os.path.isfile(new_data_file_name+\".csv\"):\n",
    "    df_new = pd.read_csv(new_data_file_name+\".csv\", encoding = \"utf-8-sig\")\n",
    "    if \"Unnamed: 0\" in df_new.columns:\n",
    "        df_new = df_new.drop(columns = \"Unnamed: 0\")\n",
    "    df_new[df_new.columns[5]] = df_new[df_new.columns[5]].apply(lambda s: np.fromstring(s[1:-1], dtype = np.float64, sep = \" \"))\n",
    "    df_new[df_new.columns[6]] = df_new[df_new.columns[6]].apply(lambda s: np.fromstring(s[1:-1], dtype = np.float64, sep = \" \"))\n",
    "else:\n",
    "    from tqdm import tqdm\n",
    "    new_data = []\n",
    "    for material_info in material_infos_new:\n",
    "        material_data = {}\n",
    "        material_data.update({\"$\\mu$\": material_info[\"$\\mu$\"]})\n",
    "        material_data.update({\"$\\lambda$\": material_info[\"$\\lambda$\"]})\n",
    "        material_data.update({\"$\\nu_1$\": material_info[\"$\\nu_1$\"]})\n",
    "        material_data.update({\"$\\nu_2$\": material_info[\"$\\nu_2$\"]})\n",
    "        material_data.update({\"$\\nu_3$\": material_info[\"$\\nu_3$\"]})\n",
    "        new_data.append(material_data)\n",
    "    get_materials_M_data(tqdm(new_data), val_r_0, val_r_1, val_Psitilde_min, val_Psitilde_max, list_len, False)\n",
    "    df_new = pd.DataFrame.from_dict(new_data)\n",
    "display(df_new)\n",
    "if not os.path.isfile(new_data_file_name+\".pickle\"):\n",
    "    df_new.to_pickle(new_data_file_name+\".pickle\")\n",
    "if not os.path.isfile(new_data_file_name+\".feather\"):\n",
    "    df_new.to_feather(new_data_file_name+\".feather\")\n",
    "if not os.path.isfile(new_data_file_name+\".csv\"):\n",
    "    df_new.to_csv(new_data_file_name+\".csv\", encoding = \"utf-8-sig\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$k_{1}$</th>\n",
       "      <th>$k_{2}$</th>\n",
       "      <th>$k_{3}$</th>\n",
       "      <th>$k_{4}$</th>\n",
       "      <th>$k_{5}$</th>\n",
       "      <th>...</th>\n",
       "      <th>$M_{10}$</th>\n",
       "      <th>$M_{11}$</th>\n",
       "      <th>$M_{12}$</th>\n",
       "      <th>$M_{13}$</th>\n",
       "      <th>$M_{14}$</th>\n",
       "      <th>$M_{15}$</th>\n",
       "      <th>$M_{16}$</th>\n",
       "      <th>$M_{17}$</th>\n",
       "      <th>$M_{18}$</th>\n",
       "      <th>$M_{19}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.799</td>\n",
       "      <td>1.158</td>\n",
       "      <td>0.36</td>\n",
       "      <td>-2.66</td>\n",
       "      <td>-1.785</td>\n",
       "      <td>1.000037</td>\n",
       "      <td>1.000148</td>\n",
       "      <td>1.000334</td>\n",
       "      <td>1.000596</td>\n",
       "      <td>1.000935</td>\n",
       "      <td>...</td>\n",
       "      <td>93.363530</td>\n",
       "      <td>101.778261</td>\n",
       "      <td>109.920949</td>\n",
       "      <td>117.762239</td>\n",
       "      <td>125.271337</td>\n",
       "      <td>132.414645</td>\n",
       "      <td>139.156506</td>\n",
       "      <td>145.457662</td>\n",
       "      <td>151.274470</td>\n",
       "      <td>156.557508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.824</td>\n",
       "      <td>1.107</td>\n",
       "      <td>-0.96</td>\n",
       "      <td>-2.54</td>\n",
       "      <td>-1.810</td>\n",
       "      <td>1.000036</td>\n",
       "      <td>1.000146</td>\n",
       "      <td>1.000329</td>\n",
       "      <td>1.000586</td>\n",
       "      <td>1.000919</td>\n",
       "      <td>...</td>\n",
       "      <td>96.486303</td>\n",
       "      <td>105.232651</td>\n",
       "      <td>113.712024</td>\n",
       "      <td>121.899358</td>\n",
       "      <td>129.760938</td>\n",
       "      <td>137.266009</td>\n",
       "      <td>144.380118</td>\n",
       "      <td>151.065636</td>\n",
       "      <td>157.280427</td>\n",
       "      <td>162.978386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 43 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\mu$  $\\lambda$  $\\nu_1$  $\\nu_2$  $\\nu_3$   $k_{1}$   $k_{2}$   $k_{3}$  \\\n",
       "0  0.799      1.158     0.36    -2.66   -1.785  1.000037  1.000148  1.000334   \n",
       "1  0.824      1.107    -0.96    -2.54   -1.810  1.000036  1.000146  1.000329   \n",
       "\n",
       "    $k_{4}$   $k_{5}$  ...   $M_{10}$    $M_{11}$    $M_{12}$    $M_{13}$  \\\n",
       "0  1.000596  1.000935  ...  93.363530  101.778261  109.920949  117.762239   \n",
       "1  1.000586  1.000919  ...  96.486303  105.232651  113.712024  121.899358   \n",
       "\n",
       "     $M_{14}$    $M_{15}$    $M_{16}$    $M_{17}$    $M_{18}$    $M_{19}$  \n",
       "0  125.271337  132.414645  139.156506  145.457662  151.274470  156.557508  \n",
       "1  129.760938  137.266009  144.380118  151.065636  157.280427  162.978386  \n",
       "\n",
       "[2 rows x 43 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_new_k = pd.DataFrame(df_new[\"$k$\"].to_list(), columns = [\"$k_{\"+str(i)+\"}$\" for i in range(list_len)])\n",
    "df_new_k = df_new_k.drop(df_new_k.columns[0], axis = 1)\n",
    "df_new_M = pd.DataFrame(df_new[\"$M$\"].to_list(), columns = [\"$M_{\"+str(i)+\"}$\" for i in range(list_len)])\n",
    "df_new_M = df_new_M.drop(df_new_M.columns[0], axis = 1)\n",
    "df_new = pd.concat([df_new.drop(columns = [\"$k$\", \"$M$\"]), df_new_k, df_new_M], axis = 1)\n",
    "list_len -= 1\n",
    "display(df_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new = np.array(df_new.iloc[:, 5:].values.tolist())\n",
    "y_new = np.array(df_new.iloc[:, :5].values.tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new = X_scaler.transform(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Коэффициент детерминации:\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.993297</td>\n",
       "      <td>-1.826413</td>\n",
       "      <td>-3.026476</td>\n",
       "      <td>-1.473709</td>\n",
       "      <td>-231.243446</td>\n",
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      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$     $\\nu_3$\n",
       "0  0.993297  -1.826413 -3.026476 -1.473709 -231.243446"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя абсолютная ошибка:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "      <th>0</th>\n",
       "      <td>0.001023</td>\n",
       "      <td>0.039583</td>\n",
       "      <td>1.14503</td>\n",
       "      <td>0.089509</td>\n",
       "      <td>0.190406</td>\n",
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       "      $\\mu$  $\\lambda$  $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
       "0  0.001023   0.039583  1.14503  0.089509  0.190406"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Корень среднеквадратической ошибки:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>0.001023</td>\n",
       "      <td>0.04287</td>\n",
       "      <td>1.324361</td>\n",
       "      <td>0.094368</td>\n",
       "      <td>0.190494</td>\n",
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       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
       "0  0.001023    0.04287  1.324361  0.094368  0.190494"
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\mu^*$</th>\n",
       "      <th>$\\mu_{APE}$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\lambda^*$</th>\n",
       "      <th>$\\lambda_{APE}$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_1^*$</th>\n",
       "      <th>${\\nu_1}_{APE}$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_2^*$</th>\n",
       "      <th>${\\nu_2}_{APE}$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$\\nu_3^*$</th>\n",
       "      <th>${\\nu_3}_{APE}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.799</td>\n",
       "      <td>0.799990</td>\n",
       "      <td>0.123899</td>\n",
       "      <td>1.158</td>\n",
       "      <td>1.101954</td>\n",
       "      <td>4.839929</td>\n",
       "      <td>0.36</td>\n",
       "      <td>-1.450492</td>\n",
       "      <td>502.914340</td>\n",
       "      <td>-2.66</td>\n",
       "      <td>-2.540599</td>\n",
       "      <td>4.488755</td>\n",
       "      <td>-1.785</td>\n",
       "      <td>-1.588804</td>\n",
       "      <td>10.991345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.824</td>\n",
       "      <td>0.825056</td>\n",
       "      <td>0.128130</td>\n",
       "      <td>1.107</td>\n",
       "      <td>1.130120</td>\n",
       "      <td>2.088563</td>\n",
       "      <td>-0.96</td>\n",
       "      <td>-1.439569</td>\n",
       "      <td>49.955072</td>\n",
       "      <td>-2.54</td>\n",
       "      <td>-2.599617</td>\n",
       "      <td>2.347110</td>\n",
       "      <td>-1.810</td>\n",
       "      <td>-1.625383</td>\n",
       "      <td>10.199828</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\mu$   $\\mu^*$  $\\mu_{APE}$  $\\lambda$  $\\lambda^*$  $\\lambda_{APE}$  \\\n",
       "0  0.799  0.799990     0.123899      1.158     1.101954         4.839929   \n",
       "1  0.824  0.825056     0.128130      1.107     1.130120         2.088563   \n",
       "\n",
       "   $\\nu_1$  $\\nu_1^*$  ${\\nu_1}_{APE}$  $\\nu_2$  $\\nu_2^*$  ${\\nu_2}_{APE}$  \\\n",
       "0     0.36  -1.450492       502.914340    -2.66  -2.540599         4.488755   \n",
       "1    -0.96  -1.439569        49.955072    -2.54  -2.599617         2.347110   \n",
       "\n",
       "   $\\nu_3$  $\\nu_3^*$  ${\\nu_3}_{APE}$  \n",
       "0   -1.785  -1.588804        10.991345  \n",
       "1   -1.810  -1.625383        10.199828  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = estimator.predict(X_new)\n",
    "prediction_data = []\n",
    "for i in range(df_new.shape[0]):\n",
    "    material_data = {}\n",
    "    material_data.update({\"$\\mu$\": y_new[i][0]})\n",
    "    material_data.update({\"$\\mu^*$\": y_pred[i][0]})\n",
    "    material_data.update({\"$\\mu_{APE}$\": np.abs((y_pred[i][0]-y_new[i][0])/y_new[i][0])*100.0})\n",
    "    material_data.update({\"$\\lambda$\": y_new[i][1]})\n",
    "    material_data.update({\"$\\lambda^*$\": y_pred[i][1]})\n",
    "    material_data.update({\"$\\lambda_{APE}$\": np.abs((y_pred[i][1]-y_new[i][1])/y_new[i][1])*100.0})\n",
    "    material_data.update({\"$\\nu_1$\": y_new[i][2]})\n",
    "    material_data.update({\"$\\nu_1^*$\": y_pred[i][2]})\n",
    "    material_data.update({\"${\\nu_1}_{APE}$\": np.abs((y_pred[i][2]-y_new[i][2])/y_new[i][2])*100.0})\n",
    "    material_data.update({\"$\\nu_2$\": y_new[i][3]})\n",
    "    material_data.update({\"$\\nu_2^*$\": y_pred[i][3]})\n",
    "    material_data.update({\"${\\nu_2}_{APE}$\": np.abs((y_pred[i][3]-y_new[i][3])/y_new[i][3])*100.0})\n",
    "    material_data.update({\"$\\nu_3$\": y_new[i][4]})\n",
    "    material_data.update({\"$\\nu_3^*$\": y_pred[i][4]})\n",
    "    material_data.update({\"${\\nu_3}_{APE}$\": np.abs((y_pred[i][4]-y_new[i][4])/y_new[i][4])*100.0})\n",
    "    prediction_data.append(material_data)\n",
    "score = r2_score(y_new, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Коэффициент детерминации:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = mean_absolute_error(y_new, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Средняя абсолютная ошибка:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = root_mean_squared_error(y_new, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Корень среднеквадратической ошибки:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "display(pd.DataFrame.from_dict(prediction_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.0 \\leq \\tilde{\\Psi} \\leq 0.15707963267949$"
      ],
      "text/plain": [
       "0.0 <= (Psitilde <= 0.15707963267949)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_Psitilde_min = 0.0\n",
    "val_Psitilde_max = 0.05*float(sym.pi)\n",
    "display(sym.Le(val_Psitilde_min, sym.Le(Psitilde, val_Psitilde_max, evaluate = False), evaluate = False))\n",
    "list_len = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$k$</th>\n",
       "      <th>$M$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.060199</td>\n",
       "      <td>1.175119</td>\n",
       "      <td>4.223309</td>\n",
       "      <td>1.954982</td>\n",
       "      <td>0.668442</td>\n",
       "      <td>[0.9999999999999977, 0.9999373850980082, 0.999...</td>\n",
       "      <td>[0.0, 12.912829627261573, 25.85718583076396, 3...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.934900</td>\n",
       "      <td>0.678878</td>\n",
       "      <td>-4.560123</td>\n",
       "      <td>-5.433176</td>\n",
       "      <td>1.955589</td>\n",
       "      <td>[1.0, 1.0000226657535052, 1.0000930136005242, ...</td>\n",
       "      <td>[0.0, 11.3698154965785, 22.66584437248048, 33....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.902725</td>\n",
       "      <td>1.077164</td>\n",
       "      <td>5.432703</td>\n",
       "      <td>1.786148</td>\n",
       "      <td>-2.231237</td>\n",
       "      <td>[0.9999999999999919, 0.9999918201764861, 0.999...</td>\n",
       "      <td>[0.0, 10.989450438011472, 21.973232221739668, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.021150</td>\n",
       "      <td>1.727626</td>\n",
       "      <td>2.655574</td>\n",
       "      <td>1.744105</td>\n",
       "      <td>1.669546</td>\n",
       "      <td>[1.0000000000000102, 0.9999295198556898, 0.999...</td>\n",
       "      <td>[0.0, 12.435725245544203, 24.89276438827456, 3...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.879959</td>\n",
       "      <td>0.614681</td>\n",
       "      <td>-0.879454</td>\n",
       "      <td>1.568620</td>\n",
       "      <td>-2.094217</td>\n",
       "      <td>[1.000000000000009, 0.9999834716323842, 0.9999...</td>\n",
       "      <td>[0.0, 10.713161467317379, 21.42593504056849, 3...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4435</th>\n",
       "      <td>0.547015</td>\n",
       "      <td>1.288573</td>\n",
       "      <td>0.044432</td>\n",
       "      <td>-7.253548</td>\n",
       "      <td>0.466119</td>\n",
       "      <td>[1.0, 1.00002976, 1.00011987, 1.00026914, 1.00...</td>\n",
       "      <td>[0.0, 6.65117534, 13.25095051, 19.74692412, 26...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4436</th>\n",
       "      <td>1.001564</td>\n",
       "      <td>0.860793</td>\n",
       "      <td>-5.493621</td>\n",
       "      <td>-1.769730</td>\n",
       "      <td>-0.165640</td>\n",
       "      <td>[1.0, 0.99999633, 0.99998535, 0.99996717, 0.99...</td>\n",
       "      <td>[0.0, 12.19247028, 24.37737865, 36.54712384, 4...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4437</th>\n",
       "      <td>0.698036</td>\n",
       "      <td>1.639603</td>\n",
       "      <td>4.362781</td>\n",
       "      <td>-5.482224</td>\n",
       "      <td>1.867839</td>\n",
       "      <td>[1.0, 0.99997071, 0.99988306, 0.99973753, 0.99...</td>\n",
       "      <td>[0.0, 8.49448977, 16.9657369, 25.39041398, 33....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4438</th>\n",
       "      <td>0.392364</td>\n",
       "      <td>1.847479</td>\n",
       "      <td>-4.406707</td>\n",
       "      <td>-2.216694</td>\n",
       "      <td>-3.537008</td>\n",
       "      <td>[1.0, 1.00012433, 1.00050107, 1.00114196, 1.00...</td>\n",
       "      <td>[0.0, 4.76634281, 9.46889631, 14.04163225, 18....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4439</th>\n",
       "      <td>0.681446</td>\n",
       "      <td>1.312102</td>\n",
       "      <td>-6.950588</td>\n",
       "      <td>-4.898579</td>\n",
       "      <td>-4.806646</td>\n",
       "      <td>[1.0, 1.00013509, 1.00054465, 1.00123746, 1.00...</td>\n",
       "      <td>[0.0, 8.28019228, 16.46242056, 24.44321339, 32...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4440 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$  \\\n",
       "0     1.060199   1.175119  4.223309  1.954982  0.668442   \n",
       "1     0.934900   0.678878 -4.560123 -5.433176  1.955589   \n",
       "2     0.902725   1.077164  5.432703  1.786148 -2.231237   \n",
       "3     1.021150   1.727626  2.655574  1.744105  1.669546   \n",
       "4     0.879959   0.614681 -0.879454  1.568620 -2.094217   \n",
       "...        ...        ...       ...       ...       ...   \n",
       "4435  0.547015   1.288573  0.044432 -7.253548  0.466119   \n",
       "4436  1.001564   0.860793 -5.493621 -1.769730 -0.165640   \n",
       "4437  0.698036   1.639603  4.362781 -5.482224  1.867839   \n",
       "4438  0.392364   1.847479 -4.406707 -2.216694 -3.537008   \n",
       "4439  0.681446   1.312102 -6.950588 -4.898579 -4.806646   \n",
       "\n",
       "                                                    $k$  \\\n",
       "0     [0.9999999999999977, 0.9999373850980082, 0.999...   \n",
       "1     [1.0, 1.0000226657535052, 1.0000930136005242, ...   \n",
       "2     [0.9999999999999919, 0.9999918201764861, 0.999...   \n",
       "3     [1.0000000000000102, 0.9999295198556898, 0.999...   \n",
       "4     [1.000000000000009, 0.9999834716323842, 0.9999...   \n",
       "...                                                 ...   \n",
       "4435  [1.0, 1.00002976, 1.00011987, 1.00026914, 1.00...   \n",
       "4436  [1.0, 0.99999633, 0.99998535, 0.99996717, 0.99...   \n",
       "4437  [1.0, 0.99997071, 0.99988306, 0.99973753, 0.99...   \n",
       "4438  [1.0, 1.00012433, 1.00050107, 1.00114196, 1.00...   \n",
       "4439  [1.0, 1.00013509, 1.00054465, 1.00123746, 1.00...   \n",
       "\n",
       "                                                    $M$  \n",
       "0     [0.0, 12.912829627261573, 25.85718583076396, 3...  \n",
       "1     [0.0, 11.3698154965785, 22.66584437248048, 33....  \n",
       "2     [0.0, 10.989450438011472, 21.973232221739668, ...  \n",
       "3     [0.0, 12.435725245544203, 24.89276438827456, 3...  \n",
       "4     [0.0, 10.713161467317379, 21.42593504056849, 3...  \n",
       "...                                                 ...  \n",
       "4435  [0.0, 6.65117534, 13.25095051, 19.74692412, 26...  \n",
       "4436  [0.0, 12.19247028, 24.37737865, 36.54712384, 4...  \n",
       "4437  [0.0, 8.49448977, 16.9657369, 25.39041398, 33....  \n",
       "4438  [0.0, 4.76634281, 9.46889631, 14.04163225, 18....  \n",
       "4439  [0.0, 8.28019228, 16.46242056, 24.44321339, 32...  \n",
       "\n",
       "[4440 rows x 7 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_data_file_name = \"Datasets/material_results_M_train_0.05Pi_4440\"\n",
    "if os.path.isfile(train_data_file_name+\".pickle\"):\n",
    "    df_train = pd.read_pickle(train_data_file_name+\".pickle\")\n",
    "elif os.path.isfile(train_data_file_name+\".feather\"):\n",
    "    df_train = pd.read_feather(train_data_file_name+\".feather\")\n",
    "elif os.path.isfile(train_data_file_name+\".csv\"):\n",
    "    df_train = pd.read_csv(train_data_file_name+\".csv\", encoding = \"utf-8-sig\")\n",
    "    if \"Unnamed: 0\" in df_train.columns:\n",
    "        df_train = df_train.drop(columns = \"Unnamed: 0\")\n",
    "    df_train[df_train.columns[5]] = df_train[df_train.columns[5]].apply(lambda s: np.fromstring(s[1:-1], dtype = np.float64, sep = \" \"))\n",
    "    df_train[df_train.columns[6]] = df_train[df_train.columns[6]].apply(lambda s: np.fromstring(s[1:-1], dtype = np.float64, sep = \" \"))\n",
    "else:\n",
    "    df_train = None\n",
    "assert df_train is not None, \"Тренировочные данные не найдены.\"\n",
    "display(df_train)\n",
    "if not os.path.isfile(train_data_file_name+\".pickle\"):\n",
    "    df_train.to_pickle(train_data_file_name+\".pickle\")\n",
    "if not os.path.isfile(train_data_file_name+\".feather\"):\n",
    "    df_train.to_feather(train_data_file_name+\".feather\")\n",
    "if not os.path.isfile(train_data_file_name+\".csv\"):\n",
    "    df_train.to_csv(train_data_file_name+\".csv\", encoding = \"utf-8-sig\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
       "      <th>$k_{1}$</th>\n",
       "      <th>$k_{2}$</th>\n",
       "      <th>$k_{3}$</th>\n",
       "      <th>$k_{4}$</th>\n",
       "      <th>$k_{5}$</th>\n",
       "      <th>...</th>\n",
       "      <th>$M_{10}$</th>\n",
       "      <th>$M_{11}$</th>\n",
       "      <th>$M_{12}$</th>\n",
       "      <th>$M_{13}$</th>\n",
       "      <th>$M_{14}$</th>\n",
       "      <th>$M_{15}$</th>\n",
       "      <th>$M_{16}$</th>\n",
       "      <th>$M_{17}$</th>\n",
       "      <th>$M_{18}$</th>\n",
       "      <th>$M_{19}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.060199</td>\n",
       "      <td>1.175119</td>\n",
       "      <td>4.223309</td>\n",
       "      <td>1.954982</td>\n",
       "      <td>0.668442</td>\n",
       "      <td>0.999937</td>\n",
       "      <td>0.999749</td>\n",
       "      <td>0.999434</td>\n",
       "      <td>0.998997</td>\n",
       "      <td>0.998432</td>\n",
       "      <td>...</td>\n",
       "      <td>134.037978</td>\n",
       "      <td>148.512525</td>\n",
       "      <td>163.272854</td>\n",
       "      <td>178.321020</td>\n",
       "      <td>193.655110</td>\n",
       "      <td>209.316135</td>\n",
       "      <td>225.272656</td>\n",
       "      <td>241.542420</td>\n",
       "      <td>258.106345</td>\n",
       "      <td>275.051207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.934900</td>\n",
       "      <td>0.678878</td>\n",
       "      <td>-4.560123</td>\n",
       "      <td>-5.433176</td>\n",
       "      <td>1.955589</td>\n",
       "      <td>1.000023</td>\n",
       "      <td>1.000093</td>\n",
       "      <td>1.000217</td>\n",
       "      <td>1.000320</td>\n",
       "      <td>1.000455</td>\n",
       "      <td>...</td>\n",
       "      <td>103.915686</td>\n",
       "      <td>112.327432</td>\n",
       "      <td>120.272428</td>\n",
       "      <td>127.662153</td>\n",
       "      <td>134.486057</td>\n",
       "      <td>140.707282</td>\n",
       "      <td>146.285371</td>\n",
       "      <td>151.175265</td>\n",
       "      <td>155.233386</td>\n",
       "      <td>158.482898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.902725</td>\n",
       "      <td>1.077164</td>\n",
       "      <td>5.432703</td>\n",
       "      <td>1.786148</td>\n",
       "      <td>-2.231237</td>\n",
       "      <td>0.999992</td>\n",
       "      <td>0.999967</td>\n",
       "      <td>0.999926</td>\n",
       "      <td>0.999869</td>\n",
       "      <td>0.999794</td>\n",
       "      <td>...</td>\n",
       "      <td>108.849433</td>\n",
       "      <td>119.470689</td>\n",
       "      <td>129.999248</td>\n",
       "      <td>140.428482</td>\n",
       "      <td>150.745805</td>\n",
       "      <td>160.919514</td>\n",
       "      <td>170.960227</td>\n",
       "      <td>180.856753</td>\n",
       "      <td>190.571989</td>\n",
       "      <td>200.081576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.021150</td>\n",
       "      <td>1.727626</td>\n",
       "      <td>2.655574</td>\n",
       "      <td>1.744105</td>\n",
       "      <td>1.669546</td>\n",
       "      <td>0.999930</td>\n",
       "      <td>0.999718</td>\n",
       "      <td>0.999364</td>\n",
       "      <td>0.998868</td>\n",
       "      <td>0.998228</td>\n",
       "      <td>...</td>\n",
       "      <td>127.740421</td>\n",
       "      <td>141.266167</td>\n",
       "      <td>154.989763</td>\n",
       "      <td>168.921302</td>\n",
       "      <td>183.060270</td>\n",
       "      <td>197.421548</td>\n",
       "      <td>212.001673</td>\n",
       "      <td>226.804974</td>\n",
       "      <td>241.815642</td>\n",
       "      <td>257.026259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.879959</td>\n",
       "      <td>0.614681</td>\n",
       "      <td>-0.879454</td>\n",
       "      <td>1.568620</td>\n",
       "      <td>-2.094217</td>\n",
       "      <td>0.999983</td>\n",
       "      <td>0.999934</td>\n",
       "      <td>0.999851</td>\n",
       "      <td>0.999735</td>\n",
       "      <td>0.999599</td>\n",
       "      <td>...</td>\n",
       "      <td>106.796984</td>\n",
       "      <td>117.325858</td>\n",
       "      <td>127.789216</td>\n",
       "      <td>138.174232</td>\n",
       "      <td>148.456043</td>\n",
       "      <td>158.610523</td>\n",
       "      <td>168.633669</td>\n",
       "      <td>178.486392</td>\n",
       "      <td>188.154242</td>\n",
       "      <td>197.608792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4435</th>\n",
       "      <td>0.547015</td>\n",
       "      <td>1.288573</td>\n",
       "      <td>0.044432</td>\n",
       "      <td>-7.253548</td>\n",
       "      <td>0.466119</td>\n",
       "      <td>1.000030</td>\n",
       "      <td>1.000120</td>\n",
       "      <td>1.000269</td>\n",
       "      <td>1.000482</td>\n",
       "      <td>1.000759</td>\n",
       "      <td>...</td>\n",
       "      <td>57.354409</td>\n",
       "      <td>60.706329</td>\n",
       "      <td>63.229154</td>\n",
       "      <td>64.723274</td>\n",
       "      <td>64.935203</td>\n",
       "      <td>63.432342</td>\n",
       "      <td>59.428503</td>\n",
       "      <td>50.591455</td>\n",
       "      <td>37.736858</td>\n",
       "      <td>37.921742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4436</th>\n",
       "      <td>1.001564</td>\n",
       "      <td>0.860793</td>\n",
       "      <td>-5.493621</td>\n",
       "      <td>-1.769730</td>\n",
       "      <td>-0.165640</td>\n",
       "      <td>0.999996</td>\n",
       "      <td>0.999985</td>\n",
       "      <td>0.999967</td>\n",
       "      <td>0.999942</td>\n",
       "      <td>0.999910</td>\n",
       "      <td>...</td>\n",
       "      <td>120.645942</td>\n",
       "      <td>132.403067</td>\n",
       "      <td>144.068337</td>\n",
       "      <td>155.631571</td>\n",
       "      <td>167.180761</td>\n",
       "      <td>178.552086</td>\n",
       "      <td>189.803678</td>\n",
       "      <td>200.927590</td>\n",
       "      <td>211.916165</td>\n",
       "      <td>222.762146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4437</th>\n",
       "      <td>0.698036</td>\n",
       "      <td>1.639603</td>\n",
       "      <td>4.362781</td>\n",
       "      <td>-5.482224</td>\n",
       "      <td>1.867839</td>\n",
       "      <td>0.999971</td>\n",
       "      <td>0.999883</td>\n",
       "      <td>0.999738</td>\n",
       "      <td>0.999535</td>\n",
       "      <td>0.999277</td>\n",
       "      <td>...</td>\n",
       "      <td>81.046636</td>\n",
       "      <td>88.178377</td>\n",
       "      <td>95.060257</td>\n",
       "      <td>101.634181</td>\n",
       "      <td>107.870398</td>\n",
       "      <td>113.738741</td>\n",
       "      <td>119.208817</td>\n",
       "      <td>124.250254</td>\n",
       "      <td>128.832978</td>\n",
       "      <td>132.920288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4438</th>\n",
       "      <td>0.392364</td>\n",
       "      <td>1.847479</td>\n",
       "      <td>-4.406707</td>\n",
       "      <td>-2.216694</td>\n",
       "      <td>-3.537008</td>\n",
       "      <td>1.000124</td>\n",
       "      <td>1.000501</td>\n",
       "      <td>1.001142</td>\n",
       "      <td>1.002068</td>\n",
       "      <td>1.003316</td>\n",
       "      <td>...</td>\n",
       "      <td>34.271639</td>\n",
       "      <td>32.063552</td>\n",
       "      <td>26.061270</td>\n",
       "      <td>27.390462</td>\n",
       "      <td>28.522763</td>\n",
       "      <td>29.504599</td>\n",
       "      <td>29.929533</td>\n",
       "      <td>30.382555</td>\n",
       "      <td>30.502594</td>\n",
       "      <td>29.212671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4439</th>\n",
       "      <td>0.681446</td>\n",
       "      <td>1.312102</td>\n",
       "      <td>-6.950588</td>\n",
       "      <td>-4.898579</td>\n",
       "      <td>-4.806646</td>\n",
       "      <td>1.000135</td>\n",
       "      <td>1.000545</td>\n",
       "      <td>1.001237</td>\n",
       "      <td>1.002237</td>\n",
       "      <td>1.003575</td>\n",
       "      <td>...</td>\n",
       "      <td>58.585236</td>\n",
       "      <td>49.638944</td>\n",
       "      <td>53.789819</td>\n",
       "      <td>57.883978</td>\n",
       "      <td>61.744858</td>\n",
       "      <td>65.243234</td>\n",
       "      <td>68.629912</td>\n",
       "      <td>71.741125</td>\n",
       "      <td>74.071427</td>\n",
       "      <td>55.659149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4440 rows × 43 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$   $k_{1}$   $k_{2}$  \\\n",
       "0     1.060199   1.175119  4.223309  1.954982  0.668442  0.999937  0.999749   \n",
       "1     0.934900   0.678878 -4.560123 -5.433176  1.955589  1.000023  1.000093   \n",
       "2     0.902725   1.077164  5.432703  1.786148 -2.231237  0.999992  0.999967   \n",
       "3     1.021150   1.727626  2.655574  1.744105  1.669546  0.999930  0.999718   \n",
       "4     0.879959   0.614681 -0.879454  1.568620 -2.094217  0.999983  0.999934   \n",
       "...        ...        ...       ...       ...       ...       ...       ...   \n",
       "4435  0.547015   1.288573  0.044432 -7.253548  0.466119  1.000030  1.000120   \n",
       "4436  1.001564   0.860793 -5.493621 -1.769730 -0.165640  0.999996  0.999985   \n",
       "4437  0.698036   1.639603  4.362781 -5.482224  1.867839  0.999971  0.999883   \n",
       "4438  0.392364   1.847479 -4.406707 -2.216694 -3.537008  1.000124  1.000501   \n",
       "4439  0.681446   1.312102 -6.950588 -4.898579 -4.806646  1.000135  1.000545   \n",
       "\n",
       "       $k_{3}$   $k_{4}$   $k_{5}$  ...    $M_{10}$    $M_{11}$    $M_{12}$  \\\n",
       "0     0.999434  0.998997  0.998432  ...  134.037978  148.512525  163.272854   \n",
       "1     1.000217  1.000320  1.000455  ...  103.915686  112.327432  120.272428   \n",
       "2     0.999926  0.999869  0.999794  ...  108.849433  119.470689  129.999248   \n",
       "3     0.999364  0.998868  0.998228  ...  127.740421  141.266167  154.989763   \n",
       "4     0.999851  0.999735  0.999599  ...  106.796984  117.325858  127.789216   \n",
       "...        ...       ...       ...  ...         ...         ...         ...   \n",
       "4435  1.000269  1.000482  1.000759  ...   57.354409   60.706329   63.229154   \n",
       "4436  0.999967  0.999942  0.999910  ...  120.645942  132.403067  144.068337   \n",
       "4437  0.999738  0.999535  0.999277  ...   81.046636   88.178377   95.060257   \n",
       "4438  1.001142  1.002068  1.003316  ...   34.271639   32.063552   26.061270   \n",
       "4439  1.001237  1.002237  1.003575  ...   58.585236   49.638944   53.789819   \n",
       "\n",
       "        $M_{13}$    $M_{14}$    $M_{15}$    $M_{16}$    $M_{17}$    $M_{18}$  \\\n",
       "0     178.321020  193.655110  209.316135  225.272656  241.542420  258.106345   \n",
       "1     127.662153  134.486057  140.707282  146.285371  151.175265  155.233386   \n",
       "2     140.428482  150.745805  160.919514  170.960227  180.856753  190.571989   \n",
       "3     168.921302  183.060270  197.421548  212.001673  226.804974  241.815642   \n",
       "4     138.174232  148.456043  158.610523  168.633669  178.486392  188.154242   \n",
       "...          ...         ...         ...         ...         ...         ...   \n",
       "4435   64.723274   64.935203   63.432342   59.428503   50.591455   37.736858   \n",
       "4436  155.631571  167.180761  178.552086  189.803678  200.927590  211.916165   \n",
       "4437  101.634181  107.870398  113.738741  119.208817  124.250254  128.832978   \n",
       "4438   27.390462   28.522763   29.504599   29.929533   30.382555   30.502594   \n",
       "4439   57.883978   61.744858   65.243234   68.629912   71.741125   74.071427   \n",
       "\n",
       "        $M_{19}$  \n",
       "0     275.051207  \n",
       "1     158.482898  \n",
       "2     200.081576  \n",
       "3     257.026259  \n",
       "4     197.608792  \n",
       "...          ...  \n",
       "4435   37.921742  \n",
       "4436  222.762146  \n",
       "4437  132.920288  \n",
       "4438   29.212671  \n",
       "4439   55.659149  \n",
       "\n",
       "[4440 rows x 43 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_train_k = pd.DataFrame(df_train[\"$k$\"].to_list(), columns = [\"$k_{\"+str(i)+\"}$\" for i in range(list_len)])\n",
    "df_train_k = df_train_k.drop(df_train_k.columns[0], axis = 1)\n",
    "df_train_M = pd.DataFrame(df_train[\"$M$\"].to_list(), columns = [\"$M_{\"+str(i)+\"}$\" for i in range(list_len)])\n",
    "df_train_M = df_train_M.drop(df_train_M.columns[0], axis = 1)\n",
    "df_train = pd.concat([df_train.drop(columns = [\"$k$\", \"$M$\"]), df_train_k, df_train_M], axis = 1)\n",
    "list_len -= 1\n",
    "display(df_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = np.array(df_train.iloc[:, 5:].values.tolist())\n",
    "y_train = np.array(df_train.iloc[:, :5].values.tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = X_scaler.transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Ridge()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;Ridge<span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Ridge()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "Ridge()"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimator = Ridge()\n",
    "estimator.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Коэффициент детерминации:\n"
     ]
    },
    {
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       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\nu_1$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_3$</th>\n",
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       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>0.999577</td>\n",
       "      <td>-0.39749</td>\n",
       "      <td>-1.050354</td>\n",
       "      <td>-69.242199</td>\n",
       "      <td>-117.684902</td>\n",
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      ],
      "text/plain": [
       "      $\\mu$  $\\lambda$   $\\nu_1$    $\\nu_2$     $\\nu_3$\n",
       "0  0.999577   -0.39749 -1.050354 -69.242199 -117.684902"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "name": "stdout",
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     "text": [
      "Средняя абсолютная ошибка:\n"
     ]
    },
    {
     "data": {
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       "      <th>0</th>\n",
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       "      <td>0.499232</td>\n",
       "      <td>0.135872</td>\n",
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       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
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     "metadata": {},
     "output_type": "display_data"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Корень среднеквадратической ошибки:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "      $\\mu$  $\\lambda$   $\\nu_1$   $\\nu_2$   $\\nu_3$\n",
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       "      <th>$\\mu_{APE}$</th>\n",
       "      <th>$\\lambda$</th>\n",
       "      <th>$\\lambda^*$</th>\n",
       "      <th>$\\lambda_{APE}$</th>\n",
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       "      <th>$\\nu_1^*$</th>\n",
       "      <th>${\\nu_1}_{APE}$</th>\n",
       "      <th>$\\nu_2$</th>\n",
       "      <th>$\\nu_2^*$</th>\n",
       "      <th>${\\nu_2}_{APE}$</th>\n",
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       "      <th>$\\nu_3^*$</th>\n",
       "      <th>${\\nu_3}_{APE}$</th>\n",
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       "      <th>0</th>\n",
       "      <td>0.799</td>\n",
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       "      <td>0.033893</td>\n",
       "      <td>1.158</td>\n",
       "      <td>1.116491</td>\n",
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       "      <td>0.36</td>\n",
       "      <td>-0.976481</td>\n",
       "      <td>371.244591</td>\n",
       "      <td>-2.66</td>\n",
       "      <td>-2.100445</td>\n",
       "      <td>21.035917</td>\n",
       "      <td>-1.785</td>\n",
       "      <td>-1.658253</td>\n",
       "      <td>7.100677</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.824</td>\n",
       "      <td>0.824243</td>\n",
       "      <td>0.029447</td>\n",
       "      <td>1.107</td>\n",
       "      <td>1.116718</td>\n",
       "      <td>0.877872</td>\n",
       "      <td>-0.96</td>\n",
       "      <td>-0.969392</td>\n",
       "      <td>0.978377</td>\n",
       "      <td>-2.54</td>\n",
       "      <td>-2.101090</td>\n",
       "      <td>17.279903</td>\n",
       "      <td>-1.810</td>\n",
       "      <td>-1.665003</td>\n",
       "      <td>8.010899</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\mu$   $\\mu^*$  $\\mu_{APE}$  $\\lambda$  $\\lambda^*$  $\\lambda_{APE}$  \\\n",
       "0  0.799  0.799271     0.033893      1.158     1.116491         3.584540   \n",
       "1  0.824  0.824243     0.029447      1.107     1.116718         0.877872   \n",
       "\n",
       "   $\\nu_1$  $\\nu_1^*$  ${\\nu_1}_{APE}$  $\\nu_2$  $\\nu_2^*$  ${\\nu_2}_{APE}$  \\\n",
       "0     0.36  -0.976481       371.244591    -2.66  -2.100445        21.035917   \n",
       "1    -0.96  -0.969392         0.978377    -2.54  -2.101090        17.279903   \n",
       "\n",
       "   $\\nu_3$  $\\nu_3^*$  ${\\nu_3}_{APE}$  \n",
       "0   -1.785  -1.658253         7.100677  \n",
       "1   -1.810  -1.665003         8.010899  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = estimator.predict(X_new)\n",
    "prediction_data = []\n",
    "for i in range(df_new.shape[0]):\n",
    "    material_data = {}\n",
    "    material_data.update({\"$\\mu$\": y_new[i][0]})\n",
    "    material_data.update({\"$\\mu^*$\": y_pred[i][0]})\n",
    "    material_data.update({\"$\\mu_{APE}$\": np.abs((y_pred[i][0]-y_new[i][0])/y_new[i][0])*100.0})\n",
    "    material_data.update({\"$\\lambda$\": y_new[i][1]})\n",
    "    material_data.update({\"$\\lambda^*$\": y_pred[i][1]})\n",
    "    material_data.update({\"$\\lambda_{APE}$\": np.abs((y_pred[i][1]-y_new[i][1])/y_new[i][1])*100.0})\n",
    "    material_data.update({\"$\\nu_1$\": y_new[i][2]})\n",
    "    material_data.update({\"$\\nu_1^*$\": y_pred[i][2]})\n",
    "    material_data.update({\"${\\nu_1}_{APE}$\": np.abs((y_pred[i][2]-y_new[i][2])/y_new[i][2])*100.0})\n",
    "    material_data.update({\"$\\nu_2$\": y_new[i][3]})\n",
    "    material_data.update({\"$\\nu_2^*$\": y_pred[i][3]})\n",
    "    material_data.update({\"${\\nu_2}_{APE}$\": np.abs((y_pred[i][3]-y_new[i][3])/y_new[i][3])*100.0})\n",
    "    material_data.update({\"$\\nu_3$\": y_new[i][4]})\n",
    "    material_data.update({\"$\\nu_3^*$\": y_pred[i][4]})\n",
    "    material_data.update({\"${\\nu_3}_{APE}$\": np.abs((y_pred[i][4]-y_new[i][4])/y_new[i][4])*100.0})\n",
    "    prediction_data.append(material_data)\n",
    "score = r2_score(y_new, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Коэффициент детерминации:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = mean_absolute_error(y_new, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Средняя абсолютная ошибка:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "score = root_mean_squared_error(y_new, y_pred, multioutput = \"raw_values\")\n",
    "score_data = {}\n",
    "score_data.update({\"$\\mu$\": score[0]})\n",
    "score_data.update({\"$\\lambda$\": score[1]})\n",
    "score_data.update({\"$\\nu_1$\": score[2]})\n",
    "score_data.update({\"$\\nu_2$\": score[3]})\n",
    "score_data.update({\"$\\nu_3$\": score[4]})\n",
    "print(\"Корень среднеквадратической ошибки:\")\n",
    "display(pd.DataFrame(score_data, index = [0]))\n",
    "display(pd.DataFrame.from_dict(prediction_data))"
   ]
  }
 ],
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