Linear algebra. Individual homework task 2.ipynb

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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "def get_leader(row):\n",
    "    for i in range(len(row)):\n",
    "        if row[i] != 0:\n",
    "            return i\n",
    "    return 1e9\n",
    "\n",
    "def add_rows(r1, r2):\n",
    "    assert len(r1.shape) == 1\n",
    "    assert len(r2.shape) == 1\n",
    "    assert(len(r1) == len(r2))\n",
    "    return np.array(list(a + b for a, b in zip(r1, r2)))\n",
    "\n",
    "def mult_row(scalar, r1):\n",
    "    return np.array(list(x * scalar for x in r1))\n",
    "\n",
    "def gaussian_transform_forward(A):\n",
    "    current_leader = A.shape[1] + 1\n",
    "    for i in range(A.shape[0]):\n",
    "        if get_leader(A[i]) < current_leader:\n",
    "            current_leader = get_leader(A[i])\n",
    "            A[0], A[i] = A[i], A[0]\n",
    "    if current_leader == A.shape[1] + 1:\n",
    "        return A\n",
    "    A[0] = mult_row(1/A[0][current_leader], A[0])\n",
    "    for i in range(1, A.shape[0]):\n",
    "        A[i] = add_rows(mult_row(-A[i][current_leader], A[0]), A[i])\n",
    "    A[1:, 1:] = gaussian_transform_forward(A[1:, 1:])\n",
    "    return A\n",
    "\n",
    "def gaussian_transform_backward(A, cur_row):\n",
    "    if cur_row == 0:\n",
    "        return A\n",
    "    current_leader = get_leader(A[cur_row])\n",
    "    if current_leader == 1e9:\n",
    "        gaussian_transform_backward(A, cur_row - 1)\n",
    "        return A\n",
    "    for i in range(cur_row):\n",
    "        A[i] = add_rows(A[i], mult_row(-A[i][current_leader], A[cur_row]))\n",
    "    gaussian_transform_backward(A, cur_row - 1)\n",
    "    return A\n",
    "\n",
    "def gaussian_transform(A):\n",
    "    return gaussian_transform_backward(gaussian_transform_forward(A), A.shape[0] - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### СЛУ 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 2. 0.]\n",
      " [0. 1. 2. 1. 0.]\n",
      " [0. 0. 0. 0. 1.]\n",
      " [0. 0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([\n",
    "    [2, 3, 6, 7, 6],\n",
    "    [-8, 5, 10, -11, 8],\n",
    "    [6, -6, -12, 6, 3],\n",
    "    [9, -7, -14, 11, 7]\n",
    "], dtype='float64')\n",
    "print(gaussian_transform(A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### СЛУ 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  2. -2.]\n",
      " [ 0.  1.  2.  1. -1.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([\n",
    "    [2, 3, 6, 7, -7],\n",
    "    [-8, 5, 10, -11, 11],\n",
    "    [6, -6, -12, 6, -6],\n",
    "    [9, -7, -14, 11, -11]\n",
    "], dtype='float64')\n",
    "print(gaussian_transform(A))"
   ]
  }
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