Fractional_to_Cartesian.ipynb

{
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   "source": [
    "#### Lattice vectors $a_1, a_2, a_3$ are the lattice vectors (basis vectors in the direct/real space) regarding cartesian coordinates. Where $a_n = a_{nx}\\hat{i} + a_{ny}\\hat{j} + a_{nz}\\hat{k}$ and $\\hat{i} = \\begin{bmatrix} 1 \\\\ 0 \\\\ 0\\end{bmatrix}, \\hat{j} = \\begin{bmatrix} 0 \\\\ 1 \\\\ 0\\end{bmatrix}, \\hat{k} = \\begin{bmatrix} 0 \\\\ 0 \\\\ 1\\end{bmatrix}$ are unit vectors in cartesian coordinate. \n",
    "#### So the transformation matrix for the crystal to its cartesian coordinate is $A = \\begin{bmatrix} a_1 \\ a_2 \\ a_3\\end{bmatrix}$. \n",
    "#### In the POSCAR file $a_is$ are arranged vertically, so I have taken the transpose of the array to get the transformation matrix (named lattice_matrix). \n",
    "#### Let $\\vec{C_1}$ is a vector (represented by the cartesian coordinate of an atom) in the cartesian space is represented by $\\vec{F_1}$ in direct space (represented by the fractional coordinate of that atom).\n",
    "\n",
    "#### $\\vec{C_1} = \\begin{bmatrix} C_{1a1} \\\\ C_{1a2} \\\\ C_{1a3}\\end{bmatrix} = C_{1a1}a_1 + C_{1a2}a_2 + C_{1a3}a_3$\n",
    "#### and \n",
    "#### $\\vec{F_1} = \\begin{bmatrix} F_{1b1} \\\\ F_{1b2} \\\\ F_{1b3}\\end{bmatrix} = F_{1b1}b_1 + F_{1b2}b_2 + F_{1b3}b_3$, where $b_1, b_2, b_3$ are basis vectors in the direct space in terms of fractional coordinates\n",
    "\n",
    "#### Then cartesian coordinate can be achieved from the fractional coordinate by $\\vec{C_1} = A\\vec{F_1}$\n",
    "#### and fractional coordinate can be achieved from the cartesian coordinate by $\\vec{F_1} = B\\vec{C_1}$,\n",
    "#### where $B = \\begin{bmatrix} b_1 \\ b_2 \\ b_3\\end{bmatrix}$ is the transformation matrix to the direct fractional coordinate space.\n",
    "#### Alternatively, $\\vec{F_1} = A^{-1}\\vec{C_1}$, therefore, $B = A^{-1}$. \n",
    "#### For a system with more than one atom, the matrix for the coordinates of the atoms is generated by putting each vector column-wise as $C = \\begin{bmatrix} C_1 \\ C_2 \\ ...\\end{bmatrix}$ or $F = \\begin{bmatrix} F_1 \\ F_2 \\ ...\\end{bmatrix}$\n",
    "\n",
    "#### In the POSCAR file $C_is$ or $F_is$ are arranged vertically. So to get the coordinate matrices ($C$ or $F$) I have taken the transpose of the arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4405374b-3132-4b33-8a5c-a3af6d8847ac",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fa7ef17d-6a95-4d40-a6c2-41096c391ac7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "with open('POSCAR_unitcell', 'r') as data:\n",
    "    file = data.readlines()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e0c30e3d-a821-48e7-b9a7-8b07f5f5701d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['K5CuSb2\\n', '   1.00000000000000     \\n', '     9.9642821371889738   -0.0078303211631481   -0.0048139447635795\\n', '     8.1951566441023420    5.6680144143786944   -0.0048139447636245\\n', '     8.1951566441022692    2.5543793416265430    5.0597980943421703\\n', '   K    Cu   Sb\\n', '   5     1    2\\n', 'Direct\\n', '  0.5000000000000000  0.5000000000000000  0.5000000000000000\\n', '  0.6354939155472525  0.6354939155472525  0.6354939155472525\\n', '  0.3645060844527478  0.3645060844527478  0.3645060844527478\\n', '  0.7819018364271487  0.7819018364271487  0.7819018364271487\\n', '  0.2180981635728510  0.2180981635728510  0.2180981635728510\\n', '  0.0000000000000000  0.0000000000000000 -0.0000000000000000\\n', '  0.9111171097102632  0.9111171097102631  0.9111171097102632\\n', '  0.0888828682897351  0.0888828682897351  0.0888828682897351\\n']\n"
     ]
    }
   ],
   "source": [
    "print(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1c935924-da01-4b11-a6e2-2472bf32366a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "lm = np.array([list(map(float, file[2:5][i].split())) for i in range(len(file[2:5]))]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6735d918-7d03-4317-a775-0a5634dd4262",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "F = np.array([list(map(float, file[8:][i].split()[:3])) for i in range(len(file[8:]))]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "11d573ec-3728-4ca0-8134-ccfb3b69ef99",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.5         0.63549392  0.36450608  0.78190184  0.21809816  0.\n",
      "   0.91111711  0.08888287]\n",
      " [ 0.5         0.63549392  0.36450608  0.78190184  0.21809816  0.\n",
      "   0.91111711  0.08888287]\n",
      " [ 0.5         0.63549392  0.36450608  0.78190184  0.21809816 -0.\n",
      "   0.91111711  0.08888287]]\n"
     ]
    }
   ],
   "source": [
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d84f1210-e249-4860-91e2-bbfde578a453",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "C = np.dot(lm, F).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "58c2beba-9c3b-44c4-b089-85d7645809fa",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[13.17729771  4.10728172  2.5250851 ]\n",
      " [16.74818504  5.22030508  3.20935244]\n",
      " [ 9.60641039  2.99425835  1.84081777]\n",
      " [20.60670656  6.42298224  3.94873736]\n",
      " [ 5.74788886  1.7915812   1.10143285]\n",
      " [ 0.          0.          0.        ]\n",
      " [24.01212281  7.48442929  4.60129648]\n",
      " [ 2.34247203  0.73013396  0.44887361]]\n"
     ]
    }
   ],
   "source": [
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6a1c2d53-f62f-4d88-8bfc-aff59dad5e22",
   "metadata": {},
   "outputs": [],
   "source": [
    "def direct_to_carte(str_file):\n",
    "    with open(str_file, 'r') as data:\n",
    "        fl = data.readlines()\n",
    "        \n",
    "        scale_factor = float(fl[1])\n",
    "        \n",
    "        lattice_matrix = scale_factor*np.array([list(map(float, i.split())) for i in fl[2:5]]).T\n",
    "        frac_coord_matrix = np.array([list(map(float, j.split()[:3])) for j in fl[8:]]).T\n",
    "        carte_coord = np.dot(lattice_matrix, frac_coord_matrix).T\n",
    "    \n",
    "    with open('poscar_carte.vasp', 'w') as output:\n",
    "        output.write(\"generated by sampad's python code\" +'\\n')\n",
    "        # for k in fl[1:7]:\n",
    "        #     output.write(k)\n",
    "        output.writelines(fl[1:7])\n",
    "            \n",
    "\n",
    "        output.write('Cartesian'+'\\n')\n",
    "        for l in carte_coord:\n",
    "            output.write('\\t'+\"{:.16f}\".format(l[0])+'\\t'+\"{:.16f}\".format(l[1])+'\\t'+\"{:.16f}\".format(l[2])+'\\n')\n",
    "\n",
    "    return carte_coord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "38363ddf-af1b-4723-8708-b3f48add6c58",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[13.17729771,  4.10728172,  2.5250851 ],\n",
       "       [16.74818504,  5.22030508,  3.20935244],\n",
       "       [ 9.60641039,  2.99425835,  1.84081777],\n",
       "       [20.60670656,  6.42298224,  3.94873736],\n",
       "       [ 5.74788886,  1.7915812 ,  1.10143285],\n",
       "       [ 0.        ,  0.        ,  0.        ],\n",
       "       [24.01212281,  7.48442929,  4.60129648],\n",
       "       [ 2.34247203,  0.73013396,  0.44887361]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "direct_to_carte('POSCAR_unitcell')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04904e1d-3c5c-4ac5-bd31-4211175064f9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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