Cartesian_to_Fractional.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e0f9a18a-2127-4604-a957-a31c46e6ac20",
   "metadata": {},
   "source": [
    "#### Lattice vectors $a_1, a_2, a_3$ are the lattice vectors (basis vectors in the real/direct 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 coordinates of an atom) in the cartesian space is represented by $\\vec{F_1}$ in direct space (represented by the fractional coordinates 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 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": "ba206165-5598-4937-aa87-74af55698222",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aa53af59-1544-4608-a9c0-31849fcca250",
   "metadata": {},
   "outputs": [],
   "source": [
    "#def "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e525bdf4-eb04-4323-bb37-7b89ffd5e974",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "with open('POSCAR_carte.vasp', 'r') as data:\n",
    "    file = data.readlines()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8f0707f7-a569-4241-a213-f4c2cb7191ca",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['K5CuSb2                                 \\n', '1.0\\n', '        9.9642868042         0.0000000000         0.0000000000\\n', '        8.1907009722         5.6744540795         0.0000000000\\n', '        8.1907009722         2.5600544114         5.0641436108\\n', '    K   Cu   Sb\\n', '    5    1    2\\n', 'Cartesian\\n', '    13.172844374         4.117254245         2.532071805\\n', '    16.742525391         5.232980197         3.218232546\\n', '     9.603164143         3.001528540         1.845911215\\n', '    20.599742414         6.438577311         3.959663189\\n', '     5.745946335         1.795931180         1.104480422\\n', '     0.000000000         0.000000000         0.000000000\\n', '    24.004008491         7.502601797         4.614028025\\n', '     2.341680454         0.731906756         0.450115623\\n']\n"
     ]
    }
   ],
   "source": [
    "print(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "39579f77-522c-4b10-9d52-c27dbc53563a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#lm = list(map(float, list(file[i] for i in file[2:5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "74e94898-3425-42f8-a20b-fdd01c445240",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['9.9642868042', '0.0000000000', '0.0000000000']\n"
     ]
    }
   ],
   "source": [
    "print(file[2].split())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "198d161a-00ea-4422-9d46-d6e9eacec3a0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.9642868042, 0.0, 0.0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(float, file[2].split()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f0f4c559-6133-4b3b-a8e5-0d9c9d3f4709",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['        9.9642868042         0.0000000000         0.0000000000\\n', '        8.1907009722         5.6744540795         0.0000000000\\n', '        8.1907009722         2.5600544114         5.0641436108\\n']\n"
     ]
    }
   ],
   "source": [
    "print(file[2:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cd412e2f-d974-4d91-ad7a-65d5a0c3b049",
   "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": 10,
   "id": "93ac1c7f-8e7a-4270-a40a-25251400b6c3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[9.9642868  8.19070097 8.19070097]\n",
      " [0.         5.67445408 2.56005441]\n",
      " [0.         0.         5.06414361]]\n"
     ]
    }
   ],
   "source": [
    "print(lm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3a3ca872-0074-43d1-9200-bc61ddf05a48",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.9642868042"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(lm[0][0]**2 + lm[1][0]**2 + lm[2][0]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c20317b0-6df5-43d9-8677-82c51d87e15b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.964286804199899"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(lm[0][1]**2 + lm[1][1]**2 + lm[2][1]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8b2dcacc-f6c3-4d16-adfc-3747a296e2b8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.964286804188903"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(lm[0][2]**2 + lm[1][2]**2 + lm[2][2]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7b076a25-53fd-4291-a43b-b71423b206e3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.10035841 -0.14486076 -0.08908798]\n",
      " [ 0.          0.17622841 -0.08908798]\n",
      " [ 0.          0.          0.19746675]]\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.inv(lm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "064936c4-6484-4052-984a-adfb33fa7e64",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "C = np.array([list(map(float, file[8:][i].split())) for i in range(len(file[8:]))]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "30e1b566-ffcf-4186-acb4-ba8eef6dce79",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[13.17284437 16.74252539  9.60316414 20.59974241  5.74594634  0.\n",
      "  24.00400849  2.34168045]\n",
      " [ 4.11725424  5.2329802   3.00152854  6.43857731  1.79593118  0.\n",
      "   7.5026018   0.73190676]\n",
      " [ 2.53207181  3.21823255  1.84591122  3.95966319  1.10448042  0.\n",
      "   4.61402802  0.45011562]]\n"
     ]
    }
   ],
   "source": [
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2fbda7d0-2af9-400e-a6c1-a2785633fa64",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.22923864945472"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(C[0][2]**2 + C[1][2]**2 + C[2][2]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fc059f70-9344-46ce-aedd-1eddcf784b14",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "F = np.dot(np.linalg.inv(lm), C).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f3e3d27b-7cfc-4163-bc5a-b6c6beba3aea",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.5        0.5        0.5       ]\n",
      " [0.63549393 0.63549393 0.63549393]\n",
      " [0.3645061  0.3645061  0.3645061 ]\n",
      " [0.78190184 0.78190184 0.78190184]\n",
      " [0.21809816 0.21809816 0.21809816]\n",
      " [0.         0.         0.        ]\n",
      " [0.91111714 0.91111714 0.91111714]\n",
      " [0.08888287 0.08888287 0.08888287]]\n"
     ]
    }
   ],
   "source": [
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6ed2bbdc-704a-428c-ae9a-32ff94834bab",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# def carte_to_frac(str_file):\n",
    "#     with open(str_file, 'r') as data:\n",
    "#         file = data.readlines()\n",
    "        \n",
    "#         lattice_matrix = np.array([list(map(float, file[2:5][i].split())) for i in range(len(file[2:5]))]).T\n",
    "#         carte_coord_matrix = np.array([list(map(float, file[8:][i].split())) for i in range(len(file[8:]))]).T\n",
    "#         fractional_coord = np.dot(np.linalg.inv(lattice_matrix), carte_coord_matrix).T\n",
    "        \n",
    "#     return fractional_coord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1a1c8c47-1735-448f-9945-281803951208",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# carte_to_frac('POSCAR_carte.vasp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4d3d2fb9-ac06-413c-8e55-6462c57d0f60",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# def carte_to_frac(str_file):\n",
    "#     with open(str_file, 'r') as data:\n",
    "#         file = data.readlines()\n",
    "        \n",
    "#         lattice_matrix = np.array([list(map(float, file[2:5][i].split())) for i in range(len(file[2:5]))]).T\n",
    "#         carte_coord_matrix = np.array([list(map(float, file[8:][i].split())) for i in range(len(file[8:]))]).T\n",
    "#         fractional_coord = np.dot(np.linalg.inv(lattice_matrix), carte_coord_matrix).T\n",
    "    \n",
    "\n",
    "#     for i in fractional_coord:\n",
    "#         print(i[0], '\\t', i[1], '\\t', i[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d755788e-1623-4d0c-890c-75c9ac2e34fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# carte_to_frac('POSCAR_carte.vasp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "510ec0c1-7b56-44a2-ba36-cc00aab8ae71",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def carte_to_frac(str_file):\n",
    "    with open(str_file, 'r') as data:\n",
    "        fl = data.readlines()\n",
    "        \n",
    "        scale_factor = float(fl[1])\n",
    "        lattice_matrix = scale_factor*np.array([list(map(float, i.split())) for i in fl[2:5]]).T\n",
    "        carte_coord_matrix = np.array([list(map(float, j.split()[:3])) for j in fl[8:]]).T\n",
    "        fractional_coord = np.dot(np.linalg.inv(lattice_matrix), carte_coord_matrix).T\n",
    "    \n",
    "    with open('poscar_frac.vasp', 'w') as output:\n",
    "        output.write('generated by sampad' +'\\n')\n",
    "        for k in fl[1:7]:\n",
    "            output.write(k)\n",
    "        # output.write(str(scale_factor)+'\\n')\n",
    "        # output.write(fl[2])\n",
    "        # output.write(fl[3])\n",
    "        # output.write(fl[4])\n",
    "        # output.write(fl[5])\n",
    "        # output.write(fl[6])\n",
    "        \n",
    "        output.write('Direct'+'\\n')       \n",
    "        for l in fractional_coord:\n",
    "            output.write('\\t'+str(l[0])+'\\t'+str(l[1])+'\\t'+str(l[2])+'\\n')\n",
    "            # output.write('\\t'+str(i[1])+'\\t')\n",
    "            # output.write('\\t'+str(i[2])+'\\n')\n",
    "    return fractional_coord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3cdb319d-9843-4379-90f9-c18926cad03a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5       , 0.5       , 0.5       ],\n",
       "       [0.63549393, 0.63549393, 0.63549393],\n",
       "       [0.3645061 , 0.3645061 , 0.3645061 ],\n",
       "       [0.78190184, 0.78190184, 0.78190184],\n",
       "       [0.21809816, 0.21809816, 0.21809816],\n",
       "       [0.        , 0.        , 0.        ],\n",
       "       [0.91111714, 0.91111714, 0.91111714],\n",
       "       [0.08888287, 0.08888287, 0.08888287]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carte_to_frac('POSCAR_carte.vasp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fd776380-481a-4479-8fc3-01df49763932",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def carte_to_frac(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",
    "        carte_coord_matrix = np.array([list(map(float, j.split())) for j in fl[8:]]).T\n",
    "        fractional_coord = np.dot(np.linalg.inv(lattice_matrix), carte_coord_matrix).T\n",
    "    \n",
    "    with open('poscar_frac.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('Direct'+'\\n')\n",
    "        for l in fractional_coord:\n",
    "            output.write('\\t'+\"{:.16f}\".format(l[0])+'\\t'+\"{:.16f}\".format(l[1])+'\\t'+\"{:.16f}\".format(l[2])+'\\n')\n",
    "\n",
    "    return fractional_coord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5ac68947-2f8c-4a8d-9ed7-83cc89b0eb6c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5       , 0.5       , 0.5       ],\n",
       "       [0.63549393, 0.63549393, 0.63549393],\n",
       "       [0.3645061 , 0.3645061 , 0.3645061 ],\n",
       "       [0.78190184, 0.78190184, 0.78190184],\n",
       "       [0.21809816, 0.21809816, 0.21809816],\n",
       "       [0.        , 0.        , 0.        ],\n",
       "       [0.91111714, 0.91111714, 0.91111714],\n",
       "       [0.08888287, 0.08888287, 0.08888287]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carte_to_frac('POSCAR_carte.vasp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bf12d527-c433-4742-b9c5-a79bf98d5884",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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