Tutorial-Finite_Difference_Derivatives-FDtable_soln.ipynb

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    "# Creating the Finite-Difference Table for Centered First and Second  Derivatives, from Second through Eighth-Order Accuracy\n",
    "\n",
    "## Courtesy Brandon Clark"
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      "Derivative Accuracy   -4     -3     -2   -1     0     1    2     3     4   \n",
      "---------- -------- ------ ------ ----- ---- ------- --- ----- ----- ------\n",
      "     First        2      0      0     0 -1/2       0 1/2     0     0      0\n",
      "     First        4      0      0  1/12 -2/3       0 2/3 -1/12     0      0\n",
      "     First        6      0  -1/60  3/20 -3/4       0 3/4 -3/20  1/60      0\n",
      "     First        8  1/280 -4/105   1/5 -4/5       0 4/5  -1/5 4/105 -1/280\n",
      "    Second        2      0      0     0    1      -2   1     0     0      0\n",
      "    Second        4      0      0 -1/12  4/3    -5/2 4/3 -1/12     0      0\n",
      "    Second        6      0   1/90 -3/20  3/2  -49/18 3/2 -3/20  1/90      0\n",
      "    Second        8 -1/560  8/315  -1/5  8/5 -205/72 8/5  -1/5 8/315 -1/560\n"
     ]
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    "# Step 0: Import needed modules\n",
    "import numpy as np\n",
    "import finite_difference as fin\n",
    "from astropy.table import Table\n",
    "\n",
    "# Step 1: Set the maximum finite-difference accuracy order\n",
    "max_fdorder = 8\n",
    "\n",
    "# Step 2: Set up table parameters\n",
    "#    One column for deriv order, one for deriv accuracy, and max_fdorder+1\n",
    "numcols = 2 + max_fdorder + 1\n",
    "#    8 rows: 4 accuracy orders per derivative order.\n",
    "numrows = 8\n",
    "#    Center column index of table will be at 2 + max_fdorder/2  (zero-offset indexing)\n",
    "column_corresponding_to_zero_fd_point = 2 + int(max_fdorder/2)\n",
    "#    The table is initialized as a matrix of zeroes in numpy:\n",
    "numpy_matrix = np.zeros((numrows, numcols), dtype=object)\n",
    "\n",
    "# Step 3: Construct the first-order derivative finite difference coefficients\n",
    "rowcount = 0\n",
    "for fdorder in range(2, max_fdorder+1, 2): # loop runs from 2 to max_fdorder inclusive, skipping odd orders.\n",
    "    numpy_matrix[rowcount, 0] = \"First\"\n",
    "    numpy_matrix[rowcount, 1] = fdorder     \n",
    "    fdcoeffs, fdstencl = fin.compute_fdcoeffs_fdstencl(\"D0\", fdorder)\n",
    "    for i in range(fdorder):\n",
    "        numpy_matrix[rowcount, column_corresponding_to_zero_fd_point + fdstencl[i][0]] = fdcoeffs[i]\n",
    "    rowcount += 1\n",
    "\n",
    "# Step 4: Construct the first-order derivative finite difference coefficients\n",
    "for fdorder in range(2, max_fdorder+1, 2): # loop runs from 2 to max_fdorder inclusive, skipping odd orders.\n",
    "    numpy_matrix[rowcount, 0] = \"Second\"\n",
    "    numpy_matrix[rowcount, 1] = fdorder\n",
    "    fdcoeffs, fdstencl = fin.compute_fdcoeffs_fdstencl(\"DD00\", fdorder)\n",
    "    for i in range(fdorder+1):\n",
    "        numpy_matrix[rowcount, column_corresponding_to_zero_fd_point + fdstencl[i][0]] = fdcoeffs[i]\n",
    "    rowcount += 1  \n",
    "\n",
    "# Step 5: Construct an astropy table from the numpy matrix with the following header info, and then print it:\n",
    "table = Table(numpy_matrix, names=('Derivative', 'Accuracy', '-4', '-3', '-2', '-1', '0', '1', '2', '3', '4'))\n",
    "print(table)"
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