Jupyter notebooks and labs

running_tables.ipynb

test_finitediff_cont_2.ipynb

test_finitediff_cont_3.ipynb

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    "# 4.\tPerforming interpolation and derivative using the variant length of the grid points\n",
    "\n",
    "In this part, it performs the behavior of interpolation and derivative results with the variation of grid length. Order 0 means the interpolation and the otherwise is derivative. Figure 22 shows the code that being used to obtain the results and Figures 23-25 are the results of 3, 4, and 5 length of the grid, respectively. Comparing figs. 23, 24, and 25, they show that the higher length of data will give the better accuracy of the result such as in data length of 3 gives low accuracy of the results that might be caused of being not optimally clear for y = x^3 in this length whereas in data length of 4 and 5 give high accuracy of the results."
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      "data: length = 3\n",
      "x = [1. 2. 3.]\n",
      "y = [ 1.  8. 27.]\n",
      "seek y, y', and y'' for x = 1.5\n",
      "y\t= x^3\n",
      "y'\t= 3x^2\n",
      "y''\t= 6x\n",
      "order =  0\n",
      "\tweights = [ 0.375  0.75  -0.125]\n",
      "\ty_exact = 3.375 and y_by_finite_diff = 3.0\n",
      "order =  1\n",
      "\tweights = [-1.  1.  0.]\n",
      "\ty_exact = 6.75 and y_by_finite_diff = 7.0\n",
      "order =  2\n",
      "\tweights = [ 1. -2.  1.]\n",
      "\ty_exact = 9.0 and y_by_finite_diff = 12.0\n",
      "________________________________________________________________________________ \n",
      "\n",
      "data: length = 4\n",
      "x = [1. 2. 3. 4.]\n",
      "y = [ 1.  8. 27. 64.]\n",
      "seek y, y', and y'' for x = 1.5\n",
      "y\t= x^3\n",
      "y'\t= 3x^2\n",
      "y''\t= 6x\n",
      "order =  0\n",
      "\tweights = [ 0.3125  0.9375 -0.3125  0.0625]\n",
      "\ty_exact = 3.375 and y_by_finite_diff = 3.375\n",
      "order =  1\n",
      "\tweights = [-0.95833333  0.875       0.125      -0.04166667]\n",
      "\ty_exact = 6.75 and y_by_finite_diff = 6.750000000000002\n",
      "order =  2\n",
      "\tweights = [ 1.5 -3.5  2.5 -0.5]\n",
      "\ty_exact = 9.0 and y_by_finite_diff = 9.0\n",
      "________________________________________________________________________________ \n",
      "\n",
      "data: length = 5\n",
      "x = [1. 2. 3. 4. 5.]\n",
      "y = [  1.   8.  27.  64. 125.]\n",
      "seek y, y', and y'' for x = 1.5\n",
      "y\t= x^3\n",
      "y'\t= 3x^2\n",
      "y''\t= 6x\n",
      "order =  0\n",
      "\tweights = [ 0.2734375  1.09375   -0.546875   0.21875   -0.0390625]\n",
      "\ty_exact = 3.375 and y_by_finite_diff = 3.375\n",
      "order =  1\n",
      "\tweights = [-0.91666667  0.70833333  0.375      -0.20833333  0.04166667]\n",
      "\ty_exact = 6.75 and y_by_finite_diff = 6.750000000000001\n",
      "order =  2\n",
      "\tweights = [ 1.79166667 -4.66666667  4.25       -1.66666667  0.29166667]\n",
      "\ty_exact = 9.0 and y_by_finite_diff = 9.0\n",
      "________________________________________________________________________________ \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from finitediff import get_weights\n",
    "import numpy as np\n",
    "\n",
    "# data\n",
    "xint = np.array([1.,2.,3.,4.,5.,6.])\n",
    "for j in range(3):\n",
    "    x = xint[:(-3+j)]\n",
    "    y = np.power(x,3) # y = x^3\n",
    "    print('data: length = {}'.format(len(x)))\n",
    "    print('x = {}'.format(x))\n",
    "    print('y = {}'.format(y))\n",
    "    # seek y, y', and y'' for x = 1.5\n",
    "    # y' = 3x^2\n",
    "    # y'' = 6x\n",
    "    x0 = 1.5\n",
    "    print(\"seek y, y', and y'' for x = {}\".format(x0))\n",
    "    print(\"y\\t= x^3\\ny'\\t= 3x^2\\ny''\\t= 6x\")\n",
    "    c = get_weights(x, x0, maxorder=2)\n",
    "    for i in range(len(c[0,:])):\n",
    "        yexact = 0\n",
    "        if i == 0:\n",
    "            yexact = x0**3\n",
    "        elif i == 1:\n",
    "            yexact = 3*x0**2\n",
    "        elif i == 2:\n",
    "            yexact = 6*x0\n",
    "        print('order = ',i)\n",
    "        print('\\tweights = {}'.format(c[:,i]))\n",
    "        yest = np.sum(y*c[:,i])\n",
    "        print('\\ty_exact = {} and y_by_finite_diff = {}'.format(yexact, yest))\n",
    "    print(\"\".join(['_' for l in range(80)]),'\\n')"
   ]
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   "cell_type": "markdown",
   "id": "2226b7eb-1b57-4b0d-9891-667662170f33",
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    "Figure 22. The code for testing interpolation (order = 0) and derivative (order != 0) by using finite difference\n",
    "\n",
    "Figure 23. The result by using the length of 3 points\n",
    "\n",
    "Figure 24. The result by using the length of 4 points\n",
    "\n",
    "Figure 25. The result by using the length of 5 points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a064bea9-c892-40ce-8616-58a6be6937c2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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test_finitediff_cont_4.ipynb

test_finitediff_cont_5.ipynb

test_to_gist.ipynb