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@yudhastyawan
Last active May 1, 2021 21:08
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Jupyter notebooks and labs
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{
"cells": [
{
"cell_type": "markdown",
"id": "eb1fc783-45ff-401f-ad91-83c3cf3e8543",
"metadata": {},
"source": [
"# 3.\tPlotting the weight coefficients with the grid points and the orders\n",
"\n",
"Figures 15 – 21 show the code and the illustration of the weight coefficient distribution along the grid points. Generally, the variation of the distribution in each figures is similar that means the largest value of weights is on/around the center points and decreasing gradually until the edge/last point in opposite directions. Besides, if assuming the center point as the separating line between opposite direction (left and right), the plot behavior seems there are a structure odd or even function for odd and even order, respectively. After that, the plots seem also each parts (left and right) tend to balance each other so that if the weights are summed into one value, it gives a very small number (except order 0 that approximately equals to 1) and close to 0 value."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9e59ce21-55c8-4f0a-bad5-11c516605288",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"orde (derivative) = 0\n",
"[-0. 0. -0. 0. 1. -0. 0. -0. 0.]\n",
"\n",
"orde (derivative) = 1\n",
"[ 3.57142857e-03 -3.80952381e-02 2.00000000e-01 -8.00000000e-01\n",
" -3.05311332e-16 8.00000000e-01 -2.00000000e-01 3.80952381e-02\n",
" -3.57142857e-03]\n",
"\n",
"orde (derivative) = 2\n",
"[-1.78571429e-03 2.53968254e-02 -2.00000000e-01 1.60000000e+00\n",
" -2.84722222e+00 1.60000000e+00 -2.00000000e-01 2.53968254e-02\n",
" -1.78571429e-03]\n",
"\n",
"orde (derivative) = 3\n",
"[-2.91666667e-02 3.00000000e-01 -1.40833333e+00 2.03333333e+00\n",
" -2.22044605e-15 -2.03333333e+00 1.40833333e+00 -3.00000000e-01\n",
" 2.91666667e-02]\n",
"\n",
"orde (derivative) = 4\n",
"[ 0.02916667 -0.4 2.81666667 -8.13333333 11.375 -8.13333333\n",
" 2.81666667 -0.4 0.02916667]\n",
"\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from finitediff import get_weights\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"c = get_weights(np.array([-4.,-3.,-2.,-1.,0,1.,2.,3.,4.]), 0, maxorder=4)\n",
"plt.figure()\n",
"for i in range(len(c[0,:])):\n",
" print('orde (derivative) = ',i)\n",
" print(c[:,i])\n",
" plt.plot(np.array([-4.,-3.,-2.,-1.,0,1.,2.,3.,4.]),c[:,i],label='order {}'.format(i))\n",
" print('')\n",
"plt.xlabel('grid points')\n",
"plt.ylabel('the weight coefficients')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "fb8437b5-ef13-4e80-92b8-db577c6a171e",
"metadata": {},
"source": [
"### Figure 15. Code for plotting the weights to the grid points based on Table 1 & Figure 16. The result of Fig. 15 "
]
},
{
"cell_type": "markdown",
"id": "5ed2a82a-1519-42c9-be0d-a312de6a001d",
"metadata": {},
"source": [
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "cf601a0e-dd75-4dd4-8d22-e2dd48a9442f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"orde (derivative) = 0\n",
"[-0.00244141 0.02392578 -0.11962891 0.59814453 0.59814453 -0.11962891\n",
" 0.02392578 -0.00244141]\n",
"\n",
"orde (derivative) = 1\n",
"[ 6.97544643e-04 -9.57031250e-03 7.97526042e-02 -1.19628906e+00\n",
" 1.19628906e+00 -7.97526042e-02 9.57031250e-03 -6.97544643e-04]\n",
"\n",
"orde (derivative) = 2\n",
"[ 0.02248264 -0.21657986 1.01484375 -0.82074653 -0.82074653 1.01484375\n",
" -0.21657986 0.02248264]\n",
"\n",
"orde (derivative) = 3\n",
"[-0.01927083 0.25989583 -2.0296875 4.92447917 -4.92447917 2.0296875\n",
" -0.25989583 0.01927083]\n",
"\n",
"orde (derivative) = 4\n",
"[-0.14583333 1.22916667 -2.8125 1.72916667 1.72916667 -2.8125\n",
" 1.22916667 -0.14583333]\n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from finitediff import get_weights\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"c = get_weights(np.array([(-7./2.),(-5./2.),(-3./2.),(-1./2.),(1./2.),(3./2.),(5./2.),(7./2.)]),\n",
" 0, maxorder=4)\n",
"plt.figure()\n",
"for i in range(len(c[0,:])):\n",
" print('orde (derivative) = ',i)\n",
" print(c[:,i])\n",
" plt.plot(np.array([(-7./2.),(-5./2.),(-3./2.),(-1./2.),(1./2.),(3./2.),(5./2.),(7./2.)]),\n",
" c[:,i],label='order {}'.format(i))\n",
" print('')\n",
"plt.xlabel('grid points')\n",
"plt.ylabel('the weight coefficients')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "a7d06b0d-380e-4e9b-a53f-2503b8fa5bb7",
"metadata": {},
"source": [
"### Figure 17. Code for plotting the weights to the grid points based on Table 2 & Figure 18. The result of Fig. 17\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f868401f-f1bc-45ad-80e4-9c69dbfc5414",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"orde (derivative) = 0\n",
"[ 1. -0. 0. -0. 0. -0. 0. -0. 0.]\n",
"\n",
"orde (derivative) = 1\n",
"[ -2.71785714 8. -14. 18.66666667 -17.5\n",
" 11.2 -4.66666667 1.14285714 -0.125 ]\n",
"\n",
"orde (derivative) = 2\n",
"[ 5.8593254 -27.48571429 62.1 -89.02222222 86.375\n",
" -56.4 23.81111111 -5.88571429 0.64821429]\n",
"\n",
"orde (derivative) = 3\n",
"[ -10.0125 58.16666667 -152.94166667 239.1 -242.83333333\n",
" 163.03333333 -70.125 17.56666667 -1.95416667]\n",
"\n",
"orde (derivative) = 4\n",
"[ 13.3625 -87.73333333 254.81666667 -428.8 458.04166667\n",
" -318.13333333 140.15 -35.73333333 4.02916667]\n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from finitediff import get_weights\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"c = get_weights(np.array([0,1,2,3,4,5,6,7,8]), 0, maxorder=4)\n",
"plt.figure()\n",
"for i in range(len(c[0,:])):\n",
" print('orde (derivative) = ',i)\n",
" print(c[:,i])\n",
" plt.plot(np.array([0,1,2,3,4,5,6,7,8]),\n",
" c[:,i],label='order {}'.format(i))\n",
" print('')\n",
"plt.xlabel('grid points')\n",
"plt.ylabel('the weight coefficients')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "00acea29-fc0e-4104-9ab9-d8827848a437",
"metadata": {},
"source": [
"### Figure 19. Code for plotting the weights to the grid points based on Table 3 & Figure 20. The result of Fig. 19"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "bef1e043-83c9-42a1-b428-fb3414182155",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"orde (derivative) = 0\n",
"[ 0.19638062 1.57104492 -1.83288574 2.19946289 -1.96380615 1.22192383\n",
" -0.49987793 0.12084961 -0.01309204]\n",
"\n",
"orde (derivative) = 1\n",
"[-0.79408482 -0.06849888 2.52376302 -3.61503906 3.45214844 -2.22558594\n",
" 0.93066406 -0.22837612 0.0250093 ]\n",
"\n",
"orde (derivative) = 2\n",
"[ 2.26637835 -7.55368304 11.85798611 -13.08359375 11.07226562\n",
" -6.65112847 2.6546875 -0.63024554 0.06733321]\n",
"\n",
"orde (derivative) = 3\n",
"[ -4.82708333 24.84739583 -58.1484375 82.53697917 -78.22135417\n",
" 50.1421875 -20.87864583 5.10677083 -0.5578125 ]\n",
"\n",
"orde (derivative) = 4\n",
"[ 7.74010417 -48.23333333 133.11875 -213.75833333 219.36979167\n",
" -147.55 63.41041667 -15.85833333 1.7609375 ]\n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from finitediff import get_weights\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"c = get_weights(np.array([(-1./2.),(1./2.),(3./2.),(5./2.),(7./2.),(9./2.),(11./2.),(13./2.),(15./2.)]),\n",
" 0, maxorder=4)\n",
"plt.figure()\n",
"for i in range(len(c[0,:])):\n",
" print('orde (derivative) = ',i)\n",
" print(c[:,i])\n",
" plt.plot(np.array([(-1./2.),(1./2.),(3./2.),(5./2.),(7./2.),(9./2.),(11./2.),(13./2.),(15./2.)]),\n",
" c[:,i],label='order {}'.format(i))\n",
" print('')\n",
"plt.xlabel('grid points')\n",
"plt.ylabel('the weight coefficients')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "b9cd72cb-e104-4543-a2e1-a6b18127580e",
"metadata": {},
"source": [
"### Figure 21. Code for plotting the weights to the grid points based on Table 4 & Figure 21. The result of Fig. 20"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "949ad8a0-49c2-4b30-a93b-04fbc9c0fab0",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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