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Final: Fix integrate(yk, x) and implement test

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Kees van Kempen
2022-03-18 16:14:01 +01:00
parent 3c1f80b41d
commit d284f0c9a8
1 changed files with 22 additions and 10 deletions
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32
Final/Final - Tight-binding propagation method.ipynb
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@ -306,7 +306,7 @@
}, },
"outputs": [], "outputs": [],
"source": [ "source": [
"def integrate(yk, x, b=None, c=None):\n", "def integrate(yk, x):\n",
" \"\"\"\n", " \"\"\"\n",
" Numerically integrates function yk over [x[0], x[-1]] using\n", " Numerically integrates function yk over [x[0], x[-1]] using\n",
" Simpson's rule over the grid provided by x.\n", " Simpson's rule over the grid provided by x.\n",
@ -326,7 +326,7 @@
" if callable(yk):\n", " if callable(yk):\n",
" yk = yk(x)\n", " yk = yk(x)\n",
" \n", " \n",
" a, b = yk[0], yk[-1]\n", " #a, b = yk[0], yk[-1]\n",
" \n", " \n",
" h = x[1:] - x[:-1]\n", " h = x[1:] - x[:-1]\n",
" \n", " \n",
@ -334,20 +334,21 @@
" # thus avoiding any issues with 2 ∤ n.\n", " # thus avoiding any issues with 2 ∤ n.\n",
" #integral = h/3*(a + 2*np.sum(yk[2:-1:2]) + 4*np.sum(yk[1:-1:2]) + b)\n", " #integral = h/3*(a + 2*np.sum(yk[2:-1:2]) + 4*np.sum(yk[1:-1:2]) + b)\n",
" \n", " \n",
" integral = 3*h/8*(a + 3*np.sum(yk[2:-1:2]) + 3*np.sum(yk[1:-1:2]) + b)\n", " #integral = 3*h/8*(a + 3*np.sum(yk[2:-1:2]) + 3*np.sum(yk[1:-1:2]) + b)\n",
" #integral = (b - a)/8*(x[0] + x[-1]) + 3*(x[1:] - x[:-1])/8*( )\n", " #integral = (b - a)/8*(x[0] + x[-1]) + 3*(x[1:] - x[:-1])/8*( )\n",
" integral = 0\n", " integral = 0\n",
" integral += 3/8*(x[1] - x[0])*yk[0]\n", " integral += 3/8*(x[1] - x[0])*yk[0]\n",
" integral += 3/8*np.sum(yk[])\n", " integral += 9/8*yk[1:-1:3]@h[1::3]\n",
" \n", " integral += 9/8*yk[2:-1:3]@h[2::3]\n",
" integral += 3/8*(x[-1] - x[-2])*yk[-1])\n", " integral += 6/8*yk[:-1:3]@h[::3]\n",
" integral += 3/8*(x[-1] - x[-2])*yk[-1]\n",
" #integral = 3/8*( (x[1] - x[0])*yk[0] + np.sum(yk[]) + (x[-1] - x[-2])*yk[-1])\n", " #integral = 3/8*( (x[1] - x[0])*yk[0] + np.sum(yk[]) + (x[-1] - x[-2])*yk[-1])\n",
" return integral" " return integral"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": 5,
"metadata": { "metadata": {
"deletable": false, "deletable": false,
"nbgrader": { "nbgrader": {
@ -362,11 +363,22 @@
"task": false "task": false
} }
}, },
"outputs": [], "outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Exact: 333333333.3333333\n",
"Integrated: 333333448.1291072\n"
]
}
],
"source": [ "source": [
"def test_integrate():\n", "def test_integrate():\n",
" # YOUR CODE HERE\n", " f = lambda x: x**2\n",
" raise NotImplementedError()\n", " x = np.logspace(0, 3, 10000000)\n",
" print(\"Exact:\", 1000**3/3)\n",
" print(\"Integrated:\", integrate(f, x))\n",
" \n", " \n",
"test_integrate()" "test_integrate()"
] ]