06: Task 1 be done.

Week 2/6 Composite Numerical Integration: Trapezoid and Simpson Rules.ipynb

@@ -39,7 +39,7 @@
    "cell_type": "raw",
    "metadata": {},
    "source": [
-    "team_members = \"\""
+    "team_members = \"Koen Vendrig, Kees van Kempen\""
    ]
   },
   {
@@ -75,7 +75,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -92,10 +92,8 @@
    },
    "outputs": [],
    "source": [
-    "# Import packages here ...\n",
-    "\n",
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "import numpy as np\n",
+    "import scipy.integrate"
    ]
   },
   {
@@ -126,7 +124,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -144,17 +142,23 @@
    "outputs": [],
    "source": [
     "def trapz(yk, dx):\n",
-    "    # YOUR CODE HERE\n",
-    "    raise NotImplementedError()\n",
+    "    a, b = yk[0], yk[-1]\n",
+    "    h = dx\n",
+    "    integral = h/2*(a + 2*np.sum(yk[1:-1]) + b)\n",
+    "    return integral\n",
     "    \n",
     "def simps(yk, dx):\n",
-    "    # YOUR CODE HERE\n",
-    "    raise NotImplementedError()"
+    "    a, b = yk[0], yk[-1]\n",
+    "    h = dx\n",
+    "    # Instead of summing over something with n/2, we use step size 2,\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",
+    "    return integral"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -171,10 +175,41 @@
    },
    "outputs": [],
    "source": [
-    "# Compare your results here ...\n",
+    "# We need a function to integrate, so here we go.\n",
+    "f = lambda x: x**2\n",
     "\n",
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "n    = 100001\n",
+    "a, b = 0, 1\n",
+    "h    = (b - a)/n\n",
+    "xk   = np.linspace(a, b, n + 1)\n",
+    "yk   = f(xk)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "For function f(x) = x^2\n",
+      "for boundaries a = 0 , b = 1 and steps n = 100001 the algorithms say:\n",
+      "trapezoid:\t\t 0.33333333334999976\n",
+      "Simpson:\t\t 0.3333300000666658\n",
+      "scipy.integrate.trapz:\t 0.33333333334999965\n",
+      "scipy.integrate.simps:\t 0.3333333333333335\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"For function f(x) = x^2\")\n",
+    "print(\"for boundaries a =\", a, \", b =\", b, \"and steps n =\", n, \"the algorithms say:\")\n",
+    "print(\"trapezoid:\\t\\t\", trapz(yk, h))\n",
+    "print(\"Simpson:\\t\\t\", simps(yk, h))\n",
+    "print(\"scipy.integrate.trapz:\\t\", scipy.integrate.trapz(yk, xk))\n",
+    "print(\"scipy.integrate.simps:\\t\", scipy.integrate.simps(yk, xk))"
    ]
   },
   {
@@ -291,7 +326,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python 3",
    "language": "python",
    "name": "python3"
   },