##// END OF EJS Templates
use better integration boundaries...
Andreas Amann -
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@@ -37,7 +37,7 b''
37 "cell_type": "code",
37 "cell_type": "code",
38 "execution_count": 2,
38 "execution_count": 2,
39 "metadata": {
39 "metadata": {
40 "collapsed": true
40 "collapsed": false
41 },
41 },
42 "outputs": [],
42 "outputs": [],
43 "source": [
43 "source": [
@@ -63,9 +63,10 b''
63 },
63 },
64 "outputs": [],
64 "outputs": [],
65 "source": [
65 "source": [
66 "a, b = 1, 9\n",
66 "a, b = 1, 8 # the left and right boundaries\n",
67 "xint = x[np.logical_and(x>=a, x<=b)][::30]\n",
67 "N = 5 # the number of points\n",
68 "yint = y[np.logical_and(x>=a, x<=b)][::30]"
68 "xint = np.linspace(a, b, N)\n",
69 "yint = f(xint)"
69 ]
70 ]
70 },
71 },
71 {
72 {
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329 ],
335 ],
330 "text/plain": [
336 "text/plain": [
331 "<matplotlib.figure.Figure at 0x107d67b90>"
337 "<matplotlib.figure.Figure at 0x7f47175e3898>"
332 ]
338 ]
333 },
339 },
334 "metadata": {},
340 "metadata": {},
@@ -337,7 +343,7 b''
337 ],
343 ],
338 "source": [
344 "source": [
339 "plt.plot(x, y, lw=2)\n",
345 "plt.plot(x, y, lw=2)\n",
340 "plt.axis([0, 10, 0, 140])\n",
346 "plt.axis([0, 9, 0, 140])\n",
341 "plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n",
347 "plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n",
342 "plt.text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);"
348 "plt.text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);"
343 ]
349 ]
@@ -360,21 +366,39 b''
360 "name": "stdout",
366 "name": "stdout",
361 "output_type": "stream",
367 "output_type": "stream",
362 "text": [
368 "text": [
363 "The integral is: 680.0 +/- 7.54951656745e-12\n",
369 "The integral is: 565.2499999999999 +/- 6.275535646693696e-12\n",
364 "The trapezoid approximation with 6 points is: 621.286411141\n"
370 "The trapezoid approximation with 5 points is: 559.890625\n"
365 ]
371 ]
366 }
372 }
367 ],
373 ],
368 "source": [
374 "source": [
369 "from __future__ import print_function\n",
375 "from __future__ import print_function\n",
370 "from scipy.integrate import quad, trapz\n",
376 "from scipy.integrate import quad\n",
371 "integral, error = quad(f, 1, 9)\n",
377 "integral, error = quad(f, a, b)\n",
378 "integral_trapezoid = sum( (xint[1:] - xint[:-1]) * (yint[1:] + yint[:-1]) ) / 2\n",
372 "print(\"The integral is:\", integral, \"+/-\", error)\n",
379 "print(\"The integral is:\", integral, \"+/-\", error)\n",
373 "print(\"The trapezoid approximation with\", len(xint), \"points is:\", trapz(yint, xint))"
380 "print(\"The trapezoid approximation with\", len(xint), \"points is:\", integral_trapezoid)"
374 ]
381 ]
375 }
382 }
376 ],
383 ],
377 "metadata": {},
384 "metadata": {
385 "kernelspec": {
386 "display_name": "Python 3",
387 "name": "python3"
388 },
389 "language_info": {
390 "codemirror_mode": {
391 "name": "ipython",
392 "version": 3
393 },
394 "file_extension": ".py",
395 "mimetype": "text/x-python",
396 "name": "python",
397 "nbconvert_exporter": "python",
398 "pygments_lexer": "ipython3",
399 "version": "3.4.2"
400 }
401 },
378 "nbformat": 4,
402 "nbformat": 4,
379 "nbformat_minor": 0
403 "nbformat_minor": 0
380 } No newline at end of file
404 }
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