{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "## Exercice:\n", "\n", "Sans utiliser de boucles :\n", "\n", " - Créer une matrice (5x6) de flottants aléatoire entre -1.0 et 1.0\n", " - Remplacer une colonne sur deux par sa valeur moins le double de la colonne suivante\n", " - Remplacer les valeurs négatives par 0 en utilisant un masque (indice conditionnel)\n", " - Calculer l'approximation de $\\pi$ avec la formule de Wallis: \n", " $$ \\pi = 2\\prod_{i=1}^{\\infty} \\frac{4i^2}{4i^2-1}$$ \n", " On peut utiliser la méthode prod() sur des vecteurs.\n", " - Même chose avec l'approximation du logarithme (pour x petit): \n", " $$ log(1+x) = \\sum_{i=1}^{\\infty} \\frac{(-1)^{i+1}x^i}{i}$$\n", " On peut utiliser la méthode sum() sur des vecteurs.\n", " Tracer la courbe de l'écart à la valeur donnée par la bibliothèque math (math.log)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.random.random((5,6))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.32614209, 0.94507492, 0.15039077, 0.49899161, 0.22801319,\n", " 0.31686311],\n", " [0.2750166 , 0.49100694, 0.07496441, 0.59162757, 0.87771134,\n", " 0.74894487],\n", " [0.75644988, 0.28702302, 0.44136848, 0.63288267, 0.13215086,\n", " 0.41129515],\n", " [0.64837241, 0.26883023, 0.41553097, 0.15214247, 0.54815496,\n", " 0.8370513 ],\n", " [0.37832411, 0.08208008, 0.69275366, 0.96025715, 0.81522655,\n", " 0.35468042]])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-1.56400774 0.94507492 -0.84759246 0.49899161 -0.40571304 0.31686311]\n", " [-0.70699728 0.49100694 -1.10829073 0.59162757 -0.62017841 0.74894487]\n", " [ 0.18240384 0.28702302 -0.82439686 0.63288267 -0.69043943 0.41129515]\n", " [ 0.11071195 0.26883023 0.11124602 0.15214247 -1.12594764 0.8370513 ]\n", " [ 0.21416396 0.08208008 -1.22776064 0.96025715 0.10586571 0.35468042]]\n" ] } ], "source": [ "a[:,::2] = a[:,::2] - 2*a[:,1::2]\n", "print(a)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0. 0.94507492 0. 0.49899161 0. 0.31686311]\n", " [0. 0.49100694 0. 0.59162757 0. 0.74894487]\n", " [0.18240384 0.28702302 0. 0.63288267 0. 0.41129515]\n", " [0.11071195 0.26883023 0.11124602 0.15214247 0. 0.8370513 ]\n", " [0.21416396 0.08208008 0. 0.96025715 0.10586571 0.35468042]]\n" ] } ], "source": [ "a[a<0] = 0\n", "print(a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Calculer l'approximation de $\\pi$ avec la formule de Wallis: \n", " $$ \\pi = 2\\prod_{i=1}^{\\infty} \\frac{4i^2}{4i^2-1}$$ \n", " On peut utiliser la méthode prod() sur des vecteurs.\n", "- Même chose avec l'approximation du logarithme (pour x petit): \n", "\n", " $$ \\log(1+x) = \\sum_{i=1}^{\\infty} \\frac{(-1)^{i+1}x^i}{i} $$\n", " \n", " On peut utiliser la méthode sum() sur des vecteurs.\n", " Tracer la courbe de l'écart à la valeur donnée par la bibliothèque math (math.log)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14\n", " 15 16 17 18 19 20 21 22 23 24 25 26 27 28\n", " 29 30 31 32 33 34 35 36 37 38 39 40 41 42\n", " 43 44 45 46 47 48 49 50 51 52 53 54 55 56\n", " 57 58 59 60 61 62 63 64 65 66 67 68 69 70\n", " 71 72 73 74 75 76 77 78 79 80 81 82 83 84\n", " 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n", " 99 100 101 102 103 104 105 106 107 108 109 110 111 112\n", " 113 114 115 116 117 118 119 120 121 122 123 124 125 126\n", " 127 128 129 130 131 132 133 134 135 136 137 138 139 140\n", " 141 142 143 144 145 146 147 148 149 150 151 152 153 154\n", " 155 156 157 158 159 160 161 162 163 164 165 166 167 168\n", " 169 170 171 172 173 174 175 176 177 178 179 180 181 182\n", " 183 184 185 186 187 188 189 190 191 192 193 194 195 196\n", " 197 198 199 200 201 202 203 204 205 206 207 208 209 210\n", " 211 212 213 214 215 216 217 218 219 220 221 222 223 224\n", " 225 226 227 228 229 230 231 232 233 234 235 236 237 238\n", " 239 240 241 242 243 244 245 246 247 248 249 250 251 252\n", " 253 254 255 256 257 258 259 260 261 262 263 264 265 266\n", " 267 268 269 270 271 272 273 274 275 276 277 278 279 280\n", " 281 282 283 284 285 286 287 288 289 290 291 292 293 294\n", " 295 296 297 298 299 300 301 302 303 304 305 306 307 308\n", " 309 310 311 312 313 314 315 316 317 318 319 320 321 322\n", " 323 324 325 326 327 328 329 330 331 332 333 334 335 336\n", " 337 338 339 340 341 342 343 344 345 346 347 348 349 350\n", " 351 352 353 354 355 356 357 358 359 360 361 362 363 364\n", " 365 366 367 368 369 370 371 372 373 374 375 376 377 378\n", " 379 380 381 382 383 384 385 386 387 388 389 390 391 392\n", " 393 394 395 396 397 398 399 400 401 402 403 404 405 406\n", " 407 408 409 410 411 412 413 414 415 416 417 418 419 420\n", " 421 422 423 424 425 426 427 428 429 430 431 432 433 434\n", " 435 436 437 438 439 440 441 442 443 444 445 446 447 448\n", " 449 450 451 452 453 454 455 456 457 458 459 460 461 462\n", " 463 464 465 466 467 468 469 470 471 472 473 474 475 476\n", " 477 478 479 480 481 482 483 484 485 486 487 488 489 490\n", " 491 492 493 494 495 496 497 498 499 500 501 502 503 504\n", " 505 506 507 508 509 510 511 512 513 514 515 516 517 518\n", " 519 520 521 522 523 524 525 526 527 528 529 530 531 532\n", " 533 534 535 536 537 538 539 540 541 542 543 544 545 546\n", " 547 548 549 550 551 552 553 554 555 556 557 558 559 560\n", " 561 562 563 564 565 566 567 568 569 570 571 572 573 574\n", " 575 576 577 578 579 580 581 582 583 584 585 586 587 588\n", " 589 590 591 592 593 594 595 596 597 598 599 600 601 602\n", " 603 604 605 606 607 608 609 610 611 612 613 614 615 616\n", " 617 618 619 620 621 622 623 624 625 626 627 628 629 630\n", " 631 632 633 634 635 636 637 638 639 640 641 642 643 644\n", " 645 646 647 648 649 650 651 652 653 654 655 656 657 658\n", " 659 660 661 662 663 664 665 666 667 668 669 670 671 672\n", " 673 674 675 676 677 678 679 680 681 682 683 684 685 686\n", " 687 688 689 690 691 692 693 694 695 696 697 698 699 700\n", " 701 702 703 704 705 706 707 708 709 710 711 712 713 714\n", " 715 716 717 718 719 720 721 722 723 724 725 726 727 728\n", " 729 730 731 732 733 734 735 736 737 738 739 740 741 742\n", " 743 744 745 746 747 748 749 750 751 752 753 754 755 756\n", " 757 758 759 760 761 762 763 764 765 766 767 768 769 770\n", " 771 772 773 774 775 776 777 778 779 780 781 782 783 784\n", " 785 786 787 788 789 790 791 792 793 794 795 796 797 798\n", " 799 800 801 802 803 804 805 806 807 808 809 810 811 812\n", " 813 814 815 816 817 818 819 820 821 822 823 824 825 826\n", " 827 828 829 830 831 832 833 834 835 836 837 838 839 840\n", " 841 842 843 844 845 846 847 848 849 850 851 852 853 854\n", " 855 856 857 858 859 860 861 862 863 864 865 866 867 868\n", " 869 870 871 872 873 874 875 876 877 878 879 880 881 882\n", " 883 884 885 886 887 888 889 890 891 892 893 894 895 896\n", " 897 898 899 900 901 902 903 904 905 906 907 908 909 910\n", " 911 912 913 914 915 916 917 918 919 920 921 922 923 924\n", " 925 926 927 928 929 930 931 932 933 934 935 936 937 938\n", " 939 940 941 942 943 944 945 946 947 948 949 950 951 952\n", " 953 954 955 956 957 958 959 960 961 962 963 964 965 966\n", " 967 968 969 970 971 972 973 974 975 976 977 978 979 980\n", " 981 982 983 984 985 986 987 988 989 990 991 992 993 994\n", " 995 996 997 998 999 1000]\n", "[1.33333333 1.06666667 1.02857143 1.01587302 1.01010101 1.00699301\n", " 1.00512821 1.00392157 1.00309598 1.00250627 1.00207039 1.00173913\n", " 1.00148148 1.00127714 1.00111235 1.00097752 1.0008658 1.0007722\n", " 1.000693 1.00062539 1.00056721 1.0005168 1.00047281 1.00043422\n", " 1.00040016 1.00036996 1.00034305 1.00031898 1.00029735 1.00027785]\n", "3.140807746030402\n" ] } ], "source": [ "n = 1000\n", "i = np.arange(n)+1\n", "print(i)\n", "b = 4*i**2\n", "v = (b/(b-1))\n", "print(v[:30])\n", "print(2*v.prod())" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "# pour notebook\n", "%pylab inline" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pylab import plot\n", "from math import pi\n", "plot((2*v.cumprod())[100:]-pi)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.551115123125783e-17" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from math import log\n", "x = 0.5\n", "i = np.arange(1000)+1\n", "base = ((-1)**(i+1)*x**i/i)\n", "approx = base.sum()\n", "log(1+x)-approx" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#print(base)\n", "plot(base.cumsum()[:100]-log(1+x))" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(base.cumsum()-log(1+x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Avec des fonctions" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.140807746030402 3.141592653589793 -0.0007849075593910904\n" ] } ], "source": [ "import numpy\n", "from math import pi\n", "\n", "def wallis(n):\n", " i = numpy.arange(n)+1 \n", " b = (4*i*i)\n", " c = b/(b-1)\n", " return c\n", "\n", "#return 2*c.prod()\n", "\n", "approx = 2*wallis(1000).prod()\n", "print(approx,pi,approx-pi)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/envs/snorkel/lib/python3.6/site-packages/IPython/core/magics/pylab.py:160: UserWarning: pylab import has clobbered these variables: ['pi', 'log']\n", "`%matplotlib` prevents importing * from pylab and numpy\n", " \"\\n`%matplotlib` prevents importing * from pylab and numpy\"\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pylab.plot(2*wallis(1000).cumprod()[:1000]-pi)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.18232155679395462\n" ] } ], "source": [ "def log_app(x,n):\n", " i = np.arange(n)+1\n", " v = (-1)**(i+1)*x**i/i\n", " return v.sum()\n", "\n", "print(log_app(0.2,1000))" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+o0OTeEt0M7PRnJSapCuf80IHM7MyTkpN0tXha0pmZuWclJqkqyPHPk/fmZkdxkmpSTo9fWdmNoqTUpN0deTY75GSmdlhnJSaZLJHSmZmozgpNUlXh5OSmVk5J6Um6ezIsf/ACCMj/vKymVmRk1KTFLdEHxgaaXJPzMxah5NSk3j7CjOz0ZyUmsRJycxsNCelJunMF3efHapR08xs4nBSapJDW6L7mpKZWZGTUpMc6fTdB25by/+878lj2SUzs6ZzUmqS4uq7sSalnzz/Ev/0b9uPZZfMzJquLklJ0lJJGyX1Srou4/NJku5Kn6+VtKDks+tT+UZJF9WKmbZIXytpU4qZr9aGpF+WtF7S4+n5/JJY309tPJYeJ9fjfIzFoem72klpaHiEXfsO8NT2PQx6CbmZHcfGnZQk5YBbgIuBRcDlkhaVVbsK2BURpwOrgJvSsYsobFt+FrAU+KykXI2YNwGrImIhsCvFrtgGsAP4tYj4BWAFcGdZ366IiMXpsW2cp2PMiiOlsWxf0b9vEIADw0Hvtj3HtF9mZs1Uj5HSEqA3Ip6OiEFgNbCsrM4y4I70+h7gAklK5asjYiAingF6U7zMmOmY81MMUsxLqrUREY9GxJZUvgHolDSpDj/3uBzJNaWdewYPvn5y68vHrE9mZs1Wj6Q0F9hc8r4vlWXWiYgh4CVgZpVjK5XPBF5MMcrbqtRGqd8AHo2IgZKyL6apu4+npDeKpJWSeiT1bN9en+s6RzJ917/XScnMJoZ6JKWsX+TlN3SrVKde5TX7IeksClN6Hy75/Io0rfeO9PhARgwi4taI6I6I7tmzZ2dVOWKd+cKpH8tIaceeQg6d0tnOE05KZnYcq0dS6gPml7yfB2ypVEdSO3AS0F/l2ErlO4BpKUZ5W5XaQNI84JvAlRHxVDFoRDyfnncDX6UwbdgQ+VwbbRrbSKk4fff218/iya0vE+GbuJrZ8akeSWkdsDCtistTWLiwpqzOGgqLDAAuBR6Mwm/WNcDytHLuNGAh8HClmOmYh1IMUsx7q7UhaRrwLeD6iPhBsUOS2iXNSq87gPcCP6nD+RgTSWPevmLn3gHa28R5r5vBrn0HeOHlgZrHmJm9GrXXrlJdRAxJuga4H8gBt0fEBkk3AD0RsQa4DbhTUi+F0cvydOwGSXcDTwBDwNURMQyQFTM1eS2wWtKNwKMpNpXaAK4BTgc+LunjqexCYC9wf0pIOeC7wOfHez6ORNcYN/rbuWeQGSfkWfTak4DCdaXXnNR5rLtnZtZw405KABFxH3BfWdkfl7zeD1xW4dhPAZ8aS8xU/jQZ02yV2oiIG4EbK3T9nArlDdE5xi3Rd6SkdMacKQA8sfVl3n1Gw75SZWbWML6jQxONdUv0nXsHmHXiJKZ2djBvepdX4JnZcctJqYnGfE1pzyAzT8wDcOacqV6BZ2bHLSelJursyI1x9d0AM08ofN930ZypPLtj75iOMzN7tXFSaqKufK7mbYb2Hxhm7+DwYSOlkYCNL+xuRBfNzBrKSamJxjJ9tzPdzWFWSkqL5kwFfGcHMzs+OSk1UVdHjn01puF2prs5FKfv5k3v4sRJ7U5KZnZcclJqos4xTN8V7+ZQnL5raxNnvGaKk5KZHZeclJqoawwLHYr3vZt14qEbm585ZypPbt3NyIhvN2RmxxcnpSYqXlOqdi+74jWl4kgJYNFrp7JnYIi+Xa8c8z6amTWSk1ITdeVzjAQMDlfeTXbnngG6OnJMzh+6+caZabGDv69kZscbJ6UmKu6ptH+wWlIq3GKo1BtOmUKbvALPzI4/TkpNVNwSvdqy8B17Bw8uBy89bsGsE8aclIaGR/i7f93iL9yaWctzUmqisWyJvnPPADNPHL17+5lzpvLkv48tKX39kT5+52uP8l/vesyLI8yspTkpNVHnGLZE37lnkJll03dQ+BLt5v5XeHn/gZrtfPXhzUzO5/jOhn/nL/5h49F32MzsGHNSaqJD03dDmZ9HBP17BzNHSsU7O/x0a/XbDT259WX+dfOL/P6Fb+DyJafy2e8/xdfX942z52Zmx0ZdkpKkpZI2SuqVdF3G55Mk3ZU+XytpQcln16fyjZIuqhUz7Ua7VtKmFDNf7zYa5eD0XYWFDrsHhhgcHhl1TQkOrcCrdV1p9cPPkc+18etvmssNy87iba+fyXXf+DHrnu0fZ+/NzOpv3ElJUg64BbgYWARcLmlRWbWrgF0RcTqwCrgpHbuIwg6xZwFLgc9KytWIeROwKiIWArtS7Hq30RC1rimV382h1ClTJzF9ckfVpLT/wDDffPR5lp79GqafkKcj18bnrjiH+dMn8+E71/Pczn01+xgRfPvxrXzmwU2se7afA1WWr5uZjVc9dp5dAvSmHWGRtBpYRmGL86JlwJ+k1/cAn5GkVL46IgaAZ9JW5sVdZUfFlPQkcD7wm6nOHSnu5+rVRlm/j6mufOFvgspJ6fD73pWSlO7sUDkp3ff4Vl7eP8TyJfMPlp00uYPbPngul9zyA/7THev4xn9+G1M7OzKPX/+zXdz4rSd49LkXD5adkM+x5LQZvP30Wbz99Fmc8ZopFE7zIRHBjj2D9O3aR9+uV9jy4ivk2sSUznamdnYwpbODKZ3t6dHBiZPaGRoZYXBohMHhEQYOFJ4Hh0YYGBpmaDhoaxO5NpFTem4T7W2irU20SYxEEFFoO4CRCEZGoPAunTOEBMXuFt8f6nd65sgWgwjVrmR2HDhl6iSmTR79R3I91SMpzQU2l7zvA95SqU5EDEl6CZiZyn9Uduzc9Dor5kzgxYgYyqhfrzYapvPg95Syk9KOKiMlKEzhfWXtzxgeCXJto38xrn54MwtmTuatr5t5WPlps07gr37rHD5w21qu/sojfPGD59KeOzRofm7nPm76zk/51uNbOXnKJP7Xb/wi71l0Cg8/s5Mf9O7kB707eGjjk0Dh7uVvff0spna207frlYOJaGDIIyqz482Nl5zNb533c8e0jXokpaw/E8v/1KxUp1J51rRitfr1bGMUSSuBlQCnnnpqVpWjUrxLQ8WR0t7R970rdeacqew/MMIzO/Zy+sknHvZZ77Y9PPxsP9cuPWPUSAbgra+fyY2XnM1133icT/79E/zpsrN5ad8BPvPQJu74l5+RaxO/e8FCVr7zdZwwqdDPpWfPYenZcwDY8uIr/KB3Bz/o3cG/PLWTweER5k+fzM+fMoXzzziZedMnM296F/OmT+a10zoJYPf+IV5+5QC79w+xe/+h5z0Dw7S3iXx7G/n2Nial53yu8NyRa2N4JBiOYGQkGBopPA9HMDwSjETQJiEVxixtEm0HR0SF0VBhFBQlo6FCWRCHjXQOjaLGxgvsbSI567VTj3kb9UhKfcD8kvfzgC0V6vRJagdOAvprHJtVvgOYJqk9jZZK69erjVEi4lbgVoDu7u66/R4a6zWl6RWGy2fOmQIUFjuUJ6W71j1He5u49Jx5FdtfvuRUnt6xl1v/6Wle3j/EQxu38dIrB7j0zfP4/QvfwGtO6qx47GundXFZ93wu655fsU65qZ0dzJ3WNeb6Zjbx1GP13TpgYVoVl6ewqGBNWZ01wIr0+lLgwSjchXQNsDytnDsNWAg8XClmOuahFIMU8956tlGH8zFmk9rTNaUK03c79wwwtbOdfHv2f6aFJ0+hI6dR98AbGBrm6488zy8vOoXZU7JHWUXXLj2D95x5Ct989HnOeu1U/v53fok/v+yNVROSmdmxMu6RUrp+cw1wP5ADbo+IDZJuAHoiYg1wG3BnWmTQTyEBkOrdTWFxwRBwdUQMA2TFTE1eC6yWdCPwaIpNndtoiLY20dnRVnFPpcIthionlXx7G6+ffeKoxQ4PPPEC/XsHWb6k9lRjrk3ccsWb2PTCHs567dTMqT4zs0apx/QdEXEfcF9Z2R+XvN4PXFbh2E8BnxpLzFT+NIdWz5WW162NRqq2+2zhFkPVV7osmjOVHzy147Cy1Q9vZu60Lt5x+qwx9WFSe46z5540tg6bmR1DvqNDkxX3VMrSv3cwczl4qTPnTOWFlwfoT/su/WznXv5f7w7ef+582jJW5JmZtTInpSbrzFdOSjv3DNYcKZXf2eGudZtpE1zWXXmBg5lZq3JSarKujlzm95SGR4L+fdn3vStVugLvwPAIf7O+j3e/4WTmnORVbmb26uOk1GSVpu927Rskgsz73pWaeeIkTpk6iSe2vMyDP93G9t0DY1rgYGbWiuqy0MGOXlc+x56B0XcJP3jfuxrXlKAwhffE1pfZtW+QU6ZO4t1vmF33fpqZNYJHSk3W1ZHL/J7Swfve1RgpQSEpbdq2h3/8t+1cds78w24ZZGb2auKRUpN15XOZ31PakVbT1Zq+g0JSGk47yr7/3LHfYcHMrNX4T+omq3RNqThSmjGG6btFabHDOxbOYv6MyfXtoJlZA3mk1GSdFb48u3PPIG2CaV3Z20qUOm3Wifz6m+ZyxXle4GBmr25OSk1Wafpu594BZpwwaUxfgM21ib98/+Jj0T0zs4by9F2TdXXkODAco3Z03blncEzXk8zMjidOSk1W3L6ifLS0c2/tuzmYmR1vnJSarDOfvafSzj0DY/qOkpnZ8cRJqckOjpQGR0/feaRkZhONk1KTTc4YKe0/MMzugaGqeymZmR2PxpWUJM2Q9ICkTel5eoV6K1KdTZJWlJSfI+lxSb2SblbaYa5SXBXcnOr/WNKbq7UhabKkb0n6qaQNkv6spP4HJW2X9Fh6fGg85+JoZW2JXtyGYuYJHimZ2cQy3pHSdcD3ImIh8L30/jCSZgCfAN5CYXO+T5Qkr88BKylsUb4QWFoj7sUldVem42u18RcRcQbwJuDtki4u6d5dEbE4Pb4wrjNxlDqLSanku0oH73vnkZKZTTDjTUrLgDvS6zuASzLqXAQ8EBH9EbELeABYKmkOMDUifhgRAXy55PhKcZcBX46CHwHTUpzMNiJiX0Q8BBARg8AjQEttNNR1cPru0E1Zd+wd+33vzMyOJ+NNSqdExFaA9HxyRp25wOaS932pbG56XV5eLW61WFnlB0maBvwahZFX0W+kacB7JDXlpnEHp+9KFjocukO4k5KZTSw17+gg6bvAazI++sMxtpF1S4KoUl73WJLaga8BN0fE06n474CvRcSApI9QGJGdn9motJLCdCGnnlrfW/lkXVM6dIdwT9+Z2cRSc6QUEe+JiLMzHvcCL6TpM9LztowQfUDpKGQesCWVz8sop0rcarGyyotuBTZFxKdLfq6dETGQ3n4eOKfKObg1Irojonv27PruVdSZL/wnKF/oMKm9jRPS1J6Z2UQx3um7NUBxNd0K4N6MOvcDF0qanhYfXAjcn6bldks6L626u7Lk+Epx1wBXplV45wEvpTiZbQBIuhE4Cfi90k4Vk17yPuDJozoD43Toe0qHktKOPYPMOnESaTGimdmEMd4bsv4ZcLekq4DngMsAJHUDH4mID0VEv6RPAuvSMTdERH96/VHgS0AX8O30qBgXuA/4FaAX2Af8NkClNiTNozDN+FPgkfRL/jNppd1/kfQ+YAjoBz44znNxVDqzpu/2DniRg5lNSONKShGxE7ggo7wH+FDJ+9uB2yvUO/sI4gZwdYW+jGojIvrIvt5ERFwPXJ/1WSN15NroyKnsmpJvxmpmE5Pv6NACyrdE37lnwIsczGxCclJqAaV7KkUEO3yHcDOboJyUWkBXye6zewaGGBwaYZbvEG5mE5CTUgvo7MgdvKZ06BZDHimZ2cTjpNQCSqfvdu71F2fNbOJyUmoBpQsddvgWQ2Y2gTkptYCukum7g9tWePrOzCYgJ6UW0JkvvaZUmL6b4ZGSmU1ATkotoKsjd/A2Qzv2DDKls51J7b7vnZlNPE5KLWBy6Uhp76C3QTezCctJqQV0dRw+fedFDmY2UTkptYDOjhz7D4wwMhLs3OO7OZjZxOWk1AKKW6LvHxpOdwj39J2ZTUxOSi2guKfSnoEh+vcOMsvTd2Y2QTkptYBiUvr3l/YzEr6bg5lNXONKSpJmSHpA0qb0PL1CvRWpziZJK0rKz5H0uKReSTenHWgrxk07zt6c6v9Y0pvH0Mb3JW2U9Fh6nJzKJ0m6K8VaK2nBeM7FeHTse0INAAAHwUlEQVSm6bu+Xa8A/uKsmU1c4x0pXQd8LyIWAt9L7w8jaQbwCeAtwBLgEyXJ63PASmBheiytEffikror0/G12gC4IiIWp8e2VHYVsCsiTgdWATeN50SMR3Gk9HxKSv7irJlNVONNSsuAO9LrO4BLMupcBDwQEf0RsQt4AFgqaQ4wNSJ+mHaU/XLJ8ZXiLgO+HAU/AqalOJltHEHf7wEuKI7UGq2YlPp27QPw95TMbMIab1I6JSK2AqTnkzPqzAU2l7zvS2Vz0+vy8mpxq8XKKi/6Ypq6+3hJ4jl4TEQMAS8BM2v9wMdCV77wn+Hg9J1HSmY2QbXXqiDpu8BrMj76wzG2kTX6iCrl9Y51RUQ8L2kK8HXgAxRGZWNuX9JKCtOFnHrqqTW6eOS6Ogr/Gfp2vUKbYNpkJyUzm5hqjpQi4j0RcXbG417ghTR9RnrelhGiD5hf8n4esCWVz8sop0rcarGyyomI59PzbuCrFK45HRZLUjtwEtBf4RzcGhHdEdE9e/bsrCrjUvye0uZd+5hxQp5cW1NmEc3Mmm6803drgOJKtxXAvRl17gculDQ9LT64ELg/TcvtlnRemlK7suT4SnHXAFemVXjnAS+lOJltSGqXNAtAUgfwXuAnGW1cCjyYrm01XPGa0r7BYWZ6G3Qzm8BqTt/V8GfA3ZKuAp4DLgOQ1A18JCI+FBH9kj4JrEvH3BARxRHJR4EvAV3At9OjYlzgPuBXgF5gH/DbAJXakHQCheTUAeSA7wKfT3VuA+6U1EthhLR8nOfiqBWTEng5uJlNbGrS4OBVq7u7O3p6euoac2BomDf80XcA+LU3vpb/e/mb6hrfzKzZJK2PiO5a9XxHhxaQz7VRvIzklXdmNpE5KbUASQen8GZ5+s7MJjAnpRZRXIE3wwsdzGwCc1JqEZ1ppOSFDmY2kTkptYjJeU/fmZk5KbWI4jUlf0/JzCYyJ6UW4ek7MzMnpZbRlc+Rb2/jxEnj/T6zmdmrl5NSi+jqyDHzhDxN2j3DzKwl+M/yFvGB836OC848pdndMDNrKielFvG202c1uwtmZk3n6TszM2sZTkpmZtYynJTMzKxlOCmZmVnLcFIyM7OW4aRkZmYtw0nJzMxahpOSmZm1DEVEs/vwqiJpO/Czozx8FrCjjt2pJ/ft6LhvR8d9Ozqv5r79XETMrhXESamBJPVERHez+5HFfTs67tvRcd+OzkTom6fvzMysZTgpmZlZy3BSaqxbm92BKty3o+O+HR337egc933zNSUzM2sZHimZmVnLcFJqEElLJW2U1Cvpumb3p5SkZyU9LukxST1N7svtkrZJ+klJ2QxJD0jalJ6nt1Df/kTS8+ncPSbpV5rUt/mSHpL0pKQNkn43lTf93FXpW9PPnaROSQ9L+tfUtz9N5adJWpvO212S8i3Uty9JeqbkvC1udN9K+piT9Kikv0/vx33enJQaQFIOuAW4GFgEXC5pUXN7Ncq7I2JxCyw3/RKwtKzsOuB7EbEQ+F563wxfYnTfAFalc7c4Iu5rcJ+KhoDfj4gzgfOAq9P/Y61w7ir1DZp/7gaA8yPijcBiYKmk84CbUt8WAruAq1qobwB/UHLeHmtC34p+F3iy5P24z5uTUmMsAXoj4umIGARWA8ua3KeWFBH/BPSXFS8D7kiv7wAuaWinkgp9awkRsTUiHkmvd1P4RTGXFjh3VfrWdFGwJ73tSI8AzgfuSeXNOm+V+tYSJM0DfhX4Qnov6nDenJQaYy6wueR9Hy3yjzIJ4B8krZe0stmdyXBKRGyFwi844OQm96fcNZJ+nKb3mjK1WErSAuBNwFpa7NyV9Q1a4NylKajHgG3AA8BTwIsRMZSqNO3fa3nfIqJ43j6VztsqSZOa0Tfg08B/B0bS+5nU4bw5KTWGMspa5i8e4O0R8WYK04tXS3pnszv0KvI54PUUple2Av+7mZ2RdCLwdeD3IuLlZvalXEbfWuLcRcRwRCwG5lGY1Tgzq1pje5UaLeubpLOB64EzgHOBGcC1je6XpPcC2yJifWlxRtUjPm9OSo3RB8wveT8P2NKkvowSEVvS8zbgmxT+YbaSFyTNAUjP25rcn4Mi4oX0i2ME+DxNPHeSOij80v9KRHwjFbfEucvqWyudu9SfF4HvU7juNU1Se/qo6f9eS/q2NE2HRkQMAF+kOeft7cD7JD1L4XLE+RRGTuM+b05KjbEOWJhWpuSB5cCaJvcJAEknSJpSfA1cCPyk+lENtwZYkV6vAO5tYl8OU/yFn/wHmnTu0nz+bcCTEfGXJR81/dxV6lsrnDtJsyVNS6+7gPdQuOb1EHBpqtas85bVt5+W/JEhCtdsGn7eIuL6iJgXEQso/D57MCKuoA7nzV+ebZC03PXTQA64PSI+1eQuASDpdRRGRwDtwFeb2TdJXwPeReGOwy8AnwD+FrgbOBV4DrgsIhq+4KBC395FYfopgGeBDxev4TS4b78E/DPwOIfm+P8HhWs3TT13Vfp2OU0+d5J+kcIF+RyFP9Lvjogb0r+L1RSmxx4FfiuNTFqhbw8CsylMlz0GfKRkQUTDSXoX8N8i4r31OG9OSmZm1jI8fWdmZi3DScnMzFqGk5KZmbUMJyUzM2sZTkpmZtYynJTMzKxlOCmZmVnLcFIyM7OW8f8BgWJdPX8q12IAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from math import log\n", "import pylab\n", "\n", "\n", "def all_app(x,n):\n", " i = np.arange(n)+1\n", " v = (-1)**(i+1)*x**i/i\n", " return v\n", "\n", "v = all_app(0.5,1000)\n", "pylab.plot(v.cumsum()[10:50]-log(1.5))" ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 1 }