Secant's Method.ipynb

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   "source": [
    "import math"
   ]
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   "source": [
    "### Secant's Method"
   ]
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   "source": [
    "def swap(a, b):\n",
    "    a = a + b\n",
    "    b = a - b\n",
    "    a = a - b\n",
    "    return a, b"
   ]
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   "source": [
    "def secant(func, a, b, M, delta, epsilon):\n",
    "    f_a = func(a)\n",
    "    f_b = func(b)\n",
    "    for k in range(2, M+1):\n",
    "        if abs(f_a) > abs(f_b):\n",
    "            f_a, f_b = swap(f_a, f_b)\n",
    "            a, b = swap(a, b)\n",
    "        s = (a - b) / (f_a - f_b)\n",
    "        b = a\n",
    "        f_b = f_a\n",
    "        a = a - s*f_a\n",
    "        f_a = func(a)\n",
    "\n",
    "        if abs(f_a) < epsilon or abs(a-b) < delta:\n",
    "            print(\"found a:\", a)\n",
    "            print(\"func(a) =\", f_a)\n",
    "            print(\"Iteration: \", k-1)\n",
    "            return\n",
    "            break\n",
    "    print(\"found a:\", a)\n",
    "    print(\"func(a) =\", f_a)\n",
    "    print(\"Iteration: \", M)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sample function\n",
    "def f1(x):\n",
    "    return math.sin(x/2)-1"
   ]
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   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
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     "text": [
      "found a: 3.132984300166466\n",
      "func(a) = -9.262954282163172e-06\n",
      "Iteration:  11\n"
     ]
    }
   ],
   "source": [
    "secant(f1, 0, 1, 1000, 10**-5, 10**-5)"
   ]
  }
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