<\/span><\/h4>\n\n\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport math\n\nrate = 1e-2\nx_in_gradient_descent = []\n\ndef diff(f, x):\n h = 1e-4\n return (f(x+h) - f(x-h)) \/ (2*h)\n\ndef gradientDescent(f, x):\n x_in_gradient_descent.append(x)\n if abs(rate * diff(f, x)) < 1e-8:\n return (x, f(x))\n next_x = x - rate * diff(f, x)\n return gradientDescent(f, next_x)\n\ndef f(x):\n return (x**2) * math.sin(x)\n\nstart = 0\nend = 8\n\nfig, ax = plt.subplots()\nax.set_xlim(start, end)\nax.plot(np.arange(start, end, 1e-4), [f(x) for x in np.arange(start, end, 1e-4)])\n\n\nmin_x, min_value = gradientDescent(f, 2.5)\n\ny_in_gradient_descent = [f(x) for x in x_in_gradient_descent]\nplt.plot(x_in_gradient_descent, y_in_gradient_descent, 'ro', markersize=1.5)\n\nplt.title('Gradient Descent at $x^{2} \\sin(x)$, start from $x=2.5$')\nplt.show()\n\nprint(min_x, min_value)<\/pre>\n\n\n\n![\"\"](\"https:\/\/stevenoh0908.pe.kr\/blog\/wp-content\/uploads\/2021\/10\/Gradient-Descent-at-x2sinx-start-from-x2.5.png\")
Gradient Descent\uc758 \uacb0\uacfc<\/figcaption><\/figure><\/div>\n\n\n\n \uc704 Gradient Descent\uc758 \uacb0\uacfc\ub85c $x \\approx 5.087$\uc5d0\uc11c $-24.08$\uc758 \uadf9\uc19f\uac12\uc744 \uac00\uc9d0\uc744 \ud655\uc778\ud560 \uc218 \uc788\uc5c8\ub2e4.<\/p>\n\n\n\n
<\/span>$f(x, y) = x^{4} + y^{4} – 4xy$\uc758 \uadf9\uc18c\uac12 \ucc3e\uae30 by Gradient Descent<\/span><\/h4>\n\n\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\n\nrate = 1e-3\ncords = []\n\n#\uc774\ubcc0\uc218 \ud568\uc218\uc758 \uac01 \ud3b8\ubbf8\ubd84\uc758 \uc218\uce58 \ubbf8\ubd84 \uacc4\uc0b0\ndef partial(f, var, x, y):\n h = 1e-4\n if var == 'x':\n return (f(x+h, y) - f(x-h, y)) \/ (2*h)\n elif var == 'y':\n return (f(x, y+h) - f(x, y-h)) \/ (2*h)\n pass\n\n#\uc774\ubcc0\uc218 \ud568\uc218\uc758 Gradient \ubca1\ud130 \uacc4\uc0b0\ndef gradient(f, x, y):\n return (partial(f, 'x', x, y), partial(f, 'y', x, y))\n\ndef gradientDescent(f, x, y):\n cords.append((x, y))\n if abs((rate * gradient(f, x, y)[0])) < 1e-4 and abs((rate * gradient(f, x, y)[1])) < 1e-4:\n return x, y, f(x, y)\n if not abs(rate * gradient(f, x, y)[0]) < 1e-4:\n nx = x - rate * gradient(f, x, y)[0]\n pass\n else:\n nx = x\n pass\n if not abs(rate * gradient(f, x, y)[1]) < 1e-4:\n ny = y - rate * gradient(f, x, y)[1]\n pass\n else:\n ny = y\n pass\n return gradientDescent(f, nx, ny)\n\ndef f(x, y):\n return x**4 + y**4 - 4*x*y\n\n# \uadf8\ub798\ud504 \uadf8\ub9ac\uae30\ndiv = 500\nx = np.linspace(-5, 5, div)\ny = np.linspace(-5, 5, div)\nz = np.zeros((len(x), len(y)))\nfor i in range(div):\n for j in range(div):\n z[j, i] = f(x[i], y[j])\n pass\n pass\n\nxx, yy = np.meshgrid(x, y)\nplt.figure(1, figsize = (10, 10))\nax = plt.subplot(111, projection='3d')\n\nax.plot_surface(xx, yy, z, alpha=0.3, color='blue', edgecolor='gray')\n\n# Gradient Descent from (start_x, start_y)\nstart_x = 4\nstart_y = 4\n\nmin_x, min_y, min_f = gradientDescent(f, start_x, start_y)\n\nprint(min_x, min_y, min_f)\nax.plot([x for x, y in cords], [y for x, y in cords], [f(x, y) for x, y in cords], 'ro', markersize=1.5)\n\nplt.title('Gradient Descent at $x^4 + y^4 - 4xy$ start from (4,4)', pad=30)\nplt.show()<\/pre>\n\n\n\n![\"\"](\"https:\/\/stevenoh0908.pe.kr\/blog\/wp-content\/uploads\/2021\/10\/Gradient-Descent-at-x^4y^4-4xy-start-from-44.png\")
Gradient Descent\uc758 \uacb0\uacfc<\/figcaption><\/figure><\/div>\n\n\n\n \uc704 Gradient Descent\uc758 \uacb0\uacfc\ub85c $(x, y) \\approx (1.012, 1.012)$\uc5d0\uc11c $-1.999$\uc758 \uadf9\uc19f\uac12\uc744 \uac00\uc9d0\uc744 \ud655\uc778\ud560 \uc218 \uc788\uc5c8\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"
\ub9c8\uce68\ub0b4 \uc5b4\uc81c \uc800\ub141\uc5d0 \ube44\ub358 \uc2dc\uac04 \ub3d9\uc548\uc5d0 Gradient Descent\ub97c \uad6c\ud604\ud560 \uc218 \uc788\uac8c \ub418\uc5c8\ub2e4. \uadfc \uba87 \uc8fc \ub3d9\uc548 \ub300\ud559\uc758 \uc218\ud559 \uac15\uc88c\uc5d0\uc11c \ub2e4\ubcc0\uc218\ud568\uc218\uc758 Gradient\uc640 \ud3b8\ubbf8\ubd84\uc758 \uac1c\ub150, \uc608\uc804\uc5d0 Machine Learning \uac15\uc88c\uc5d0\uc11c \uc8fc\uc6cc \ub4e4\uc5c8\ub358 Gradient Descent\uc5d0 \ub300\ud55c \uac1c\ub150, \uadf8\ub9ac\uace0 \uc218\uce58 \ubbf8\ubd84\uc5d0 \uad00\ud55c \uba87 \uac00\uc9c0 \uac80\uc0c9 \uc815\ubcf4\ub97c \ud65c\uc6a9\ud588\ub2e4. Python\uc758 matplotlib\uc640 numpy\ub97c \uc774\uc6a9\ud588\uace0, \ub2e4\uc74c\uacfc \uac19\uc740 \ucf54\ub4dc\ub4e4\ub85c \uc544\ub798\uc758 \uc774\ubbf8\uc9c0\uc640 \uac19\uc740 \uacb0\uacfc\ub97c \uc5bb\uc744 \uc218 \uc788\uc5c8\ub2e4. […]<\/a><\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0","_share_on_mastodon_status":"## [%title%](%permalink%)\r\n\r\n%excerpt%"},"categories":[45],"tags":[],"series":[],"class_list":["post-2942","post","type-post","status-publish","format-standard","hentry","category-chalkboard"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t