{"id":1948,"date":"2023-07-24T08:20:22","date_gmt":"2023-07-24T08:20:22","guid":{"rendered":"https:\/\/statorials.org\/pl\/numpy-iloczyn-kropkowy\/"},"modified":"2023-07-24T08:20:22","modified_gmt":"2023-07-24T08:20:22","slug":"numpy-iloczyn-kropkowy","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/numpy-iloczyn-kropkowy\/","title":{"rendered":"Jak obliczy\u0107 iloczyn skalarny za pomoc\u0105 numpy"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bior\u0105c pod uwag\u0119 wektor <em>a<\/em> = [a <sub>1<\/sub> , a <sub>2<\/sub> , a <sub>3<\/sub> ] i wektor <em>b<\/em> = [b <sub>1<\/sub> , b <sub>2<\/sub> , b <sub>3<\/sub> ], <strong>iloczyn skalarny<\/strong> wektor\u00f3w, oznaczonych <strong>a \u00b7 b<\/strong> , jest dany wzorem:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab<\/strong> = za <sub>1<\/sub> * b <sub>1<\/sub> + za <sub>2<\/sub> * b <sub>2<\/sub> + za <sub>3<\/sub> * b <sub>3<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad, je\u015bli <em>a<\/em> = [2, 5, 6] i <em>b<\/em> = [4, 3, 2], to iloczyn skalarny <em>a<\/em> i <em>b<\/em> b\u0119dzie r\u00f3wny:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab =<\/strong> 2*4 + 5*3 + 6*2<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab =<\/strong> 8 + 15 + 12<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>odb =<\/strong> 35<\/span><\/p>\n<p> <span style=\"color: #000000;\">M\u00f3wi\u0105c najpro\u015bciej, iloczyn skalarny to suma iloczyn\u00f3w odpowiednich wpis\u00f3w w dw\u00f3ch wektorach.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W Pythonie mo\u017cesz u\u017cy\u0107 funkcji <strong>numpy.dot()<\/strong> , aby szybko obliczy\u0107 iloczyn skalarny mi\u0119dzy dwoma wektorami:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<\/span>\n<\/span>n.p. <span style=\"color: #3366ff;\">dowry<\/span> (a, b)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak w praktyce wykorzysta\u0107 t\u0119 funkcj\u0119.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: oblicz iloczyn skalarny mi\u0119dzy dwoma wektorami<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cywa\u0107 <strong>numpy.dot()<\/strong> do obliczania iloczynu skalarnego mi\u0119dzy dwoma wektorami:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#definevectors<\/span>\na = [7, 2, 2]\nb = [1, 4, 9]\n\n<span style=\"color: #008080;\">#calculate dot product between vectors<\/span>\nn.p. <span style=\"color: #3366ff;\">dowry<\/span> (a, b)\n\n33\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Oto jak obliczono t\u0119 warto\u015b\u0107:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>ab =<\/strong> 7*1 + 2*4 + 2*9<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>ab =<\/strong> 7 + 8 + 18<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>odb =<\/strong> 33<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: oblicz iloczyn skalarny mi\u0119dzy dwiema kolumnami<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cywa\u0107 <strong>numpy.dot()<\/strong> do obliczania iloczynu skalarnego mi\u0119dzy dwiema kolumnami w ramce DataFrame pandy:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import <span style=\"color: #000000;\">pandas <span style=\"color: #008000;\">as<\/span> pd<\/span>\nimport<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#createDataFrame<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">A<\/span> ': [4, 6, 7, 7, 9],\n                   ' <span style=\"color: #ff0000;\">B<\/span> ': [5, 7, 7, 2, 2],\n                   ' <span style=\"color: #ff0000;\">C<\/span> ': [11, 8, 9, 6, 1]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span>df\n\n\tA B C\n0 4 5 11\n1 6 7 8\n2 7 7 9\n3 7 2 6\n4 9 2 1\n\n<span style=\"color: #008080;\">#calculate dot product between column A and column C<\/span>\nn.p. <span style=\"color: #3366ff;\">dot<\/span> (df. <span style=\"color: #3366ff;\">A<\/span> , df. <span style=\"color: #3366ff;\">C<\/span> )\n\n206\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Oto jak obliczono t\u0119 warto\u015b\u0107:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>AC =<\/strong> 4*11 + 6*8 + 7*9 + 7*6 + 9*1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>AC =<\/strong> 44 + 48 + 63 + 42 + 9<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>A \u00b7 C =<\/strong> 206<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Uwaga:<\/strong> Pami\u0119taj, \u017ce Python zg\u0142osi b\u0142\u0105d, je\u015bli dwa wektory, dla kt\u00f3rych obliczasz iloczyn skalarny, maj\u0105 r\u00f3\u017cn\u0105 d\u0142ugo\u015b\u0107.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/pandy-dodaja-linie-do-ramki-danych\/\" target=\"_blank\" rel=\"noopener\">Jak doda\u0107 wiersze do ramki danych Pandas<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/dodaj-tablice-numpy-do-ramki-danych-pand\/\" target=\"_blank\" rel=\"noopener\">Jak doda\u0107 tablic\u0119 Numpy do ramki danych Pandas<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/\u0142ozysko-korelacyjne-pandy\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 korelacj\u0119 przesuwn\u0105 w pandach<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bior\u0105c pod uwag\u0119 wektor a = [a 1 , a 2 , a 3 ] i wektor b = [b 1 , b 2 , b 3 ], iloczyn skalarny wektor\u00f3w, oznaczonych a \u00b7 b , jest dany wzorem: ab = za 1 * b 1 + za 2 * b 2 + za 3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1948","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak obliczy\u0107 iloczyn skalarny za pomoc\u0105 NumPy - 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