{"id":30323,"date":"2025-09-26T17:06:27","date_gmt":"2025-09-26T14:06:27","guid":{"rendered":"https:\/\/fatihsoysal.com\/blog\/?p=30323"},"modified":"2025-09-26T17:28:04","modified_gmt":"2025-09-26T14:28:04","slug":"numpy-matris-carpimi-detayli-bir-inceleme","status":"publish","type":"post","link":"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/","title":{"rendered":"NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme"},"content":{"rendered":"

<\/p>\n

NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme<\/h2>\n

NumPy (Numerical Python), Python programlama dilinde bilimsel hesaplamalar i\u00e7in temel bir k\u00fct\u00fcphanedir. \u00d6zellikle \u00e7ok boyutlu diziler (ndarray) ve bu diziler \u00fczerinde y\u00fcksek performansl\u0131 matematiksel i\u015flemler i\u00e7in optimize edilmi\u015ftir. Veri bilimi, makine \u00f6\u011frenimi, m\u00fchendislik ve fizik gibi alanlarda matrisler ve vekt\u00f6rler temel yap\u0131 ta\u015flar\u0131 oldu\u011fundan, NumPy’nin matris i\u015flemleri, \u00f6zellikle matris \u00e7arp\u0131m\u0131 yetenekleri, b\u00fcy\u00fck \u00f6nem ta\u015f\u0131r. Bu makalede, NumPy’de matris \u00e7arp\u0131m\u0131n\u0131n farkl\u0131 y\u00f6ntemlerini, performans \u00f6zelliklerini ve yayg\u0131n kullan\u0131m senaryolar\u0131n\u0131 ayr\u0131nt\u0131l\u0131 olarak inceleyece\u011fiz.<\/p>\n

NumPy ve Matrislerin Temelleri<\/h3>\n

NumPy’nin kalbinde ndarray<\/code> nesnesi bulunur. Bu nesne, ayn\u0131 veri tipindeki \u00f6\u011felerden olu\u015fan, sabit boyutlu, \u00e7ok boyutlu bir dizidir. Matrisler, iki boyutlu ndarray<\/code>‘ler olarak temsil edilir.<\/p>\n

NumPy Dizisi (Matris) Olu\u015fturma<\/h4>\n

NumPy’de matris olu\u015fturman\u0131n bir\u00e7ok yolu vard\u0131r:<\/p>\n

* Do\u011frudan listelerden:<\/strong><\/p>\n

import numpy as np\r\n\r\n    # 2x3 boyutunda bir matris\r\n    matris_a = np.array([[1, 2, 3],\r\n                         [4, 5, 6]])\r\n    print(\"Matris A:\\n\", matris_a)\r\n    print(\"Boyut (shape):\", matris_a.shape)<\/code><\/pre>\n
*   \u00d6zel fonksiyonlar ile:<\/strong><\/p>\n
# S\u0131f\u0131rlardan olu\u015fan 3x3 bir matris\r\n    sifir_matris = np.zeros((3, 3))\r\n    print(\"\\nS\u0131f\u0131r Matris:\\n\", sifir_matris)\r\n\r\n    # Birlerden olu\u015fan 2x4 bir matris\r\n    bir_matris = np.ones((2, 4))\r\n    print(\"\\nBir Matris:\\n\", bir_matris)\r\n\r\n    # Birim matris (k\u00f6\u015fegenleri 1, di\u011ferleri 0)\r\n    birim_matris = np.eye(3)\r\n    print(\"\\nBirim Matris:\\n\", birim_matris)\r\n\r\n    # Rastgele say\u0131lardan olu\u015fan matris\r\n    rastgele_matris = np.random.rand(2, 2)\r\n    print(\"\\nRastgele Matris:\\n\", rastgele_matris)<\/code><\/pre>\n
Bir matrisin shape<\/code> \u00f6zelli\u011fi, boyutlar\u0131n\u0131 (sat\u0131r ve s\u00fctun say\u0131s\u0131) bir demet (tuple) olarak verir. ndim<\/code> \u00f6zelli\u011fi, matrisin ka\u00e7 boyuta sahip oldu\u011funu g\u00f6sterir (matrisler i\u00e7in 2). dtype<\/code> ise elemanlar\u0131n veri tipini belirtir.<\/p>\n
Matris \u00c7arp\u0131m\u0131n\u0131n Temel Kavramlar\u0131<\/h3>\n
NumPy’de “\u00e7arp\u0131m” denildi\u011finde iki farkl\u0131 i\u015flem akla gelir:<\/p>\n
1.  Eleman bazl\u0131 \u00e7arp\u0131m (Hadamard \u00e7arp\u0131m\u0131):<\/strong> Matrislerin kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131n\u0131n \u00e7arp\u0131lmas\u0131.
\n2.  Matris \u00e7arp\u0131m\u0131 (Nokta \u00e7arp\u0131m\u0131):<\/strong> Lineer cebirdeki standart matris \u00e7arp\u0131m\u0131.<\/p>\n
Bu iki i\u015flem aras\u0131ndaki fark\u0131 anlamak, NumPy’de do\u011fru i\u015flemi se\u00e7mek i\u00e7in kritik \u00f6neme sahiptir.<\/p>\n
Eleman Bazl\u0131 \u00c7arp\u0131m (Hadamard \u00c7arp\u0131m\u0131)<\/h4>\n
Eleman bazl\u0131 \u00e7arp\u0131m, iki matrisin ayn\u0131 boyutlara sahip olmas\u0131 durumunda, kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131n\u0131n \u00e7arp\u0131lmas\u0131yla ger\u00e7ekle\u015fir. Sonu\u00e7 matrisi de giri\u015f matrisleriyle ayn\u0131 boyutlara sahip olur.<\/p>\n
   <\/em><\/code> operat\u00f6r\u00fc:<\/strong><\/p>\n
matris_x = np.array([[1, 2],\r\n                         [3, 4]])\r\n    matris_y = np.array([[5, 6],\r\n                         [7, 8]])\r\n\r\n    eleman_bazli_carpim = matris_x * matris_y\r\n    print(\"Eleman Bazl\u0131 \u00c7arp\u0131m:\\n\", eleman_bazli_carpim)\r\n    # \u00c7\u0131kt\u0131:\r\n    # [[ 5 12]\r\n    #  [21 32]]<\/code><\/pre>\n
*   np.multiply()<\/code> fonksiyonu:<\/strong><\/p>\n
eleman_bazli_carpim_func = np.multiply(matris_x, matris_y)\r\n    print(\"Eleman Bazl\u0131 \u00c7arp\u0131m (np.multiply):\\n\", eleman_bazli_carpim_func)<\/code><\/pre>\n
Bu i\u015flem, g\u00f6r\u00fcnt\u00fclerde piksellerin parlakl\u0131\u011f\u0131n\u0131 ayarlama veya belirli \u00f6zellik vekt\u00f6rlerini \u00f6l\u00e7eklendirme gibi durumlarda kullan\u0131\u015fl\u0131d\u0131r.<\/p>\n
Matris \u00c7arp\u0131m\u0131 (Nokta \u00c7arp\u0131m\u0131)<\/h4>\n
Lineer cebirdeki matris \u00e7arp\u0131m\u0131, daha karma\u015f\u0131k bir i\u015flemdir ve belirli boyut uyumlulu\u011fu kurallar\u0131na uymas\u0131 gerekir. A matrisi m x n<\/code> boyutunda ve B matrisi n x p<\/code> boyutunda ise, A ve B’nin \u00e7arp\u0131m\u0131 olan C matrisi m x p<\/code> boyutunda olacakt\u0131r. Buradaki kritik kural, ilk matrisin s\u00fctun say\u0131s\u0131n\u0131n (n<\/code>), ikinci matrisin sat\u0131r say\u0131s\u0131na (n<\/code>) e\u015fit olmas\u0131d\u0131r.<\/p>\n
Her C_ij<\/code> eleman\u0131, A matrisinin i<\/code>. sat\u0131r\u0131 ile B matrisinin j<\/code>. s\u00fctununun eleman bazl\u0131 \u00e7arp\u0131mlar\u0131n\u0131n toplam\u0131 olarak hesaplan\u0131r.<\/p>\n
Matematiksel olarak:
\n$C_{ij} = \\sum_{k=1}^{n} A_{ik} B_{kj}$<\/p>\n
NumPy’de Matris \u00c7arp\u0131m\u0131 Y\u00f6ntemleri<\/h3>\n
NumPy, matris \u00e7arp\u0131m\u0131 i\u00e7in birden fazla y\u00f6ntem sunar. Her birinin kendine \u00f6zg\u00fc kullan\u0131m durumlar\u0131 ve n\u00fcanslar\u0131 vard\u0131r.<\/p>\n
@<\/code> Operat\u00f6r\u00fc (Python 3.5+)<\/h4>\n
Python 3.5 ve sonraki s\u00fcr\u00fcmlerde tan\u0131t\u0131lan @<\/code> operat\u00f6r\u00fc, NumPy’de matris \u00e7arp\u0131m\u0131 i\u00e7in en modern, okunabilir ve \u00f6nerilen y\u00f6ntemdir. Do\u011frudan matris \u00e7arp\u0131m\u0131n\u0131 ifade eder ve karma\u015f\u0131k kod yaz\u0131m\u0131n\u0131 basitle\u015ftirir.<\/p>\n
matris_a = np.array([[1, 2],\r\n                     [3, 4]])\r\nmatris_b = np.array([[5, 6],\r\n                     [7, 8]])\r\n\r\n
@ operat\u00f6r\u00fc ile matris \u00e7arp\u0131m\u0131<\/h2>\r\ncarpim_at = matris_a @ matris_b\r\nprint(\"Matris \u00c7arp\u0131m\u0131 (@ operat\u00f6r\u00fc ile):\\n\", carpim_at)\r\n
\u00c7\u0131kt\u0131:<\/h2>\r\n
[[19 22]<\/h2>\r\n
[43 50]]<\/code><\/pre>\n<\/h2>\n
Bu \u00f6rnekte:
\n$(15) + (2<\/em>7) = 5 + 14 = 19$
\n$(16) + (2<\/em>8) = 6 + 16 = 22$
\n$(35) + (4<\/em>7) = 15 + 28 = 43$
\n$(36) + (4<\/em>8) = 18 + 32 = 50$<\/p>\n
@<\/code> operat\u00f6r\u00fc, hem 2D matrisler hem de daha y\u00fcksek boyutlu tens\u00f6rler (matris y\u0131\u011f\u0131nlar\u0131) i\u00e7in matris \u00e7arp\u0131m\u0131 semanti\u011fini korur.<\/p>\n
numpy.dot()<\/code> Fonksiyonu<\/h4>\n
numpy.dot()<\/code> fonksiyonu, NumPy’deki en eski ve \u00e7ok y\u00f6nl\u00fc \u00e7arp\u0131m fonksiyonlar\u0131ndan biridir. Giri\u015f dizilerinin boyutlar\u0131na ba\u011fl\u0131 olarak farkl\u0131 davran\u0131\u015flar sergiler:<\/p>\n
*   Skalerler i\u00e7in:<\/strong> Standart \u00e7arp\u0131m.
\n*   1D diziler (vekt\u00f6rler) i\u00e7in:<\/strong> Vekt\u00f6rlerin nokta \u00e7arp\u0131m\u0131n\u0131 (skaler sonu\u00e7) hesaplar.
\n*   2D diziler (matrisler) i\u00e7in:<\/strong> Standart matris \u00e7arp\u0131m\u0131n\u0131 ger\u00e7ekle\u015ftirir.
\n*   Kar\u0131\u015f\u0131k boyutlar i\u00e7in:<\/strong> Daha karma\u015f\u0131k i\u015flemler yapabilir (\u00f6rne\u011fin, matris-vekt\u00f6r \u00e7arp\u0131m\u0131).<\/p>\n
Matris-Matris \u00c7arp\u0131m\u0131:<\/strong><\/p>\n
carpim_dot = np.dot(matris_a, matris_b)\r\nprint(\"Matris \u00c7arp\u0131m\u0131 (np.dot ile):\\n\", carpim_dot)<\/code><\/pre>\n
np.dot()<\/code> fonksiyonu, 2D diziler i\u00e7in @<\/code> operat\u00f6r\u00fc ile ayn\u0131 sonucu verir.<\/p>\n
Vekt\u00f6r-Vekt\u00f6r \u00c7arp\u0131m\u0131 (Nokta \u00dcr\u00fcn):<\/strong><\/p>\n
vektor_v = np.array([1, 2, 3])\r\nvektor_w = np.array([4, 5, 6])\r\n\r\nnokta_urun = np.dot(vektor_v, vektor_w)\r\nprint(\"\\nVekt\u00f6r Nokta \u00dcr\u00fcn\u00fc (np.dot ile):\", nokta_urun)\r\n
\u00c7\u0131kt\u0131: (14) + (2<\/em>5) + (3*6) = 4 + 10 + 18 = 32<\/code><\/pre>\n<\/h2>\n
Burada np.dot<\/code> bir skaler de\u011fer d\u00f6nd\u00fcr\u00fcr.<\/p>\n
Matris-Vekt\u00f6r \u00c7arp\u0131m\u0131:<\/strong><\/p>\n
matris_m = np.array([[1, 2, 3],\r\n                     [4, 5, 6]]) # 2x3 matris\r\nvektor_x = np.array([7, 8, 9])  # 3 boyutlu vekt\u00f6r\r\n\r\nmatris_vektor_carpim = np.dot(matris_m, vektor_x)\r\nprint(\"\\nMatris-Vekt\u00f6r \u00c7arp\u0131m\u0131 (np.dot ile):\\n\", matris_vektor_carpim)\r\n
\u00c7\u0131kt\u0131:<\/h2>\r\n
[(17)+(2<\/em>8)+(3*9)] = [7+16+27] = [50]<\/h2>\r\n
[(47)+(5<\/em>8)+(6*9)] = [28+40+54] = [122]<\/code><\/pre>\n<\/h2>\n
Sonu\u00e7, matrisin sat\u0131r say\u0131s\u0131 boyutunda bir vekt\u00f6rd\u00fcr (2 boyutlu).<\/p>\n
numpy.matmul()<\/code> Fonksiyonu<\/h4>\n
numpy.matmul()<\/code> (matrix multiply) fonksiyonu, np.dot()<\/code>‘un matris \u00e7arp\u0131m\u0131na \u00f6zel bir versiyonudur. \u00d6zellikle daha y\u00fcksek boyutlu diziler (tens\u00f6rler) i\u00e7in matris \u00e7arp\u0131m\u0131 semanti\u011fini daha tutarl\u0131 bir \u015fekilde uygular.<\/p>\n
np.matmul()<\/code>‘un np.dot()<\/code>‘tan temel farklar\u0131:<\/p>\n
1.  Skalerler ile:<\/strong> np.matmul()<\/code> skalerlerle \u00e7al\u0131\u015fmaz, hata verir. np.dot()<\/code> ise skaler \u00e7arp\u0131m\u0131 yapar.
\n2.  1D diziler (vekt\u00f6rler) ile:<\/strong>
\n    *   np.dot(v1, v2)<\/code> iki vekt\u00f6r\u00fcn nokta \u00e7arp\u0131m\u0131n\u0131 (skaler) verir.
\n    *   np.matmul(v1, v2)<\/code> hata verir \u00e7\u00fcnk\u00fc matmul<\/code> vekt\u00f6rleri matris gibi ele almaya \u00e7al\u0131\u015f\u0131r ve boyut uyumsuzlu\u011fu olu\u015fur (1D dizileri 2D matris gibi kabul etmez). Matris \u00e7arp\u0131m\u0131 i\u00e7in en az 2D olmalar\u0131 beklenir. E\u011fer vekt\u00f6rleri matris gibi davranmas\u0131n\u0131 istiyorsak, onlar\u0131 a\u00e7\u0131k\u00e7a 2D hale getirmeliyiz (\u00f6rne\u011fin v1.reshape(1, -1)<\/code> veya v1[:, np.newaxis]<\/code>).
\n3.  Y\u00fcksek boyutlu diziler (Batch Matrix Multiplication):<\/strong> np.matmul()<\/code>‘un en b\u00fcy\u00fck avantaj\u0131, “y\u0131\u011f\u0131n matris \u00e7arp\u0131m\u0131” (batched matrix multiplication) yetene\u011fidir. E\u011fer giri\u015f dizileri 2D’den b\u00fcy\u00fckse, np.matmul()<\/code> son iki boyutu matris olarak kabul eder ve di\u011fer boyutlar\u0131 “y\u0131\u011f\u0131n” boyutlar\u0131 olarak ele alarak her y\u0131\u011f\u0131n i\u00e7in matris \u00e7arp\u0131m\u0131 yapar.<\/p>\n
Matris-Matris \u00c7arp\u0131m\u0131:<\/strong><\/p>\n
carpim_matmul = np.matmul(matris_a, matris_b)\r\nprint(\"Matris \u00c7arp\u0131m\u0131 (np.matmul ile):\\n\", carpim_matmul)<\/code><\/pre>\n
2D matrisler i\u00e7in np.matmul()<\/code> da @<\/code> operat\u00f6r\u00fc ve np.dot()<\/code> ile ayn\u0131 sonucu verir.<\/p>\n
Y\u00fcksek Boyutlu Diziler (Batch Matrix Multiplication):<\/strong>
\nBu, derin \u00f6\u011frenme gibi alanlarda \u00e7ok \u00f6nemlidir, \u00e7\u00fcnk\u00fc genellikle ayn\u0131 anda birden fazla matris \u00e7arp\u0131m\u0131 yapmak gerekir.<\/p>\n
# 2 adet 2x3 matris i\u00e7eren bir y\u0131\u011f\u0131n\r\nbatch_a = np.random.rand(2, 2, 3) # (batch_size, rows, cols)\r\n
2 adet 3x4 matris i\u00e7eren bir y\u0131\u011f\u0131n<\/h2>\r\nbatch_b = np.random.rand(2, 3, 4)\r\n\r\n
batch_a'n\u0131n (2,3) ve batch_b'nin (3,4) matris \u00e7arp\u0131m\u0131 her y\u0131\u011f\u0131n i\u00e7in ayr\u0131 ayr\u0131 yap\u0131l\u0131r.<\/h2>\r\n
Sonu\u00e7 (2, 2, 4) boyutunda olacakt\u0131r.<\/h2>\r\nbatch_carpim = np.matmul(batch_a, batch_b)\r\nprint(\"\\nBatch Matris \u00c7arp\u0131m\u0131 (np.matmul ile):\\n\", batch_carpim.shape)\r\n
\u00c7\u0131kt\u0131: (2, 2, 4)<\/code><\/pre>\n<\/h2>\n
np.dot()<\/code> da y\u00fcksek boyutlu dizileri i\u015fleyebilir, ancak np.matmul()<\/code>‘un y\u0131\u011f\u0131n matris \u00e7arp\u0131m\u0131 davran\u0131\u015f\u0131 daha sezgiseldir ve genellikle bu t\u00fcr senaryolar i\u00e7in tercih edilir. np.dot()<\/code>‘un y\u00fcksek boyutlu dizilerdeki davran\u0131\u015f\u0131, son ekseni ilk dizinin ikinci-sondan-sonraki ekseniyle \u00e7arpma e\u011filimindedir, bu da matmul<\/code>‘dan farkl\u0131 olabilir.<\/p>\n
ndarray.dot()<\/code> Metodu<\/h4>\n
NumPy dizilerinin (ndarray) kendi \u00fczerinde bir .dot()<\/code> metodu da bulunur. Bu, np.dot(a, b)<\/code> yerine a.dot(b)<\/code> \u015feklinde kullan\u0131labilir. \u0130\u015flevsellik olarak np.dot()<\/code> ile ayn\u0131d\u0131r.<\/p>\n
carpim_method = matris_a.dot(matris_b)\r\nprint(\"Matris \u00c7arp\u0131m\u0131 (ndarray.dot() metodu ile):\\n\", carpim_method)<\/code><\/pre>\n
Bu y\u00f6ntem, \u00f6zellikle bir dizi nesnesi \u00fczerinde zincirleme i\u015flemler yaparken kullan\u0131\u015fl\u0131 olabilir.<\/p>\n
Performans Konular\u0131<\/h3>\n
NumPy’nin en b\u00fcy\u00fck avantajlar\u0131ndan biri, y\u00fcksek performans\u0131d\u0131r. Matris \u00e7arp\u0131m\u0131 gibi yo\u011fun hesaplama gerektiren i\u015flemler, NumPy’nin C veya Fortran’da yaz\u0131lm\u0131\u015f optimize edilmi\u015f alt katmanlar\u0131 sayesinde saf Python d\u00f6ng\u00fclerine g\u00f6re katlarca daha h\u0131zl\u0131d\u0131r.<\/p>\n
NumPy, genellikle BLAS (Basic Linear Algebra Subprograms) ve LAPACK (Linear Algebra Package) gibi optimize edilmi\u015f k\u00fct\u00fcphaneleri kullan\u0131r. Bu k\u00fct\u00fcphaneler, i\u015flemciye \u00f6zg\u00fc optimizasyonlar i\u00e7erir ve matris i\u015flemlerini inan\u0131lmaz derecede verimli hale getirir. \u00d6rne\u011fin, Intel’in MKL (Math Kernel Library) veya OpenBLAS gibi uygulamalar\u0131, NumPy’nin arkas\u0131ndaki motoru olu\u015fturabilir.<\/p>\n
Neden NumPy h\u0131zl\u0131d\u0131r?<\/strong><\/p>\n
*   Vekt\u00f6rle\u015ftirme:<\/strong> NumPy, d\u00f6ng\u00fcleri Python seviyesinde yazmak yerine, C seviyesindeki h\u0131zl\u0131, vekt\u00f6rle\u015ftirilmi\u015f i\u015flemleri kullan\u0131r. Bu, Python yorumlay\u0131c\u0131s\u0131n\u0131n getirdi\u011fi ek y\u00fck\u00fc ortadan kald\u0131r\u0131r.
\n*   Bellek D\u00fczeni:<\/strong> NumPy dizileri bellekte biti\u015fik olarak saklan\u0131r. Bu, CPU’nun \u00f6nbellek (cache) mekanizmalar\u0131n\u0131 daha verimli kullanmas\u0131n\u0131 sa\u011flar, bu da veri eri\u015fimini h\u0131zland\u0131r\u0131r.
\n*   Harici K\u00fct\u00fcphaneler:<\/strong> Yukar\u0131da bahsedildi\u011fi gibi, BLAS\/LAPACK gibi kan\u0131tlanm\u0131\u015f ve optimize edilmi\u015f k\u00fct\u00fcphaneleri kullan\u0131r.<\/p>\n
K\u00fc\u00e7\u00fck bir kar\u015f\u0131la\u015ft\u0131rma:<\/p>\n
import time\r\n\r\n
B\u00fcy\u00fck matrisler olu\u015ftural\u0131m<\/h2>\r\nsize = 500\r\nmat_a = np.random.rand(size, size)\r\nmat_b = np.random.rand(size, size)\r\n\r\n
NumPy ile \u00e7arp\u0131m<\/h2>\r\nstart_time = time.time()\r\nresult_np = mat_a @ mat_b\r\nend_time = time.time()\r\nprint(f\"\\nNumPy ile matris \u00e7arp\u0131m\u0131 s\u00fcresi: {end_time - start_time:.4f} saniye\")\r\n\r\n
Saf Python ile (sadece konsepti g\u00f6stermek i\u00e7in, ger\u00e7ekte \u00e7ok yava\u015f olacakt\u0131r)<\/h2>\r\n
Bu kod \u00e7ok yava\u015f \u00e7al\u0131\u015faca\u011f\u0131 i\u00e7in, genellikle b\u00fcy\u00fck boyutlarda \u00e7al\u0131\u015ft\u0131r\u0131lmaz.<\/h2>\r\n
Ancak fark\u0131 g\u00f6stermek i\u00e7in, \u00e7ok daha k\u00fc\u00e7\u00fck bir boyutta deneyebiliriz.<\/h2>\r\nsmall_size = 50\r\nsmall_mat_a = [[np.random.rand() for _ in range(small_size)] for _ in range(small_size)]\r\nsmall_mat_b = [[np.random.rand() for _ in range(small_size)] for _ in range(small_size)]\r\nresult_py = [[0 for _ in range(small_size)] for _ in range(small_size)]\r\n\r\nstart_time_py = time.time()\r\nfor i in range(small_size):\r\n    for j in range(small_size):\r\n        for k in range(small_size):\r\n            result_py[i][j] += small_mat_a[i][k] * small_mat_b[k][j]\r\nend_time_py = time.time()\r\nprint(f\"Saf Python ile matris \u00e7arp\u0131m\u0131 s\u00fcresi ({small_size}x{small_size}): {end_time_py - start_time_py:.4f} saniye\")\r\n
NumPy'nin ayn\u0131 boyuttaki performans\u0131:<\/h2>\r\n
start_time_np_small = time.time()<\/h2>\r\n
result_np_small = np.array(small_mat_a) @ np.array(small_mat_b)<\/h2>\r\n
end_time_np_small = time.time()<\/h2>\r\n
print(f\"NumPy ile matris \u00e7arp\u0131m\u0131 s\u00fcresi ({small_size}x{small_size}): {end_time_np_small - start_time_np_small:.6f} saniye\")<\/code><\/pre>\n<\/h2>\n
Yukar\u0131daki \u00f6rnekte, NumPy’nin h\u0131z fark\u0131 a\u00e7\u0131k\u00e7a g\u00f6r\u00fclecektir. Saf Python d\u00f6ng\u00fcleri, \u00f6zellikle b\u00fcy\u00fck matrisler i\u00e7in pratik de\u011fildir.<\/p>\n
\u0130leri Konular ve \u00d6zel Durumlar<\/h3>\n
Matris \u00e7arp\u0131m\u0131, bir\u00e7ok lineer cebir i\u015fleminin temelidir. NumPy, bu i\u015flemleri de y\u00fcksek performansla sunar.<\/p>\n
Matris Transpozisyonu<\/h4>\n
Bir matrisin sat\u0131r ve s\u00fctunlar\u0131n\u0131n yer de\u011fi\u015ftirmesine transpozisyon denir. A<\/code> matrisinin transpozu A^T<\/code> veya A'<\/code> ile g\u00f6sterilir. NumPy’de A.T<\/code> veya np.transpose(A)<\/code> ile elde edilir.<\/p>\n
matris_c = np.array([[1, 2, 3],\r\n                     [4, 5, 6]])\r\ntranspoze_c = matris_c.T\r\nprint(\"\\nMatris C:\\n\", matris_c)\r\nprint(\"Transpoze C:\\n\", transpoze_c)<\/code><\/pre>\n
Transpozisyon, matris \u00e7arp\u0131m\u0131n\u0131n boyut gereksinimlerini kar\u015f\u0131lamak veya belirli algoritmalar\u0131 uygulamak i\u00e7in s\u0131k\u00e7a kullan\u0131l\u0131r. \u00d6rne\u011fin, $A^T A$ \u00e7arp\u0131m\u0131, kareler toplam\u0131n\u0131 minimize etmede (en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi) yayg\u0131n olarak kullan\u0131l\u0131r.<\/p>\n
Ters Matris (Inverse Matrix)<\/h4>\n
Bir $A$ matrisinin tersi olan $A^{-1}$ matrisi, $A A^{-1} = A^{-1} A = I$ e\u015fitli\u011fini sa\u011flar, burada $I$ birim matristir. Ters matris sadece kare ve tekil olmayan (determinant\u0131 s\u0131f\u0131r olmayan) matrisler i\u00e7in tan\u0131ml\u0131d\u0131r.<\/p>\n
NumPy’de np.linalg.inv()<\/code> fonksiyonu ile hesaplan\u0131r:<\/p>\n
kare_matris = np.array([[1, 2],\r\n                        [3, 4]])\r\nters_matris = np.linalg.inv(kare_matris)\r\nprint(\"\\nKare Matris:\\n\", kare_matris)\r\nprint(\"Ters Matris:\\n\", ters_matris)\r\n\r\n
Do\u011frulama: matris @ ters_matris yakla\u015f\u0131k olarak birim matris olmal\u0131<\/h2>\r\ndogrulama = kare_matris @ ters_matris\r\nprint(\"Do\u011frulama (Matris @ Ters Matris):\\n\", dogrulama)\r\n
Floating point hatalar\u0131 nedeniyle tam olarak [1,0],[0,1] olmayabilir,<\/h2>\r\n
ancak \u00e7ok yak\u0131n de\u011ferler olacakt\u0131r. np.allclose() ile kontrol edilebilir.<\/code><\/pre>\n<\/h2>\n
Ters matris, lineer denklem sistemlerini \u00e7\u00f6zmek i\u00e7in teorik olarak kullan\u0131labilir ($Ax=b \\implies x = A^{-1}b$). Ancak, say\u0131sal olarak np.linalg.solve()<\/code> kullanmak daha kararl\u0131 ve verimlidir.<\/p>\n
Lineer Denklem Sistemlerini \u00c7\u00f6zme<\/h4>\n
$Ax=b$ formundaki bir lineer denklem sistemini \u00e7\u00f6zmek i\u00e7in np.linalg.solve()<\/code> fonksiyonu tercih edilmelidir. Bu fonksiyon, ters matrisi a\u00e7\u0131k\u00e7a hesaplamadan daha optimize ve say\u0131sal olarak daha kararl\u0131 y\u00f6ntemler kullan\u0131r.<\/p>\n
# A matrisi\r\nA = np.array([[3, 1],\r\n              [1, 2]])\r\n
b vekt\u00f6r\u00fc<\/h2>\r\nb = np.array([9, 8])\r\n\r\n
Ax = b denklemini \u00e7\u00f6z<\/h2>\r\nx = np.linalg.solve(A, b)\r\nprint(\"\\nDenklem sistemi \u00e7\u00f6z\u00fcm\u00fc (x):\\n\", x)\r\n\r\n
Do\u011frulama: A @ x yakla\u015f\u0131k olarak b'ye e\u015fit olmal\u0131<\/h2>\r\ndogrulama_cozum = A @ x\r\nprint(\"Do\u011frulama (A @ x):\\n\", dogrulama_cozum)<\/code><\/pre>\n
Yayg\u0131n Hatalar ve En \u0130yi Uygulamalar<\/h3>\n
   Eleman bazl\u0131 \u00e7arp\u0131m ile matris \u00e7arp\u0131m\u0131n\u0131 kar\u0131\u015ft\u0131rmak:<\/strong> Bu, yeni ba\u015flayanlar\u0131n yapt\u0131\u011f\u0131 en yayg\u0131n hatad\u0131r. <\/em><\/code> eleman bazl\u0131 \u00e7arp\u0131m, @<\/code> ise matris \u00e7arp\u0131m\u0131d\u0131r.
\n*   Boyut uyumsuzluklar\u0131:<\/strong> Matris \u00e7arp\u0131m\u0131 yaparken boyutlar\u0131n uyumlu oldu\u011fundan emin olun (ilk matrisin s\u00fctun say\u0131s\u0131, ikinci matrisin sat\u0131r say\u0131s\u0131na e\u015fit olmal\u0131). Uyumsuzluk durumunda NumPy ValueError<\/code> hatas\u0131 verir.
\n*   np.matrix<\/code> kullanmaktan ka\u00e7\u0131nmak:<\/strong> NumPy’nin eski bir \u00f6zelli\u011fi olan np.matrix<\/code> tipi, matris i\u015flemlerini basitle\u015ftirmek i\u00e7in tasarlanm\u0131\u015ft\u0131, ancak ndarray<\/code> ile kar\u0131\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda tutars\u0131zl\u0131klara yol a\u00e7ar ve art\u0131k \u00f6nerilmez. T\u00fcm yeni kodlarda np.array<\/code> kullan\u0131n.
\n*   Do\u011fru \u00e7arp\u0131m y\u00f6ntemini se\u00e7mek:<\/strong>
\n    *   Genel matris \u00e7arp\u0131mlar\u0131 i\u00e7in Python 3.5+ kullan\u0131yorsan\u0131z @<\/code> operat\u00f6r\u00fc en okunabilir ve \u00f6nerilen y\u00f6ntemdir.
\n    *   Vekt\u00f6rlerin nokta \u00e7arp\u0131m\u0131 veya farkl\u0131 boyutlardaki (skaler, vekt\u00f6r, matris) dizilerle esnek i\u015flemler i\u00e7in np.dot()<\/code> kullan\u0131labilir.
\n    *   Y\u0131\u011f\u0131n matris \u00e7arp\u0131mlar\u0131 (batch matrix multiplication) i\u00e7in np.matmul()<\/code> en uygunudur.<\/p>\n
Sonu\u00e7<\/h3>\n
NumPy, Python’da matris i\u015flemlerini, \u00f6zellikle matris \u00e7arp\u0131m\u0131n\u0131, son derece verimli ve kolay bir \u015fekilde ger\u00e7ekle\u015ftirmek i\u00e7in vazge\u00e7ilmez bir ara\u00e7t\u0131r. @<\/code> operat\u00f6r\u00fc, np.dot()<\/code> ve np.matmul()<\/code> gibi \u00e7e\u015fitli y\u00f6ntemler sunarak, geli\u015ftiricilere farkl\u0131 kullan\u0131m senaryolar\u0131na uygun esneklik sa\u011flar. Matris \u00e7arp\u0131m\u0131n\u0131n temelini ve bu farkl\u0131 y\u00f6ntemlerin n\u00fcanslar\u0131n\u0131 anlamak, veri bilimi, makine \u00f6\u011frenimi ve bilimsel hesaplama alanlar\u0131nda \u00e7al\u0131\u015fan herkes i\u00e7in temel bir beceridir. NumPy’nin optimize edilmi\u015f C\/Fortran tabanl\u0131 alt yap\u0131s\u0131 sayesinde, karma\u015f\u0131k lineer cebir problemleri bile saniyeler i\u00e7inde \u00e7\u00f6z\u00fclebilir, bu da modern hesaplama d\u00fcnyas\u0131nda b\u00fcy\u00fck bir avantaj sunar. Matris \u00e7arp\u0131m\u0131n\u0131n \u00f6tesinde, NumPy’nin sundu\u011fu di\u011fer lineer cebir fonksiyonlar\u0131 (ters alma, determinant, \u00f6zde\u011fer\/\u00f6zvekt\u00f6r hesaplama vb.) ile birle\u015fti\u011finde, neredeyse t\u00fcm say\u0131sal problemlerin \u00fcstesinden gelinebilir.<\/p>\n
<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme\nNumPy (Numerical Python), Python programlama dilinde bilimsel hesaplamalar i\u00e7in temel bir k\u00fct\u00fcph","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_page_header_type":"","csco_page_load_nextpost":"","csco_page_subscribe_form":"","csco_page_contact_form":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-30323","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"\nNumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme - Kodlar\u0131n Gizemli D\u00fcnyas\u0131<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme\" \/>\n<meta property=\"og:description\" content=\"NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme  NumPy (Numerical Python), Python programlama dilinde bilimsel hesaplamalar i\u00e7in temel bir k\u00fct\u00fcph\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/\" \/>\n<meta property=\"og:site_name\" content=\"Kodlar\u0131n Gizemli D\u00fcnyas\u0131\" \/>\n<meta property=\"article:published_time\" content=\"2025-09-26T14:06:27+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-26T14:28:04+00:00\" \/>\n<meta name=\"author\" content=\"Fatih Soysal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Fatih Soysal\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/\"},\"author\":{\"name\":\"Fatih Soysal\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"headline\":\"NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme\",\"datePublished\":\"2025-09-26T14:06:27+00:00\",\"dateModified\":\"2025-09-26T14:28:04+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/\"},\"wordCount\":1725,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/#respond\"]}],\"copyrightYear\":\"2025\",\"copyrightHolder\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/numpy-matris-carpimi-detayli-bir-inceleme\/\",\"name\":\"NumPy Matris \u00c7arp\u0131m\u0131: Detayl\u0131 Bir \u0130nceleme - 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