py list matrix 2d mul 2
Perkalian dua buah matriks dalam Pyton dapat dilakukan menggunakan pengulangan bersarang [ 1 ] atau paket numerik NumPy [ 2 ]. Di sini akan dibahas dengan pengulangan bersarang pada list untuk perkalian matriks, dan karena memang hanya untuk tujuan pembelajaran, diterapkan untuk matriks berukuran kecil.
matrix multiplication with matrix
Terdapat matriks
\begin{equation}\label{eqn:matrix-a} A = \left[ \begin{array}{ccc} a_{11} & a_{12} & a_{13} \newline a_{21} & a_{22} & a_{23} \newline \end{array} \right] \end{equation}
dan
\begin{equation}\label{eqn:matrix-b} B = \left[ \begin{array}{ccc} b_{11} & b_{12} & b_{13} & b_{14} \newline b_{21} & b_{22} & b_{23} & b_{24} \newline b_{31} & b_{32} & b_{33} & b_{34} \end{array} \right], \end{equation}
yang akan dikalikan
\begin{equation}\label{eqn:matrix-c=ab-element} C = AB \end{equation}
dan memberikan
\begin{equation}\label{eqn:matrix-c} C = \left[ \begin{array}{ccc} c_{11} & c_{12} & c_{13} & c_{14} \newline c_{21} & c_{22} & c_{23} & c_{24} \end{array} \right], \end{equation}
yang berlaku
\begin{equation}\label{eqn:matrix-b=ca-element} c_{ij} = \sum_k a_{ik} b_{kj}, \end{equation}
untuk setiap elemennya.
a code
Suatu pustaka matrix.py berisikan
# matrix.py
# Simple matrix library using list
# 20220216 Create this example.
# print only two-dimension matrix in form of a list
def printmat(m):
# assume that all rows have the same columns
row = len(m)
col = len(m[0])
# iterate through rows then colums
for r in range(row):
for c in range(col):
print(m[r][c], end='\t')
print()
# create an new two-dimension matrix in form of a list filled with zero
def newmat(row, col):
# create empty matrix
m = []
# iterate through rows then colums
for r in range(row):
newrow = []
for c in range(col):
newrow.append(0)
m.append(newrow)
return m
diperlukan agar dapat menggunakan printmat dan newmat dalam program berikut
# 0480-matrix-no-numpy-mul2.py
# Multiply a matrix with a matrix
# 20220216 Create this example.
import matrix as mat
# multiply a matrix with a matrix
def mulmat2(m1, m2):
# assume colum of 1st and row of 2nd are matched
row = len(m1)
mid = len(m1[0])
col = len(m2[0])
m3 = mat.newmat(row, col)
# iterate through rows then colums
for r in range(row):
for c in range(col):
temp = 0
for m in range(mid):
temp = temp + m1[r][m] * m2[m][c]
m3[r][c] = temp
return m3
# define a list as two-dimension matrix
m1 = [
[1, 1, 1],
[1, 2, 1],
]
m2 = [
[1, 1],
[1, 2],
[1, 1],
]
m3 = mulmat2(m1, m2)
# display results
print("m1:")
mat.printmat(m1)
print("m2:")
mat.printmat(m2)
print("m3:")
mat.printmat(m3)
yang memberikan hasil
==== RESTART: 0480-matrix-no-numpy-mul2.py ====
m1:
1 1 1
1 2 1
m2:
1 1
1 2
1 1
m3:
3 4
4 6
saat dijalankan.
Modifikasi kode di atas, sehingga mat dapat tetap digunakan, dapat dijalankan di OneCompiler
3xtm9tpf4
, yang memerlukan definisi suatu namespace mat berisikan fungsi yang diperlukan untuk menggantikan baris import matrix as mat
#import matrix as mat
class mat:
# print only two-dimension matrix in form of a list
def printmat(m):
# assume that all rows have the same number of columns
row = len(m)
col = len(m[0])
# iterate through rows then colums
for r in range(row):
for c in range(col):
print(m[r][c], end='\t')
print()
# create an new two-dimension matrix in form of a list filled with zero
def newmat(row, col):
# create empty matrix
m = []
# iterate through rows then colums
for r in range(row):
newrow = []
for c in range(col):
newrow.append(0)
m.append(newrow)
return m
agar tidak perlu mengubah baris kode yang lain. Penggunaan paket matrix ini adalah untuk menyembuyikan fungsi-fungsi yang bukan menjadi fokus pembahasan di sini sehingga contoh program dapat masih cukup ringkas.
exer
- Apa syarat dua buah matriks dapat dikalikan? Perhatikan Persamaan \eqref{eqn:matrix-b=ca-element}.
note
- SHARIQ_JMI, psbishnu1, anikakapoor, “Python program to multiply two matrices”, GeeksforGeeks, 11 Aug 2021, url https://www.geeksforgeeks.org/python-program-multiply-two-matrices/ [20220217].
- Erin Schaffer, “NumPy matrix multiplication: Get started in 5 minutes”, Educative, Inc., 03 Sep 2021, url https://www.educative.io/blog/numpy-matrix-multiplication [20220217].