Menampilkan Rumus Operasi Matriks menggunakan SciPy dan NumPy

Hallo guys, Berjumpa dengan Miniblog dari Inzaghi's Blog! Jika sebelumnya sudah membahas tentang cara menampilkan Rumus Plot Trigonometri menggunakan NumPy, SciPy, dan Matplotlib, kali ini kita akan menampilkan Rumus Operasi Matriks menggunakan SciPy dan NumPy.

Berikut ini adalah Program Python untuk Menampilkan Rumus Operasi Matriks menggunakan SciPy dan NumPy.

1. Import Library

import numpy as np
import scipy.linalg as la

2. Mendefinisikan Vektor dan Matriks

# Define the vectors and matrix
vec1 = np.array([-1., 4., -9.])
mat1 = np.array([[1., 3., 5.], [7., -9., 2.], [4., 6., 8.]])

3. Menghitung Vektor

# 1. Multiply vec1 by a constant (np.pi/4)
vec2 = (np.pi/4) * vec1
# 2. Apply the cosine function to vec2
vec2 = np.cos(vec2)
# 3. Add vec1 and 2 times vec2
vec3 = vec1 + 2 * vec2
# 4. Calculate the Euclidean norm of vec3
euclidean_norm = la.norm(vec3)

4. Menghitung Matriks

# 5. Perform matrix-vector multiplication between mat1 and vec3
vec4 = np.dot(mat1, vec3)
# 6. Compute the transpose of mat1
mat1_transpose = mat1.T
# 7. Compute the determinant of mat1
mat1_det = la.det(mat1)
# 8. Compute the trace of mat1
mat1_trace = np.trace(mat1)

5. Mencari Elemen Terkecil dari Vektor dan Matriks

# 9. Find the smallest element in vec1
smallest_element_vec1 = np.min(vec1)
# 10. Find the index of the smallest element in vec1
index_smallest_element_vec1 = np.argmin(vec1)
# 11. Find the smallest element in mat1
smallest_element_mat1 = np.min(mat1)

6. Memeriksa dan mem-Verifikasi Penjumlahan Matriks

# 12. Verify if mat1 is a magic square
row_sums = np.sum(mat1, axis=1)
col_sums = np.sum(mat1, axis=0)
diagonal_sum1 = np.trace(mat1)
diagonal_sum2 = np.trace(np.fliplr(mat1))
# Check if all sums are the same
is_magic_square = (len(set(row_sums)) == 1 and len(set(col_sums)) == 1 and
                   row_sums[0] == col_sums[0] == diagonal_sum1 == diagonal_sum2)

7. Mencetak Vektor dan Matriks

print("1. Resulting vec2:", vec2)
print("2. Resulting vec2 after applying cosine:", vec2)
print("3. Resulting vec3:", vec3)
print("4. Euclidean norm of vec3:", euclidean_norm)
print("5. Resulting vec4:", vec4)
print("6. Transpose of mat1:\n", mat1_transpose)
print("7. Determinant of mat1:", mat1_det)
print("8. Trace of mat1:", mat1_trace)
print("9. Smallest element in vec1:", smallest_element_vec1)
print("10. Index of the smallest element in vec1:", index_smallest_element_vec1)
print("11. Smallest element in mat1:", smallest_element_mat1)
print("12. Is mat1 a magic square?", is_magic_square)

Output :

1. Resulting vec2: [ 0.70710678 -1.          0.70710678]
2. Resulting vec2 after applying cosine: [ 0.70710678 -1.          0.70710678]
3. Resulting vec3: [ 0.41421356  2.         -7.58578644]
4. Euclidean norm of vec3: 7.855935892848037
5. Resulting vec4: [-31.51471863 -30.27207794 -47.02943725]
6. Transpose of mat1:
 [[ 1.  7.  4.]
 [ 3. -9.  6.]
 [ 5.  2.  8.]]
7. Determinant of mat1: 161.99999999999997
8. Trace of mat1: 0.0
9. Smallest element in vec1: -9.0
10. Index of the smallest element in vec1: 2
11. Smallest element in mat1: -9.0
12. Is mat1 a magic square? False

8. Konstruksi dan Generasi Matriks dan Submatriks

# 13. Construct a 10x10 matrix named M filled with random numbers
M = np.random.rand(10, 10)
# 14. Generate the four 5x5 sub-matrices
# Upper Left Quarter (MUL)
MUL = M[:5, :5]
# Upper Right Quarter (MUR)
MUR = M[:5, 5:]
# Lower Left Quarter (MLL)
MLL = M[5:, :5]
# Lower Right Quarter (MLR)
MLR = M[5:, 5:]

9. Menampilkan Submatriks

# Display the sub-matrices
print("Upper Left Quarter (MUL):\n", MUL)
print("\nUpper Right Quarter (MUR):\n", MUR)
print("\nLower Left Quarter (MLL):\n", MLL)
print("\nLower Right Quarter (MLR):\n", MLR)

Output :

Upper Left Quarter (MUL):
 [[0.39613543 0.06659083 0.1353606  0.03575032 0.78565856]
 [0.83856055 0.07156087 0.61407801 0.45584335 0.18366205]
 [0.67648104 0.47251966 0.20641843 0.48942973 0.23163408]
 [0.80090565 0.77390097 0.85108114 0.72952116 0.73008316]
 [0.43021931 0.34048256 0.5292398  0.43191999 0.93864353]]

Upper Right Quarter (MUR):
 [[0.73586742 0.54266173 0.10776348 0.79440221 0.51642669]
 [0.13423576 0.60392076 0.33561124 0.68250265 0.46730018]
 [0.58423521 0.76363396 0.21959778 0.8774659  0.09996112]
 [0.0157255  0.36378884 0.38811041 0.93804427 0.52344093]
 [0.07392527 0.07770546 0.04661559 0.47845337 0.74419622]]

Lower Left Quarter (MLL):
 [[0.27387088 0.13349402 0.03315354 0.04740001 0.64161455]
 [0.12377607 0.4194496  0.06505218 0.6973751  0.60539034]
 [0.9890294  0.35747239 0.36983188 0.11420733 0.78528483]
 [0.54299472 0.95740632 0.23606324 0.42562606 0.92802738]
 [0.28227684 0.86046471 0.96920774 0.78395278 0.03091222]]

Lower Right Quarter (MLR):
 [[0.66121549 0.40610742 0.56539897 0.40851901 0.10947693]
 [0.26124489 0.22191262 0.0951539  0.34172111 0.61695321]
 [0.39979312 0.52719262 0.03263554 0.06680715 0.45924553]
 [0.97422601 0.03391992 0.1604091  0.85942077 0.9710585 ]
 [0.35692984 0.14346116 0.6271265  0.51228915 0.04226928]]

10. Hasil di Jupyter Notebook

Mohon maaf apabila ada kesalahan sedikit pun pada Kode Program ini.

Terima Kasih 😀😊😘👌👍 :)