BudiajiMatrix

BudiajiMatrix adalah library Python untuk pengolahan matrix yang lengkap dan mudah digunakan. Cocok untuk keperluan analisis time series, GSTAR, VARIMA, dan berbagai analisis statistik lainnya.

🚀 Fitur Utama

• Operasi Dasar: Penjumlahan, pengurangan, perkalian, pembagian matrix
• Dekomposisi: Cholesky, QR, LU, SVD, Eigendecomposition, Schur
• Nilai Karakteristik: Determinant, trace, rank, norm, condition number, eigenvalues, eigenvectors
• Properti Matrix: Cek simetris, positif definit, orthogonal, singular, diagonal
• Statistik: Mean, variance, standard deviation, covariance, correlation
• Normalisasi: Normalisasi baris/kolom, standardisasi
• Solving Systems: Linear system solver, least squares
• Matrix Power: Pangkat, exponential, logarithm, square root
• Dan banyak lagi!

📦 Instalasi

pip install budiajimatrix

💡 Cara Penggunaan

Import Library

import numpy as np
from budiajimatrix import transpose, multiply, eigenvalues, inverse, covariance

Contoh Penggunaan Dasar

import numpy as np
from budiajimatrix import transpose, multiply, add

# Buat matrix
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

# Transpose
print("Transpose A:")
print(transpose(A))
# Output:
# [[1 3]
#  [2 4]]

# Perkalian matrix
print("A × B:")
print(multiply(A, B))
# Output:
# [[19 22]
#  [43 50]]

# Penjumlahan
print("A + B:")
print(add(A, B))
# Output:
# [[ 6  8]
#  [10 12]]

Eigenvalues dan Eigenvectors

from budiajimatrix import eigenvalues, eigenvectors

A = np.array([[4, 2], [1, 3]])

# Hitung eigenvalues (akar ciri)
eig_vals = eigenvalues(A)
print("Eigenvalues:", eig_vals)

# Hitung eigenvectors (vektor ciri)
eig_vecs = eigenvectors(A)
print("Eigenvectors:")
print(eig_vecs)

Dekomposisi Matrix

from budiajimatrix import svd, qr_decomposition, cholesky

# Singular Value Decomposition
A = np.array([[1, 2], [3, 4], [5, 6]])
U, S, Vt = svd(A)
print("U:", U)
print("S:", S)
print("Vt:", Vt)

# QR Decomposition
A = np.array([[12, -51, 4], [6, 167, -68], [-4, 24, -41]])
Q, R = qr_decomposition(A)
print("Q:", Q)
print("R:", R)

# Cholesky (untuk matrix positif definit)
A = np.array([[4, 12], [12, 37]])
L = cholesky(A)
print("L:", L)

Statistik Matrix

from budiajimatrix import covariance, correlation, mean, std

# Data matrix (observasi × variabel)
data = np.array([[1, 2, 3],
                 [4, 5, 6],
                 [7, 8, 9],
                 [10, 11, 12]])

# Covariance matrix
cov_matrix = covariance(data)
print("Covariance Matrix:")
print(cov_matrix)

# Correlation matrix
corr_matrix = correlation(data)
print("Correlation Matrix:")
print(corr_matrix)

# Mean per kolom
print("Mean:", mean(data, axis=0))

# Standard deviation per kolom
print("Std:", std(data, axis=0))

Normalisasi dan Standardisasi

from budiajimatrix import standardize, normalize_rows

data = np.array([[1, 2, 3],
                 [4, 5, 6],
                 [7, 8, 9]])

# Standardisasi (mean=0, std=1)
standardized = standardize(data)
print("Standardized:")
print(standardized)

# Normalisasi per baris
normalized = normalize_rows(data)
print("Normalized Rows:")
print(normalized)

Properti Matrix

from budiajimatrix import is_symmetric, is_positive_definite, rank, determinant

A = np.array([[2, 1], [1, 2]])

# Cek simetris
print("Symmetric?", is_symmetric(A))

# Cek positif definit
print("Positive Definite?", is_positive_definite(A))

# Rank
print("Rank:", rank(A))

# Determinant
print("Determinant:", determinant(A))

Solving Linear Systems

from budiajimatrix import solve_linear_system, least_squares

# Solve Ax = b
A = np.array([[3, 1], [1, 2]])
b = np.array([9, 8])
x = solve_linear_system(A, b)
print("Solution x:", x)

# Least squares (untuk overdetermined system)
A = np.array([[1, 1], [1, 2], [1, 3]])
b = np.array([2, 3, 4])
x = least_squares(A, b)
print("Least Squares Solution:", x)

📚 Dokumentasi Lengkap

Operasi Dasar

• add(matrix1, matrix2) - Penjumlahan matrix
• subtract(matrix1, matrix2) - Pengurangan matrix
• multiply(matrix1, matrix2) - Perkalian matrix
• element_multiply(matrix1, matrix2) - Perkalian elemen per elemen
• scalar_multiply(matrix, scalar) - Perkalian dengan skalar
• divide(matrix, scalar) - Pembagian dengan skalar

Transformasi

• transpose(matrix) - Transpose matrix
• inverse(matrix) - Inverse matrix
• pseudo_inverse(matrix) - Moore-Penrose pseudo-inverse
• conjugate(matrix) - Konjugat matrix
• adjoint(matrix) - Adjoint matrix

Dekomposisi

• cholesky(matrix) - Dekomposisi Cholesky
• qr_decomposition(matrix) - Dekomposisi QR
• lu_decomposition(matrix) - Dekomposisi LU
• svd(matrix) - Singular Value Decomposition
• eigendecomposition(matrix) - Dekomposisi Eigen
• schur(matrix) - Dekomposisi Schur

Nilai Karakteristik

• determinant(matrix) - Determinan
• trace(matrix) - Trace
• rank(matrix) - Rank
• norm(matrix, ord) - Norm matrix
• condition_number(matrix) - Condition number
• eigenvalues(matrix) - Eigenvalues (akar ciri)
• eigenvectors(matrix) - Eigenvectors (vektor ciri)

Properti Matrix

• is_symmetric(matrix) - Cek simetris
• is_positive_definite(matrix) - Cek positif definit
• is_orthogonal(matrix) - Cek orthogonal
• is_singular(matrix) - Cek singular
• is_diagonal(matrix) - Cek diagonal

Matrix Khusus

• identity(n) - Identity matrix n×n
• zeros(shape) - Matrix nol
• ones(shape) - Matrix satu
• diagonal(values) - Diagonal matrix
• random_matrix(shape, distribution) - Random matrix

Statistik

• mean(matrix, axis) - Mean
• variance(matrix, axis) - Variance
• std(matrix, axis) - Standard deviation
• covariance(matrix) - Covariance matrix
• correlation(matrix) - Correlation matrix

Operasi Baris/Kolom

• row_sum(matrix) - Jumlah per baris
• col_sum(matrix) - Jumlah per kolom
• row_mean(matrix) - Mean per baris
• col_mean(matrix) - Mean per kolom
• normalize_rows(matrix) - Normalisasi per baris
• normalize_cols(matrix) - Normalisasi per kolom
• standardize(matrix) - Standardisasi matrix

Solving Systems

• solve_linear_system(A, b) - Solve Ax = b
• least_squares(A, b) - Least squares solution

Matrix Power

• matrix_power(matrix, n) - Matrix pangkat n
• matrix_exp(matrix) - Matrix exponential
• matrix_log(matrix) - Matrix logarithm
• matrix_sqrt(matrix) - Matrix square root

Distance/Similarity

• frobenius_distance(matrix1, matrix2) - Jarak Frobenius
• cosine_similarity(vector1, vector2) - Cosine similarity

🛠️ Requirements

• Python >= 3.7
• NumPy >= 1.18.0
• SciPy >= 1.4.0

📝 License

This project is licensed under the MIT License - see the LICENSE file for details.

👨‍💻 Author

Budi Aji

🤝 Contributing

Contributions, issues, and feature requests are welcome!

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