NumPyの基本：配列と数学演算
NumPy配列を作成・操作し、ベクトル化された算術演算を実行して、数値データを効率的に扱うためのブロードキャストを理解します。
「NumPyの基本：配列と数学演算」はCoddyKit上の無料Machine Learning Academyレッスンです。 これはレッスン2/4です。 下記で完全なレッスンを無料で読むことができます。その後、ブラウザ内の組み込みコードエディタと24時間対応のAIチューターでハンズオン演習できます。 これはMachine Learning Academy学習パスの一部であり、ウェブとCoddyKitアプリ全体で進捗が同期されます。 Machine Learning Academyコースには全4レッスンが含まれています。
このレッスンの一部はまだ翻訳されておらず、英語で表示されています。
Why NumPy Is the Foundation of ML
NumPy is the foundation under every ML library. Its superpower is vectorized math: it works on whole arrays at once in fast C code, leaving Python loops in the dust.
import numpy as np
import time
# Speed comparison: NumPy vs Python list
n = 1_000_000
python_list = list(range(n))
np_array = np.arange(n)
# Python loop (slow)
start = time.time()
result = [x * 2 for x in python_list]
print(f'Python loop: {time.time() - start:.3f}s')
# NumPy vectorised (fast)
start = time.time()
result = np_array * 2
print(f'NumPy vectorised: {time.time() - start:.4f}s')Creating NumPy Arrays
The core NumPy object is the array. Its most important trait is shape — a tuple giving the size of each dimension, like (rows, cols). The code shows how to make them.
import numpy as np
# From Python list
a = np.array([1, 2, 3, 4, 5])
print('1D array:', a, '| shape:', a.shape) # (5,)
# 2D matrix from nested list
M = np.array([[1, 2, 3], [4, 5, 6]])
print('2D matrix shape:', M.shape) # (2, 3)
# Built-in generators
zeros = np.zeros((3, 4)) # 3x4 matrix of zeros
ones = np.ones((2, 5)) # 2x5 matrix of ones
range_arr = np.arange(0, 10, 2) # [0 2 4 6 8]
linspace = np.linspace(0, 1, 5) # 5 evenly spaced points
random = np.random.randn(3, 3) # 3x3 standard normalArray Indexing and Slicing
You index arrays with [row, col] and slice with start:stop:step. One gotcha: a slice is a view, not a copy — change it and you change the original. Use .copy() to be safe.
import numpy as np
M = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12]])
# Single element
print(M[1, 2]) # 7 (row 1, column 2)
# Slice rows and columns
print(M[0:2, 1:3]) # rows 0-1, columns 1-2 -> [[2,3],[6,7]]
# All rows, last column
print(M[:, -1]) # [4, 8, 12]
# Boolean indexing
print(M[M > 6]) # [7, 8, 9, 10, 11, 12]Vectorised Arithmetic Operations
NumPy math is element-wise by default: a + b adds matching elements with no loop. It runs in compiled C, which is why it flies on millions of numbers. See the code.
import numpy as np
a = np.array([1.0, 2.0, 3.0, 4.0])
b = np.array([10.0, 20.0, 30.0, 40.0])
print('Addition:', a + b) # [11. 22. 33. 44.]
print('Multiply:', a * b) # [10. 40. 90. 160.]
print('Power:', a ** 2) # [ 1. 4. 9. 16.]
print('Divide:', b / a) # [10. 10. 10. 10.]
# Scalar operations apply to all elements
print('Add scalar:', a + 100) # [101. 102. 103. 104.]
print('Square root:', np.sqrt(a)) # [1. 1.41 1.73 2.]Broadcasting: Operating on Different Shapes
Broadcasting lets NumPy combine different shapes by stretching the smaller one to fit. It's how you add a bias vector to a whole batch without writing any loops.
import numpy as np
# Matrix + vector (broadcasting)
matrix = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]) # shape (3, 3)
bias = np.array([10, 20, 30]) # shape (3,) -> broadcasts to (3, 3)
result = matrix + bias
print(result)
# [[11 22 33]
# [14 25 36]
# [17 28 39]]
# Normalize each column to zero mean (ML preprocessing)
mean = matrix.mean(axis=0) # shape (3,)
centered = matrix - mean # broadcasts across rowsAggregation Functions
Aggregations like mean and sum collapse an array down. The axis picks the direction: axis=0 goes down columns, axis=1 goes across rows. The code shows both.
import numpy as np
X = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]], dtype=float)
print('Global mean:', X.mean()) # 5.0
print('Column means:', X.mean(axis=0)) # [4. 5. 6.]
print('Row means:', X.mean(axis=1)) # [2. 5. 8.]
print('Global std:', X.std()) # ~2.58
print('Column max:', X.max(axis=0)) # [7. 8. 9.]
print('Row sum:', X.sum(axis=1)) # [ 6. 15. 24.]Matrix Multiplication: The Heart of ML
Matrix multiplication is the heart of ML — every neural net layer and prediction is one. Use @ (not *, which is element-wise). Inner shapes must match: (m,k) by (k,n).
import numpy as np
# Linear regression prediction: y_hat = X @ weights + bias
X = np.random.randn(100, 5) # 100 samples, 5 features
weights = np.random.randn(5) # one weight per feature
bias = 0.5
y_hat = X @ weights + bias # shape: (100,)
print('Predictions shape:', y_hat.shape)
# Matrix-matrix multiplication (e.g., two weight layers)
A = np.random.randn(4, 3) # (4, 3)
B = np.random.randn(3, 5) # (3, 5)
C = A @ B # (4, 5)
print('A @ B shape:', C.shape)Reshaping and Stacking Arrays
Reshaping changes an array's shape without touching its data — like flattening a 28x28 image into 784 numbers. Stacking with vstack or hstack joins arrays together.
import numpy as np
# Reshape: 1D to 2D
a = np.arange(12) # [0, 1, ..., 11]
matrix = a.reshape(3, 4) # shape (3, 4)
print('Reshaped:', matrix.shape)
# Use -1 to infer one dimension automatically
flat = matrix.reshape(-1) # back to 1D (12,)
row = matrix.reshape(1, -1) # shape (1, 12)
col = matrix.reshape(-1, 1) # shape (12, 1)
# Stack two arrays row-wise
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
stacked = np.vstack([A, B]) # shape (4, 2)Random Number Generation for ML
Random numbers drive weight init, shuffling, and train-test splits. Always set a seed so results repeat — without it, every run differs and debugging gets painful.
import numpy as np
# Set seed for reproducibility
rng = np.random.default_rng(seed=42)
# Common distributions used in ML
uniform = rng.uniform(0, 1, size=(3, 3)) # Uniform [0, 1)
normal = rng.normal(0, 1, size=(3, 3)) # Standard normal
integers = rng.integers(0, 10, size=5) # Random integers
# Shuffle an array
data = np.arange(10)
rng.shuffle(data)
print('Shuffled:', data)
# Random sampling without replacement
idxs = rng.choice(100, size=20, replace=False) # 20 unique indicesBoolean Masks and Fancy Indexing
Boolean masking filters arrays in one clean line: compare to a condition, then select the matches. Fancy indexing picks elements by an explicit list of positions.
import numpy as np
scores = np.array([85, 42, 91, 67, 55, 78, 33, 95])
# Boolean mask: select scores above 70
mask = scores > 70
print('Mask:', mask) # [T F T F F T F T]
print('High scores:', scores[mask]) # [85 91 78 95]
# Count how many passed
print('Passed:', mask.sum()) # 4
# Fancy indexing: select by explicit indices
indices = np.array([0, 2, 7])
print('Selected:', scores[indices]) # [85 91 95]
# Replace outliers
scores[scores < 50] = 50 # clip low scores to 50NumPy in scikit-learn Workflows
scikit-learn wants shapes right: X as 2D (samples, features), y as 1D (samples). A shape like (100,) instead of (100, 1) is a classic error — reshape(-1, 1) fixes it.
import numpy as np
from sklearn.linear_model import LinearRegression
# X must be 2D: (n_samples, n_features)
X = np.array([1, 2, 3, 4, 5]) # shape (5,) -- WRONG
# Fix:
X = X.reshape(-1, 1) # shape (5, 1) -- CORRECT
y = np.array([2.1, 4.0, 5.9, 8.1, 10.0]) # shape (5,) -- correct
model = LinearRegression()
model.fit(X, y)
print('Learned slope:', round(model.coef_[0], 2)) # ~2.0Quick Check
Test your understanding of Machine Learning with Python concepts from this lesson.
Lesson Recap
You learned the core of NumPy: arrays underpin all ML, vectorized math and broadcasting kill slow loops, and the @ operator runs every model. Next up: Pandas. 🐼
よくある質問
「NumPyの基本：配列と数学演算」レッスンは無料ですか？
はい。「NumPyの基本：配列と数学演算」の完全なテキストはこのウェブで無料で読めます。インタラクティブに演習し（組み込みコードエディタと24時間対応のAIチューター）、Machine Learning Academyコースの残りをアンロックするには、CoddyKit PROにアップグレードしてください。 Machine Learning Academyコースには全4レッスンが含まれています。
「NumPyの基本：配列と数学演算」で何を学びますか？
NumPy配列を作成・操作し、ベクトル化された算術演算を実行して、数値データを効率的に扱うためのブロードキャストを理解します。 ブラウザで直接実行するハンズオンコードでMachine Learning Academyを演習し、24時間対応のAIチューターがレッスンを進める中での質問に答えます。
Machine Learning Academyを始めるのに経験は必要ですか？
事前経験は必要ありません。CoddyKitのMachine Learning Academyは初級者から上級者向けに構成されているため、ここから始めるか最初から始めて、自分のペースで進むことができます。 これはレッスン2/4です。
「NumPyの基本：配列と数学演算」レッスンにはどのくらい時間がかかりますか？
ほとんどのCoddyKitレッスンは約5～10分かかります。各レッスンはコンパクトでインタラクティブなので、着実に進歩し、ウェブとアプリ全体で正確に前回の場所から再開できます。
このMachine Learning Academyレッスンでコードを書いて実行できますか？
はい。すべてのMachine Learning Academyレッスンに組み込みコードエディタが含まれているため、ブラウザでリアルコードを書いて実行し、即座のAIフィードバックを取得できます。ローカル設定は不要です。