المتجهات والمصفوفات

import math
from typing import List

# ─── Vector ────────────────────────────────────────────────
class Vector:
    def __init__(self, data: List[float]):
        self.data = data
        self.dim  = len(data)

    def __repr__(self) -> str:
        vals = ", ".join(f"{x:.2f}" for x in self.data)
        return f"Vector([{vals}])"

    def magnitude(self) -> float:
        return math.sqrt(sum(x**2 for x in self.data))

    def normalize(self) -> "Vector":
        mag = self.magnitude()
        return Vector([x / mag for x in self.data]) if mag > 0 else Vector([0.0]*self.dim)

    def dot(self, other: "Vector") -> float:
        return sum(a * b for a, b in zip(self.data, other.data))

    def cosine_similarity(self, other: "Vector") -> float:
        denom = self.magnitude() * other.magnitude()
        return self.dot(other) / denom if denom > 0 else 0.0

    def __add__(self, other: "Vector") -> "Vector":
        return Vector([a + b for a, b in zip(self.data, other.data)])

    def scale(self, s: float) -> "Vector":
        return Vector([x * s for x in self.data])

# ─── Matrix ────────────────────────────────────────────────
class Matrix:
    def __init__(self, data: List[List[float]]):
        self.data = data
        self.rows = len(data)
        self.cols = len(data[0]) if data else 0

    @classmethod
    def zeros(cls, r: int, c: int) -> "Matrix":
        return cls([[0.0]*c for _ in range(r)])

    @classmethod
    def identity(cls, n: int) -> "Matrix":
        m = cls.zeros(n, n)
        for i in range(n): m.data[i][i] = 1.0
        return m

    def transpose(self) -> "Matrix":
        return Matrix([[self.data[r][c] for r in range(self.rows)]
                       for c in range(self.cols)])

    def matmul(self, B: "Matrix") -> "Matrix":
        C = Matrix.zeros(self.rows, B.cols)
        for i in range(self.rows):
            for j in range(B.cols):
                C.data[i][j] = sum(self.data[i][k] * B.data[k][j] for k in range(self.cols))
        return C

    def show(self, name: str = ""):
        shape = f"{self.rows}×{self.cols}"
        if name: print(f"\n{name} ({shape}):")
        for row in self.data:
            cells = "  ".join(f"{x:6.2f}" for x in row)
            print(f"  [ {cells} ]")

# ─── Embeddings ────────────────────────────────────────────
print("🔢 المتجهات في AI — Word Embeddings:")
print("=" * 52)

words = {
    "ملك":   Vector([0.90, 0.10, 0.80, 0.20]),
    "ملكة":  Vector([0.90, 0.90, 0.80, 0.20]),
    "رجل":   Vector([0.80, 0.10, 0.10, 0.30]),
    "امرأة": Vector([0.80, 0.90, 0.10, 0.30]),
}

print("\n📐 Cosine Similarity بين الكلمات:")
keys = list(words.keys())
for i in range(len(keys)):
    for j in range(i+1, len(keys)):
        w1, w2 = keys[i], keys[j]
        sim = words[w1].cosine_similarity(words[w2])
        bar = "█" * int(sim * 10)
        print(f"  {w1:<8} ↔ {w2:<8}: {sim:.3f} {bar}")

# ─── Matrix Operations ─────────────────────────────────────
print(f"\n\n📊 المصفوفات في Neural Networks:")
# Input: 3 samples × 4 features
X = Matrix([[1.0, 0.5, 0.8, 0.2],
            [0.3, 0.9, 0.1, 0.7],
            [0.7, 0.4, 0.6, 0.5]])
# Weights: 4 → 2
W = Matrix([[0.1, 0.4],
            [0.3, 0.2],
            [0.2, 0.5],
            [0.4, 0.1]])

X.show("X (3 عينات × 4 ميزات)")
W.show("W (4 → 2 أوزان)")
Z = X.matmul(W)
Z.show("Z = X @ W (3 عينات × 2 مخرجات)")

# Transpose
WT = W.transpose()
WT.show("Wᵀ (2 × 4)")
print(f"\n✅ فهم المتجهات = فهم كيف يفكر النموذج!")