File size: 9,039 Bytes
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import site
import sys
from pathlib import Path
_VENDOR_ROOT = Path(__file__).resolve().parent.parent / ".vendor"
for _vendor_path in (_VENDOR_ROOT / "python", _VENDOR_ROOT / "sitepkgs"):
if _vendor_path.exists():
vendor_text = str(_vendor_path)
if vendor_text not in sys.path:
sys.path.insert(0, vendor_text)
try:
import numpy as np
except ModuleNotFoundError:
user_site = site.getusersitepackages()
if user_site and user_site not in sys.path:
sys.path.append(user_site)
try:
import numpy as np
except ModuleNotFoundError:
np = None
if np is not None and not hasattr(np, "asarray"):
np = None
Matrix = list[list[float]]
Vector = list[float]
SUMPROD = getattr(math, "sumprod", None)
def zeros(rows: int, cols: int) -> Matrix:
return [[0.0 for _ in range(cols)] for _ in range(rows)]
def zeros_vector(size: int) -> Vector:
return [0.0 for _ in range(size)]
def identity(size: int) -> Matrix:
matrix = zeros(size, size)
for index in range(size):
matrix[index][index] = 1.0
return matrix
def copy_matrix(matrix: Matrix) -> Matrix:
return [row[:] for row in matrix]
def transpose(matrix: Matrix) -> Matrix:
if not matrix:
return []
if np is not None:
return np.asarray(matrix, dtype=np.float64).T.tolist()
return [list(column) for column in zip(*matrix)]
def matvec(matrix: Matrix, vector: Vector) -> Vector:
if np is not None:
return (np.asarray(matrix, dtype=np.float64) @ np.asarray(vector, dtype=np.float64)).tolist()
if SUMPROD is not None:
return [SUMPROD(row, vector) for row in matrix]
return [sum(value * vector[idx] for idx, value in enumerate(row)) for row in matrix]
def matmul(left: Matrix, right: Matrix) -> Matrix:
if not left or not right:
return []
if np is not None:
return (np.asarray(left, dtype=np.float64) @ np.asarray(right, dtype=np.float64)).tolist()
right_t = transpose(right)
if SUMPROD is not None:
return [[SUMPROD(row, column) for column in right_t] for row in left]
return [
[sum(a * b for a, b in zip(row, column)) for column in right_t]
for row in left
]
def add_matrices(left: Matrix, right: Matrix) -> Matrix:
return [
[left[row][col] + right[row][col] for col in range(len(left[row]))]
for row in range(len(left))
]
def subtract_matrices(left: Matrix, right: Matrix) -> Matrix:
return [
[left[row][col] - right[row][col] for col in range(len(left[row]))]
for row in range(len(left))
]
def scale_matrix(matrix: Matrix, scalar: float) -> Matrix:
return [[scalar * value for value in row] for row in matrix]
def dot(left: Vector, right: Vector) -> float:
if np is not None:
return float(np.dot(np.asarray(left, dtype=np.float64), np.asarray(right, dtype=np.float64)))
if SUMPROD is not None:
return SUMPROD(left, right)
return sum(a * b for a, b in zip(left, right))
def norm(vector: Vector) -> float:
return math.sqrt(dot(vector, vector))
def outer(left: Vector, right: Vector) -> Matrix:
if np is not None:
return np.outer(np.asarray(left, dtype=np.float64), np.asarray(right, dtype=np.float64)).tolist()
return [[a * b for b in right] for a in left]
def mean(values: Vector) -> float:
return sum(values) / len(values) if values else 0.0
def trace(matrix: Matrix) -> float:
return sum(matrix[index][index] for index in range(min(len(matrix), len(matrix[0]))))
def covariance_matrix(samples: list[Vector]) -> Matrix:
if not samples:
return []
if np is not None:
sample_array = np.asarray(samples, dtype=np.float64)
centered = sample_array - sample_array.mean(axis=0, keepdims=True)
denominator = max(len(samples) - 1, 1)
return ((centered.T @ centered) / denominator).tolist()
feature_count = len(samples[0])
sample_count = len(samples)
means = [
sum(sample[feature] for sample in samples) / sample_count
for feature in range(feature_count)
]
covariance = zeros(feature_count, feature_count)
for sample in samples:
centered = [sample[index] - means[index] for index in range(feature_count)]
for row in range(feature_count):
for col in range(feature_count):
covariance[row][col] += centered[row] * centered[col]
denominator = max(sample_count - 1, 1)
return scale_matrix(covariance, 1.0 / denominator)
def solve_linear_system(matrix: Matrix, vector: Vector) -> Vector:
if np is not None:
return np.linalg.solve(
np.asarray(matrix, dtype=np.float64),
np.asarray(vector, dtype=np.float64),
).tolist()
size = len(matrix)
augmented = [matrix[row][:] + [vector[row]] for row in range(size)]
for pivot_index in range(size):
pivot_row = max(
range(pivot_index, size),
key=lambda row_index: abs(augmented[row_index][pivot_index]),
)
augmented[pivot_index], augmented[pivot_row] = augmented[pivot_row], augmented[pivot_index]
pivot_value = augmented[pivot_index][pivot_index]
if abs(pivot_value) < 1e-12:
raise ValueError("Singular matrix encountered while solving linear system.")
inverse_pivot = 1.0 / pivot_value
augmented[pivot_index] = [value * inverse_pivot for value in augmented[pivot_index]]
for row_index in range(size):
if row_index == pivot_index:
continue
factor = augmented[row_index][pivot_index]
augmented[row_index] = [
augmented[row_index][col] - factor * augmented[pivot_index][col]
for col in range(size + 1)
]
return [augmented[row][-1] for row in range(size)]
def invert_matrix(matrix: Matrix) -> Matrix:
if np is not None:
return np.linalg.inv(np.asarray(matrix, dtype=np.float64)).tolist()
size = len(matrix)
inverse_columns = []
for basis_index in range(size):
basis_vector = [0.0 for _ in range(size)]
basis_vector[basis_index] = 1.0
inverse_columns.append(solve_linear_system(matrix, basis_vector))
return transpose(inverse_columns)
def dominant_eigenpair_symmetric(
matrix: Matrix,
max_iterations: int = 64,
tolerance: float = 1e-10,
) -> tuple[float, Vector]:
size = len(matrix)
if size == 0:
return 0.0, []
if np is not None:
values, vectors = np.linalg.eigh(np.asarray(matrix, dtype=np.float64))
index = int(np.argmax(values))
eigenvalue = float(values[index])
if eigenvalue <= tolerance:
return 0.0, zeros_vector(size)
return eigenvalue, vectors[:, index].astype(float).tolist()
vector = [1.0 / math.sqrt(size) for _ in range(size)]
for _ in range(max_iterations):
next_vector = matvec(matrix, vector)
next_norm = norm(next_vector)
if next_norm < tolerance:
return 0.0, zeros_vector(size)
next_vector = [value / next_norm for value in next_vector]
delta = max(abs(a - b) for a, b in zip(vector, next_vector))
vector = next_vector
if delta < tolerance:
break
eigenvalue = dot(vector, matvec(matrix, vector))
return eigenvalue, vector
def top_k_eigenpairs_symmetric(matrix: Matrix, k: int) -> list[tuple[float, Vector]]:
if np is not None and matrix:
values, vectors = np.linalg.eigh(np.asarray(matrix, dtype=np.float64))
ranked = sorted(
(
(float(values[index]), vectors[:, index].astype(float).tolist())
for index in range(len(values))
if float(values[index]) > 1e-9
),
key=lambda item: item[0],
reverse=True,
)
return ranked[: min(k, len(ranked))]
working = copy_matrix(matrix)
eigenpairs: list[tuple[float, Vector]] = []
for _ in range(min(k, len(working))):
eigenvalue, eigenvector = dominant_eigenpair_symmetric(working)
if eigenvalue <= 1e-9 or not eigenvector:
break
eigenpairs.append((eigenvalue, eigenvector))
deflation = scale_matrix(outer(eigenvector, eigenvector), eigenvalue)
working = subtract_matrices(working, deflation)
return eigenpairs
def softmax(logits: Vector) -> Vector:
if not logits:
return []
if np is not None:
values = np.asarray(logits, dtype=np.float64)
shifted = np.exp(values - values.max())
total = float(shifted.sum())
if total == 0.0:
return [1.0 / len(logits) for _ in logits]
return (shifted / total).tolist()
max_logit = max(logits)
shifted = [math.exp(logit - max_logit) for logit in logits]
total = sum(shifted)
if total == 0.0:
return [1.0 / len(logits) for _ in logits]
return [value / total for value in shifted]
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