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Linear Algebra Tool - Các phép toán đại số tuyến tính.
===========================================
Dùng numpy lazy import. Hỗ trợ: dot, matmul, det, inv, eigen, svd, norm,
transpose, trace, solve, rank, qr.
Author: Hieu Louis (2026)
"""
from __future__ import annotations
from typing import Any, Dict, List, Optional
from .base import Tool, ToolResult, ToolContext, ToolCategory, ToolSafety
OPERATIONS = {
"dot", "matmul", "det", "inv", "eigen", "svd", "norm", "transpose",
"trace", "solve", "rank", "qr", "lu", "identity", "ones", "zeros",
}
def _to_matrix(data: Any) -> List[List[float]]:
"""Ép list[list|list-of-rows] → list[list[float]]. / Coerce to 2D float matrix."""
if not isinstance(data, (list, tuple)):
raise ValueError(f"matrix phải là list, got {type(data).__name__}")
if not data:
return []
# 1D → 2D row vector / promote 1D to row vector
if not isinstance(data[0], (list, tuple)):
return [[float(x) for x in data]]
return [[float(x) for x in row] for row in data]
class LinearAlgebraTool(Tool):
"""Đại số tuyến tính: dot, matmul, det, inv, eigen, svd, norm, ..."""
category = ToolCategory.MATH
safety = ToolSafety.SAFE
@property
def name(self) -> str:
return "linear_algebra"
@property
def description(self) -> str:
return "Linear algebra: dot/matmul/det/inv/eigen/svd/norm/solve/qr/lu (numpy backend)."
@property
def parameters(self) -> Dict[str, Any]:
return {
"type": "object",
"properties": {
"matrix_a": {"type": "array", "items": {"type": "array", "items": {"type": "number"}}},
"matrix_b": {"type": "array", "items": {"type": "array", "items": {"type": "number"}}},
"operation": {
"type": "string",
"enum": sorted(OPERATIONS),
"default": "matmul",
},
"params": {"type": "object"},
},
"required": ["operation"],
}
def validate_args(self, args: Dict[str, Any]) -> Optional[str]:
op = args.get("operation", "matmul")
if op not in OPERATIONS:
return f"Invalid operation='{op}'. Supported: {sorted(OPERATIONS)}"
# Phép toán 2 ngôi / binary ops require matrix_b
if op in ("matmul", "dot", "solve") and not args.get("matrix_b"):
return f"Missing required arg: matrix_b (cho operation='{op}')"
# Phép 1 ngôi cần matrix_a / unary ops require matrix_a
if op not in ("identity", "ones", "zeros") and not args.get("matrix_a"):
return f"Missing required arg: matrix_a (cho operation='{op}')"
if op in ("identity", "ones", "zeros"):
params = args.get("params", {}) or {}
if not params.get("shape"):
return f"Missing required param: params.shape (cho operation='{op}')"
return None
def _to_serializable(self, obj: Any) -> Any:
"""Convert numpy object sang JSON-safe (list/number). / Convert numpy → JSON-safe."""
try:
import numpy as np # type: ignore
if isinstance(obj, np.ndarray):
return obj.tolist()
if isinstance(obj, np.generic):
return obj.item()
except ImportError:
pass
if hasattr(obj, "tolist"):
try:
return obj.tolist()
except Exception:
pass
if isinstance(obj, (list, tuple)):
return [self._to_serializable(x) for x in obj]
if isinstance(obj, complex):
return {"real": obj.real, "imag": obj.imag}
return obj
def execute(self, args: Dict[str, Any], context: ToolContext) -> ToolResult:
op = args.get("operation", "matmul")
params: Dict[str, Any] = args.get("params", {}) or {}
if context.dry_run:
return ToolResult(
success=True,
output=f"[dry-run] linear_algebra op='{op}'",
metadata={"operation": op, "dry_run": True},
)
try:
import numpy as np # type: ignore
except ImportError:
return ToolResult(
success=False,
error="numpy chưa cài. Cài đặt: pip install numpy",
return_code=127,
)
try:
# Parse matrices / parse matrices
if op in ("identity", "ones", "zeros"):
shape = params["shape"]
if isinstance(shape, int):
shape = (shape, shape)
if op == "identity":
result: Any = np.identity(int(shape[0])).tolist()
elif op == "ones":
result = np.ones(tuple(int(s) for s in shape)).tolist()
else:
result = np.zeros(tuple(int(s) for s in shape)).tolist()
return ToolResult(success=True, output=str(result), metadata={"operation": op, "result": result})
A = np.array(_to_matrix(args["matrix_a"]), dtype=float)
B = None
if args.get("matrix_b"):
B = np.array(_to_matrix(args["matrix_b"]), dtype=float)
if op in ("matmul", "dot"):
if B is None:
return ToolResult(success=False, error=f"matrix_b required for {op}", return_code=1)
result = A @ B if op == "matmul" else np.dot(A, B)
elif op == "det":
result = float(np.linalg.det(A))
elif op == "inv":
result = np.linalg.inv(A)
elif op == "eigen":
# Trả về values + vectors / return both eigenvalues and eigenvectors
w, v = np.linalg.eig(A)
result = {"eigenvalues": self._to_serializable(w), "eigenvectors": self._to_serializable(v)}
elif op == "svd":
U, S, Vt = np.linalg.svd(A)
result = {
"U": self._to_serializable(U),
"singular_values": self._to_serializable(S),
"Vt": self._to_serializable(Vt),
}
elif op == "norm":
ord_val = params.get("ord", "fro") # type: ignore[assignment]
result = float(np.linalg.norm(A, ord=ord_val))
elif op == "transpose":
result = A.T
elif op == "trace":
result = float(np.trace(A))
elif op == "solve":
# Solve Ax = B cho x / solve linear system
if B is None:
return ToolResult(success=False, error="matrix_b required for solve", return_code=1)
if B.ndim == 1:
result = np.linalg.solve(A, B)
else:
result = np.linalg.solve(A, B)
elif op == "rank":
result = int(np.linalg.matrix_rank(A))
elif op == "qr":
Q, R = np.linalg.qr(A)
result = {"Q": self._to_serializable(Q), "R": self._to_serializable(R)}
elif op == "lu":
try:
from scipy.linalg import lu # type: ignore
P, L, U = lu(A)
result = {
"P": self._to_serializable(P),
"L": self._to_serializable(L),
"U": self._to_serializable(U),
}
except ImportError:
return ToolResult(
success=False,
error="scipy chưa cài cho lu decomposition. Cài đặt: pip install scipy",
return_code=127,
)
else:
return ToolResult(success=False, error=f"Unknown operation: {op}", return_code=1)
serializable = self._to_serializable(result)
return ToolResult(
success=True,
output=str(serializable),
metadata={
"operation": op,
"shape_a": list(A.shape),
"shape_b": list(B.shape) if B is not None else None,
"result": serializable,
},
)
except np.linalg.LinAlgError as e:
return ToolResult(success=False, error=f"LinAlgError: {e}", return_code=1)
except ValueError as e:
return ToolResult(success=False, error=f"ValueError: {e}", return_code=1)
except Exception as e:
return ToolResult(success=False, error=f"Compute failed: {e}", return_code=1)
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