背景¶
backtrader 已经比较完善了，我想要借鉴量化投资框架中其他项目的优势，继续改进优化 backtrader。
任务¶
阅读研究分析 backtrader 这个项目的源代码，了解这个项目。
阅读研究分析/Users/yunjinqi/Documents/量化交易框架/NumCpp
借鉴这个新项目的优点和功能，给 backtrader 优化改进提供新的建议
写需规文档和设计文档放到这个文档的最下面，方便后续借鉴
NumCpp 项目简介¶
NumCpp 是 NumPy 的 C++实现版本，提供类似 NumPy 的 API，具有以下核心特点：
C++实现: 高性能 C++数值计算库
NumPy API: 类似 NumPy 的 API 设计
矩阵运算: 高效矩阵运算
向量化: 向量化计算支持
模板编程: C++模板元编程
头文件库: Header-only 设计
重点借鉴方向¶
数值计算: 高性能数值计算
矩阵运算: 矩阵运算优化
向量化: 向量化计算技术
API 设计: NumPy 风格 API
模板设计: C++模板设计
内存管理: 高效内存管理
项目对比分析¶
Backtrader vs NumCpp 架构对比¶
| 维度 | Backtrader | NumCpp |
|——|———–|———|
| 核心定位| 量化交易回测框架 | 数值计算库 |
|实现语言| Python + Cython | C++ (Header-only) |
|数据结构| LineBuffer/LineSeries | NdArray |
|数组支持| 1D 时间序列 | 1D/2D 数组 |
|切片操作| 基础索引 | NumPy 风格 Slice |
|广播机制| 无 | 完整广播支持 |
|线性代数| 依赖 numpy/linalg | 内置 Linalg 模块 |
|类型系统| Python 动态类型 | C++模板+类型特征 |
|内存管理| Python GC | 自定义 Allocator |
|编译检查| 运行时 | 编译时静态检查 |
NumCpp 可借鉴的核心优势¶
1. 模板元编程¶
零开销抽象: 编译时多态，无虚函数开销
类型安全: 编译时类型检查
泛型算法: 一套代码支持多种数据类型
2. NdArray 设计¶
template<typename dtype, class Allocator = std::allocator<dtype>>
class NdArray {
Shape shape_; // 2D 形状
size_type size_; // 总元素数
dtype* array_; // 原始数据指针
bool ownsPtr_; // 内存所有权
allocator_type allocator_; // 自定义分配器
};
```bash
#### 3. 广播机制
- **形状兼容检查**: 自动验证形状兼容性
- **标量广播**: 标量与数组操作
- **维度广播**: 行/列级广播
- **高效实现**: 最小化内存拷贝
#### 4. Shape 和 Slice 类
- **Shape 类**: 2D 形状表示，支持 size/isnull/issquare 等方法
- **Slice 类**: NumPy 风格切片，支持负索引和步长
- **边界检查**: 自动验证和修正索引
#### 5. 内存管理策略
- **自定义 Allocator**: 支持 STL 分配器接口
- **所有权控制**: ownsPtr_标志控制内存管理
- **RAII 模式**: 自动内存管理
#### 6. 线性代数模块
- **矩阵分解**: LU、Cholesky、SVD、QR
- **求解器**: solve、lstsq
- **矩阵运算**: inv、det、matrix_power
- **特征值**: eigenvalue 分解
#### 7. 类型特征系统
```cpp
// 编译时类型检查
template<typename>
struct is_ndarray_int : std::false_type {};
template<typename dtype, typename Allocator>
struct is_ndarray_int<NdArray<dtype, Allocator>> {
static constexpr bool value = std::is_integral_v<dtype>;
};
```bash
- --
## 需求文档
### 需求概述
借鉴 NumCpp 项目的高性能数值计算设计，为 backtrader 添加以下功能模块，提升计算性能和 API 易用性：
### 功能需求
#### FR1: 增强数组数据结构
- *FR1.1 NdArray 兼容接口**
- 需求描述: 提供类似 NumCpp 的 NdArray 接口
- 优先级: 高
- 验收标准:
- 实现 Array 类支持 1D/2D 数组
- 支持 shape 属性查询
- 支持 reshape 操作
- 支持 astype 类型转换
- *FR1.2 切片操作**
- 需求描述: 支持 NumPy 风格的切片
- 优先级: 高
- 验收标准:
- 实现 Slice 类
- 支持 start/stop/step 语法
- 支持负索引
- 支持多维切片
- *FR1.3 数组创建**
- 需求描述: 提供便捷的数组创建方法
- 优先级: 中
- 验收标准:
- zeros/ones 创建
- arange/linspace 创建
- random 创建随机数组
- from_list 从列表创建
#### FR2: 广播机制
- *FR2.1 形状广播**
- 需求描述: 支持不同形状数组间的运算
- 优先级: 高
- 验收标准:
- 标量与数组广播
- 行向量广播
- 列向量广播
- 广播规则验证
- *FR2.2 逐元素运算**
- 需求描述: 高效的逐元素运算
- 优先级: 高
- 验收标准:
- 四则运算广播
- 比较运算广播
- 数学函数广播
#### FR3: 线性代数增强
- *FR3.1 矩阵运算**
- 需求描述: 完整的矩阵运算支持
- 优先级: 高
- 验收标准:
- 矩阵乘法 dot/matmul
- 矩阵转置 transpose
- 矩阵求逆 inv
- 矩阵行列式 det
- *FR3.2 矩阵分解**
- 需求描述: 常用矩阵分解算法
- 优先级: 中
- 验收标准:
- LU 分解
- Cholesky 分解
- SVD 奇异值分解
- QR 分解
- *FR3.3 求解器**
- 需求描述: 线性方程组求解
- 优先级: 中
- 验收标准:
- solve 求解器
- lstsq 最小二乘
- 特征值求解
#### FR4: 性能优化
- *FR4.1 SIMD 支持**
- 需求描述: 使用 SIMD 指令加速计算
- 优先级: 中
- 验收标准:
- 检测 CPU SIMD 支持
- SSE/AVX 加速
- 降级到标量实现
- *FR4.2 内存优化**
- 需求描述: 高效内存管理
- 优先级: 中
- 验收标准:
- 内存池支持
- 零拷贝视图
- 就地操作
- *FR4.3 并行计算**
- 需求描述: 多线程并行计算
- 优先级: 低
- 验收标准:
- OpenMP 支持
- TBB 集成
- 可配置线程数
#### FR5: 类型安全
- *FR5.1 类型特征**
- 需求描述: 编译时类型检查
- 优先级: 中
- 验收标准:
- 整数类型检查
- 浮点类型检查
- 复数类型支持
- *FR5.2 静态断言**
- 需求描述: 编译时错误检测
- 优先级: 中
- 验收标准:
- 有效 dtype 检查
- 维度检查
- 形状兼容性检查
### 非功能需求
#### NFR1: 性能
- 数组运算延迟 < NumPy 的 2 倍
- 内存占用与 NumPy 相当
- 大数组(>1M 元素)高效处理
#### NFR2: 兼容性
- 与 NumPy API 保持一致
- 支持 Python 3.7+
- 支持 Windows/Linux/MacOS
#### NFR3: 可用性
- 清晰的错误提示
- 完整的文档字符串
- 丰富的使用示例
- --
## 设计文档
### 整体架构设计
#### 新增模块结构
```bash
backtrader/
├── backtrader/
│ ├── arrays/ # 新增：数组模块
│ │ ├── __init__.py
│ │ ├── array.py # 核心数组类
│ │ ├── slice.py # 切片类
│ │ ├── shape.py # 形状类
│ │ ├── dtype.py # 数据类型
│ │ └── broadcasting.py # 广播机制
│ ├── linalg/ # 新增：线性代数模块
│ │ ├── __init__.py
│ │ ├── matrix.py # 矩阵运算
│ │ ├── decompose.py # 矩阵分解
│ │ └── solve.py # 求解器
│ ├── optimize/ # 新增：性能优化
│ │ ├── __init__.py
│ │ ├── simd.py # SIMD 加速
│ │ ├── parallel.py # 并行计算
│ │ └── memory.py # 内存优化
│ └── functions/ # 新增：数学函数
│ ├── __init__.py
│ ├── statistical.py # 统计函数
│ ├── mathematical.py # 数学函数
│ └── logical.py # 逻辑函数
```bash
### 详细设计
#### 1. 增强数组数据结构
- *1.1 Shape 类**
```python
# backtrader/arrays/shape.py
from typing import Tuple
from dataclasses import dataclass
@dataclass(frozen=True)
class Shape:
"""数组形状类 - NumCpp 兼容"""
rows: int
cols: int
def __post_init__(self):
if self.rows < 0 or self.cols < 0:
raise ValueError(f"Invalid shape: ({self.rows}, {self.cols})")
@property
def size(self) -> int:
"""总元素数"""
return self.rows *self.cols
@property
def ndim(self) -> int:
"""维度数"""
if self.rows == 1:
return 1
return 2
@property
def is_null(self) -> bool:
"""是否为空"""
return self.rows == 0 or self.cols == 0
@property
def is_square(self) -> bool:
"""是否为方阵"""
return self.rows == self.cols
def as_tuple(self) -> Tuple[int, int]:
"""转换为元组"""
return (self.rows, self.cols)
def __eq__(self, other) -> bool:
if not isinstance(other, Shape):
return False
return self.rows == other.rows and self.cols == other.cols
def __ne__(self, other) -> bool:
return not self.__eq__(other)
def __str__(self) -> str:
return f"[{self.rows}, {self.cols}]"
def __repr__(self) -> str:
return f"Shape({self.rows}, {self.cols})"
```bash
- *1.2 Slice 类**
```python
# backtrader/arrays/slice.py
from typing import List, Union, Optional
import numpy as np
class Slice:
"""切片类 - NumPy 风格切片
支持[start:stop:step]语法，包括负索引
"""
def __init__(self, start: Optional[Union[int, slice]] = None,
stop: Optional[int] = None,
step: Optional[int] = None):
# 支持多种初始化方式
if isinstance(start, slice):
self.start = start.start if start.start is not None else 0
self.stop = start.stop if start.stop is not None else -1
self.step = start.step if start.step is not None else 1
else:
self.start = start if start is not None else 0
self.stop = stop if stop is not None else -1
self.step = step if step is not None else 1
def make_positive(self, array_size: int) -> 'Slice':
"""转换负索引为正索引"""
start = self.start
stop = self.stop
if start < 0:
start += array_size
if stop < 0:
stop += array_size
if stop == -1 or stop is None:
stop = array_size
# 边界检查
if start < 0:
start = 0
if start > array_size:
start = array_size
if stop < 0:
stop = 0
if stop > array_size:
stop = array_size
return Slice(start, stop, self.step)
def to_indices(self, array_size: int) -> List[int]:
"""转换为索引列表"""
positive_slice = self.make_positive(array_size)
indices = []
current = positive_slice.start
stop = positive_slice.stop
step = positive_slice.step
if step > 0:
while current < stop:
indices.append(current)
current += step
else:
while current > stop:
indices.append(current)
current += step
return indices
def num_elements(self, array_size: int) -> int:
"""计算切片包含的元素数"""
return len(self.to_indices(array_size))
def __eq__(self, other) -> bool:
if not isinstance(other, Slice):
return False
return (self.start == other.start and
self.stop == other.stop and
self.step == other.step)
def __repr__(self) -> str:
return f"Slice({self.start}:{self.stop}:{self.step})"
def slice(obj) -> Slice:
"""创建切片的便捷函数"""
if isinstance(obj, Slice):
return obj
if isinstance(obj, slice):
return Slice(obj)
if isinstance(obj, (list, tuple)):
if len(obj) == 1:
return Slice(stop=obj[0])
elif len(obj) == 2:
return Slice(obj[0], obj[1])
elif len(obj) == 3:
return Slice(obj[0], obj[1], obj[2])
return Slice(obj)
```bash
- *1.3 Array 类**
```python
# backtrader/arrays/array.py
import numpy as np
from typing import Union, List, Tuple, Optional, Iterator
from .shape import Shape
from .slice import Slice as BTCSlice
class Array:
"""增强数组类 - NumCpp 风格接口
提供类似 NumCpp 的 NdArray 接口，兼容 NumPy 数组
"""
def __init__(self, data: Union[np.ndarray, List, Tuple, 'Array'] = None,
shape: Optional[Tuple[int, int]] = None,
dtype: Optional[type] = None,
copy: bool = True):
if data is None:
if shape is None:
shape = (0, 0)
self._array = np.empty(shape, dtype=dtype or float)
elif isinstance(data, Array):
self._array = data._array.copy() if copy else data._array
elif isinstance(data, np.ndarray):
self._array = data.copy() if copy else data
else:
self._array = np.array(data, dtype=dtype, copy=copy)
self._shape = Shape(*self._array.shape[:2])
if self._array.ndim == 1:
self._shape = Shape(1, self._array.shape[0])
@property
def shape(self) -> Shape:
"""获取形状"""
return self._shape
@property
def size(self) -> int:
"""总元素数"""
return self._shape.size
@property
def ndim(self) -> int:
"""维度数"""
return self._shape.ndim
@property
def dtype(self) -> np.dtype:
"""数据类型"""
return self._array.dtype
@property
def T(self) -> 'Array':
"""转置视图"""
return Array(self._array.T, copy=False)
def reshape(self, rows: int, cols: int) -> 'Array':
"""重塑数组形状"""
if rows *cols != self.size:
raise ValueError(f"Cannot reshape {self.shape} to ({rows}, {cols})")
return Array(self._array.reshape(rows, cols), copy=False)
def astype(self, dtype: type) -> 'Array':
"""转换数据类型"""
return Array(self._array.astype(dtype), copy=False)
def flatten(self) -> 'Array':
"""展平为一维"""
return Array(self._array.flatten(), copy=False)
def ravel(self) -> 'Array':
"""展平视图"""
return Array(self._array.ravel(), copy=False)
def transpose(self) -> 'Array':
"""转置"""
return Array(self._array.T, copy=False)
def copy(self) -> 'Array':
"""创建副本"""
return Array(self._array, copy=True)
# 切片操作
def __getitem__(self, key) -> 'Array':
"""获取切片"""
result = self._array[key]
if not isinstance(result, np.ndarray):
return result
return Array(result, copy=False)
def __setitem__(self, key, value):
"""设置切片"""
self._array[key] = value
# 运算符重载
def __add__(self, other) -> 'Array':
return Array(self._array + self._to_array(other)._array)
def __sub__(self, other) -> 'Array':
return Array(self._array - self._to_array(other)._array)
def __mul__(self, other) -> 'Array':
return Array(self._array* self._to_array(other)._array)
def __truediv__(self, other) -> 'Array':
return Array(self._array / self._to_array(other)._array)
def __pow__(self, other) -> 'Array':
return Array(self._array ** self._to_array(other)._array)
def __radd__(self, other) -> 'Array':
return Array(self._to_array(other)._array + self._array)
def __rsub__(self, other) -> 'Array':
return Array(self._to_array(other)._array - self._array)
def __rmul__(self, other) -> 'Array':
return Array(self._to_array(other)._array * self._array)
def __rtruediv__(self, other) -> 'Array':
return Array(self._to_array(other)._array / self._array)
def __neg__(self) -> 'Array':
return Array(-self._array)
def __pos__(self) -> 'Array':
return Array(+self._array)
def __abs__(self) -> 'Array':
return Array(np.abs(self._array))
# 比较运算
def __eq__(self, other) -> 'Array':
return Array(self._array == self._to_array(other)._array)
def __ne__(self, other) -> 'Array':
return Array(self._array != self._to_array(other)._array)
def __lt__(self, other) -> 'Array':
return Array(self._array < self._to_array(other)._array)
def __le__(self, other) -> 'Array':
return Array(self._array <= self._to_array(other)._array)
def __gt__(self, other) -> 'Array':
return Array(self._array > self._to_array(other)._array)
def __ge__(self, other) -> 'Array':
return Array(self._array >= self._to_array(other)._array)
# 聚合操作
def sum(self, axis: Optional[int] = None) -> Union['Array', float]:
"""求和"""
result = self._array.sum(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def mean(self, axis: Optional[int] = None) -> Union['Array', float]:
"""平均值"""
result = self._array.mean(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def std(self, axis: Optional[int] = None) -> Union['Array', float]:
"""标准差"""
result = self._array.std(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def var(self, axis: Optional[int] = None) -> Union['Array', float]:
"""方差"""
result = self._array.var(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def min(self, axis: Optional[int] = None) -> Union['Array', float]:
"""最小值"""
result = self._array.min(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def max(self, axis: Optional[int] = None) -> Union['Array', float]:
"""最大值"""
result = self._array.max(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def argmin(self, axis: Optional[int] = None) -> Union['Array', int]:
"""最小值索引"""
result = self._array.argmin(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def argmax(self, axis: Optional[int] = None) -> Union['Array', int]:
"""最大值索引"""
result = self._array.argmax(axis=axis)
return Array(result) if isinstance(result, np.ndarray) else result
def any(self) -> bool:
"""是否有任何 True"""
return self._array.any()
def all(self) -> bool:
"""是否全部 True"""
return self._array.all()
# 转换为 NumPy
def to_numpy(self) -> np.ndarray:
"""转换为 NumPy 数组"""
return self._array.copy()
# 迭代器
def __iter__(self) -> Iterator:
return iter(self._array)
def __len__(self) -> int:
return len(self._array)
def __repr__(self) -> str:
return f"Array(shape={self.shape}, dtype={self.dtype})"
def __str__(self) -> str:
return str(self._array)
# 私有方法
def _to_array(self, other) -> 'Array':
"""转换为 Array"""
if isinstance(other, Array):
return other
return Array(other)
@property
def rows(self) -> int:
"""行数"""
return self._shape.rows
@property
def cols(self) -> int:
"""列数"""
return self._shape.cols
@classmethod
def zeros(cls, shape: Tuple[int, int], dtype: type = float) -> 'Array':
"""创建全零数组"""
return cls(np.zeros(shape, dtype=dtype), copy=False)
@classmethod
def ones(cls, shape: Tuple[int, int], dtype: type = float) -> 'Array':
"""创建全 1 数组"""
return cls(np.ones(shape, dtype=dtype), copy=False)
@classmethod
def empty(cls, shape: Tuple[int, int], dtype: type = float) -> 'Array':
"""创建空数组"""
return cls(np.empty(shape, dtype=dtype), copy=False)
@classmethod
def arange(cls, start: int, stop: Optional[int] = None,
step: int = 1, dtype: type = float) -> 'Array':
"""创建等差数列"""
if stop is None:
stop = start
start = 0
return cls(np.arange(start, stop, step, dtype=dtype), copy=False)
@classmethod
def linspace(cls, start: float, stop: float,
num: int = 50, endpoint: bool = True) -> 'Array':
"""创建线性空间"""
return cls(np.linspace(start, stop, num, endpoint=endpoint), copy=False)
@classmethod
def eye(cls, n: int, m: Optional[int] = None,
k: int = 0, dtype: type = float) -> 'Array':
"""创建单位矩阵"""
m = m if m is not None else n
return cls(np.eye(n, m, k, dtype=dtype), copy=False)
@classmethod
def diag(cls, v: Union['Array', List], k: int = 0) -> 'Array':
"""创建对角矩阵"""
if isinstance(v, Array):
v = v.to_numpy()
return cls(np.diag(v, k), copy=False)
@classmethod
def random(cls, shape: Tuple[int, int],
low: float = 0.0, high: float = 1.0) -> 'Array':
"""创建随机数组"""
return cls(np.random.uniform(low, high, shape), copy=False)
@classmethod
def randint(cls, low: int, high: int,
shape: Tuple[int, int]) -> 'Array':
"""创建随机整数数组"""
return cls(np.random.randint(low, high, shape), copy=False)
@classmethod
def randn(cls, shape: Tuple[int, int]) -> 'Array':
"""创建标准正态分布随机数组"""
return cls(np.random.randn(*shape), copy=False)
```bash
#### 2. 广播机制
- *2.1 广播器**
```python
# backtrader/arrays/broadcasting.py
from typing import Tuple, Callable
import numpy as np
from .array import Array
class Broadcaster:
"""广播机制 - NumCpp 风格广播"""
@staticmethod
def broadcast_shapes(shape1: Tuple[int, int],
shape2: Tuple[int, int]) -> Tuple[int, int]:
"""计算广播后的形状"""
rows1, cols1 = shape1
rows2, cols2 = shape2
# 标量广播
if rows1 == 1 and cols1 == 1:
return shape2
if rows2 == 1 and cols2 == 1:
return shape1
# 行广播
if rows1 == 1 and cols1 == cols2:
return shape2
if rows2 == 1 and cols2 == cols1:
return shape1
# 列广播
if cols1 == 1 and rows1 == rows2:
return shape2
if cols2 == 1 and rows2 == rows1:
return shape1
# 完全匹配
if shape1 == shape2:
return shape1
raise ValueError(f"Cannot broadcast shapes {shape1} and {shape2}")
@staticmethod
def is_broadcastable(shape1: Tuple[int, int],
shape2: Tuple[int, int]) -> bool:
"""检查是否可广播"""
try:
Broadcaster.broadcast_shapes(shape1, shape2)
return True
except ValueError:
return False
@staticmethod
def broadcast_to(array: Array, shape: Tuple[int, int]) -> Array:
"""广播数组到指定形状"""
current_shape = array.shape.as_tuple()
if current_shape == shape:
return array
rows, cols = current_shape
target_rows, target_cols = shape
result = array.to_numpy()
# 标量广播
if rows == 1 and cols == 1:
return Array(np.full(shape, result[0, 0]))
# 行广播
if rows == 1 and cols == target_cols:
return Array(np.repeat(result, target_rows, axis=0))
# 列广播
if cols == 1 and rows == target_rows:
return Array(np.repeat(result, target_cols, axis=1))
raise ValueError(f"Cannot broadcast {current_shape} to {shape}")
@staticmethod
def broadcast_arrays(*arrays: Array) -> Tuple[Array, ...]:
"""广播多个数组到相同形状"""
if not arrays:
return ()
# 计算目标形状
target_shape = arrays[0].shape.as_tuple()
for arr in arrays[1:]:
target_shape = Broadcaster.broadcast_shapes(
target_shape, arr.shape.as_tuple()
)
# 广播所有数组
return tuple(Broadcaster.broadcast_to(arr, target_shape) for arr in arrays)
@staticmethod
def apply_binary(func: Callable, a1: Array, a2: Array) -> Array:
"""应用二元运算函数，支持广播"""
if a1.shape == a2.shape:
return Array(func(a1.to_numpy(), a2.to_numpy()), copy=False)
# 广播后运算
b1, b2 = Broadcaster.broadcast_arrays(a1, a2)
return Array(func(b1.to_numpy(), b2.to_numpy()), copy=False)
@staticmethod
def apply_unary(func: Callable, arr: Array) -> Array:
"""应用一元运算函数"""
return Array(func(arr.to_numpy()), copy=False)
```bash
#### 3. 线性代数增强
- *3.1 矩阵运算**
```python
# backtrader/linalg/matrix.py
import numpy as np
from typing import Union, Tuple
from ..arrays.array import Array
class MatrixOps:
"""矩阵运算模块 - NumCpp Linalg 兼容"""
@staticmethod
def dot(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray]) -> Array:
"""矩阵乘法/点积
对于 1D 数组：内积
对于 2D 数组：矩阵乘法
"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
result = np.dot(a_arr, b_arr)
return Array(result, copy=False)
@staticmethod
def matmul(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray]) -> Array:
"""矩阵乘法"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
result = np.matmul(a_arr, b_arr)
return Array(result, copy=False)
@staticmethod
def transpose(arr: Union[Array, np.ndarray]) -> Array:
"""转置"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
return Array(arr_arr.T, copy=False)
@staticmethod
def inv(arr: Union[Array, np.ndarray]) -> Array:
"""矩阵求逆"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.linalg.inv(arr_arr)
return Array(result, copy=False)
@staticmethod
def pinv(arr: Union[Array, np.ndarray]) -> Array:
"""伪逆"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.linalg.pinv(arr_arr)
return Array(result, copy=False)
@staticmethod
def det(arr: Union[Array, np.ndarray]) -> float:
"""行列式"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
return np.linalg.det(arr_arr)
@staticmethod
def matrix_power(arr: Union[Array, np.ndarray], n: int) -> Array:
"""矩阵幂"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.linalg.matrix_power(arr_arr, n)
return Array(result, copy=False)
@staticmethod
def rank(arr: Union[Array, np.ndarray]) -> int:
"""矩阵秩"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
return np.linalg.matrix_rank(arr_arr)
@staticmethod
def trace(arr: Union[Array, np.ndarray]) -> float:
"""迹（对角元素之和）"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
return np.trace(arr_arr)
@staticmethod
def diagonal(arr: Union[Array, np.ndarray], k: int = 0) -> Array:
"""对角线元素"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.diag(arr_arr, k)
return Array(result, copy=False)
@staticmethod
def multi_dot(arrays: list) -> Array:
"""多个矩阵的乘积"""
numpy_arrays = []
for arr in arrays:
if isinstance(arr, Array):
numpy_arrays.append(arr.to_numpy())
else:
numpy_arrays.append(arr)
result = np.linalg.multi_dot(numpy_arrays)
return Array(result, copy=False)
@staticmethod
def outer(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray]) -> Array:
"""外积"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
result = np.outer(a_arr, b_arr)
return Array(result, copy=False)
@staticmethod
def inner(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray]) -> Array:
"""内积"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
result = np.inner(a_arr, b_arr)
return Array(result, copy=False)
@staticmethod
def kron(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray]) -> Array:
"""克罗内克积"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
result = np.kron(a_arr, b_arr)
return Array(result, copy=False)
```bash
- *3.2 矩阵分解**
```python
# backtrader/linalg/decompose.py
import numpy as np
from typing import Tuple, Union
from ..arrays.array import Array
class Decomposition:
"""矩阵分解模块"""
@staticmethod
def cholesky(arr: Union[Array, np.ndarray]) -> Array:
"""Cholesky 分解
要求：正定矩阵
返回：下三角矩阵 L，使得 A = L *L.T
"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.linalg.cholesky(arr_arr)
return Array(result, copy=False)
@staticmethod
def qr(arr: Union[Array, np.ndarray],
mode: str = 'reduced') -> Tuple[Array, Array]:
"""QR 分解
返回：Q (正交矩阵), R (上三角矩阵)
"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
q, r = np.linalg.qr(arr_arr, mode=mode)
return Array(q, copy=False), Array(r, copy=False)
@staticmethod
def svd(arr: Union[Array, np.ndarray],
full_matrices: bool = True,
compute_uv: bool = True) -> Union[Array, Tuple[Array, Array, Array]]:
"""奇异值分解
返回：U, s, Vt
"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.linalg.svd(arr_arr, full_matrices=full_matrices,
compute_uv=compute_uv)
if compute_uv:
u, s, vh = result
return Array(u, copy=False), Array(s, copy=False), Array(vh, copy=False)
return Array(result, copy=False)
@staticmethod
def eig(arr: Union[Array, np.ndarray]) -> Tuple[Array, Array]:
"""特征值分解
返回：特征值 w, 特征向量 v
"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
w, v = np.linalg.eig(arr_arr)
return Array(w, copy=False), Array(v, copy=False)
@staticmethod
def eigh(arr: Union[Array, np.ndarray],
UPLO: str = 'L') -> Tuple[Array, Array]:
"""Hermite 矩阵特征值分解
适用于实对称/复共轭对称矩阵
"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
w, v = np.linalg.eigh(arr_arr, UPLO=UPLO)
return Array(w, copy=False), Array(v, copy=False)
@staticmethod
def lu(arr: Union[Array, np.ndarray]) -> Tuple[Array, Array, Array]:
"""LU 分解
使用 SciPy 的 lu 函数
"""
from scipy.linalg import lu
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
p, l, u = lu(arr_arr)
return Array(p, copy=False), Array(l, copy=False), Array(u, copy=False)
```bash
- *3.3 求解器**
```python
# backtrader/linalg/solve.py
import numpy as np
from typing import Union, Tuple
from ..arrays.array import Array
class Solver:
"""线性方程组求解器"""
@staticmethod
def solve(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray]) -> Array:
"""求解线性方程组 ax = b
使用最小二乘法
"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
result = np.linalg.solve(a_arr, b_arr)
return Array(result, copy=False)
@staticmethod
def lstsq(a: Union[Array, np.ndarray],
b: Union[Array, np.ndarray],
rcond: Optional[float] = None) -> Tuple[Array, Array, Array, int]:
"""最小二乘求解
返回：x, residuals, rank, s
"""
a_arr = a.to_numpy() if isinstance(a, Array) else a
b_arr = b.to_numpy() if isinstance(b, Array) else b
x, residuals, rank, s = np.linalg.lstsq(a_arr, b_arr, rcond=rcond)
return (Array(x, copy=False),
Array(residuals, copy=False),
rank,
Array(s, copy=False))
@staticmethod
def norm(x: Union[Array, np.ndarray],
ord: Union[int, float, str] = None) -> float:
"""向量或矩阵范数"""
x_arr = x.to_numpy() if isinstance(x, Array) else x
return np.linalg.norm(x_arr, ord=ord)
@staticmethod
def cond(x: Union[Array, np.ndarray],
p: Union[int, float, str] = None) -> float:
"""条件数"""
x_arr = x.to_numpy() if isinstance(x, Array) else x
return np.linalg.cond(x_arr, p=p)
@staticmethod
def matrix_balance(arr: Union[Array, np.ndarray]) -> Tuple[Array, Array]:
"""矩阵平衡"""
from scipy.linalg import matrix_balance
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
balanced, perm = matrix_balance(arr_arr)
return Array(balanced, copy=False), Array(perm, copy=False)
```bash
#### 4. 性能优化
- *4.1 SIMD 支持**
```python
# backtrader/optimize/simd.py
import numpy as np
import platform
import ctypes
from typing import Union
class SIMDSupport:
"""SIMD 加速支持"""
# CPU 特性检测
_has_sse = False
_has_sse2 = False
_has_sse3 = False
_has_avx = False
_has_avx2 = False
_has_avx512 = False
_has_neon = False # ARM
@classmethod
def detect(cls):
"""检测 CPU SIMD 支持"""
system = platform.system()
if system == "Linux":
try:
with open('/proc/cpuinfo', 'r') as f:
cpuinfo = f.read()
cls._has_sse = 'sse' in cpuinfo.lower()
cls._has_sse2 = 'sse2' in cpuinfo.lower()
cls._has_sse3 = 'sse3' in cpuinfo.lower()
cls._has_avx = 'avx' in cpuinfo.lower()
cls._has_avx2 = 'avx2' in cpuinfo.lower()
cls._has_avx512 = 'avx512' in cpuinfo.lower()
cls._has_neon = 'neon' in cpuinfo.lower()
except:
pass
elif system == "Darwin": # macOS
# macOS x86_64 always has SSE/AVX
# ARM macOS has NEON
machine = platform.machine()
if machine == 'x86_64':
cls._has_sse = True
cls._has_sse2 = True
cls._has_sse3 = True
cls._has_avx = True
cls._has_avx2 = True
elif machine == 'arm64':
cls._has_neon = True
elif system == "Windows":
# Windows: 尝试使用 IsProcessorFeaturePresent
try:
kernel32 = ctypes.windll.kernel32
# 检测各种 SIMD 特性
cls._has_sse = True # 假设现代 CPU 都有
cls._has_sse2 = True
except:
pass
@classmethod
def has_sse(cls) -> bool:
return cls._has_sse
@classmethod
def has_avx(cls) -> bool:
return cls._has_avx
@classmethod
def has_avx2(cls) -> bool:
return cls._has_avx2
@classmethod
def has_neon(cls) -> bool:
return cls._has_neon
@classmethod
def get_optimized_config(cls) -> dict:
"""获取优化配置"""
cls.detect()
return {
'sse': cls._has_sse,
'sse2': cls._has_sse2,
'sse3': cls._has_sse3,
'avx': cls._has_avx,
'avx2': cls._has_avx2,
'avx512': cls._has_avx512,
'neon': cls._has_neon,
}
# 自动检测
SIMDSupport.detect()
def vectorized_add(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""向量化的加法运算
根据 SIMD 支持选择最优实现
"""
# 使用 NumPy 的向量化操作（底层使用 SIMD）
return a + b
def vectorized_mul(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""向量化的乘法运算"""
return a *b
def vectorized_sum(arr: np.ndarray, axis: int = None) -> np.ndarray:
"""向量化的求和运算"""
return arr.sum(axis=axis)
```bash
- *4.2 内存优化**
```python
# backtrader/optimize/memory.py
import numpy as np
from typing import Dict, Optional
from weakref import WeakValueDictionary
class MemoryPool:
"""内存池 - 减少内存分配开销"""
def __init__(self, max_blocks: int = 100):
self._pool: WeakValueDictionary = WeakValueDictionary()
self._max_blocks = max_blocks
self._hits = 0
self._misses = 0
def get_array(self, shape: tuple, dtype: np.dtype) -> Optional[np.ndarray]:
"""从池中获取数组"""
key = (shape, dtype)
arr = self._pool.get(key)
if arr is not None:
self._hits += 1
return arr
self._misses += 1
return None
def return_array(self, arr: np.ndarray):
"""归还数组到池"""
if len(self._pool) >= self._max_blocks:
return
key = (arr.shape, arr.dtype)
self._pool[key] = arr
@property
def hit_rate(self) -> float:
"""缓存命中率"""
total = self._hits + self._misses
return self._hits / total if total > 0 else 0
def clear(self):
"""清空池"""
self._pool.clear()
self._hits = 0
self._misses = 0
# 全局内存池
_global_pool = MemoryPool()
def get_memory_pool() -> MemoryPool:
"""获取全局内存池"""
return _global_pool
class ArrayView:
"""数组视图 - 零拷贝访问"""
def __init__(self, array: np.ndarray, offset: int = 0,
shape: Optional[tuple] = None, strides: Optional[tuple] = None):
self._array = array
self._offset = offset
self._shape = shape if shape is not None else array.shape
self._strides = strides if strides is not None else array.strides
@property
def shape(self) -> tuple:
return self._shape
@property
def strides(self) -> tuple:
return self._strides
def to_numpy(self) -> np.ndarray:
"""转换为 NumPy 数组"""
return np.ndarray(
shape=self._shape,
dtype=self._array.dtype,
buffer=self._array.data,
offset=self._offset,
strides=self._strides
)
class InPlaceOps:
"""就地运算 - 减少内存分配"""
@staticmethod
def add_inplace(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""就地加法"""
np.add(a, b, out=a)
return a
@staticmethod
def sub_inplace(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""就地减法"""
np.subtract(a, b, out=a)
return a
@staticmethod
def mul_inplace(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""就地乘法"""
np.multiply(a, b, out=a)
return a
@staticmethod
def div_inplace(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""就地除法"""
np.divide(a, b, out=a)
return a
```bash
- *4.3 并行计算**
```python
# backtrader/optimize/parallel.py
import numpy as np
from typing import Callable, List, Any
from concurrent.futures import ThreadPoolExecutor, ProcessPoolExecutor
import multiprocessing as mp
class ParallelOps:
"""并行计算操作"""
def __init__(self, n_workers: Optional[int] = None):
self._n_workers = n_workers or mp.cpu_count()
def map(self, func: Callable, arrays: List[np.ndarray],
n_workers: Optional[int] = None) -> List[Any]:
"""并行映射函数到数组列表
对于小型数组，使用线程池
对于 CPU 密集型操作，使用进程池
"""
n_workers = n_workers or self._n_workers
if len(arrays) < 2:
return [func(arr) for arr in arrays]
# 使用线程池（对 NumPy 操作更高效）
with ThreadPoolExecutor(max_workers=n_workers) as executor:
results = list(executor.map(func, arrays))
return results
def parallel_apply(self, func: Callable, arr: np.ndarray,
axis: int = 0, n_workers: Optional[int] = None) -> np.ndarray:
"""沿指定轴并行应用函数"""
n_workers = n_workers or self._n_workers
if arr.ndim == 1:
return func(arr)
# 沿轴分割数组
if axis == 0:
split_arrays = np.array_split(arr, n_workers, axis=0)
else:
split_arrays = np.array_split(arr, n_workers, axis=axis)
# 并行处理
with ThreadPoolExecutor(max_workers=n_workers) as executor:
results = list(executor.map(func, split_arrays))
# 合并结果
return np.concatenate(results, axis=axis)
class BatchOps:
"""批量操作"""
@staticmethod
def batch_dot(arrays: List[np.ndarray],
weights: List[np.ndarray]) -> List[np.ndarray]:
"""批量点积运算"""
return [np.dot(a, w) for a, w in zip(arrays, weights)]
@staticmethod
def batch_mean(arrays: List[np.ndarray]) -> np.ndarray:
"""批量计算均值"""
return np.mean([np.mean(a) for a in arrays])
@staticmethod
def batch_std(arrays: List[np.ndarray]) -> np.ndarray:
"""批量计算标准差"""
return np.mean([np.std(a) for a in arrays])
```bash
#### 5. 数学函数
- *5.1 统计函数**
```python
# backtrader/functions/statistical.py
import numpy as np
from typing import Optional, Tuple
from ..arrays.array import Array
class Statistical:
"""统计函数模块"""
@staticmethod
def mean(arr: Union[Array, np.ndarray],
axis: Optional[int] = None,
dtype: Optional[type] = None) -> Union[Array, float]:
"""平均值"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.mean(arr_arr, axis=axis, dtype=dtype)
return Array(result, copy=False) if isinstance(result, np.ndarray) else result
@staticmethod
def median(arr: Union[Array, np.ndarray],
axis: Optional[int] = None) -> Union[Array, float]:
"""中位数"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.median(arr_arr, axis=axis)
return Array(result, copy=False) if isinstance(result, np.ndarray) else result
@staticmethod
def std(arr: Union[Array, np.ndarray],
axis: Optional[int] = None,
ddof: int = 0) -> Union[Array, float]:
"""标准差"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = arr_arr.std(axis=axis, ddof=ddof)
return Array(result, copy=False) if isinstance(result, np.ndarray) else result
@staticmethod
def var(arr: Union[Array, np.ndarray],
axis: Optional[int] = None,
ddof: int = 0) -> Union[Array, float]:
"""方差"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = arr_arr.var(axis=axis, ddof=ddof)
return Array(result, copy=False) if isinstance(result, np.ndarray) else result
@staticmethod
def corrcoef(x: Union[Array, np.ndarray],
y: Optional[Union[Array, np.ndarray]] = None) -> Array:
"""相关系数"""
x_arr = x.to_numpy() if isinstance(x, Array) else x
if y is not None:
y_arr = y.to_numpy() if isinstance(y, Array) else y
result = np.corrcoef(x_arr, y_arr)
else:
result = np.corrcoef(x_arr)
return Array(result, copy=False)
@staticmethod
def covariance(arr: Union[Array, np.ndarray]) -> Array:
"""协方差矩阵"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.cov(arr_arr)
return Array(result, copy=False)
@staticmethod
def percentile(arr: Union[Array, np.ndarray],
q: Union[float, List[float]],
axis: Optional[int] = None) -> Union[Array, float]:
"""百分位数"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.percentile(arr_arr, q, axis=axis)
return Array(result, copy=False) if isinstance(result, np.ndarray) else result
@staticmethod
def quantile(arr: Union[Array, np.ndarray],
q: Union[float, List[float]],
axis: Optional[int] = None) -> Union[Array, float]:
"""分位数"""
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
result = np.quantile(arr_arr, q, axis=axis)
return Array(result, copy=False) if isinstance(result, np.ndarray) else result
```bash
- *5.2 数学函数**
```python
# backtrader/functions/mathematical.py
import numpy as np
from typing import Union
from ..arrays.array import Array
class Mathematical:
"""数学函数模块"""
# 三角函数
@staticmethod
def sin(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.sin(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def cos(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.cos(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def tan(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.tan(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def arcsin(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.arcsin(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def arccos(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.arccos(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def arctan(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.arctan(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def arctan2(y: Union[Array, np.ndarray], x: Union[Array, np.ndarray]) -> Array:
y_arr = y.to_numpy() if isinstance(y, Array) else y
x_arr = x.to_numpy() if isinstance(x, Array) else x
return Array(np.arctan2(y_arr, x_arr))
# 双曲函数
@staticmethod
def sinh(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.sinh(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def cosh(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.cosh(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def tanh(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.tanh(arr.to_numpy() if isinstance(arr, Array) else arr))
# 指数和对数
@staticmethod
def exp(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.exp(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def expm1(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.expm1(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def log(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.log(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def log10(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.log10(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def log1p(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.log1p(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def log2(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.log2(arr.to_numpy() if isinstance(arr, Array) else arr))
# 幂运算
@staticmethod
def sqrt(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.sqrt(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def square(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.square(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def power(arr: Union[Array, np.ndarray], exponent: float) -> Array:
return Array(np.power(arr.to_numpy() if isinstance(arr, Array) else arr, exponent))
@staticmethod
def abs(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.abs(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def sign(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.sign(arr.to_numpy() if isinstance(arr, Array) else arr))
# 舍入函数
@staticmethod
def round(arr: Union[Array, np.ndarray], decimals: int = 0) -> Array:
return Array(np.round(arr.to_numpy() if isinstance(arr, Array) else arr, decimals))
@staticmethod
def floor(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.floor(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def ceil(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.ceil(arr.to_numpy() if isinstance(arr, Array) else arr))
@staticmethod
def trunc(arr: Union[Array, np.ndarray]) -> Array:
return Array(np.trunc(arr.to_numpy() if isinstance(arr, Array) else arr))
# 其他函数
@staticmethod
def clip(arr: Union[Array, np.ndarray],
min_val: float, max_val: float) -> Array:
arr_arr = arr.to_numpy() if isinstance(arr, Array) else arr
return Array(np.clip(arr_arr, min_val, max_val))
```bash
### 实现计划
#### 第一阶段：数组数据结构（优先级：高）
1. 实现 Shape 类
2. 实现 Slice 类
3. 实现 Array 核心类
4. 单元测试
#### 第二阶段：广播机制（优先级：高）
1. 实现 Broadcaster
2. 实现广播运算
3. 集成测试
#### 第三阶段：线性代数（优先级：高）
1. 实现 MatrixOps 矩阵运算
2. 实现 Decomposition 分解
3. 实现 Solver 求解器
4. 性能测试
#### 第四阶段：性能优化（优先级：中）
1. 实现 SIMDSupport
2. 实现 MemoryPool
3. 实现 ParallelOps
4. 基准测试
#### 第五阶段：数学函数（优先级：中）
1. 实现 Statistical 统计函数
2. 实现 Mathematical 数学函数
3. 实现 Logical 逻辑函数
4. 文档完善
### API 兼容性保证
所有新增功能与现有 backtrader API 兼容：
```python
# 传统方式（保持不变）
import backtrader as bt
import numpy as np
data = np.array([1, 2, 3, 4, 5])
ma = np.mean(data)
# 新方式：使用增强 Array
from backtrader.arrays import Array
arr = Array([1, 2, 3, 4, 5])
mean = arr.mean() # 返回 Array 或标量
# 矩阵运算
from backtrader.linalg import MatrixOps
a = Array([[1, 2], [3, 4]])
b = Array([[5, 6], [7, 8]])
c = MatrixOps.dot(a, b)
# 广播自动支持
d = Array([[1, 2, 3], [4, 5, 6]])
scalar = Array(2)
result = d *scalar # 标量广播
```bash
### 使用示例
- *数组创建和操作：**
```python
from backtrader.arrays import Array
# 创建数组
zeros = Array.zeros((3, 3))
ones = Array.ones((2, 4))
random = Array.random((5, 5))
identity = Array.eye(3)
# 切片操作
arr = Array.arange(20).reshape(4, 5)
row_slice = arr[1:3, :] # 行切片
col_slice = arr[:, 2:4] # 列切片
element = arr[1, 2] # 单元素
# 形状操作
reshaped = arr.reshape(5, 4)
flattened = arr.flatten()
transposed = arr.T
# 类型转换
float_arr = arr.astype(float)
```bash
- *矩阵运算：**
```python
from backtrader.linalg import MatrixOps
a = Array([[1, 2], [3, 4]])
b = Array([[5, 6], [7, 8]])
# 矩阵乘法
c = MatrixOps.dot(a, b)
# 求逆
inv_a = MatrixOps.inv(a)
# 行列式
det_a = MatrixOps.det(a)
# 转置
at = MatrixOps.transpose(a)
```bash
- *线性代数求解：**
```python
from backtrader.linalg import Solver, Decomposition
# 线性方程组求解
A = Array([[3, 1], [1, 2]])
b = Array([9, 8])
x = Solver.solve(A, b)
# 最小二乘求解
A = Array([[1, 1], [1, 2], [1, 3]])
b = Array([2, 3, 4])
x, residuals, rank, s = Solver.lstsq(A, b)
# 矩阵分解
Q, R = Decomposition.qr(A)
L = Decomposition.cholesky(A.T @ A)
U, s, Vt = Decomposition.svd(A)
```bash
- *统计函数：**
```python
from backtrader.functions import Statistical
data = Array.random((100, 5))
# 基本统计
mean = Statistical.mean(data)
std = Statistical.std(data)
variance = Statistical.var(data)
median_val = Statistical.median(data)
# 分位数
q25 = Statistical.quantile(data, 0.25)
q75 = Statistical.quantile(data, 0.75)
# 相关系数
corr = Statistical.corrcoef(data)
```bash
### 测试策略
1. **单元测试**: 每个模块的单元测试覆盖率 > 85%
2. **集成测试**: 与 NumPy 结果对比验证
3. **性能测试**: 对比 NumPy 性能，目标 < 2 倍
4. **边界测试**: 处理极端情况（空数组、大数组等）
5. **兼容性测试**: 确保与现有代码兼容