NumPy -数组属性与形状操作

数组属性与形状操作

目录

• 数组属性
• 形状操作
• 维度操作
• 转置操作
• 实际应用示例

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数组属性

基本属性

import numpy as np

arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

print(f"数组:\n{arr}")
print(f"形状 (shape): {arr.shape}")        # (3, 3)
print(f"维度 (ndim): {arr.ndim}")          # 2
print(f"大小 (size): {arr.size}")          # 9
print(f"数据类型 (dtype): {arr.dtype}")    # int64
print(f"元素大小 (itemsize): {arr.itemsize}")  # 8 字节
print(f"总内存 (nbytes): {arr.nbytes}")    # 72 字节
print(f"标志 (flags):\n{arr.flags}")

数据访问属性

import numpy as np

arr = np.array([1, 2, 3, 4, 5])

# 数据指针
print(f"数据指针: {arr.ctypes.data}")

# 数据是否连续存储
print(f"是否连续: {arr.flags['C_CONTIGUOUS']}")

# 是否只读
arr_readonly = arr.copy()
arr_readonly.flags.writeable = False
print(f"是否只读: {arr_readonly.flags['WRITEABLE']}")

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形状操作

reshape 方法

import numpy as np

# 创建一维数组
arr = np.arange(12)
print(f"原数组: {arr}")
print(f"形状: {arr.shape}")

# 重塑为二维数组
arr_2d = arr.reshape(3, 4)
print(f"\n重塑为 (3, 4):\n{arr_2d}")

# 重塑为三维数组
arr_3d = arr.reshape(2, 2, 3)
print(f"\n重塑为 (2, 2, 3):\n{arr_3d}")

# 使用 -1 自动计算维度
arr_auto = arr.reshape(3, -1)
print(f"\n自动计算列数:\n{arr_auto}")

# 一维化
arr_flat = arr_2d.reshape(-1)
print(f"\n一维化: {arr_flat}")

resize 方法

import numpy as np

arr = np.array([[1, 2, 3], [4, 5, 6]])
print(f"原数组:\n{arr}")

# resize 会修改原数组
arr.resize(3, 2)
print(f"\nresize 后:\n{arr}")

# 如果新大小更大，用0填充
arr.resize(4, 3)
print(f"\n扩大后（用0填充）:\n{arr}")

flatten 和 ravel 方法

import numpy as np

arr = np.array([[1, 2, 3], [4, 5, 6]])
print(f"原数组:\n{arr}")

# flatten：返回副本
arr_flat1 = arr.flatten()
arr_flat1[0] = 999
print(f"\nflatten (修改后):\n{arr_flat1}")
print(f"原数组未变:\n{arr}")

# ravel：返回视图（如果可能）
arr_flat2 = arr.ravel()
arr_flat2[0] = 888
print(f"\nravel (修改后):\n{arr_flat2}")
print(f"原数组已变:\n{arr}")

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维度操作

增加维度

import numpy as np

arr = np.array([1, 2, 3, 4])
print(f"原数组: {arr}")
print(f"形状: {arr.shape}")

# 使用 newaxis 增加维度
arr_row = arr[np.newaxis, :]
print(f"\n行向量:\n{arr_row}")
print(f"形状: {arr_row.shape}")

arr_col = arr[:, np.newaxis]
print(f"\n列向量:\n{arr_col}")
print(f"形状: {arr_col.shape}")

# 使用 expand_dims
arr_expanded = np.expand_dims(arr, axis=0)
print(f"\nexpand_dims (axis=0):\n{arr_expanded}")
print(f"形状: {arr_expanded.shape}")

arr_expanded = np.expand_dims(arr, axis=1)
print(f"\nexpand_dims (axis=1):\n{arr_expanded}")
print(f"形状: {arr_expanded.shape}")

减少维度

import numpy as np

arr = np.array([[[1, 2, 3]]])
print(f"原数组: {arr}")
print(f"形状: {arr.shape}")

# squeeze：移除长度为1的维度
arr_squeezed = np.squeeze(arr)
print(f"\nsqueeze 后: {arr_squeezed}")
print(f"形状: {arr_squeezed.shape}")

# 指定 axis
arr2 = np.array([[[1]], [[2]], [[3]]])
print(f"\n原数组形状: {arr2.shape}")
arr2_squeezed = np.squeeze(arr2, axis=2)
print(f"squeeze (axis=2) 后形状: {arr2_squeezed.shape}")

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转置操作

transpose 方法

import numpy as np

arr = np.array([[1, 2, 3], [4, 5, 6]])
print(f"原数组:\n{arr}")
print(f"形状: {arr.shape}")

# 转置
arr_T = arr.T
print(f"\n转置:\n{arr_T}")
print(f"形状: {arr_T.shape}")

# 使用 transpose 方法
arr_T2 = arr.transpose()
print(f"\n使用 transpose:\n{arr_T2}")

# 多维数组转置
arr_3d = np.arange(24).reshape(2, 3, 4)
print(f"\n三维数组形状: {arr_3d.shape}")

# 交换轴
arr_T3d = arr_3d.transpose(2, 0, 1)
print(f"转置后形状: {arr_T3d.shape}")

swapaxes 方法

import numpy as np

arr = np.arange(24).reshape(2, 3, 4)
print(f"原数组形状: {arr.shape}")

# 交换轴
arr_swapped = np.swapaxes(arr, 0, 2)
print(f"交换轴 0 和 2 后形状: {arr_swapped.shape}")

arr_swapped = np.swapaxes(arr, 1, 2)
print(f"交换轴 1 和 2 后形状: {arr_swapped.shape}")

moveaxis 方法

import numpy as np

arr = np.arange(24).reshape(2, 3, 4)
print(f"原数组形状: {arr.shape}")

# 移动轴
arr_moved = np.moveaxis(arr, 0, -1)
print(f"移动轴 0 到最后: {arr_moved.shape}")

arr_moved = np.moveaxis(arr, [0, 1], [1, 0])
print(f"交换轴 0 和 1: {arr_moved.shape}")

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实际应用示例

示例 1：图像处理中的形状操作

import numpy as np

# 模拟图像数据 (高度, 宽度, 通道)
image = np.random.randint(0, 255, size=(480, 640, 3), dtype=np.uint8)
print(f"原始图像形状: {image.shape}")

# 转换为灰度图（简单平均）
gray = image.mean(axis=2).astype(np.uint8)
print(f"灰度图形状: {gray.shape}")

# 调整大小（下采样）
small = gray[::2, ::2]
print(f"下采样后形状: {small.shape}")

# 重塑为一维特征向量
features = small.flatten()
print(f"特征向量形状: {features.shape}")

示例 2：矩阵运算中的形状操作

import numpy as np

# 创建数据矩阵
data = np.random.randn(100, 10)
print(f"数据矩阵形状: {data.shape}")

# 添加偏置项（需要在每行前加1）
bias = np.ones((100, 1))
data_with_bias = np.concatenate([bias, data], axis=1)
print(f"添加偏置后形状: {data_with_bias.shape}")

# 转置用于矩阵乘法
data_T = data_with_bias.T
print(f"转置后形状: {data_T.shape}")

# 计算协方差矩阵（需要中心化）
data_centered = data - data.mean(axis=0)
cov_matrix = np.dot(data_centered.T, data_centered) / (data.shape[0] - 1)
print(f"协方差矩阵形状: {cov_matrix.shape}")

示例 3：批量数据处理

import numpy as np

# 创建批次数据
batch_size = 32
features = np.random.randn(1000, 784)  # 1000个样本，每个784维特征
print(f"原始数据形状: {features.shape}")

# 重塑为批次
num_batches = features.shape[0] // batch_size
features_batched = features[:num_batches * batch_size].reshape(num_batches, batch_size, 784)
print(f"批次数据形状: {features_batched.shape}")

# 处理每个批次
for i, batch in enumerate(features_batched):
    print(f"批次 {i}: 形状 {batch.shape}")
    # 这里可以进行批量处理

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总结

数组属性与形状操作要点：

1. 属性：shape, ndim, size, dtype, itemsize, nbytes
2. 形状操作：reshape, resize, flatten, ravel
3. 维度操作：newaxis, expand_dims, squeeze
4. 转置操作：T, transpose, swapaxes, moveaxis

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