PyTorch – 如何计算矩阵的奇异值分解 (SVD)?
火炬。linalg.svd()计算矩阵或一批矩阵的奇异值分解(SVD)。奇异值分解表示为命名元组(U,S,Vh)。
U和Vh对于实矩阵是正交的,对于输入复矩阵是酉矩阵。
当V是实数值时Vh是V的转置,当V是复数时是共轭转置。
即使输入是复数,S也始终是实数值。
语法
U, S, Vh = torch.linalg.svd(A, full_matrices=True)
参数
A–PyTorch张量(矩阵或矩阵批次)。
full_matrices–如果为True,则输出为完整的SVD,否则为简化的SVD。默认为真。
输出结果
它返回一个命名元组(U,S,Vh)。
脚步
导入所需的库。
import torch
创建一个矩阵或一批矩阵。
A = torch.randn(3,4)
计算上面创建的矩阵或矩阵批次的SVD。
U, S, Vh = torch.linalg.svd(A)
显示U、S和Vh。
print("U:\n",U) print("S:\n",S) print("Vh:\n",Vh)
示例1
以下Python程序展示了如何计算矩阵的SVD。
# import necessary library import torch # create a matrix A = torch.randn(3,4) print("Matrix:\n", A) # compute SVD U, S, Vh = torch.linalg.svd(A) # print U, S, and Vh print("U:\n",U) print("S:\n",S) print("Vh:\n",Vh)输出结果
Matrix: tensor([[-1.5122, -0.4714, -0.1173, -0.3914], [ 0.4288, -1.9329, 0.9171, -1.0288], [ 0.1143, 0.1989, 0.3290, 0.3031]]) U: tensor([[ 0.1769, 0.9716, 0.1569], [ 0.9815, -0.1860, 0.0448], [-0.0728, -0.1460, 0.9866]]) S: tensor([2.4383, 1.6226, 0.4119]) Vh: tensor([[ 0.0595, -0.8182, 0.3508, -0.4516], [-0.9649, -0.0787, -0.2050, -0.1438], [-0.2554, 0.0864, 0.8433, 0.4650], [ 0.0092, -0.5629, -0.3519, 0.7478]])
示例2
以下Python程序展示了如何计算复矩阵的SVD。
# import necessary library import torch # create a matrix of complex random number A = torch.randn(2,2, dtype = torch.cfloat) print("Complex Matrix:\n", A) # compute SVD U, S, Vh = torch.linalg.svd(A) # print U, S, and Vh print("U:\n",U) print("S:\n",S) print("Vh:\n",Vh)输出结果
Complex Matrix: tensor([[-0.2761-0.6619j, -1.4248-0.3026j], [-0.2797+0.2036j, 0.2143+1.3459j]]) U: tensor([[-0.2670-0.7083j, 0.3372+0.5597j], [-0.4943+0.4273j, -0.4737+0.5905j]]) S: tensor([2.1358, 0.2259]) Vh: tensor([[ 0.3595+0.0000j, 0.4981-0.7891j], [-0.9332+0.0000j, 0.1919-0.3040j]])
示例3
以下Python程序展示了如何计算一批三个矩阵的SVD。
# import necessary library import torch # create a batch of three 2x3 matrices A = torch.randn(3,2,3) print("Matrices:\n", A) # compute SVD U, S, Vh = torch.linalg.svd(A) #print U, S, and Vh print("U:\n",U) print("S:\n",S) print("Vh:\n",Vh)输出结果
Matrices: tensor([[[ 0.2195, -1.3015, -1.0770], [-0.5884, -0.8269, 0.0135]], [[ 1.0753, -1.7080, -0.3692], [-1.3024, 0.2581, -1.2018]], [[-0.3576, -1.0531, -0.6192], [ 0.8453, 0.4187, -0.1622]]]) U: tensor([[[ 0.9242, -0.3818], [ 0.3818, 0.9242]], [[ 0.8178, 0.5755], [-0.5755, 0.8178]], [[ 0.8604, 0.5097], [-0.5097, 0.8604]]]) S: tensor([[1.8131, 0.8030], [2.2789, 1.4912], [1.4146, 0.7317]]) Vh: tensor([[[-0.0120, -0.8376, -0.5462], [-0.7815, -0.3329, 0.5276], [ 0.6237, -0.4332, 0.6506]], [[ 0.7148, -0.6781, 0.1710], [-0.2993, -0.5176, -0.8015], [-0.6321, -0.5217, 0.5730]], [[-0.5221, -0.7913, -0.3182], [ 0.7448, -0.2413, -0.6221], [ 0.4155, -0.5617, 0.7154]]])