- paddle.linalg. svd ( x, full_matrices=False, name=None )
Computes the singular value decomposition of one matrix or a batch of regular matrices.
Let \(X\) be the input matrix or a batch of input matrices, the output should satisfies:\[X = U * diag(S) * VT\]
x (Tensor) – The input tensor. Its shape should be […, N, M], where … is zero or more batch dimensions. N and M can be arbitraty positive number. Note that if x is sigular matrices, the grad is numerical instable. The data type of x should be float32 or float64.
full_matrices (bool) – A flag to control the behavor of svd. If full_matrices = True, svd op will compute full U and V matrics, which means shape of U is […, N, N], shape of V is […, M, M]. K = min(M, N). If full_matrices = False, svd op will use a economic method to store U and V. which means shape of U is […, N, K], shape of V is […, M, K]. K = min(M, N).
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.
(U, S, VH). VH is the conjugate transpose of V. S is the singlar value vectors of matrics with shape […, K]
- Return type
Tuple of 3 tensors
import paddle x = paddle.to_tensor([[1.0, 2.0], [1.0, 3.0], [4.0, 6.0]]).astype('float64') x = x.reshape([3, 2]) u, s, vh = paddle.linalg.svd(x) print (u) #U = [[ 0.27364809, -0.21695147 ], # [ 0.37892198, -0.87112408 ], # [ 0.8840446 , 0.44053933 ]] print (s) #S = [8.14753743, 0.78589688] print (vh) #VT= [[ 0.51411221, 0.85772294], # [ 0.85772294, -0.51411221]] # one can verify : U * S * VT == X # U * UH == I # V * VH == I