svd

paddle.linalg. svd ( x, full_matrices=False, name=None ) [source]

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:

\[X = U * diag(S) * VT\]
Parameters

  • x (Tensor) – The input tensor. Its shape should be […, N, M], where … is zero or more batch dimensions. N and M can be arbitrary positive number. Note that if x is singular matrices, the grad is numerical instable. The data type of x should be float32 or float64.

  • full_matrices (bool, optional) – A flag to control the behavior of svd. If full_matrices = True, svd op will compute full U and V matrices, 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). Default value is False.

  • name (str, optional) – Name for the operation. For more information, please refer to Name. Default value is None.

Returns

  • U (Tensor), is the singular value decomposition result U.

  • S (Tensor), is the singular value decomposition result S.

  • VH (Tensor), VH is the conjugate transpose of V, which is the singular value decomposition result V.

Tuple of 3 tensors(U, S, VH): VH is the conjugate transpose of V. S is the singular value vectors of matrices with shape […, K]

Examples

>>> 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)
Tensor(shape=[3, 2], dtype=float64, place=Place(cpu), stop_gradient=True,
[[-0.27364809, -0.21695147],
 [-0.37892198, -0.87112408],
 [-0.88404460,  0.44053933]])

>>> print (s)
Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=True,
[8.14753743, 0.78589688])

>>> print (vh)
Tensor(shape=[2, 2], dtype=float64, place=Place(cpu), stop_gradient=True,
[[-0.51411221, -0.85772294],
 [ 0.85772294, -0.51411221]])

>>> # one can verify : U * S * VT == X
>>> #                  U * UH == I
>>> #                  V * VH == I