torch.svd¶

torch.
svd
(input, some=True, compute_uv=True, *, out=None) > (Tensor, Tensor, Tensor)¶ Computes the singular value decomposition of either a matrix or batch of matrices
input
. The singular value decomposition is represented as a namedtuple (U,S,V), such thatinput
= U diag(S) Vᴴ, where Vᴴ is the transpose of V for the realvalued inputs, or the conjugate transpose of V for the complexvalued inputs. Ifinput
is a batch of tensors, then U, S, and V are also batched with the same batch dimensions asinput
.If
some
isTrue
(default), the method returns the reduced singular value decomposition i.e., if the last two dimensions ofinput
are m and n, then the returned U and V matrices will contain only min(n, m) orthonormal columns.If
compute_uv
isFalse
, the returned U and V will be zerofilled matrices of shape (m × m) and (n × n) respectively, and the same device asinput
. Thesome
argument has no effect whencompute_uv
isFalse
.Supports input of float, double, cfloat and cdouble data types. The dtypes of U and V are the same as
input
’s. S will always be realvalued, even ifinput
is complex.Warning
torch.svd()
is deprecated. Please usetorch.linalg.svd()
instead, which is similar to NumPy’snumpy.linalg.svd
.Note
Differences with
torch.linalg.svd()
:some
is the opposite oftorch.linalg.svd()
’sfull_matricies
. Note that default value for both isTrue
, so the default behavior is effectively the opposite.torch.svd()
returns V, whereastorch.linalg.svd()
returns Vᴴ.If
compute_uv=False
,torch.svd()
returns zerofilled tensors forU
andVh
, whereastorch.linalg.svd()
returns empty tensors.
Note
The singular values are returned in descending order. If
input
is a batch of matrices, then the singular values of each matrix in the batch is returned in descending order.Note
The implementation of SVD on CPU uses the LAPACK routine ?gesdd (a divideandconquer algorithm) instead of ?gesvd for speed. Analogously, the SVD on GPU uses the cuSOLVER routines gesvdj and gesvdjBatched on CUDA 10.1.243 and later, and uses the MAGMA routine gesdd on earlier versions of CUDA.
Note
The returned matrix U will be transposed, i.e. with strides
U.contiguous().transpose(2, 1).stride()
.Note
Gradients computed using U and V may be unstable if
input
is not full rank or has nonunique singular values.Note
When
some
=False
, the gradients onU[..., :, min(m, n):]
andV[..., :, min(m, n):]
will be ignored in backward as those vectors can be arbitrary bases of the subspaces.Note
The S tensor can only be used to compute gradients if
compute_uv
is True.Note
With the complexvalued input the backward operation works correctly only for gauge invariant loss functions. Please look at Gauge problem in AD for more details.
Note
Since U and V of an SVD is not unique, each vector can be multiplied by an arbitrary phase factor $e^{i \phi}$ while the SVD result is still correct. Different platforms, like Numpy, or inputs on different device types, may produce different U and V tensors.
 Parameters
input (Tensor) – the input tensor of size (*, m, n) where * is zero or more batch dimensions consisting of (m × n) matrices.
some (bool, optional) – controls whether to compute the reduced or full decomposition, and consequently the shape of returned U and V. Defaults to True.
compute_uv (bool, optional) – option whether to compute U and V or not. Defaults to True.
 Keyword Arguments
out (tuple, optional) – the output tuple of tensors
Example:
>>> a = torch.randn(5, 3) >>> a tensor([[ 0.2364, 0.7752, 0.6372], [ 1.7201, 0.7394, 0.0504], [0.3371, 1.0584, 0.5296], [ 0.3550, 0.4022, 1.5569], [ 0.2445, 0.0158, 1.1414]]) >>> u, s, v = torch.svd(a) >>> u tensor([[ 0.4027, 0.0287, 0.5434], [0.1946, 0.8833, 0.3679], [ 0.4296, 0.2890, 0.5261], [ 0.6604, 0.2717, 0.2618], [ 0.4234, 0.2481, 0.4733]]) >>> s tensor([2.3289, 2.0315, 0.7806]) >>> v tensor([[0.0199, 0.8766, 0.4809], [0.5080, 0.4054, 0.7600], [ 0.8611, 0.2594, 0.4373]]) >>> torch.dist(a, torch.mm(torch.mm(u, torch.diag(s)), v.t())) tensor(8.6531e07) >>> a_big = torch.randn(7, 5, 3) >>> u, s, v = torch.svd(a_big) >>> torch.dist(a_big, torch.matmul(torch.matmul(u, torch.diag_embed(s)), v.transpose(2, 1))) tensor(2.6503e06)