Creating Complex Tensors¶

We support two complex dtypes: torch.cfloat and torch.cdouble

>>> x = torch.randn(2,2, dtype=torch.cfloat)
>>> x
tensor([[-0.4621-0.0303j, -0.2438-0.5874j],
     [ 0.7706+0.1421j,  1.2110+0.1918j]])

All factory functions apart from torch.linspace(), torch.logspace(), and torch.arange() are supported for complex tensors.

Transition from the old representation¶

Users who currently worked around the lack of complex tensors with real tensors of shape $(..., 2)$ can easily to switch using the complex tensors in their code using torch.view_as_complex() and torch.view_as_real(). Note that these functions don’t perform any copy and return a view of the input tensor.

>>> x = torch.randn(3, 2)
>>> x
tensor([[ 0.6125, -0.1681],
     [-0.3773,  1.3487],
     [-0.0861, -0.7981]])
>>> y = torch.view_as_complex(x)
>>> y
tensor([ 0.6125-0.1681j, -0.3773+1.3487j, -0.0861-0.7981j])
>>> torch.view_as_real(y)
tensor([[ 0.6125, -0.1681],
     [-0.3773,  1.3487],
     [-0.0861, -0.7981]])

Accessing real and imag¶

The real and imaginary values of a complex tensor can be accessed using the real and imag.

>>> y.real
tensor([ 0.6125, -0.3773, -0.0861])
>>> y.imag
tensor([-0.1681,  1.3487, -0.7981])

>>> y.real.mul_(2)
tensor([ 1.2250, -0.7546, -0.1722])
>>> y
tensor([ 1.2250-0.1681j, -0.7546+1.3487j, -0.1722-0.7981j])
>>> y.real.stride()
(2,)

Angle and abs¶

The angle and absolute values of a complex tensor can be computed using torch.angle() and torch.abs.

>>> x1=torch.tensor([3j, 4+4j])
>>> x1.abs()
tensor([3.0000, 5.6569])
>>> x1.angle()
tensor([1.5708, 0.7854])

Linear Algebra¶

Currently, there is very minimal linear algebra operation support for complex tensors. We currently support torch.mv(), torch.svd(), torch.qr(), and torch.inverse() (the latter three are only supported on CPU). However we are working to add support for more functions soon: torch.matmul(), torch.solve(), torch.eig(), torch.symeig(). If any of these would help your use case, please search if an issue has already been filed and if not, file one.

Serialization¶

Complex tensors can be serialized, allowing data to be saved as complex values.

>>> torch.save(y, 'complex_tensor.pt')
>>> torch.load('complex_tensor.pt')
tensor([ 0.6125-0.1681j, -0.3773+1.3487j, -0.0861-0.7981j])

Autograd¶

PyTorch supports autograd for complex tensors. The autograd APIs can be used for both holomorphic and non-holomorphic functions. For holomorphic functions, you get the regular complex gradient. For $C → R$ real-valued loss functions, grad.conj() gives a descent direction. For more details, check out the note Autograd for Complex Numbers.

We do not support the following subsystems:

• Quantization

• JIT

• Sparse Tensors

• Distributed

If any of these would help your use case, please search if an issue has already been filed and if not, file one.