torch¶

The torch package contains data structures for multi-dimensional tensors and mathematical operations over these are defined. Additionally, it provides many utilities for efficient serializing of Tensors and arbitrary types, and other useful utilities.

It has a CUDA counterpart, that enables you to run your tensor computations on an NVIDIA GPU with compute capability >= 3.0.

Tensors¶

torch.is_tensor(obj)[source]¶

Returns True if obj is a PyTorch tensor.

Parameters: obj (Object) – Object to test

torch.is_storage(obj)[source]¶

Returns True if obj is a PyTorch storage object.

Parameters: obj (Object) – Object to test

torch.is_complex(input) -> (bool)¶

Returns True if the data type of input is a complex data type i.e., one of torch.complex64, and torch.complex128.

Parameters: input (Tensor) – the PyTorch tensor to test

torch.is_floating_point(input) -> (bool)¶

Returns True if the data type of input is a floating point data type i.e., one of torch.float64, torch.float32 and torch.float16.

Parameters: input (Tensor) – the PyTorch tensor to test

torch.set_default_dtype(d)[source]¶

Sets the default floating point dtype to d. This type will be used as default floating point type for type inference in torch.tensor().

The default floating point dtype is initially torch.float32.

Parameters: d (torch.dtype) – the floating point dtype to make the default

Example:

>>> torch.tensor([1.2, 3]).dtype           # initial default for floating point is torch.float32
torch.float32
>>> torch.set_default_dtype(torch.float64)
>>> torch.tensor([1.2, 3]).dtype           # a new floating point tensor
torch.float64

torch.get_default_dtype() → torch.dtype¶

Get the current default floating point torch.dtype.

Example:

>>> torch.get_default_dtype()  # initial default for floating point is torch.float32
torch.float32
>>> torch.set_default_dtype(torch.float64)
>>> torch.get_default_dtype()  # default is now changed to torch.float64
torch.float64
>>> torch.set_default_tensor_type(torch.FloatTensor)  # setting tensor type also affects this
>>> torch.get_default_dtype()  # changed to torch.float32, the dtype for torch.FloatTensor
torch.float32

torch.set_default_tensor_type(t)[source]¶

Sets the default torch.Tensor type to floating point tensor type t. This type will also be used as default floating point type for type inference in torch.tensor().

The default floating point tensor type is initially torch.FloatTensor.

Parameters: t (type or string) – the floating point tensor type or its name

Example:

>>> torch.tensor([1.2, 3]).dtype    # initial default for floating point is torch.float32
torch.float32
>>> torch.set_default_tensor_type(torch.DoubleTensor)
>>> torch.tensor([1.2, 3]).dtype    # a new floating point tensor
torch.float64

torch.numel(input) → int¶

Returns the total number of elements in the input tensor.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(1, 2, 3, 4, 5)
>>> torch.numel(a)
120
>>> a = torch.zeros(4,4)
>>> torch.numel(a)
16

torch.set_printoptions(precision=None, threshold=None, edgeitems=None, linewidth=None, profile=None, sci_mode=None)[source]¶

Set options for printing. Items shamelessly taken from NumPy

Parameters

precision – Number of digits of precision for floating point output (default = 4).
threshold – Total number of array elements which trigger summarization rather than full repr (default = 1000).
edgeitems – Number of array items in summary at beginning and end of each dimension (default = 3).
linewidth – The number of characters per line for the purpose of inserting line breaks (default = 80). Thresholded matrices will ignore this parameter.
profile – Sane defaults for pretty printing. Can override with any of the above options. (any one of default, short, full)
sci_mode – Enable (True) or disable (False) scientific notation. If None (default) is specified, the value is defined by _Formatter

torch.set_flush_denormal(mode) → bool¶

Disables denormal floating numbers on CPU.

Returns True if your system supports flushing denormal numbers and it successfully configures flush denormal mode. set_flush_denormal() is only supported on x86 architectures supporting SSE3.

Parameters: mode (bool) – Controls whether to enable flush denormal mode or not

Example:

>>> torch.set_flush_denormal(True)
True
>>> torch.tensor([1e-323], dtype=torch.float64)
tensor([ 0.], dtype=torch.float64)
>>> torch.set_flush_denormal(False)
True
>>> torch.tensor([1e-323], dtype=torch.float64)
tensor(9.88131e-324 *
       [ 1.0000], dtype=torch.float64)

Creation Ops¶

Note

Random sampling creation ops are listed under Random sampling and include: torch.rand() torch.rand_like() torch.randn() torch.randn_like() torch.randint() torch.randint_like() torch.randperm() You may also use torch.empty() with the In-place random sampling methods to create torch.Tensor s with values sampled from a broader range of distributions.

torch.tensor(data, dtype=None, device=None, requires_grad=False, pin_memory=False) → Tensor¶

Constructs a tensor with data.

Warning

torch.tensor() always copies data. If you have a Tensor data and want to avoid a copy, use torch.Tensor.requires_grad_() or torch.Tensor.detach(). If you have a NumPy ndarray and want to avoid a copy, use torch.as_tensor().

Warning

When data is a tensor x, torch.tensor() reads out ‘the data’ from whatever it is passed, and constructs a leaf variable. Therefore torch.tensor(x) is equivalent to x.clone().detach() and torch.tensor(x, requires_grad=True) is equivalent to x.clone().detach().requires_grad_(True). The equivalents using clone() and detach() are recommended.

Parameters

data (array_like) – Initial data for the tensor. Can be a list, tuple, NumPy ndarray, scalar, and other types.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, infers data type from data.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
pin_memory (bool, optional) – If set, returned tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False.

Example:

>>> torch.tensor([[0.1, 1.2], [2.2, 3.1], [4.9, 5.2]])
tensor([[ 0.1000,  1.2000],
        [ 2.2000,  3.1000],
        [ 4.9000,  5.2000]])

>>> torch.tensor([0, 1])  # Type inference on data
tensor([ 0,  1])

>>> torch.tensor([[0.11111, 0.222222, 0.3333333]],
                 dtype=torch.float64,
                 device=torch.device('cuda:0'))  # creates a torch.cuda.DoubleTensor
tensor([[ 0.1111,  0.2222,  0.3333]], dtype=torch.float64, device='cuda:0')

>>> torch.tensor(3.14159)  # Create a scalar (zero-dimensional tensor)
tensor(3.1416)

>>> torch.tensor([])  # Create an empty tensor (of size (0,))
tensor([])

torch.sparse_coo_tensor(indices, values, size=None, dtype=None, device=None, requires_grad=False) → Tensor¶

Constructs a sparse tensors in COO(rdinate) format with non-zero elements at the given indices with the given values. A sparse tensor can be uncoalesced, in that case, there are duplicate coordinates in the indices, and the value at that index is the sum of all duplicate value entries: torch.sparse.

Parameters

indices (array_like) – Initial data for the tensor. Can be a list, tuple, NumPy ndarray, scalar, and other types. Will be cast to a torch.LongTensor internally. The indices are the coordinates of the non-zero values in the matrix, and thus should be two-dimensional where the first dimension is the number of tensor dimensions and the second dimension is the number of non-zero values.
values (array_like) – Initial values for the tensor. Can be a list, tuple, NumPy ndarray, scalar, and other types.
size (list, tuple, or torch.Size, optional) – Size of the sparse tensor. If not provided the size will be inferred as the minimum size big enough to hold all non-zero elements.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, infers data type from values.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> i = torch.tensor([[0, 1, 1],
                      [2, 0, 2]])
>>> v = torch.tensor([3, 4, 5], dtype=torch.float32)
>>> torch.sparse_coo_tensor(i, v, [2, 4])
tensor(indices=tensor([[0, 1, 1],
                       [2, 0, 2]]),
       values=tensor([3., 4., 5.]),
       size=(2, 4), nnz=3, layout=torch.sparse_coo)

>>> torch.sparse_coo_tensor(i, v)  # Shape inference
tensor(indices=tensor([[0, 1, 1],
                       [2, 0, 2]]),
       values=tensor([3., 4., 5.]),
       size=(2, 3), nnz=3, layout=torch.sparse_coo)

>>> torch.sparse_coo_tensor(i, v, [2, 4],
                            dtype=torch.float64,
                            device=torch.device('cuda:0'))
tensor(indices=tensor([[0, 1, 1],
                       [2, 0, 2]]),
       values=tensor([3., 4., 5.]),
       device='cuda:0', size=(2, 4), nnz=3, dtype=torch.float64,
       layout=torch.sparse_coo)

# Create an empty sparse tensor with the following invariants:
#   1. sparse_dim + dense_dim = len(SparseTensor.shape)
#   2. SparseTensor._indices().shape = (sparse_dim, nnz)
#   3. SparseTensor._values().shape = (nnz, SparseTensor.shape[sparse_dim:])
#
# For instance, to create an empty sparse tensor with nnz = 0, dense_dim = 0 and
# sparse_dim = 1 (hence indices is a 2D tensor of shape = (1, 0))
>>> S = torch.sparse_coo_tensor(torch.empty([1, 0]), [], [1])
tensor(indices=tensor([], size=(1, 0)),
       values=tensor([], size=(0,)),
       size=(1,), nnz=0, layout=torch.sparse_coo)

# and to create an empty sparse tensor with nnz = 0, dense_dim = 1 and
# sparse_dim = 1
>>> S = torch.sparse_coo_tensor(torch.empty([1, 0]), torch.empty([0, 2]), [1, 2])
tensor(indices=tensor([], size=(1, 0)),
       values=tensor([], size=(0, 2)),
       size=(1, 2), nnz=0, layout=torch.sparse_coo)

torch.as_tensor(data, dtype=None, device=None) → Tensor¶

Convert the data into a torch.Tensor. If the data is already a Tensor with the same dtype and device, no copy will be performed, otherwise a new Tensor will be returned with computational graph retained if data Tensor has requires_grad=True. Similarly, if the data is an ndarray of the corresponding dtype and the device is the cpu, no copy will be performed.

Parameters

data (array_like) – Initial data for the tensor. Can be a list, tuple, NumPy ndarray, scalar, and other types.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, infers data type from data.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.

Example:

>>> a = numpy.array([1, 2, 3])
>>> t = torch.as_tensor(a)
>>> t
tensor([ 1,  2,  3])
>>> t[0] = -1
>>> a
array([-1,  2,  3])

>>> a = numpy.array([1, 2, 3])
>>> t = torch.as_tensor(a, device=torch.device('cuda'))
>>> t
tensor([ 1,  2,  3])
>>> t[0] = -1
>>> a
array([1,  2,  3])

torch.as_strided(input, size, stride, storage_offset=0) → Tensor¶

Create a view of an existing torch.Tensor input with specified size, stride and storage_offset.

Warning

More than one element of a created tensor may refer to a single memory location. As a result, in-place operations (especially ones that are vectorized) may result in incorrect behavior. If you need to write to the tensors, please clone them first.

Many PyTorch functions, which return a view of a tensor, are internally implemented with this function. Those functions, like torch.Tensor.expand(), are easier to read and are therefore more advisable to use.

Parameters

input (Tensor) – the input tensor.
size (tuple or ints) – the shape of the output tensor
stride (tuple or ints) – the stride of the output tensor
storage_offset (int, optional) – the offset in the underlying storage of the output tensor

Example:

>>> x = torch.randn(3, 3)
>>> x
tensor([[ 0.9039,  0.6291,  1.0795],
        [ 0.1586,  2.1939, -0.4900],
        [-0.1909, -0.7503,  1.9355]])
>>> t = torch.as_strided(x, (2, 2), (1, 2))
>>> t
tensor([[0.9039, 1.0795],
        [0.6291, 0.1586]])
>>> t = torch.as_strided(x, (2, 2), (1, 2), 1)
tensor([[0.6291, 0.1586],
        [1.0795, 2.1939]])

torch.from_numpy(ndarray) → Tensor¶

Creates a Tensor from a numpy.ndarray.

The returned tensor and ndarray share the same memory. Modifications to the tensor will be reflected in the ndarray and vice versa. The returned tensor is not resizable.

It currently accepts ndarray with dtypes of numpy.float64, numpy.float32, numpy.float16, numpy.int64, numpy.int32, numpy.int16, numpy.int8, numpy.uint8, and numpy.bool.

Example:

>>> a = numpy.array([1, 2, 3])
>>> t = torch.from_numpy(a)
>>> t
tensor([ 1,  2,  3])
>>> t[0] = -1
>>> a
array([-1,  2,  3])

torch.zeros(*size, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a tensor filled with the scalar value 0, with the shape defined by the variable argument size.

Parameters

size (int...) – a sequence of integers defining the shape of the output tensor. Can be a variable number of arguments or a collection like a list or tuple.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.zeros(2, 3)
tensor([[ 0.,  0.,  0.],
        [ 0.,  0.,  0.]])

>>> torch.zeros(5)
tensor([ 0.,  0.,  0.,  0.,  0.])

torch.zeros_like(input, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) → Tensor¶

Returns a tensor filled with the scalar value 0, with the same size as input. torch.zeros_like(input) is equivalent to torch.zeros(input.size(), dtype=input.dtype, layout=input.layout, device=input.device).

Warning

As of 0.4, this function does not support an out keyword. As an alternative, the old torch.zeros_like(input, out=output) is equivalent to torch.zeros(input.size(), out=output).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

Example:

>>> input = torch.empty(2, 3)
>>> torch.zeros_like(input)
tensor([[ 0.,  0.,  0.],
        [ 0.,  0.,  0.]])

torch.ones(*size, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a tensor filled with the scalar value 1, with the shape defined by the variable argument size.

Parameters

size (int...) – a sequence of integers defining the shape of the output tensor. Can be a variable number of arguments or a collection like a list or tuple.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.ones(2, 3)
tensor([[ 1.,  1.,  1.],
        [ 1.,  1.,  1.]])

>>> torch.ones(5)
tensor([ 1.,  1.,  1.,  1.,  1.])

torch.ones_like(input, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) → Tensor¶

Returns a tensor filled with the scalar value 1, with the same size as input. torch.ones_like(input) is equivalent to torch.ones(input.size(), dtype=input.dtype, layout=input.layout, device=input.device).

Warning

As of 0.4, this function does not support an out keyword. As an alternative, the old torch.ones_like(input, out=output) is equivalent to torch.ones(input.size(), out=output).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

Example:

>>> input = torch.empty(2, 3)
>>> torch.ones_like(input)
tensor([[ 1.,  1.,  1.],
        [ 1.,  1.,  1.]])

torch.arange(start=0, end, step=1, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a 1-D tensor of size $\left\lceil \frac{\text{end} - \text{start}}{\text{step}} \right\rceil$ with values from the interval [start, end) taken with common difference step beginning from start.

Note that non-integer step is subject to floating point rounding errors when comparing against end; to avoid inconsistency, we advise adding a small epsilon to end in such cases.

\text{out}_{{i+1}} = \text{out}_{i} + \text{step}

Parameters

start (Number) – the starting value for the set of points. Default: 0.
end (Number) – the ending value for the set of points
step (Number) – the gap between each pair of adjacent points. Default: 1.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()). If dtype is not given, infer the data type from the other input arguments. If any of start, end, or stop are floating-point, the dtype is inferred to be the default dtype, see get_default_dtype(). Otherwise, the dtype is inferred to be torch.int64.
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.arange(5)
tensor([ 0,  1,  2,  3,  4])
>>> torch.arange(1, 4)
tensor([ 1,  2,  3])
>>> torch.arange(1, 2.5, 0.5)
tensor([ 1.0000,  1.5000,  2.0000])

torch.range(start=0, end, step=1, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a 1-D tensor of size $\left\lfloor \frac{\text{end} - \text{start}}{\text{step}} \right\rfloor + 1$ with values from start to end with step step. Step is the gap between two values in the tensor.

\text{out}_{i+1} = \text{out}_i + \text{step}.

Warning

This function is deprecated in favor of torch.arange().

Parameters

start (float) – the starting value for the set of points. Default: 0.
end (float) – the ending value for the set of points
step (float) – the gap between each pair of adjacent points. Default: 1.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()). If dtype is not given, infer the data type from the other input arguments. If any of start, end, or stop are floating-point, the dtype is inferred to be the default dtype, see get_default_dtype(). Otherwise, the dtype is inferred to be torch.int64.
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.range(1, 4)
tensor([ 1.,  2.,  3.,  4.])
>>> torch.range(1, 4, 0.5)
tensor([ 1.0000,  1.5000,  2.0000,  2.5000,  3.0000,  3.5000,  4.0000])

torch.linspace(start, end, steps=100, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a one-dimensional tensor of steps equally spaced points between start and end.

The output tensor is 1-D of size steps.

Parameters

start (float) – the starting value for the set of points
end (float) – the ending value for the set of points
steps (int) – number of points to sample between start and end. Default: 100.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.linspace(3, 10, steps=5)
tensor([  3.0000,   4.7500,   6.5000,   8.2500,  10.0000])
>>> torch.linspace(-10, 10, steps=5)
tensor([-10.,  -5.,   0.,   5.,  10.])
>>> torch.linspace(start=-10, end=10, steps=5)
tensor([-10.,  -5.,   0.,   5.,  10.])
>>> torch.linspace(start=-10, end=10, steps=1)
tensor([-10.])

torch.logspace(start, end, steps=100, base=10.0, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a one-dimensional tensor of steps points logarithmically spaced with base base between ${\text{base}}^{\text{start}}$ and ${\text{base}}^{\text{end}}$ .

The output tensor is 1-D of size steps.

Parameters

start (float) – the starting value for the set of points
end (float) – the ending value for the set of points
steps (int) – number of points to sample between start and end. Default: 100.
base (float) – base of the logarithm function. Default: 10.0.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.logspace(start=-10, end=10, steps=5)
tensor([ 1.0000e-10,  1.0000e-05,  1.0000e+00,  1.0000e+05,  1.0000e+10])
>>> torch.logspace(start=0.1, end=1.0, steps=5)
tensor([  1.2589,   2.1135,   3.5481,   5.9566,  10.0000])
>>> torch.logspace(start=0.1, end=1.0, steps=1)
tensor([1.2589])
>>> torch.logspace(start=2, end=2, steps=1, base=2)
tensor([4.0])

torch.eye(n, m=None, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a 2-D tensor with ones on the diagonal and zeros elsewhere.

Parameters

n (int) – the number of rows
m (int, optional) – the number of columns with default being n
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Returns

A 2-D tensor with ones on the diagonal and zeros elsewhere

Return type

Tensor

Example:

>>> torch.eye(3)
tensor([[ 1.,  0.,  0.],
        [ 0.,  1.,  0.],
        [ 0.,  0.,  1.]])

torch.empty(*size, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False, pin_memory=False) → Tensor¶

Returns a tensor filled with uninitialized data. The shape of the tensor is defined by the variable argument size.

Parameters

size (int...) – a sequence of integers defining the shape of the output tensor. Can be a variable number of arguments or a collection like a list or tuple.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
pin_memory (bool, optional) – If set, returned tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.contiguous_format.

Example:

>>> torch.empty(2, 3)
tensor(1.00000e-08 *
       [[ 6.3984,  0.0000,  0.0000],
        [ 0.0000,  0.0000,  0.0000]])

torch.empty_like(input, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) → Tensor¶

Returns an uninitialized tensor with the same size as input. torch.empty_like(input) is equivalent to torch.empty(input.size(), dtype=input.dtype, layout=input.layout, device=input.device).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

Example:

>>> torch.empty((2,3), dtype=torch.int64)
tensor([[ 9.4064e+13,  2.8000e+01,  9.3493e+13],
        [ 7.5751e+18,  7.1428e+18,  7.5955e+18]])

torch.empty_strided(size, stride, dtype=None, layout=None, device=None, requires_grad=False, pin_memory=False) → Tensor¶

Returns a tensor filled with uninitialized data. The shape and strides of the tensor is defined by the variable argument size and stride respectively. torch.empty_strided(size, stride) is equivalent to torch.empty(size).as_strided(size, stride).

Warning

More than one element of the created tensor may refer to a single memory location. As a result, in-place operations (especially ones that are vectorized) may result in incorrect behavior. If you need to write to the tensors, please clone them first.

Parameters

size (tuple of python:ints) – the shape of the output tensor
stride (tuple of python:ints) – the strides of the output tensor
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
pin_memory (bool, optional) – If set, returned tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False.

Example:

>>> a = torch.empty_strided((2, 3), (1, 2))
>>> a
tensor([[8.9683e-44, 4.4842e-44, 5.1239e+07],
        [0.0000e+00, 0.0000e+00, 3.0705e-41]])
>>> a.stride()
(1, 2)
>>> a.size()
torch.Size([2, 3])

torch.full(size, fill_value, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a tensor of size size filled with fill_value.

Warning

In PyTorch 1.5 a bool or integral fill_value will produce a warning if dtype or out are not set. In a future PyTorch release, when dtype and out are not set a bool fill_value will return a tensor of torch.bool dtype, and an integral fill_value will return a tensor of torch.long dtype.

Parameters

size (int...) – a list, tuple, or torch.Size of integers defining the shape of the output tensor.
fill_value – the number to fill the output tensor with.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.full((2, 3), 3.141592)
tensor([[ 3.1416,  3.1416,  3.1416],
        [ 3.1416,  3.1416,  3.1416]])

torch.full_like()¶

full_like(input, fill_value, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns a tensor with the same size as input filled with fill_value. torch.full_like(input, fill_value) is equivalent to torch.full(input.size(), fill_value, dtype=input.dtype, layout=input.layout, device=input.device).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
fill_value – the number to fill the output tensor with.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

torch.quantize_per_tensor(input, scale, zero_point, dtype) → Tensor¶

Converts a float tensor to quantized tensor with given scale and zero point.

Parameters

input (Tensor) – float tensor to quantize
scale (float) – scale to apply in quantization formula
zero_point (int) – offset in integer value that maps to float zero
dtype (torch.dtype) – the desired data type of returned tensor. Has to be one of the quantized dtypes: torch.quint8, torch.qint8, torch.qint32

Returns

A newly quantized tensor

Return type

Tensor

Example:

>>> torch.quantize_per_tensor(torch.tensor([-1.0, 0.0, 1.0, 2.0]), 0.1, 10, torch.quint8)
tensor([-1.,  0.,  1.,  2.], size=(4,), dtype=torch.quint8,
       quantization_scheme=torch.per_tensor_affine, scale=0.1, zero_point=10)
>>> torch.quantize_per_tensor(torch.tensor([-1.0, 0.0, 1.0, 2.0]), 0.1, 10, torch.quint8).int_repr()
tensor([ 0, 10, 20, 30], dtype=torch.uint8)

torch.quantize_per_channel(input, scales, zero_points, axis, dtype) → Tensor¶

Converts a float tensor to per-channel quantized tensor with given scales and zero points.

Parameters

input (Tensor) – float tensor to quantize
scales (Tensor) – float 1D tensor of scales to use, size should match input.size(axis)
zero_points (int) – integer 1D tensor of offset to use, size should match input.size(axis)
axis (int) – dimension on which apply per-channel quantization
dtype (torch.dtype) – the desired data type of returned tensor. Has to be one of the quantized dtypes: torch.quint8, torch.qint8, torch.qint32

Returns

A newly quantized tensor

Return type

Tensor

Example:

>>> x = torch.tensor([[-1.0, 0.0], [1.0, 2.0]])
>>> torch.quantize_per_channel(x, torch.tensor([0.1, 0.01]), torch.tensor([10, 0]), 0, torch.quint8)
tensor([[-1.,  0.],
        [ 1.,  2.]], size=(2, 2), dtype=torch.quint8,
       quantization_scheme=torch.per_channel_affine,
       scale=tensor([0.1000, 0.0100], dtype=torch.float64),
       zero_point=tensor([10,  0]), axis=0)
>>> torch.quantize_per_channel(x, torch.tensor([0.1, 0.01]), torch.tensor([10, 0]), 0, torch.quint8).int_repr()
tensor([[  0,  10],
        [100, 200]], dtype=torch.uint8)

Indexing, Slicing, Joining, Mutating Ops¶

torch.cat(tensors, dim=0, out=None) → Tensor¶

Concatenates the given sequence of seq tensors in the given dimension. All tensors must either have the same shape (except in the concatenating dimension) or be empty.

torch.cat() can be seen as an inverse operation for torch.split() and torch.chunk().

torch.cat() can be best understood via examples.

Parameters

tensors (sequence of Tensors) – any python sequence of tensors of the same type. Non-empty tensors provided must have the same shape, except in the cat dimension.
dim (int, optional) – the dimension over which the tensors are concatenated
out (Tensor, optional) – the output tensor.

Example:

>>> x = torch.randn(2, 3)
>>> x
tensor([[ 0.6580, -1.0969, -0.4614],
        [-0.1034, -0.5790,  0.1497]])
>>> torch.cat((x, x, x), 0)
tensor([[ 0.6580, -1.0969, -0.4614],
        [-0.1034, -0.5790,  0.1497],
        [ 0.6580, -1.0969, -0.4614],
        [-0.1034, -0.5790,  0.1497],
        [ 0.6580, -1.0969, -0.4614],
        [-0.1034, -0.5790,  0.1497]])
>>> torch.cat((x, x, x), 1)
tensor([[ 0.6580, -1.0969, -0.4614,  0.6580, -1.0969, -0.4614,  0.6580,
         -1.0969, -0.4614],
        [-0.1034, -0.5790,  0.1497, -0.1034, -0.5790,  0.1497, -0.1034,
         -0.5790,  0.1497]])

torch.chunk(input, chunks, dim=0) → List of Tensors¶

Splits a tensor into a specific number of chunks. Each chunk is a view of the input tensor.

Last chunk will be smaller if the tensor size along the given dimension dim is not divisible by chunks.

Parameters

input (Tensor) – the tensor to split
chunks (int) – number of chunks to return
dim (int) – dimension along which to split the tensor

torch.gather(input, dim, index, out=None, sparse_grad=False) → Tensor¶

Gathers values along an axis specified by dim.

For a 3-D tensor the output is specified by:

out[i][j][k] = input[index[i][j][k]][j][k]  # if dim == 0
out[i][j][k] = input[i][index[i][j][k]][k]  # if dim == 1
out[i][j][k] = input[i][j][index[i][j][k]]  # if dim == 2

If input is an n-dimensional tensor with size $(x_0, x_1..., x_{i-1}, x_i, x_{i+1}, ..., x_{n-1})$ and dim = i, then index must be an $n$ -dimensional tensor with size $(x_0, x_1, ..., x_{i-1}, y, x_{i+1}, ..., x_{n-1})$ where $y \geq 1$ and out will have the same size as index.

Parameters

input (Tensor) – the source tensor
dim (int) – the axis along which to index
index (LongTensor) – the indices of elements to gather
out (Tensor, optional) – the destination tensor
sparse_grad (bool,optional) – If True, gradient w.r.t. input will be a sparse tensor.

Example:

>>> t = torch.tensor([[1,2],[3,4]])
>>> torch.gather(t, 1, torch.tensor([[0,0],[1,0]]))
tensor([[ 1,  1],
        [ 4,  3]])

torch.index_select(input, dim, index, out=None) → Tensor¶

Returns a new tensor which indexes the input tensor along dimension dim using the entries in index which is a LongTensor.

The returned tensor has the same number of dimensions as the original tensor (input). The dimth dimension has the same size as the length of index; other dimensions have the same size as in the original tensor.

Note

The returned tensor does not use the same storage as the original tensor. If out has a different shape than expected, we silently change it to the correct shape, reallocating the underlying storage if necessary.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension in which we index
index (LongTensor) – the 1-D tensor containing the indices to index
out (Tensor, optional) – the output tensor.

Example:

>>> x = torch.randn(3, 4)
>>> x
tensor([[ 0.1427,  0.0231, -0.5414, -1.0009],
        [-0.4664,  0.2647, -0.1228, -1.1068],
        [-1.1734, -0.6571,  0.7230, -0.6004]])
>>> indices = torch.tensor([0, 2])
>>> torch.index_select(x, 0, indices)
tensor([[ 0.1427,  0.0231, -0.5414, -1.0009],
        [-1.1734, -0.6571,  0.7230, -0.6004]])
>>> torch.index_select(x, 1, indices)
tensor([[ 0.1427, -0.5414],
        [-0.4664, -0.1228],
        [-1.1734,  0.7230]])

torch.masked_select(input, mask, out=None) → Tensor¶

Returns a new 1-D tensor which indexes the input tensor according to the boolean mask mask which is a BoolTensor.

The shapes of the mask tensor and the input tensor don’t need to match, but they must be broadcastable.

Note

The returned tensor does not use the same storage as the original tensor

Parameters

input (Tensor) – the input tensor.
mask (BoolTensor) – the tensor containing the binary mask to index with
out (Tensor, optional) – the output tensor.

Example:

>>> x = torch.randn(3, 4)
>>> x
tensor([[ 0.3552, -2.3825, -0.8297,  0.3477],
        [-1.2035,  1.2252,  0.5002,  0.6248],
        [ 0.1307, -2.0608,  0.1244,  2.0139]])
>>> mask = x.ge(0.5)
>>> mask
tensor([[False, False, False, False],
        [False, True, True, True],
        [False, False, False, True]])
>>> torch.masked_select(x, mask)
tensor([ 1.2252,  0.5002,  0.6248,  2.0139])

torch.narrow(input, dim, start, length) → Tensor¶

Returns a new tensor that is a narrowed version of input tensor. The dimension dim is input from start to start + length. The returned tensor and input tensor share the same underlying storage.

Parameters

input (Tensor) – the tensor to narrow
dim (int) – the dimension along which to narrow
start (int) – the starting dimension
length (int) – the distance to the ending dimension

Example:

>>> x = torch.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> torch.narrow(x, 0, 0, 2)
tensor([[ 1,  2,  3],
        [ 4,  5,  6]])
>>> torch.narrow(x, 1, 1, 2)
tensor([[ 2,  3],
        [ 5,  6],
        [ 8,  9]])

torch.nonzero(input, *, out=None, as_tuple=False) → LongTensor or tuple of LongTensors¶

Note

torch.nonzero(..., as_tuple=False) (default) returns a 2-D tensor where each row is the index for a nonzero value.

torch.nonzero(..., as_tuple=True) returns a tuple of 1-D index tensors, allowing for advanced indexing, so x[x.nonzero(as_tuple=True)] gives all nonzero values of tensor x. Of the returned tuple, each index tensor contains nonzero indices for a certain dimension.

See below for more details on the two behaviors.

When as_tuple is ``False`` (default):

Returns a tensor containing the indices of all non-zero elements of input. Each row in the result contains the indices of a non-zero element in input. The result is sorted lexicographically, with the last index changing the fastest (C-style).

If input has $n$ dimensions, then the resulting indices tensor out is of size $(z \times n)$ , where $z$ is the total number of non-zero elements in the input tensor.

When as_tuple is ``True``:

Returns a tuple of 1-D tensors, one for each dimension in input, each containing the indices (in that dimension) of all non-zero elements of input .

If input has $n$ dimensions, then the resulting tuple contains $n$ tensors of size $z$ , where $z$ is the total number of non-zero elements in the input tensor.

As a special case, when input has zero dimensions and a nonzero scalar value, it is treated as a one-dimensional tensor with one element.

Parameters

input (Tensor) – the input tensor.
out (LongTensor, optional) – the output tensor containing indices

Returns

If as_tuple is False, the output tensor containing indices. If as_tuple is True, one 1-D tensor for each dimension, containing the indices of each nonzero element along that dimension.

Return type

LongTensor or tuple of LongTensor

Example:

>>> torch.nonzero(torch.tensor([1, 1, 1, 0, 1]))
tensor([[ 0],
        [ 1],
        [ 2],
        [ 4]])
>>> torch.nonzero(torch.tensor([[0.6, 0.0, 0.0, 0.0],
                                [0.0, 0.4, 0.0, 0.0],
                                [0.0, 0.0, 1.2, 0.0],
                                [0.0, 0.0, 0.0,-0.4]]))
tensor([[ 0,  0],
        [ 1,  1],
        [ 2,  2],
        [ 3,  3]])
>>> torch.nonzero(torch.tensor([1, 1, 1, 0, 1]), as_tuple=True)
(tensor([0, 1, 2, 4]),)
>>> torch.nonzero(torch.tensor([[0.6, 0.0, 0.0, 0.0],
                                [0.0, 0.4, 0.0, 0.0],
                                [0.0, 0.0, 1.2, 0.0],
                                [0.0, 0.0, 0.0,-0.4]]), as_tuple=True)
(tensor([0, 1, 2, 3]), tensor([0, 1, 2, 3]))
>>> torch.nonzero(torch.tensor(5), as_tuple=True)
(tensor([0]),)

torch.reshape(input, shape) → Tensor¶

Returns a tensor with the same data and number of elements as input, but with the specified shape. When possible, the returned tensor will be a view of input. Otherwise, it will be a copy. Contiguous inputs and inputs with compatible strides can be reshaped without copying, but you should not depend on the copying vs. viewing behavior.

See torch.Tensor.view() on when it is possible to return a view.

A single dimension may be -1, in which case it’s inferred from the remaining dimensions and the number of elements in input.

Parameters

input (Tensor) – the tensor to be reshaped
shape (tuple of python:ints) – the new shape

Example:

>>> a = torch.arange(4.)
>>> torch.reshape(a, (2, 2))
tensor([[ 0.,  1.],
        [ 2.,  3.]])
>>> b = torch.tensor([[0, 1], [2, 3]])
>>> torch.reshape(b, (-1,))
tensor([ 0,  1,  2,  3])

torch.split(tensor, split_size_or_sections, dim=0)[source]¶

Splits the tensor into chunks. Each chunk is a view of the original tensor.

If split_size_or_sections is an integer type, then tensor will be split into equally sized chunks (if possible). Last chunk will be smaller if the tensor size along the given dimension dim is not divisible by split_size.

If split_size_or_sections is a list, then tensor will be split into len(split_size_or_sections) chunks with sizes in dim according to split_size_or_sections.

Parameters

tensor (Tensor) – tensor to split.
split_size_or_sections (int) or (list(int)) – size of a single chunk or list of sizes for each chunk
dim (int) – dimension along which to split the tensor.

torch.squeeze(input, dim=None, out=None) → Tensor¶

Returns a tensor with all the dimensions of input of size 1 removed.

For example, if input is of shape: $(A \times 1 \times B \times C \times 1 \times D)$ then the out tensor will be of shape: $(A \times B \times C \times D)$ .

When dim is given, a squeeze operation is done only in the given dimension. If input is of shape: $(A \times 1 \times B)$ , squeeze(input, 0) leaves the tensor unchanged, but squeeze(input, 1) will squeeze the tensor to the shape $(A \times B)$ .

Note

The returned tensor shares the storage with the input tensor, so changing the contents of one will change the contents of the other.

Parameters

input (Tensor) – the input tensor.
dim (int, optional) – if given, the input will be squeezed only in this dimension
out (Tensor, optional) – the output tensor.

Example:

>>> x = torch.zeros(2, 1, 2, 1, 2)
>>> x.size()
torch.Size([2, 1, 2, 1, 2])
>>> y = torch.squeeze(x)
>>> y.size()
torch.Size([2, 2, 2])
>>> y = torch.squeeze(x, 0)
>>> y.size()
torch.Size([2, 1, 2, 1, 2])
>>> y = torch.squeeze(x, 1)
>>> y.size()
torch.Size([2, 2, 1, 2])

torch.stack(tensors, dim=0, out=None) → Tensor¶

Concatenates sequence of tensors along a new dimension.

All tensors need to be of the same size.

Parameters

tensors (sequence of Tensors) – sequence of tensors to concatenate
dim (int) – dimension to insert. Has to be between 0 and the number of dimensions of concatenated tensors (inclusive)
out (Tensor, optional) – the output tensor.

torch.t(input) → Tensor¶

Expects input to be <= 2-D tensor and transposes dimensions 0 and 1.

0-D and 1-D tensors are returned as is. When input is a 2-D tensor this is equivalent to transpose(input, 0, 1).

Parameters: input (Tensor) – the input tensor.

Example:

>>> x = torch.randn(())
>>> x
tensor(0.1995)
>>> torch.t(x)
tensor(0.1995)
>>> x = torch.randn(3)
>>> x
tensor([ 2.4320, -0.4608,  0.7702])
>>> torch.t(x)
tensor([ 2.4320, -0.4608,  0.7702])
>>> x = torch.randn(2, 3)
>>> x
tensor([[ 0.4875,  0.9158, -0.5872],
        [ 0.3938, -0.6929,  0.6932]])
>>> torch.t(x)
tensor([[ 0.4875,  0.3938],
        [ 0.9158, -0.6929],
        [-0.5872,  0.6932]])

torch.take(input, index) → Tensor¶

Returns a new tensor with the elements of input at the given indices. The input tensor is treated as if it were viewed as a 1-D tensor. The result takes the same shape as the indices.

Parameters

input (Tensor) – the input tensor.
indices (LongTensor) – the indices into tensor

Example:

>>> src = torch.tensor([[4, 3, 5],
                        [6, 7, 8]])
>>> torch.take(src, torch.tensor([0, 2, 5]))
tensor([ 4,  5,  8])

torch.transpose(input, dim0, dim1) → Tensor¶

Returns a tensor that is a transposed version of input. The given dimensions dim0 and dim1 are swapped.

The resulting out tensor shares it’s underlying storage with the input tensor, so changing the content of one would change the content of the other.

Parameters

input (Tensor) – the input tensor.
dim0 (int) – the first dimension to be transposed
dim1 (int) – the second dimension to be transposed

Example:

>>> x = torch.randn(2, 3)
>>> x
tensor([[ 1.0028, -0.9893,  0.5809],
        [-0.1669,  0.7299,  0.4942]])
>>> torch.transpose(x, 0, 1)
tensor([[ 1.0028, -0.1669],
        [-0.9893,  0.7299],
        [ 0.5809,  0.4942]])

torch.unbind(input, dim=0) → seq¶

Removes a tensor dimension.

Returns a tuple of all slices along a given dimension, already without it.

Parameters

input (Tensor) – the tensor to unbind
dim (int) – dimension to remove

Example:

>>> torch.unbind(torch.tensor([[1, 2, 3],
>>>                            [4, 5, 6],
>>>                            [7, 8, 9]]))
(tensor([1, 2, 3]), tensor([4, 5, 6]), tensor([7, 8, 9]))

torch.unsqueeze(input, dim) → Tensor¶

Returns a new tensor with a dimension of size one inserted at the specified position.

The returned tensor shares the same underlying data with this tensor.

A dim value within the range [-input.dim() - 1, input.dim() + 1) can be used. Negative dim will correspond to unsqueeze() applied at dim = dim + input.dim() + 1.

Parameters

input (Tensor) – the input tensor.
dim (int) – the index at which to insert the singleton dimension

Example:

>>> x = torch.tensor([1, 2, 3, 4])
>>> torch.unsqueeze(x, 0)
tensor([[ 1,  2,  3,  4]])
>>> torch.unsqueeze(x, 1)
tensor([[ 1],
        [ 2],
        [ 3],
        [ 4]])

torch.where()¶

torch.where(condition, x, y) → Tensor

Return a tensor of elements selected from either x or y, depending on condition.

The operation is defined as:

\text{out}_i = \begin{cases} \text{x}_i & \text{if } \text{condition}_i \\ \text{y}_i & \text{otherwise} \\ \end{cases}

Note

The tensors condition, x, y must be broadcastable.

Parameters

condition (BoolTensor) – When True (nonzero), yield x, otherwise yield y
x (Tensor) – values selected at indices where condition is True
y (Tensor) – values selected at indices where condition is False

Returns

A tensor of shape equal to the broadcasted shape of condition, x, y

Return type

Tensor

Example:

>>> x = torch.randn(3, 2)
>>> y = torch.ones(3, 2)
>>> x
tensor([[-0.4620,  0.3139],
        [ 0.3898, -0.7197],
        [ 0.0478, -0.1657]])
>>> torch.where(x > 0, x, y)
tensor([[ 1.0000,  0.3139],
        [ 0.3898,  1.0000],
        [ 0.0478,  1.0000]])

torch.where(condition) → tuple of LongTensor

torch.where(condition) is identical to torch.nonzero(condition, as_tuple=True).

Note

Generators¶

class torch._C.Generator(device='cpu') → Generator¶

Creates and returns a generator object which manages the state of the algorithm that produces pseudo random numbers. Used as a keyword argument in many In-place random sampling functions.

Parameters: device (torch.device, optional) – the desired device for the generator.
Returns: An torch.Generator object.
Return type: Generator

Example:

>>> g_cpu = torch.Generator()
>>> g_cuda = torch.Generator(device='cuda')

device¶

Generator.device -> device

Gets the current device of the generator.

Example:

>>> g_cpu = torch.Generator()
>>> g_cpu.device
device(type='cpu')

get_state() → Tensor¶

Returns the Generator state as a torch.ByteTensor.

Returns: A torch.ByteTensor which contains all the necessary bits to restore a Generator to a specific point in time.
Return type: Tensor

Example:

>>> g_cpu = torch.Generator()
>>> g_cpu.get_state()

initial_seed() → int¶

Returns the initial seed for generating random numbers.

Example:

>>> g_cpu = torch.Generator()
>>> g_cpu.initial_seed()
2147483647

manual_seed(seed) → Generator¶

Sets the seed for generating random numbers. Returns a torch.Generator object. It is recommended to set a large seed, i.e. a number that has a good balance of 0 and 1 bits. Avoid having many 0 bits in the seed.

Parameters: seed (int) – The desired seed.
Returns: An torch.Generator object.
Return type: Generator

Example:

>>> g_cpu = torch.Generator()
>>> g_cpu.manual_seed(2147483647)

seed() → int¶

Gets a non-deterministic random number from std::random_device or the current time and uses it to seed a Generator.

Example:

>>> g_cpu = torch.Generator()
>>> g_cpu.seed()
1516516984916

set_state(new_state) → void¶

Sets the Generator state.

Parameters: new_state (torch.ByteTensor) – The desired state.

Example:

>>> g_cpu = torch.Generator()
>>> g_cpu_other = torch.Generator()
>>> g_cpu.set_state(g_cpu_other.get_state())

Random sampling¶

torch.seed()[source]¶: Sets the seed for generating random numbers to a non-deterministic random number. Returns a 64 bit number used to seed the RNG.

torch.manual_seed(seed)[source]¶

Sets the seed for generating random numbers. Returns a torch.Generator object.

Parameters: seed (int) – The desired seed.

torch.initial_seed()[source]¶: Returns the initial seed for generating random numbers as a Python long.

torch.get_rng_state()[source]¶: Returns the random number generator state as a torch.ByteTensor.

torch.set_rng_state(new_state)[source]¶

Sets the random number generator state.

Parameters: new_state (torch.ByteTensor) – The desired state

torch.default_generator Returns the default CPU torch.Generator¶

torch.bernoulli(input, *, generator=None, out=None) → Tensor¶

Draws binary random numbers (0 or 1) from a Bernoulli distribution.

The input tensor should be a tensor containing probabilities to be used for drawing the binary random number. Hence, all values in input have to be in the range: $0 \leq \text{input}_i \leq 1$ .

The $\text{i}^{th}$ element of the output tensor will draw a value $1$ according to the $\text{i}^{th}$ probability value given in input.

\text{out}_{i} \sim \mathrm{Bernoulli}(p = \text{input}_{i})

The returned out tensor only has values 0 or 1 and is of the same shape as input.

out can have integral dtype, but input must have floating point dtype.

Parameters

input (Tensor) – the input tensor of probability values for the Bernoulli distribution
generator (torch.Generator, optional) – a pseudorandom number generator for sampling
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.empty(3, 3).uniform_(0, 1)  # generate a uniform random matrix with range [0, 1]
>>> a
tensor([[ 0.1737,  0.0950,  0.3609],
        [ 0.7148,  0.0289,  0.2676],
        [ 0.9456,  0.8937,  0.7202]])
>>> torch.bernoulli(a)
tensor([[ 1.,  0.,  0.],
        [ 0.,  0.,  0.],
        [ 1.,  1.,  1.]])

>>> a = torch.ones(3, 3) # probability of drawing "1" is 1
>>> torch.bernoulli(a)
tensor([[ 1.,  1.,  1.],
        [ 1.,  1.,  1.],
        [ 1.,  1.,  1.]])
>>> a = torch.zeros(3, 3) # probability of drawing "1" is 0
>>> torch.bernoulli(a)
tensor([[ 0.,  0.,  0.],
        [ 0.,  0.,  0.],
        [ 0.,  0.,  0.]])

torch.multinomial(input, num_samples, replacement=False, *, generator=None, out=None) → LongTensor¶

Returns a tensor where each row contains num_samples indices sampled from the multinomial probability distribution located in the corresponding row of tensor input.

Note

The rows of input do not need to sum to one (in which case we use the values as weights), but must be non-negative, finite and have a non-zero sum.

Indices are ordered from left to right according to when each was sampled (first samples are placed in first column).

If input is a vector, out is a vector of size num_samples.

If input is a matrix with m rows, out is an matrix of shape $(m \times \text{num\_samples})$ .

If replacement is True, samples are drawn with replacement.

If not, they are drawn without replacement, which means that when a sample index is drawn for a row, it cannot be drawn again for that row.

Note

When drawn without replacement, num_samples must be lower than number of non-zero elements in input (or the min number of non-zero elements in each row of input if it is a matrix).

Parameters

input (Tensor) – the input tensor containing probabilities
num_samples (int) – number of samples to draw
replacement (bool, optional) – whether to draw with replacement or not
generator (torch.Generator, optional) – a pseudorandom number generator for sampling
out (Tensor, optional) – the output tensor.

Example:

>>> weights = torch.tensor([0, 10, 3, 0], dtype=torch.float) # create a tensor of weights
>>> torch.multinomial(weights, 2)
tensor([1, 2])
>>> torch.multinomial(weights, 4) # ERROR!
RuntimeError: invalid argument 2: invalid multinomial distribution (with replacement=False,
not enough non-negative category to sample) at ../aten/src/TH/generic/THTensorRandom.cpp:320
>>> torch.multinomial(weights, 4, replacement=True)
tensor([ 2,  1,  1,  1])

torch.normal()¶

torch.normal(mean, std, *, generator=None, out=None) → Tensor

Returns a tensor of random numbers drawn from separate normal distributions whose mean and standard deviation are given.

The mean is a tensor with the mean of each output element’s normal distribution

The std is a tensor with the standard deviation of each output element’s normal distribution

The shapes of mean and std don’t need to match, but the total number of elements in each tensor need to be the same.

Note

When the shapes do not match, the shape of mean is used as the shape for the returned output tensor

Parameters

mean (Tensor) – the tensor of per-element means
std (Tensor) – the tensor of per-element standard deviations
generator (torch.Generator, optional) – a pseudorandom number generator for sampling
out (Tensor, optional) – the output tensor.

Example:

>>> torch.normal(mean=torch.arange(1., 11.), std=torch.arange(1, 0, -0.1))
tensor([  1.0425,   3.5672,   2.7969,   4.2925,   4.7229,   6.2134,
          8.0505,   8.1408,   9.0563,  10.0566])

torch.normal(mean=0.0, std, out=None) → Tensor

Similar to the function above, but the means are shared among all drawn elements.

Parameters

mean (float, optional) – the mean for all distributions
std (Tensor) – the tensor of per-element standard deviations
out (Tensor, optional) – the output tensor.

Example:

>>> torch.normal(mean=0.5, std=torch.arange(1., 6.))
tensor([-1.2793, -1.0732, -2.0687,  5.1177, -1.2303])

torch.normal(mean, std=1.0, out=None) → Tensor

Similar to the function above, but the standard-deviations are shared among all drawn elements.

Parameters

mean (Tensor) – the tensor of per-element means
std (float, optional) – the standard deviation for all distributions
out (Tensor, optional) – the output tensor

Example:

>>> torch.normal(mean=torch.arange(1., 6.))
tensor([ 1.1552,  2.6148,  2.6535,  5.8318,  4.2361])

torch.normal(mean, std, size, *, out=None) → Tensor

Similar to the function above, but the means and standard deviations are shared among all drawn elements. The resulting tensor has size given by size.

Parameters

mean (float) – the mean for all distributions
std (float) – the standard deviation for all distributions
size (int...) – a sequence of integers defining the shape of the output tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.normal(2, 3, size=(1, 4))
tensor([[-1.3987, -1.9544,  3.6048,  0.7909]])

torch.poisson(input *, generator=None) → Tensor¶

Returns a tensor of the same size as input with each element sampled from a Poisson distribution with rate parameter given by the corresponding element in input i.e.,

\text{out}_i \sim \text{Poisson}(\text{input}_i)

Parameters

input (Tensor) – the input tensor containing the rates of the Poisson distribution
generator (torch.Generator, optional) – a pseudorandom number generator for sampling

Example:

>>> rates = torch.rand(4, 4) * 5  # rate parameter between 0 and 5
>>> torch.poisson(rates)
tensor([[9., 1., 3., 5.],
        [8., 6., 6., 0.],
        [0., 4., 5., 3.],
        [2., 1., 4., 2.]])

torch.rand(*size, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a tensor filled with random numbers from a uniform distribution on the interval $[0, 1)$

The shape of the tensor is defined by the variable argument size.

Parameters

size (int...) – a sequence of integers defining the shape of the output tensor. Can be a variable number of arguments or a collection like a list or tuple.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.rand(4)
tensor([ 0.5204,  0.2503,  0.3525,  0.5673])
>>> torch.rand(2, 3)
tensor([[ 0.8237,  0.5781,  0.6879],
        [ 0.3816,  0.7249,  0.0998]])

torch.rand_like(input, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) → Tensor¶

Returns a tensor with the same size as input that is filled with random numbers from a uniform distribution on the interval $[0, 1)$ . torch.rand_like(input) is equivalent to torch.rand(input.size(), dtype=input.dtype, layout=input.layout, device=input.device).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

torch.randint()¶

randint(low=0, high, size, *, generator=None, out=None,: dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a tensor filled with random integers generated uniformly between low (inclusive) and high (exclusive).

The shape of the tensor is defined by the variable argument size.

Parameters

low (int, optional) – Lowest integer to be drawn from the distribution. Default: 0.
high (int) – One above the highest integer to be drawn from the distribution.
size (tuple) – a tuple defining the shape of the output tensor.
generator (torch.Generator, optional) – a pseudorandom number generator for sampling
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.randint(3, 5, (3,))
tensor([4, 3, 4])


>>> torch.randint(10, (2, 2))
tensor([[0, 2],
        [5, 5]])


>>> torch.randint(3, 10, (2, 2))
tensor([[4, 5],
        [6, 7]])

torch.randint_like()¶

randint_like(input, low=0, high, dtype=None, layout=torch.strided, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns a tensor with the same shape as Tensor input filled with random integers generated uniformly between low (inclusive) and high (exclusive).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
low (int, optional) – Lowest integer to be drawn from the distribution. Default: 0.
high (int) – One above the highest integer to be drawn from the distribution.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

torch.randn(*size, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Returns a tensor filled with random numbers from a normal distribution with mean 0 and variance 1 (also called the standard normal distribution).

\text{out}_{i} \sim \mathcal{N}(0, 1)

The shape of the tensor is defined by the variable argument size.

Parameters

size (int...) – a sequence of integers defining the shape of the output tensor. Can be a variable number of arguments or a collection like a list or tuple.
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()).
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.randn(4)
tensor([-2.1436,  0.9966,  2.3426, -0.6366])
>>> torch.randn(2, 3)
tensor([[ 1.5954,  2.8929, -1.0923],
        [ 1.1719, -0.4709, -0.1996]])

torch.randn_like(input, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) → Tensor¶

Returns a tensor with the same size as input that is filled with random numbers from a normal distribution with mean 0 and variance 1. torch.randn_like(input) is equivalent to torch.randn(input.size(), dtype=input.dtype, layout=input.layout, device=input.device).

Parameters

input (Tensor) – the size of input will determine size of the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned Tensor. Default: if None, defaults to the dtype of input.
layout (torch.layout, optional) – the desired layout of returned tensor. Default: if None, defaults to the layout of input.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, defaults to the device of input.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.
memory_format (torch.memory_format, optional) – the desired memory format of returned Tensor. Default: torch.preserve_format.

torch.randperm(n, out=None, dtype=torch.int64, layout=torch.strided, device=None, requires_grad=False) → LongTensor¶

Returns a random permutation of integers from 0 to n - 1.

Parameters

n (int) – the upper bound (exclusive)
out (Tensor, optional) – the output tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: torch.int64.
layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Example:

>>> torch.randperm(4)
tensor([2, 1, 0, 3])

In-place random sampling¶

There are a few more in-place random sampling functions defined on Tensors as well. Click through to refer to their documentation:

torch.Tensor.bernoulli_() - in-place version of torch.bernoulli()
torch.Tensor.cauchy_() - numbers drawn from the Cauchy distribution
torch.Tensor.exponential_() - numbers drawn from the exponential distribution
torch.Tensor.geometric_() - elements drawn from the geometric distribution
torch.Tensor.log_normal_() - samples from the log-normal distribution
torch.Tensor.normal_() - in-place version of torch.normal()
torch.Tensor.random_() - numbers sampled from the discrete uniform distribution
torch.Tensor.uniform_() - numbers sampled from the continuous uniform distribution

Quasi-random sampling¶

class torch.quasirandom.SobolEngine(dimension, scramble=False, seed=None)[source]¶

The torch.quasirandom.SobolEngine is an engine for generating (scrambled) Sobol sequences. Sobol sequences are an example of low discrepancy quasi-random sequences.

This implementation of an engine for Sobol sequences is capable of sampling sequences up to a maximum dimension of 1111. It uses direction numbers to generate these sequences, and these numbers have been adapted from here.

References

Art B. Owen. Scrambling Sobol and Niederreiter-Xing points. Journal of Complexity, 14(4):466-489, December 1998.
I. M. Sobol. The distribution of points in a cube and the accurate evaluation of integrals. Zh. Vychisl. Mat. i Mat. Phys., 7:784-802, 1967.

Parameters

dimension (Int) – The dimensionality of the sequence to be drawn
scramble (bool, optional) – Setting this to True will produce scrambled Sobol sequences. Scrambling is capable of producing better Sobol sequences. Default: False.
seed (Int, optional) – This is the seed for the scrambling. The seed of the random number generator is set to this, if specified. Otherwise, it uses a random seed. Default: None

Examples:

>>> soboleng = torch.quasirandom.SobolEngine(dimension=5)
>>> soboleng.draw(3)
tensor([[0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.7500, 0.2500, 0.7500, 0.2500, 0.7500],
        [0.2500, 0.7500, 0.2500, 0.7500, 0.2500]])

draw(n=1, out=None, dtype=torch.float32)[source]¶

Function to draw a sequence of n points from a Sobol sequence. Note that the samples are dependent on the previous samples. The size of the result is $(n, dimension)$ .

Parameters

n (Int, optional) – The length of sequence of points to draw. Default: 1
out (Tensor, optional) – The output tensor
dtype (torch.dtype, optional) – the desired data type of the returned tensor. Default: torch.float32

fast_forward(n)[source]¶

Function to fast-forward the state of the SobolEngine by n steps. This is equivalent to drawing n samples without using the samples.

Parameters: n (Int) – The number of steps to fast-forward by.

reset()[source]¶: Function to reset the SobolEngine to base state.

Serialization¶

torch.save(obj, f, pickle_module=pickle, pickle_protocol=2, _use_new_zipfile_serialization=False)[source]¶

Saves an object to a disk file.

Parameters

obj – saved object
f – a file-like object (has to implement write and flush) or a string containing a file name
pickle_module – module used for pickling metadata and objects
pickle_protocol – can be specified to override the default protocol

Warning

If you are using Python 2, torch.save() does NOT support StringIO.StringIO as a valid file-like object. This is because the write method should return the number of bytes written; StringIO.write() does not do this.

Please use something like io.BytesIO instead.

Example

>>> # Save to file
>>> x = torch.tensor([0, 1, 2, 3, 4])
>>> torch.save(x, 'tensor.pt')
>>> # Save to io.BytesIO buffer
>>> buffer = io.BytesIO()
>>> torch.save(x, buffer)

torch.load(f, map_location=None, pickle_module=pickle, **pickle_load_args)[source]¶

Loads an object saved with torch.save() from a file.

torch.load() uses Python’s unpickling facilities but treats storages, which underlie tensors, specially. They are first deserialized on the CPU and are then moved to the device they were saved from. If this fails (e.g. because the run time system doesn’t have certain devices), an exception is raised. However, storages can be dynamically remapped to an alternative set of devices using the map_location argument.

If map_location is a callable, it will be called once for each serialized storage with two arguments: storage and location. The storage argument will be the initial deserialization of the storage, residing on the CPU. Each serialized storage has a location tag associated with it which identifies the device it was saved from, and this tag is the second argument passed to map_location. The builtin location tags are 'cpu' for CPU tensors and 'cuda:device_id' (e.g. 'cuda:2') for CUDA tensors. map_location should return either None or a storage. If map_location returns a storage, it will be used as the final deserialized object, already moved to the right device. Otherwise, torch.load() will fall back to the default behavior, as if map_location wasn’t specified.

If map_location is a torch.device object or a string containing a device tag, it indicates the location where all tensors should be loaded.

Otherwise, if map_location is a dict, it will be used to remap location tags appearing in the file (keys), to ones that specify where to put the storages (values).

User extensions can register their own location tags and tagging and deserialization methods using torch.serialization.register_package().

Parameters

f – a file-like object (has to implement read(), :meth`readline`, :meth`tell`, and :meth`seek`), or a string containing a file name
map_location – a function, torch.device, string or a dict specifying how to remap storage locations
pickle_module – module used for unpickling metadata and objects (has to match the pickle_module used to serialize file)
pickle_load_args – (Python 3 only) optional keyword arguments passed over to pickle_module.load() and pickle_module.Unpickler(), e.g., errors=....

Warning

torch.load() uses pickle module implicitly, which is known to be insecure. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling. Never load data that could have come from an untrusted source, or that could have been tampered with. Only load data you trust.

Note

When you call torch.load() on a file which contains GPU tensors, those tensors will be loaded to GPU by default. You can call torch.load(.., map_location='cpu') and then load_state_dict() to avoid GPU RAM surge when loading a model checkpoint.

Note

By default, we decode byte strings as utf-8. This is to avoid a common error case UnicodeDecodeError: 'ascii' codec can't decode byte 0x... when loading files saved by Python 2 in Python 3. If this default is incorrect, you may use an extra encoding keyword argument to specify how these objects should be loaded, e.g., encoding='latin1' decodes them to strings using latin1 encoding, and encoding='bytes' keeps them as byte arrays which can be decoded later with byte_array.decode(...).

Example

>>> torch.load('tensors.pt')
# Load all tensors onto the CPU
>>> torch.load('tensors.pt', map_location=torch.device('cpu'))
# Load all tensors onto the CPU, using a function
>>> torch.load('tensors.pt', map_location=lambda storage, loc: storage)
# Load all tensors onto GPU 1
>>> torch.load('tensors.pt', map_location=lambda storage, loc: storage.cuda(1))
# Map tensors from GPU 1 to GPU 0
>>> torch.load('tensors.pt', map_location={'cuda:1':'cuda:0'})
# Load tensor from io.BytesIO object
>>> with open('tensor.pt', 'rb') as f:
        buffer = io.BytesIO(f.read())
>>> torch.load(buffer)
# Load a module with 'ascii' encoding for unpickling
>>> torch.load('module.pt', encoding='ascii')

Parallelism¶

torch.get_num_threads() → int¶: Returns the number of threads used for parallelizing CPU operations

torch.set_num_threads(int)¶: Sets the number of threads used for intraop parallelism on CPU. WARNING: To ensure that the correct number of threads is used, set_num_threads must be called before running eager, JIT or autograd code.

torch.get_num_interop_threads() → int¶: Returns the number of threads used for inter-op parallelism on CPU (e.g. in JIT interpreter)

torch.set_num_interop_threads(int)¶: Sets the number of threads used for interop parallelism (e.g. in JIT interpreter) on CPU. WARNING: Can only be called once and before any inter-op parallel work is started (e.g. JIT execution).

Locally disabling gradient computation¶

The context managers torch.no_grad(), torch.enable_grad(), and torch.set_grad_enabled() are helpful for locally disabling and enabling gradient computation. See Locally disabling gradient computation for more details on their usage. These context managers are thread local, so they won’t work if you send work to another thread using the threading module, etc.

Examples:

>>> x = torch.zeros(1, requires_grad=True)
>>> with torch.no_grad():
...     y = x * 2
>>> y.requires_grad
False

>>> is_train = False
>>> with torch.set_grad_enabled(is_train):
...     y = x * 2
>>> y.requires_grad
False

>>> torch.set_grad_enabled(True)  # this can also be used as a function
>>> y = x * 2
>>> y.requires_grad
True

>>> torch.set_grad_enabled(False)
>>> y = x * 2
>>> y.requires_grad
False

torch.no_grad()[source]¶

Context-manager that disabled gradient calculation.

Disabling gradient calculation is useful for inference, when you are sure that you will not call Tensor.backward(). It will reduce memory consumption for computations that would otherwise have requires_grad=True.

In this mode, the result of every computation will have requires_grad=False, even when the inputs have requires_grad=True.

This mode has no effect when using enable_grad context manager .

This context manager is thread local; it will not affect computation in other threads.

Also functions as a decorator. (Make sure to instantiate with parenthesis.)

Example:

>>> x = torch.tensor([1], requires_grad=True)
>>> with torch.no_grad():
...   y = x * 2
>>> y.requires_grad
False
>>> @torch.no_grad()
... def doubler(x):
...     return x * 2
>>> z = doubler(x)
>>> z.requires_grad
False

torch.enable_grad()[source]¶

Context-manager that enables gradient calculation.

Enables gradient calculation, if it has been disabled via no_grad or set_grad_enabled.

This context manager is thread local; it will not affect computation in other threads.

Also functions as a decorator. (Make sure to instantiate with parenthesis.)

Example:

>>> x = torch.tensor([1], requires_grad=True)
>>> with torch.no_grad():
...   with torch.enable_grad():
...     y = x * 2
>>> y.requires_grad
True
>>> y.backward()
>>> x.grad
>>> @torch.enable_grad()
... def doubler(x):
...     return x * 2
>>> with torch.no_grad():
...     z = doubler(x)
>>> z.requires_grad
True

torch.set_grad_enabled(mode)[source]¶

Context-manager that sets gradient calculation to on or off.

set_grad_enabled will enable or disable grads based on its argument mode. It can be used as a context-manager or as a function.

When using enable_grad context manager, set_grad_enabled(False) has no effect.

This context manager is thread local; it will not affect computation in other threads.

Parameters: mode (bool) – Flag whether to enable grad (True), or disable (False). This can be used to conditionally enable gradients.

Example:

>>> x = torch.tensor([1], requires_grad=True)
>>> is_train = False
>>> with torch.set_grad_enabled(is_train):
...   y = x * 2
>>> y.requires_grad
False
>>> torch.set_grad_enabled(True)
>>> y = x * 2
>>> y.requires_grad
True
>>> torch.set_grad_enabled(False)
>>> y = x * 2
>>> y.requires_grad
False

Math operations¶

Pointwise Ops¶

torch.abs(input, out=None) → Tensor¶

Computes the element-wise absolute value of the given input tensor.

\text{out}_{i} = |\text{input}_{i}|

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.abs(torch.tensor([-1, -2, 3]))
tensor([ 1,  2,  3])

torch.acos(input, out=None) → Tensor¶

Returns a new tensor with the arccosine of the elements of input.

\text{out}_{i} = \cos^{-1}(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.3348, -0.5889,  0.2005, -0.1584])
>>> torch.acos(a)
tensor([ 1.2294,  2.2004,  1.3690,  1.7298])

torch.add()¶

torch.add(input, other, out=None)

Adds the scalar other to each element of the input input and returns a new resulting tensor.

\text{out} = \text{input} + \text{other}

If input is of type FloatTensor or DoubleTensor, other must be a real number, otherwise it should be an integer.

Parameters

input (Tensor) – the input tensor.
value (Number) – the number to be added to each element of input

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.0202,  1.0985,  1.3506, -0.6056])
>>> torch.add(a, 20)
tensor([ 20.0202,  21.0985,  21.3506,  19.3944])

torch.add(input, other, *, alpha=1, out=None)

Each element of the tensor other is multiplied by the scalar alpha and added to each element of the tensor input. The resulting tensor is returned.

The shapes of input and other must be broadcastable.

\text{out} = \text{input} + \text{alpha} \times \text{other}

If other is of type FloatTensor or DoubleTensor, alpha must be a real number, otherwise it should be an integer.

Parameters

input (Tensor) – the first input tensor
other (Tensor) – the second input tensor
alpha (Number) – the scalar multiplier for other

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-0.9732, -0.3497,  0.6245,  0.4022])
>>> b = torch.randn(4, 1)
>>> b
tensor([[ 0.3743],
        [-1.7724],
        [-0.5811],
        [-0.8017]])
>>> torch.add(a, b, alpha=10)
tensor([[  2.7695,   3.3930,   4.3672,   4.1450],
        [-18.6971, -18.0736, -17.0994, -17.3216],
        [ -6.7845,  -6.1610,  -5.1868,  -5.4090],
        [ -8.9902,  -8.3667,  -7.3925,  -7.6147]])

torch.addcdiv(input, tensor1, tensor2, *, value=1, out=None) → Tensor¶

Performs the element-wise division of tensor1 by tensor2, multiply the result by the scalar value and add it to input.

Warning

Integer division with addcdiv is deprecated, and in a future release addcdiv will perform a true division of tensor1 and tensor2. The current addcdiv behavior can be replicated using floor_divide() for integral inputs (input + value * tensor1 // tensor2) and div() for float inputs (input + value * tensor1 / tensor2). The new addcdiv behavior can be implemented with true_divide() (input + value * torch.true_divide(tensor1, tensor2).

\text{out}_i = \text{input}_i + \text{value} \times \frac{\text{tensor1}_i}{\text{tensor2}_i}

The shapes of input, tensor1, and tensor2 must be broadcastable.

For inputs of type FloatTensor or DoubleTensor, value must be a real number, otherwise an integer.

Parameters

input (Tensor) – the tensor to be added
tensor1 (Tensor) – the numerator tensor
tensor2 (Tensor) – the denominator tensor
value (Number, optional) – multiplier for $\text{tensor1} / \text{tensor2}$
out (Tensor, optional) – the output tensor.

Example:

>>> t = torch.randn(1, 3)
>>> t1 = torch.randn(3, 1)
>>> t2 = torch.randn(1, 3)
>>> torch.addcdiv(t, t1, t2, value=0.1)
tensor([[-0.2312, -3.6496,  0.1312],
        [-1.0428,  3.4292, -0.1030],
        [-0.5369, -0.9829,  0.0430]])

torch.addcmul(input, tensor1, tensor2, *, value=1, out=None) → Tensor¶

Performs the element-wise multiplication of tensor1 by tensor2, multiply the result by the scalar value and add it to input.

\text{out}_i = \text{input}_i + \text{value} \times \text{tensor1}_i \times \text{tensor2}_i

The shapes of tensor, tensor1, and tensor2 must be broadcastable.

For inputs of type FloatTensor or DoubleTensor, value must be a real number, otherwise an integer.

Parameters

input (Tensor) – the tensor to be added
tensor1 (Tensor) – the tensor to be multiplied
tensor2 (Tensor) – the tensor to be multiplied
value (Number, optional) – multiplier for $tensor1 .* tensor2$
out (Tensor, optional) – the output tensor.

Example:

>>> t = torch.randn(1, 3)
>>> t1 = torch.randn(3, 1)
>>> t2 = torch.randn(1, 3)
>>> torch.addcmul(t, t1, t2, value=0.1)
tensor([[-0.8635, -0.6391,  1.6174],
        [-0.7617, -0.5879,  1.7388],
        [-0.8353, -0.6249,  1.6511]])

torch.angle(input, out=None) → Tensor¶

Computes the element-wise angle (in radians) of the given input tensor.

\text{out}_{i} = angle(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.angle(torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j]))*180/3.14159
tensor([ 135.,  135,  -45])

torch.asin(input, out=None) → Tensor¶

Returns a new tensor with the arcsine of the elements of input.

\text{out}_{i} = \sin^{-1}(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-0.5962,  1.4985, -0.4396,  1.4525])
>>> torch.asin(a)
tensor([-0.6387,     nan, -0.4552,     nan])

torch.atan(input, out=None) → Tensor¶

Returns a new tensor with the arctangent of the elements of input.

\text{out}_{i} = \tan^{-1}(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.2341,  0.2539, -0.6256, -0.6448])
>>> torch.atan(a)
tensor([ 0.2299,  0.2487, -0.5591, -0.5727])

torch.atan2(input, other, out=None) → Tensor¶

Element-wise arctangent of $\text{input}_{i} / \text{other}_{i}$ with consideration of the quadrant. Returns a new tensor with the signed angles in radians between vector $(\text{other}_{i}, \text{input}_{i})$ and vector $(1, 0)$ . (Note that $\text{other}_{i}$ , the second parameter, is the x-coordinate, while $\text{input}_{i}$ , the first parameter, is the y-coordinate.)

The shapes of input and other must be broadcastable.

Parameters

input (Tensor) – the first input tensor
other (Tensor) – the second input tensor
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.9041,  0.0196, -0.3108, -2.4423])
>>> torch.atan2(a, torch.randn(4))
tensor([ 0.9833,  0.0811, -1.9743, -1.4151])

torch.bitwise_not(input, out=None) → Tensor¶

Computes the bitwise NOT of the given input tensor. The input tensor must be of integral or Boolean types. For bool tensors, it computes the logical NOT.

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example

>>> torch.bitwise_not(torch.tensor([-1, -2, 3], dtype=torch.int8))
tensor([ 0,  1, -4], dtype=torch.int8)

torch.bitwise_and(input, other, out=None) → Tensor¶

Computes the bitwise AND of input and other. The input tensor must be of integral or Boolean types. For bool tensors, it computes the logical AND.

Parameters

input – the first input tensor
other – the second input tensor
out (Tensor, optional) – the output tensor.

Example

>>> torch.bitwise_and(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
tensor([1, 0,  3], dtype=torch.int8)
>>> torch.bitwise_and(torch.tensor([True, True, False]), torch.tensor([False, True, False]))
tensor([ False, True, False])

torch.bitwise_or(input, other, out=None) → Tensor¶

Computes the bitwise OR of input and other. The input tensor must be of integral or Boolean types. For bool tensors, it computes the logical OR.

Parameters

input – the first input tensor
other – the second input tensor
out (Tensor, optional) – the output tensor.

Example

>>> torch.bitwise_or(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
tensor([-1, -2,  3], dtype=torch.int8)
>>> torch.bitwise_or(torch.tensor([True, True, False]), torch.tensor([False, True, False]))
tensor([ True, True, False])

torch.bitwise_xor(input, other, out=None) → Tensor¶

Computes the bitwise XOR of input and other. The input tensor must be of integral or Boolean types. For bool tensors, it computes the logical XOR.

Parameters

input – the first input tensor
other – the second input tensor
out (Tensor, optional) – the output tensor.

Example

>>> torch.bitwise_xor(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
tensor([-2, -2,  0], dtype=torch.int8)
>>> torch.bitwise_xor(torch.tensor([True, True, False]), torch.tensor([False, True, False]))
tensor([ True, False, False])

torch.ceil(input, out=None) → Tensor¶

Returns a new tensor with the ceil of the elements of input, the smallest integer greater than or equal to each element.

\text{out}_{i} = \left\lceil \text{input}_{i} \right\rceil = \left\lfloor \text{input}_{i} \right\rfloor + 1

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-0.6341, -1.4208, -1.0900,  0.5826])
>>> torch.ceil(a)
tensor([-0., -1., -1.,  1.])

torch.clamp(input, min, max, out=None) → Tensor¶

Clamp all elements in input into the range [ min, max ] and return a resulting tensor:

y_i = \begin{cases} \text{min} & \text{if } x_i < \text{min} \\ x_i & \text{if } \text{min} \leq x_i \leq \text{max} \\ \text{max} & \text{if } x_i > \text{max} \end{cases}

If input is of type FloatTensor or DoubleTensor, args min and max must be real numbers, otherwise they should be integers.

Parameters

input (Tensor) – the input tensor.
min (Number) – lower-bound of the range to be clamped to
max (Number) – upper-bound of the range to be clamped to
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-1.7120,  0.1734, -0.0478, -0.0922])
>>> torch.clamp(a, min=-0.5, max=0.5)
tensor([-0.5000,  0.1734, -0.0478, -0.0922])

torch.clamp(input, *, min, out=None) → Tensor

Clamps all elements in input to be larger or equal min.

If input is of type FloatTensor or DoubleTensor, value should be a real number, otherwise it should be an integer.

Parameters

input (Tensor) – the input tensor.
value (Number) – minimal value of each element in the output
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-0.0299, -2.3184,  2.1593, -0.8883])
>>> torch.clamp(a, min=0.5)
tensor([ 0.5000,  0.5000,  2.1593,  0.5000])

torch.clamp(input, *, max, out=None) → Tensor

Clamps all elements in input to be smaller or equal max.

If input is of type FloatTensor or DoubleTensor, value should be a real number, otherwise it should be an integer.

Parameters

input (Tensor) – the input tensor.
value (Number) – maximal value of each element in the output
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.7753, -0.4702, -0.4599,  1.1899])
>>> torch.clamp(a, max=0.5)
tensor([ 0.5000, -0.4702, -0.4599,  0.5000])

torch.conj(input, out=None) → Tensor¶

Computes the element-wise conjugate of the given input tensor.

\text{out}_{i} = conj(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.conj(torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j]))
tensor([-1 - 1j, -2 - 2j, 3 + 3j])

torch.cos(input, out=None) → Tensor¶

Returns a new tensor with the cosine of the elements of input.

\text{out}_{i} = \cos(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 1.4309,  1.2706, -0.8562,  0.9796])
>>> torch.cos(a)
tensor([ 0.1395,  0.2957,  0.6553,  0.5574])

torch.cosh(input, out=None) → Tensor¶

Returns a new tensor with the hyperbolic cosine of the elements of input.

\text{out}_{i} = \cosh(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.1632,  1.1835, -0.6979, -0.7325])
>>> torch.cosh(a)
tensor([ 1.0133,  1.7860,  1.2536,  1.2805])

torch.div()¶

torch.div(input, other, out=None) → Tensor

Divides each element of the input input with the scalar other and returns a new resulting tensor.

Warning

Integer division using div is deprecated, and in a future release div will perform true division like torch.true_divide(). Use torch.floor_divide() (// in Python) to perform integer division, instead.

\text{out}_i = \frac{\text{input}_i}{\text{other}}

If the torch.dtype of input and other differ, the torch.dtype of the result tensor is determined following rules described in the type promotion documentation. If out is specified, the result must be castable to the torch.dtype of the specified output tensor. Integral division by zero leads to undefined behavior.

Parameters

input (Tensor) – the input tensor.
other (Number) – the number to be divided to each element of input

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(5)
>>> a
tensor([ 0.3810,  1.2774, -0.2972, -0.3719,  0.4637])
>>> torch.div(a, 0.5)
tensor([ 0.7620,  2.5548, -0.5944, -0.7439,  0.9275])

torch.div(input, other, out=None) → Tensor

Each element of the tensor input is divided by each element of the tensor other. The resulting tensor is returned.

\text{out}_i = \frac{\text{input}_i}{\text{other}_i}

The shapes of input and other must be broadcastable. If the torch.dtype of input and other differ, the torch.dtype of the result tensor is determined following rules described in the type promotion documentation. If out is specified, the result must be castable to the torch.dtype of the specified output tensor. Integral division by zero leads to undefined behavior.

Parameters

input (Tensor) – the numerator tensor
other (Tensor) – the denominator tensor

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[-0.3711, -1.9353, -0.4605, -0.2917],
        [ 0.1815, -1.0111,  0.9805, -1.5923],
        [ 0.1062,  1.4581,  0.7759, -1.2344],
        [-0.1830, -0.0313,  1.1908, -1.4757]])
>>> b = torch.randn(4)
>>> b
tensor([ 0.8032,  0.2930, -0.8113, -0.2308])
>>> torch.div(a, b)
tensor([[-0.4620, -6.6051,  0.5676,  1.2637],
        [ 0.2260, -3.4507, -1.2086,  6.8988],
        [ 0.1322,  4.9764, -0.9564,  5.3480],
        [-0.2278, -0.1068, -1.4678,  6.3936]])

torch.digamma(input, out=None) → Tensor¶

Computes the logarithmic derivative of the gamma function on input.

\psi(x) = \frac{d}{dx} \ln\left(\Gamma\left(x\right)\right) = \frac{\Gamma'(x)}{\Gamma(x)}

Parameters: input (Tensor) – the tensor to compute the digamma function on

Example:

>>> a = torch.tensor([1, 0.5])
>>> torch.digamma(a)
tensor([-0.5772, -1.9635])

torch.erf(input, out=None) → Tensor¶

Computes the error function of each element. The error function is defined as follows:

\mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^2} dt

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.erf(torch.tensor([0, -1., 10.]))
tensor([ 0.0000, -0.8427,  1.0000])

torch.erfc(input, out=None) → Tensor¶

Computes the complementary error function of each element of input. The complementary error function is defined as follows:

\mathrm{erfc}(x) = 1 - \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^2} dt

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.erfc(torch.tensor([0, -1., 10.]))
tensor([ 1.0000, 1.8427,  0.0000])

torch.erfinv(input, out=None) → Tensor¶

Computes the inverse error function of each element of input. The inverse error function is defined in the range $(-1, 1)$ as:

\mathrm{erfinv}(\mathrm{erf}(x)) = x

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.erfinv(torch.tensor([0, 0.5, -1.]))
tensor([ 0.0000,  0.4769,    -inf])

torch.exp(input, out=None) → Tensor¶

Returns a new tensor with the exponential of the elements of the input tensor input.

y_{i} = e^{x_{i}}

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.exp(torch.tensor([0, math.log(2.)]))
tensor([ 1.,  2.])

torch.expm1(input, out=None) → Tensor¶

Returns a new tensor with the exponential of the elements minus 1 of input.

y_{i} = e^{x_{i}} - 1

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.expm1(torch.tensor([0, math.log(2.)]))
tensor([ 0.,  1.])

torch.floor(input, out=None) → Tensor¶

Returns a new tensor with the floor of the elements of input, the largest integer less than or equal to each element.

\text{out}_{i} = \left\lfloor \text{input}_{i} \right\rfloor

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-0.8166,  1.5308, -0.2530, -0.2091])
>>> torch.floor(a)
tensor([-1.,  1., -1., -1.])

torch.floor_divide(input, other, out=None) → Tensor¶

Return the division of the inputs rounded down to the nearest integer. See torch.div() for type promotion and broadcasting rules.

\text{{out}}_i = \left\lfloor \frac{{\text{{input}}_i}}{{\text{{other}}_i}} \right\rfloor

Parameters

input (Tensor) – the numerator tensor
other (Tensor or Scalar) – the denominator

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.tensor([4.0, 3.0])
>>> b = torch.tensor([2.0, 2.0])
>>> torch.floor_divide(a, b)
tensor([2.0, 1.0])
>>> torch.floor_divide(a, 1.4)
tensor([2.0, 2.0])

torch.fmod(input, other, out=None) → Tensor¶

Computes the element-wise remainder of division.

The dividend and divisor may contain both for integer and floating point numbers. The remainder has the same sign as the dividend input.

When other is a tensor, the shapes of input and other must be broadcastable.

Parameters

input (Tensor) – the dividend
other (Tensor or float) – the divisor, which may be either a number or a tensor of the same shape as the dividend
out (Tensor, optional) – the output tensor.

Example:

>>> torch.fmod(torch.tensor([-3., -2, -1, 1, 2, 3]), 2)
tensor([-1., -0., -1.,  1.,  0.,  1.])
>>> torch.fmod(torch.tensor([1., 2, 3, 4, 5]), 1.5)
tensor([ 1.0000,  0.5000,  0.0000,  1.0000,  0.5000])

torch.frac(input, out=None) → Tensor¶

Computes the fractional portion of each element in input.

\text{out}_{i} = \text{input}_{i} - \left\lfloor |\text{input}_{i}| \right\rfloor * \operatorname{sgn}(\text{input}_{i})

Example:

>>> torch.frac(torch.tensor([1, 2.5, -3.2]))
tensor([ 0.0000,  0.5000, -0.2000])

torch.imag(input, out=None) → Tensor¶

Returns the imaginary part of the input tensor.

Warning

Not yet implemented.

\text{out}_{i} = imag(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

torch.lerp(input, end, weight, out=None)¶

Does a linear interpolation of two tensors start (given by input) and end based on a scalar or tensor weight and returns the resulting out tensor.

\text{out}_i = \text{start}_i + \text{weight}_i \times (\text{end}_i - \text{start}_i)

The shapes of start and end must be broadcastable. If weight is a tensor, then the shapes of weight, start, and end must be broadcastable.

Parameters

input (Tensor) – the tensor with the starting points
end (Tensor) – the tensor with the ending points
weight (float or tensor) – the weight for the interpolation formula
out (Tensor, optional) – the output tensor.

Example:

>>> start = torch.arange(1., 5.)
>>> end = torch.empty(4).fill_(10)
>>> start
tensor([ 1.,  2.,  3.,  4.])
>>> end
tensor([ 10.,  10.,  10.,  10.])
>>> torch.lerp(start, end, 0.5)
tensor([ 5.5000,  6.0000,  6.5000,  7.0000])
>>> torch.lerp(start, end, torch.full_like(start, 0.5))
tensor([ 5.5000,  6.0000,  6.5000,  7.0000])

torch.lgamma(input, out=None) → Tensor¶

Computes the logarithm of the gamma function on input.

\text{out}_{i} = \log \Gamma(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.arange(0.5, 2, 0.5)
>>> torch.lgamma(a)
tensor([ 0.5724,  0.0000, -0.1208])

torch.log(input, out=None) → Tensor¶

Returns a new tensor with the natural logarithm of the elements of input.

y_{i} = \log_{e} (x_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(5)
>>> a
tensor([-0.7168, -0.5471, -0.8933, -1.4428, -0.1190])
>>> torch.log(a)
tensor([ nan,  nan,  nan,  nan,  nan])

torch.log10(input, out=None) → Tensor¶

Returns a new tensor with the logarithm to the base 10 of the elements of input.

y_{i} = \log_{10} (x_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.rand(5)
>>> a
tensor([ 0.5224,  0.9354,  0.7257,  0.1301,  0.2251])


>>> torch.log10(a)
tensor([-0.2820, -0.0290, -0.1392, -0.8857, -0.6476])

torch.log1p(input, out=None) → Tensor¶

Returns a new tensor with the natural logarithm of (1 + input).

y_i = \log_{e} (x_i + 1)

Note

This function is more accurate than torch.log() for small values of input

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(5)
>>> a
tensor([-1.0090, -0.9923,  1.0249, -0.5372,  0.2492])
>>> torch.log1p(a)
tensor([    nan, -4.8653,  0.7055, -0.7705,  0.2225])

torch.log2(input, out=None) → Tensor¶

Returns a new tensor with the logarithm to the base 2 of the elements of input.

y_{i} = \log_{2} (x_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.rand(5)
>>> a
tensor([ 0.8419,  0.8003,  0.9971,  0.5287,  0.0490])


>>> torch.log2(a)
tensor([-0.2483, -0.3213, -0.0042, -0.9196, -4.3504])

torch.logical_and(input, other, out=None) → Tensor¶

Computes the element-wise logical AND of the given input tensors. Zeros are treated as False and nonzeros are treated as True.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the tensor to compute AND with
out (Tensor, optional) – the output tensor.

Example:

>>> torch.logical_and(torch.tensor([True, False, True]), torch.tensor([True, False, False]))
tensor([ True, False, False])
>>> a = torch.tensor([0, 1, 10, 0], dtype=torch.int8)
>>> b = torch.tensor([4, 0, 1, 0], dtype=torch.int8)
>>> torch.logical_and(a, b)
tensor([False, False,  True, False])
>>> torch.logical_and(a.double(), b.double())
tensor([False, False,  True, False])
>>> torch.logical_and(a.double(), b)
tensor([False, False,  True, False])
>>> torch.logical_and(a, b, out=torch.empty(4, dtype=torch.bool))
tensor([False, False,  True, False])

torch.logical_not(input, out=None) → Tensor¶

Computes the element-wise logical NOT of the given input tensor. If not specified, the output tensor will have the bool dtype. If the input tensor is not a bool tensor, zeros are treated as False and non-zeros are treated as True.

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> torch.logical_not(torch.tensor([True, False]))
tensor([False,  True])
>>> torch.logical_not(torch.tensor([0, 1, -10], dtype=torch.int8))
tensor([ True, False, False])
>>> torch.logical_not(torch.tensor([0., 1.5, -10.], dtype=torch.double))
tensor([ True, False, False])
>>> torch.logical_not(torch.tensor([0., 1., -10.], dtype=torch.double), out=torch.empty(3, dtype=torch.int16))
tensor([1, 0, 0], dtype=torch.int16)

torch.logical_or(input, other, out=None) → Tensor¶

Computes the element-wise logical OR of the given input tensors. Zeros are treated as False and nonzeros are treated as True.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the tensor to compute OR with
out (Tensor, optional) – the output tensor.

Example:

>>> torch.logical_or(torch.tensor([True, False, True]), torch.tensor([True, False, False]))
tensor([ True, False,  True])
>>> a = torch.tensor([0, 1, 10, 0], dtype=torch.int8)
>>> b = torch.tensor([4, 0, 1, 0], dtype=torch.int8)
>>> torch.logical_or(a, b)
tensor([ True,  True,  True, False])
>>> torch.logical_or(a.double(), b.double())
tensor([ True,  True,  True, False])
>>> torch.logical_or(a.double(), b)
tensor([ True,  True,  True, False])
>>> torch.logical_or(a, b, out=torch.empty(4, dtype=torch.bool))
tensor([ True,  True,  True, False])

torch.logical_xor(input, other, out=None) → Tensor¶

Computes the element-wise logical XOR of the given input tensors. Zeros are treated as False and nonzeros are treated as True.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the tensor to compute XOR with
out (Tensor, optional) – the output tensor.

Example:

>>> torch.logical_xor(torch.tensor([True, False, True]), torch.tensor([True, False, False]))
tensor([False, False,  True])
>>> a = torch.tensor([0, 1, 10, 0], dtype=torch.int8)
>>> b = torch.tensor([4, 0, 1, 0], dtype=torch.int8)
>>> torch.logical_xor(a, b)
tensor([ True,  True, False, False])
>>> torch.logical_xor(a.double(), b.double())
tensor([ True,  True, False, False])
>>> torch.logical_xor(a.double(), b)
tensor([ True,  True, False, False])
>>> torch.logical_xor(a, b, out=torch.empty(4, dtype=torch.bool))
tensor([ True,  True, False, False])

torch.mul()¶

torch.mul(input, other, out=None)

Multiplies each element of the input input with the scalar other and returns a new resulting tensor.

\text{out}_i = \text{other} \times \text{input}_i

If input is of type FloatTensor or DoubleTensor, other should be a real number, otherwise it should be an integer

Parameters

{input} –
value (Number) – the number to be multiplied to each element of input
{out} –

Example:

>>> a = torch.randn(3)
>>> a
tensor([ 0.2015, -0.4255,  2.6087])
>>> torch.mul(a, 100)
tensor([  20.1494,  -42.5491,  260.8663])

torch.mul(input, other, out=None)

Each element of the tensor input is multiplied by the corresponding element of the Tensor other. The resulting tensor is returned.

The shapes of input and other must be broadcastable.

\text{out}_i = \text{input}_i \times \text{other}_i

Parameters

input (Tensor) – the first multiplicand tensor
other (Tensor) – the second multiplicand tensor
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4, 1)
>>> a
tensor([[ 1.1207],
        [-0.3137],
        [ 0.0700],
        [ 0.8378]])
>>> b = torch.randn(1, 4)
>>> b
tensor([[ 0.5146,  0.1216, -0.5244,  2.2382]])
>>> torch.mul(a, b)
tensor([[ 0.5767,  0.1363, -0.5877,  2.5083],
        [-0.1614, -0.0382,  0.1645, -0.7021],
        [ 0.0360,  0.0085, -0.0367,  0.1567],
        [ 0.4312,  0.1019, -0.4394,  1.8753]])

torch.mvlgamma(input, p) → Tensor¶

Computes the multivariate log-gamma function) with dimension $p$ element-wise, given by

\log(\Gamma_{p}(a)) = C + \displaystyle \sum_{i=1}^{p} \log\left(\Gamma\left(a - \frac{i - 1}{2}\right)\right)

where $C = \log(\pi) \times \frac{p (p - 1)}{4}$ and $\Gamma(\cdot)$ is the Gamma function.

All elements must be greater than $\frac{p - 1}{2}$ , otherwise an error would be thrown.

Parameters

input (Tensor) – the tensor to compute the multivariate log-gamma function
p (int) – the number of dimensions

Example:

>>> a = torch.empty(2, 3).uniform_(1, 2)
>>> a
tensor([[1.6835, 1.8474, 1.1929],
        [1.0475, 1.7162, 1.4180]])
>>> torch.mvlgamma(a, 2)
tensor([[0.3928, 0.4007, 0.7586],
        [1.0311, 0.3901, 0.5049]])

torch.neg(input, out=None) → Tensor¶

Returns a new tensor with the negative of the elements of input.

\text{out} = -1 \times \text{input}

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(5)
>>> a
tensor([ 0.0090, -0.2262, -0.0682, -0.2866,  0.3940])
>>> torch.neg(a)
tensor([-0.0090,  0.2262,  0.0682,  0.2866, -0.3940])

torch.polygamma(n, input, out=None) → Tensor¶

Computes the $n^{th}$ derivative of the digamma function on input. $n \geq 0$ is called the order of the polygamma function.

\psi^{(n)}(x) = \frac{d^{(n)}}{dx^{(n)}} \psi(x)

Note

This function is not implemented for $n \geq 2$ .

Parameters

n (int) – the order of the polygamma function
input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example::

>>> a = torch.tensor([1, 0.5])
>>> torch.polygamma(1, a)
tensor([1.64493, 4.9348])

torch.pow()¶

torch.pow(input, exponent, out=None) → Tensor

Takes the power of each element in input with exponent and returns a tensor with the result.

exponent can be either a single float number or a Tensor with the same number of elements as input.

When exponent is a scalar value, the operation applied is:

\text{out}_i = x_i ^ \text{exponent}

When exponent is a tensor, the operation applied is:

\text{out}_i = x_i ^ {\text{exponent}_i}

When exponent is a tensor, the shapes of input and exponent must be broadcastable.

Parameters

input (Tensor) – the input tensor.
exponent (float or tensor) – the exponent value
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.4331,  1.2475,  0.6834, -0.2791])
>>> torch.pow(a, 2)
tensor([ 0.1875,  1.5561,  0.4670,  0.0779])
>>> exp = torch.arange(1., 5.)

>>> a = torch.arange(1., 5.)
>>> a
tensor([ 1.,  2.,  3.,  4.])
>>> exp
tensor([ 1.,  2.,  3.,  4.])
>>> torch.pow(a, exp)
tensor([   1.,    4.,   27.,  256.])

torch.pow(self, exponent, out=None) → Tensor

self is a scalar float value, and exponent is a tensor. The returned tensor out is of the same shape as exponent

The operation applied is:

\text{out}_i = \text{self} ^ {\text{exponent}_i}

Parameters

self (float) – the scalar base value for the power operation
exponent (Tensor) – the exponent tensor
out (Tensor, optional) – the output tensor.

Example:

>>> exp = torch.arange(1., 5.)
>>> base = 2
>>> torch.pow(base, exp)
tensor([  2.,   4.,   8.,  16.])

torch.real(input, out=None) → Tensor¶

Returns the real part of the input tensor. If input is a real (non-complex) tensor, this function just returns it.

Warning

Not yet implemented for complex tensors.

\text{out}_{i} = real(\text{input}_{i})

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

torch.reciprocal(input, out=None) → Tensor¶

Returns a new tensor with the reciprocal of the elements of input

\text{out}_{i} = \frac{1}{\text{input}_{i}}

Parameters

input (Tensor) – the input tensor.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([-0.4595, -2.1219, -1.4314,  0.7298])
>>> torch.reciprocal(a)
tensor([-2.1763, -0.4713, -0.6986,  1.3702])

torch.remainder(input, other, out=None) → Tensor¶

Computes the element-wise remainder of division.

The divisor and dividend may contain both for integer and floating point numbers. The remainder has the same sign as the divisor.

When other is a tensor, the shapes of input and other must be broadcastable.

Parameters

input (Tensor) – the dividend
other (Tensor or float) – the divisor that may be either a number or a Tensor of the same shape as the dividend
out (Tensor, optional) – the output tensor.

Example:

>>> torch.remainder(torch.tensor([-3., -2, -1, 1, 2, 3]), 2)
tensor([ 1.,  0.,  1.,  1.,  0.,  1.])
>>> torch.remainder(torch.tensor([1., 2, 3, 4, 5]), 1.5)
tensor([ 1.0000,  0.5000,  0.0000,  1.0000,  0.5000])

Reduction Ops¶

torch.argmax()¶

torch.argmax(input) → LongTensor

Returns the indices of the maximum value of all elements in the input tensor.

This is the second value returned by torch.max(). See its documentation for the exact semantics of this method.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 1.3398,  0.2663, -0.2686,  0.2450],
        [-0.7401, -0.8805, -0.3402, -1.1936],
        [ 0.4907, -1.3948, -1.0691, -0.3132],
        [-1.6092,  0.5419, -0.2993,  0.3195]])
>>> torch.argmax(a)
tensor(0)

torch.argmax(input, dim, keepdim=False) → LongTensor

Returns the indices of the maximum values of a tensor across a dimension.

This is the second value returned by torch.max(). See its documentation for the exact semantics of this method.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce. If None, the argmax of the flattened input is returned.
keepdim (bool) – whether the output tensor has dim retained or not. Ignored if dim=None.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 1.3398,  0.2663, -0.2686,  0.2450],
        [-0.7401, -0.8805, -0.3402, -1.1936],
        [ 0.4907, -1.3948, -1.0691, -0.3132],
        [-1.6092,  0.5419, -0.2993,  0.3195]])
>>> torch.argmax(a, dim=1)
tensor([ 0,  2,  0,  1])

torch.argmin()¶

torch.argmin(input) → LongTensor

Returns the indices of the minimum value of all elements in the input tensor.

This is the second value returned by torch.min(). See its documentation for the exact semantics of this method.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.1139,  0.2254, -0.1381,  0.3687],
        [ 1.0100, -1.1975, -0.0102, -0.4732],
        [-0.9240,  0.1207, -0.7506, -1.0213],
        [ 1.7809, -1.2960,  0.9384,  0.1438]])
>>> torch.argmin(a)
tensor(13)

torch.argmin(input, dim, keepdim=False, out=None) → LongTensor

Returns the indices of the minimum values of a tensor across a dimension.

This is the second value returned by torch.min(). See its documentation for the exact semantics of this method.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce. If None, the argmin of the flattened input is returned.
keepdim (bool) – whether the output tensor has dim retained or not. Ignored if dim=None.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.1139,  0.2254, -0.1381,  0.3687],
        [ 1.0100, -1.1975, -0.0102, -0.4732],
        [-0.9240,  0.1207, -0.7506, -1.0213],
        [ 1.7809, -1.2960,  0.9384,  0.1438]])
>>> torch.argmin(a, dim=1)
tensor([ 2,  1,  3,  1])

torch.dist(input, other, p=2) → Tensor¶

Returns the p-norm of (input - other)

The shapes of input and other must be broadcastable.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the Right-hand-side input tensor
p (float, optional) – the norm to be computed

Example:

>>> x = torch.randn(4)
>>> x
tensor([-1.5393, -0.8675,  0.5916,  1.6321])
>>> y = torch.randn(4)
>>> y
tensor([ 0.0967, -1.0511,  0.6295,  0.8360])
>>> torch.dist(x, y, 3.5)
tensor(1.6727)
>>> torch.dist(x, y, 3)
tensor(1.6973)
>>> torch.dist(x, y, 0)
tensor(inf)
>>> torch.dist(x, y, 1)
tensor(2.6537)

torch.logsumexp(input, dim, keepdim=False, out=None)¶

Returns the log of summed exponentials of each row of the input tensor in the given dimension dim. The computation is numerically stabilized.

For summation index $j$ given by dim and other indices $i$ , the result is

$\text{logsumexp}(x)_{i} = \log \sum_j \exp(x_{ij})$

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
out (Tensor, optional) – the output tensor.

Example::

>>> a = torch.randn(3, 3)
>>> torch.logsumexp(a, 1)
tensor([ 0.8442,  1.4322,  0.8711])

torch.mean()¶

torch.mean(input) → Tensor

Returns the mean value of all elements in the input tensor.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[ 0.2294, -0.5481,  1.3288]])
>>> torch.mean(a)
tensor(0.3367)

torch.mean(input, dim, keepdim=False, out=None) → Tensor

Returns the mean value of each row of the input tensor in the given dimension dim. If dim is a list of dimensions, reduce over all of them.

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[-0.3841,  0.6320,  0.4254, -0.7384],
        [-0.9644,  1.0131, -0.6549, -1.4279],
        [-0.2951, -1.3350, -0.7694,  0.5600],
        [ 1.0842, -0.9580,  0.3623,  0.2343]])
>>> torch.mean(a, 1)
tensor([-0.0163, -0.5085, -0.4599,  0.1807])
>>> torch.mean(a, 1, True)
tensor([[-0.0163],
        [-0.5085],
        [-0.4599],
        [ 0.1807]])

torch.median()¶

torch.median(input) → Tensor

Returns the median value of all elements in the input tensor.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[ 1.5219, -1.5212,  0.2202]])
>>> torch.median(a)
tensor(0.2202)

torch.median(input, dim=-1, keepdim=False, out=None) -> (Tensor, LongTensor)

Returns a namedtuple (values, indices) where values is the median value of each row of the input tensor in the given dimension dim. And indices is the index location of each median value found.

By default, dim is the last dimension of the input tensor.

If keepdim is True, the output tensors are of the same size as input except in the dimension dim where they are of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the outputs tensor having 1 fewer dimension than input.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
out (tuple, optional) – the result tuple of two output tensors (max, max_indices)

Example:

>>> a = torch.randn(4, 5)
>>> a
tensor([[ 0.2505, -0.3982, -0.9948,  0.3518, -1.3131],
        [ 0.3180, -0.6993,  1.0436,  0.0438,  0.2270],
        [-0.2751,  0.7303,  0.2192,  0.3321,  0.2488],
        [ 1.0778, -1.9510,  0.7048,  0.4742, -0.7125]])
>>> torch.median(a, 1)
torch.return_types.median(values=tensor([-0.3982,  0.2270,  0.2488,  0.4742]), indices=tensor([1, 4, 4, 3]))

torch.mode(input, dim=-1, keepdim=False, out=None) -> (Tensor, LongTensor)¶

Returns a namedtuple (values, indices) where values is the mode value of each row of the input tensor in the given dimension dim, i.e. a value which appears most often in that row, and indices is the index location of each mode value found.

By default, dim is the last dimension of the input tensor.

If keepdim is True, the output tensors are of the same size as input except in the dimension dim where they are of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensors having 1 fewer dimension than input.

Note

This function is not defined for torch.cuda.Tensor yet.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
out (tuple, optional) – the result tuple of two output tensors (values, indices)

Example:

>>> a = torch.randint(10, (5,))
>>> a
tensor([6, 5, 1, 0, 2])
>>> b = a + (torch.randn(50, 1) * 5).long()
>>> torch.mode(b, 0)
torch.return_types.mode(values=tensor([6, 5, 1, 0, 2]), indices=tensor([2, 2, 2, 2, 2]))

torch.norm(input, p='fro', dim=None, keepdim=False, out=None, dtype=None)[source]¶

Returns the matrix norm or vector norm of a given tensor.

Parameters

input (Tensor) – the input tensor
p (int, float, inf, -inf, 'fro', 'nuc', optional) –
the order of norm. Default: 'fro' The following norms can be calculated:

ord

matrix norm

vector norm

None

Frobenius norm

2-norm

’fro’

Frobenius norm

–

‘nuc’

nuclear norm

–

Other

as vec norm when dim is None

sum(abs(x)**ord)**(1./ord)
dim (int, 2-tuple of python:ints, 2-list of python:ints, optional) – If it is an int, vector norm will be calculated, if it is 2-tuple of ints, matrix norm will be calculated. If the value is None, matrix norm will be calculated when the input tensor only has two dimensions, vector norm will be calculated when the input tensor only has one dimension. If the input tensor has more than two dimensions, the vector norm will be applied to last dimension.
keepdim (bool, optional) – whether the output tensors have dim retained or not. Ignored if dim = None and out = None. Default: False
out (Tensor, optional) – the output tensor. Ignored if dim = None and out = None.
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to :attr:’dtype’ while performing the operation. Default: None.

Example:

>>> import torch
>>> a = torch.arange(9, dtype= torch.float) - 4
>>> b = a.reshape((3, 3))
>>> torch.norm(a)
tensor(7.7460)
>>> torch.norm(b)
tensor(7.7460)
>>> torch.norm(a, float('inf'))
tensor(4.)
>>> torch.norm(b, float('inf'))
tensor(4.)
>>> c = torch.tensor([[ 1, 2, 3],[-1, 1, 4]] , dtype= torch.float)
>>> torch.norm(c, dim=0)
tensor([1.4142, 2.2361, 5.0000])
>>> torch.norm(c, dim=1)
tensor([3.7417, 4.2426])
>>> torch.norm(c, p=1, dim=1)
tensor([6., 6.])
>>> d = torch.arange(8, dtype= torch.float).reshape(2,2,2)
>>> torch.norm(d, dim=(1,2))
tensor([ 3.7417, 11.2250])
>>> torch.norm(d[0, :, :]), torch.norm(d[1, :, :])
(tensor(3.7417), tensor(11.2250))

torch.prod()¶

torch.prod(input, dtype=None) → Tensor

Returns the product of all elements in the input tensor.

Parameters

input (Tensor) – the input tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[-0.8020,  0.5428, -1.5854]])
>>> torch.prod(a)
tensor(0.6902)

torch.prod(input, dim, keepdim=False, dtype=None) → Tensor

Returns the product of each row of the input tensor in the given dimension dim.

If keepdim is True, the output tensor is of the same size as input except in the dimension dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 fewer dimension than input.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

Example:

>>> a = torch.randn(4, 2)
>>> a
tensor([[ 0.5261, -0.3837],
        [ 1.1857, -0.2498],
        [-1.1646,  0.0705],
        [ 1.1131, -1.0629]])
>>> torch.prod(a, 1)
tensor([-0.2018, -0.2962, -0.0821, -1.1831])

torch.std()¶

torch.std(input, unbiased=True) → Tensor

Returns the standard-deviation of all elements in the input tensor.

If unbiased is False, then the standard-deviation will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
unbiased (bool) – whether to use the unbiased estimation or not

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[-0.8166, -1.3802, -0.3560]])
>>> torch.std(a)
tensor(0.5130)

torch.std(input, dim, unbiased=True, keepdim=False, out=None) → Tensor

Returns the standard-deviation of each row of the input tensor in the dimension dim. If dim is a list of dimensions, reduce over all of them.

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

If unbiased is False, then the standard-deviation will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
unbiased (bool) – whether to use the unbiased estimation or not
keepdim (bool) – whether the output tensor has dim retained or not.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.2035,  1.2959,  1.8101, -0.4644],
        [ 1.5027, -0.3270,  0.5905,  0.6538],
        [-1.5745,  1.3330, -0.5596, -0.6548],
        [ 0.1264, -0.5080,  1.6420,  0.1992]])
>>> torch.std(a, dim=1)
tensor([ 1.0311,  0.7477,  1.2204,  0.9087])

torch.std_mean()¶

torch.std_mean(input, unbiased=True) -> (Tensor, Tensor)

Returns the standard-deviation and mean of all elements in the input tensor.

If unbiased is False, then the standard-deviation will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
unbiased (bool) – whether to use the unbiased estimation or not

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[0.3364, 0.3591, 0.9462]])
>>> torch.std_mean(a)
(tensor(0.3457), tensor(0.5472))

torch.std_mean(input, dim, unbiased=True, keepdim=False) -> (Tensor, Tensor)

Returns the standard-deviation and mean of each row of the input tensor in the dimension dim. If dim is a list of dimensions, reduce over all of them.

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

If unbiased is False, then the standard-deviation will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
unbiased (bool) – whether to use the unbiased estimation or not
keepdim (bool) – whether the output tensor has dim retained or not.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.5648, -0.5984, -1.2676, -1.4471],
        [ 0.9267,  1.0612,  1.1050, -0.6014],
        [ 0.0154,  1.9301,  0.0125, -1.0904],
        [-1.9711, -0.7748, -1.3840,  0.5067]])
>>> torch.std_mean(a, 1)
(tensor([0.9110, 0.8197, 1.2552, 1.0608]), tensor([-0.6871,  0.6229,  0.2169, -0.9058]))

torch.sum()¶

torch.sum(input, dtype=None) → Tensor

Returns the sum of all elements in the input tensor.

Parameters

input (Tensor) – the input tensor.
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[ 0.1133, -0.9567,  0.2958]])
>>> torch.sum(a)
tensor(-0.5475)

torch.sum(input, dim, keepdim=False, dtype=None) → Tensor

Returns the sum of each row of the input tensor in the given dimension dim. If dim is a list of dimensions, reduce over all of them.

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.0569, -0.2475,  0.0737, -0.3429],
        [-0.2993,  0.9138,  0.9337, -1.6864],
        [ 0.1132,  0.7892, -0.1003,  0.5688],
        [ 0.3637, -0.9906, -0.4752, -1.5197]])
>>> torch.sum(a, 1)
tensor([-0.4598, -0.1381,  1.3708, -2.6217])
>>> b = torch.arange(4 * 5 * 6).view(4, 5, 6)
>>> torch.sum(b, (2, 1))
tensor([  435.,  1335.,  2235.,  3135.])

torch.unique(input, sorted=True, return_inverse=False, return_counts=False, dim=None)[source]¶

Returns the unique elements of the input tensor.

Note

This function is different from torch.unique_consecutive() in the sense that this function also eliminates non-consecutive duplicate values.

Note

Currently in the CUDA implementation and the CPU implementation when dim is specified, torch.unique always sort the tensor at the beginning regardless of the sort argument. Sorting could be slow, so if your input tensor is already sorted, it is recommended to use torch.unique_consecutive() which avoids the sorting.

Parameters

input (Tensor) – the input tensor
sorted (bool) – Whether to sort the unique elements in ascending order before returning as output.
return_inverse (bool) – Whether to also return the indices for where elements in the original input ended up in the returned unique list.
return_counts (bool) – Whether to also return the counts for each unique element.
dim (int) – the dimension to apply unique. If None, the unique of the flattened input is returned. default: None

Returns

A tensor or a tuple of tensors containing

output (Tensor): the output list of unique scalar elements.

inverse_indices (Tensor): (optional) if return_inverse is True, there will be an additional returned tensor (same shape as input) representing the indices for where elements in the original input map to in the output; otherwise, this function will only return a single tensor.

counts (Tensor): (optional) if return_counts is True, there will be an additional returned tensor (same shape as output or output.size(dim), if dim was specified) representing the number of occurrences for each unique value or tensor.

Return type

(Tensor, Tensor (optional), Tensor (optional))

Example:

>>> output = torch.unique(torch.tensor([1, 3, 2, 3], dtype=torch.long))
>>> output
tensor([ 2,  3,  1])

>>> output, inverse_indices = torch.unique(
        torch.tensor([1, 3, 2, 3], dtype=torch.long), sorted=True, return_inverse=True)
>>> output
tensor([ 1,  2,  3])
>>> inverse_indices
tensor([ 0,  2,  1,  2])

>>> output, inverse_indices = torch.unique(
        torch.tensor([[1, 3], [2, 3]], dtype=torch.long), sorted=True, return_inverse=True)
>>> output
tensor([ 1,  2,  3])
>>> inverse_indices
tensor([[ 0,  2],
        [ 1,  2]])

torch.unique_consecutive(input, return_inverse=False, return_counts=False, dim=None)[source]¶

Eliminates all but the first element from every consecutive group of equivalent elements.

Note

This function is different from torch.unique() in the sense that this function only eliminates consecutive duplicate values. This semantics is similar to std::unique in C++.

Parameters

input (Tensor) – the input tensor
return_inverse (bool) – Whether to also return the indices for where elements in the original input ended up in the returned unique list.
return_counts (bool) – Whether to also return the counts for each unique element.
dim (int) – the dimension to apply unique. If None, the unique of the flattened input is returned. default: None

Returns

A tensor or a tuple of tensors containing

output (Tensor): the output list of unique scalar elements.

inverse_indices (Tensor): (optional) if return_inverse is True, there will be an additional returned tensor (same shape as input) representing the indices for where elements in the original input map to in the output; otherwise, this function will only return a single tensor.

counts (Tensor): (optional) if return_counts is True, there will be an additional returned tensor (same shape as output or output.size(dim), if dim was specified) representing the number of occurrences for each unique value or tensor.

Return type

(Tensor, Tensor (optional), Tensor (optional))

Example:

>>> x = torch.tensor([1, 1, 2, 2, 3, 1, 1, 2])
>>> output = torch.unique_consecutive(x)
>>> output
tensor([1, 2, 3, 1, 2])

>>> output, inverse_indices = torch.unique_consecutive(x, return_inverse=True)
>>> output
tensor([1, 2, 3, 1, 2])
>>> inverse_indices
tensor([0, 0, 1, 1, 2, 3, 3, 4])

>>> output, counts = torch.unique_consecutive(x, return_counts=True)
>>> output
tensor([1, 2, 3, 1, 2])
>>> counts
tensor([2, 2, 1, 2, 1])

torch.var()¶

torch.var(input, unbiased=True) → Tensor

Returns the variance of all elements in the input tensor.

If unbiased is False, then the variance will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
unbiased (bool) – whether to use the unbiased estimation or not

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[-0.3425, -1.2636, -0.4864]])
>>> torch.var(a)
tensor(0.2455)

torch.var(input, dim, keepdim=False, unbiased=True, out=None) → Tensor

Returns the variance of each row of the input tensor in the given dimension dim.

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

If unbiased is False, then the variance will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
unbiased (bool) – whether to use the unbiased estimation or not
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[-0.3567,  1.7385, -1.3042,  0.7423],
        [ 1.3436, -0.1015, -0.9834, -0.8438],
        [ 0.6056,  0.1089, -0.3112, -1.4085],
        [-0.7700,  0.6074, -0.1469,  0.7777]])
>>> torch.var(a, 1)
tensor([ 1.7444,  1.1363,  0.7356,  0.5112])

torch.var_mean()¶

torch.var_mean(input, unbiased=True) -> (Tensor, Tensor)

Returns the variance and mean of all elements in the input tensor.

If unbiased is False, then the variance will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
unbiased (bool) – whether to use the unbiased estimation or not

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[0.0146, 0.4258, 0.2211]])
>>> torch.var_mean(a)
(tensor(0.0423), tensor(0.2205))

torch.var_mean(input, dim, keepdim=False, unbiased=True) -> (Tensor, Tensor)

Returns the variance and mean of each row of the input tensor in the given dimension dim.

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

If unbiased is False, then the variance will be calculated via the biased estimator. Otherwise, Bessel’s correction will be used.

Parameters

input (Tensor) – the input tensor.
dim (int or tuple of python:ints) – the dimension or dimensions to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
unbiased (bool) – whether to use the unbiased estimation or not

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[-1.5650,  2.0415, -0.1024, -0.5790],
        [ 0.2325, -2.6145, -1.6428, -0.3537],
        [-0.2159, -1.1069,  1.2882, -1.3265],
        [-0.6706, -1.5893,  0.6827,  1.6727]])
>>> torch.var_mean(a, 1)
(tensor([2.3174, 1.6403, 1.4092, 2.0791]), tensor([-0.0512, -1.0946, -0.3403,  0.0239]))

Comparison Ops¶

torch.allclose(input, other, rtol=1e-05, atol=1e-08, equal_nan=False) → bool¶

This function checks if all input and other satisfy the condition:

\lvert \text{input} - \text{other} \rvert \leq \texttt{atol} + \texttt{rtol} \times \lvert \text{other} \rvert

elementwise, for all elements of input and other. The behaviour of this function is analogous to numpy.allclose

Parameters

input (Tensor) – first tensor to compare
other (Tensor) – second tensor to compare
atol (float, optional) – absolute tolerance. Default: 1e-08
rtol (float, optional) – relative tolerance. Default: 1e-05
equal_nan (bool, optional) – if True, then two NaN s will be compared as equal. Default: False

Example:

>>> torch.allclose(torch.tensor([10000., 1e-07]), torch.tensor([10000.1, 1e-08]))
False
>>> torch.allclose(torch.tensor([10000., 1e-08]), torch.tensor([10000.1, 1e-09]))
True
>>> torch.allclose(torch.tensor([1.0, float('nan')]), torch.tensor([1.0, float('nan')]))
False
>>> torch.allclose(torch.tensor([1.0, float('nan')]), torch.tensor([1.0, float('nan')]), equal_nan=True)
True

torch.argsort(input, dim=-1, descending=False) → LongTensor¶

Returns the indices that sort a tensor along a given dimension in ascending order by value.

This is the second value returned by torch.sort(). See its documentation for the exact semantics of this method.

Parameters

input (Tensor) – the input tensor.
dim (int, optional) – the dimension to sort along
descending (bool, optional) – controls the sorting order (ascending or descending)

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.0785,  1.5267, -0.8521,  0.4065],
        [ 0.1598,  0.0788, -0.0745, -1.2700],
        [ 1.2208,  1.0722, -0.7064,  1.2564],
        [ 0.0669, -0.2318, -0.8229, -0.9280]])


>>> torch.argsort(a, dim=1)
tensor([[2, 0, 3, 1],
        [3, 2, 1, 0],
        [2, 1, 0, 3],
        [3, 2, 1, 0]])

torch.eq(input, other, out=None) → Tensor¶

Computes element-wise equality

The second argument can be a number or a tensor whose shape is broadcastable with the first argument.

Parameters

input (Tensor) – the tensor to compare
other (Tensor or float) – the tensor or value to compare
out (Tensor, optional) – the output tensor. Must be a ByteTensor

Returns

A torch.BoolTensor containing a True at each location where comparison is true

Return type

Tensor

Example:

>>> torch.eq(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
tensor([[ True, False],
        [False, True]])

torch.equal(input, other) → bool¶

True if two tensors have the same size and elements, False otherwise.

Example:

>>> torch.equal(torch.tensor([1, 2]), torch.tensor([1, 2]))
True

torch.ge(input, other, out=None) → Tensor¶

Computes $\text{input} \geq \text{other}$ element-wise.

The second argument can be a number or a tensor whose shape is broadcastable with the first argument.

Parameters

input (Tensor) – the tensor to compare
other (Tensor or float) – the tensor or value to compare
out (Tensor, optional) – the output tensor that must be a BoolTensor

Returns

A torch.BoolTensor containing a True at each location where comparison is true

Return type

Tensor

Example:

>>> torch.ge(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
tensor([[True, True], [False, True]])

torch.gt(input, other, out=None) → Tensor¶

Computes $\text{input} > \text{other}$ element-wise.

The second argument can be a number or a tensor whose shape is broadcastable with the first argument.

Parameters

input (Tensor) – the tensor to compare
other (Tensor or float) – the tensor or value to compare
out (Tensor, optional) – the output tensor that must be a BoolTensor

Returns

A torch.BoolTensor containing a True at each location where comparison is true

Return type

Tensor

Example:

>>> torch.gt(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
tensor([[False, True], [False, False]])

torch.isfinite()¶

Returns a new tensor with boolean elements representing if each element is Finite or not.

Arguments:
tensor (Tensor): A tensor to check

Returns:
Tensor: A torch.Tensor with dtype torch.bool containing a True at each location of finite elements and False otherwise

Example:
>>> torch.isfinite(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')]))
tensor([True,  False,  True,  False,  False])

torch.isinf()¶

Returns a new tensor with boolean elements representing if each element is +/-INF or not.

Arguments:
tensor (Tensor): A tensor to check

Returns:
Tensor: A torch.Tensor with dtype torch.bool containing a True at each location of +/-INF elements and False otherwise

Example:
>>> torch.isinf(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')]))
tensor([False,  True,  False,  True,  False])

torch.isnan()¶

Returns a new tensor with boolean elements representing if each element is NaN or not.

Parameters: input (Tensor) – A tensor to check
Returns: A torch.BoolTensor containing a True at each location of NaN elements.
Return type: Tensor

Example:

>>> torch.isnan(torch.tensor([1, float('nan'), 2]))
tensor([False, True, False])

torch.kthvalue(input, k, dim=None, keepdim=False, out=None) -> (Tensor, LongTensor)¶

Returns a namedtuple (values, indices) where values is the k th smallest element of each row of the input tensor in the given dimension dim. And indices is the index location of each element found.

If dim is not given, the last dimension of the input is chosen.

If keepdim is True, both the values and indices tensors are the same size as input, except in the dimension dim where they are of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in both the values and indices tensors having 1 fewer dimension than the input tensor.

Parameters

input (Tensor) – the input tensor.
k (int) – k for the k-th smallest element
dim (int, optional) – the dimension to find the kth value along
keepdim (bool) – whether the output tensor has dim retained or not.
out (tuple, optional) – the output tuple of (Tensor, LongTensor) can be optionally given to be used as output buffers

Example:

>>> x = torch.arange(1., 6.)
>>> x
tensor([ 1.,  2.,  3.,  4.,  5.])
>>> torch.kthvalue(x, 4)
torch.return_types.kthvalue(values=tensor(4.), indices=tensor(3))

>>> x=torch.arange(1.,7.).resize_(2,3)
>>> x
tensor([[ 1.,  2.,  3.],
        [ 4.,  5.,  6.]])
>>> torch.kthvalue(x, 2, 0, True)
torch.return_types.kthvalue(values=tensor([[4., 5., 6.]]), indices=tensor([[1, 1, 1]]))

torch.le(input, other, out=None) → Tensor¶

Computes $\text{input} \leq \text{other}$ element-wise.

The second argument can be a number or a tensor whose shape is broadcastable with the first argument.

Parameters

input (Tensor) – the tensor to compare
other (Tensor or float) – the tensor or value to compare
out (Tensor, optional) – the output tensor that must be a BoolTensor

Returns

A torch.BoolTensor containing a True at each location where comparison is true

Return type

Tensor

Example:

>>> torch.le(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
tensor([[True, False], [True, True]])

torch.lt(input, other, out=None) → Tensor¶

Computes $\text{input} < \text{other}$ element-wise.

The second argument can be a number or a tensor whose shape is broadcastable with the first argument.

Parameters

input (Tensor) – the tensor to compare
other (Tensor or float) – the tensor or value to compare
out (Tensor, optional) – the output tensor that must be a BoolTensor

Returns

A torch.BoolTensor containing a True at each location where comparison is true

Return type

Tensor

Example:

>>> torch.lt(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
tensor([[False, False], [True, False]])

torch.max()¶

torch.max(input) → Tensor

Returns the maximum value of all elements in the input tensor.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[ 0.6763,  0.7445, -2.2369]])
>>> torch.max(a)
tensor(0.7445)

torch.max(input, dim, keepdim=False, out=None) -> (Tensor, LongTensor)

Returns a namedtuple (values, indices) where values is the maximum value of each row of the input tensor in the given dimension dim. And indices is the index location of each maximum value found (argmax).

Warning

indices does not necessarily contain the first occurrence of each maximal value found, unless it is unique. The exact implementation details are device-specific. Do not expect the same result when run on CPU and GPU in general.

If keepdim is True, the output tensors are of the same size as input except in the dimension dim where they are of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensors having 1 fewer dimension than input.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce.
keepdim (bool) – whether the output tensor has dim retained or not. Default: False.
out (tuple, optional) – the result tuple of two output tensors (max, max_indices)

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[-1.2360, -0.2942, -0.1222,  0.8475],
        [ 1.1949, -1.1127, -2.2379, -0.6702],
        [ 1.5717, -0.9207,  0.1297, -1.8768],
        [-0.6172,  1.0036, -0.6060, -0.2432]])
>>> torch.max(a, 1)
torch.return_types.max(values=tensor([0.8475, 1.1949, 1.5717, 1.0036]), indices=tensor([3, 0, 0, 1]))

torch.max(input, other, out=None) → Tensor

Each element of the tensor input is compared with the corresponding element of the tensor other and an element-wise maximum is taken.

The shapes of input and other don’t need to match, but they must be broadcastable.

\text{out}_i = \max(\text{tensor}_i, \text{other}_i)

Note

When the shapes do not match, the shape of the returned output tensor follows the broadcasting rules.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the second input tensor
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.2942, -0.7416,  0.2653, -0.1584])
>>> b = torch.randn(4)
>>> b
tensor([ 0.8722, -1.7421, -0.4141, -0.5055])
>>> torch.max(a, b)
tensor([ 0.8722, -0.7416,  0.2653, -0.1584])

torch.min()¶

torch.min(input) → Tensor

Returns the minimum value of all elements in the input tensor.

Parameters: input (Tensor) – the input tensor.

Example:

>>> a = torch.randn(1, 3)
>>> a
tensor([[ 0.6750,  1.0857,  1.7197]])
>>> torch.min(a)
tensor(0.6750)

torch.min(input, dim, keepdim=False, out=None) -> (Tensor, LongTensor)

Returns a namedtuple (values, indices) where values is the minimum value of each row of the input tensor in the given dimension dim. And indices is the index location of each minimum value found (argmin).

Warning

indices does not necessarily contain the first occurrence of each minimal value found, unless it is unique. The exact implementation details are device-specific. Do not expect the same result when run on CPU and GPU in general.

If keepdim is True, the output tensors are of the same size as input except in the dimension dim where they are of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensors having 1 fewer dimension than input.

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to reduce.
keepdim (bool) – whether the output tensor has dim retained or not.
out (tuple, optional) – the tuple of two output tensors (min, min_indices)

Example:

>>> a = torch.randn(4, 4)
>>> a
tensor([[-0.6248,  1.1334, -1.1899, -0.2803],
        [-1.4644, -0.2635, -0.3651,  0.6134],
        [ 0.2457,  0.0384,  1.0128,  0.7015],
        [-0.1153,  2.9849,  2.1458,  0.5788]])
>>> torch.min(a, 1)
torch.return_types.min(values=tensor([-1.1899, -1.4644,  0.0384, -0.1153]), indices=tensor([2, 0, 1, 0]))

torch.min(input, other, out=None) → Tensor

Each element of the tensor input is compared with the corresponding element of the tensor other and an element-wise minimum is taken. The resulting tensor is returned.

The shapes of input and other don’t need to match, but they must be broadcastable.

\text{out}_i = \min(\text{tensor}_i, \text{other}_i)

Note

When the shapes do not match, the shape of the returned output tensor follows the broadcasting rules.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the second input tensor
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4)
>>> a
tensor([ 0.8137, -1.1740, -0.6460,  0.6308])
>>> b = torch.randn(4)
>>> b
tensor([-0.1369,  0.1555,  0.4019, -0.1929])
>>> torch.min(a, b)
tensor([-0.1369, -1.1740, -0.6460, -0.1929])

torch.ne(input, other, out=None) → Tensor¶

Computes $input \neq other$ element-wise.

The second argument can be a number or a tensor whose shape is broadcastable with the first argument.

Parameters

input (Tensor) – the tensor to compare
other (Tensor or float) – the tensor or value to compare
out (Tensor, optional) – the output tensor that must be a BoolTensor

Returns

A torch.BoolTensor containing a True at each location where comparison is true.

Return type

Tensor

Example:

>>> torch.ne(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
tensor([[False, True], [True, False]])

torch.sort(input, dim=-1, descending=False, out=None) -> (Tensor, LongTensor)¶

Sorts the elements of the input tensor along a given dimension in ascending order by value.

If dim is not given, the last dimension of the input is chosen.

If descending is True then the elements are sorted in descending order by value.

A namedtuple of (values, indices) is returned, where the values are the sorted values and indices are the indices of the elements in the original input tensor.

Parameters

input (Tensor) – the input tensor.
dim (int, optional) – the dimension to sort along
descending (bool, optional) – controls the sorting order (ascending or descending)
out (tuple, optional) – the output tuple of (Tensor, LongTensor) that can be optionally given to be used as output buffers

Example:

>>> x = torch.randn(3, 4)
>>> sorted, indices = torch.sort(x)
>>> sorted
tensor([[-0.2162,  0.0608,  0.6719,  2.3332],
        [-0.5793,  0.0061,  0.6058,  0.9497],
        [-0.5071,  0.3343,  0.9553,  1.0960]])
>>> indices
tensor([[ 1,  0,  2,  3],
        [ 3,  1,  0,  2],
        [ 0,  3,  1,  2]])

>>> sorted, indices = torch.sort(x, 0)
>>> sorted
tensor([[-0.5071, -0.2162,  0.6719, -0.5793],
        [ 0.0608,  0.0061,  0.9497,  0.3343],
        [ 0.6058,  0.9553,  1.0960,  2.3332]])
>>> indices
tensor([[ 2,  0,  0,  1],
        [ 0,  1,  1,  2],
        [ 1,  2,  2,  0]])

torch.topk(input, k, dim=None, largest=True, sorted=True, out=None) -> (Tensor, LongTensor)¶

Returns the k largest elements of the given input tensor along a given dimension.

If dim is not given, the last dimension of the input is chosen.

If largest is False then the k smallest elements are returned.

A namedtuple of (values, indices) is returned, where the indices are the indices of the elements in the original input tensor.

The boolean option sorted if True, will make sure that the returned k elements are themselves sorted

Parameters

input (Tensor) – the input tensor.
k (int) – the k in “top-k”
dim (int, optional) – the dimension to sort along
largest (bool, optional) – controls whether to return largest or smallest elements
sorted (bool, optional) – controls whether to return the elements in sorted order
out (tuple, optional) – the output tuple of (Tensor, LongTensor) that can be optionally given to be used as output buffers

Example:

>>> x = torch.arange(1., 6.)
>>> x
tensor([ 1.,  2.,  3.,  4.,  5.])
>>> torch.topk(x, 3)
torch.return_types.topk(values=tensor([5., 4., 3.]), indices=tensor([4, 3, 2]))

Spectral Ops¶

torch.fft(input, signal_ndim, normalized=False) → Tensor¶

Complex-to-complex Discrete Fourier Transform

This method computes the complex-to-complex discrete Fourier transform. Ignoring the batch dimensions, it computes the following expression:

X[\omega_1, \dots, \omega_d] = \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d] e^{-j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},

where $d$ = signal_ndim is number of dimensions for the signal, and $N_i$ is the size of signal dimension $i$ .

This method supports 1D, 2D and 3D complex-to-complex transforms, indicated by signal_ndim. input must be a tensor with last dimension of size 2, representing the real and imaginary components of complex numbers, and should have at least signal_ndim + 1 dimensions with optionally arbitrary number of leading batch dimensions. If normalized is set to True, this normalizes the result by dividing it with $\sqrt{\prod_{i=1}^K N_i}$ so that the operator is unitary.

Returns the real and the imaginary parts together as one tensor of the same shape of input.

The inverse of this function is ifft().

Note

For CUDA tensors, an LRU cache is used for cuFFT plans to speed up repeatedly running FFT methods on tensors of same geometry with same configuration. See cuFFT plan cache for more details on how to monitor and control the cache.

Warning

For CPU tensors, this method is currently only available with MKL. Use torch.backends.mkl.is_available() to check if MKL is installed.

Parameters

input (Tensor) – the input tensor of at least signal_ndim + 1 dimensions
signal_ndim (int) – the number of dimensions in each signal. signal_ndim can only be 1, 2 or 3
normalized (bool, optional) – controls whether to return normalized results. Default: False

Returns

A tensor containing the complex-to-complex Fourier transform result

Return type

Tensor

Example:

>>> # unbatched 2D FFT
>>> x = torch.randn(4, 3, 2)
>>> torch.fft(x, 2)
tensor([[[-0.0876,  1.7835],
         [-2.0399, -2.9754],
         [ 4.4773, -5.0119]],

        [[-1.5716,  2.7631],
         [-3.8846,  5.2652],
         [ 0.2046, -0.7088]],

        [[ 1.9938, -0.5901],
         [ 6.5637,  6.4556],
         [ 2.9865,  4.9318]],

        [[ 7.0193,  1.1742],
         [-1.3717, -2.1084],
         [ 2.0289,  2.9357]]])
>>> # batched 1D FFT
>>> torch.fft(x, 1)
tensor([[[ 1.8385,  1.2827],
         [-0.1831,  1.6593],
         [ 2.4243,  0.5367]],

        [[-0.9176, -1.5543],
         [-3.9943, -2.9860],
         [ 1.2838, -2.9420]],

        [[-0.8854, -0.6860],
         [ 2.4450,  0.0808],
         [ 1.3076, -0.5768]],

        [[-0.1231,  2.7411],
         [-0.3075, -1.7295],
         [-0.5384, -2.0299]]])
>>> # arbitrary number of batch dimensions, 2D FFT
>>> x = torch.randn(3, 3, 5, 5, 2)
>>> y = torch.fft(x, 2)
>>> y.shape
torch.Size([3, 3, 5, 5, 2])

torch.ifft(input, signal_ndim, normalized=False) → Tensor¶

Complex-to-complex Inverse Discrete Fourier Transform

This method computes the complex-to-complex inverse discrete Fourier transform. Ignoring the batch dimensions, it computes the following expression:

X[\omega_1, \dots, \omega_d] = \frac{1}{\prod_{i=1}^d N_i} \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d] e^{\ j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},

where $d$ = signal_ndim is number of dimensions for the signal, and $N_i$ is the size of signal dimension $i$ .

The argument specifications are almost identical with fft(). However, if normalized is set to True, this instead returns the results multiplied by $\sqrt{\prod_{i=1}^d N_i}$ , to become a unitary operator. Therefore, to invert a fft(), the normalized argument should be set identically for fft().

Returns the real and the imaginary parts together as one tensor of the same shape of input.

The inverse of this function is fft().

Note

For CUDA tensors, an LRU cache is used for cuFFT plans to speed up repeatedly running FFT methods on tensors of same geometry with same configuration. See cuFFT plan cache for more details on how to monitor and control the cache.

Warning

For CPU tensors, this method is currently only available with MKL. Use torch.backends.mkl.is_available() to check if MKL is installed.

Parameters

input (Tensor) – the input tensor of at least signal_ndim + 1 dimensions
signal_ndim (int) – the number of dimensions in each signal. signal_ndim can only be 1, 2 or 3
normalized (bool, optional) – controls whether to return normalized results. Default: False

Returns

A tensor containing the complex-to-complex inverse Fourier transform result

Return type

Tensor

Example:

>>> x = torch.randn(3, 3, 2)
>>> x
tensor([[[ 1.2766,  1.3680],
         [-0.8337,  2.0251],
         [ 0.9465, -1.4390]],

        [[-0.1890,  1.6010],
         [ 1.1034, -1.9230],
         [-0.9482,  1.0775]],

        [[-0.7708, -0.8176],
         [-0.1843, -0.2287],
         [-1.9034, -0.2196]]])
>>> y = torch.fft(x, 2)
>>> torch.ifft(y, 2)  # recover x
tensor([[[ 1.2766,  1.3680],
         [-0.8337,  2.0251],
         [ 0.9465, -1.4390]],

        [[-0.1890,  1.6010],
         [ 1.1034, -1.9230],
         [-0.9482,  1.0775]],

        [[-0.7708, -0.8176],
         [-0.1843, -0.2287],
         [-1.9034, -0.2196]]])

torch.rfft(input, signal_ndim, normalized=False, onesided=True) → Tensor¶

Real-to-complex Discrete Fourier Transform

This method computes the real-to-complex discrete Fourier transform. It is mathematically equivalent with fft() with differences only in formats of the input and output.

This method supports 1D, 2D and 3D real-to-complex transforms, indicated by signal_ndim. input must be a tensor with at least signal_ndim dimensions with optionally arbitrary number of leading batch dimensions. If normalized is set to True, this normalizes the result by dividing it with $\sqrt{\prod_{i=1}^K N_i}$ so that the operator is unitary, where $N_i$ is the size of signal dimension $i$ .

The real-to-complex Fourier transform results follow conjugate symmetry:

X[\omega_1, \dots, \omega_d] = X^*[N_1 - \omega_1, \dots, N_d - \omega_d],

where the index arithmetic is computed modulus the size of the corresponding dimension, $\ ^*$ is the conjugate operator, and $d$ = signal_ndim. onesided flag controls whether to avoid redundancy in the output results. If set to True (default), the output will not be full complex result of shape $(*, 2)$ , where $*$ is the shape of input, but instead the last dimension will be halfed as of size $\lfloor \frac{N_d}{2} \rfloor + 1$ .

The inverse of this function is irfft().

Note

For CUDA tensors, an LRU cache is used for cuFFT plans to speed up repeatedly running FFT methods on tensors of same geometry with same configuration. See cuFFT plan cache for more details on how to monitor and control the cache.

Warning

For CPU tensors, this method is currently only available with MKL. Use torch.backends.mkl.is_available() to check if MKL is installed.

Parameters

input (Tensor) – the input tensor of at least signal_ndim dimensions
signal_ndim (int) – the number of dimensions in each signal. signal_ndim can only be 1, 2 or 3
normalized (bool, optional) – controls whether to return normalized results. Default: False
onesided (bool, optional) – controls whether to return half of results to avoid redundancy. Default: True

Returns

A tensor containing the real-to-complex Fourier transform result

Return type

Tensor

Example:

>>> x = torch.randn(5, 5)
>>> torch.rfft(x, 2).shape
torch.Size([5, 3, 2])
>>> torch.rfft(x, 2, onesided=False).shape
torch.Size([5, 5, 2])

torch.irfft(input, signal_ndim, normalized=False, onesided=True, signal_sizes=None) → Tensor¶

Complex-to-real Inverse Discrete Fourier Transform

This method computes the complex-to-real inverse discrete Fourier transform. It is mathematically equivalent with ifft() with differences only in formats of the input and output.

The argument specifications are almost identical with ifft(). Similar to ifft(), if normalized is set to True, this normalizes the result by multiplying it with $\sqrt{\prod_{i=1}^K N_i}$ so that the operator is unitary, where $N_i$ is the size of signal dimension $i$ .

Note

Due to the conjugate symmetry, input do not need to contain the full complex frequency values. Roughly half of the values will be sufficient, as is the case when input is given by rfft() with rfft(signal, onesided=True). In such case, set the onesided argument of this method to True. Moreover, the original signal shape information can sometimes be lost, optionally set signal_sizes to be the size of the original signal (without the batch dimensions if in batched mode) to recover it with correct shape.

Therefore, to invert an rfft(), the normalized and onesided arguments should be set identically for irfft(), and preferably a signal_sizes is given to avoid size mismatch. See the example below for a case of size mismatch.

See rfft() for details on conjugate symmetry.

The inverse of this function is rfft().

Warning

Generally speaking, input to this function should contain values following conjugate symmetry. Note that even if onesided is True, often symmetry on some part is still needed. When this requirement is not satisfied, the behavior of irfft() is undefined. Since torch.autograd.gradcheck() estimates numerical Jacobian with point perturbations, irfft() will almost certainly fail the check.

Note

For CUDA tensors, an LRU cache is used for cuFFT plans to speed up repeatedly running FFT methods on tensors of same geometry with same configuration. See cuFFT plan cache for more details on how to monitor and control the cache.

Warning

For CPU tensors, this method is currently only available with MKL. Use torch.backends.mkl.is_available() to check if MKL is installed.

Parameters

input (Tensor) – the input tensor of at least signal_ndim + 1 dimensions
signal_ndim (int) – the number of dimensions in each signal. signal_ndim can only be 1, 2 or 3
normalized (bool, optional) – controls whether to return normalized results. Default: False
onesided (bool, optional) – controls whether input was halfed to avoid redundancy, e.g., by rfft(). Default: True
signal_sizes (list or torch.Size, optional) – the size of the original signal (without batch dimension). Default: None

Returns

A tensor containing the complex-to-real inverse Fourier transform result

Return type

Tensor

Example:

>>> x = torch.randn(4, 4)
>>> torch.rfft(x, 2, onesided=True).shape
torch.Size([4, 3, 2])
>>>
>>> # notice that with onesided=True, output size does not determine the original signal size
>>> x = torch.randn(4, 5)

>>> torch.rfft(x, 2, onesided=True).shape
torch.Size([4, 3, 2])
>>>
>>> # now we use the original shape to recover x
>>> x
tensor([[-0.8992,  0.6117, -1.6091, -0.4155, -0.8346],
        [-2.1596, -0.0853,  0.7232,  0.1941, -0.0789],
        [-2.0329,  1.1031,  0.6869, -0.5042,  0.9895],
        [-0.1884,  0.2858, -1.5831,  0.9917, -0.8356]])
>>> y = torch.rfft(x, 2, onesided=True)
>>> torch.irfft(y, 2, onesided=True, signal_sizes=x.shape)  # recover x
tensor([[-0.8992,  0.6117, -1.6091, -0.4155, -0.8346],
        [-2.1596, -0.0853,  0.7232,  0.1941, -0.0789],
        [-2.0329,  1.1031,  0.6869, -0.5042,  0.9895],
        [-0.1884,  0.2858, -1.5831,  0.9917, -0.8356]])

torch.stft(input, n_fft, hop_length=None, win_length=None, window=None, center=True, pad_mode='reflect', normalized=False, onesided=True)[source]¶

Short-time Fourier transform (STFT).

Ignoring the optional batch dimension, this method computes the following expression:

X[m, \omega] = \sum_{k = 0}^{\text{win\_length-1}}% \text{window}[k]\ \text{input}[m \times \text{hop\_length} + k]\ % \exp\left(- j \frac{2 \pi \cdot \omega k}{\text{win\_length}}\right),

where $m$ is the index of the sliding window, and $\omega$ is the frequency that $0 \leq \omega < \text{n\_fft}$ . When onesided is the default value True,

input must be either a 1-D time sequence or a 2-D batch of time sequences.
If hop_length is None (default), it is treated as equal to floor(n_fft / 4).
If win_length is None (default), it is treated as equal to n_fft.
window can be a 1-D tensor of size win_length, e.g., from torch.hann_window(). If window is None (default), it is treated as if having $1$ everywhere in the window. If $\text{win\_length} < \text{n\_fft}$ , window will be padded on both sides to length n_fft before being applied.
If center is True (default), input will be padded on both sides so that the $t$ -th frame is centered at time $t \times \text{hop\_length}$ . Otherwise, the $t$ -th frame begins at time $t \times \text{hop\_length}$ .
pad_mode determines the padding method used on input when center is True. See torch.nn.functional.pad() for all available options. Default is "reflect".
If onesided is True (default), only values for $\omega$ in $\left[0, 1, 2, \dots, \left\lfloor \frac{\text{n\_fft}}{2} \right\rfloor + 1\right]$ are returned because the real-to-complex Fourier transform satisfies the conjugate symmetry, i.e., $X[m, \omega] = X[m, \text{n\_fft} - \omega]^*$ .
If normalized is True (default is False), the function returns the normalized STFT results, i.e., multiplied by $(\text{frame\_length})^{-0.5}$ .

Returns the real and the imaginary parts together as one tensor of size $(* \times N \times T \times 2)$ , where $*$ is the optional batch size of input, $N$ is the number of frequencies where STFT is applied, $T$ is the total number of frames used, and each pair in the last dimension represents a complex number as the real part and the imaginary part.

Warning

This function changed signature at version 0.4.1. Calling with the previous signature may cause error or return incorrect result.

Parameters

input (Tensor) – the input tensor
n_fft (int) – size of Fourier transform
hop_length (int, optional) – the distance between neighboring sliding window frames. Default: None (treated as equal to floor(n_fft / 4))
win_length (int, optional) – the size of window frame and STFT filter. Default: None (treated as equal to n_fft)
window (Tensor, optional) – the optional window function. Default: None (treated as window of all $1$ s)
center (bool, optional) – whether to pad input on both sides so that the $t$ -th frame is centered at time $t \times \text{hop\_length}$ . Default: True
pad_mode (string, optional) – controls the padding method used when center is True. Default: "reflect"
normalized (bool, optional) – controls whether to return the normalized STFT results Default: False
onesided (bool, optional) – controls whether to return half of results to avoid redundancy Default: True

Returns

A tensor containing the STFT result with shape described above

Return type

Tensor

torch.bartlett_window(window_length, periodic=True, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Bartlett window function.

w[n] = 1 - \left| \frac{2n}{N-1} - 1 \right| = \begin{cases} \frac{2n}{N - 1} & \text{if } 0 \leq n \leq \frac{N - 1}{2} \\ 2 - \frac{2n}{N - 1} & \text{if } \frac{N - 1}{2} < n < N \\ \end{cases},

where $N$ is the full window size.

The input window_length is a positive integer controlling the returned window size. periodic flag determines whether the returned window trims off the last duplicate value from the symmetric window and is ready to be used as a periodic window with functions like torch.stft(). Therefore, if periodic is true, the $N$ in above formula is in fact $\text{window\_length} + 1$ . Also, we always have torch.bartlett_window(L, periodic=True) equal to torch.bartlett_window(L + 1, periodic=False)[:-1]).

Note

If window_length $=1$ , the returned window contains a single value 1.

Parameters

window_length (int) – the size of returned window
periodic (bool, optional) – If True, returns a window to be used as periodic function. If False, return a symmetric window.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()). Only floating point types are supported.
layout (torch.layout, optional) – the desired layout of returned window tensor. Only torch.strided (dense layout) is supported.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Returns

A 1-D tensor of size $(\text{window\_length},)$ containing the window

Return type

Tensor

torch.blackman_window(window_length, periodic=True, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Blackman window function.

w[n] = 0.42 - 0.5 \cos \left( \frac{2 \pi n}{N - 1} \right) + 0.08 \cos \left( \frac{4 \pi n}{N - 1} \right)

where $N$ is the full window size.

The input window_length is a positive integer controlling the returned window size. periodic flag determines whether the returned window trims off the last duplicate value from the symmetric window and is ready to be used as a periodic window with functions like torch.stft(). Therefore, if periodic is true, the $N$ in above formula is in fact $\text{window\_length} + 1$ . Also, we always have torch.blackman_window(L, periodic=True) equal to torch.blackman_window(L + 1, periodic=False)[:-1]).

Note

If window_length $=1$ , the returned window contains a single value 1.

Parameters

window_length (int) – the size of returned window
periodic (bool, optional) – If True, returns a window to be used as periodic function. If False, return a symmetric window.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()). Only floating point types are supported.
layout (torch.layout, optional) – the desired layout of returned window tensor. Only torch.strided (dense layout) is supported.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Returns

A 1-D tensor of size $(\text{window\_length},)$ containing the window

Return type

Tensor

torch.hamming_window(window_length, periodic=True, alpha=0.54, beta=0.46, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Hamming window function.

w[n] = \alpha - \beta\ \cos \left( \frac{2 \pi n}{N - 1} \right),

where $N$ is the full window size.

The input window_length is a positive integer controlling the returned window size. periodic flag determines whether the returned window trims off the last duplicate value from the symmetric window and is ready to be used as a periodic window with functions like torch.stft(). Therefore, if periodic is true, the $N$ in above formula is in fact $\text{window\_length} + 1$ . Also, we always have torch.hamming_window(L, periodic=True) equal to torch.hamming_window(L + 1, periodic=False)[:-1]).

Note

If window_length $=1$ , the returned window contains a single value 1.

Note

This is a generalized version of torch.hann_window().

Parameters

window_length (int) – the size of returned window
periodic (bool, optional) – If True, returns a window to be used as periodic function. If False, return a symmetric window.
alpha (float, optional) – The coefficient $\alpha$ in the equation above
beta (float, optional) – The coefficient $\beta$ in the equation above
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()). Only floating point types are supported.
layout (torch.layout, optional) – the desired layout of returned window tensor. Only torch.strided (dense layout) is supported.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Returns

A 1-D tensor of size $(\text{window\_length},)$ containing the window

Return type

Tensor

torch.hann_window(window_length, periodic=True, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor¶

Hann window function.

w[n] = \frac{1}{2}\ \left[1 - \cos \left( \frac{2 \pi n}{N - 1} \right)\right] = \sin^2 \left( \frac{\pi n}{N - 1} \right),

where $N$ is the full window size.

The input window_length is a positive integer controlling the returned window size. periodic flag determines whether the returned window trims off the last duplicate value from the symmetric window and is ready to be used as a periodic window with functions like torch.stft(). Therefore, if periodic is true, the $N$ in above formula is in fact $\text{window\_length} + 1$ . Also, we always have torch.hann_window(L, periodic=True) equal to torch.hann_window(L + 1, periodic=False)[:-1]).

Note

If window_length $=1$ , the returned window contains a single value 1.

Parameters

window_length (int) – the size of returned window
periodic (bool, optional) – If True, returns a window to be used as periodic function. If False, return a symmetric window.
dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None, uses a global default (see torch.set_default_tensor_type()). Only floating point types are supported.
layout (torch.layout, optional) – the desired layout of returned window tensor. Only torch.strided (dense layout) is supported.
device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.
requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Returns

A 1-D tensor of size $(\text{window\_length},)$ containing the window

Return type

Tensor

Other Operations¶

torch.bincount(input, weights=None, minlength=0) → Tensor¶

Count the frequency of each value in an array of non-negative ints.

The number of bins (size 1) is one larger than the largest value in input unless input is empty, in which case the result is a tensor of size 0. If minlength is specified, the number of bins is at least minlength and if input is empty, then the result is tensor of size minlength filled with zeros. If n is the value at position i, out[n] += weights[i] if weights is specified else out[n] += 1.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters

input (Tensor) – 1-d int tensor
weights (Tensor) – optional, weight for each value in the input tensor. Should be of same size as input tensor.
minlength (int) – optional, minimum number of bins. Should be non-negative.

Returns

a tensor of shape Size([max(input) + 1]) if input is non-empty, else Size(0)

Return type

output (Tensor)

Example:

>>> input = torch.randint(0, 8, (5,), dtype=torch.int64)
>>> weights = torch.linspace(0, 1, steps=5)
>>> input, weights
(tensor([4, 3, 6, 3, 4]),
 tensor([ 0.0000,  0.2500,  0.5000,  0.7500,  1.0000])

>>> torch.bincount(input)
tensor([0, 0, 0, 2, 2, 0, 1])

>>> input.bincount(weights)
tensor([0.0000, 0.0000, 0.0000, 1.0000, 1.0000, 0.0000, 0.5000])

torch.broadcast_tensors(*tensors) → List of Tensors[source]¶

Broadcasts the given tensors according to Broadcasting semantics.

Parameters: *tensors – any number of tensors of the same type

Warning

More than one element of a broadcasted tensor may refer to a single memory location. As a result, in-place operations (especially ones that are vectorized) may result in incorrect behavior. If you need to write to the tensors, please clone them first.

Example:

>>> x = torch.arange(3).view(1, 3)
>>> y = torch.arange(2).view(2, 1)
>>> a, b = torch.broadcast_tensors(x, y)
>>> a.size()
torch.Size([2, 3])
>>> a
tensor([[0, 1, 2],
        [0, 1, 2]])

torch.cartesian_prod(*tensors)[source]¶

Do cartesian product of the given sequence of tensors. The behavior is similar to python’s itertools.product.

Parameters

*tensors – any number of 1 dimensional tensors.

Returns

A tensor equivalent to converting all the input tensors into lists,: do itertools.product on these lists, and finally convert the resulting list into tensor.

Return type

Tensor

Example:

>>> a = [1, 2, 3]
>>> b = [4, 5]
>>> list(itertools.product(a, b))
[(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)]
>>> tensor_a = torch.tensor(a)
>>> tensor_b = torch.tensor(b)
>>> torch.cartesian_prod(tensor_a, tensor_b)
tensor([[1, 4],
        [1, 5],
        [2, 4],
        [2, 5],
        [3, 4],
        [3, 5]])

torch.cdist(x1, x2, p=2.0, compute_mode='use_mm_for_euclid_dist_if_necessary')[source]¶

Computes batched the p-norm distance between each pair of the two collections of row vectors.

Parameters

x1 (Tensor) – input tensor of shape $B \times P \times M$ .
x2 (Tensor) – input tensor of shape $B \times R \times M$ .
p – p value for the p-norm distance to calculate between each vector pair $\in [0, \infty]$ .
compute_mode – ‘use_mm_for_euclid_dist_if_necessary’ - will use matrix multiplication approach to calculate euclidean distance (p = 2) if P > 25 or R > 25 ‘use_mm_for_euclid_dist’ - will always use matrix multiplication approach to calculate euclidean distance (p = 2) ‘donot_use_mm_for_euclid_dist’ - will never use matrix multiplication approach to calculate euclidean distance (p = 2) Default: use_mm_for_euclid_dist_if_necessary.

If x1 has shape $B \times P \times M$ and x2 has shape $B \times R \times M$ then the output will have shape $B \times P \times R$ .

This function is equivalent to scipy.spatial.distance.cdist(input,’minkowski’, p=p) if $p \in (0, \infty)$ . When $p = 0$ it is equivalent to scipy.spatial.distance.cdist(input, ‘hamming’) * M. When $p = \infty$ , the closest scipy function is scipy.spatial.distance.cdist(xn, lambda x, y: np.abs(x - y).max()).

Example

>>> a = torch.tensor([[0.9041,  0.0196], [-0.3108, -2.4423], [-0.4821,  1.059]])
>>> a
tensor([[ 0.9041,  0.0196],
        [-0.3108, -2.4423],
        [-0.4821,  1.0590]])
>>> b = torch.tensor([[-2.1763, -0.4713], [-0.6986,  1.3702]])
>>> b
tensor([[-2.1763, -0.4713],
        [-0.6986,  1.3702]])
>>> torch.cdist(a, b, p=2)
tensor([[3.1193, 2.0959],
        [2.7138, 3.8322],
        [2.2830, 0.3791]])

torch.combinations(input, r=2, with_replacement=False) → seq¶

Compute combinations of length $r$ of the given tensor. The behavior is similar to python’s itertools.combinations when with_replacement is set to False, and itertools.combinations_with_replacement when with_replacement is set to True.

Parameters

input (Tensor) – 1D vector.
r (int, optional) – number of elements to combine
with_replacement (boolean, optional) – whether to allow duplication in combination

Returns

A tensor equivalent to converting all the input tensors into lists, do itertools.combinations or itertools.combinations_with_replacement on these lists, and finally convert the resulting list into tensor.

Return type

Tensor

Example:

>>> a = [1, 2, 3]
>>> list(itertools.combinations(a, r=2))
[(1, 2), (1, 3), (2, 3)]
>>> list(itertools.combinations(a, r=3))
[(1, 2, 3)]
>>> list(itertools.combinations_with_replacement(a, r=2))
[(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)]
>>> tensor_a = torch.tensor(a)
>>> torch.combinations(tensor_a)
tensor([[1, 2],
        [1, 3],
        [2, 3]])
>>> torch.combinations(tensor_a, r=3)
tensor([[1, 2, 3]])
>>> torch.combinations(tensor_a, with_replacement=True)
tensor([[1, 1],
        [1, 2],
        [1, 3],
        [2, 2],
        [2, 3],
        [3, 3]])

torch.cross(input, other, dim=-1, out=None) → Tensor¶

Returns the cross product of vectors in dimension dim of input and other.

input and other must have the same size, and the size of their dim dimension should be 3.

If dim is not given, it defaults to the first dimension found with the size 3.

Parameters

input (Tensor) – the input tensor.
other (Tensor) – the second input tensor
dim (int, optional) – the dimension to take the cross-product in.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(4, 3)
>>> a
tensor([[-0.3956,  1.1455,  1.6895],
        [-0.5849,  1.3672,  0.3599],
        [-1.1626,  0.7180, -0.0521],
        [-0.1339,  0.9902, -2.0225]])
>>> b = torch.randn(4, 3)
>>> b
tensor([[-0.0257, -1.4725, -1.2251],
        [-1.1479, -0.7005, -1.9757],
        [-1.3904,  0.3726, -1.1836],
        [-0.9688, -0.7153,  0.2159]])
>>> torch.cross(a, b, dim=1)
tensor([[ 1.0844, -0.5281,  0.6120],
        [-2.4490, -1.5687,  1.9792],
        [-0.8304, -1.3037,  0.5650],
        [-1.2329,  1.9883,  1.0551]])
>>> torch.cross(a, b)
tensor([[ 1.0844, -0.5281,  0.6120],
        [-2.4490, -1.5687,  1.9792],
        [-0.8304, -1.3037,  0.5650],
        [-1.2329,  1.9883,  1.0551]])

torch.cummax(input, dim, out=None) -> (Tensor, LongTensor)¶

Returns a namedtuple (values, indices) where values is the cumulative maximum of elements of input in the dimension dim. And indices is the index location of each maximum value found in the dimension dim.

y_i = max(x_1, x_2, x_3, \dots, x_i)

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to do the operation over
out (tuple, optional) – the result tuple of two output tensors (values, indices)

Example:

>>> a = torch.randn(10)
>>> a
tensor([-0.3449, -1.5447,  0.0685, -1.5104, -1.1706,  0.2259,  1.4696, -1.3284,
     1.9946, -0.8209])
>>> torch.cummax(a, dim=0)
torch.return_types.cummax(
    values=tensor([-0.3449, -0.3449,  0.0685,  0.0685,  0.0685,  0.2259,  1.4696,  1.4696,
     1.9946,  1.9946]),
    indices=tensor([0, 0, 2, 2, 2, 5, 6, 6, 8, 8]))

torch.cummin(input, dim, out=None) -> (Tensor, LongTensor)¶

Returns a namedtuple (values, indices) where values is the cumulative minimum of elements of input in the dimension dim. And indices is the index location of each maximum value found in the dimension dim.

y_i = min(x_1, x_2, x_3, \dots, x_i)

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to do the operation over
out (tuple, optional) – the result tuple of two output tensors (values, indices)

Example:

>>> a = torch.randn(10)
>>> a
tensor([-0.2284, -0.6628,  0.0975,  0.2680, -1.3298, -0.4220, -0.3885,  1.1762,
     0.9165,  1.6684])
>>> torch.cummin(a, dim=0)
torch.return_types.cummin(
    values=tensor([-0.2284, -0.6628, -0.6628, -0.6628, -1.3298, -1.3298, -1.3298, -1.3298,
    -1.3298, -1.3298]),
    indices=tensor([0, 1, 1, 1, 4, 4, 4, 4, 4, 4]))

torch.cumprod(input, dim, out=None, dtype=None) → Tensor¶

Returns the cumulative product of elements of input in the dimension dim.

For example, if input is a vector of size N, the result will also be a vector of size N, with elements.

y_i = x_1 \times x_2\times x_3\times \dots \times x_i

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to do the operation over
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(10)
>>> a
tensor([ 0.6001,  0.2069, -0.1919,  0.9792,  0.6727,  1.0062,  0.4126,
        -0.2129, -0.4206,  0.1968])
>>> torch.cumprod(a, dim=0)
tensor([ 0.6001,  0.1241, -0.0238, -0.0233, -0.0157, -0.0158, -0.0065,
         0.0014, -0.0006, -0.0001])

>>> a[5] = 0.0
>>> torch.cumprod(a, dim=0)
tensor([ 0.6001,  0.1241, -0.0238, -0.0233, -0.0157, -0.0000, -0.0000,
         0.0000, -0.0000, -0.0000])

torch.cumsum(input, dim, out=None, dtype=None) → Tensor¶

Returns the cumulative sum of elements of input in the dimension dim.

For example, if input is a vector of size N, the result will also be a vector of size N, with elements.

y_i = x_1 + x_2 + x_3 + \dots + x_i

Parameters

input (Tensor) – the input tensor.
dim (int) – the dimension to do the operation over
dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.
out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(10)
>>> a
tensor([-0.8286, -0.4890,  0.5155,  0.8443,  0.1865, -0.1752, -2.0595,
         0.1850, -1.1571, -0.4243])
>>> torch.cumsum(a, dim=0)
tensor([-0.8286, -1.3175, -0.8020,  0.0423,  0.2289,  0.0537, -2.0058,
        -1.8209, -2.9780, -3.4022])

torch.diag(input, diagonal=0, out=None) → Tensor¶

If input is a vector (1-D tensor), then returns a 2-D square tensor with the elements of input as the diagonal.
If input is a matrix (2-D tensor), then returns a 1-D tensor with the diagonal elements of input.

The argument diagonal controls which diagonal to consider:

If diagonal = 0, it is the main diagonal.
If diagonal > 0, it is above the main diagonal.
If diagonal < 0, it is below the main diagonal.

Parameters

input (Tensor) – the input tensor.
diagonal (int, optional) – the diagonal to consider
out (Tensor, optional) – the output tensor.

BLAS and LAPACK Operations¶

torch.addbmm(input, batch1, batch2, *, beta=1, alpha=1, out=None) → Tensor¶

Performs a batch matrix-matrix product of matrices stored in batch1 and batch2, with a reduced add step (all matrix multiplications get accumulated along the first dimension). input is added to the final result.

batch1 and batch2 must be 3-D tensors each containing the same number of matrices.

If batch1 is a $(b \times n \times m)$ tensor, batch2 is a $(b \times m \times p)$ tensor, input must be broadcastable with a $(n \times p)$ tensor and out will be a $(n \times p)$ tensor.

out = \beta\ \text{input} + \alpha\ (\sum_{i=0}^{b-1} \text{batch1}_i \mathbin{@} \text{batch2}_i)

For inputs of type FloatTensor or DoubleTensor, arguments beta and alpha must be real numbers, otherwise they should be integers.

Parameters

batch1 (Tensor) – the first batch of matrices to be multiplied
batch2 (Tensor) – the second batch of matrices to be multiplied
beta (Number, optional) – multiplier for input ( $\beta$ )
input (Tensor) – matrix to be added
alpha (Number, optional) – multiplier for batch1 @ batch2 ( $\alpha$ )
out (Tensor, optional) – the output tensor.

Example:

>>> M = torch.randn(3, 5)
>>> batch1 = torch.randn(10, 3, 4)
>>> batch2 = torch.randn(10, 4, 5)
>>> torch.addbmm(M, batch1, batch2)
tensor([[  6.6311,   0.0503,   6.9768, -12.0362,  -2.1653],
        [ -4.8185,  -1.4255,  -6.6760,   8.9453,   2.5743],
        [ -3.8202,   4.3691,   1.0943,  -1.1109,   5.4730]])

torch.addmm(input, mat1, mat2, *, beta=1, alpha=1, out=None) → Tensor¶

Performs a matrix multiplication of the matrices mat1 and mat2. The matrix input is added to the final result.

If mat1 is a $(n \times m)$ tensor, mat2 is a $(m \times p)$ tensor, then input must be broadcastable with a $(n \times p)$ tensor and out will be a $(n \times p)$ tensor.

alpha and beta are scaling factors on matrix-vector product between mat1 and mat2 and the added matrix input respectively.

\text{out} = \beta\ \text{input} + \alpha\ (\text{mat1}_i \mathbin{@} \text{mat2}_i)

For inputs of type FloatTensor or DoubleTensor, arguments beta and alpha must be real numbers, otherwise they should be integers.

Parameters

input (Tensor) – matrix to be added
mat1 (Tensor) – the first matrix to be multiplied
mat2 (Tensor) – the second matrix to be multiplied
beta (Number, optional) – multiplier for input ( $\beta$ )
alpha (Number, optional) – multiplier for $mat1 @ mat2$ ( $\alpha$ )
out (Tensor, optional) – the output tensor.

Example:

>>> M = torch.randn(2, 3)
>>> mat1 = torch.randn(2, 3)
>>> mat2 = torch.randn(3, 3)
>>> torch.addmm(M, mat1, mat2)
tensor([[-4.8716,  1.4671, -1.3746],
        [ 0.7573, -3.9555, -2.8681]])

torch.addmv(input, mat, vec, *, beta=1, alpha=1, out=None) → Tensor¶

Performs a matrix-vector product of the matrix mat and the vector vec. The vector input is added to the final result.

If mat is a $(n \times m)$ tensor, vec is a 1-D tensor of size m, then input must be broadcastable with a 1-D tensor of size n and out will be 1-D tensor of size n.

alpha and beta are scaling factors on matrix-vector product between mat and vec and the added tensor input respectively.

\text{out} = \beta\ \text{input} + \alpha\ (\text{mat} \mathbin{@} \text{vec})

For inputs of type FloatTensor or DoubleTensor, arguments beta and alpha must be real numbers, otherwise they should be integers

Parameters

input (Tensor) – vector to be added
mat (Tensor) – matrix to be multiplied
vec (Tensor) – vector to be multiplied
beta (Number, optional) – multiplier for input ( $\beta$ )
alpha (Number, optional) – multiplier for $mat @ vec$ ( $\alpha$ )
out (Tensor, optional) – the output tensor.

Example:

>>> M = torch.randn(2)
>>> mat = torch.randn(2, 3)
>>> vec = torch.randn(3)
>>> torch.addmv(M, mat, vec)
tensor([-0.3768, -5.5565])

torch.addr(input, vec1, vec2, *, beta=1, alpha=1, out=None) → Tensor¶

Performs the outer-product of vectors vec1 and vec2 and adds it to the matrix input.

Optional values beta and alpha are scaling factors on the outer product between vec1 and vec2 and the added matrix input respectively.

\text{out} = \beta\ \text{input} + \alpha\ (\text{vec1} \otimes \text{vec2})

If vec1 is a vector of size n and vec2 is a vector of size m, then input must be broadcastable with a matrix of size $(n \times m)$ and out will be a matrix of size $(n \times m)$ .

For inputs of type FloatTensor or DoubleTensor, arguments beta and alpha must be real numbers, otherwise they should be integers

Parameters

input (Tensor) – matrix to be added
vec1 (Tensor) – the first vector of the outer product
vec2 (Tensor) – the second vector of the outer product
beta (Number, optional) – multiplier for input ( $\beta$ )
alpha (Number, optional) – multiplier for $\text{vec1} \otimes \text{vec2}$ ( $\alpha$ )
out (Tensor, optional) – the output tensor.

Example:

>>> vec1 = torch.arange(1., 4.)
>>> vec2 = torch.arange(1., 3.)
>>> M = torch.zeros(3, 2)
>>> torch.addr(M, vec1, vec2)
tensor([[ 1.,  2.],
        [ 2.,  4.],
        [ 3.,  6.]])

torch.baddbmm(input, batch1, batch2, *, beta=1, alpha=1, out=None) → Tensor¶

Performs a batch matrix-matrix product of matrices in batch1 and batch2. input is added to the final result.

batch1 and batch2 must be 3-D tensors each containing the same number of matrices.

If batch1 is a $(b \times n \times m)$ tensor, batch2 is a $(b \times m \times p)$ tensor, then input must be broadcastable with a $(b \times n \times p)$ tensor and out will be a $(b \times n \times p)$ tensor. Both alpha and beta mean the same as the scaling factors used in torch.addbmm().

\text{out}_i = \beta\ \text{input}_i + \alpha\ (\text{batch1}_i \mathbin{@} \text{batch2}_i)

For inputs of type FloatTensor or DoubleTensor, arguments beta and alpha must be real numbers, otherwise they should be integers.

Parameters

input (Tensor) – the tensor to be added
batch1 (Tensor) – the first batch of matrices to be multiplied
batch2 (Tensor) – the second batch of matrices to be multiplied
beta (Number, optional) – multiplier for input ( $\beta$ )
alpha (Number, optional) – multiplier for $\text{batch1} \mathbin{@} \text{batch2}$ ( $\alpha$ )
out (Tensor, optional) – the output tensor.

Example:

>>> M = torch.randn(10, 3, 5)
>>> batch1 = torch.randn(10, 3, 4)
>>> batch2 = torch.randn(10, 4, 5)
>>> torch.baddbmm(M, batch1, batch2).size()
torch.Size([10, 3, 5])

torch.bmm(input, mat2, out=None) → Tensor¶

Performs a batch matrix-matrix product of matrices stored in input and mat2.

input and mat2 must be 3-D tensors each containing the same number of matrices.

If input is a $(b \times n \times m)$ tensor, mat2 is a $(b \times m \times p)$ tensor, out will be a $(b \times n \times p)$ tensor.

\text{out}_i = \text{input}_i \mathbin{@} \text{mat2}_i

Note

This function does not broadcast. For broadcasting matrix products, see torch.matmul().

Parameters

input (Tensor) – the first batch of matrices to be multiplied
mat2 (Tensor) – the second batch of matrices to be multiplied
out (Tensor, optional) – the output tensor.

Example:

>>> input = torch.randn(10, 3, 4)
>>> mat2 = torch.randn(10, 4, 5)
>>> res = torch.bmm(input, mat2)
>>> res.size()
torch.Size([10, 3, 5])

torch.chain_matmul(*matrices)[source]¶

Returns the matrix product of the $N$ 2-D tensors. This product is efficiently computed using the matrix chain order algorithm which selects the order in which incurs the lowest cost in terms of arithmetic operations ([CLRS]). Note that since this is a function to compute the product, $N$ needs to be greater than or equal to 2; if equal to 2 then a trivial matrix-matrix product is returned. If $N$ is 1, then this is a no-op - the original matrix is returned as is.

Parameters: matrices (Tensors...) – a sequence of 2 or more 2-D tensors whose product is to be determined.
Returns: if the $i^{th}$ tensor was of dimensions $p_{i} \times p_{i + 1}$ , then the product would be of dimensions $p_{1} \times p_{N + 1}$ .
Return type: Tensor

Example:

>>> a = torch.randn(3, 4)
>>> b = torch.randn(4, 5)
>>> c = torch.randn(5, 6)
>>> d = torch.randn(6, 7)
>>> torch.chain_matmul(a, b, c, d)
tensor([[ -2.3375,  -3.9790,  -4.1119,  -6.6577,   9.5609, -11.5095,  -3.2614],
        [ 21.4038,   3.3378,  -8.4982,  -5.2457, -10.2561,  -2.4684,   2.7163],
        [ -0.9647,  -5.8917,  -2.3213,  -5.2284,  12.8615, -12.2816,  -2.5095]])

torch.cholesky(input, upper=False, out=None) → Tensor¶

Computes the Cholesky decomposition of a symmetric positive-definite matrix $A$ or for batches of symmetric positive-definite matrices.

If upper is True, the returned matrix U is upper-triangular, and the decomposition has the form:

A = U^TU

If upper is False, the returned matrix L is lower-triangular, and the decomposition has the form:

A = LL^T

If upper is True, and $A$ is a batch of symmetric positive-definite matrices, then the returned tensor will be composed of upper-triangular Cholesky factors of each of the individual matrices. Similarly, when upper is False, the returned tensor will be composed of lower-triangular Cholesky factors of each of the individual matrices.

Parameters

input (Tensor) – the input tensor $A$ of size $(*, n, n)$ where * is zero or more batch dimensions consisting of symmetric positive-definite matrices.
upper (bool, optional) – flag that indicates whether to return a upper or lower triangular matrix. Default: False
out (Tensor, optional) – the output matrix

Example:

>>> a = torch.randn(3, 3)
>>> a = torch.mm(a, a.t()) # make symmetric positive-definite
>>> l = torch.cholesky(a)
>>> a
tensor([[ 2.4112, -0.7486,  1.4551],
        [-0.7486,  1.3544,  0.1294],
        [ 1.4551,  0.1294,  1.6724]])
>>> l
tensor([[ 1.5528,  0.0000,  0.0000],
        [-0.4821,  1.0592,  0.0000],
        [ 0.9371,  0.5487,  0.7023]])
>>> torch.mm(l, l.t())
tensor([[ 2.4112, -0.7486,  1.4551],
        [-0.7486,  1.3544,  0.1294],
        [ 1.4551,  0.1294,  1.6724]])
>>> a = torch.randn(3, 2, 2)
>>> a = torch.matmul(a, a.transpose(-1, -2)) + 1e-03 # make symmetric positive-definite
>>> l = torch.cholesky(a)
>>> z = torch.matmul(l, l.transpose(-1, -2))
>>> torch.max(torch.abs(z - a)) # Max non-zero
tensor(2.3842e-07)

torch.cholesky_inverse(input, upper=False, out=None) → Tensor¶

Computes the inverse of a symmetric positive-definite matrix $A$ using its Cholesky factor $u$ : returns matrix inv. The inverse is computed using LAPACK routines dpotri and spotri (and the corresponding MAGMA routines).

If upper is False, $u$ is lower triangular such that the returned tensor is

inv = (uu^{{T}})^{{-1}}

If upper is True or not provided, $u$ is upper triangular such that the returned tensor is

inv = (u^T u)^{{-1}}

Parameters

input (Tensor) – the input 2-D tensor $u$ , a upper or lower triangular Cholesky factor
upper (bool, optional) – whether to return a lower (default) or upper triangular matrix
out (Tensor, optional) – the output tensor for inv

Example:

>>> a = torch.randn(3, 3)
>>> a = torch.mm(a, a.t()) + 1e-05 * torch.eye(3) # make symmetric positive definite
>>> u = torch.cholesky(a)
>>> a
tensor([[  0.9935,  -0.6353,   1.5806],
        [ -0.6353,   0.8769,  -1.7183],
        [  1.5806,  -1.7183,  10.6618]])
>>> torch.cholesky_inverse(u)
tensor([[ 1.9314,  1.2251, -0.0889],
        [ 1.2251,  2.4439,  0.2122],
        [-0.0889,  0.2122,  0.1412]])
>>> a.inverse()
tensor([[ 1.9314,  1.2251, -0.0889],
        [ 1.2251,  2.4439,  0.2122],
        [-0.0889,  0.2122,  0.1412]])

torch.cholesky_solve(input, input2, upper=False, out=None) → Tensor¶

Solves a linear system of equations with a positive semidefinite matrix to be inverted given its Cholesky factor matrix $u$ .

If upper is False, $u$ is and lower triangular and c is returned such that:

c = (u u^T)^{{-1}} b

If upper is True or not provided, $u$ is upper triangular and c is returned such that:

c = (u^T u)^{{-1}} b

torch.cholesky_solve(b, u) can take in 2D inputs b, u or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs c

Parameters

input (Tensor) – input matrix $b$ of size $(*, m, k)$ , where $*$ is zero or more batch dimensions
input2 (Tensor) – input matrix $u$ of size $(*, m, m)$ , where $*$ is zero of more batch dimensions composed of upper or lower triangular Cholesky factor
upper (bool, optional) – whether to consider the Cholesky factor as a lower or upper triangular matrix. Default: False.
out (Tensor, optional) – the output tensor for c

Example:

>>> a = torch.randn(3, 3)
>>> a = torch.mm(a, a.t()) # make symmetric positive definite
>>> u = torch.cholesky(a)
>>> a
tensor([[ 0.7747, -1.9549,  1.3086],
        [-1.9549,  6.7546, -5.4114],
        [ 1.3086, -5.4114,  4.8733]])
>>> b = torch.randn(3, 2)
>>> b
tensor([[-0.6355,  0.9891],
        [ 0.1974,  1.4706],
        [-0.4115, -0.6225]])
>>> torch.cholesky_solve(b, u)
tensor([[ -8.1625,  19.6097],
        [ -5.8398,  14.2387],
        [ -4.3771,  10.4173]])
>>> torch.mm(a.inverse(), b)
tensor([[ -8.1626,  19.6097],
        [ -5.8398,  14.2387],
        [ -4.3771,  10.4173]])

torch.dot(input, tensor) → Tensor¶

Computes the dot product (inner product) of two tensors.

Note

This function does not broadcast.

Example:

>>> torch.dot(torch.tensor([2, 3]), torch.tensor([2, 1]))
tensor(7)

torch.eig(input, eigenvectors=False, out=None) -> (Tensor, Tensor)¶

Computes the eigenvalues and eigenvectors of a real square matrix.

Note

Since eigenvalues and eigenvectors might be complex, backward pass is supported only for torch.symeig()

Parameters

input (Tensor) – the square matrix of shape $(n \times n)$ for which the eigenvalues and eigenvectors will be computed
eigenvectors (bool) – True to compute both eigenvalues and eigenvectors; otherwise, only eigenvalues will be computed
out (tuple, optional) – the output tensors

Returns

A namedtuple (eigenvalues, eigenvectors) containing

eigenvalues (Tensor): Shape $(n \times 2)$ . Each row is an eigenvalue of input, where the first element is the real part and the second element is the imaginary part. The eigenvalues are not necessarily ordered.

eigenvectors (Tensor): If eigenvectors=False, it’s an empty tensor. Otherwise, this tensor of shape $(n \times n)$ can be used to compute normalized (unit length) eigenvectors of corresponding eigenvalues as follows. If the corresponding eigenvalues[j] is a real number, column eigenvectors[:, j] is the eigenvector corresponding to eigenvalues[j]. If the corresponding eigenvalues[j] and eigenvalues[j + 1] form a complex conjugate pair, then the true eigenvectors can be computed as $\text{true eigenvector}[j] = eigenvectors[:, j] + i \times eigenvectors[:, j + 1]$ , $\text{true eigenvector}[j + 1] = eigenvectors[:, j] - i \times eigenvectors[:, j + 1]$ .

Return type

(Tensor, Tensor)

torch.geqrf(input, out=None) -> (Tensor, Tensor)¶

This is a low-level function for calling LAPACK directly. This function returns a namedtuple (a, tau) as defined in LAPACK documentation for geqrf .

You’ll generally want to use torch.qr() instead.

Computes a QR decomposition of input, but without constructing $Q$ and $R$ as explicit separate matrices.

Rather, this directly calls the underlying LAPACK function ?geqrf which produces a sequence of ‘elementary reflectors’.

See LAPACK documentation for geqrf for further details.

Parameters

input (Tensor) – the input matrix
out (tuple, optional) – the output tuple of (Tensor, Tensor)

torch.ger(input, vec2, out=None) → Tensor¶

Outer product of input and vec2. If input is a vector of size $n$ and vec2 is a vector of size $m$ , then out must be a matrix of size $(n \times m)$ .

Note

This function does not broadcast.

Parameters

input (Tensor) – 1-D input vector
vec2 (Tensor) – 1-D input vector
out (Tensor, optional) – optional output matrix

Example:

>>> v1 = torch.arange(1., 5.)
>>> v2 = torch.arange(1., 4.)
>>> torch.ger(v1, v2)
tensor([[  1.,   2.,   3.],
        [  2.,   4.,   6.],
        [  3.,   6.,   9.],
        [  4.,   8.,  12.]])

torch.inverse(input, out=None) → Tensor¶

Takes the inverse of the square matrix input. input can be batches of 2D square tensors, in which case this function would return a tensor composed of individual inverses.

Note

Irrespective of the original strides, the returned tensors will be transposed, i.e. with strides like input.contiguous().transpose(-2, -1).stride()

Parameters

input (Tensor) – the input tensor of size $(*, n, n)$ where * is zero or more batch dimensions
out (Tensor, optional) – the output tensor.

Example:

>>> x = torch.rand(4, 4)
>>> y = torch.inverse(x)
>>> z = torch.mm(x, y)
>>> z
tensor([[ 1.0000, -0.0000, -0.0000,  0.0000],
        [ 0.0000,  1.0000,  0.0000,  0.0000],
        [ 0.0000,  0.0000,  1.0000,  0.0000],
        [ 0.0000, -0.0000, -0.0000,  1.0000]])
>>> torch.max(torch.abs(z - torch.eye(4))) # Max non-zero
tensor(1.1921e-07)
>>> # Batched inverse example
>>> x = torch.randn(2, 3, 4, 4)
>>> y = torch.inverse(x)
>>> z = torch.matmul(x, y)
>>> torch.max(torch.abs(z - torch.eye(4).expand_as(x))) # Max non-zero
tensor(1.9073e-06)

torch.det(input) → Tensor¶

Calculates determinant of a square matrix or batches of square matrices.

Note

Backward through det() internally uses SVD results when input is not invertible. In this case, double backward through det() will be unstable in when input doesn’t have distinct singular values. See svd() for details.

Parameters: input (Tensor) – the input tensor of size (*, n, n) where * is zero or more batch dimensions.

Example:

>>> A = torch.randn(3, 3)
>>> torch.det(A)
tensor(3.7641)

>>> A = torch.randn(3, 2, 2)
>>> A
tensor([[[ 0.9254, -0.6213],
         [-0.5787,  1.6843]],

        [[ 0.3242, -0.9665],
         [ 0.4539, -0.0887]],

        [[ 1.1336, -0.4025],
         [-0.7089,  0.9032]]])
>>> A.det()
tensor([1.1990, 0.4099, 0.7386])

torch.logdet(input) → Tensor¶

Calculates log determinant of a square matrix or batches of square matrices.

Note

Result is -inf if input has zero log determinant, and is nan if input has negative determinant.

Note

Backward through logdet() internally uses SVD results when input is not invertible. In this case, double backward through logdet() will be unstable in when input doesn’t have distinct singular values. See svd() for details.

Parameters: input (Tensor) – the input tensor of size (*, n, n) where * is zero or more batch dimensions.

Example:

>>> A = torch.randn(3, 3)
>>> torch.det(A)
tensor(0.2611)
>>> torch.logdet(A)
tensor(-1.3430)
>>> A
tensor([[[ 0.9254, -0.6213],
         [-0.5787,  1.6843]],

        [[ 0.3242, -0.9665],
         [ 0.4539, -0.0887]],

        [[ 1.1336, -0.4025],
         [-0.7089,  0.9032]]])
>>> A.det()
tensor([1.1990, 0.4099, 0.7386])
>>> A.det().log()
tensor([ 0.1815, -0.8917, -0.3031])

torch.slogdet(input) -> (Tensor, Tensor)¶

Calculates the sign and log absolute value of the determinant(s) of a square matrix or batches of square matrices.

Note

If input has zero determinant, this returns (0, -inf).

Note

Backward through slogdet() internally uses SVD results when input is not invertible. In this case, double backward through slogdet() will be unstable in when input doesn’t have distinct singular values. See svd() for details.

Parameters: input (Tensor) – the input tensor of size (*, n, n) where * is zero or more batch dimensions.
Returns: A namedtuple (sign, logabsdet) containing the sign of the determinant, and the log value of the absolute determinant.

Example:

>>> A = torch.randn(3, 3)
>>> A
tensor([[ 0.0032, -0.2239, -1.1219],
        [-0.6690,  0.1161,  0.4053],
        [-1.6218, -0.9273, -0.0082]])
>>> torch.det(A)
tensor(-0.7576)
>>> torch.logdet(A)
tensor(nan)
>>> torch.slogdet(A)
torch.return_types.slogdet(sign=tensor(-1.), logabsdet=tensor(-0.2776))

torch.lstsq(input, A, out=None) → Tensor¶

Computes the solution to the least squares and least norm problems for a full rank matrix $A$ of size $(m \times n)$ and a matrix $B$ of size $(m \times k)$ .

If $m \geq n$ , lstsq() solves the least-squares problem:

\begin{array}{ll} \min_X & \|AX-B\|_2. \end{array}

If $m < n$ , lstsq() solves the least-norm problem:

\begin{array}{ll} \min_X & \|X\|_2 & \text{subject to} & AX = B. \end{array}

Returned tensor $X$ has shape $(\max(m, n) \times k)$ . The first $n$ rows of $X$ contains the solution. If $m \geq n$ , the residual sum of squares for the solution in each column is given by the sum of squares of elements in the remaining $m - n$ rows of that column.

Note

The case when $m < n$ is not supported on the GPU.

Parameters

input (Tensor) – the matrix $B$
A (Tensor) – the $m$ by $n$ matrix $A$
out (tuple, optional) – the optional destination tensor

Returns

A namedtuple (solution, QR) containing:

solution (Tensor): the least squares solution

QR (Tensor): the details of the QR factorization

Return type

(Tensor, Tensor)

Note

The returned matrices will always be transposed, irrespective of the strides of the input matrices. That is, they will have stride (1, m) instead of (m, 1).

Example:

>>> A = torch.tensor([[1., 1, 1],
                      [2, 3, 4],
                      [3, 5, 2],
                      [4, 2, 5],
                      [5, 4, 3]])
>>> B = torch.tensor([[-10., -3],
                      [ 12, 14],
                      [ 14, 12],
                      [ 16, 16],
                      [ 18, 16]])
>>> X, _ = torch.lstsq(B, A)
>>> X
tensor([[  2.0000,   1.0000],
        [  1.0000,   1.0000],
        [  1.0000,   2.0000],
        [ 10.9635,   4.8501],
        [  8.9332,   5.2418]])

torch.lu(*args, **kwargs)¶

Computes the LU factorization of a matrix or batches of matrices A. Returns a tuple containing the LU factorization and pivots of A. Pivoting is done if pivot is set to True.

Note

The pivots returned by the function are 1-indexed. If pivot is False, then the returned pivots is a tensor filled with zeros of the appropriate size.

Note

LU factorization with pivot = False is not available for CPU, and attempting to do so will throw an error. However, LU factorization with pivot = False is available for CUDA.

Note

This function does not check if the factorization was successful or not if get_infos is True since the status of the factorization is present in the third element of the return tuple.

Note

In the case of batches of square matrices with size less or equal to 32 on a CUDA device, the LU factorization is repeated for singular matrices due to the bug in the MAGMA library (see magma issue 13).

Parameters

A (Tensor) – the tensor to factor of size $(*, m, n)$
pivot (bool, optional) – controls whether pivoting is done. Default: True
get_infos (bool, optional) – if set to True, returns an info IntTensor. Default: False
out (tuple, optional) – optional output tuple. If get_infos is True, then the elements in the tuple are Tensor, IntTensor, and IntTensor. If get_infos is False, then the elements in the tuple are Tensor, IntTensor. Default: None

Returns

A tuple of tensors containing

factorization (Tensor): the factorization of size $(*, m, n)$

pivots (IntTensor): the pivots of size $(*, m)$

infos (IntTensor, optional): if get_infos is True, this is a tensor of size $(*)$ where non-zero values indicate whether factorization for the matrix or each minibatch has succeeded or failed

Return type

(Tensor, IntTensor, IntTensor (optional))

Example:

>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = torch.lu(A)
>>> A_LU
tensor([[[ 1.3506,  2.5558, -0.0816],
         [ 0.1684,  1.1551,  0.1940],
         [ 0.1193,  0.6189, -0.5497]],

        [[ 0.4526,  1.2526, -0.3285],
         [-0.7988,  0.7175, -0.9701],
         [ 0.2634, -0.9255, -0.3459]]])
>>> pivots
tensor([[ 3,  3,  3],
        [ 3,  3,  3]], dtype=torch.int32)
>>> A_LU, pivots, info = torch.lu(A, get_infos=True)
>>> if info.nonzero().size(0) == 0:
...   print('LU factorization succeeded for all samples!')
LU factorization succeeded for all samples!

torch.lu_solve(input, LU_data, LU_pivots, out=None) → Tensor¶

Returns the LU solve of the linear system $Ax = b$ using the partially pivoted LU factorization of A from torch.lu().

Parameters

b (Tensor) – the RHS tensor of size $(*, m, k)$ , where $*$ is zero or more batch dimensions.
LU_data (Tensor) – the pivoted LU factorization of A from torch.lu() of size $(*, m, m)$ , where $*$ is zero or more batch dimensions.
LU_pivots (IntTensor) – the pivots of the LU factorization from torch.lu() of size $(*, m)$ , where $*$ is zero or more batch dimensions. The batch dimensions of LU_pivots must be equal to the batch dimensions of LU_data.
out (Tensor, optional) – the output tensor.

Example:

>>> A = torch.randn(2, 3, 3)
>>> b = torch.randn(2, 3, 1)
>>> A_LU = torch.lu(A)
>>> x = torch.lu_solve(b, *A_LU)
>>> torch.norm(torch.bmm(A, x) - b)
tensor(1.00000e-07 *
       2.8312)

torch.lu_unpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True)[source]¶

Unpacks the data and pivots from a LU factorization of a tensor.

Returns a tuple of tensors as (the pivots, the L tensor, the U tensor).

Parameters

LU_data (Tensor) – the packed LU factorization data
LU_pivots (Tensor) – the packed LU factorization pivots
unpack_data (bool) – flag indicating if the data should be unpacked
unpack_pivots (bool) – flag indicating if the pivots should be unpacked

Examples:

>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = A.lu()
>>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
>>>
>>> # can recover A from factorization
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))

>>> # LU factorization of a rectangular matrix:
>>> A = torch.randn(2, 3, 2)
>>> A_LU, pivots = A.lu()
>>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
>>> P
tensor([[[1., 0., 0.],
         [0., 1., 0.],
         [0., 0., 1.]],

        [[0., 0., 1.],
         [0., 1., 0.],
         [1., 0., 0.]]])
>>> A_L
tensor([[[ 1.0000,  0.0000],
         [ 0.4763,  1.0000],
         [ 0.3683,  0.1135]],

        [[ 1.0000,  0.0000],
         [ 0.2957,  1.0000],
         [-0.9668, -0.3335]]])
>>> A_U
tensor([[[ 2.1962,  1.0881],
         [ 0.0000, -0.8681]],

        [[-1.0947,  0.3736],
         [ 0.0000,  0.5718]]])
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))
>>> torch.norm(A_ - A)
tensor(2.9802e-08)

torch.matmul(input, other, out=None) → Tensor¶

Matrix product of two tensors.

The behavior depends on the dimensionality of the tensors as follows:

If both tensors are 1-dimensional, the dot product (scalar) is returned.
If both arguments are 2-dimensional, the matrix-matrix product is returned.
If the first argument is 1-dimensional and the second argument is 2-dimensional, a 1 is prepended to its dimension for the purpose of the matrix multiply. After the matrix multiply, the prepended dimension is removed.
If the first argument is 2-dimensional and the second argument is 1-dimensional, the matrix-vector product is returned.
If both arguments are at least 1-dimensional and at least one argument is N-dimensional (where N > 2), then a batched matrix multiply is returned. If the first argument is 1-dimensional, a 1 is prepended to its dimension for the purpose of the batched matrix multiply and removed after. If the second argument is 1-dimensional, a 1 is appended to its dimension for the purpose of the batched matrix multiple and removed after. The non-matrix (i.e. batch) dimensions are broadcasted (and thus must be broadcastable). For example, if input is a $(j \times 1 \times n \times m)$ tensor and other is a $(k \times m \times p)$ tensor, out will be an $(j \times k \times n \times p)$ tensor.

Note

The 1-dimensional dot product version of this function does not support an out parameter.

Parameters

input (Tensor) – the first tensor to be multiplied
other (Tensor) – the second tensor to be multiplied
out (Tensor, optional) – the output tensor.

Example:

>>> # vector x vector
>>> tensor1 = torch.randn(3)
>>> tensor2 = torch.randn(3)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([])
>>> # matrix x vector
>>> tensor1 = torch.randn(3, 4)
>>> tensor2 = torch.randn(4)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([3])
>>> # batched matrix x broadcasted vector
>>> tensor1 = torch.randn(10, 3, 4)
>>> tensor2 = torch.randn(4)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([10, 3])
>>> # batched matrix x batched matrix
>>> tensor1 = torch.randn(10, 3, 4)
>>> tensor2 = torch.randn(10, 4, 5)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([10, 3, 5])
>>> # batched matrix x broadcasted matrix
>>> tensor1 = torch.randn(10, 3, 4)
>>> tensor2 = torch.randn(4, 5)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([10, 3, 5])

torch.matrix_power(input, n) → Tensor¶

Returns the matrix raised to the power n for square matrices. For batch of matrices, each individual matrix is raised to the power n.

If n is negative, then the inverse of the matrix (if invertible) is raised to the power n. For a batch of matrices, the batched inverse (if invertible) is raised to the power n. If n is 0, then an identity matrix is returned.

Parameters

input (Tensor) – the input tensor.
n (int) – the power to raise the matrix to

Example:

>>> a = torch.randn(2, 2, 2)
>>> a
tensor([[[-1.9975, -1.9610],
         [ 0.9592, -2.3364]],

        [[-1.2534, -1.3429],
         [ 0.4153, -1.4664]]])
>>> torch.matrix_power(a, 3)
tensor([[[  3.9392, -23.9916],
         [ 11.7357,  -0.2070]],

        [[  0.2468,  -6.7168],
         [  2.0774,  -0.8187]]])

torch.matrix_rank(input, tol=None, symmetric=False) → Tensor¶

Returns the numerical rank of a 2-D tensor. The method to compute the matrix rank is done using SVD by default. If symmetric is True, then input is assumed to be symmetric, and the computation of the rank is done by obtaining the eigenvalues.

tol is the threshold below which the singular values (or the eigenvalues when symmetric is True) are considered to be 0. If tol is not specified, tol is set to S.max() * max(S.size()) * eps where S is the singular values (or the eigenvalues when symmetric is True), and eps is the epsilon value for the datatype of input.

Parameters

input (Tensor) – the input 2-D tensor
tol (float, optional) – the tolerance value. Default: None
symmetric (bool, optional) – indicates whether input is symmetric. Default: False

Example:

>>> a = torch.eye(10)
>>> torch.matrix_rank(a)
tensor(10)
>>> b = torch.eye(10)
>>> b[0, 0] = 0
>>> torch.matrix_rank(b)
tensor(9)

torch.mm(input, mat2, out=None) → Tensor¶

Performs a matrix multiplication of the matrices input and mat2.

If input is a $(n \times m)$ tensor, mat2 is a $(m \times p)$ tensor, out will be a $(n \times p)$ tensor.

Note

This function does not broadcast. For broadcasting matrix products, see torch.matmul().

Parameters

input (Tensor) – the first matrix to be multiplied
mat2 (Tensor) – the second matrix to be multiplied
out (Tensor, optional) – the output tensor.

Example:

>>> mat1 = torch.randn(2, 3)
>>> mat2 = torch.randn(3, 3)
>>> torch.mm(mat1, mat2)
tensor([[ 0.4851,  0.5037, -0.3633],
        [-0.0760, -3.6705,  2.4784]])

torch.mv(input, vec, out=None) → Tensor¶

Performs a matrix-vector product of the matrix input and the vector vec.

If input is a $(n \times m)$ tensor, vec is a 1-D tensor of size $m$ , out will be 1-D of size $n$ .

Note

This function does not broadcast.

Parameters

input (Tensor) – matrix to be multiplied
vec (Tensor) – vector to be multiplied
out (Tensor, optional) – the output tensor.

Example:

>>> mat = torch.randn(2, 3)
>>> vec = torch.randn(3)
>>> torch.mv(mat, vec)
tensor([ 1.0404, -0.6361])

torch.orgqr(input, input2) → Tensor¶

Computes the orthogonal matrix Q of a QR factorization, from the (input, input2) tuple returned by torch.geqrf().

This directly calls the underlying LAPACK function ?orgqr. See LAPACK documentation for orgqr for further details.

Parameters

input (Tensor) – the a from torch.geqrf().
input2 (Tensor) – the tau from torch.geqrf().

torch.ormqr(input, input2, input3, left=True, transpose=False) → Tensor¶

Multiplies mat (given by input3) by the orthogonal Q matrix of the QR factorization formed by torch.geqrf() that is represented by (a, tau) (given by (input, input2)).

This directly calls the underlying LAPACK function ?ormqr. See LAPACK documentation for ormqr for further details.

Parameters

input (Tensor) – the a from torch.geqrf().
input2 (Tensor) – the tau from torch.geqrf().
input3 (Tensor) – the matrix to be multiplied.

torch.pinverse(input, rcond=1e-15) → Tensor¶

Calculates the pseudo-inverse (also known as the Moore-Penrose inverse) of a 2D tensor. Please look at Moore-Penrose inverse for more details

Note

This method is implemented using the Singular Value Decomposition.

Note

The pseudo-inverse is not necessarily a continuous function in the elements of the matrix [1]. Therefore, derivatives are not always existent, and exist for a constant rank only [2]. However, this method is backprop-able due to the implementation by using SVD results, and could be unstable. Double-backward will also be unstable due to the usage of SVD internally. See svd() for more details.

Parameters

input (Tensor) – The input tensor of size $(*, m, n)$ where $*$ is zero or more batch dimensions
rcond (float) – A floating point value to determine the cutoff for small singular values. Default: 1e-15

Returns

The pseudo-inverse of input of dimensions $(*, n, m)$

Example:

>>> input = torch.randn(3, 5)
>>> input
tensor([[ 0.5495,  0.0979, -1.4092, -0.1128,  0.4132],
        [-1.1143, -0.3662,  0.3042,  1.6374, -0.9294],
        [-0.3269, -0.5745, -0.0382, -0.5922, -0.6759]])
>>> torch.pinverse(input)
tensor([[ 0.0600, -0.1933, -0.2090],
        [-0.0903, -0.0817, -0.4752],
        [-0.7124, -0.1631, -0.2272],
        [ 0.1356,  0.3933, -0.5023],
        [-0.0308, -0.1725, -0.5216]])
>>> # Batched pinverse example
>>> a = torch.randn(2,6,3)
>>> b = torch.pinverse(a)
>>> torch.matmul(b, a)
tensor([[[ 1.0000e+00,  1.6391e-07, -1.1548e-07],
        [ 8.3121e-08,  1.0000e+00, -2.7567e-07],
        [ 3.5390e-08,  1.4901e-08,  1.0000e+00]],

        [[ 1.0000e+00, -8.9407e-08,  2.9802e-08],
        [-2.2352e-07,  1.0000e+00,  1.1921e-07],
        [ 0.0000e+00,  8.9407e-08,  1.0000e+00]]])

torch.qr(input, some=True, out=None) -> (Tensor, Tensor)¶

Computes the QR decomposition of a matrix or a batch of matrices input, and returns a namedtuple (Q, R) of tensors such that $\text{input} = Q R$ with $Q$ being an orthogonal matrix or batch of orthogonal matrices and $R$ being an upper triangular matrix or batch of upper triangular matrices.

If some is True, then this function returns the thin (reduced) QR factorization. Otherwise, if some is False, this function returns the complete QR factorization.

Note

precision may be lost if the magnitudes of the elements of input are large

Note

While it should always give you a valid decomposition, it may not give you the same one across platforms - it will depend on your LAPACK implementation.

Parameters

input (Tensor) – the input tensor of size $(*, m, n)$ where * is zero or more batch dimensions consisting of matrices of dimension $m \times n$ .
some (bool, optional) – Set to True for reduced QR decomposition and False for complete QR decomposition.
out (tuple, optional) – tuple of Q and R tensors satisfying input = torch.matmul(Q, R). The dimensions of Q and R are $(*, m, k)$ and $(*, k, n)$ respectively, where $k = \min(m, n)$ if some: is True and $k = m$ otherwise.

Example:

>>> a = torch.tensor([[12., -51, 4], [6, 167, -68], [-4, 24, -41]])
>>> q, r = torch.qr(a)
>>> q
tensor([[-0.8571,  0.3943,  0.3314],
        [-0.4286, -0.9029, -0.0343],
        [ 0.2857, -0.1714,  0.9429]])
>>> r
tensor([[ -14.0000,  -21.0000,   14.0000],
        [   0.0000, -175.0000,   70.0000],
        [   0.0000,    0.0000,  -35.0000]])
>>> torch.mm(q, r).round()
tensor([[  12.,  -51.,    4.],
        [   6.,  167.,  -68.],
        [  -4.,   24.,  -41.]])
>>> torch.mm(q.t(), q).round()
tensor([[ 1.,  0.,  0.],
        [ 0.,  1., -0.],
        [ 0., -0.,  1.]])
>>> a = torch.randn(3, 4, 5)
>>> q, r = torch.qr(a, some=False)
>>> torch.allclose(torch.matmul(q, r), a)
True
>>> torch.allclose(torch.matmul(q.transpose(-2, -1), q), torch.eye(5))
True

torch.solve(input, A, out=None) -> (Tensor, Tensor)¶

This function returns the solution to the system of linear equations represented by $AX = B$ and the LU factorization of A, in order as a namedtuple solution, LU.

LU contains L and U factors for LU factorization of A.

torch.solve(B, A) can take in 2D inputs B, A or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs solution, LU.

Note

Irrespective of the original strides, the returned matrices solution and LU will be transposed, i.e. with strides like B.contiguous().transpose(-1, -2).stride() and A.contiguous().transpose(-1, -2).stride() respectively.

Parameters

input (Tensor) – input matrix $B$ of size $(*, m, k)$ , where $*$ is zero or more batch dimensions.
A (Tensor) – input square matrix of size $(*, m, m)$ , where $*$ is zero or more batch dimensions.
out ((Tensor, Tensor), optional) – optional output tuple.

Example:

>>> A = torch.tensor([[6.80, -2.11,  5.66,  5.97,  8.23],
                      [-6.05, -3.30,  5.36, -4.44,  1.08],
                      [-0.45,  2.58, -2.70,  0.27,  9.04],
                      [8.32,  2.71,  4.35,  -7.17,  2.14],
                      [-9.67, -5.14, -7.26,  6.08, -6.87]]).t()
>>> B = torch.tensor([[4.02,  6.19, -8.22, -7.57, -3.03],
                      [-1.56,  4.00, -8.67,  1.75,  2.86],
                      [9.81, -4.09, -4.57, -8.61,  8.99]]).t()
>>> X, LU = torch.solve(B, A)
>>> torch.dist(B, torch.mm(A, X))
tensor(1.00000e-06 *
       7.0977)

>>> # Batched solver example
>>> A = torch.randn(2, 3, 1, 4, 4)
>>> B = torch.randn(2, 3, 1, 4, 6)
>>> X, LU = torch.solve(B, A)
>>> torch.dist(B, A.matmul(X))
tensor(1.00000e-06 *
   3.6386)

torch.svd(input, some=True, compute_uv=True, out=None) -> (Tensor, Tensor, Tensor)¶

This function returns a namedtuple (U, S, V) which is the singular value decomposition of a input real matrix or batches of real matrices input such that $input = U \times diag(S) \times V^T$ .

If some is True (default), the method returns the reduced singular value decomposition i.e., if the last two dimensions of input are m and n, then the returned U and V matrices will contain only $min(n, m)$ orthonormal columns.

If compute_uv is False, the returned U and V matrices will be zero matrices of shape $(m \times m)$ and $(n \times n)$ respectively. some will be ignored here.

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 divide-and-conquer algorithm) instead of ?gesvd for speed. Analogously, the SVD on GPU uses the MAGMA routine gesdd as well.

Note

Irrespective of the original strides, the returned matrix U will be transposed, i.e. with strides U.contiguous().transpose(-2, -1).stride()

Note

Extra care needs to be taken when backward through U and V outputs. Such operation is really only stable when input is full rank with all distinct singular values. Otherwise, NaN can appear as the gradients are not properly defined. Also, notice that double backward will usually do an additional backward through U and V even if the original backward is only on S.

Note

When some = False, the gradients on U[..., :, min(m, n):] and V[..., :, min(m, n):] will be ignored in backward as those vectors can be arbitrary bases of the subspaces.

Note

When compute_uv = False, backward cannot be performed since U and V from the forward pass is required for the backward operation.

Parameters

input (Tensor) – the input tensor of size $(*, m, n)$ where * is zero or more batch dimensions consisting of $m \times n$ matrices.
some (bool, optional) – controls the shape of returned U and V
compute_uv (bool, optional) – option whether to compute U and V or not
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(8.6531e-07)
>>> 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(2.6503e-06)

torch.svd_lowrank(A, q=6, niter=2, M=None)[source]¶

Return the singular value decomposition (U, S, V) of a matrix, batches of matrices, or a sparse matrix $A$ such that . In case $M$ is given, then SVD is computed for the matrix $A - M$ .

Note

The implementation is based on the Algorithm 5.1 from Halko et al, 2009.

Note

To obtain repeatable results, reset the seed for the pseudorandom number generator

Note

The input is assumed to be a low-rank matrix.

Note

In general, use the full-rank SVD implementation torch.svd for dense matrices due to its 10-fold higher performance characteristics. The low-rank SVD will be useful for huge sparse matrices that torch.svd cannot handle.

Arguments::

A (Tensor): the input tensor of size $(*, m, n)$

q (int, optional): a slightly overestimated rank of A.

niter (int, optional): the number of subspace iterations to: conduct; niter must be a nonnegative integer, and defaults to 2
M (Tensor, optional): the input tensor’s mean of size: $(*, 1, n)$ .

References::

Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp, Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions, arXiv:0909.4061 [math.NA; math.PR], 2009 (available at arXiv).

torch.pca_lowrank(A, q=None, center=True, niter=2)[source]¶

Performs linear Principal Component Analysis (PCA) on a low-rank matrix, batches of such matrices, or sparse matrix.

This function returns a namedtuple (U, S, V) which is the nearly optimal approximation of a singular value decomposition of a centered matrix $A$ such that $A = U diag(S) V^T$ .

Note

The relation of (U, S, V) to PCA is as follows:

$A$ is a data matrix with m samples and n features
the $V$ columns represent the principal directions
$S ** 2 / (m - 1)$ contains the eigenvalues of $A^T A / (m - 1)$ which is the covariance of A when center=True is provided.
matmul(A, V[:, :k]) projects data to the first k principal components

Note

Different from the standard SVD, the size of returned matrices depend on the specified rank and q values as follows:

$U$ is m x q matrix

$S$ is q-vector

$V$ is n x q matrix

Note

To obtain repeatable results, reset the seed for the pseudorandom number generator

Parameters

A (Tensor) – the input tensor of size $(*, m, n)$
q (int, optional) – a slightly overestimated rank of $A$ . By default, q = min(6, m, n).
center (bool, optional) – if True, center the input tensor, otherwise, assume that the input is centered.
niter (int, optional) – the number of subspace iterations to conduct; niter must be a nonnegative integer, and defaults to 2.

References:

- Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp, Finding
  structure with randomness: probabilistic algorithms for
  constructing approximate matrix decompositions,
  arXiv:0909.4061 [math.NA; math.PR], 2009 (available at
  `arXiv <http://arxiv.org/abs/0909.4061>`_).

torch.symeig(input, eigenvectors=False, upper=True, out=None) -> (Tensor, Tensor)¶

This function returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices, represented by a namedtuple (eigenvalues, eigenvectors).

This function calculates all eigenvalues (and vectors) of input such that $\text{input} = V \text{diag}(e) V^T$ .

The boolean argument eigenvectors defines computation of both eigenvectors and eigenvalues or eigenvalues only.

If it is False, only eigenvalues are computed. If it is True, both eigenvalues and eigenvectors are computed.

Since the input matrix input is supposed to be symmetric, only the upper triangular portion is used by default.

If upper is False, then lower triangular portion is used.

Note

The eigenvalues are returned in ascending order. If input is a batch of matrices, then the eigenvalues of each matrix in the batch is returned in ascending order.

Note

Irrespective of the original strides, the returned matrix V will be transposed, i.e. with strides V.contiguous().transpose(-1, -2).stride().

Note

Extra care needs to be taken when backward through outputs. Such operation is really only stable when all eigenvalues are distinct. Otherwise, NaN can appear as the gradients are not properly defined.

Parameters

input (Tensor) – the input tensor of size $(*, n, n)$ where * is zero or more batch dimensions consisting of symmetric matrices.
eigenvectors (boolean, optional) – controls whether eigenvectors have to be computed
upper (boolean, optional) – controls whether to consider upper-triangular or lower-triangular region
out (tuple, optional) – the output tuple of (Tensor, Tensor)

Returns

A namedtuple (eigenvalues, eigenvectors) containing

eigenvalues (Tensor): Shape $(*, m)$ . The eigenvalues in ascending order.

eigenvectors (Tensor): Shape $(*, m, m)$ . If eigenvectors=False, it’s an empty tensor. Otherwise, this tensor contains the orthonormal eigenvectors of the input.

Return type

(Tensor, Tensor)

Examples:

>>> a = torch.randn(5, 5)
>>> a = a + a.t()  # To make a symmetric
>>> a
tensor([[-5.7827,  4.4559, -0.2344, -1.7123, -1.8330],
        [ 4.4559,  1.4250, -2.8636, -3.2100, -0.1798],
        [-0.2344, -2.8636,  1.7112, -5.5785,  7.1988],
        [-1.7123, -3.2100, -5.5785, -2.6227,  3.1036],
        [-1.8330, -0.1798,  7.1988,  3.1036, -5.1453]])
>>> e, v = torch.symeig(a, eigenvectors=True)
>>> e
tensor([-13.7012,  -7.7497,  -2.3163,   5.2477,   8.1050])
>>> v
tensor([[ 0.1643,  0.9034, -0.0291,  0.3508,  0.1817],
        [-0.2417, -0.3071, -0.5081,  0.6534,  0.4026],
        [-0.5176,  0.1223, -0.0220,  0.3295, -0.7798],
        [-0.4850,  0.2695, -0.5773, -0.5840,  0.1337],
        [ 0.6415, -0.0447, -0.6381, -0.0193, -0.4230]])
>>> a_big = torch.randn(5, 2, 2)
>>> a_big = a_big + a_big.transpose(-2, -1)  # To make a_big symmetric
>>> e, v = a_big.symeig(eigenvectors=True)
>>> torch.allclose(torch.matmul(v, torch.matmul(e.diag_embed(), v.transpose(-2, -1))), a_big)
True

torch.lobpcg(A, k=None, B=None, X=None, n=None, iK=None, niter=None, tol=None, largest=None, method=None, tracker=None, ortho_iparams=None, ortho_fparams=None, ortho_bparams=None)[source]¶

Find the k largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric positive defined generalized eigenvalue problem using matrix-free LOBPCG methods.

This function is a front-end to the following LOBPCG algorithms selectable via method argument:

method=”basic” - the LOBPCG method introduced by Andrew Knyazev, see [Knyazev2001]. A less robust method, may fail when Cholesky is applied to singular input.

method=”ortho” - the LOBPCG method with orthogonal basis selection [StathopoulosEtal2002]. A robust method.

Supported inputs are dense, sparse, and batches of dense matrices.

Note

In general, the basic method spends least time per iteration. However, the robust methods converge much faster and are more stable. So, the usage of the basic method is generally not recommended but there exist cases where the usage of the basic method may be preferred.

Parameters

A (Tensor) – the input tensor of size $(*, m, m)$
B (Tensor, optional) – the input tensor of size $(*, m, m)$ . When not specified, B is interpereted as identity matrix.
X (tensor, optional) – the input tensor of size $(*, m, n)$ where k <= n <= m. When specified, it is used as initial approximation of eigenvectors. X must be a dense tensor.
iK (tensor, optional) – the input tensor of size $(*, m, m)$ . When specified, it will be used as preconditioner.
k (integer, optional) – the number of requested eigenpairs. Default is the number of $X$ columns (when specified) or 1.
n (integer, optional) – if $X$ is not specified then n specifies the size of the generated random approximation of eigenvectors. Default value for n is k. If $X$ is specifed, the value of n (when specified) must be the number of $X$ columns.
tol (float, optional) – residual tolerance for stopping criterion. Default is feps ** 0.5 where feps is smallest non-zero floating-point number of the given input tensor A data type.
largest (bool, optional) – when True, solve the eigenproblem for the largest eigenvalues. Otherwise, solve the eigenproblem for smallest eigenvalues. Default is True.
method (str, optional) – select LOBPCG method. See the description of the function above. Default is “ortho”.
niter (int, optional) – maximum number of iterations. When reached, the iteration process is hard-stopped and the current approximation of eigenpairs is returned. For infinite iteration but until convergence criteria is met, use -1.
tracker (callable, optional) –
a function for tracing the iteration process. When specified, it is called at each iteration step with LOBPCG instance as an argument. The LOBPCG instance holds the full state of the iteration process in the following attributes:

iparams, fparams, bparams - dictionaries of integer, float, and boolean valued input parameters, respectively

ivars, fvars, bvars, tvars - dictionaries of integer, float, boolean, and Tensor valued iteration variables, respectively.

A, B, iK - input Tensor arguments.

E, X, S, R - iteration Tensor variables.

For instance:

ivars[“istep”] - the current iteration step X - the current approximation of eigenvectors E - the current approximation of eigenvalues R - the current residual ivars[“converged_count”] - the current number of converged eigenpairs tvars[“rerr”] - the current state of convergence criteria

Note that when tracker stores Tensor objects from the LOBPCG instance, it must make copies of these.

If tracker sets bvars[“force_stop”] = True, the iteration process will be hard-stopped.
ortho_fparams, ortho_bparams (ortho_iparams,) – various parameters to LOBPCG algorithm when using method=”ortho”.

Returns

tensor of eigenvalues of size $(*, k)$

X (Tensor): tensor of eigenvectors of size $(*, m, k)$

Return type

E (Tensor)

References

[Knyazev2001] Andrew V. Knyazev. (2001) Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method. SIAM J. Sci. Comput., 23(2), 517-541. (25 pages) `https://epubs.siam.org/doi/abs/10.1137/S1064827500366124`_

[StathopoulosEtal2002] Andreas Stathopoulos and Kesheng Wu. (2002) A Block Orthogonalization Procedure with Constant Synchronization Requirements. SIAM J. Sci. Comput., 23(6), 2165-2182. (18 pages) `https://epubs.siam.org/doi/10.1137/S1064827500370883`_

[DuerschEtal2018] Jed A. Duersch, Meiyue Shao, Chao Yang, Ming Gu. (2018) A Robust and Efficient Implementation of LOBPCG. SIAM J. Sci. Comput., 40(5), C655-C676. (22 pages) `https://epubs.siam.org/doi/abs/10.1137/17M1129830`_

torch.trapz()¶

torch.trapz(y, x, *, dim=-1) → Tensor

Estimate $\int y\,dx$ along dim, using the trapezoid rule.

Parameters

y (Tensor) – The values of the function to integrate
x (Tensor) – The points at which the function y is sampled. If x is not in ascending order, intervals on which it is decreasing contribute negatively to the estimated integral (i.e., the convention $\int_a^b f = -\int_b^a f$ is followed).
dim (int) – The dimension along which to integrate. By default, use the last dimension.

Returns

A Tensor with the same shape as the input, except with dim removed. Each element of the returned tensor represents the estimated integral $\int y\,dx$ along dim.

Example:

>>> y = torch.randn((2, 3))
>>> y
tensor([[-2.1156,  0.6857, -0.2700],
        [-1.2145,  0.5540,  2.0431]])
>>> x = torch.tensor([[1, 3, 4], [1, 2, 3]])
>>> torch.trapz(y, x)
tensor([-1.2220,  0.9683])

torch.trapz(y, *, dx=1, dim=-1) → Tensor

As above, but the sample points are spaced uniformly at a distance of dx.

Parameters

y (Tensor) – The values of the function to integrate
dx (float) – The distance between points at which y is sampled.
dim (int) – The dimension along which to integrate. By default, use the last dimension.

Returns

A Tensor with the same shape as the input, except with dim removed. Each element of the returned tensor represents the estimated integral $\int y\,dx$ along dim.

torch.triangular_solve(input, A, upper=True, transpose=False, unitriangular=False) -> (Tensor, Tensor)¶

Solves a system of equations with a triangular coefficient matrix $A$ and multiple right-hand sides $b$ .

In particular, solves $AX = b$ and assumes $A$ is upper-triangular with the default keyword arguments.

torch.triangular_solve(b, A) can take in 2D inputs b, A or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs X

Parameters

input (Tensor) – multiple right-hand sides of size $(*, m, k)$ where $*$ is zero of more batch dimensions ( $b$ )
A (Tensor) – the input triangular coefficient matrix of size $(*, m, m)$ where $*$ is zero or more batch dimensions
upper (bool, optional) – whether to solve the upper-triangular system of equations (default) or the lower-triangular system of equations. Default: True.
transpose (bool, optional) – whether $A$ should be transposed before being sent into the solver. Default: False.
unitriangular (bool, optional) – whether $A$ is unit triangular. If True, the diagonal elements of $A$ are assumed to be 1 and not referenced from $A$ . Default: False.

Returns

A namedtuple (solution, cloned_coefficient) where cloned_coefficient is a clone of $A$ and solution is the solution $X$ to $AX = b$ (or whatever variant of the system of equations, depending on the keyword arguments.)

Examples:

>>> A = torch.randn(2, 2).triu()
>>> A
tensor([[ 1.1527, -1.0753],
        [ 0.0000,  0.7986]])
>>> b = torch.randn(2, 3)
>>> b
tensor([[-0.0210,  2.3513, -1.5492],
        [ 1.5429,  0.7403, -1.0243]])
>>> torch.triangular_solve(b, A)
torch.return_types.triangular_solve(
solution=tensor([[ 1.7841,  2.9046, -2.5405],
        [ 1.9320,  0.9270, -1.2826]]),
cloned_coefficient=tensor([[ 1.1527, -1.0753],
        [ 0.0000,  0.7986]]))

Utilities¶

torch.compiled_with_cxx11_abi()[source]¶: Returns whether PyTorch was built with _GLIBCXX_USE_CXX11_ABI=1

torch.result_type(tensor1, tensor2) → dtype¶

Returns the torch.dtype that would result from performing an arithmetic operation on the provided input tensors. See type promotion documentation for more information on the type promotion logic.

Parameters

tensor1 (Tensor or Number) – an input tensor or number
tensor2 (Tensor or Number) – an input tensor or number

Example:

>>> torch.result_type(torch.tensor([1, 2], dtype=torch.int), 1.0)
torch.float32
>>> torch.result_type(torch.tensor([1, 2], dtype=torch.uint8), torch.tensor(1))
torch.uint8

torch.can_cast(from, to) → bool¶

Determines if a type conversion is allowed under PyTorch casting rules described in the type promotion documentation.

Parameters

from (dpython:type) – The original torch.dtype.
to (dpython:type) – The target torch.dtype.

Example:

>>> torch.can_cast(torch.double, torch.float)
True
>>> torch.can_cast(torch.float, torch.int)
False

torch.promote_types(type1, type2) → dtype¶

Returns the torch.dtype with the smallest size and scalar kind that is not smaller nor of lower kind than either type1 or type2. See type promotion documentation for more information on the type promotion logic.

Parameters

type1 (torch.dtype) –
type2 (torch.dtype) –

Example:

>>> torch.promote_types(torch.int32, torch.float32))
torch.float32
>>> torch.promote_types(torch.uint8, torch.long)
torch.long

torch¶

Tensors¶

Creation Ops¶

Indexing, Slicing, Joining, Mutating Ops¶

Generators¶

Random sampling¶

In-place random sampling¶

Quasi-random sampling¶

Serialization¶

Parallelism¶

Locally disabling gradient computation¶

Math operations¶

Pointwise Ops¶

Reduction Ops¶

Comparison Ops¶

Spectral Ops¶

Other Operations¶

BLAS and LAPACK Operations¶

Utilities¶

Docs

Tutorials

Resources

ord	matrix norm	vector norm
None	Frobenius norm	2-norm
’fro’	Frobenius norm	–
‘nuc’	nuclear norm	–
Other	as vec norm when dim is None	sum(abs(x)ord)(1./ord)