import torch import torch.nn.functional as F from torch._six import inf from operator import mul from functools import reduce import math import warnings __all__ = [ 'argmax', 'argmin', 'argsort', 'btriunpack', 'chain_matmul', 'einsum', 'broadcast_tensors', 'isfinite', 'isinf', 'isnan', 'norm', 'meshgrid', 'potrf', 'split', 'stft', 'tensordot', 'unique', ] def broadcast_tensors(*tensors): r"""broadcast_tensors(*tensors) -> List of Tensors Broadcasts the given tensors according to :ref:`_broadcasting-semantics`. Args: *tensors: any number of tensors of the same type 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]]) """ return torch._C._VariableFunctions.broadcast_tensors(tensors) def split(tensor, split_size_or_sections, dim=0): r"""Splits the tensor into chunks. If :attr:`split_size_or_sections` is an integer type, then :attr:`tensor` will be split into equally sized chunks (if possible). Last chunk will be smaller if the tensor size along the given dimension :attr:`dim` is not divisible by :attr:`split_size`. If :attr:`split_size_or_sections` is a list, then :attr:`tensor` will be split into ``len(split_size_or_sections)`` chunks with sizes in :attr:`dim` according to :attr:`split_size_or_sections`. Arguments: 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. """ # Overwriting reason: # This dispatches to two ATen functions depending on the type of # split_size_or_sections. The branching code is in tensor.py, which we # call here. return tensor.split(split_size_or_sections, dim) def btriunpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True): r"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor. Returns a tuple of tensors as ``(the pivots, the L tensor, the U tensor)``. Arguments: 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 Example:: >>> A = torch.randn(2, 3, 3) >>> A_LU, pivots = A.btrifact() >>> P, A_L, A_U = torch.btriunpack(A_LU, pivots) >>> >>> # can recover A from factorization >>> A_ = torch.bmm(P, torch.bmm(A_L, A_U)) """ nBatch, sz, _ = LU_data.size() if unpack_data: I_U = torch.triu(torch.ones(sz, sz)).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz) I_L = 1 - I_U L = LU_data.new(LU_data.size()).zero_() U = LU_data.new(LU_data.size()).zero_() I_diag = torch.eye(sz).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz) L[I_diag] = 1.0 L[I_L] = LU_data[I_L] U[I_U] = LU_data[I_U] else: L = U = None if unpack_pivots: P = torch.eye(sz).type_as(LU_data).unsqueeze(0).repeat(nBatch, 1, 1) for i in range(nBatch): for j in range(sz): k = int(LU_pivots[i, j] - 1) t = P[i, :, j].clone() P[i, :, j] = P[i, :, k] P[i, :, k] = t else: P = None return P, L, U def einsum(equation, *operands): r"""einsum(equation, *operands) -> Tensor This function provides a way of computing multilinear expressions (i.e. sums of products) using the Einstein summation convention. Args: equation (string): The equation is given in terms of lower case letters (indices) to be associated with each dimension of the operands and result. The left hand side lists the operands dimensions, separated by commas. There should be one index letter per tensor dimension. The right hand side follows after `->` and gives the indices for the output. If the `->` and right hand side are omitted, it implicitly defined as the alphabetically sorted list of all indices appearing exactly once in the left hand side. The indices not apprearing in the output are summed over after multiplying the operands entries. If an index appears several times for the same operand, a diagonal is taken. Ellipses `...` represent a fixed number of dimensions. If the right hand side is inferred, the ellipsis dimensions are at the beginning of the output. operands (list of Tensors): The operands to compute the Einstein sum of. Note that the operands are passed as a list, not as individual arguments. Examples:: >>> x = torch.randn(5) >>> y = torch.randn(4) >>> torch.einsum('i,j->ij', x, y) # outer product tensor([[-0.0570, -0.0286, -0.0231, 0.0197], [ 1.2616, 0.6335, 0.5113, -0.4351], [ 1.4452, 0.7257, 0.5857, -0.4984], [-0.4647, -0.2333, -0.1883, 0.1603], [-1.1130, -0.5588, -0.4510, 0.3838]]) >>> A = torch.randn(3,5,4) >>> l = torch.randn(2,5) >>> r = torch.randn(2,4) >>> torch.einsum('bn,anm,bm->ba', l, A, r) # compare torch.nn.functional.bilinear tensor([[-0.3430, -5.2405, 0.4494], [ 0.3311, 5.5201, -3.0356]]) >>> As = torch.randn(3,2,5) >>> Bs = torch.randn(3,5,4) >>> torch.einsum('bij,bjk->bik', As, Bs) # batch matrix multiplication tensor([[[-1.0564, -1.5904, 3.2023, 3.1271], [-1.6706, -0.8097, -0.8025, -2.1183]], [[ 4.2239, 0.3107, -0.5756, -0.2354], [-1.4558, -0.3460, 1.5087, -0.8530]], [[ 2.8153, 1.8787, -4.3839, -1.2112], [ 0.3728, -2.1131, 0.0921, 0.8305]]]) >>> A = torch.randn(3, 3) >>> torch.einsum('ii->i', A) # diagonal tensor([-0.7825, 0.8291, -0.1936]) >>> A = torch.randn(4, 3, 3) >>> torch.einsum('...ii->...i', A) # batch diagonal tensor([[-1.0864, 0.7292, 0.0569], [-0.9725, -1.0270, 0.6493], [ 0.5832, -1.1716, -1.5084], [ 0.4041, -1.1690, 0.8570]]) >>> A = torch.randn(2, 3, 4, 5) >>> torch.einsum('...ij->...ji', A).shape # batch permute torch.Size([2, 3, 5, 4]) """ if len(operands) == 1 and isinstance(operands[0], (list, tuple)): # the old interface of passing the operands as one list argument operands = operands[0] return torch._C._VariableFunctions.einsum(equation, operands) def isfinite(tensor): r"""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.ByteTensor`` containing a 1 at each location of finite elements and 0 otherwise Example:: >>> torch.isfinite(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')])) tensor([ 1, 0, 1, 0, 0], dtype=torch.uint8) """ if not isinstance(tensor, torch.Tensor): raise ValueError("The argument is not a tensor", str(tensor)) # Support int input, nan and inf are concepts in floating point numbers. # Numpy uses type 'Object' when the int overflows long, but we don't # have a similar concept. It's safe to assume any created LongTensor doesn't # overflow and it's finite. if not tensor.is_floating_point(): return torch.ones_like(tensor, dtype=torch.uint8) return (tensor == tensor) & (tensor.abs() != inf) def isinf(tensor): r"""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.ByteTensor`` containing a 1 at each location of `+/-INF` elements and 0 otherwise Example:: >>> torch.isinf(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')])) tensor([ 0, 1, 0, 1, 0], dtype=torch.uint8) """ if not isinstance(tensor, torch.Tensor): raise ValueError("The argument is not a tensor", str(tensor)) return tensor.abs() == inf def meshgrid(*tensors, **kwargs): r"""Take :math:`N` tensors, each of which can be either scalar or 1-dimensional vector, and create :math:`N` N-dimensional grids, where the :math:`i`th grid is defined by expanding the :math:`i`th input over dimensions defined by other inputs. Args: tensors (list of Tensor): list of scalars or 1 dimensional tensors. Scalars will be treated as tensors of size :math:`(1,)` automatically Returns: seq (sequence of Tensors): If the input has :math:`k` tensors of size :math:`(N_1,), (N_2,), \ldots , (N_k,)`, then the output would also has :math:`k` tensors, where all tensors are of size :math:`(N_1, N_2, \ldots , N_k)`. Example:: >>> x = torch.tensor([1, 2, 3]) >>> y = torch.tensor([4, 5, 6]) >>> grid_x, grid_y = torch.meshgrid(x, y) >>> grid_x tensor([[1, 1, 1], [2, 2, 2], [3, 3, 3]]) >>> grid_y tensor([[4, 5, 6], [4, 5, 6], [4, 5, 6]]) """ if kwargs: raise TypeError("meshgrid() got an unexpected keyword argument '%s'" % (list(kwargs)[0],)) if len(tensors) == 1 and isinstance(tensors[0], (list, tuple)): # the old interface of passing the operands as one list argument tensors = tensors[0] return torch._C._VariableFunctions.meshgrid(tensors) def stft(input, n_fft, hop_length=None, win_length=None, window=None, center=True, pad_mode='reflect', normalized=False, onesided=True): r"""Short-time Fourier transform (STFT). Ignoring the optional batch dimension, this method computes the following expression: .. math:: X[m, \omega] = \sum_{k = 0}^{\text{win\_length}}% \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 :math:`m` is the index of the sliding window, and :math:`\omega` is the frequency that :math:`0 \leq \omega < \text{n\_fft}`. When :attr:`onesided` is the default value ``True``, * :attr:`input` must be either a 1-D time sequence or a 2-D batch of time sequences. * If :attr:`hop_length` is ``None`` (default), it is treated as equal to ``floor(n_fft / 4)``. * If :attr:`win_length` is ``None`` (default), it is treated as equal to :attr:`n_fft`. * :attr:`window` can be a 1-D tensor of size :attr:`win_length`, e.g., from :meth:`torch.hann_window`. If :attr:`window` is ``None`` (default), it is treated as if having :math:`1` everywhere in the window. If :math:`\text{win\_length} < \text{n\_fft}`, :attr:`window` will be padded on both sides to length :attr:`n_fft` before being applied. * If :attr:`center` is ``True`` (default), :attr:`input` will be padded on both sides so that the :math:`t`-th frame is centered at time :math:`t \times \text{hop\_length}`. Otherwise, the :math:`t`-th frame begins at time :math:`t \times \text{hop\_length}`. * :attr:`pad_mode` determines the padding method used on :attr:`input` when :attr:`center` is ``True``. See :meth:`torch.nn.functional.pad` for all available options. Default is ``"reflect"``. * If :attr:`onesided` is ``True`` (default), only values for :math:`\omega` in :math:`\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., :math:`X[m, \omega] = X[m, \text{n\_fft} - \omega]^*`. * If :attr:`normalized` is ``True`` (default is ``False``), the function returns the normalized STFT results, i.e., multiplied by :math:`(\text{frame\_length})^{-0.5}`. Returns the real and the imaginary parts together as one tensor of size :math:`(* \times N \times T \times 2)`, where :math:`*` is the optional batch size of :attr:`input`, :math:`N` is the number of frequencies where STFT is applied, :math:`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. Arguments: 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 :attr:`n_fft`) window (Tensor, optional): the optional window function. Default: ``None`` (treated as window of all :math:`1` s) center (bool, optional): whether to pad :attr:`input` on both sides so that the :math:`t`-th frame is centered at time :math:`t \times \text{hop\_length}`. Default: ``True`` pad_mode (string, optional): controls the padding method used when :attr:`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: Tensor: A tensor containing the STFT result with shape described above """ # TODO: after having proper ways to map Python strings to ATen Enum, move # this and F.pad to ATen. if center: signal_dim = input.dim() extended_shape = [1] * (3 - signal_dim) + list(input.size()) pad = int(n_fft // 2) input = F.pad(input.view(extended_shape), (pad, pad), pad_mode) input = input.view(input.shape[-signal_dim:]) return torch._C._VariableFunctions.stft(input, n_fft, hop_length, win_length, window, normalized, onesided) def isnan(tensor): r"""Returns a new tensor with boolean elements representing if each element is `NaN` or not. Arguments: tensor (Tensor): A tensor to check Returns: Tensor: A ``torch.ByteTensor`` containing a 1 at each location of `NaN` elements. Example:: >>> torch.isnan(torch.tensor([1, float('nan'), 2])) tensor([ 0, 1, 0], dtype=torch.uint8) """ if not isinstance(tensor, torch.Tensor): raise ValueError("The argument is not a tensor", str(tensor)) return tensor != tensor def unique(input, sorted=False, return_inverse=False, dim=None): r"""Returns the unique scalar elements of the input tensor as a 1-D tensor. Arguments: 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. dim (int): the dimension to apply unique. If ``None``, the unique of the flattened input is returned. default: ``None`` Returns: (Tensor, Tensor (optional)): A tensor or a tuple of tensors containing - **output** (*Tensor*): the output list of unique scalar elements. - **inverse_indices** (*Tensor*): (optional) if :attr:`return_inverse` is True, there will be a 2nd 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. 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]]) """ if dim is not None: output, inverse_indices = torch._unique_dim( input, dim, sorted=sorted, return_inverse=return_inverse ) else: output, inverse_indices = torch._unique( input, sorted=sorted, return_inverse=return_inverse, ) if return_inverse: return output, inverse_indices else: return output def argmax(input, dim=None, keepdim=False): r"""Returns the indices of the maximum values of a tensor across a dimension. This is the second value returned by :meth:`torch.max`. See its documentation for the exact semantics of this method. Args: 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 tensors have :attr:`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]) """ if dim is None: return torch._argmax(input.contiguous().view(-1), dim=0, keepdim=False) return torch._argmax(input, dim, keepdim) def argmin(input, dim=None, keepdim=False): r"""Returns the indices of the minimum values of a tensor across a dimension. This is the second value returned by :meth:`torch.min`. See its documentation for the exact semantics of this method. Args: 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 tensors have :attr:`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]) """ if dim is None: return torch._argmin(input.contiguous().view(-1), dim=0, keepdim=False) return torch._argmin(input, dim, keepdim) def tensordot(a, b, dims=2): r"""Returns a contraction of a and b over multiple dimensions. :attr:`tensordot` implements a generalizes the matrix product. Args: a (Tensor): Left tensor to contract b (Tensor): Right tensor to contract dims (int or tuple of two lists of integers): number of dimensions to contract or explicit lists of dimensions for :attr:`a` and :attr:`b` respectively When called with an integer argument :attr:`dims` = :math:`d`, and the number of dimensions of :attr:`a` and :attr:`b` is :math:`m` and :math:`n`, respectively, it computes .. math:: r_{i_0,...,i_{m-d}, i_d,...,i_n} = \sum_{k_0,...,k_{d-1}} a_{i_0,...,i_{m-d},k_0,...,k_{d-1}} \times b_{k_0,...,k_{d-1}, i_d,...,i_n}. When called with :attr:`dims` of the list form, the given dimensions will be contracted in place of the last :math:`d` of :attr:`a` and the first :math:`d` of :math:`b`. The sizes in these dimensions must match, but :attr:`tensordot` will deal with broadcasted dimensions. Examples:: >>> a = torch.arange(60.).reshape(3, 4, 5) >>> b = torch.arange(24.).reshape(4, 3, 2) >>> torch.tensordot(a, b, dims=([1, 0], [0, 1])) tensor([[4400., 4730.], [4532., 4874.], [4664., 5018.], [4796., 5162.], [4928., 5306.]]) >>> a = torch.randn(3, 4, 5, device='cuda') >>> b = torch.randn(4, 5, 6, device='cuda') >>> c = torch.tensordot(a, b, dims=2).cpu() tensor([[ 8.3504, -2.5436, 6.2922, 2.7556, -1.0732, 3.2741], [ 3.3161, 0.0704, 5.0187, -0.4079, -4.3126, 4.8744], [ 0.8223, 3.9445, 3.2168, -0.2400, 3.4117, 1.7780]]) """ if isinstance(dims, (list, tuple)) or \ (isinstance(dims, torch.Tensor) and dims.numel() > 1): dims_a, dims_b = dims else: if isinstance(dims, torch.Tensor): dims = dims.item() dims_a = list(range(-dims, 0)) dims_b = list(range(dims)) return torch._C._VariableFunctions.tensordot(a, b, dims_a, dims_b) def argsort(input, dim=None, descending=False): r"""Returns the indices that sort a tensor along a given dimension in ascending order by value. This is the second value returned by :meth:`torch.sort`. See its documentation for the exact semantics of this method. Args: 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]]) """ if dim is None: return torch.sort(input, -1, descending)[1] return torch.sort(input, dim, descending)[1] def norm(input, p="fro", dim=None, keepdim=False, out=None): r"""Returns the matrix norm or vector norm of a given tensor. Args: 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 ints, 2-list of 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 :attr:`dim` retained or not. Ignored if :attr:`dim` = ``None`` and :attr:`out` = ``None``. Default: ``False`` out (Tensor, optional): the output tensor. Ignored if :attr:`dim` = ``None`` and :attr:`out` = ``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., 3., 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)) """ ndim = input.dim() # catch default case if dim is None and out is None: if p == "fro": return torch._C._VariableFunctions.frobenius_norm(input) elif p != "nuc": return torch._C._VariableFunctions.norm(input, p) if p == "fro": if dim is None: dim = tuple(range(ndim)) if out is None: return torch._C._VariableFunctions.frobenius_norm(input, dim, keepdim=keepdim) return torch._C._VariableFunctions.frobenius_norm(input, dim, keepdim=keepdim, out=out) elif p == "nuc": if out is None: torch._C._VariableFunctions.nuclear_norm(input, keepdim=keepdim) return torch._C._VariableFunctions.nuclear_norm(input, keepdim=keepdim, out=out) else: if out is None: return torch._C._VariableFunctions.norm(input, p, dim, keepdim=keepdim) return torch._C._VariableFunctions.norm(input, p, dim, keepdim=keepdim, out=out) def chain_matmul(*matrices): r"""Returns the matrix product of the :math:`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, :math:`N` needs to be greater than or equal to 2; if equal to 2 then a trivial matrix-matrix product is returned. If :math:`N` is 1, then this is a no-op - the original matrix is returned as is. Args: matrices (Tensors...): a sequence of 2 or more 2-D tensors whose product is to be determined. Returns: Tensor: if the :math:`i^{th}` tensor was of dimensions :math:`p_{i} \times p_{i + 1}`, then the product would be of dimensions :math:`p_{1} \times p_{N + 1}`. 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]]) .. _`[CLRS]`: https://mitpress.mit.edu/books/introduction-algorithms-third-edition """ return torch._C._VariableFunctions.chain_matmul(matrices) def potrf(a, upper=True, out=None): r"""Computes the Cholesky decomposition of a symmetric positive-definite matrix :math:`A`. For more information, regarding :func:`torch.potrf`, please check :func:`torch.cholesky`. .. warning:: torch.potrf is deprecated in favour of torch.cholesky and will be removed in the next release. Please use torch.cholesky instead and note that the :attr:`upper` argument in torch.cholesky defaults to ``False``. """ warnings.warn("torch.potrf is deprecated in favour of torch.cholesky and will be removed in the next " "release. Please use torch.cholesky instead and note that the :attr:`upper` argument in" " torch.cholesky defaults to ``False``.", stacklevel=2) return torch.cholesky(a, upper=upper, out=out)