104 lines
2.4 KiB
Python
104 lines
2.4 KiB
Python
"""Various linear algebra utility methods for internal use.
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"""
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from torch import Tensor
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import torch
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from typing import Optional, Tuple
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def is_sparse(A):
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"""Check if tensor A is a sparse tensor"""
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if isinstance(A, torch.Tensor):
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return A.layout == torch.sparse_coo
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error_str = "expected Tensor"
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if not torch.jit.is_scripting():
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error_str += " but got {}".format(type(A))
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raise TypeError(error_str)
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def get_floating_dtype(A):
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"""Return the floating point dtype of tensor A.
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Integer types map to float32.
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"""
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dtype = A.dtype
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if dtype in (torch.float16, torch.float32, torch.float64):
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return dtype
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return torch.float32
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def matmul(A: Optional[Tensor], B: Tensor) -> Tensor:
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"""Multiply two matrices.
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If A is None, return B. A can be sparse or dense. B is always
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dense.
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"""
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if A is None:
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return B
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if is_sparse(A):
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return torch.sparse.mm(A, B)
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return torch.matmul(A, B)
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def conjugate(A):
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"""Return conjugate of tensor A.
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.. note:: If A's dtype is not complex, A is returned.
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"""
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if A.is_complex():
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return A.conj()
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return A
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def transpose(A):
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"""Return transpose of a matrix or batches of matrices.
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"""
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ndim = len(A.shape)
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return A.transpose(ndim - 1, ndim - 2)
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def transjugate(A):
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"""Return transpose conjugate of a matrix or batches of matrices.
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"""
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return conjugate(transpose(A))
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def bform(X: Tensor, A: Optional[Tensor], Y: Tensor) -> Tensor:
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"""Return bilinear form of matrices: :math:`X^T A Y`.
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"""
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return matmul(transpose(X), matmul(A, Y))
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def qform(A: Optional[Tensor], S: Tensor):
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"""Return quadratic form :math:`S^T A S`.
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"""
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return bform(S, A, S)
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def basis(A):
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"""Return orthogonal basis of A columns.
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"""
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if A.is_cuda:
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# torch.orgqr is not available in CUDA
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Q, _ = torch.qr(A, some=True)
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else:
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Q = torch.orgqr(*torch.geqrf(A))
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return Q
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def symeig(A: Tensor, largest: Optional[bool] = False, eigenvectors: Optional[bool] = True) -> Tuple[Tensor, Tensor]:
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"""Return eigenpairs of A with specified ordering.
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"""
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if largest is None:
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largest = False
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if eigenvectors is None:
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eigenvectors = True
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E, Z = torch.symeig(A, eigenvectors, True)
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# assuming that E is ordered
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if largest:
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E = torch.flip(E, dims=(-1,))
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Z = torch.flip(Z, dims=(-1,))
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return E, Z
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