_linalg_utils.py

"""Various linear algebra utility methods for internal use.

"""

from torch import Tensor
import torch

from typing import Optional, Tuple


def is_sparse(A):
    """Check if tensor A is a sparse tensor"""
    if isinstance(A, torch.Tensor):
        return A.layout == torch.sparse_coo

    error_str = "expected Tensor"
    if not torch.jit.is_scripting():
        error_str += " but got {}".format(type(A))
    raise TypeError(error_str)

def get_floating_dtype(A):
    """Return the floating point dtype of tensor A.

    Integer types map to float32.
    """
    dtype = A.dtype
    if dtype in (torch.float16, torch.float32, torch.float64):
        return dtype
    return torch.float32


def matmul(A: Optional[Tensor], B: Tensor) -> Tensor:
    """Multiply two matrices.

    If A is None, return B. A can be sparse or dense. B is always
    dense.
    """
    if A is None:
        return B
    if is_sparse(A):
        return torch.sparse.mm(A, B)
    return torch.matmul(A, B)


def conjugate(A):
    """Return conjugate of tensor A.

    .. note:: If A's dtype is not complex, A is returned.
    """
    if A.is_complex():
        return A.conj()
    return A


def transpose(A):
    """Return transpose of a matrix or batches of matrices.
    """
    ndim = len(A.shape)
    return A.transpose(ndim - 1, ndim - 2)


def transjugate(A):
    """Return transpose conjugate of a matrix or batches of matrices.
    """
    return conjugate(transpose(A))


def bform(X: Tensor, A: Optional[Tensor], Y: Tensor) -> Tensor:
    """Return bilinear form of matrices: :math:`X^T A Y`.
    """
    return matmul(transpose(X), matmul(A, Y))


def qform(A: Optional[Tensor], S: Tensor):
    """Return quadratic form :math:`S^T A S`.
    """
    return bform(S, A, S)


def basis(A):
    """Return orthogonal basis of A columns.
    """
    if A.is_cuda:
        # torch.orgqr is not available in CUDA
        Q = torch.linalg.qr(A).Q
    else:
        Q = torch.orgqr(*torch.geqrf(A))
    return Q


def symeig(A: Tensor, largest: Optional[bool] = False) -> Tuple[Tensor, Tensor]:
    """Return eigenpairs of A with specified ordering.
    """
    if largest is None:
        largest = False
    E, Z = torch.linalg.eigh(A, UPLO='U')
    # assuming that E is ordered
    if largest:
        E = torch.flip(E, dims=(-1,))
        Z = torch.flip(Z, dims=(-1,))
    return E, Z