# Contains code from opt_einsum, which is licensed under the MIT License.
# The MIT License (MIT)
# Copyright (c) 2014 Daniel Smith
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import numpy as np
from .wrappers import contract, transpose_add
[docs]
def einsum(*operands, out=None, optimize="greedy", complex_real_contractions=False, **kwargs):
"""
einsum(subscripts, *operands, out=None, order='K',
optimize='greedy')
Evaluates the Einstein summation convention on the operands.
Drop-in replacement for numpy.einsum, using TBLIS for tensor contractions.
Parameters
----------
subscripts : str
Specifies the subscripts for summation as comma separated list of
subscript labels. An implicit (classical Einstein summation)
calculation is performed unless the explicit indicator '->' is
included as well as subscript labels of the precise output form.
operands : list of array_like
These are the arrays for the operation.
out : ndarray, optional
If provided, the calculation is done into this array.
order : {'C', 'F', 'A', 'K'}, optional
Controls the memory layout of the output. 'C' means it should
be C contiguous. 'F' means it should be Fortran contiguous,
'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
'K' means it should be as close to the layout as the inputs as
is possible, including arbitrarily permuted axes.
Default is 'K'.
optimize : {'greedy', 'optimal'}, default 'greedy'
Controls the optimization strategy used to compute the contraction.
complex_real_contractions : bool, default False
If True, handle contractions between complex and real tensors by performing
separate contractions for the real and imaginary parts of the complex tensor.
Returns
-------
output : ndarray
The calculation based on the Einstein summation convention.
"""
specified_out = out is not None
assert optimize in ("greedy", "optimal"), "optimize must be 'greedy' or 'optimal'"
# Check the kwargs to avoid a more cryptic error later, without having to
# repeat default values here
valid_einsum_kwargs = ["order"]
unknown_kwargs = [k for (k, v) in kwargs.items() if k not in valid_einsum_kwargs]
if unknown_kwargs:
msg = f"Did not understand the following kwargs: {unknown_kwargs}"
raise TypeError(msg)
# Build the contraction list and operand
operands, contraction_list = np.einsum_path(*operands, optimize=optimize, einsum_call=True)
# Handle order kwarg for output array, c_einsum allows mixed case
output_order = kwargs.pop("order", "K")
if output_order.upper() == "A":
output_order = "F" if all(arr.flags.f_contiguous for arr in operands) else "C"
# Start contraction loop
for num, contraction in enumerate(contraction_list):
if len(contraction) == 3: # numpy 2.4.0 and newer.
inds, einsum_str, _ = contraction
else: # numpy 2.3.x and older.
inds, _, einsum_str, _, _ = contraction
tmp_operands = [operands.pop(x) for x in inds]
# Do we need to deal with the output?
handle_out = specified_out and ((num + 1) == len(contraction_list))
out_kwarg = None
if handle_out:
out_kwarg = out
if len(tmp_operands) == 2:
new_view = contract(
einsum_str,
*tmp_operands,
out=out_kwarg,
allow_partial_trace=True,
complex_real_contractions=complex_real_contractions,
)
elif len(tmp_operands) == 1:
# check if only a transpose
einsum_str = einsum_str.replace(" ", "")
subscript_a, subscript_b = einsum_str.split("->")
if sorted(subscript_a) == sorted(subscript_b):
# only a transpose, use numpy for this (should return view)
new_view = np.einsum(einsum_str, tmp_operands[0], out=out_kwarg, **kwargs)
else:
# may involve a trace or replication, use tblis transpose_add for this
new_view = transpose_add(einsum_str, tmp_operands[0], out=out_kwarg, **kwargs)
else:
# fallback to numpy einsum
# e.g. contractions of 3 tensors
out_kwarg = None
if handle_out:
out_kwarg = out
new_view = np.einsum(einsum_str, *tmp_operands, out=out_kwarg, **kwargs)
# Append new items and dereference what we can
operands.append(new_view)
del tmp_operands, new_view
if specified_out:
return out
return operands[0]