# 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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from contextlib import nullcontext
import numpy as np
from .defaultorder import _default_order, get_default_array_order, use_default_array_order
from .numpy_einsumpath import einsum_path
from .wrappers import contract, transpose_add
[docs]
def einsum(*operands, out=None, optimize=True, complex_real_contractions=True, **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' is ignored, for now.
Default is 'C'.
optimize : {False, True, 'greedy', 'optimal'}, default True
Controls the optimization strategy used to compute the contraction.
complex_real_contractions : bool, default True
If True, handle contractions between complex and real tensors by performing
separate contractions for the real and imaginary parts of the complex tensor.
This avoids NumPy type promotion if the complex and real tensors
have the same precision (e.g., complex128 and float64).
Returns
-------
output : ndarray
The calculation based on the Einstein summation convention.
"""
specified_out = out is not None
if optimize not in (False, True, "greedy", "optimal"):
raise ValueError("optimize must be one of False, True, '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)
# calculate contraction path
operands, contraction_list = einsum_path(*operands, optimize=optimize, einsum_call=True)
# Handle order kwarg for output array, c_einsum allows mixed case
order_given = "order" in kwargs
output_order = kwargs.get("order", _default_order.get())
if output_order not in ("C", "F", "A", "K"):
raise ValueError("order must be one of 'C', 'F', 'A', or 'K'")
if output_order == "A":
output_order = "F" if all(arr.flags.f_contiguous for arr in operands) else "C"
elif output_order == "K":
# ignore K.
output_order = get_default_array_order()
# Start contraction loop
for num, contraction in enumerate(contraction_list):
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))
if handle_out:
out_kwarg = out
else:
out_kwarg = None
if ((num + 1) == len(contraction_list)) and order_given:
# Set the requested output order on the final contraction.
order_context = use_default_array_order(output_order)
else:
order_context = nullcontext()
if len(tmp_operands) == 2:
# two operands: use contract
with order_context:
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
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)
# may involve a trace or replication, use tblis transpose_add for this
else:
with order_context:
new_view = transpose_add(einsum_str, tmp_operands[0], out=out_kwarg)
else:
# 3 or more operands, fall back to numpy einsum
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]