From aa3dd9acc3e46fe6e0a08a07270dc1eeb5d437df Mon Sep 17 00:00:00 2001
From: Roman Novak <44512421+romanngg@users.noreply.github.com>
Date: Sat, 9 Jul 2022 09:01:16 -0700
Subject: [PATCH] Fix `dp` to work for contractions with no sized axes (scalars
 only). (#195)

* Fix `dp` to work for contractions with no sized axes (scalars only).

* Add comma for linter

* Bug fixes and tweaks for v3.4.0 (#192)

* Unpins MyPy, now appears stable

* Minor typing tweaks

* Skips unicode surrogates, fixes #182

* Adds simple validation to BranchBound, fixes #136

* More accurate branch bound exception handler

* Update opt_einsum/paths.py

Co-authored-by: Daniel Smith <dgasmith@icloud.com>
---
 opt_einsum/paths.py               | 2 +-
 opt_einsum/tests/test_contract.py | 1 +
 opt_einsum/tests/test_paths.py    | 1 +
 3 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/opt_einsum/paths.py b/opt_einsum/paths.py
index eac36301..ac8ccd5d 100644
--- a/opt_einsum/paths.py
+++ b/opt_einsum/paths.py
@@ -1217,7 +1217,7 @@ def __call__(
         output = frozenset(symbol2int[c] for c in output_)
         size_dict_canonical = {symbol2int[c]: v for c, v in size_dict_.items() if c in symbol2int}
         size_dict = [size_dict_canonical[j] for j in range(len(size_dict_canonical))]
-        naive_cost = naive_scale * len(inputs) * functools.reduce(operator.mul, size_dict)
+        naive_cost = naive_scale * len(inputs) * functools.reduce(operator.mul, size_dict, 1)
 
         inputs, inputs_done, inputs_contractions = _dp_parse_out_single_term_ops(inputs, all_inds, ind_counts)
 
diff --git a/opt_einsum/tests/test_contract.py b/opt_einsum/tests/test_contract.py
index 453a7790..ef3ee5de 100644
--- a/opt_einsum/tests/test_contract.py
+++ b/opt_einsum/tests/test_contract.py
@@ -13,6 +13,7 @@
     "a,->a",
     "ab,->ab",
     ",ab,->ab",
+    ",,->",
     # Test hadamard-like products
     "a,ab,abc->abc",
     "a,b,ab->ab",
diff --git a/opt_einsum/tests/test_paths.py b/opt_einsum/tests/test_paths.py
index c6fef4f5..eb4b18bb 100644
--- a/opt_einsum/tests/test_paths.py
+++ b/opt_einsum/tests/test_paths.py
@@ -58,6 +58,7 @@
     ["ab,->ab", 1],
     [",a,->a", 2],
     [",,a,->a", 3],
+    [",,->", 2],
 ]