two version of R2R are here HEAD master

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diff --git a/.venv/lib/python3.12/site-packages/numpy/core/einsumfunc.py b/.venv/lib/python3.12/site-packages/numpy/core/einsumfunc.py
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+"""
+Implementation of optimized einsum.
+
+"""
+import itertools
+import operator
+
+from numpy.core.multiarray import c_einsum
+from numpy.core.numeric import asanyarray, tensordot
+from numpy.core.overrides import array_function_dispatch
+
+__all__ = ['einsum', 'einsum_path']
+
+einsum_symbols = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+einsum_symbols_set = set(einsum_symbols)
+
+
+def _flop_count(idx_contraction, inner, num_terms, size_dictionary):
+    """
+    Computes the number of FLOPS in the contraction.
+
+    Parameters
+    ----------
+    idx_contraction : iterable
+        The indices involved in the contraction
+    inner : bool
+        Does this contraction require an inner product?
+    num_terms : int
+        The number of terms in a contraction
+    size_dictionary : dict
+        The size of each of the indices in idx_contraction
+
+    Returns
+    -------
+    flop_count : int
+        The total number of FLOPS required for the contraction.
+
+    Examples
+    --------
+
+    >>> _flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
+    30
+
+    >>> _flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
+    60
+
+    """
+
+    overall_size = _compute_size_by_dict(idx_contraction, size_dictionary)
+    op_factor = max(1, num_terms - 1)
+    if inner:
+        op_factor += 1
+
+    return overall_size * op_factor
+
+def _compute_size_by_dict(indices, idx_dict):
+    """
+    Computes the product of the elements in indices based on the dictionary
+    idx_dict.
+
+    Parameters
+    ----------
+    indices : iterable
+        Indices to base the product on.
+    idx_dict : dictionary
+        Dictionary of index sizes
+
+    Returns
+    -------
+    ret : int
+        The resulting product.
+
+    Examples
+    --------
+    >>> _compute_size_by_dict('abbc', {'a': 2, 'b':3, 'c':5})
+    90
+
+    """
+    ret = 1
+    for i in indices:
+        ret *= idx_dict[i]
+    return ret
+
+
+def _find_contraction(positions, input_sets, output_set):
+    """
+    Finds the contraction for a given set of input and output sets.
+
+    Parameters
+    ----------
+    positions : iterable
+        Integer positions of terms used in the contraction.
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+
+    Returns
+    -------
+    new_result : set
+        The indices of the resulting contraction
+    remaining : list
+        List of sets that have not been contracted, the new set is appended to
+        the end of this list
+    idx_removed : set
+        Indices removed from the entire contraction
+    idx_contraction : set
+        The indices used in the current contraction
+
+    Examples
+    --------
+
+    # A simple dot product test case
+    >>> pos = (0, 1)
+    >>> isets = [set('ab'), set('bc')]
+    >>> oset = set('ac')
+    >>> _find_contraction(pos, isets, oset)
+    ({'a', 'c'}, [{'a', 'c'}], {'b'}, {'a', 'b', 'c'})
+
+    # A more complex case with additional terms in the contraction
+    >>> pos = (0, 2)
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set('ac')
+    >>> _find_contraction(pos, isets, oset)
+    ({'a', 'c'}, [{'a', 'c'}, {'a', 'c'}], {'b', 'd'}, {'a', 'b', 'c', 'd'})
+    """
+
+    idx_contract = set()
+    idx_remain = output_set.copy()
+    remaining = []
+    for ind, value in enumerate(input_sets):
+        if ind in positions:
+            idx_contract |= value
+        else:
+            remaining.append(value)
+            idx_remain |= value
+
+    new_result = idx_remain & idx_contract
+    idx_removed = (idx_contract - new_result)
+    remaining.append(new_result)
+
+    return (new_result, remaining, idx_removed, idx_contract)
+
+
+def _optimal_path(input_sets, output_set, idx_dict, memory_limit):
+    """
+    Computes all possible pair contractions, sieves the results based
+    on ``memory_limit`` and returns the lowest cost path. This algorithm
+    scales factorial with respect to the elements in the list ``input_sets``.
+
+    Parameters
+    ----------
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+    idx_dict : dictionary
+        Dictionary of index sizes
+    memory_limit : int
+        The maximum number of elements in a temporary array
+
+    Returns
+    -------
+    path : list
+        The optimal contraction order within the memory limit constraint.
+
+    Examples
+    --------
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set()
+    >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    >>> _optimal_path(isets, oset, idx_sizes, 5000)
+    [(0, 2), (0, 1)]
+    """
+
+    full_results = [(0, [], input_sets)]
+    for iteration in range(len(input_sets) - 1):
+        iter_results = []
+
+        # Compute all unique pairs
+        for curr in full_results:
+            cost, positions, remaining = curr
+            for con in itertools.combinations(range(len(input_sets) - iteration), 2):
+
+                # Find the contraction
+                cont = _find_contraction(con, remaining, output_set)
+                new_result, new_input_sets, idx_removed, idx_contract = cont
+
+                # Sieve the results based on memory_limit
+                new_size = _compute_size_by_dict(new_result, idx_dict)
+                if new_size > memory_limit:
+                    continue
+
+                # Build (total_cost, positions, indices_remaining)
+                total_cost =  cost + _flop_count(idx_contract, idx_removed, len(con), idx_dict)
+                new_pos = positions + [con]
+                iter_results.append((total_cost, new_pos, new_input_sets))
+
+        # Update combinatorial list, if we did not find anything return best
+        # path + remaining contractions
+        if iter_results:
+            full_results = iter_results
+        else:
+            path = min(full_results, key=lambda x: x[0])[1]
+            path += [tuple(range(len(input_sets) - iteration))]
+            return path
+
+    # If we have not found anything return single einsum contraction
+    if len(full_results) == 0:
+        return [tuple(range(len(input_sets)))]
+
+    path = min(full_results, key=lambda x: x[0])[1]
+    return path
+
+def _parse_possible_contraction(positions, input_sets, output_set, idx_dict, memory_limit, path_cost, naive_cost):
+    """Compute the cost (removed size + flops) and resultant indices for
+    performing the contraction specified by ``positions``.
+
+    Parameters
+    ----------
+    positions : tuple of int
+        The locations of the proposed tensors to contract.
+    input_sets : list of sets
+        The indices found on each tensors.
+    output_set : set
+        The output indices of the expression.
+    idx_dict : dict
+        Mapping of each index to its size.
+    memory_limit : int
+        The total allowed size for an intermediary tensor.
+    path_cost : int
+        The contraction cost so far.
+    naive_cost : int
+        The cost of the unoptimized expression.
+
+    Returns
+    -------
+    cost : (int, int)
+        A tuple containing the size of any indices removed, and the flop cost.
+    positions : tuple of int
+        The locations of the proposed tensors to contract.
+    new_input_sets : list of sets
+        The resulting new list of indices if this proposed contraction is performed.
+
+    """
+
+    # Find the contraction
+    contract = _find_contraction(positions, input_sets, output_set)
+    idx_result, new_input_sets, idx_removed, idx_contract = contract
+
+    # Sieve the results based on memory_limit
+    new_size = _compute_size_by_dict(idx_result, idx_dict)
+    if new_size > memory_limit:
+        return None
+
+    # Build sort tuple
+    old_sizes = (_compute_size_by_dict(input_sets[p], idx_dict) for p in positions)
+    removed_size = sum(old_sizes) - new_size
+
+    # NB: removed_size used to be just the size of any removed indices i.e.:
+    #     helpers.compute_size_by_dict(idx_removed, idx_dict)
+    cost = _flop_count(idx_contract, idx_removed, len(positions), idx_dict)
+    sort = (-removed_size, cost)
+
+    # Sieve based on total cost as well
+    if (path_cost + cost) > naive_cost:
+        return None
+
+    # Add contraction to possible choices
+    return [sort, positions, new_input_sets]
+
+
+def _update_other_results(results, best):
+    """Update the positions and provisional input_sets of ``results`` based on
+    performing the contraction result ``best``. Remove any involving the tensors
+    contracted.
+
+    Parameters
+    ----------
+    results : list
+        List of contraction results produced by ``_parse_possible_contraction``.
+    best : list
+        The best contraction of ``results`` i.e. the one that will be performed.
+
+    Returns
+    -------
+    mod_results : list
+        The list of modified results, updated with outcome of ``best`` contraction.
+    """
+
+    best_con = best[1]
+    bx, by = best_con
+    mod_results = []
+
+    for cost, (x, y), con_sets in results:
+
+        # Ignore results involving tensors just contracted
+        if x in best_con or y in best_con:
+            continue
+
+        # Update the input_sets
+        del con_sets[by - int(by > x) - int(by > y)]
+        del con_sets[bx - int(bx > x) - int(bx > y)]
+        con_sets.insert(-1, best[2][-1])
+
+        # Update the position indices
+        mod_con = x - int(x > bx) - int(x > by), y - int(y > bx) - int(y > by)
+        mod_results.append((cost, mod_con, con_sets))
+
+    return mod_results
+
+def _greedy_path(input_sets, output_set, idx_dict, memory_limit):
+    """
+    Finds the path by contracting the best pair until the input list is
+    exhausted. The best pair is found by minimizing the tuple
+    ``(-prod(indices_removed), cost)``.  What this amounts to is prioritizing
+    matrix multiplication or inner product operations, then Hadamard like
+    operations, and finally outer operations. Outer products are limited by
+    ``memory_limit``. This algorithm scales cubically with respect to the
+    number of elements in the list ``input_sets``.
+
+    Parameters
+    ----------
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+    idx_dict : dictionary
+        Dictionary of index sizes
+    memory_limit : int
+        The maximum number of elements in a temporary array
+
+    Returns
+    -------
+    path : list
+        The greedy contraction order within the memory limit constraint.
+
+    Examples
+    --------
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set()
+    >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    >>> _greedy_path(isets, oset, idx_sizes, 5000)
+    [(0, 2), (0, 1)]
+    """
+
+    # Handle trivial cases that leaked through
+    if len(input_sets) == 1:
+        return [(0,)]
+    elif len(input_sets) == 2:
+        return [(0, 1)]
+
+    # Build up a naive cost
+    contract = _find_contraction(range(len(input_sets)), input_sets, output_set)
+    idx_result, new_input_sets, idx_removed, idx_contract = contract
+    naive_cost = _flop_count(idx_contract, idx_removed, len(input_sets), idx_dict)
+
+    # Initially iterate over all pairs
+    comb_iter = itertools.combinations(range(len(input_sets)), 2)
+    known_contractions = []
+
+    path_cost = 0
+    path = []
+
+    for iteration in range(len(input_sets) - 1):
+
+        # Iterate over all pairs on first step, only previously found pairs on subsequent steps
+        for positions in comb_iter:
+
+            # Always initially ignore outer products
+            if input_sets[positions[0]].isdisjoint(input_sets[positions[1]]):
+                continue
+
+            result = _parse_possible_contraction(positions, input_sets, output_set, idx_dict, memory_limit, path_cost,
+                                                 naive_cost)
+            if result is not None:
+                known_contractions.append(result)
+
+        # If we do not have a inner contraction, rescan pairs including outer products
+        if len(known_contractions) == 0:
+
+            # Then check the outer products
+            for positions in itertools.combinations(range(len(input_sets)), 2):
+                result = _parse_possible_contraction(positions, input_sets, output_set, idx_dict, memory_limit,
+                                                     path_cost, naive_cost)
+                if result is not None:
+                    known_contractions.append(result)
+
+            # If we still did not find any remaining contractions, default back to einsum like behavior
+            if len(known_contractions) == 0:
+                path.append(tuple(range(len(input_sets))))
+                break
+
+        # Sort based on first index
+        best = min(known_contractions, key=lambda x: x[0])
+
+        # Now propagate as many unused contractions as possible to next iteration
+        known_contractions = _update_other_results(known_contractions, best)
+
+        # Next iteration only compute contractions with the new tensor
+        # All other contractions have been accounted for
+        input_sets = best[2]
+        new_tensor_pos = len(input_sets) - 1
+        comb_iter = ((i, new_tensor_pos) for i in range(new_tensor_pos))
+
+        # Update path and total cost
+        path.append(best[1])
+        path_cost += best[0][1]
+
+    return path
+
+
+def _can_dot(inputs, result, idx_removed):
+    """
+    Checks if we can use BLAS (np.tensordot) call and its beneficial to do so.
+
+    Parameters
+    ----------
+    inputs : list of str
+        Specifies the subscripts for summation.
+    result : str
+        Resulting summation.
+    idx_removed : set
+        Indices that are removed in the summation
+
+
+    Returns
+    -------
+    type : bool
+        Returns true if BLAS should and can be used, else False
+
+    Notes
+    -----
+    If the operations is BLAS level 1 or 2 and is not already aligned
+    we default back to einsum as the memory movement to copy is more
+    costly than the operation itself.
+
+
+    Examples
+    --------
+
+    # Standard GEMM operation
+    >>> _can_dot(['ij', 'jk'], 'ik', set('j'))
+    True
+
+    # Can use the standard BLAS, but requires odd data movement
+    >>> _can_dot(['ijj', 'jk'], 'ik', set('j'))
+    False
+
+    # DDOT where the memory is not aligned
+    >>> _can_dot(['ijk', 'ikj'], '', set('ijk'))
+    False
+
+    """
+
+    # All `dot` calls remove indices
+    if len(idx_removed) == 0:
+        return False
+
+    # BLAS can only handle two operands
+    if len(inputs) != 2:
+        return False
+
+    input_left, input_right = inputs
+
+    for c in set(input_left + input_right):
+        # can't deal with repeated indices on same input or more than 2 total
+        nl, nr = input_left.count(c), input_right.count(c)
+        if (nl > 1) or (nr > 1) or (nl + nr > 2):
+            return False
+
+        # can't do implicit summation or dimension collapse e.g.
+        #     "ab,bc->c" (implicitly sum over 'a')
+        #     "ab,ca->ca" (take diagonal of 'a')
+        if nl + nr - 1 == int(c in result):
+            return False
+
+    # Build a few temporaries
+    set_left = set(input_left)
+    set_right = set(input_right)
+    keep_left = set_left - idx_removed
+    keep_right = set_right - idx_removed
+    rs = len(idx_removed)
+
+    # At this point we are a DOT, GEMV, or GEMM operation
+
+    # Handle inner products
+
+    # DDOT with aligned data
+    if input_left == input_right:
+        return True
+
+    # DDOT without aligned data (better to use einsum)
+    if set_left == set_right:
+        return False
+
+    # Handle the 4 possible (aligned) GEMV or GEMM cases
+
+    # GEMM or GEMV no transpose
+    if input_left[-rs:] == input_right[:rs]:
+        return True
+
+    # GEMM or GEMV transpose both
+    if input_left[:rs] == input_right[-rs:]:
+        return True
+
+    # GEMM or GEMV transpose right
+    if input_left[-rs:] == input_right[-rs:]:
+        return True
+
+    # GEMM or GEMV transpose left
+    if input_left[:rs] == input_right[:rs]:
+        return True
+
+    # Einsum is faster than GEMV if we have to copy data
+    if not keep_left or not keep_right:
+        return False
+
+    # We are a matrix-matrix product, but we need to copy data
+    return True
+
+
+def _parse_einsum_input(operands):
+    """
+    A reproduction of einsum c side einsum parsing in python.
+
+    Returns
+    -------
+    input_strings : str
+        Parsed input strings
+    output_string : str
+        Parsed output string
+    operands : list of array_like
+        The operands to use in the numpy contraction
+
+    Examples
+    --------
+    The operand list is simplified to reduce printing:
+
+    >>> np.random.seed(123)
+    >>> a = np.random.rand(4, 4)
+    >>> b = np.random.rand(4, 4, 4)
+    >>> _parse_einsum_input(('...a,...a->...', a, b))
+    ('za,xza', 'xz', [a, b]) # may vary
+
+    >>> _parse_einsum_input((a, [Ellipsis, 0], b, [Ellipsis, 0]))
+    ('za,xza', 'xz', [a, b]) # may vary
+    """
+
+    if len(operands) == 0:
+        raise ValueError("No input operands")
+
+    if isinstance(operands[0], str):
+        subscripts = operands[0].replace(" ", "")
+        operands = [asanyarray(v) for v in operands[1:]]
+
+        # Ensure all characters are valid
+        for s in subscripts:
+            if s in '.,->':
+                continue
+            if s not in einsum_symbols:
+                raise ValueError("Character %s is not a valid symbol." % s)
+
+    else:
+        tmp_operands = list(operands)
+        operand_list = []
+        subscript_list = []
+        for p in range(len(operands) // 2):
+            operand_list.append(tmp_operands.pop(0))
+            subscript_list.append(tmp_operands.pop(0))
+
+        output_list = tmp_operands[-1] if len(tmp_operands) else None
+        operands = [asanyarray(v) for v in operand_list]
+        subscripts = ""
+        last = len(subscript_list) - 1
+        for num, sub in enumerate(subscript_list):
+            for s in sub:
+                if s is Ellipsis:
+                    subscripts += "..."
+                else:
+                    try:
+                        s = operator.index(s)
+                    except TypeError as e:
+                        raise TypeError("For this input type lists must contain "
+                                        "either int or Ellipsis") from e
+                    subscripts += einsum_symbols[s]
+            if num != last:
+                subscripts += ","
+
+        if output_list is not None:
+            subscripts += "->"
+            for s in output_list:
+                if s is Ellipsis:
+                    subscripts += "..."
+                else:
+                    try:
+                        s = operator.index(s)
+                    except TypeError as e:
+                        raise TypeError("For this input type lists must contain "
+                                        "either int or Ellipsis") from e
+                    subscripts += einsum_symbols[s]
+    # Check for proper "->"
+    if ("-" in subscripts) or (">" in subscripts):
+        invalid = (subscripts.count("-") > 1) or (subscripts.count(">") > 1)
+        if invalid or (subscripts.count("->") != 1):
+            raise ValueError("Subscripts can only contain one '->'.")
+
+    # Parse ellipses
+    if "." in subscripts:
+        used = subscripts.replace(".", "").replace(",", "").replace("->", "")
+        unused = list(einsum_symbols_set - set(used))
+        ellipse_inds = "".join(unused)
+        longest = 0
+
+        if "->" in subscripts:
+            input_tmp, output_sub = subscripts.split("->")
+            split_subscripts = input_tmp.split(",")
+            out_sub = True
+        else:
+            split_subscripts = subscripts.split(',')
+            out_sub = False
+
+        for num, sub in enumerate(split_subscripts):
+            if "." in sub:
+                if (sub.count(".") != 3) or (sub.count("...") != 1):
+                    raise ValueError("Invalid Ellipses.")
+
+                # Take into account numerical values
+                if operands[num].shape == ():
+                    ellipse_count = 0
+                else:
+                    ellipse_count = max(operands[num].ndim, 1)
+                    ellipse_count -= (len(sub) - 3)
+
+                if ellipse_count > longest:
+                    longest = ellipse_count
+
+                if ellipse_count < 0:
+                    raise ValueError("Ellipses lengths do not match.")
+                elif ellipse_count == 0:
+                    split_subscripts[num] = sub.replace('...', '')
+                else:
+                    rep_inds = ellipse_inds[-ellipse_count:]
+                    split_subscripts[num] = sub.replace('...', rep_inds)
+
+        subscripts = ",".join(split_subscripts)
+        if longest == 0:
+            out_ellipse = ""
+        else:
+            out_ellipse = ellipse_inds[-longest:]
+
+        if out_sub:
+            subscripts += "->" + output_sub.replace("...", out_ellipse)
+        else:
+            # Special care for outputless ellipses
+            output_subscript = ""
+            tmp_subscripts = subscripts.replace(",", "")
+            for s in sorted(set(tmp_subscripts)):
+                if s not in (einsum_symbols):
+                    raise ValueError("Character %s is not a valid symbol." % s)
+                if tmp_subscripts.count(s) == 1:
+                    output_subscript += s
+            normal_inds = ''.join(sorted(set(output_subscript) -
+                                         set(out_ellipse)))
+
+            subscripts += "->" + out_ellipse + normal_inds
+
+    # Build output string if does not exist
+    if "->" in subscripts:
+        input_subscripts, output_subscript = subscripts.split("->")
+    else:
+        input_subscripts = subscripts
+        # Build output subscripts
+        tmp_subscripts = subscripts.replace(",", "")
+        output_subscript = ""
+        for s in sorted(set(tmp_subscripts)):
+            if s not in einsum_symbols:
+                raise ValueError("Character %s is not a valid symbol." % s)
+            if tmp_subscripts.count(s) == 1:
+                output_subscript += s
+
+    # Make sure output subscripts are in the input
+    for char in output_subscript:
+        if char not in input_subscripts:
+            raise ValueError("Output character %s did not appear in the input"
+                             % char)
+
+    # Make sure number operands is equivalent to the number of terms
+    if len(input_subscripts.split(',')) != len(operands):
+        raise ValueError("Number of einsum subscripts must be equal to the "
+                         "number of operands.")
+
+    return (input_subscripts, output_subscript, operands)
+
+
+def _einsum_path_dispatcher(*operands, optimize=None, einsum_call=None):
+    # NOTE: technically, we should only dispatch on array-like arguments, not
+    # subscripts (given as strings). But separating operands into
+    # arrays/subscripts is a little tricky/slow (given einsum's two supported
+    # signatures), so as a practical shortcut we dispatch on everything.
+    # Strings will be ignored for dispatching since they don't define
+    # __array_function__.
+    return operands
+
+
+@array_function_dispatch(_einsum_path_dispatcher, module='numpy')
+def einsum_path(*operands, optimize='greedy', einsum_call=False):
+    """
+    einsum_path(subscripts, *operands, optimize='greedy')
+
+    Evaluates the lowest cost contraction order for an einsum expression by
+    considering the creation of intermediate arrays.
+
+    Parameters
+    ----------
+    subscripts : str
+        Specifies the subscripts for summation.
+    *operands : list of array_like
+        These are the arrays for the operation.
+    optimize : {bool, list, tuple, 'greedy', 'optimal'}
+        Choose the type of path. If a tuple is provided, the second argument is
+        assumed to be the maximum intermediate size created. If only a single
+        argument is provided the largest input or output array size is used
+        as a maximum intermediate size.
+
+        * if a list is given that starts with ``einsum_path``, uses this as the
+          contraction path
+        * if False no optimization is taken
+        * if True defaults to the 'greedy' algorithm
+        * 'optimal' An algorithm that combinatorially explores all possible
+          ways of contracting the listed tensors and chooses the least costly
+          path. Scales exponentially with the number of terms in the
+          contraction.
+        * 'greedy' An algorithm that chooses the best pair contraction
+          at each step. Effectively, this algorithm searches the largest inner,
+          Hadamard, and then outer products at each step. Scales cubically with
+          the number of terms in the contraction. Equivalent to the 'optimal'
+          path for most contractions.
+
+        Default is 'greedy'.
+
+    Returns
+    -------
+    path : list of tuples
+        A list representation of the einsum path.
+    string_repr : str
+        A printable representation of the einsum path.
+
+    Notes
+    -----
+    The resulting path indicates which terms of the input contraction should be
+    contracted first, the result of this contraction is then appended to the
+    end of the contraction list. This list can then be iterated over until all
+    intermediate contractions are complete.
+
+    See Also
+    --------
+    einsum, linalg.multi_dot
+
+    Examples
+    --------
+
+    We can begin with a chain dot example. In this case, it is optimal to
+    contract the ``b`` and ``c`` tensors first as represented by the first
+    element of the path ``(1, 2)``. The resulting tensor is added to the end
+    of the contraction and the remaining contraction ``(0, 1)`` is then
+    completed.
+
+    >>> np.random.seed(123)
+    >>> a = np.random.rand(2, 2)
+    >>> b = np.random.rand(2, 5)
+    >>> c = np.random.rand(5, 2)
+    >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy')
+    >>> print(path_info[0])
+    ['einsum_path', (1, 2), (0, 1)]
+    >>> print(path_info[1])
+      Complete contraction:  ij,jk,kl->il # may vary
+             Naive scaling:  4
+         Optimized scaling:  3
+          Naive FLOP count:  1.600e+02
+      Optimized FLOP count:  5.600e+01
+       Theoretical speedup:  2.857
+      Largest intermediate:  4.000e+00 elements
+    -------------------------------------------------------------------------
+    scaling                  current                                remaining
+    -------------------------------------------------------------------------
+       3                   kl,jk->jl                                ij,jl->il
+       3                   jl,ij->il                                   il->il
+
+
+    A more complex index transformation example.
+
+    >>> I = np.random.rand(10, 10, 10, 10)
+    >>> C = np.random.rand(10, 10)
+    >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C,
+    ...                            optimize='greedy')
+
+    >>> print(path_info[0])
+    ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)]
+    >>> print(path_info[1]) 
+      Complete contraction:  ea,fb,abcd,gc,hd->efgh # may vary
+             Naive scaling:  8
+         Optimized scaling:  5
+          Naive FLOP count:  8.000e+08
+      Optimized FLOP count:  8.000e+05
+       Theoretical speedup:  1000.000
+      Largest intermediate:  1.000e+04 elements
+    --------------------------------------------------------------------------
+    scaling                  current                                remaining
+    --------------------------------------------------------------------------
+       5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+       5               bcde,fb->cdef                         gc,hd,cdef->efgh
+       5               cdef,gc->defg                            hd,defg->efgh
+       5               defg,hd->efgh                               efgh->efgh
+    """
+
+    # Figure out what the path really is
+    path_type = optimize
+    if path_type is True:
+        path_type = 'greedy'
+    if path_type is None:
+        path_type = False
+
+    explicit_einsum_path = False
+    memory_limit = None
+
+    # No optimization or a named path algorithm
+    if (path_type is False) or isinstance(path_type, str):
+        pass
+
+    # Given an explicit path
+    elif len(path_type) and (path_type[0] == 'einsum_path'):
+        explicit_einsum_path = True
+
+    # Path tuple with memory limit
+    elif ((len(path_type) == 2) and isinstance(path_type[0], str) and
+            isinstance(path_type[1], (int, float))):
+        memory_limit = int(path_type[1])
+        path_type = path_type[0]
+
+    else:
+        raise TypeError("Did not understand the path: %s" % str(path_type))
+
+    # Hidden option, only einsum should call this
+    einsum_call_arg = einsum_call
+
+    # Python side parsing
+    input_subscripts, output_subscript, operands = _parse_einsum_input(operands)
+
+    # Build a few useful list and sets
+    input_list = input_subscripts.split(',')
+    input_sets = [set(x) for x in input_list]
+    output_set = set(output_subscript)
+    indices = set(input_subscripts.replace(',', ''))
+
+    # Get length of each unique dimension and ensure all dimensions are correct
+    dimension_dict = {}
+    broadcast_indices = [[] for x in range(len(input_list))]
+    for tnum, term in enumerate(input_list):
+        sh = operands[tnum].shape
+        if len(sh) != len(term):
+            raise ValueError("Einstein sum subscript %s does not contain the "
+                             "correct number of indices for operand %d."
+                             % (input_subscripts[tnum], tnum))
+        for cnum, char in enumerate(term):
+            dim = sh[cnum]
+
+            # Build out broadcast indices
+            if dim == 1:
+                broadcast_indices[tnum].append(char)
+
+            if char in dimension_dict.keys():
+                # For broadcasting cases we always want the largest dim size
+                if dimension_dict[char] == 1:
+                    dimension_dict[char] = dim
+                elif dim not in (1, dimension_dict[char]):
+                    raise ValueError("Size of label '%s' for operand %d (%d) "
+                                     "does not match previous terms (%d)."
+                                     % (char, tnum, dimension_dict[char], dim))
+            else:
+                dimension_dict[char] = dim
+
+    # Convert broadcast inds to sets
+    broadcast_indices = [set(x) for x in broadcast_indices]
+
+    # Compute size of each input array plus the output array
+    size_list = [_compute_size_by_dict(term, dimension_dict)
+                 for term in input_list + [output_subscript]]
+    max_size = max(size_list)
+
+    if memory_limit is None:
+        memory_arg = max_size
+    else:
+        memory_arg = memory_limit
+
+    # Compute naive cost
+    # This isn't quite right, need to look into exactly how einsum does this
+    inner_product = (sum(len(x) for x in input_sets) - len(indices)) > 0
+    naive_cost = _flop_count(indices, inner_product, len(input_list), dimension_dict)
+
+    # Compute the path
+    if explicit_einsum_path:
+        path = path_type[1:]
+    elif (
+        (path_type is False)
+        or (len(input_list) in [1, 2])
+        or (indices == output_set)
+    ):
+        # Nothing to be optimized, leave it to einsum
+        path = [tuple(range(len(input_list)))]
+    elif path_type == "greedy":
+        path = _greedy_path(input_sets, output_set, dimension_dict, memory_arg)
+    elif path_type == "optimal":
+        path = _optimal_path(input_sets, output_set, dimension_dict, memory_arg)
+    else:
+        raise KeyError("Path name %s not found", path_type)
+
+    cost_list, scale_list, size_list, contraction_list = [], [], [], []
+
+    # Build contraction tuple (positions, gemm, einsum_str, remaining)
+    for cnum, contract_inds in enumerate(path):
+        # Make sure we remove inds from right to left
+        contract_inds = tuple(sorted(list(contract_inds), reverse=True))
+
+        contract = _find_contraction(contract_inds, input_sets, output_set)
+        out_inds, input_sets, idx_removed, idx_contract = contract
+
+        cost = _flop_count(idx_contract, idx_removed, len(contract_inds), dimension_dict)
+        cost_list.append(cost)
+        scale_list.append(len(idx_contract))
+        size_list.append(_compute_size_by_dict(out_inds, dimension_dict))
+
+        bcast = set()
+        tmp_inputs = []
+        for x in contract_inds:
+            tmp_inputs.append(input_list.pop(x))
+            bcast |= broadcast_indices.pop(x)
+
+        new_bcast_inds = bcast - idx_removed
+
+        # If we're broadcasting, nix blas
+        if not len(idx_removed & bcast):
+            do_blas = _can_dot(tmp_inputs, out_inds, idx_removed)
+        else:
+            do_blas = False
+
+        # Last contraction
+        if (cnum - len(path)) == -1:
+            idx_result = output_subscript
+        else:
+            sort_result = [(dimension_dict[ind], ind) for ind in out_inds]
+            idx_result = "".join([x[1] for x in sorted(sort_result)])
+
+        input_list.append(idx_result)
+        broadcast_indices.append(new_bcast_inds)
+        einsum_str = ",".join(tmp_inputs) + "->" + idx_result
+
+        contraction = (contract_inds, idx_removed, einsum_str, input_list[:], do_blas)
+        contraction_list.append(contraction)
+
+    opt_cost = sum(cost_list) + 1
+
+    if len(input_list) != 1:
+        # Explicit "einsum_path" is usually trusted, but we detect this kind of
+        # mistake in order to prevent from returning an intermediate value.
+        raise RuntimeError(
+            "Invalid einsum_path is specified: {} more operands has to be "
+            "contracted.".format(len(input_list) - 1))
+
+    if einsum_call_arg:
+        return (operands, contraction_list)
+
+    # Return the path along with a nice string representation
+    overall_contraction = input_subscripts + "->" + output_subscript
+    header = ("scaling", "current", "remaining")
+
+    speedup = naive_cost / opt_cost
+    max_i = max(size_list)
+
+    path_print  = "  Complete contraction:  %s\n" % overall_contraction
+    path_print += "         Naive scaling:  %d\n" % len(indices)
+    path_print += "     Optimized scaling:  %d\n" % max(scale_list)
+    path_print += "      Naive FLOP count:  %.3e\n" % naive_cost
+    path_print += "  Optimized FLOP count:  %.3e\n" % opt_cost
+    path_print += "   Theoretical speedup:  %3.3f\n" % speedup
+    path_print += "  Largest intermediate:  %.3e elements\n" % max_i
+    path_print += "-" * 74 + "\n"
+    path_print += "%6s %24s %40s\n" % header
+    path_print += "-" * 74
+
+    for n, contraction in enumerate(contraction_list):
+        inds, idx_rm, einsum_str, remaining, blas = contraction
+        remaining_str = ",".join(remaining) + "->" + output_subscript
+        path_run = (scale_list[n], einsum_str, remaining_str)
+        path_print += "\n%4d    %24s %40s" % path_run
+
+    path = ['einsum_path'] + path
+    return (path, path_print)
+
+
+def _einsum_dispatcher(*operands, out=None, optimize=None, **kwargs):
+    # Arguably we dispatch on more arguments than we really should; see note in
+    # _einsum_path_dispatcher for why.
+    yield from operands
+    yield out
+
+
+# Rewrite einsum to handle different cases
+@array_function_dispatch(_einsum_dispatcher, module='numpy')
+def einsum(*operands, out=None, optimize=False, **kwargs):
+    """
+    einsum(subscripts, *operands, out=None, dtype=None, order='K',
+           casting='safe', optimize=False)
+
+    Evaluates the Einstein summation convention on the operands.
+
+    Using the Einstein summation convention, many common multi-dimensional,
+    linear algebraic array operations can be represented in a simple fashion.
+    In *implicit* mode `einsum` computes these values.
+
+    In *explicit* mode, `einsum` provides further flexibility to compute
+    other array operations that might not be considered classical Einstein
+    summation operations, by disabling, or forcing summation over specified
+    subscript labels.
+
+    See the notes and examples for clarification.
+
+    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.
+    dtype : {data-type, None}, optional
+        If provided, forces the calculation to use the data type specified.
+        Note that you may have to also give a more liberal `casting`
+        parameter to allow the conversions. Default is None.
+    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'.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur.  Setting this to
+        'unsafe' is not recommended, as it can adversely affect accumulations.
+
+          * 'no' means the data types should not be cast at all.
+          * 'equiv' means only byte-order changes are allowed.
+          * 'safe' means only casts which can preserve values are allowed.
+          * 'same_kind' means only safe casts or casts within a kind,
+            like float64 to float32, are allowed.
+          * 'unsafe' means any data conversions may be done.
+
+        Default is 'safe'.
+    optimize : {False, True, 'greedy', 'optimal'}, optional
+        Controls if intermediate optimization should occur. No optimization
+        will occur if False and True will default to the 'greedy' algorithm.
+        Also accepts an explicit contraction list from the ``np.einsum_path``
+        function. See ``np.einsum_path`` for more details. Defaults to False.
+
+    Returns
+    -------
+    output : ndarray
+        The calculation based on the Einstein summation convention.
+
+    See Also
+    --------
+    einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
+    einops :
+        similar verbose interface is provided by
+        `einops <https://github.com/arogozhnikov/einops>`_ package to cover
+        additional operations: transpose, reshape/flatten, repeat/tile,
+        squeeze/unsqueeze and reductions.
+    opt_einsum :
+        `opt_einsum <https://optimized-einsum.readthedocs.io/en/stable/>`_
+        optimizes contraction order for einsum-like expressions
+        in backend-agnostic manner.
+
+    Notes
+    -----
+    .. versionadded:: 1.6.0
+
+    The Einstein summation convention can be used to compute
+    many multi-dimensional, linear algebraic array operations. `einsum`
+    provides a succinct way of representing these.
+
+    A non-exhaustive list of these operations,
+    which can be computed by `einsum`, is shown below along with examples:
+
+    * Trace of an array, :py:func:`numpy.trace`.
+    * Return a diagonal, :py:func:`numpy.diag`.
+    * Array axis summations, :py:func:`numpy.sum`.
+    * Transpositions and permutations, :py:func:`numpy.transpose`.
+    * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`.
+    * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`.
+    * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`.
+    * Tensor contractions, :py:func:`numpy.tensordot`.
+    * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`.
+
+    The subscripts string is a comma-separated list of subscript labels,
+    where each label refers to a dimension of the corresponding operand.
+    Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
+    is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
+    appears only once, it is not summed, so ``np.einsum('i', a)`` produces a
+    view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)``
+    describes traditional matrix multiplication and is equivalent to
+    :py:func:`np.matmul(a,b) <numpy.matmul>`. Repeated subscript labels in one
+    operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent
+    to :py:func:`np.trace(a) <numpy.trace>`.
+
+    In *implicit mode*, the chosen subscripts are important
+    since the axes of the output are reordered alphabetically.  This
+    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
+    ``np.einsum('ji', a)`` takes its transpose. Additionally,
+    ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
+    ``np.einsum('ij,jh', a, b)`` returns the transpose of the
+    multiplication since subscript 'h' precedes subscript 'i'.
+
+    In *explicit mode* the output can be directly controlled by
+    specifying output subscript labels.  This requires the
+    identifier '->' as well as the list of output subscript labels.
+    This feature increases the flexibility of the function since
+    summing can be disabled or forced when required. The call
+    ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) <numpy.sum>`,
+    and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) <numpy.diag>`.
+    The difference is that `einsum` does not allow broadcasting by default.
+    Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
+    order of the output subscript labels and therefore returns matrix
+    multiplication, unlike the example above in implicit mode.
+
+    To enable and control broadcasting, use an ellipsis.  Default
+    NumPy-style broadcasting is done by adding an ellipsis
+    to the left of each term, like ``np.einsum('...ii->...i', a)``.
+    To take the trace along the first and last axes,
+    you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
+    product with the left-most indices instead of rightmost, one can do
+    ``np.einsum('ij...,jk...->ik...', a, b)``.
+
+    When there is only one operand, no axes are summed, and no output
+    parameter is provided, a view into the operand is returned instead
+    of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
+    produces a view (changed in version 1.10.0).
+
+    `einsum` also provides an alternative way to provide the subscripts
+    and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
+    If the output shape is not provided in this format `einsum` will be
+    calculated in implicit mode, otherwise it will be performed explicitly.
+    The examples below have corresponding `einsum` calls with the two
+    parameter methods.
+
+    .. versionadded:: 1.10.0
+
+    Views returned from einsum are now writeable whenever the input array
+    is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
+    have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
+    and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
+    of a 2D array.
+
+    .. versionadded:: 1.12.0
+
+    Added the ``optimize`` argument which will optimize the contraction order
+    of an einsum expression. For a contraction with three or more operands this
+    can greatly increase the computational efficiency at the cost of a larger
+    memory footprint during computation.
+
+    Typically a 'greedy' algorithm is applied which empirical tests have shown
+    returns the optimal path in the majority of cases. In some cases 'optimal'
+    will return the superlative path through a more expensive, exhaustive search.
+    For iterative calculations it may be advisable to calculate the optimal path
+    once and reuse that path by supplying it as an argument. An example is given
+    below.
+
+    See :py:func:`numpy.einsum_path` for more details.
+
+    Examples
+    --------
+    >>> a = np.arange(25).reshape(5,5)
+    >>> b = np.arange(5)
+    >>> c = np.arange(6).reshape(2,3)
+
+    Trace of a matrix:
+
+    >>> np.einsum('ii', a)
+    60
+    >>> np.einsum(a, [0,0])
+    60
+    >>> np.trace(a)
+    60
+
+    Extract the diagonal (requires explicit form):
+
+    >>> np.einsum('ii->i', a)
+    array([ 0,  6, 12, 18, 24])
+    >>> np.einsum(a, [0,0], [0])
+    array([ 0,  6, 12, 18, 24])
+    >>> np.diag(a)
+    array([ 0,  6, 12, 18, 24])
+
+    Sum over an axis (requires explicit form):
+
+    >>> np.einsum('ij->i', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [0,1], [0])
+    array([ 10,  35,  60,  85, 110])
+    >>> np.sum(a, axis=1)
+    array([ 10,  35,  60,  85, 110])
+
+    For higher dimensional arrays summing a single axis can be done with ellipsis:
+
+    >>> np.einsum('...j->...', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
+    array([ 10,  35,  60,  85, 110])
+
+    Compute a matrix transpose, or reorder any number of axes:
+
+    >>> np.einsum('ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum('ij->ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum(c, [1,0])
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.transpose(c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+
+    Vector inner products:
+
+    >>> np.einsum('i,i', b, b)
+    30
+    >>> np.einsum(b, [0], b, [0])
+    30
+    >>> np.inner(b,b)
+    30
+
+    Matrix vector multiplication:
+
+    >>> np.einsum('ij,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum(a, [0,1], b, [1])
+    array([ 30,  80, 130, 180, 230])
+    >>> np.dot(a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum('...j,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+
+    Broadcasting and scalar multiplication:
+
+    >>> np.einsum('..., ...', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(',ij', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.multiply(3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+
+    Vector outer product:
+
+    >>> np.einsum('i,j', np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.einsum(np.arange(2)+1, [0], b, [1])
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.outer(np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+
+    Tensor contraction:
+
+    >>> a = np.arange(60.).reshape(3,4,5)
+    >>> b = np.arange(24.).reshape(4,3,2)
+    >>> np.einsum('ijk,jil->kl', a, b)
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+    >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+    >>> np.tensordot(a,b, axes=([1,0],[0,1]))
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+
+    Writeable returned arrays (since version 1.10.0):
+
+    >>> a = np.zeros((3, 3))
+    >>> np.einsum('ii->i', a)[:] = 1
+    >>> a
+    array([[1., 0., 0.],
+           [0., 1., 0.],
+           [0., 0., 1.]])
+
+    Example of ellipsis use:
+
+    >>> a = np.arange(6).reshape((3,2))
+    >>> b = np.arange(12).reshape((4,3))
+    >>> np.einsum('ki,jk->ij', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('ki,...k->i...', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('k...,jk', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+
+    Chained array operations. For more complicated contractions, speed ups
+    might be achieved by repeatedly computing a 'greedy' path or pre-computing the
+    'optimal' path and repeatedly applying it, using an
+    `einsum_path` insertion (since version 1.12.0). Performance improvements can be
+    particularly significant with larger arrays:
+
+    >>> a = np.ones(64).reshape(2,4,8)
+
+    Basic `einsum`: ~1520ms  (benchmarked on 3.1GHz Intel i5.)
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)
+
+    Sub-optimal `einsum` (due to repeated path calculation time): ~330ms
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')
+
+    Greedy `einsum` (faster optimal path approximation): ~160ms
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy')
+
+    Optimal `einsum` (best usage pattern in some use cases): ~110ms
+
+    >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')[0]
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path)
+
+    """
+    # Special handling if out is specified
+    specified_out = out is not None
+
+    # If no optimization, run pure einsum
+    if optimize is False:
+        if specified_out:
+            kwargs['out'] = out
+        return c_einsum(*operands, **kwargs)
+
+    # Check the kwargs to avoid a more cryptic error later, without having to
+    # repeat default values here
+    valid_einsum_kwargs = ['dtype', 'order', 'casting']
+    unknown_kwargs = [k for (k, v) in kwargs.items() if
+                      k not in valid_einsum_kwargs]
+    if len(unknown_kwargs):
+        raise TypeError("Did not understand the following kwargs: %s"
+                        % unknown_kwargs)
+
+    # Build the contraction list and operand
+    operands, contraction_list = 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':
+        if all(arr.flags.f_contiguous for arr in operands):
+            output_order = 'F'
+        else:
+            output_order = 'C'
+
+    # Start contraction loop
+    for num, contraction in enumerate(contraction_list):
+        inds, idx_rm, einsum_str, remaining, blas = 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))
+
+        # Call tensordot if still possible
+        if blas:
+            # Checks have already been handled
+            input_str, results_index = einsum_str.split('->')
+            input_left, input_right = input_str.split(',')
+
+            tensor_result = input_left + input_right
+            for s in idx_rm:
+                tensor_result = tensor_result.replace(s, "")
+
+            # Find indices to contract over
+            left_pos, right_pos = [], []
+            for s in sorted(idx_rm):
+                left_pos.append(input_left.find(s))
+                right_pos.append(input_right.find(s))
+
+            # Contract!
+            new_view = tensordot(*tmp_operands, axes=(tuple(left_pos), tuple(right_pos)))
+
+            # Build a new view if needed
+            if (tensor_result != results_index) or handle_out:
+                if handle_out:
+                    kwargs["out"] = out
+                new_view = c_einsum(tensor_result + '->' + results_index, new_view, **kwargs)
+
+        # Call einsum
+        else:
+            # If out was specified
+            if handle_out:
+                kwargs["out"] = out
+
+            # Do the contraction
+            new_view = c_einsum(einsum_str, *tmp_operands, **kwargs)
+
+        # Append new items and dereference what we can
+        operands.append(new_view)
+        del tmp_operands, new_view
+
+    if specified_out:
+        return out
+    else:
+        return asanyarray(operands[0], order=output_order)