numpy.einsum_path(subscripts, *operands, optimize='greedy')
[source]
Evaluates the lowest cost contraction order for an einsum expression by considering the creation of intermediate arrays.
Parameters: 


Returns: 

See also
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.
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
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https://docs.scipy.org/doc/numpy1.17.0/reference/generated/numpy.einsum_path.html