Metadata-Version: 2.1
Name: opt-einsum
Version: 0+unknown
Summary: Optimizing numpys einsum function
Home-page: https://github.com/dgasmith/opt_einsum
Author: Daniel Smith
Author-email: dgasmith@icloud.com
License: MIT
Description: 
        Einsum is a very powerful function for contracting tensors of arbitrary
        dimension and index. However, it is only optimized to contract two terms
        at a time resulting in non-optimal scaling.
        
        For example, consider the following index transformation:
        ``M_{pqrs} = C_{pi} C_{qj} I_{ijkl} C_{rk} C_{sl}``
        
        Consider two different algorithms:
        
        .. code:: python
        
            import numpy as np
            N = 10
            C = np.random.rand(N, N)
            I = np.random.rand(N, N, N, N)
        
            def naive(I, C):
                # N^8 scaling
                return np.einsum('pi,qj,ijkl,rk,sl->pqrs', C, C, I, C, C)
        
            def optimized(I, C):
                # N^5 scaling
                K = np.einsum('pi,ijkl->pjkl', C, I)
                K = np.einsum('qj,pjkl->pqkl', C, K)
                K = np.einsum('rk,pqkl->pqrl', C, K)
                K = np.einsum('sl,pqrl->pqrs', C, K)
                return K
        
        The einsum function does not consider building intermediate arrays;
        therefore, helping einsum out by building these intermediate arrays can result
        in a considerable cost savings even for small N (N=10):
        
        .. code:: python
        
            >> np.allclose(naive(I, C), optimized(I, C))
            True
        
            %timeit naive(I, C)
            1 loops, best of 3: 1.18 s per loop
        
            %timeit optimized(I, C)
            1000 loops, best of 3: 612 µs per loop
        
        The index transformation is a well known contraction that leads to
        straightforward intermediates. This contraction can be further
        complicated by considering that the shape of the C matrices need not be
        the same, in this case the ordering in which the indices are transformed
        matters greatly. Logic can be built that optimizes the ordering;
        however, this is a lot of time and effort for a single expression.
        
        The opt_einsum package is a drop in replacement for the ``np.einsum`` function
        and can handle all of the logic for you:
        
        .. code:: python
        
            from opt_einsum import contract
        
            contract('pi,qj,ijkl,rk,sl->pqrs', C, C, I, C, C)
        
        The above will automatically find the optimal contraction order, in this case
        identical to that of the optimized function above, and compute the products for
        you. In this case, it even uses `np.dot` under the hood to exploit any vendor
        BLAS functionality that your NumPy build has!
        
        We can then view more details about the optimized contraction order:
        
        .. code:: python
        
            >>> from opt_einsum import contract_path
        
            >>> path_info = oe.contract_path('pi,qj,ijkl,rk,sl->pqrs', C, C, I, C, C)
        
            >>> print(path_info[0])
            [(0, 2), (0, 3), (0, 2), (0, 1)]
        
            >>> print(path_info[1])
              Complete contraction:  pi,qj,ijkl,rk,sl->pqrs
                     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   BLAS                  current                                remaining
            --------------------------------------------------------------------------------
               5      GEMM            ijkl,pi->jklp                      qj,rk,sl,jklp->pqrs
               5      GEMM            jklp,qj->klpq                         rk,sl,klpq->pqrs
               5      GEMM            klpq,rk->lpqr                            sl,lpqr->pqrs
               5      GEMM            lpqr,sl->pqrs                               pqrs->pqrs
        
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Provides-Extra: docs
Provides-Extra: tests
