Einstein Summation Numpy API

This is evaluates the einstein summation on the operands. It is analogous to numpy.einsum, and uses the same notation.

Examples for all the possible use cases are provided below.

omtools.std.einsum.einsum(*operands: List[omtools.core.variable.Variable], subscripts: str, partial_format='dense')

The Einstein Summation function performs the equivalent of numpy.einsum

Parameters

operands: Variable(s)

The Variable(s) which you would like to perform an einsum with.

subscripts: str

Specifies the subscripts for summation as comma separated list of subscript labels

partial_format: str

Denotes whether to compute ‘dense’ partials or ‘sparse’ partials

Inner Products

• Vector-Vector Inner Product using Einsum
• Vector-Vector Inner Product using Einsum with Sparse Partials
• Tensor-Vector Inner Product using Einsum
• Tensor-Vector Inner Product using Einsum with Sparse Partials

Outer Products

• Vector-Vector Outer Product using Einsum
• Vector-Vector Outer Product using Einsum with Sparse Partials
• Tensor-Vector Outer Product using Einsum
• Tensor-Vector Outer Product using Einsum with Sparse Partials

Reorder Operations

• Reordering a Matrix using Einsum
• Reordering a Matrix using Einsum with Sparse Partials
• Reordering a Tensor using Einsum
• Reordering a Tensor using Einsum with Sparse Partials

Summation Operations

• Single Vector Summation using Einsum
• Single Vector Summation using Einsum with Sparse Partials
• Single Tensor Summation using Einsum
• Single Tensor Summation using Einsum with Sparse Partials

Special Operations

• Multiple Vector Summation using Einsum
• Multiple Vector Summation using Einsum with Sparse Partials