Einsums Python Tensor Algebra#

This page will discuss functions and classes relating to tensor algebra calls in Python.

einsums.core.compile_plan(C_indices: str, A_indices: str, B_indices: str) → einsums.core.EinsumsGenericPlan#

Inspects the indices passed in the strings and determines any optimizations that can be done to the subsequent operations with this plan. The call will look something like \(C_{abc\cdots} = \alpha C_{abc\cdots} + \beta A_{def\cdots} B_{ghi\cdots}\), though we don’t have to specify the prefactors here. Only the indices need to be specified.

As an example on how to use this, here is a matrix multiplication.

>>> import einsums
>>> plan = einsums.core.compile_plan("ij", "ik", "kj")
>>> A = einsums.util.create_random_tensor("A", [3, 3])
>>> B = einsums.util.create_random_tensor("B", [3, 3])
>>> C = einsums.util.create_random_tensor("C", [3, 3])
>>> plan.execute(0, C, 1, A, B)
Parameters:

  • C_indices – The indices on the output tensor.

  • A_indices – The indices on the left input tensor.

  • B_indices – The indices on the right input tensor.

Returns:

A plan which can execute the given tensor operation.

class einsums.core.EinsumsGenericPlan#

This is the base for all plans. It is also the fall-back when a plan that normally could be optimized is passed values that it can’t handle, such as tensors with different types or tensor views whose smallest stride is more than one element (usually).

execute(C_prefactor, C, AB_prefactor, A, B) → None#

Execute the plan. This can work when C_prefactor and AB_prefactor can be cast to numbers, as well as when A, B, and C are either all buffer objects or all einsums.core.GPUView objects. If they are all einsums.core.GPUView objects, make sure to watch the state of the synchronization of the objects, as they may become desynchronized.

class einsums.core.EinsumsDotPlan#

This plan optimizes calls that are equivalent to dot products. At this time, C cannot be a scalar value. This may change in the future. This does not conjugate A or B, meaning this is not a true dot product. The form of the dot product is this: \(C = \alpha C + \beta A_{i} B_{i}\).

execute(C_prefactor, C, AB_prefactor, A, B) → None#

Execute the plan. This can work when C_prefactor and AB_prefactor can be cast to numbers, as well as when A, B, and C are either all buffer objects or all einsums.core.GPUView objects. If they are all einsums.core.GPUView objects, make sure to watch the state of the synchronization of the objects, as they may become desynchronized.

class einsums.core.EinsumsDirectProductPlan#

This plan optimizes calls that are equivalent to direct products. The ideal form of the direct product is this: \(C_{i} = \alpha C_{i} + \beta A_{i} B_{i}\).

execute(C_prefactor, C, AB_prefactor, A, B) → None#

Execute the plan. This can work when C_prefactor and AB_prefactor can be cast to numbers, as well as when A, B, and C are either all buffer objects or all einsums.core.GPUView objects. If they are all einsums.core.GPUView objects, make sure to watch the state of the synchronization of the objects, as they may become desynchronized.

class einsums.core.EinsumsGerPlan#

This plan optimizes calls that are equivalent to outer products, calling BLAS’s ger at its core. The ideal form of the direct product is this: \(C_{ij} = \alpha C_{ij} + \beta A_{i} B_{j}\).

execute(C_prefactor, C, AB_prefactor, A, B) → None#

Execute the plan. This can work when C_prefactor and AB_prefactor can be cast to numbers, as well as when A, B, and C are either all buffer objects or all einsums.core.GPUView objects. If they are all einsums.core.GPUView objects, make sure to watch the state of the synchronization of the objects, as they may become desynchronized.

class einsums.core.EinsumsGemvPlan#

This plan optimizes calls that are equivalent to matrix-vector products, calling BLAS’s gemv at its core. The ideal form of the direct product is this: \(C_{i} = \alpha C_{i} + \beta A_{ij} B_{j}\).

execute(C_prefactor, C, AB_prefactor, A, B) → None#

Execute the plan. This can work when C_prefactor and AB_prefactor can be cast to numbers, as well as when A, B, and C are either all buffer objects or all einsums.core.GPUView objects. If they are all einsums.core.GPUView objects, make sure to watch the state of the synchronization of the objects, as they may become desynchronized.

class einsums.core.EinsumsGemmPlan#

This plan optimizes calls that are equivalent to matrix products, calling BLAS’s gemm at its core. The ideal form of the direct product is this: \(C_{ij} = \alpha C_{ij} + \beta A_{ik} B_{kj}\).

execute(C_prefactor, C, AB_prefactor, A, B) → None#

Execute the plan. This can work when C_prefactor and AB_prefactor can be cast to numbers, as well as when A, B, and C are either all buffer objects or all einsums.core.GPUView objects. If they are all einsums.core.GPUView objects, make sure to watch the state of the synchronization of the objects, as they may become desynchronized.