| 1 | /**
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| 2 | * @license
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| 3 | * Copyright 2021 Google LLC. All Rights Reserved.
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| 4 | * Licensed under the Apache License, Version 2.0 (the "License");
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| 5 | * you may not use this file except in compliance with the License.
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| 6 | * You may obtain a copy of the License at
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| 7 | *
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| 8 | * http://www.apache.org/licenses/LICENSE-2.0
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| 9 | *
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| 10 | * Unless required by applicable law or agreed to in writing, software
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| 11 | * distributed under the License is distributed on an "AS IS" BASIS,
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| 12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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| 13 | * See the License for the specific language governing permissions and
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| 14 | * limitations under the License.
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| 15 | * =============================================================================
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| 16 | */
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| 17 | /// <amd-module name="@tensorflow/tfjs-core/dist/ops/einsum" />
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| 18 | import { Tensor } from '../tensor';
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| 19 | /**
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| 20 | * Tensor contraction over specified indices and outer product.
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| 21 | *
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| 22 | * `einsum` allows defining Tensors by defining their element-wise computation.
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| 23 | * This computation is based on
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| 24 | * [Einstein summation](https://en.wikipedia.org/wiki/Einstein_notation).
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| 25 | *
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| 26 | * Some special cases include:
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| 27 | *
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| 28 | * Matrix multiplication:
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| 29 | * ```js
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| 30 | * const x = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
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| 31 | * const y = tf.tensor2d([[0, 1], [2, 3], [4, 5]]);
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| 32 | * x.print();
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| 33 | * y.print();
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| 34 | * tf.einsum('ij,jk->ik', x, y).print();
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| 35 | * ```
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| 36 | *
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| 37 | * Dot product:
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| 38 | * ```js
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| 39 | * const x = tf.tensor1d([1, 2, 3]);
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| 40 | * const y = tf.tensor1d([0, 1, 2]);
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| 41 | * x.print();
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| 42 | * y.print();
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| 43 | * tf.einsum('i,i->', x, y).print();
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| 44 | * ```
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| 45 | *
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| 46 | * Batch dot product:
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| 47 | * ```js
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| 48 | * const x = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
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| 49 | * const y = tf.tensor2d([[0, 1, 2], [3, 4, 5]]);
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| 50 | * x.print();
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| 51 | * y.print();
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| 52 | * tf.einsum('bi,bi->b', x, y).print();
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| 53 | * ```
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| 54 | *
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| 55 | * Outer prouduct:
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| 56 | * ```js
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| 57 | * const x = tf.tensor1d([1, 3, 5]);
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| 58 | * const y = tf.tensor1d([2, 4, 6]);
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| 59 | * x.print();
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| 60 | * y.print();
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| 61 | * tf.einsum('i,j->ij', x, y).print();
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| 62 | * ```
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| 63 | *
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| 64 | * Matrix transpose:
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| 65 | * ```js
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| 66 | * const x = tf.tensor2d([[1, 2], [3, 4]]);
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| 67 | * x.print();
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| 68 | * tf.einsum('ij->ji', x).print();
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| 69 | * ```
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| 70 | *
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| 71 | * Batch matrix transpose:
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| 72 | * ```js
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| 73 | * const x = tf.tensor3d([[[1, 2], [3, 4]], [[-1, -2], [-3, -4]]]);
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| 74 | * x.print();
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| 75 | * tf.einsum('bij->bji', x).print();
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| 76 | * ```
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| 77 | *
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| 78 | * Limitations:
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| 79 | *
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| 80 | * This implementation of einsum has the following limitations:
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| 81 | *
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| 82 | * - Does not support >2 input tensors.
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| 83 | * - Does not support duplicate axes for any given input tensor. E.g., equation
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| 84 | * 'ii->' is not suppoted.
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| 85 | * - The `...` notation is not supported.
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| 86 | *
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| 87 | * @param equation a string describing the contraction, in the same format as
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| 88 | * [numpy.einsum](https://numpy.org/doc/stable/reference/generated/numpy.einsum.html).
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| 89 | * @param tensors the input(s) to contract (each one a Tensor), whose shapes
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| 90 | * should be consistent with equation.
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| 91 | * @returns The output tensor.
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| 92 | *
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| 93 | * @doc {heading: 'Tensors', subheading: 'Matrices'}
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| 94 | */
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| 95 | export declare function einsum_(equation: string, ...tensors: Tensor[]): Tensor;
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| 96 | export declare const einsum: typeof einsum_;
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