1 | /**
|
2 | * @license
|
3 | * Copyright 2021 Google LLC. All Rights Reserved.
|
4 | * Licensed under the Apache License, Version 2.0 (the "License");
|
5 | * you may not use this file except in compliance with the License.
|
6 | * You may obtain a copy of the License at
|
7 | *
|
8 | * http://www.apache.org/licenses/LICENSE-2.0
|
9 | *
|
10 | * Unless required by applicable law or agreed to in writing, software
|
11 | * distributed under the License is distributed on an "AS IS" BASIS,
|
12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
13 | * See the License for the specific language governing permissions and
|
14 | * limitations under the License.
|
15 | * =============================================================================
|
16 | */
|
17 | import { ENGINE } from '../engine';
|
18 | import { Einsum } from '../kernel_names';
|
19 | import { convertToTensor } from '../tensor_util_env';
|
20 | import { op } from './operation';
|
21 | /**
|
22 | * Tensor contraction over specified indices and outer product.
|
23 | *
|
24 | * `einsum` allows defining Tensors by defining their element-wise computation.
|
25 | * This computation is based on
|
26 | * [Einstein summation](https://en.wikipedia.org/wiki/Einstein_notation).
|
27 | *
|
28 | * Some special cases include:
|
29 | *
|
30 | * Matrix multiplication:
|
31 | * ```js
|
32 | * const x = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
|
33 | * const y = tf.tensor2d([[0, 1], [2, 3], [4, 5]]);
|
34 | * x.print();
|
35 | * y.print();
|
36 | * tf.einsum('ij,jk->ik', x, y).print();
|
37 | * ```
|
38 | *
|
39 | * Dot product:
|
40 | * ```js
|
41 | * const x = tf.tensor1d([1, 2, 3]);
|
42 | * const y = tf.tensor1d([0, 1, 2]);
|
43 | * x.print();
|
44 | * y.print();
|
45 | * tf.einsum('i,i->', x, y).print();
|
46 | * ```
|
47 | *
|
48 | * Batch dot product:
|
49 | * ```js
|
50 | * const x = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
|
51 | * const y = tf.tensor2d([[0, 1, 2], [3, 4, 5]]);
|
52 | * x.print();
|
53 | * y.print();
|
54 | * tf.einsum('bi,bi->b', x, y).print();
|
55 | * ```
|
56 | *
|
57 | * Outer prouduct:
|
58 | * ```js
|
59 | * const x = tf.tensor1d([1, 3, 5]);
|
60 | * const y = tf.tensor1d([2, 4, 6]);
|
61 | * x.print();
|
62 | * y.print();
|
63 | * tf.einsum('i,j->ij', x, y).print();
|
64 | * ```
|
65 | *
|
66 | * Matrix transpose:
|
67 | * ```js
|
68 | * const x = tf.tensor2d([[1, 2], [3, 4]]);
|
69 | * x.print();
|
70 | * tf.einsum('ij->ji', x).print();
|
71 | * ```
|
72 | *
|
73 | * Batch matrix transpose:
|
74 | * ```js
|
75 | * const x = tf.tensor3d([[[1, 2], [3, 4]], [[-1, -2], [-3, -4]]]);
|
76 | * x.print();
|
77 | * tf.einsum('bij->bji', x).print();
|
78 | * ```
|
79 | *
|
80 | * Limitations:
|
81 | *
|
82 | * This implementation of einsum has the following limitations:
|
83 | *
|
84 | * - Does not support >2 input tensors.
|
85 | * - Does not support duplicate axes for any given input tensor. E.g., equation
|
86 | * 'ii->' is not suppoted.
|
87 | * - The `...` notation is not supported.
|
88 | *
|
89 | * @param equation a string describing the contraction, in the same format as
|
90 | * [numpy.einsum](https://numpy.org/doc/stable/reference/generated/numpy.einsum.html).
|
91 | * @param tensors the input(s) to contract (each one a Tensor), whose shapes
|
92 | * should be consistent with equation.
|
93 | * @returns The output tensor.
|
94 | *
|
95 | * @doc {heading: 'Tensors', subheading: 'Matrices'}
|
96 | */
|
97 | export function einsum_(equation, ...tensors) {
|
98 | const $tensors = tensors.map((t, i) => convertToTensor(t, `tensors${i}`, 'einsum'));
|
99 | const attrs = { equation };
|
100 | return ENGINE.runKernel(Einsum, $tensors, attrs);
|
101 | }
|
102 | export const einsum = op({ einsum_ });
|
103 | //# sourceMappingURL=einsum.js.map |
\ | No newline at end of file |