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| /**
| * @license
| * Copyright 2021 Google LLC. All Rights Reserved.
| * Licensed under the Apache License, Version 2.0 (the "License");
| * you may not use this file except in compliance with the License.
| * You may obtain a copy of the License at
| *
| * http://www.apache.org/licenses/LICENSE-2.0
| *
| * Unless required by applicable law or agreed to in writing, software
| * distributed under the License is distributed on an "AS IS" BASIS,
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
| * See the License for the specific language governing permissions and
| * limitations under the License.
| * =============================================================================
| */
| import * as tf from '../index';
| import { ALL_ENVS, describeWithFlags } from '../jasmine_util';
| import { expectArraysClose } from '../test_util';
| import { tensor1d, tensor2d, tensor3d } from './ops';
| describeWithFlags('einsum', ALL_ENVS, () => {
| it('two scalars', async () => {
| const x = tf.scalar(2);
| const y = tf.scalar(3);
| const out = tf.einsum(',->', x, y);
| expectArraysClose(await out.data(), 6);
| });
| it('1D tensor and scalars: reduce', async () => {
| const x = tensor1d([2, 3]);
| const y = tf.scalar(4);
| const out = tf.einsum('i,->', x, y);
| expectArraysClose(await out.data(), 20);
| });
| it('1D tensor and scalars: multiply', async () => {
| const x = tensor1d([2, 3]);
| const y = tf.scalar(4);
| const out = tf.einsum('i,->i', x, y);
| expectArraysClose(await out.data(), [8, 12]);
| });
| it('1d reduce sum', async () => {
| const x = tensor1d([2, 4, 6]);
| const out = tf.einsum('i->', x);
| expectArraysClose(await out.data(), 12);
| });
| it('2d matrix reduce sum', async () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| const out = tf.einsum('ij->', x);
| expectArraysClose(await out.data(), 10);
| });
| it('2d matrices multiply and reduce summing', async () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| const y = tensor2d([[4, 3], [2, 1]]);
| const out = tf.einsum('ij,ji->', x, y);
| expectArraysClose(await out.data(), 21);
| });
| it('2d matrix times scalar and reduce summing', async () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| const y = tf.scalar(5);
| const out = tf.einsum('ij,->', x, y);
| expectArraysClose(await out.data(), 50);
| });
| it('two 1d tensors dot', async () => {
| const x = tensor1d([1, 3, 5]);
| const y = tensor1d([2, 4, 6]);
| const out = tf.einsum('i,i->', x, y);
| expectArraysClose(await out.data(), 44);
| });
| it('two 1d tensors outer', async () => {
| const x = tensor1d([1, 3, 5]);
| const y = tensor1d([2, 4, 6]);
| const out = tf.einsum('i,j->ij', x, y);
| expectArraysClose(await out.data(), [[2, 4, 6], [6, 12, 18], [10, 20, 30]]);
| });
| it('2d matrix calculate trace: duplicate axes not implemented yet', () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| expect(() => tf.einsum('ii->', x)).toThrowError(/not implemented yet/);
| });
| it('2d and 1d matrix & vector multiply', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor1d([2, 4, 6]);
| const out = tf.einsum('ij,j->i', x, y);
| expectArraysClose(await out.data(), [28, 64]);
| });
| it('2d matrix sum along columns', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const out = tf.einsum('ij->j', x);
| expectArraysClose(await out.data(), [5, 7, 9]);
| });
| it('2d matrix sum along rows', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const out = tf.einsum('ij->i', x);
| expectArraysClose(await out.data(), [6, 15]);
| });
| it('2d matrix transposing', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const out = tf.einsum('ij->ji', x);
| expectArraysClose(await out.data(), [[1, 4], [2, 5], [3, 6]]);
| });
| it('2d matrix multiply', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1], [2, 3], [4, 5]]);
| const out = tf.einsum('ij,jk->ik', x, y);
| expectArraysClose(await out.data(), [[16, 22], [34, 49]]);
| });
| it('2d matrix multiply and transposing', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1], [2, 3], [4, 5]]);
| const out = tf.einsum('ij,jk->ki', x, y);
| expectArraysClose(await out.data(), [[16, 34], [22, 49]]);
| });
| it('two 2d matrices batch dot', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1, 2], [3, 4, 5]]);
| const out = tf.einsum('bi,bi->b', x, y);
| expectArraysClose(await out.data(), [8, 62]);
| });
| it('two 2d matrices batch outer', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1, 2], [3, 4, 5]]);
| const out = tf.einsum('bi,bj->bij', x, y);
| expectArraysClose(await out.data(), [
| [[0, 1, 2], [0, 2, 4], [0, 3, 6]],
| [[12, 16, 20], [15, 20, 25], [18, 24, 30]]
| ]);
| });
| it('two 3d tensors batch matmul', async () => {
| const x = tf.reshape(tf.range(1, 13), [2, 2, 3]);
| const y = tf.reshape(tf.range(1, 19), [2, 3, 3]);
| const out = tf.einsum('bij,bjk->bik', x, y);
| expectArraysClose(await out.data(), [[[30, 36, 42], [66, 81, 96]], [[318, 342, 366], [435, 468, 501]]]);
| });
| it('two 3d tensors A', async () => {
| const x = tf.reshape(tf.range(1, 9), [2, 2, 2]);
| const y = tf.reshape(tf.range(1, 13), [2, 3, 2]);
| const out = tf.einsum('adc,abc->abd', x, y);
| expectArraysClose(await out.data(), [[[5, 11], [11, 25], [17, 39]], [[83, 113], [105, 143], [127, 173]]]);
| });
| it('two 3d tensors B', async () => {
| const x = tf.reshape(tf.range(1, 9), [2, 2, 2]);
| const y = tf.reshape(tf.range(1, 13), [2, 3, 2]);
| const out = tf.einsum('adc,abc->adb', x, y);
| expectArraysClose(await out.data(), [[[5, 11, 17], [11, 25, 39]], [[83, 105, 127], [113, 143, 173]]]);
| });
| it('one 3d tensor: batch matrix transposing', async () => {
| const x = tensor3d([[[1, 2], [3, 4]], [[-1, -2], [-3, -4]]]);
| const out = tf.einsum('bij->bji', x);
| expectArraysClose(await out.data(), [[[1, 3], [2, 4]], [[-1, -3], [-2, -4]]]);
| });
| it('4d tensor and 3d tensor, contracting two dimensions', async () => {
| const x = tf.reshape(tf.range(1, 33), [2, 4, 2, 2]);
| const y = tf.reshape(tf.range(1, 9), [2, 2, 2]);
| const out = tf.einsum('abcd,cde->abe', x, y);
| expectArraysClose(await out.data(), [
| [[50, 60], [114, 140], [178, 220], [242, 300]],
| [[306, 380], [370, 460], [434, 540], [498, 620]]
| ]);
| });
| it('two 4d tensors, contracting one dimension', async () => {
| const x = tf.reshape(tf.range(1, 33), [2, 4, 2, 2]);
| const y = tf.reshape(tf.range(1, 25), [2, 3, 2, 2]);
| const out = tf.einsum('aecd,abcd->acbe', x, y);
| expectArraysClose(await out.data(), [
| [
| [[5, 17, 29, 41], [17, 61, 105, 149], [29, 105, 181, 257]],
| [[25, 53, 81, 109], [53, 113, 173, 233], [81, 173, 265, 357]]
| ],
| [
| [[473, 581, 689, 797], [613, 753, 893, 1033], [753, 925, 1097, 1269]],
| [[605, 729, 853, 977], [761, 917, 1073, 1229], [917, 1105, 1293, 1481]]
| ]
| ]);
| });
| it('two 4d tensors, contracting two dimensions', async () => {
| const x = tf.reshape(tf.range(1, 33), [2, 4, 2, 2]);
| const y = tf.reshape(tf.range(1, 25), [2, 3, 2, 2]);
| const out = tf.einsum('aecd,abcd->abe', x, y);
| expectArraysClose(await out.data(), [
| [[30, 70, 110, 150], [70, 174, 278, 382], [110, 278, 446, 614]],
| [
| [1078, 1310, 1542, 1774], [1374, 1670, 1966, 2262],
| [1670, 2030, 2390, 2750]
| ]
| ]);
| });
| it('mismatched dimensions throws error', () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1], [2, 3]]);
| expect(() => tf.einsum('ij,jk->ik', x, y))
| .toThrowError(/dimension 3 at axis 0 of (the )?input shaped \[2,2\]/);
| });
| it('incorrect equation throws error', () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| const y = tensor2d([[0, 1], [2, 3]]);
| expect(() => tf.einsum('', x, y))
| .toThrowError(/Equations without an arrow|Expecting exactly one/);
| expect(() => tf.einsum('ij,jk>ik', x, y))
| .toThrowError(/Equations without an arrow|Expecting exactly one/);
| });
| it('incorrect number of tensors throws error', () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| const y = tensor2d([[0, 1], [2, 3]]);
| expect(() => tf.einsum('ij->ji', x, y))
| .toThrowError(/Expected 1 inputs? (tensors, received)?(but got:)? 2/);
| });
| it('more than two input tensors throws error', async () => {
| const x = tensor2d([[1, 2], [3, 4]]);
| const y = tensor2d([[0, 1], [2, 3]]);
| const z = tensor2d([[-1, 0], [1, 2]]);
| expect(() => tf.einsum('ij,jk,kl->il', x, y, z))
| .toThrowError(/(more than 2 input tensors)|(Expecting 1 or 2 input)/);
| });
| it('nonexistent dimension throws error', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1], [2, 3], [4, 5]]);
| expect(() => tf.einsum('ij,jk->in', x, y))
| .toThrowError('Output subscripts contain the label n not present in ' +
| 'the input subscripts.');
| });
| it('two arrows in equation throws error', async () => {
| const x = tensor2d([[1, 2, 3], [4, 5, 6]]);
| const y = tensor2d([[0, 1], [2, 3], [4, 5]]);
| expect(() => tf.einsum('ij,jk->ik->i', x, y)).toThrowError(/exactly one/);
| });
| });
| //# 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* @license\n * Copyright 2021 Google LLC. All Rights Reserved.\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.\n * You may obtain a copy of the License at\n *\n * http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n * See the License for the specific language governing permissions and\n * limitations under the License.\n * =============================================================================\n */\n\nimport * as tf from '../index';\nimport {ALL_ENVS, describeWithFlags} from '../jasmine_util';\nimport {expectArraysClose} from '../test_util';\n\nimport {tensor1d, tensor2d, tensor3d} from './ops';\n\ndescribeWithFlags('einsum', ALL_ENVS, () => {\n  it('two scalars', async () => {\n    const x = tf.scalar(2);\n    const y = tf.scalar(3);\n    const out = tf.einsum(',->', x, y);\n    expectArraysClose(await out.data(), 6);\n  });\n\n  it('1D tensor and scalars: reduce', async () => {\n    const x = tensor1d([2, 3]);\n    const y = tf.scalar(4);\n    const out = tf.einsum('i,->', x, y);\n    expectArraysClose(await out.data(), 20);\n  });\n\n  it('1D tensor and scalars: multiply', async () => {\n    const x = tensor1d([2, 3]);\n    const y = tf.scalar(4);\n    const out = tf.einsum('i,->i', x, y);\n    expectArraysClose(await out.data(), [8, 12]);\n  });\n\n  it('1d reduce sum', async () => {\n    const x = tensor1d([2, 4, 6]);\n    const out = tf.einsum('i->', x);\n    expectArraysClose(await out.data(), 12);\n  });\n\n  it('2d matrix reduce sum', async () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    const out = tf.einsum('ij->', x);\n    expectArraysClose(await out.data(), 10);\n  });\n\n  it('2d matrices multiply and reduce summing', async () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    const y = tensor2d([[4, 3], [2, 1]]);\n    const out = tf.einsum('ij,ji->', x, y);\n    expectArraysClose(await out.data(), 21);\n  });\n\n  it('2d matrix times scalar and reduce summing', async () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    const y = tf.scalar(5);\n    const out = tf.einsum('ij,->', x, y);\n    expectArraysClose(await out.data(), 50);\n  });\n\n  it('two 1d tensors dot', async () => {\n    const x = tensor1d([1, 3, 5]);\n    const y = tensor1d([2, 4, 6]);\n    const out = tf.einsum('i,i->', x, y);\n    expectArraysClose(await out.data(), 44);\n  });\n\n  it('two 1d tensors outer', async () => {\n    const x = tensor1d([1, 3, 5]);\n    const y = tensor1d([2, 4, 6]);\n    const out = tf.einsum('i,j->ij', x, y);\n    expectArraysClose(await out.data(), [[2, 4, 6], [6, 12, 18], [10, 20, 30]]);\n  });\n\n  it('2d matrix calculate trace: duplicate axes not implemented yet', () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    expect(() => tf.einsum('ii->', x)).toThrowError(/not implemented yet/);\n  });\n\n  it('2d and 1d matrix & vector multiply', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor1d([2, 4, 6]);\n    const out = tf.einsum('ij,j->i', x, y);\n    expectArraysClose(await out.data(), [28, 64]);\n  });\n\n  it('2d matrix sum along columns', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const out = tf.einsum('ij->j', x);\n    expectArraysClose(await out.data(), [5, 7, 9]);\n  });\n\n  it('2d matrix sum along rows', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const out = tf.einsum('ij->i', x);\n    expectArraysClose(await out.data(), [6, 15]);\n  });\n\n  it('2d matrix transposing', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const out = tf.einsum('ij->ji', x);\n    expectArraysClose(await out.data(), [[1, 4], [2, 5], [3, 6]]);\n  });\n\n  it('2d matrix multiply', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1], [2, 3], [4, 5]]);\n    const out = tf.einsum('ij,jk->ik', x, y);\n    expectArraysClose(await out.data(), [[16, 22], [34, 49]]);\n  });\n\n  it('2d matrix multiply and transposing', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1], [2, 3], [4, 5]]);\n    const out = tf.einsum('ij,jk->ki', x, y);\n    expectArraysClose(await out.data(), [[16, 34], [22, 49]]);\n  });\n\n  it('two 2d matrices batch dot', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1, 2], [3, 4, 5]]);\n    const out = tf.einsum('bi,bi->b', x, y);\n    expectArraysClose(await out.data(), [8, 62]);\n  });\n\n  it('two 2d matrices batch outer', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1, 2], [3, 4, 5]]);\n    const out = tf.einsum('bi,bj->bij', x, y);\n    expectArraysClose(await out.data(), [\n      [[0, 1, 2], [0, 2, 4], [0, 3, 6]],\n      [[12, 16, 20], [15, 20, 25], [18, 24, 30]]\n    ]);\n  });\n\n  it('two 3d tensors batch matmul', async () => {\n    const x = tf.reshape(tf.range(1, 13), [2, 2, 3]);\n    const y = tf.reshape(tf.range(1, 19), [2, 3, 3]);\n    const out = tf.einsum('bij,bjk->bik', x, y);\n    expectArraysClose(\n        await out.data(),\n        [[[30, 36, 42], [66, 81, 96]], [[318, 342, 366], [435, 468, 501]]]);\n  });\n\n  it('two 3d tensors A', async () => {\n    const x = tf.reshape(tf.range(1, 9), [2, 2, 2]);\n    const y = tf.reshape(tf.range(1, 13), [2, 3, 2]);\n    const out = tf.einsum('adc,abc->abd', x, y);\n    expectArraysClose(\n        await out.data(),\n        [[[5, 11], [11, 25], [17, 39]], [[83, 113], [105, 143], [127, 173]]]);\n  });\n\n  it('two 3d tensors B', async () => {\n    const x = tf.reshape(tf.range(1, 9), [2, 2, 2]);\n    const y = tf.reshape(tf.range(1, 13), [2, 3, 2]);\n    const out = tf.einsum('adc,abc->adb', x, y);\n    expectArraysClose(\n        await out.data(),\n        [[[5, 11, 17], [11, 25, 39]], [[83, 105, 127], [113, 143, 173]]]);\n  });\n\n  it('one 3d tensor: batch matrix transposing', async () => {\n    const x = tensor3d([[[1, 2], [3, 4]], [[-1, -2], [-3, -4]]]);\n    const out = tf.einsum('bij->bji', x);\n    expectArraysClose(\n        await out.data(), [[[1, 3], [2, 4]], [[-1, -3], [-2, -4]]]);\n  });\n\n  it('4d tensor and 3d tensor, contracting two dimensions', async () => {\n    const x = tf.reshape(tf.range(1, 33), [2, 4, 2, 2]);\n    const y = tf.reshape(tf.range(1, 9), [2, 2, 2]);\n    const out = tf.einsum('abcd,cde->abe', x, y);\n    expectArraysClose(await out.data(), [\n      [[50, 60], [114, 140], [178, 220], [242, 300]],\n      [[306, 380], [370, 460], [434, 540], [498, 620]]\n    ]);\n  });\n\n  it('two 4d tensors, contracting one dimension', async () => {\n    const x = tf.reshape(tf.range(1, 33), [2, 4, 2, 2]);\n    const y = tf.reshape(tf.range(1, 25), [2, 3, 2, 2]);\n    const out = tf.einsum('aecd,abcd->acbe', x, y);\n    expectArraysClose(await out.data(), [\n      [\n        [[5, 17, 29, 41], [17, 61, 105, 149], [29, 105, 181, 257]],\n        [[25, 53, 81, 109], [53, 113, 173, 233], [81, 173, 265, 357]]\n      ],\n      [\n        [[473, 581, 689, 797], [613, 753, 893, 1033], [753, 925, 1097, 1269]],\n        [[605, 729, 853, 977], [761, 917, 1073, 1229], [917, 1105, 1293, 1481]]\n      ]\n    ]);\n  });\n\n  it('two 4d tensors, contracting two dimensions', async () => {\n    const x = tf.reshape(tf.range(1, 33), [2, 4, 2, 2]);\n    const y = tf.reshape(tf.range(1, 25), [2, 3, 2, 2]);\n    const out = tf.einsum('aecd,abcd->abe', x, y);\n    expectArraysClose(await out.data(), [\n      [[30, 70, 110, 150], [70, 174, 278, 382], [110, 278, 446, 614]],\n      [\n        [1078, 1310, 1542, 1774], [1374, 1670, 1966, 2262],\n        [1670, 2030, 2390, 2750]\n      ]\n    ]);\n  });\n\n  it('mismatched dimensions throws error', () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1], [2, 3]]);\n    expect(() => tf.einsum('ij,jk->ik', x, y))\n        .toThrowError(/dimension 3 at axis 0 of (the )?input shaped \\[2,2\\]/);\n  });\n\n  it('incorrect equation throws error', () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    const y = tensor2d([[0, 1], [2, 3]]);\n    expect(() => tf.einsum('', x, y))\n        .toThrowError(/Equations without an arrow|Expecting exactly one/);\n    expect(() => tf.einsum('ij,jk>ik', x, y))\n        .toThrowError(/Equations without an arrow|Expecting exactly one/);\n  });\n\n  it('incorrect number of tensors throws error', () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    const y = tensor2d([[0, 1], [2, 3]]);\n    expect(() => tf.einsum('ij->ji', x, y))\n        .toThrowError(/Expected 1 inputs? (tensors, received)?(but got:)? 2/);\n  });\n\n  it('more than two input tensors throws error', async () => {\n    const x = tensor2d([[1, 2], [3, 4]]);\n    const y = tensor2d([[0, 1], [2, 3]]);\n    const z = tensor2d([[-1, 0], [1, 2]]);\n    expect(() => tf.einsum('ij,jk,kl->il', x, y, z))\n        .toThrowError(/(more than 2 input tensors)|(Expecting 1 or 2 input)/);\n  });\n\n  it('nonexistent dimension throws error', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1], [2, 3], [4, 5]]);\n    expect(() => tf.einsum('ij,jk->in', x, y))\n        .toThrowError(\n            'Output subscripts contain the label n not present in ' +\n            'the input subscripts.');\n  });\n\n  it('two arrows in equation throws error', async () => {\n    const x = tensor2d([[1, 2, 3], [4, 5, 6]]);\n    const y = tensor2d([[0, 1], [2, 3], [4, 5]]);\n    expect(() => tf.einsum('ij,jk->ik->i', x, y)).toThrowError(/exactly one/);\n  });\n});\n"]}
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