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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(\n 'Expected dimension 3 at axis 0 of input shaped [2,2], ' +\n 'but got dimension 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 are not supported.');\n expect(() => tf.einsum('ij,jk>ik', x, y))\n .toThrowError('Equations without an arrow are not supported.');\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 input tensors, received 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/);\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))\n .toThrowError(/exactly one arrow/);\n });\n});\n"]} |