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| /**
| * @license
| * Copyright 2020 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 { scalar, tensor1d, tensor2d, tensor3d, tensor4d } from '../ops';
| describeWithFlags('qr', ALL_ENVS, () => {
| it('1x1', async () => {
| const x = tensor2d([[10]], [1, 1]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [[-1]]);
| expectArraysClose(await r.array(), [[-10]]);
| });
| it('2x2', async () => {
| const x = tensor2d([[1, 3], [-2, -4]], [2, 2]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [[-0.4472, -0.8944], [0.8944, -0.4472]]);
| expectArraysClose(await r.array(), [[-2.2361, -4.9193], [0, -0.8944]]);
| });
| it('2x2x2', async () => {
| const x = tensor3d([[[-1, -3], [2, 4]], [[1, 3], [-2, -4]]], [2, 2, 2]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [
| [[-0.4472, -0.8944], [0.8944, -0.4472]],
| [[-0.4472, -0.8944], [0.8944, -0.4472]]
| ]);
| expectArraysClose(await r.array(), [[[2.2361, 4.9193], [0, 0.8944]], [[-2.2361, -4.9193], [0, -0.8944]]]);
| });
| it('2x1x2x2', async () => {
| const x = tensor4d([[[[-1, -3], [2, 4]]], [[[1, 3], [-2, -4]]]], [2, 1, 2, 2]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [
| [[[-0.4472, -0.8944], [0.8944, -0.4472]]],
| [[[-0.4472, -0.8944], [0.8944, -0.4472]]],
| ]);
| expectArraysClose(await r.array(), [
| [[[2.2361, 4.9193], [0, 0.8944]]], [[[-2.2361, -4.9193], [0, -0.8944]]]
| ]);
| });
| it('3x3', async () => {
| const x = tensor2d([[1, 3, 2], [-2, 0, 7], [8, -9, 4]], [3, 3]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [
| [-0.1204, 0.8729, 0.4729], [0.2408, -0.4364, 0.8669],
| [-0.9631, -0.2182, 0.1576]
| ]);
| expectArraysClose(await r.array(), [[-8.3066, 8.3066, -2.4077], [0, 4.5826, -2.1822], [0, 0, 7.6447]]);
| });
| it('3x3, zero on diagonal', async () => {
| const x = tensor2d([[0, 2, 2], [1, 1, 1], [0, 1, 2]], [3, 3]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.data(), [
| [0., -0.89442719, 0.4472136], [1., 0., 0.], [0., -0.4472136, -0.89442719]
| ]);
| expectArraysClose(await r.data(), [[1., 1., 1.], [0., -2.23606798, -2.68328157], [0., 0., -0.89442719]]);
| });
| it('3x2, fullMatrices = default false', async () => {
| const x = tensor2d([[1, 2], [3, -3], [-2, 1]], [3, 2]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [[-0.2673, 0.9221], [-0.8018, -0.3738], [0.5345, -0.0997]]);
| expectArraysClose(await r.array(), [[-3.7417, 2.4054], [0, 2.8661]]);
| });
| it('3x2, fullMatrices = true', async () => {
| const x = tensor2d([[1, 2], [3, -3], [-2, 1]], [3, 2]);
| const [q, r] = tf.linalg.qr(x, true);
| expectArraysClose(await q.array(), [
| [-0.2673, 0.9221, 0.2798], [-0.8018, -0.3738, 0.4663],
| [0.5345, -0.0997, 0.8393]
| ]);
| expectArraysClose(await r.array(), [[-3.7417, 2.4054], [0, 2.8661], [0, 0]]);
| });
| it('2x3, fullMatrices = default false', async () => {
| const x = tensor2d([[1, 2, 3], [-3, -2, 1]], [2, 3]);
| const [q, r] = tf.linalg.qr(x);
| expectArraysClose(await q.array(), [[-0.3162278, -0.9486833], [0.9486833, -0.31622773]]);
| expectArraysClose(await r.array(), [[-3.162, -2.5298, -2.3842e-07], [0, -1.2649, -3.162]]);
| });
| it('2x3, fullMatrices = true', async () => {
| const x = tensor2d([[1, 2, 3], [-3, -2, 1]], [2, 3]);
| const [q, r] = tf.linalg.qr(x, true);
| expectArraysClose(await q.array(), [[-0.3162278, -0.9486833], [0.9486833, -0.31622773]]);
| expectArraysClose(await r.array(), [[-3.162, -2.5298, -2.3842e-07], [0, -1.2649, -3.162]]);
| });
| it('Does not leak memory', () => {
| const x = tensor2d([[1, 3], [-2, -4]], [2, 2]);
| // The first call to qr creates and keeps internal singleton tensors.
| // Subsequent calls should always create exactly two tensors.
| tf.linalg.qr(x);
| // Count before real call.
| const numTensors = tf.memory().numTensors;
| tf.linalg.qr(x);
| expect(tf.memory().numTensors).toEqual(numTensors + 2);
| });
| it('Insuffient input tensor rank leads to error', () => {
| const x1 = scalar(12);
| expect(() => tf.linalg.qr(x1)).toThrowError(/rank >= 2.*got rank 0/);
| const x2 = tensor1d([12]);
| expect(() => tf.linalg.qr(x2)).toThrowError(/rank >= 2.*got rank 1/);
| });
| });
| //# 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* @license\n * Copyright 2020 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 {scalar, tensor1d, tensor2d, tensor3d, tensor4d} from '../ops';\n\ndescribeWithFlags('qr', ALL_ENVS, () => {\n  it('1x1', async () => {\n    const x = tensor2d([[10]], [1, 1]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(await q.array(), [[-1]]);\n    expectArraysClose(await r.array(), [[-10]]);\n  });\n\n  it('2x2', async () => {\n    const x = tensor2d([[1, 3], [-2, -4]], [2, 2]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(await q.array(), [[-0.4472, -0.8944], [0.8944, -0.4472]]);\n    expectArraysClose(await r.array(), [[-2.2361, -4.9193], [0, -0.8944]]);\n  });\n\n  it('2x2x2', async () => {\n    const x = tensor3d([[[-1, -3], [2, 4]], [[1, 3], [-2, -4]]], [2, 2, 2]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(await q.array(), [\n      [[-0.4472, -0.8944], [0.8944, -0.4472]],\n      [[-0.4472, -0.8944], [0.8944, -0.4472]]\n    ]);\n    expectArraysClose(\n        await r.array(),\n        [[[2.2361, 4.9193], [0, 0.8944]], [[-2.2361, -4.9193], [0, -0.8944]]]);\n  });\n\n  it('2x1x2x2', async () => {\n    const x =\n        tensor4d([[[[-1, -3], [2, 4]]], [[[1, 3], [-2, -4]]]], [2, 1, 2, 2]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(await q.array(), [\n      [[[-0.4472, -0.8944], [0.8944, -0.4472]]],\n      [[[-0.4472, -0.8944], [0.8944, -0.4472]]],\n    ]);\n    expectArraysClose(await r.array(), [\n      [[[2.2361, 4.9193], [0, 0.8944]]], [[[-2.2361, -4.9193], [0, -0.8944]]]\n    ]);\n  });\n\n  it('3x3', async () => {\n    const x = tensor2d([[1, 3, 2], [-2, 0, 7], [8, -9, 4]], [3, 3]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(await q.array(), [\n      [-0.1204, 0.8729, 0.4729], [0.2408, -0.4364, 0.8669],\n      [-0.9631, -0.2182, 0.1576]\n    ]);\n    expectArraysClose(\n        await r.array(),\n        [[-8.3066, 8.3066, -2.4077], [0, 4.5826, -2.1822], [0, 0, 7.6447]]);\n  });\n\n  it('3x3, zero on diagonal', async () => {\n    const x = tensor2d([[0, 2, 2], [1, 1, 1], [0, 1, 2]], [3, 3]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(await q.data(), [\n      [0., -0.89442719, 0.4472136], [1., 0., 0.], [0., -0.4472136, -0.89442719]\n    ]);\n    expectArraysClose(\n        await r.data(),\n        [[1., 1., 1.], [0., -2.23606798, -2.68328157], [0., 0., -0.89442719]]);\n  });\n\n  it('3x2, fullMatrices = default false', async () => {\n    const x = tensor2d([[1, 2], [3, -3], [-2, 1]], [3, 2]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(\n        await q.array(),\n        [[-0.2673, 0.9221], [-0.8018, -0.3738], [0.5345, -0.0997]]);\n    expectArraysClose(await r.array(), [[-3.7417, 2.4054], [0, 2.8661]]);\n  });\n\n  it('3x2, fullMatrices = true', async () => {\n    const x = tensor2d([[1, 2], [3, -3], [-2, 1]], [3, 2]);\n    const [q, r] = tf.linalg.qr(x, true);\n    expectArraysClose(await q.array(), [\n      [-0.2673, 0.9221, 0.2798], [-0.8018, -0.3738, 0.4663],\n      [0.5345, -0.0997, 0.8393]\n    ]);\n    expectArraysClose(\n        await r.array(), [[-3.7417, 2.4054], [0, 2.8661], [0, 0]]);\n  });\n\n  it('2x3, fullMatrices = default false', async () => {\n    const x = tensor2d([[1, 2, 3], [-3, -2, 1]], [2, 3]);\n    const [q, r] = tf.linalg.qr(x);\n    expectArraysClose(\n        await q.array(), [[-0.3162278, -0.9486833], [0.9486833, -0.31622773]]);\n    expectArraysClose(\n        await r.array(),\n        [[-3.162, -2.5298, -2.3842e-07], [0, -1.2649, -3.162]]);\n  });\n\n  it('2x3, fullMatrices = true', async () => {\n    const x = tensor2d([[1, 2, 3], [-3, -2, 1]], [2, 3]);\n    const [q, r] = tf.linalg.qr(x, true);\n    expectArraysClose(\n        await q.array(), [[-0.3162278, -0.9486833], [0.9486833, -0.31622773]]);\n    expectArraysClose(\n        await r.array(),\n        [[-3.162, -2.5298, -2.3842e-07], [0, -1.2649, -3.162]]);\n  });\n\n  it('Does not leak memory', () => {\n    const x = tensor2d([[1, 3], [-2, -4]], [2, 2]);\n    // The first call to qr creates and keeps internal singleton tensors.\n    // Subsequent calls should always create exactly two tensors.\n    tf.linalg.qr(x);\n    // Count before real call.\n    const numTensors = tf.memory().numTensors;\n    tf.linalg.qr(x);\n    expect(tf.memory().numTensors).toEqual(numTensors + 2);\n  });\n\n  it('Insuffient input tensor rank leads to error', () => {\n    const x1 = scalar(12);\n    expect(() => tf.linalg.qr(x1)).toThrowError(/rank >= 2.*got rank 0/);\n    const x2 = tensor1d([12]);\n    expect(() => tf.linalg.qr(x2)).toThrowError(/rank >= 2.*got rank 1/);\n  });\n});\n"]}
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