@tensorflow/tfjs-core
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Hardware-accelerated JavaScript library for machine intelligence
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TypeScript
/**
* @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.
* =============================================================================
*/
/// <amd-module name="@tensorflow/tfjs-core/dist/ops/linalg/gram_schmidt" />
import { Tensor1D, Tensor2D } from '../../tensor';
/**
* Gram-Schmidt orthogonalization.
*
* ```js
* const x = tf.tensor2d([[1, 2], [3, 4]]);
* let y = tf.linalg.gramSchmidt(x);
* y.print();
* console.log('Orthogonalized:');
* y.dot(y.transpose()).print(); // should be nearly the identity matrix.
* console.log('First row direction maintained:');
* const data = await y.array();
* console.log(data[0][1] / data[0][0]); // should be nearly 2.
* ```
*
* @param xs The vectors to be orthogonalized, in one of the two following
* formats:
* - An Array of `tf.Tensor1D`.
* - A `tf.Tensor2D`, i.e., a matrix, in which case the vectors are the rows
* of `xs`.
* In each case, all the vectors must have the same length and the length
* must be greater than or equal to the number of vectors.
* @returns The orthogonalized and normalized vectors or matrix.
* Orthogonalization means that the vectors or the rows of the matrix
* are orthogonal (zero inner products). Normalization means that each
* vector or each row of the matrix has an L2 norm that equals `1`.
*
* @doc {heading:'Operations', subheading:'Linear Algebra', namespace:'linalg'}
*/
declare function gramSchmidt_(xs: Tensor1D[] | Tensor2D): Tensor1D[] | Tensor2D;
export declare const gramSchmidt: typeof gramSchmidt_;
export {};