/// <amd-module name="@tensorflow/tfjs-core/dist/ops/linalg/qr" />
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import { Tensor } from '../../tensor';
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/**
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* Compute QR decomposition of m-by-n matrix using Householder transformation.
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*
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* Implementation based on
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* [http://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf]
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* (http://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf)
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*
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* ```js
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* const a = tf.tensor2d([[1, 2], [3, 4]]);
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* let [q, r] = tf.linalg.qr(a);
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* console.log('Q');
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* q.print();
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* console.log('R');
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* r.print();
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* console.log('Orthogonalized');
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* q.dot(q.transpose()).print() // should be nearly the identity matrix.
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* console.log('Reconstructed');
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* q.dot(r).print(); // should be nearly [[1, 2], [3, 4]];
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* ```
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*
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* @param x The `tf.Tensor` to be QR-decomposed. Must have rank >= 2. Suppose
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* it has the shape `[..., M, N]`.
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* @param fullMatrices An optional boolean parameter. Defaults to `false`.
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* If `true`, compute full-sized `Q`. If `false` (the default),
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* compute only the leading N columns of `Q` and `R`.
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* @returns An `Array` of two `tf.Tensor`s: `[Q, R]`. `Q` is a unitary matrix,
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* i.e., its columns all have unit norm and are mutually orthogonal.
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* If `M >= N`,
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* If `fullMatrices` is `false` (default),
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* - `Q` has a shape of `[..., M, N]`,
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* - `R` has a shape of `[..., N, N]`.
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* If `fullMatrices` is `true` (default),
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* - `Q` has a shape of `[..., M, M]`,
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* - `R` has a shape of `[..., M, N]`.
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* If `M < N`,
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* - `Q` has a shape of `[..., M, M]`,
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* - `R` has a shape of `[..., M, N]`.
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* @throws If the rank of `x` is less than 2.
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*
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* @doc {heading:'Operations',
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* subheading:'Linear Algebra',
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* namespace:'linalg'}
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*/
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declare function qr_(x: Tensor, fullMatrices?: boolean): [Tensor, Tensor];
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export declare const qr: typeof qr_;
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export {};
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