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‎lib/node_modules/@stdlib/lapack/base/dorg2r/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dorg2r
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> LAPACK routine to generate an M-by-N real matrix Q with orthonormal columns.
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<section class="usage">
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## Usage
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```javascript
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var dorg2r = require( '@stdlib/lapack/base/dorg2r' );
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```
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#### dorg2r( order, M, N, K, A, LDA, tau, work )
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Generates an M-by-N real matrix Q with orthonormal columns. The matrix Q is defined as the first N columns of a product of K elementary reflectors of order M. `Q = H(1) H(2) . . . H(K)` as returned by `dgeqrf`.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var tau = new Float64Array( [ 0.0, 0.0 ] );
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var work = new Float64Array( 10 );
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dorg2r( 'column-major', 3, 2, 2, A, 3, tau, work );
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// A => <Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **M**: number of rows in matrix `A`.
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- **N**: number of columns in matrix `A`.
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- **K**: number of elementary reflectors whose product defines the matrix Q.
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- **A**: input matrix (overwritten by Householder vectors from `dgeqrf`) stored in linear memory as a [`Float64Array`][mdn-float64array].
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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- **tau**: vector of K scalar factors of the elementary reflectors as a [`Float64Array`][mdn-float64array].
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- **work**: workspace array as a [`Float64Array`][mdn-float64array].
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The function returns the input matrix `A` overwritten with the orthogonal matrix Q.
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#### dorg2r.ndarray( M, N, K, A, sa1, sa2, oa, tau, st, ot, work, sw, ow )
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Generates an M-by-N real matrix Q with orthonormal columns using alternative indexing semantics. The matrix Q is defined as the first N columns of a product of K elementary reflectors of order M. `Q = H(1) H(2) . . . H(K)` as returned by `dgeqrf`.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var tau = new Float64Array( [ 0.0, 0.0 ] );
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var work = new Float64Array( 10 );
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dorg2r.ndarray( 3, 2, 2, A, 1, 3, 0, tau, 1, 0, work, 1, 0 );
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// A => <Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
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```
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The function has the following additional parameters:
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- **M**: number of rows in matrix `A`.
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- **N**: number of columns in matrix `A`.
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- **K**: number of elementary reflectors whose product defines the matrix Q.
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- **A**: input matrix (overwritten by Householder vectors from `dgeqrf`) stored in linear memory as a [`Float64Array`][mdn-float64array].
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- **sa1**: stride of the first dimension of `A`.
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- **sa2**: stride of the second dimension of `A`.
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- **oa**: index offset for `A`.
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- **tau**: vector of K scalar factors of the elementary reflectors as a [`Float64Array`][mdn-float64array].
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- **st**: stride length for `tau`.
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- **ot**: index offset for `tau`.
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- **work**: workspace array as a [`Float64Array`][mdn-float64array].
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- **sw**: stride length for `work`.
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- **ow**: index offset for `work`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var tau = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
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var work = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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dorg2r.ndarray( 3, 2, 2, A, 1, 3, 3, tau, 1, 2, work, 1, 0 );
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// A => <Float64Array>[ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notess
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- The function overwrites the input matrix `A` with the orthogonal matrix `Q`.
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- The matrix Q is generated from the Householder vectors and scalar factors returned by `dgeqrf`.
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- `dorg2r()` corresponds to the [LAPACK][LAPACK] function [`dorg2r`][lapack-dorg2r].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
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var dorg2r = require( '@stdlib/lapack/base/dorg2r' );
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// Specify matrix meta data:
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var M = 4;
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var N = 3;
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var K = 2;
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// Create a matrix stored in linear memory:
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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console.log( 'Original matrix A containing Householder vectors:' );
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console.log( ndarray2array( A, [ M, N ], [ 1, M ], 0, 'column-major' ) );
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// Define scalar factors of the elementary reflectors:
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var tau = new Float64Array( [ 1.2, 0.8 ] );
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// Create workspace array:
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var work = new Float64Array( N );
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// Generate the orthogonal matrix Q:
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dorg2r( 'column-major', M, N, K, A, M, tau, work );
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console.log( 'Resulting orthogonal matrix Q:' );
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console.log( ndarray2array( A, [ M, N ], [ 1, M ], 0, 'column-major' ) );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[lapack-dorg2r]: https://netlib.org/lapack/explore-html/da/da2/group__ung2r_ga8877e79ab6e262ae7497f11d8534635c.html#ga8877e79ab6e262ae7497f11d8534635c
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/lapack/base/dorg2r/docs/repl.txt‎

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{{alias}}( order, M, N, K, A, LDA, tau, work )
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Generates an M-by-N real matrix Q with orthonormal columns. The matrix Q
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is defined as the first N columns of a product of K elementary reflectors
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of order M. Q = H(1) H(2) . . . H(K) as returned by dgeqrf.
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The function overwrites the input matrix A with the orthogonal matrix Q.
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Parameters
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----------
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order: string
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Row-major (C-style) or column-major (Fortran-style) order. Must be
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either 'row-major' or 'column-major'.
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M: integer
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Number of rows in matrix A.
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N: integer
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Number of columns in matrix A.
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K: integer
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Number of elementary reflectors whose product defines the matrix Q.
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A: Float64Array
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Input matrix (overwritten by Householder vectors from dgeqrf).
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LDA: integer
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Stride of the first dimension of A (a.k.a., leading dimension of the
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matrix A).
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tau: Float64Array
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Vector of K scalar factors of the elementary reflectors.
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work: Float64Array
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Workspace array.
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Returns
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-------
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A: Float64Array
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Mutated input matrix overwritten with the orthogonal matrix Q.
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Examples
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--------
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> var A = new {{alias:@stdlib/array/float64}}([ 1.0,2.0,3.0,4.0,5.0,6.0 ]);
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> var tau = new {{alias:@stdlib/array/float64}}( [ 0.0, 0.0 ] );
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> var work = new {{alias:@stdlib/array/float64}}( 10 );
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> {{alias}}( 'column-major', 3, 2, 2, A, 3, tau, work )
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<Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
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{{alias}}.ndarray( M, N, K, A, sa1, sa2, oa, tau, st, ot, work, sw, ow )
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Generates an M-by-N real matrix Q with orthonormal columns using
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alternative indexing semantics. The matrix Q is defined as the first N
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columns of a product of K elementary reflectors of order M.
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`Q = H(1) H(2) . . . H(K)` as returned by `dgeqrf`.
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While typed array views mandate a view offset based on the underlying
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buffer, the offset parameters support indexing semantics based on starting
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indices.
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Parameters
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----------
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M: integer
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Number of rows in matrix A.
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N: integer
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Number of columns in matrix A.
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K: integer
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Number of elementary reflectors whose product defines the matrix Q.
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A: Float64Array
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Input matrix.
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sa1: integer
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Stride of the first dimension of A.
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sa2: integer
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Stride of the second dimension of A.
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oa: integer
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Index offset for A.
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tau: Float64Array
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Vector of K scalar factors of the elementary reflectors.
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st: integer
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Stride length for tau.
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ot: integer
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Index offset for tau.
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work: Float64Array
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Workspace array.
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sw: integer
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Stride length for work.
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ow: integer
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Index offset for work.
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Returns
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-------
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A: Float64Array
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Mutated input matrix overwritten with the orthogonal matrix Q.
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Examples
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--------
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> var A = new {{alias:@stdlib/array/float64}}([ 1.0,2.0,3.0,4.0,5.0,6.0 ]);
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> var tau = new {{alias:@stdlib/array/float64}}( [ 0.0, 0.0 ] );
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> var work = new {{alias:@stdlib/array/float64}}( 10 );
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> {{alias}}.ndarray( 3, 2, 2, A, 1, 3, 0, tau, 1, 0, work, 1, 0 )
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<Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
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See Also
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--------

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