feat: add lapack/base/dorgqr

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+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.
+
+-->
+
+# dorgqr
+
+> Generate an `M-by-N` real matrix `Q` with orthonormal columns, which is defined as the first `N` columns of a product of `K` elementary reflectors of order `M`.
+
+<section class="intro">
+
+The `dorgqr` routine generates the orthogonal matrix `Q` from the elementary reflectors returned by the QR factorization routine `dgeqrf`.
+
+<!-- <equation class="equation" label="eq:Q" align="center" raw="Q  =  H(1) H(2) . . . H(k)" alt="Equation for Q."> -->
+
+```math
+Q  =  H(1) H(2) . . . H(k)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dorgqr = require( '@stdlib/lapack/base/dorgqr' );
+```
+
+#### dorgqr( order, M, N, K, A, LDA, TAU, WORK, LWORK )
+
+Generates an `M-by-N` real matrix `Q` with orthonormal columns, which is defined as the first `N` columns of a product of `K` elementary reflectors of order `M`.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ] );
+var TAU = new Float64Array( [ 2.0, 2.0 ] );
+var WORK = new Float64Array( 10 );
+
+dorgqr( 'column-major', 3, 2, 2, A, 3, TAU, WORK, 10 );
+// A => <Float64Array>[ -1.0, 0.0, 0.0, 0.0, -1.0, 0.0 ]
+// WORK[ 0 ] => 2.0
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout. Must be `'row-major'` or `'column-major'`.
+-   **M**: number of rows of `Q`.
+-   **N**: number of columns of `Q`. Must be less than or equal to `M`.
+-   **K**: number of elementary reflectors whose product defines the matrix `Q`. Must be less than or equal to `N`.
+-   **A**: input/output matrix of size `M×N` stored in linear memory as a [`Float64Array`][@stdlib/array/float64]. On entry, the i-th column of `A` must contain the reflector vector for `H(i)`, as returned by `dgeqrf`. On exit, `A` is overwritten by the `M-by-N` orthogonal matrix `Q`.
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`). Must be at least `max(1,M)` when `order` is `'column-major'` and at least `max(1,N)` when `order` is `'row-major'`.
+-   **TAU**: scalar factors of the elementary reflectors as a [`Float64Array`][@stdlib/array/float64] of length `K`.
+-   **WORK**: workspace array as a [`Float64Array`][@stdlib/array/float64].
+-   **LWORK**: dimension of the array `WORK`. Must be at least `max(1,N)`, unless equal to `-1`, in which case a workspace query is performed and the optimal size of `WORK` is returned in `WORK[0]`.
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments, max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ] );
+var TAU0 = new Float64Array( [ 0.0, 2.0, 2.0 ] );
+var WORK0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create offset views...
+var A = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var TAU = new Float64Array( TAU0.buffer, TAU0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var WORK = new Float64Array( WORK0.buffer, WORK0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dorgqr( 'column-major', 3, 2, 2, A, 3, TAU, WORK, 10 );
+// A0 => <Float64Array>[ 0.0, -1.0, 0.0, 0.0, 0.0, -1.0, 0.0 ]
+// WORK0[ 1 ] => 2.0
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dorgqr.ndarray( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK )
+
+Generates an `M-by-N` real matrix `Q` with orthonormal columns using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ] );
+var TAU = new Float64Array( [ 2.0, 2.0 ] );
+var WORK = new Float64Array( 10 );
+
+dorgqr.ndarray( 3, 2, 2, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+// A => <Float64Array>[ -1.0, 0.0, 0.0, 0.0, -1.0, 0.0 ]
+// WORK[ 0 ] => 2.0
+```
+
+The function has the following additional parameters:
+
+-   **strideA1**: stride length for the first dimension of `A`.
+-   **strideA2**: stride length for the second dimension of `A`.
+-   **offsetA**: starting index for `A`.
+-   **strideTAU**: stride length for `TAU`.
+-   **offsetTAU**: starting index for `TAU`.
+-   **strideWORK**: stride length for `WORK`.
+-   **offsetWORK**: starting index for `WORK`.
+
+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,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ] );
+var TAU = new Float64Array( [ 0.0, 2.0, 2.0 ] );
+var WORK = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+dorgqr.ndarray( 3, 2, 2, A, 1, 3, 1, TAU, 1, 1, WORK, 1, 1, 10 );
+// A => <Float64Array>[ 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0 ]
+// WORK[ 1 ] => 2.0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input arrays `A`, `TAU`, and `WORK`.
+
+-   Both functions return a status code indicating success (`0`) or failure.
+
+-   `dorgqr()` corresponds to the [LAPACK][LAPACK] routine [`dorgqr`][lapack-dorgqr].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var dorgqr = require( '@stdlib/lapack/base/dorgqr' );
+
+// Define matrix dimensions:
+var M = 6;
+var N = 4;
+var K = 4;
+var shape = [ M, N ];
+var order = 'row-major';
+var strides = shape2strides( shape, order );
+
+// Create the matrix A containing elementary reflector vectors from dgeqrf:
+var A = new Float64Array( [
+    5.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+    0.0, 4.0, 0.0, 0.0, 0.0, 0.0,
+    0.0, 0.0, 3.0, 0.0, 0.0, 0.0,
+    0.0, 0.0, 0.0, 2.0, 0.0, 0.0
+] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+// Define the scalar factors and workspace array:
+var TAU = new Float64Array( [ 2.0, 2.0, 2.0, 2.0 ] );
+var WORK = new Float64Array( 20 );
+
+// Generate the orthogonal matrix Q:
+var info = dorgqr( order, M, N, K, A, strides[ 0 ], TAU, WORK, WORK.length );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+console.log( info );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dorgqr]: https://www.netlib.org/lapack/explore-html/d4/dfc/group__ungqr_ga9f4abcfe1543a5d6d90fcd4dd21f12f0.html
+
+[@stdlib/array/float64]: https://stdlib.io/docs/api/latest/@stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->