stdlib-js · prajjwalbajpai · Aug 8, 2026
diff --git a/lib/node_modules/@stdlib/lapack/base/dgelqf/README.md b/lib/node_modules/@stdlib/lapack/base/dgelqf/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.
+
+-->
+
+# dgelqf
+
+> LAPACK routine to compute an LQ factorization of a real `M`-by-`N` matrix `A`.
+
+<section class="intro">
+
+`dgelqf` computes an LQ factorization of a real `M`-by-`N` matrix `A`:
+
+```math
+A = \begin{pmatrix} L & 0 \end{pmatrix} \cdot Q
+```
+
+where
+
+-   **Q** is an `N`-by-`N` orthogonal matrix,
+-   **L** is a lower-triangular `M`-by-`M` matrix, and
+-   **0** is an `M`-by-`(N-M)` zero matrix if `M < N`.
+
+The matrix `Q` is represented as a product of elementary reflectors
+
+```math
+Q = H(k) . . . H(2) H(1)
+```
+
+where `k = min(m,n)`.
+
+Each `H(i)` has the form
+
+```math
+H(i) = I - \tau \cdot v \cdot v^T
+```
+
+where `\tau` is a real scalar, and `v` is a real vector with `v(1:i-1) = 0` and `v(i) = 1`; `v(i+1:n)` is stored on exit in `A(i,i+1:n)`, and `\tau` in `TAU(i)`.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dgelqf = require( '@stdlib/lapack/base/dgelqf' );
+```
+
+#### dgelqf( order, M, N, A, LDA, TAU, WORK, LWORK )
+
+Computes an LQ factorization of a real `M`-by-`N` matrix `A`.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU = new Float64Array( 3 );
+var WORK = new Float64Array( 4 );
+
+dgelqf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+// A => <Float64Array>[ ~-5.477, ~-12.78, ~-20.083, ~0.309, ~-3.266, ~-6.532, ~0.463, ~-0.327, ~0.0, ~0.618, ~-0.789, ~0.618 ]
+// TAU => <Float64Array>[ ~1.183, ~1.156, ~1.447 ]
+// WORK => <Float64Array>[ 3.0, ~24.593, 0.0, 0.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input/output matrix.
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **TAU**: output array.
+-   **WORK**: workspace array.
+-   **LWORK**: dimension of the array `WORK`. If `min(M,N) = 0`, `LWORK` must be at least `1`; otherwise, `LWORK` must be at least `max(1,M)`. For optimal performance, `LWORK` should be at least `M * NB` where `NB` is the optimal block size. If `LWORK = -1`, a workspace query is assumed; the routine only calculates the optimal size of the `WORK` array, returns this value as the first entry of the `WORK` array.
+
+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, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU0 = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+var WORK0 = new Float64Array( [ 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*0 );
+var WORK = new Float64Array( WORK0.buffer, WORK0.BYTES_PER_ELEMENT*0 );
+
+dgelqf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+// A0 => <Float64Array>[ 0.0, ~-5.477, ~-12.78, ~-20.083, ~0.309, ~-3.266, ~-6.532, ~0.463, ~-0.327, ~0.0, ~0.618, ~-0.789, ~0.618 ]
+// TAU0 => <Float64Array>[ ~1.183, ~1.156, ~1.447 ]
+// WORK0 => <Float64Array>[ 3.0, ~24.593, 0.0, 0.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dgelqf.ndarray( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK )
+
+Computes an LQ factorization of a real `M`-by-`N` matrix `A` using alternative indexing semantics.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU = new Float64Array( 3 );
+var WORK = new Float64Array( 4 );
+
+dgelqf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
+// A => <Float64Array>[ ~-5.477, ~-12.78, ~-20.083, ~0.309, ~-3.266, ~-6.532, ~0.463, ~-0.327, ~0.0, ~0.618, ~-0.789, ~0.618 ]
+// TAU => <Float64Array>[ ~1.183, ~1.156, ~1.447 ]
+// WORK => <Float64Array>[ 3.0, ~24.593, 0.0, 0.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input/output matrix as a [`Float64Array`][@stdlib/array/float64].
+-   **strideA1**: stride of the first dimension of `A`.
+-   **strideA2**: stride of the second dimension of `A`.
+-   **offsetA**: starting index for `A`.
+-   **TAU**: output array as a [`Float64Array`][@stdlib/array/float64].
+-   **strideTAU**: stride for `TAU`.
+-   **offsetTAU**: starting index for `TAU`.
+-   **WORK**: workspace array as a [`Float64Array`][@stdlib/array/float64].
+-   **strideWORK**: stride for `WORK`.
+-   **offsetWORK**: starting index for `WORK`.
+-   **LWORK**: dimension of the array `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, 0.0, 0.0, 0.0, 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+var WORK = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
+
+dgelqf.ndarray( 3, 4, A, 1, 3, 4, TAU, 1, 0, WORK, 1, 0, 4 );
+// A => <Float64Array>[ 0.0, ~-5.477, ~-12.78, ~-20.083, ~0.309, ~-3.266, ~-6.532, ~0.463, ~-0.327, ~0.0, ~0.618, ~-0.789, ~0.618 ]
+// TAU => <Float64Array>[ ~1.183, ~1.156, ~1.447 ]
+// WORK => <Float64Array>[ 3.0, ~24.593, 0.0, 0.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dgelqf()` corresponds to the [LAPACK][lapack] routine [`dgelqf`][lapack-dgelqf].
+
+</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 min = require( '@stdlib/math/base/special/min' );
+var dgelqf = require( '@stdlib/lapack/base/dgelqf' );
+
+// Specify matrix meta data:
+var shape = [ 3, 4 ];
+var order = 'row-major';
+var strides = shape2strides( shape, order );
+
+// Create a matrix stored in linear memory:
+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 ] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+// Output arrays:
+var TAU = new Float64Array( min( shape[ 0 ], shape[ 1 ] ) );
+var WORK = new Float64Array( shape[ 1 ] );
+
+// Compute the LQ factorization in-place:
+var info = dgelqf( order, shape[ 0 ], shape[ 1 ], A, strides[ 0 ], TAU, WORK, WORK.length );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+console.log( TAU );
+console.log( WORK );
+```
+
+</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-dgelqf]: https://www.netlib.org/lapack/explore-html/dc/dc1/group__gelqf_ga4c447bceb0a6a307f0eb746f40e9fe28.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 -->