diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/README.md b/lib/node_modules/@stdlib/lapack/base/dorgbr/README.md
new file mode 100644
index 000000000000..22288aeec958
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/README.md
@@ -0,0 +1,318 @@
+
+
+# dorgbr
+
+> Generate one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form.
+
+
+
+The `dorgbr` routine generates one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`. `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+
+
+
+```math
+A = Q B P^{T}
+```
+
+
+
+If `vect = 'Q'`, `A` is assumed to have been an `M-by-K` matrix, and `Q` is of order `M`:
+
+
+
+```math
+Q = H(1) H(2) \ldots H(k)
+```
+
+
+
+If `vect = 'P'`, `A` is assumed to have been a `K-by-N` matrix, and `P^T` is of order `N`:
+
+
+
+```math
+P^{T} = G(k) \ldots G(2) G(1)
+```
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var dorgbr = require( '@stdlib/lapack/base/dorgbr' );
+```
+
+#### dorgbr( order, vect, M, N, K, A, LDA, TAU, WORK, LWORK )
+
+Generates one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form.
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+var WORK = new Float64Array( 10 );
+
+dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
+// A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+// WORK[ 0 ] => 96.0
+```
+
+The function has the following parameters:
+
+- **order**: storage layout. Must be `'row-major'` or `'column-major'`.
+- **vect**: specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`. Must be `'Q'` or `'P'`.
+- **M**: number of rows of `Q` or `P^T`.
+- **N**: number of columns of `Q` or `P^T`. If `vect` is `'Q'`, must be greater than or equal to `min(M,K)` and smaller than or equal to `M`. If `vect` is `'P'`, must be greater than or equal to `M`, and `M` must be greater than or equal to `min(N,K)`.
+- **K**: if `vect` is `'Q'`, the number of columns in the original `M-by-K` matrix reduced by `dgebrd`; if `vect` is `'P'`, the number of rows in the original `K-by-N` matrix reduced by `dgebrd`.
+- **A**: input/output matrix of size `M×N` stored in linear memory as a [`Float64Array`][@stdlib/array/float64]. On entry, `A` contains the vectors which define the elementary reflectors, as returned by `dgebrd`. On exit, `A` is overwritten by the `M-by-N` matrix `Q` or `P^T`.
+- **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]. Must have length `min(M,K)` if `vect` is `'Q'` and length `min(N,K)` if `vect` is `'P'`.
+- **WORK**: workspace array as a [`Float64Array`][@stdlib/array/float64].
+- **LWORK**: dimension of the array `WORK`. Must be at least `max(1,min(M,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.
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+var TAU0 = new Float64Array( [ 0.0, 1.3, 0.9, 1.1 ] );
+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
+
+dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
+// A0 => [ 0.0, -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+// WORK0[ 1 ] => 96.0
+```
+
+
+
+#### dorgbr.ndarray( vect, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK )
+
+Generates one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+var WORK = new Float64Array( 10 );
+
+dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+// A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+// WORK[ 0 ] => 96.0
+```
+
+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,
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 0.0, 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+var TAU = new Float64Array( [ 0.0, 1.3, 0.9, 1.1 ] );
+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 ] );
+
+dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 1, TAU, 1, 1, WORK, 1, 1, 10 );
+// A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+// WORK[ 1 ] => 96.0
+```
+
+
+
+
+
+
+
+## Notes
+
+- Both functions mutate the input arrays `A` and `WORK`.
+
+- Both functions return a status code indicating success (`0`) or failure.
+
+- `dorgbr()` corresponds to the [LAPACK][LAPACK] routine [`dorgbr`][lapack-dorgbr].
+
+
+
+
+
+
+
+## Examples
+
+
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var dorgbr = require( '@stdlib/lapack/base/dorgbr' );
+
+// Define matrix dimensions:
+var M = 4;
+var N = 3;
+var K = 3;
+var shape = [ M, N ];
+var order = 'column-major';
+var strides = shape2strides( shape, order );
+
+// Create the matrix A containing the elementary reflector vectors returned by dgebrd:
+var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+// Define the scalar factors and workspace array:
+var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+var WORK = new Float64Array( 10 );
+
+// Generate the orthogonal matrix Q:
+var info = dorgbr( order, 'Q', M, N, K, A, strides[ 1 ], TAU, WORK, WORK.length );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+console.log( info );
+```
+
+
+
+
+
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+TODO
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dorgbr]: https://www.netlib.org/lapack/explore-html/dc/d45/group__ungbr_gae61b2be52b4a8e82f4cf8ec3779b8a90.html
+
+[@stdlib/array/float64]: https://stdlib.io/docs/api/latest/@stdlib/array/float64
+
+[@stdlib/lapack/base/dgebrd]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/lapack/base/dgebrd
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+
+
+
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/benchmark/benchmark.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/benchmark/benchmark.js
new file mode 100644
index 000000000000..dfda928f9b34
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/benchmark/benchmark.js
@@ -0,0 +1,126 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dorgbr = require( './../lib/dorgbr.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+ 'row-major',
+ 'column-major'
+];
+var VECTORS = [
+ 'Q',
+ 'P'
+];
+var opts = {
+ 'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {string} vect - specifies whether to generate the matrix `Q` or the matrix `P^T`
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, vect, N ) {
+ var WORK = new Float64Array( N * 32 );
+ var TAU = discreteUniform( N, 0.0, 10.0, opts );
+ var A = discreteUniform( N*N, 0.0, 10.0, opts );
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var i;
+ var z;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ z = dorgbr( order, vect, N, N, N, A, N, TAU, WORK, WORK.length );
+ if ( z < 0 ) {
+ b.fail( 'should return a success status code' );
+ }
+ }
+ b.toc();
+ if ( z < 0 ) {
+ b.fail( 'should return a success status code' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var vect;
+ var min;
+ var max;
+ var ord;
+ var N;
+ var f;
+ var i;
+ var j;
+ var k;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( j = 0; j < LAYOUTS.length; j++ ) {
+ ord = LAYOUTS[ j ];
+ for ( k = 0; k < VECTORS.length; k++ ) {
+ vect = VECTORS[ k ];
+ for ( i = min; i <= max; i++ ) {
+ N = floor( pow( pow( 10, i ), 1.0/3.0 ) );
+ f = createBenchmark( ord, vect, N );
+ bench( format( '%s::square_matrix:order=%s,vect=%s,size=%d', pkg, ord, vect, N*N ), f );
+ }
+ }
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/benchmark/benchmark.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/benchmark/benchmark.ndarray.js
new file mode 100644
index 000000000000..2b860df48e5a
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/benchmark/benchmark.ndarray.js
@@ -0,0 +1,140 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
+var Float64Array = require( '@stdlib/array/float64' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dorgbr = require( './../lib/ndarray.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+ 'row-major',
+ 'column-major'
+];
+var VECTORS = [
+ 'Q',
+ 'P'
+];
+var opts = {
+ 'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {string} vect - specifies whether to generate the matrix `Q` or the matrix `P^T`
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, vect, N ) {
+ var WORK;
+ var sa1;
+ var sa2;
+ var TAU;
+ var A;
+
+ WORK = new Float64Array( N * 32 );
+ TAU = discreteUniform( N, 0.0, 10.0, opts );
+ A = discreteUniform( N*N, 0.0, 10.0, opts );
+ if ( isColumnMajor( order ) ) {
+ sa1 = 1;
+ sa2 = N;
+ } else { // order === 'row-major'
+ sa1 = N;
+ sa2 = 1;
+ }
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var i;
+ var z;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ z = dorgbr( vect, N, N, N, A, sa1, sa2, 0, TAU, 1, 0, WORK, 1, 0, WORK.length ); // eslint-disable-line max-len
+ if ( z < 0 ) {
+ b.fail( 'should return a success status code' );
+ }
+ }
+ b.toc();
+ if ( z < 0 ) {
+ b.fail( 'should return a success status code' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var vect;
+ var min;
+ var max;
+ var ord;
+ var N;
+ var f;
+ var i;
+ var j;
+ var k;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( j = 0; j < LAYOUTS.length; j++ ) {
+ ord = LAYOUTS[ j ];
+ for ( k = 0; k < VECTORS.length; k++ ) {
+ vect = VECTORS[ k ];
+ for ( i = min; i <= max; i++ ) {
+ N = floor( pow( pow( 10, i ), 1.0/23.0 ) );
+ f = createBenchmark( ord, vect, N );
+ bench( format( '%s::square_matrix:ndarray:order=%s,vect=%s,size=%d', pkg, ord, vect, N*N ), f );
+ }
+ }
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/repl.txt b/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/repl.txt
new file mode 100644
index 000000000000..ce66a3303519
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/repl.txt
@@ -0,0 +1,168 @@
+{{alias}}( order, vect, M, N, K, A, LDA, TAU, WORK, LWORK )
+ Generates one of the real orthogonal matrices `Q` or `P**T` determined
+ by `DGEBRD` when reducing a real matrix `A` to bidiagonal form:
+ `A = Q * B * P**T`.
+
+ `Q` and `P**T` are defined as products of elementary reflectors `H(i)`
+ or `G(i)` respectively.
+
+ Indexing is relative to the first index. To introduce an offset, use typed
+ array views.
+
+ The function mutates `A` and `WORK`.
+
+ Parameters
+ ----------
+ order: string
+ Storage layout. Must be either 'row-major' or 'column-major'.
+
+ vect: string
+ Specifies whether the matrix `Q` or the matrix `P**T` is returned in
+ `A`. Must be either 'Q' or 'P'.
+
+ M: integer
+ Number of rows of `Q` or `P**T`.
+
+ N: integer
+ Number of columns of `Q` or `P**T`.
+
+ If `vect` is 'Q', `N` must be greater than or equal to `min(M,K)` and
+ smaller than or equal to `M`. If `vect` is 'P', `N` must be greater
+ than or equal to `M`, and `M` must be greater than or equal to
+ `min(N,K)`.
+
+ K: integer
+ If `vect` is 'Q', the number of columns in the original `M-by-K`
+ matrix reduced by `DGEBRD`. If `vect` is 'P', the number of rows in
+ the original `K-by-N` matrix reduced by `DGEBRD`.
+
+ A: Float64Array
+ Input/output matrix. On entry, `A` contains the vectors which define
+ the elementary reflectors, as returned by `DGEBRD`. On exit, `A` is
+ overwritten by the `M-by-N` matrix `Q` or `P**T`.
+
+ LDA: integer
+ 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: Float64Array
+ Scalar factors of the elementary reflectors. Must have length
+ `min(M,K)` if `vect` is 'Q' and length `min(N,K)` if `vect` is 'P'.
+
+ WORK: Float64Array
+ Workspace array.
+
+ LWORK: integer
+ Dimension of the array `WORK`. Must be at least `max(1,min(M,N))`,
+ unless equal to `-1`, in which case a workspace query is performed and
+ the optimal size of `WORK` is returned in `WORK[0]`.
+
+ Returns
+ -------
+ info: integer
+ Status code. A status code of `0` indicates success.
+
+ Examples
+ --------
+ > var A = new {{alias:@stdlib/array/float64}}([ 1,0,0,-1,-2,0 ]);
+ > var TAU = new {{alias:@stdlib/array/float64}}( [ 1, 1 ] );
+ > var WORK = new {{alias:@stdlib/array/float64}}( 10 );
+ > {{alias}}( 'column-major', 'P', 2, 3, 2, A, 2, TAU, WORK, 10 )
+ 0
+ > A
+ [ 0, 0, 0, 0, 2, 0 ]
+ > WORK[ 0 ]
+ 64
+
+
+{{alias}}.ndarray(vect,M,N,K,A,sA1,sA2,oA,TAU,sTAU,oTAU, WORK,sWORK,oWORK,LWORK)
+ Generates one of the real orthogonal matrices `Q` or `P**T` determined
+ by `DGEBRD` when reducing a real matrix `A` to bidiagonal form using
+ alternative indexing semantics.
+
+ While typed array views mandate a view offset based on the underlying
+ buffer, the offset parameters support indexing semantics based on starting
+ indices.
+
+ The function mutates `A` and `WORK`.
+
+ Parameters
+ ----------
+ vect: string
+ Specifies whether the matrix `Q` or the matrix `P**T` is returned in
+ `A`. Must be either 'Q' or 'P'.
+
+ M: integer
+ Number of rows of `Q` or `P**T`.
+
+ N: integer
+ Number of columns of `Q` or `P**T`.
+
+ If `vect` is 'Q', `N` must be greater than or equal to `min(M,K)` and
+ smaller than or equal to `M`. If `vect` is 'P', `N` must be greater
+ than or equal to `M`, and `M` must be greater than or equal to
+ `min(N,K)`.
+
+ K: integer
+ If `vect` is 'Q', the number of columns in the original `M-by-K`
+ matrix reduced by `DGEBRD`. If `vect` is 'P', the number of rows in
+ the original `K-by-N` matrix reduced by `DGEBRD`.
+
+ A: Float64Array
+ Input/output matrix. On entry, `A` contains the vectors which define
+ the elementary reflectors, as returned by `DGEBRD`. On exit, `A` is
+ overwritten by the `M-by-N` matrix `Q` or `P**T`.
+
+ sA1: integer
+ Stride length for the first dimension of `A`.
+
+ sA2: integer
+ Stride length for the second dimension of `A`.
+
+ oA: integer
+ Starting index for `A`.
+
+ TAU: Float64Array
+ Scalar factors of the elementary reflectors. Must have length
+ `min(M,K)` if `vect` is 'Q' and length `min(N,K)` if `vect` is 'P'.
+
+ sTAU: integer
+ Stride length for `TAU`.
+
+ oTAU: integer
+ Starting index for `TAU`.
+
+ WORK: Float64Array
+ Workspace array.
+
+ sWORK: integer
+ Stride length for `WORK`.
+
+ oWORK: integer
+ Starting index for `WORK`.
+
+ LWORK: integer
+ Dimension of the array `WORK`. Must be at least `max(1,min(M,N))`,
+ unless equal to `-1`, in which case a workspace query is performed and
+ the optimal size of `WORK` is returned in `WORK[0]`.
+
+ Returns
+ -------
+ info: integer
+ Status code. A status code of `0` indicates success.
+
+ Examples
+ --------
+ > var A = new {{alias:@stdlib/array/float64}}([ 1,0,0,-1,-2,0 ]);
+ > var TAU = new {{alias:@stdlib/array/float64}}( [ 1, 1 ] );
+ > var WORK = new {{alias:@stdlib/array/float64}}( 10 );
+ > {{alias}}.ndarray( `P`, 2, 3, 2, A, 1, 2, 0, TAU, 1, 0, WORK, 1, 0, 10 )
+ 0
+ > A
+ [ 0, 0, 0, 0, 2, 0 ]
+ > WORK[ 0 ]
+ 64
+
+ See Also
+ --------
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/types/index.d.ts b/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/types/index.d.ts
new file mode 100644
index 000000000000..5f35dde2ec96
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/types/index.d.ts
@@ -0,0 +1,154 @@
+/*
+* @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.
+*/
+
+// TypeScript Version: 4.1
+
+///
+
+import { Layout } from '@stdlib/types/blas';
+
+/**
+* Interface describing `dorgbr`.
+*/
+interface Routine {
+ /**
+ * Generates one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`.
+ *
+ * ## Notes
+ *
+ * - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+ * - On exit, `A` is overwritten by the `M-by-N` matrix `Q` or `P^T`.
+ * - `WORK` must have length, `LWORK >= max(1,min(M,N))`. For optimum performance `LWORK >= min(M,N)*NB`, where `NB` is the optimal blocksize.
+ * - If `LWORK = -1`, then a workspace query is assumed.
+ *
+ * @param order - storage layout
+ * @param vect - specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`
+ * @param M - number of rows of `Q` or `P^T`
+ * @param N - number of columns of `Q` or `P^T`
+ * @param K - number of elementary reflectors
+ * @param A - input/output matrix
+ * @param LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
+ * @param TAU - scalar factors of the elementary reflectors
+ * @param WORK - workspace array
+ * @param LWORK - dimension of the array `WORK`
+ * @returns status code
+ *
+ * @example
+ * var Float64Array = require( '@stdlib/array/float64' );
+ *
+ * var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ * var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ * var WORK = new Float64Array( 10 );
+ *
+ * dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
+ * // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+ * // WORK[ 0 ] => 96.0
+ */
+ ( order: Layout, vect: 'Q' | 'P', M: number, N: number, K: number, A: Float64Array, LDA: number, TAU: Float64Array, WORK: Float64Array, LWORK: number ): number;
+
+ /**
+ * Generates one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form using alternative indexing semantics.
+ *
+ * ## Notes
+ *
+ * - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+ * - On exit, `A` is overwritten by the `M-by-N` matrix `Q` or `P^T`.
+ * - `WORK` must have length, `LWORK >= max(1,min(M,N))`. For optimum performance `LWORK >= min(M,N)*NB`, where `NB` is the optimal blocksize.
+ * - If `LWORK = -1`, then a workspace query is assumed.
+ *
+ * @param vect - specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`
+ * @param M - number of rows of `Q` or `P^T`
+ * @param N - number of columns of `Q` or `P^T`
+ * @param K - number of elementary reflectors
+ * @param A - input/output matrix
+ * @param strideA1 - stride length for the first dimension of `A`
+ * @param strideA2 - stride length for the second dimension of `A`
+ * @param offsetA - starting index of `A`
+ * @param TAU - scalar factors of the elementary reflectors
+ * @param strideTAU - stride length for `TAU`
+ * @param offsetTAU - starting index of `TAU`
+ * @param WORK - workspace array
+ * @param strideWORK - stride length for `WORK`
+ * @param offsetWORK - starting index of `WORK`
+ * @param LWORK - dimension of the array `WORK`
+ * @returns status code
+ *
+ * @example
+ * var Float64Array = require( '@stdlib/array/float64' );
+ *
+ * var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ * var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ * var WORK = new Float64Array( 10 );
+ *
+ * dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+ * // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+ * // WORK[ 0 ] => 96.0
+ */
+ ndarray( vect: 'Q' | 'P', M: number, N: number, K: number, A: Float64Array, strideA1: number, strideA2: number, offsetA: number, TAU: Float64Array, strideTAU: number, offsetTAU: number, WORK: Float64Array, strideWORK: number, offsetWORK: number, LWORK: number ): number;
+}
+
+/**
+* LAPACK routine to generate one of the real orthogonal matrices `Q` or `P^T` determined by `dgebrd` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`.
+*
+* ## Notes
+*
+* - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+* - On exit, `A` is overwritten by the `M-by-N` matrix `Q` or `P^T`.
+* - `WORK` must have length, `LWORK >= max(1,min(M,N))`. For optimum performance `LWORK >= min(M,N)*NB`, where `NB` is the optimal blocksize.
+* - If `LWORK = -1`, then a workspace query is assumed.
+*
+* @param order - storage layout
+* @param vect - specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`
+* @param M - number of rows of `Q` or `P^T`
+* @param N - number of columns of `Q` or `P^T`
+* @param K - number of elementary reflectors
+* @param A - input/output matrix
+* @param LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
+* @param TAU - scalar factors of the elementary reflectors
+* @param WORK - workspace array
+* @param LWORK - dimension of the array `WORK`
+* @returns status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+* var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
+* // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+* // WORK[ 0 ] => 96.0
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+* var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+* // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+* // WORK[ 0 ] => 96.0
+*/
+declare var dorgbr: Routine;
+
+
+// EXPORTS //
+
+export = dorgbr;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/types/test.ts b/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/types/test.ts
new file mode 100644
index 000000000000..c0568be930c3
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/docs/types/test.ts
@@ -0,0 +1,330 @@
+/*
+* @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.
+*/
+
+// TypeScript Version: 4.1
+
+import dorgbr = require( './index' );
+
+// TESTS //
+
+// The function returns a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectType number
+ dorgbr( 'column-major', 'P', 4, 4, 5, A, 4, TAU, WORK, 10 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a valid order...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'foo', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 5, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( true, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( false, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( null, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( undefined, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( [], 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( {}, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( ( x: number ): number => x, 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is neither 'Q' nor 'P'...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'foo', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'q', 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 5, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', true, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', false, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', null, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', undefined, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', [], 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', {}, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', ( x: number ): number => x, 4, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a third argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', '5', 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', true, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', false, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', null, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', undefined, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', [], 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', {}, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', ( x: number ): number => x, 3, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fourth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, '5', 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, true, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, false, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, null, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, undefined, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, [], 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, {}, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, ( x: number ): number => x, 3, A, 4, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fifth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, 3, '5', A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, true, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, false, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, null, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, undefined, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, [], A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, {}, A, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, ( x: number ): number => x, A, 4, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a sixth argument which is not a Float64Array...
+{
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, 3, 3, '5', 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, 5, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, true, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, false, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, null, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, undefined, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, [], 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, {}, 4, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, ( x: number ): number => x, 4, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a seventh argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, '5', TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, true, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, false, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, null, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, undefined, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, [], TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, {}, TAU, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, ( x: number ): number => x, TAU, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an eighth argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, '5', WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, 5, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, true, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, false, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, null, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, undefined, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, [], WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, {}, WORK, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, ( x: number ): number => x, WORK, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a ninth argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, '5', 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, 5, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, true, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, false, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, null, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, undefined, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, [], 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, {}, 10 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, ( x: number ): number => x, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a tenth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, '5' ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, true ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, false ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, null ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, undefined ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, [] ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, {} ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr(); // $ExpectError
+ dorgbr( 'column-major' ); // $ExpectError
+ dorgbr( 'column-major', 'Q' ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4 ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK ); // $ExpectError
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10, 10 ); // $ExpectError
+}
+
+// Attached to the main export is an `ndarray` method which returns a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectType number
+ dorgbr.ndarray( 'P', 4, 4, 5, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectType number
+}
+
+// The compiler throws an error if the `ndarray` method is provided a first argument which is neither 'Q' nor 'P'...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr.ndarray( 'foo', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 5, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( true, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( false, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( null, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( undefined, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( [], 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( {}, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( ( x: number ): number => x, 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a second argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr.ndarray( 'Q', '5', 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', true, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', false, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', null, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', undefined, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', [], 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', {}, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', ( x: number ): number => x, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a fifth argument which is not a Float64Array...
+{
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr.ndarray( 'Q', 4, 3, 3, '5', 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, 5, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, true, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, false, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, null, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, undefined, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, [], 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, {}, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, ( x: number ): number => x, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a ninth argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, '5', 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, 5, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, true, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, false, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, null, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, undefined, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, [], 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, {}, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, ( x: number ): number => x, 1, 0, WORK, 1, 0, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a twelfth argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, '5', 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, 5, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, true, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, false, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, null, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, undefined, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, [], 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, {}, 1, 0, 10 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, ( x: number ): number => x, 1, 0, 10 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided an unsupported number of arguments...
+{
+ const A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+ const TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ const WORK = new Float64Array( 10 );
+
+ dorgbr.ndarray(); // $ExpectError
+ dorgbr.ndarray( 'Q' ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0 ); // $ExpectError
+ dorgbr.ndarray( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10, 10 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/examples/index.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/examples/index.js
new file mode 100644
index 000000000000..7395c45ab154
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/examples/index.js
@@ -0,0 +1,69 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var dorgbr = require( './../lib' );
+
+// Generate the orthogonal matrix `Q` determined by `dgebrd` when reducing a real `M-by-K` matrix, where `m >= k`:
+
+// Define matrix dimensions:
+var M = 4;
+var N = 3;
+var K = 3;
+var shape = [ M, N ];
+var order = 'column-major';
+var strides = shape2strides( shape, order );
+
+// Create the matrix `A` containing the elementary reflector vectors returned by `dgebrd`:
+var A = new Float64Array( [ 1.0, 0.2, -0.1, 0.3, 0.0, 1.0, 0.4, -0.2, 0.0, 0.0, 1.0, 0.5 ] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+// Define the scalar factors and workspace array:
+var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+var WORK = new Float64Array( 10 );
+
+// Generate the orthogonal matrix `Q`:
+var info = dorgbr( order, 'Q', M, N, K, A, strides[ 1 ], TAU, WORK, WORK.length );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+console.log( info );
+
+// Generate the matrix `P^T` determined by `dgebrd` when reducing a real `K-by-N` matrix, where `k >= n`:
+
+// Define matrix dimensions:
+M = 4;
+N = 4;
+K = 5;
+shape = [ M, N ];
+strides = shape2strides( shape, order );
+
+// Create the matrix `A` containing the elementary reflector vectors returned by `dgebrd`:
+A = new Float64Array( [ 1.0, 0.5, 0.8, 1.1, 0.2, 2.0, 0.9, 1.2, 0.3, 0.6, 3.0, 1.3, 0.4, 0.7, 1.0, 4.0 ] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+// Define the scalar factors and workspace array:
+TAU = new Float64Array( [ 1.5, 0.9, 1.3, 0.0 ] );
+WORK = new Float64Array( 10 );
+
+// Generate the matrix `P^T`:
+info = dorgbr( order, 'P', M, N, K, A, strides[ 1 ], TAU, WORK, WORK.length );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+console.log( info );
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/base.js
new file mode 100644
index 000000000000..0436d8d35d33
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/base.js
@@ -0,0 +1,178 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-params */
+
+'use strict';
+
+// MODULES //
+
+var max = require( '@stdlib/math/base/special/max' );
+var min = require( '@stdlib/math/base/special/min' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var dorglq = require( './dorglq.js' );
+var dorgqr = require( './dorgqr.js' );
+
+
+// MAIN //
+
+/**
+* Generates one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bi-diagonal form: `A = Q * B * P^T`.
+*
+* ## Notes
+*
+* - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+*
+* - If `vect = 'Q'`,
+*
+* - A is assumed to have been an M-by-K matrix, and Q is of order M.
+* - if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n columns of Q, where m >= n >= k;
+* - if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M matrix.
+*
+* - If `vect = 'P'`,
+*
+* - A is assumed to have been a K-by-N matrix, and P**T is of order N
+* - if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m rows of P**T, where n >= m >= k
+* - if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as an N-by-N matrix.
+*
+* - LWORK >= max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB, where NB is the optimal blocksize.
+*
+* - If LWORK = -1, then 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
+*
+* @private
+* @param {string} vect - specifies whether the matrix Q or the matrix P**T is returned in `A`
+* @param {NonNegativeInteger} M - number of rows of `Q` or `P^T`
+* @param {NonNegativeInteger} N - number of columns of `Q` or `P^T`
+* @param {NonNegativeInteger} K - number of elementary reflectors
+* @param {Float64Array} A - input/output matrix
+* @param {integer} strideA1 - stride length of the first dimension of `A`
+* @param {integer} strideA2 - stride length of the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - starting index for `A`
+* @param {Float64Array} TAU - scalar factors of elementary reflectors
+* @param {integer} strideTAU - stride length of `TAU`
+* @param {NonNegativeInteger} offsetTAU - starting index for `TAU`
+* @param {Float64Array} WORK - workspace array
+* @param {integer} strideWORK - stride length of `WORK`
+* @param {NonNegativeInteger} offsetWORK - starting index for `WORK`
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 0, 0, -1, -2, 0 ] );
+* var TAU = new Float64Array( [ 1, 1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* var info = dorgbr( `P`, 2, 3, 2, A, 1, 2, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+* // A => [ 0, 0, 0, 0, 2, 0 ]
+* // info => 0
+* // WORK[ 0 ] => 96
+*/
+function dorgbr( vect, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) {
+ var lquery;
+ var lwkopt;
+ var wantq;
+ var mn;
+ var i;
+ var j;
+
+ wantq = ( vect === 'Q' );
+ mn = min( M, N );
+ lquery = ( LWORK === -1 );
+
+ WORK[ offsetWORK ] = 1;
+ if ( wantq ) {
+ if ( M >= K ) {
+ dorgqr( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
+ } else if ( M > 1 ) {
+ dorgqr( M - 1, M - 1, M - 1, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
+ }
+ } else if ( K < N ) {
+ dorglq( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
+ } else if ( N > 1 ) {
+ dorglq( N - 1, N - 1, N - 1, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
+ }
+
+ lwkopt = floor( WORK[ offsetWORK ] );
+ lwkopt = max( lwkopt, mn );
+
+ if ( lquery ) {
+ WORK[ offsetWORK ] = lwkopt;
+ return 0;
+ }
+ if ( M === 0 || N === 0 ) {
+ WORK[ offsetWORK ] = 1;
+ return 0;
+ }
+
+ if ( wantq ) {
+ // Form Q, determined by a call to DGEBRD to reduce an `M-by-K` matrix...
+
+ if ( M >= K ) {
+ // If M >= K, assume M >= N >= K:
+ dorgqr( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
+ } else {
+ // If M < K, assume M = N; Shift the vectors which define the elementary reflectors one column to the right, and set the first row and column of Q to those of the unit matrix...
+ for ( j = M - 1; j >= 1; j-- ) {
+ A[ offsetA + ( j * strideA2 ) ] = 0.0;
+
+ for ( i = j + 1; i < M; i++ ) {
+ A[ offsetA + ( i * strideA1 ) + ( j * strideA2 ) ] = A[ offsetA + ( i * strideA1 ) + ( ( j - 1 ) * strideA2 ) ];
+ }
+ }
+ A[ offsetA ] = 1.0;
+ for ( i = 1; i < M; i++ ) {
+ A[ offsetA + ( i * strideA1 ) ] = 0.0;
+ }
+ if ( M > 1 ) {
+ // Form Q(2:m,2:m):
+ dorgqr( M - 1, M - 1, M - 1, A, strideA1, strideA2, offsetA + strideA1 + strideA2, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
+ }
+ }
+ } else if ( K < N ) {
+ // If k < n, assume k <= m <= n:
+ dorglq( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
+ } else {
+ // If k >= n, assume m = n; Shift the vectors which define the elementary reflectors one row downward, and set the first row and column of P**T to those of the unit matrix...
+ A[ offsetA ] = 1.0;
+ for ( i = 1; i < N; i++ ) {
+ A[ offsetA + ( i * strideA1 ) ] = 0.0;
+ }
+ for ( j = 1; j < N; j++ ) {
+ for ( i = j - 1; i >= 1; i-- ) {
+ A[ offsetA + ( i * strideA1 ) + ( j * strideA2 ) ] = A[ offsetA + ( ( i - 1 ) * strideA1 ) + ( j * strideA2 ) ];
+ }
+ // A(0, j) = 0
+ A[ offsetA + ( j * strideA2 ) ] = 0.0;
+ }
+
+ if ( N > 1 ) {
+ // Form P**T(2:n,2:n)
+ dorglq( N - 1, N - 1, N - 1, A, strideA1, strideA2, offsetA + strideA1 + strideA2, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
+ }
+ }
+ WORK[ offsetWORK ] = lwkopt;
+
+ return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dorgbr;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarf1f.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarf1f.js
new file mode 100644
index 000000000000..1c1fcb234d65
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarf1f.js
@@ -0,0 +1,184 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+/* eslint-disable max-len */
+
+// MODULES //
+
+var iladlc = require( '@stdlib/lapack/base/iladlc' ).ndarray;
+var iladlr = require( '@stdlib/lapack/base/iladlr' ).ndarray;
+var dgemv = require( '@stdlib/blas/base/dgemv' ).ndarray;
+var dger = require( '@stdlib/blas/base/dger' ).ndarray;
+var daxpy = require( '@stdlib/blas/base/daxpy' ).ndarray;
+var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
+
+
+// FUNCTIONS //
+
+/**
+* Tests whether an operation should be applied to the left side.
+*
+* @private
+* @param {string} side - operation side
+* @returns {boolean} boolean indicating if an operation should be applied to the left side
+*/
+function isLeftSide( side ) {
+ return side === 'left';
+}
+
+
+// MAIN //
+
+/**
+* Applies a real elementary reflector `H = I - tau * v * v^T` to a real M by N matrix `C`.
+*
+* ## Notes
+*
+* - If `side = 'left'`,
+*
+* - `work` should have `N` indexed elements.
+* - `V` should have `1 + (M-1) * abs(strideV)` indexed elements.
+* - `C` is overwritten by `H * C`.
+*
+* - If `side = 'right'`,
+*
+* - `work` should have `M` indexed elements.
+* - `V` should have `1 + (N-1) * abs(strideV)` indexed elements.
+* - `C` is overwritten by `C * H`.
+*
+* @private
+* @param {string} side - specifies the side of multiplication with `C`
+* @param {NonNegativeInteger} M - number of rows in `C`
+* @param {NonNegativeInteger} N - number of columns in `C`
+* @param {Float64Array} V - the vector `v`
+* @param {integer} strideV - stride length for `V`
+* @param {NonNegativeInteger} offsetV - starting index for `V`
+* @param {number} tau - scalar constant
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of `C`
+* @param {integer} strideC2 - stride of the second dimension of `C`
+* @param {NonNegativeInteger} offsetC - starting index for `C`
+* @param {Float64Array} work - workspace array
+* @param {integer} strideWork - stride length for `work`
+* @param {NonNegativeInteger} offsetWork - starting index for `work`
+* @returns {Float64Array} `C * H` or `H * C`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var C = 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 V = new Float64Array( [ 0.5, 0.5, 0.5, 0.5 ] );
+* var work = new Float64Array( 3 );
+*
+* var out = dlarf1f( 'left', 4, 3, V, 1, 0, 1.0, C, 3, 1, 0, work, 1, 0 );
+* // returns [ -4.5, -10.5, -16.5, -0.75, -1.75, -2.75, 0.25, -0.75, -1.75, 1.25, 0.25, -0.75 ]
+*/
+function dlarf1f( side, M, N, V, strideV, offsetV, tau, C, strideC1, strideC2, offsetC, work, strideWork, offsetWork ) { // eslint-disable-line max-params
+ var lastv;
+ var lastc;
+ var i;
+
+ if ( tau === 0.0 ) {
+ return C;
+ }
+ lastc = 0;
+ if ( isLeftSide( side ) ) {
+ lastv = M;
+ } else {
+ lastv = N;
+ }
+ // Initialize `i` to point to the last element in `V`:
+ i = offsetV + ( ( lastv-1 ) * strideV );
+
+ // Move `i` to the last non-zero element in `V`, where we assume that V[0] = 1, and it is not stored, so we shouldn't access it...
+ while ( lastv > 1 && V[ i ] === 0.0 ) {
+ lastv -= 1;
+ i -= strideV;
+ }
+ if ( isLeftSide( side ) ) {
+ // Scan for the last non-zero column in `C`:
+ lastc = iladlc( lastv + 1, N, C, strideC1, strideC2, offsetC ) + 1; // adjust by `+1` to account for the difference between zero-based and one-based indexing
+ } else {
+ // Scan for the last non-zero row in `C`:
+ lastc = iladlr( M, lastv + 1, C, strideC1, strideC2, offsetC ) + 1; // // adjust by `+1` to account for the difference between zero-based and one-based indexing
+ }
+ // Return `C` unchanged if all elements in `C` are zero...
+ if ( lastc === 0 ) {
+ return C;
+ }
+ if ( isLeftSide( side ) ) {
+ // Form: H*C
+
+ // If `lastv = 1`, this means `V = 1`, so we just need to compute `C = H*C = (1-tau)*C`...
+ if ( lastv === 1 ) {
+ // C[0,0:lastc] = (1-tau)*C[0,0:lastc]
+ dscal( lastc, 1.0-tau, C, strideC2, offsetC ); // scale the first row
+ } else {
+ // work[0:lastc,0] = C[0:lastv,0:lastc]^T * V[0:lastv,0]
+
+ // work[0:lastc,0] = C[1:lastv,0:lastc]^T * V[1:lastv,0]
+ dgemv( 'transpose', lastv-1, lastc, 1.0, C, strideC1, strideC2, offsetC+strideC1, V, strideV, offsetV+strideV, 0.0, work, strideWork, offsetWork );
+
+ // work[0:lastc,0] += C[0,0:lastc]^T * V[0,0] = C[0,0:lastc]^T
+ daxpy( lastc, 1.0, C, strideC2, offsetC, work, strideWork, offsetWork ); // operates on the first row of C
+
+ // C[0:lastv,0:lastc] = C[...] - ( tau * V[0:lastv,0] * work[0:lastc,0]^T)
+
+ // C[0,0:lastc] = C[...] - ( tau * V[0,0] * work[0:lastc,0]^^T ) = C[...] - ( tau * work[0:lastc,0]^T )
+ daxpy( lastc, -tau, work, strideWork, offsetWork, C, strideC2, offsetC ); // operates on the first row of C
+
+ // C[1:lastv,0:lastc] = C[...] - ( tau * V[1:lastv,0] * work[0:lastc,0]^T )
+ dger( lastv-1, lastc, -tau, V, strideV, offsetV+strideV, work, strideWork, offsetWork, C, strideC1, strideC2, offsetC+strideC1 );
+ }
+ return C;
+ }
+ // side === 'right'
+
+ // Form: C*H
+
+ // If `lastv = 1`, then `V = 1`, so we just need to compute `C = CH = C*(1-tau)`...
+ if ( lastv === 1 ) {
+ // C[0:lastc,0] = ( 1-tau ) * C[0:lastc,0]
+ dscal( lastc, 1.0-tau, C, strideC1, offsetC ); // scale the first column
+ return C;
+ }
+ // work[0:lastc,0] = ( 1-tau ) * C[0:lastc,0]
+
+ // work[0:lastc,0] = C[0:lastc,1:lastv] * V[1:lastv,0]
+ dgemv( 'no-transpose', lastc, lastv-1, 1.0, C, strideC1, strideC2, offsetC+strideC2, V, strideV, offsetV+strideV, 0.0, work, strideWork, offsetWork );
+
+ // work[0:lastc,0] += C[0:lastc,0] * V[0,0] = C[0:lastc,0]
+ daxpy( lastc, 1.0, C, strideC1, offsetC, work, strideWork, offsetWork ); // operates on the first column of C
+
+ // C[0:lastc,0:lastv] = C[...] - ( tau * work[0:lastc,0] * V[0:lastv,0]^T )
+
+ // C[0:lastc,0] = C[...] - ( tau * work[0:lastc,0] * V[0,0]^T ) = C[...] - ( tau * work[0:lastc,0] )
+ daxpy( lastc, -tau, work, strideWork, offsetWork, C, strideC1, offsetC ); // operates on the first column of C
+
+ // C[0:lastc,1:lastv] = C[...] - ( tau * work[0:lastc,0] * V[1:lastv]^T )
+ dger( lastc, lastv-1, -tau, work, strideWork, offsetWork, V, strideV, offsetV+strideV, C, strideC1, strideC2, offsetC+strideC2 );
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = dlarf1f;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarfb.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarfb.js
new file mode 100644
index 000000000000..9829013b213b
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarfb.js
@@ -0,0 +1,118 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-params */
+
+'use strict';
+
+// MODULES //
+
+var leftForwardColumns = require( './left_forward_columns.js' );
+var leftBackwardColumns = require( './left_backward_columns.js' );
+var leftForwardRows = require( './left_forward_rows.js' );
+var leftBackwardRows = require( './left_backward_rows.js' );
+var rightForwardColumns = require( './right_forward_columns.js' );
+var rightBackwardColumns = require( './right_backward_columns.js' );
+var rightForwardRows = require( './right_forward_rows.js' );
+var rightBackwardRows = require( './right_backward_rows.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector `H` or its transpose `H^T` to a real `M` by `N` matrix `C`, from either the left or the right.
+*
+* ## Notes
+*
+* - `V` is a double-precision array with dimension `(LDV,K)` if `storev = 'C'`, `(LDV,M)` if `storev = 'R'` and `side = 'L'`, or `(LDV,N)` if `storev = 'R'` and `side = 'R'`.
+* - `T` is a double-precision array with dimension `(LDT,K)`. The triangular `K` by `K` matrix `T` in the representation of the block reflector.
+* - `C` is a double-precision array with dimension `(LDC,N)`. On entry, the `M` by `N` matrix `C`. On exit, `C` is overwritten by the desired matrix product.
+* - `work` is a double-precision array with dimension `(LDWORK,K)`.
+*
+* @private
+* @param {string} side - specifies whether `H` or `H^T` is applied from the left or right
+* @param {string} trans - specifies whether to apply `H` or `H^T`
+* @param {string} direct - indicates how `H` is formed from a product of elementary reflectors
+* @param {string} storev - indicates how the vectors which define the elementary reflectors are stored
+* @param {NonNegativeInteger} M - number of rows of the matrix `C`
+* @param {NonNegativeInteger} N - number of columns of the matrix `C`
+* @param {NonNegativeInteger} K - order of the matrix `T`
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of `V`
+* @param {integer} strideV2 - stride of the second dimension of `V`
+* @param {integer} offsetV - index offset for `V`
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of `T`
+* @param {integer} strideT2 - stride of the second dimension of `T`
+* @param {integer} offsetT - index offset for `T`
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of `C`
+* @param {integer} strideC2 - stride of the second dimension of `C`
+* @param {integer} offsetC - index offset for `C`
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of `work`
+* @param {integer} strideWork2 - stride of the second dimension of `work`
+* @param {integer} offsetWork - index offset for `work`
+* @returns {Float64Array} updated matrix `C`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* dlarfb( 'left', 'transpose', 'forward', 'columns', 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0 );
+*
+* // C => [ -1350.00, -1400.00, -1450.00, -30961.00, -32102.00, -33243.00, -266612.00, -275464.00, -284316.00 ]
+*/
+function dlarfb( side, trans, direct, storev, M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork ) {
+ // Quick return if possible
+ if ( M <= 0 || N <= 0 ) {
+ return C;
+ }
+
+ if ( side === 'left' ) {
+ if ( storev === 'columns') {
+ if ( direct === 'forward' ) {
+ return leftForwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ return leftBackwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ if ( direct === 'forward' ) {
+ return leftForwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ return leftBackwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ if ( storev === 'columns') {
+ if ( direct === 'forward' ) {
+ return rightForwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ return rightBackwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ if ( direct === 'forward' ) {
+ return rightForwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+ }
+ return rightBackwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans );
+}
+
+
+// EXPORTS //
+
+module.exports = dlarfb;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarft.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarft.js
new file mode 100644
index 000000000000..75afd916fb30
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dlarft.js
@@ -0,0 +1,571 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-params */
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dlacpy = require( '@stdlib/lapack/base/dlacpy' ).ndarray;
+var floor = require( '@stdlib/math/base/special/floor' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Forms the triangular factor T of a real block reflector H of order N, which is defined as a product of K elementary reflectors.
+*
+* ## Notes
+*
+* - If `direct` = 'forward', `H = H(1) H(2) . . . H(k)` and `T` is upper triangular.
+* - If `direct` = 'backward', `H = H(k) . . . H(2) H(1)` and `T` is lower triangular.
+* - If `storev` = 'columns', the vector which defines the elementary reflector `H(i)` is stored in the i-th column of the array `V`, and `H = I - V * T * V**T`.
+* - If `storev` = 'rows', the vector which defines the elementary reflector `H(i)` is stored in the i-th row of the array `V`, and `H = I - V**T * T * V`.
+*
+* ## Method
+*
+* ### QR Case
+*
+* - Break \\(V\\) apart into six components
+*
+* ```tex
+* V = \left[
+* \begin{array}{cc}
+* V_{1,1} & 0 \\
+* V_{2,1} & V_{2,2} \\
+* V_{3,1} & V_{3,2}
+* \end{array}
+* \right]
+* ```
+*
+* where
+*
+* - \\(V_{1,1} \in \mathbb{R}^{l,l}\\) is unit lower triangular
+* - \\(V_{2,1} \in \mathbb{R}^{k-l,l}\\) is rectangular
+* - \\(V_{3,1} \in \mathbb{R}^{n-k,l}\\) is rectangular
+* - \\(V_{2,2} \in \mathbb{R}^{k-l,k-l}\\) is unit lower triangular
+* - \\(V_{3,2} \in \mathbb{R}^{n-k,k-l}\\) is rectangular
+*
+* - We construct the \\(T\\) matrix
+*
+* ```tex
+* T = \left[
+* \begin{array}{cc}
+* T_{1,1} & T_{1,2} \\
+* 0 & T_{2,2}
+* \end{array}
+* \right]
+* ```
+*
+* where \\(T\\) is the triangular factor obtained from block reflectors.
+*
+* - Assume we have already computed \\(T_{1,1}\\) and \\(T_{2,2}\\), and collect the associated reflectors in \\(V_1\\) and \\(V_2\\)
+*
+* ```tex
+* \begin{aligned}
+* T_{1,1} &\in \mathbb{R}^{l,l} && \text{upper triangular} \\
+* T_{2,2} &\in \mathbb{R}^{k-l,k-l} && \text{upper triangular} \\
+* T_{1,2} &\in \mathbb{R}^{l,k-l} && \text{rectangular}
+* \end{aligned}
+* ```
+*
+* with \\(l = \lfloor k/2 \rfloor\\).
+*
+* - Consider the product
+*
+* ```tex
+* \begin{aligned}
+* (I - V_1 T_{1,1} V_1^T)(I - V_2 T_{2,2} V_2^T)
+* = I - V_1 T_{1,1} V_1^T - V_2 T_{2,2} V_2^T + V_1 T_{1,1} V_1^T V_2 T_{2,2} V_2^T
+* \end{aligned}
+* ```
+*
+* - Define
+*
+* ```tex
+* T_{1,2} = -T_{1,1} V_1^T V_2 T_{2,2}
+* ```
+*
+* - Define the matrix \\(V\\) as
+*
+* ```tex
+* V = \left[
+* \begin{array}{cc}
+* V_1 & V_2
+* \end{array}
+* \right]
+* ```
+*
+* so the product is equivalent to \\(I - V T V^T\\).
+*
+* This means we can compute \\(T_{1,1}\\) and \\(T_{2,2}\\) recursively, then use this information to compute \\(T_{1,2}\\).
+*
+* ### LQ Case
+*
+* - Break \\(V\\) apart into six components
+*
+* ```tex
+* V = \left[
+* \begin{array}{ccc}
+* V_{1,1} & V_{1,2} & V_{1,3} \\
+* 0 & V_{2,2} & V_{2,3}
+* \end{array}
+* \right]
+* ```
+*
+* where
+*
+* - \\(V_{1,1} \in \mathbb{R}^{l,l}\\) is unit upper triangular
+* - \\(V_{1,2} \in \mathbb{R}^{l,k-l}\\) is rectangular
+* - \\(V_{1,3} \in \mathbb{R}^{l,n-k}\\) is rectangular
+* - \\(V_{2,2} \in \mathbb{R}^{k-l,k-l}\\) is unit upper triangular
+* - \\(V_{2,3} \in \mathbb{R}^{k-l,n-k}\\) is rectangular
+*
+* with \\(l = \lfloor k/2 \rfloor\\).
+*
+* - We construct the \\(T\\) matrix
+*
+* ```tex
+* T = \left[
+* \begin{array}{cc}
+* T_{1,1} & T_{1,2} \\
+* 0 & T_{2,2}
+* \end{array}
+* \right]
+* ```
+*
+* where \\(T\\) is the triangular factor obtained from block reflectors.
+*
+* - Assume we have already computed \\(T_{1,1}\\) and \\(T_{2,2}\\), and collect the associated reflectors in \\(V_1\\) and \\(V_2\\)
+*
+* ```tex
+* \begin{aligned}
+* T_{1,1} &\in \mathbb{R}^{l,l} && \text{upper triangular} \\
+* T_{2,2} &\in \mathbb{R}^{k-l,k-l} && \text{upper triangular} \\
+* T_{1,2} &\in \mathbb{R}^{l,k-l} && \text{rectangular}
+* \end{aligned}
+* ```
+*
+* - Consider the product
+*
+* ```tex
+* \begin{aligned}
+* (I - V_1^T T_{1,1} V_1)(I - V_2^T T_{2,2} V_2)
+* = I - V_1^T T_{1,1} V_1 - V_2^T T_{2,2} V_2 + V_1^T T_{1,1} V_1 V_2^T T_{2,2} V_2
+* \end{aligned}
+* ```
+*
+* - Define
+*
+* ```tex
+* T_{1,2} = -T_{1,1} V_1 V_2^T T_{2,2}
+* ```
+*
+* - Define the matrix \\(V\\) as
+*
+* ```tex
+* V = \left[
+* \begin{array}{c}
+* V_1 \\
+* V_2
+* \end{array}
+* \right]
+* ```
+*
+* so the product is equivalent to \\(I - V^T T V\\).
+*
+* This means we can compute \\(T_{1,1}\\) and \\(T_{2,2}\\) recursively, then use this information to compute \\(T_{1,2}\\).
+*
+* ### QL Case
+*
+* - Break \\(V\\) apart into six components
+*
+* ```tex
+* V = \left[
+* \begin{array}{cc}
+* V_{1,1} & V_{1,2} \\
+* V_{2,1} & V_{2,2} \\
+* 0 & V_{3,2}
+* \end{array}
+* \right]
+* ```
+*
+* where
+*
+* - \\(V_{1,1} \in \mathbb{R}^{n-k,k-l}\\) is rectangular
+* - \\(V_{2,1} \in \mathbb{R}^{k-l,k-l}\\) is unit upper triangular
+* - \\(V_{1,2} \in \mathbb{R}^{n-k,l}\\) is rectangular
+* - \\(V_{2,2} \in \mathbb{R}^{k-l,l}\\) is rectangular
+* - \\(V_{3,2} \in \mathbb{R}^{l,l}\\) is unit upper triangular
+*
+* - We construct the \\(T\\) matrix
+*
+* ```tex
+* T = \left[
+* \begin{array}{cc}
+* T_{1,1} & 0 \\
+* T_{2,1} & T_{2,2}
+* \end{array}
+* \right]
+* ```
+*
+* where \\(T\\) is the triangular factor obtained from block reflectors.
+*
+* - Assume we have already computed \\(T_{1,1}\\) and \\(T_{2,2}\\), and collect the associated reflectors in \\(V_1\\) and \\(V_2\\)
+*
+* ```tex
+* \begin{aligned}
+* T_{1,1} &\in \mathbb{R}^{k-l,k-l} && \text{non-unit lower triangular} \\
+* T_{2,2} &\in \mathbb{R}^{l,l} && \text{non-unit lower triangular} \\
+* T_{2,1} &\in \mathbb{R}^{l,k-l} && \text{rectangular}
+* \end{aligned}
+* ```
+*
+* with \\(l = \lfloor k/2 \rfloor\\).
+*
+* - Consider the product
+*
+* ```tex
+* \begin{aligned}
+* (I - V_2 T_{2,2} V_2^T)(I - V_1 T_{1,1} V_1^T)
+* = I - V_2 T_{2,2} V_2^T - V_1 T_{1,1} V_1^T + V_2 T_{2,2} V_2^T V_1 T_{1,1} V_1^T
+* \end{aligned}
+* ```
+*
+* - Define
+*
+* ```tex
+* T_{2,1} = -T_{2,2} V_2^T V_1 T_{1,1}
+* ```
+*
+* - Define the matrix \\(V\\) as
+*
+* ```tex
+* V = \left[
+* \begin{array}{cc}
+* V_1 & V_2
+* \end{array}
+* \right]
+* ```
+*
+* so the product is equivalent to \\(I - V T V^T\\).
+*
+* This means we can compute \\(T_{1,1}\\) and \\(T_{2,2}\\) recursively, then use this information to compute \\(T_{2,1}\\).
+*
+* ### RQ Case
+*
+* - Break \\(V\\) apart into six components
+*
+* ```tex
+* V = \left[
+* \begin{array}{ccc}
+* V_{1,1} & V_{1,2} & 0 \\
+* V_{2,1} & V_{2,2} & V_{2,3}
+* \end{array}
+* \right]
+* ```
+*
+* where
+*
+* - \\(V_{1,1} \in \mathbb{R}^{k-l,n-k}\\) is rectangular
+* - \\(V_{1,2} \in \mathbb{R}^{k-l,k-l}\\) is unit lower triangular
+* - \\(V_{2,1} \in \mathbb{R}^{l,n-k}\\) is rectangular
+* - \\(V_{2,2} \in \mathbb{R}^{l,k-l}\\) is rectangular
+* - \\(V_{2,3} \in \mathbb{R}^{l,l}\\) is unit lower triangular
+*
+* - We construct the \\(T\\) matrix
+*
+* ```tex
+* T = \left[
+* \begin{array}{cc}
+* T_{1,1} & 0 \\
+* T_{2,1} & T_{2,2}
+* \end{array}
+* \right]
+* ```
+*
+* where \\(T\\) is the triangular factor obtained from block reflectors.
+*
+* - Assume we have already computed \\(T_{1,1}\\) and \\(T_{2,2}\\), and collect the associated reflectors in \\(V_1\\) and \\(V_2\\)
+*
+* ```tex
+* \begin{aligned}
+* T_{1,1} &\in \mathbb{R}^{k-l,k-l} && \text{non-unit lower triangular} \\
+* T_{2,2} &\in \mathbb{R}^{l,l} && \text{non-unit lower triangular} \\
+* T_{2,1} &\in \mathbb{R}^{l,k-l} && \text{rectangular}
+* \end{aligned}
+* ```
+*
+* with \\(l = \lfloor k/2 \rfloor\\).
+*
+* - Consider the product
+*
+* ```tex
+* \begin{aligned}
+* (I - V_2^T T_{2,2} V_2)(I - V_1^T T_{1,1} V_1)
+* = I - V_2^T T_{2,2} V_2 - V_1^T T_{1,1} V_1 + V_2^T T_{2,2} V_2 V_1^T T_{1,1} V_1
+* \end{aligned}
+* ```
+*
+* - Define
+*
+* ```tex
+* T_{2,1} = -T_{2,2} V_2 V_1^T T_{1,1}
+* ```
+*
+* - Define the matrix \\(V\\) as
+*
+* ```tex
+* V = \left[
+* \begin{array}{c}
+* V_1 \\
+* V_2
+* \end{array}
+* \right]
+* ```
+*
+* so the product is equivalent to \\(I - V^T T V\\).
+*
+* This means we can compute \\(T_{1,1}\\) and \\(T_{2,2}\\) recursively, then use this information to compute \\(T_{2,1}\\).
+*
+* @private
+* @param {string} direct - specifies the order in which the elementary reflectors are multiplied to form the block reflector `H`
+* @param {string} storev - specifies how the vectors which define the elementary reflectors are stored
+* @param {NonNegativeInteger} N - order of the block reflector `H`
+* @param {NonNegativeInteger} K - order of the triangular factor `T` (the number of elementary reflectors)
+* @param {Float64Array} V - matrix of reflector vectors
+* @param {integer} strideV1 - stride of first dimension of `V`
+* @param {integer} strideV2 - stride of second dimension of `V`
+* @param {NonNegativeInteger} offsetV - starting index for `V`
+* @param {Float64Array} TAU - array of scalar factors of the elementary reflector `H(i)`
+* @param {integer} strideTAU - stride length for `TAU`
+* @param {NonNegativeInteger} offsetTAU - starting index for `TAU`
+* @param {Float64Array} T - output triangular matrix
+* @param {integer} strideT1 - stride of first dimension of `T`
+* @param {integer} strideT2 - stride of second dimension of `T`
+* @param {NonNegativeInteger} offsetT - starting index for `T`
+* @returns {Float64Array} `T`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 1.0, 0.2, 0.3, -0.4, 0.5, 0.0, 1.0, -0.6, 0.7, -0.8, 0.0, 0.0, 1.0, 0.9, 1.1 ] );
+* var TAU = new Float64Array( [ 1.2, 0.7, 1.5 ] );
+* var T = new Float64Array( 9 );
+*
+* dlarft( 'forward', 'rows', 5, 3, V, 5, 1, 0, TAU, 1, 0, T, 3, 1, 0 );
+* // T => [ ~1.2, ~0.5544, ~-0.17514, 0.0, 0.7, 0.8925, 0.0, 0.0, 1.5 ]
+*/
+function dlarft( direct, storev, N, K, V, strideV1, strideV2, offsetV, TAU, strideTAU, offsetTAU, T, strideT1, strideT2, offsetT ) {
+ var colv;
+ var dirf;
+ var i0;
+ var i1;
+ var i2;
+ var i3;
+ var lq;
+ var ql;
+ var qr;
+ var i;
+ var j;
+ var l;
+
+ if ( N === 0 || K === 0 ) {
+ return T;
+ }
+
+ if ( N === 1 || K === 1 ) {
+ T[ offsetT ] = TAU[ offsetTAU ];
+ return T;
+ }
+
+ l = floor( K / 2 );
+
+ if ( direct === 'forward' ) {
+ dirf = true;
+ }
+ else {
+ dirf = false;
+ }
+
+ if ( storev === 'columns') {
+ colv = true;
+ }
+ else {
+ colv = false;
+ }
+
+ // QR happens when we have forward direction in column storage
+ qr = dirf & colv;
+
+ // LQ happens when we have forward direction in row storage
+ lq = dirf & ( !colv );
+
+ // QL happens when we have backward direction in column storage
+ ql = ( !dirf ) & colv;
+
+ // The last case is RQ. Due to how we structured this, if the above 3 are false, then RQ must be true, so we never store this RQ happens when we have backward direction in row storage `RQ = ( !dirf ) & ( !colv )`
+ if ( qr ) {
+ // Compute T_{1,1} recursively
+ dlarft( direct, storev, N, l, V, strideV1, strideV2, offsetV, TAU, strideTAU, offsetTAU, T, strideT1, strideT2, offsetT );
+
+ // Compute T_{2,2} recursively
+ dlarft( direct, storev, N - l, K - l, V, strideV1, strideV2, offsetV + ( ( strideV1 + strideV2 ) * l ), TAU, strideTAU, offsetTAU + ( strideTAU * l ), T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * l ) );
+
+ // Compute T_{1,2} = V_{2,1}
+ i0 = offsetT + ( strideT2 * l );
+ i1 = offsetV + ( strideV1 * l );
+ for ( j = 0; j < l; j++ ) {
+ i2 = i0;
+ i3 = i1;
+ for ( i = 0; i < K - l; i++ ) {
+ T[ i2 ] = V[ i3 ];
+ i2 += strideT2;
+ i3 += strideV1;
+ }
+ i0 += strideT1;
+ i1 += strideV2;
+ }
+
+ // T_{1,2} = T_{1,2}*V_{2,2}
+ dtrmm( 'right', 'lower', 'no-transpose', 'unit', l, K - l, 1, V, strideV1, strideV2, offsetV + ( ( strideV1 + strideV2 ) * l ), T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ // T_{1,2} = V_{3,1}'*V_{3,2} + T_{1,2}
+
+ // Note: We assume K <= N, and GEMM will do nothing if N=K
+ dgemm( 'transpose', 'no-transpose', l, K - l, N - K, 1, V, strideV1, strideV2, offsetV + ( strideV1 * K ), V, strideV1, strideV2, offsetV + ( strideV1 * K ) + ( strideV2 * l ), 1, T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ /*
+ At this point, we have that T_{1,2} = V_1'*V_2
+ All that is left is to pre and post multiply by -T_{1,1} and T_{2,2} respectively.
+
+ T_{1,2} = -T_{1,1}*T_{1,2}
+ */
+ dtrmm( 'left', 'upper', 'no-transpose', 'non-unit', l, K - l, -1, T, strideT1, strideT2, offsetT, T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ // T_{1,2} = T_{1,2}*T_{2,2}
+ dtrmm( 'right', 'upper', 'no-transpose', 'non-unit', l, K - l, 1, T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * l ), T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+ } else if ( lq ) {
+ // Compute T_{1,1} recursively
+ dlarft( direct, storev, N, l, V, strideV1, strideV2, offsetV, TAU, strideTAU, offsetTAU, T, strideT1, strideT2, offsetT );
+
+ // Compute T_{2,2} recursively
+ dlarft( direct, storev, N - l, K - l, V, strideV1, strideV2, offsetV + ( ( strideV1 + strideV2 ) * l ), TAU, strideTAU, offsetTAU + ( strideTAU * l ), T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * l ) );
+
+ // Compute T_{1,2} = V_{1,2}
+ dlacpy( 'all', l, K - l, V, strideV1, strideV2, offsetV + ( strideV2 * l ), T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ // T_{1,2} = T_{1,2}*V_{2,2}
+ dtrmm( 'right', 'upper', 'transpose', 'unit', l, K - l, 1, V, strideV1, strideV2, offsetV + ( ( strideV1 + strideV2 ) * l ), T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ // T_{1,2} = V_{1,3}*V_{2,3}' + T_{1,2}
+
+ // Note: We assume K <= N, and GEMM will do nothing if N=K
+ dgemm( 'no-transpose', 'transpose', l, K - l, N - K, 1, V, strideV1, strideV2, offsetV + ( strideV2 * K ), V, strideV1, strideV2, offsetV + ( strideV1 * l ) + ( strideV2 * K ), 1, T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ /*
+ At this point, we have that T_{1,2} = V_1*V_2'
+ All that is left is to pre and post multiply by -T_{1,1} and T_{2,2} respectively.
+
+ T_{1,2} = -T_{1,1}*T_{1,2}
+ */
+ dtrmm( 'left', 'upper', 'no-transpose', 'non-unit', l, K - l, -1, T, strideT1, strideT2, offsetT, T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+
+ // T_{1,2} = T_{1,2}*T_{2,2}
+ dtrmm( 'right', 'upper', 'no-transpose', 'non-unit', l, K - l, 1, T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * l ), T, strideT1, strideT2, offsetT + ( strideT2 * l ) );
+ } else if ( ql ) {
+ // Compute T_{1,1} recursively
+ dlarft( direct, storev, N - l, K - l, V, strideV1, strideV2, offsetV, TAU, strideTAU, offsetTAU, T, strideT1, strideT2, offsetT );
+
+ // Compute T_{2,2} recursively
+ dlarft( direct, storev, N - l, K - l, V, strideV1, strideV2, offsetV + ( ( strideV1 + strideV2 ) * l ), TAU, strideTAU, offsetTAU + ( strideTAU * l ), T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * l ) );
+
+ // Compute T_{2,1} = V_{2,2}
+ i0 = offsetT + ( strideT1 * ( K - l ) );
+ i1 = offsetV + ( strideV1 * ( N - K ) ) + ( strideV2 * ( K - l ) );
+ for ( j = 0; j < K - l; j++ ) {
+ i2 = i0;
+ i3 = i1;
+ for ( i = 0; i < l; i++ ) {
+ T[ i2 ] = V[ i3 ];
+ i2 += strideT1;
+ i3 += strideV2;
+ }
+ i0 += strideT2;
+ i1 += strideV1;
+ }
+
+ // T_{2,1} = T_{2,1}*V_{2,1}
+ dtrmm( 'right', 'upper', 'no-transpose', 'unit', l, K - l, 1, V, strideV1, strideV2, offsetV + ( strideV1 * ( N - K ) ), T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ // T_{2,1} = V_{2,2}'*V_{2,1} + T_{2,1}
+
+ // Note: We assume K <= N, and GEMM will do nothing if N=K
+ dgemm( 'transpose', 'no-transpose', l, K - l, N - K, 1, V, strideV1, strideV2, offsetV + ( strideV2 * ( K - l ) ), V, strideV1, strideV2, offsetV, 1, T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ /*
+ At this point, we have that T_{2,1} = V_2'*V_1
+ All that is left is to pre and post multiply by -T_{2,2} and T_{1,1} respectively.
+
+ T_{2,1} = -T_{2,2}*T_{2,1}
+ */
+ dtrmm( 'left', 'lower', 'no-transpose', 'non-unit', l, K - l, -1, T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * ( K - l ) ), T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ // T_{2,1} = T_{2,1}*T_{1,1}
+ dtrmm( 'right', 'lower', 'no-transpose', 'non-unit', l, K - l, 1, T, strideT1, strideT2, offsetT, T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+ } else {
+ // Else means RQ case
+
+ // Compute T_{1,1} recursively
+ dlarft( direct, storev, N - l, K - l, V, strideV1, strideV2, offsetV, TAU, strideTAU, offsetTAU, T, strideT1, strideT2, offsetT );
+
+ // Compute T_{2,2} recursively
+ dlarft( direct, storev, N, l, V, strideV1, strideV2, offsetV + ( strideV1 * ( K - l ) ), TAU, strideTAU, offsetTAU + ( strideTAU * ( K - l ) ), T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * ( K - l ) ) );
+
+ // Compute T_{2,1} = V_{2,2}
+ dlacpy( 'all', l, K - l, V, strideV1, strideV2, offsetV + ( strideV1 * ( K - l ) ) + ( strideV2 * ( N - K ) ), T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ // T_{2,1} = T_{2,1}*V_{1,2}
+ dtrmm( 'right', 'lower', 'transpose', 'unit', l, K - l, 1, V, strideV1, strideV2, offsetV + ( strideV2 * ( N - K ) ), T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ // T_{2,1} = V_{2,1}*V_{1,1}' + T_{2,1}
+
+ // Note: We assume K <= N, and GEMM will do nothing if N=K
+ dgemm('no-transpose', 'transpose', l, K - l, N - K, 1, V, strideV1, strideV2, offsetV + ( strideV1 * ( K - l ) ), V, strideV1, strideV2, offsetV, 1, T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ /*
+ At this point, we have that T_{2,1} = V_2*V_1'
+ All that is left is to pre and post multiply by -T_{2,2} and T_{1,1} respectively.
+
+ T_{2,1} = -T_{2,2}*T_{2,1}
+ */
+ dtrmm( 'left', 'lower', 'no-transpose', 'non-unit', l, K - l, -1, T, strideT1, strideT2, offsetT + ( ( strideT1 + strideT2 ) * ( K - l ) ), T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+
+ // T_{2,1} = T_{2,1}*T_{1,1}
+ dtrmm( 'right', 'lower', 'no-transpose', 'non-unit', l, K - l, 1, T, strideT1, strideT2, offsetT, T, strideT1, strideT2, offsetT + ( strideT1 * ( K - l ) ) );
+ }
+ return T;
+}
+
+
+// EXPORTS //
+
+module.exports = dlarft;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorg2r.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorg2r.js
new file mode 100644
index 000000000000..d4c59f618c27
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorg2r.js
@@ -0,0 +1,113 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
+var dlarf1f = require( './dlarf1f.js' );
+var initUnitColumns = require( './init_unit_columns.js' );
+
+
+// MAIN //
+
+/**
+* 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`.
+*
+* @private
+* @param {PositiveInteger} M - number of rows in matrix `A`
+* @param {PositiveInteger} N - number of columns in matrix `A`
+* @param {NonNegativeInteger} K - number of elementary reflectors whose product defines the matrix Q
+* @param {Float64Array} A - input matrix
+* @param {integer} strideA1 - stride of the first dimension of `A`
+* @param {integer} strideA2 - stride of the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - index offset for `A`
+* @param {Float64Array} tau - vector of K scalar factors of the elementary reflectors
+* @param {integer} strideTau - stride length for `tau`
+* @param {NonNegativeInteger} offsetTau - index offset for `tau`
+* @param {Float64Array} work - workspace array
+* @param {integer} strideWork - stride length for `work`
+* @param {NonNegativeInteger} offsetWork - index offset for `work`
+* @returns {Float64Array} matrix `A` overwritten with the orthogonal matrix Q
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+* var tau = new Float64Array( [ 0.0, 0.0 ] );
+* var work = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+*
+* dorg2r( 3, 2, 2, A, 1, 3, 0, tau, 1, 0, work, 1, 0 );
+* // A => [ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
+*/
+function dorg2r( M, N, K, A, strideA1, strideA2, offsetA, tau, strideTau, offsetTau, work, strideWork, offsetWork ) { // eslint-disable-line max-len, max-params
+ var ia1;
+ var ia3;
+ var del;
+ var ia2;
+ var it;
+ var i;
+ var j;
+
+ if ( N <= 0 ) {
+ return A;
+ }
+
+ // Initialize columns k+1:n to columns of the unit matrix
+ initUnitColumns( M, N, K, A, strideA1, strideA2, offsetA );
+
+ del = strideA1 + strideA2;
+ it = offsetTau + ((K-1)*strideTau);
+ ia1 = offsetA + ((K-1)*(strideA1+strideA2));
+ ia2 = offsetA + ((K-1)*strideA2);
+
+ // Apply H(i) to A(i:m,i:n) from the left
+ for ( i = K-1; i >= 0; i-- ) {
+ if ( i < N ) {
+ // Apply H(i) to A(i:m,i+1:n) from the left
+ dlarf1f( 'left', M-i, N-i-1, A, strideA1, ia1, tau[ it ], A, strideA1, strideA2, ia1 + strideA2, work, strideWork, offsetWork );
+ }
+ if ( i < M ) {
+ // Scale A(i+1:m,i) by -tau(i)
+ dscal( M-i-1, -tau[ it ], A, strideA1, ia1 + strideA1 );
+ }
+
+ // Set A(i,i) = 1 - tau(i)
+ A[ ia1 ] = 1.0 - tau[ it ];
+
+ ia3 = 0;
+
+ // Set A(0:i-1,i) to zero
+ for ( j = 0; j < i; j++ ) {
+ A[ ia2 + ia3 ] = 0.0;
+ ia3 += strideA1;
+ }
+ it -= strideTau;
+
+ ia1 -= del;
+ ia2 -= strideA2;
+ }
+
+ return A;
+}
+
+
+// EXPORTS //
+
+module.exports = dorg2r;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgbr.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgbr.js
new file mode 100644
index 000000000000..3ac51945fb44
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgbr.js
@@ -0,0 +1,133 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var isLayout = require( '@stdlib/blas/base/assert/is-layout' );
+var format = require( '@stdlib/string/format' );
+var max = require( '@stdlib/math/base/special/fast/max' );
+var min = require( '@stdlib/math/base/special/min' );
+var base = require( './base.js' );
+
+
+// MAIN //
+
+/**
+* Generates one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`.
+*
+* ## Notes
+*
+* - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+*
+* - If `vect = 'Q'`,
+*
+* - `A` is assumed to have been an `M-by-K` matrix, and `Q` is of order `M`.
+* - if `m >= k`, `Q = H(1) H(2) . . . H(k)` and `dorgbr` returns the first `n` columns of `Q`, where `m >= n >= k`.
+* - if `m < k`, `Q = H(1) H(2) . . . H(m-1)` and `dorgbr` returns `Q` as an `M-by-M` matrix.
+*
+* - If `vect = 'P'`,
+*
+* - `A` is assumed to have been a `K-by-N` matrix, and `P^T` is of order `N`.
+* - if `k < n`, `P^T = G(k) . . . G(2) G(1)` and `dorgbr` returns the first `m` rows of `P^T`, where `n >= m >= k`.
+* - if `k >= n`, `P^T = G(n-1) . . . G(2) G(1)` and `dorgbr` returns `P^T` as an `N-by-N` matrix.
+*
+* - `WORK` must have length, `LWORK >= max(1,min(M,N))`. For optimum performance `LWORK >= min(M,N)*NB`, where `NB` is the optimal blocksize.
+*
+* - If `LWORK = -1`, then 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, and no error message related to `LWORK` is issued.
+*
+* @param {string} order - storage layout
+* @param {string} vect - specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`
+* @param {NonNegativeInteger} M - number of rows of `Q` or `P^T`
+* @param {NonNegativeInteger} N - number of columns of `Q` or `P^T`
+* @param {NonNegativeInteger} K - number of elementary reflectors
+* @param {Float64Array} A - input/output matrix
+* @param {integer} LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
+* @param {Float64Array} TAU - scalar factors of elementary reflectors
+* @param {Float64Array} WORK - workspace array
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @throws {TypeError} first argument must be a valid order
+* @throws {TypeError} second argument must be either `'Q'` or `'P'`
+* @throws {RangeError} third argument must be a non-negative integer
+* @throws {RangeError} fourth argument must be a non-negative integer satisfying the constraints for the given `vect` argument
+* @throws {RangeError} fifth argument must be a non-negative integer
+* @throws {RangeError} seventh argument must be a valid `LDA` value
+* @throws {RangeError} tenth argument must be a valid `LWORK` value
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 0.2, -0.1, 0.3, 0, 1, 0.4, -0.2, 0, 0, 1, 0.5 ] );
+* var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* var info = dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
+* // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+* // info => 0
+* // WORK[ 0 ] => 64
+*/
+function dorgbr( order, vect, M, N, K, A, LDA, TAU, WORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point
+ var wantq;
+ var sa1;
+ var sa2;
+
+ if ( !isLayout( order ) ) {
+ throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
+ }
+ if ( vect !== 'Q' && vect !== 'P' ) {
+ throw new TypeError( format( 'invalid argument. Second argument must be either `\'Q\'` or `\'P\'`. Value: `%s`.', vect ) );
+ }
+ wantq = ( vect === 'Q' );
+ if ( M < 0 ) {
+ throw new RangeError( format( 'invalid argument. Third argument must be a nonnegative integer. Value: `%d`.', M ) );
+ }
+ if ( wantq ) {
+ if ( N < min( M, K ) || N > M ) {
+ throw new RangeError( format( 'invalid argument. Fourth argument must be greater than or equal to `min(M,K)` and smaller than or equal to `M`. Value: `%d`.', N ) );
+ }
+ } else if ( N < M || M < min( N, K ) ) {
+ throw new RangeError( format( 'invalid argument. Fourth argument must be greater than or equal to `M`, and `M` must be greater than or equal to `min(N,K)`. Value: `%d`.', N ) );
+ }
+ if ( K < 0 ) {
+ throw new RangeError( format( 'invalid argument. Fifth argument must be a nonnegative integer. Value: `%d`.', K ) );
+ }
+ if ( order === 'column-major' ) {
+ if ( LDA < max( 1, M ) ) {
+ throw new RangeError( format( 'invalid argument. Seventh argument must be greater than or equal to `max(1,M)`. Value: `%d`.', LDA ) );
+ }
+ sa1 = 1;
+ sa2 = LDA;
+ } else { // row-major
+ if ( LDA < max( 1, N ) ) {
+ throw new RangeError( format( 'invalid argument. Seventh argument must be greater than or equal to `max(1,N)`. Value: `%d`.', LDA ) );
+ }
+ sa1 = LDA;
+ sa2 = 1;
+ }
+ if ( LWORK < max( 1, min( M, N ) ) && LWORK !== -1 ) {
+ throw new RangeError( format( 'invalid argument. Tenth argument must be greater than or equal to `max(1,min(M,N))` except when equal to -1. Value: `%d`.', LWORK ) );
+ }
+ return base( vect, M, N, K, A, sa1, sa2, 0, TAU, 1, 0, WORK, 1, 0, LWORK );
+}
+
+
+// EXPORTS //
+
+module.exports = dorgbr;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgl2.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgl2.js
new file mode 100644
index 000000000000..46d8bcedef9c
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgl2.js
@@ -0,0 +1,143 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-params */
+
+'use strict';
+
+// MODULES //
+
+var dlarf1f = require( '@stdlib/lapack/base/dlarf1f' ).ndarray;
+var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
+var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
+
+
+// MAIN //
+
+/**
+* Generate an M-by-N real orthogonal matrix `Q` from the elementary reflectors returned by `DGELQF`/`DGELQ2` (LQ factorization, unblocked).
+*
+* ## Notes
+*
+* - On entry, the i-th row of A must contain the vector which defines the elementary reflector H(i), for i = 1, 2, ..., K, as returned by `DGELQF` in the first K rows of its array argument A.
+*
+* - Q is defined as the product of K elementary reflectors:
+*
+* - Q = H(K) ... H(2) H(1), where each H(i) has the form `H(i) = I - tau(i)*v*v^T`, and v is stored as row i of the input matrix A.
+*
+* - On exit, A contains the M-by-N matrix Q.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of Q (0 <= M <= N)
+* @param {NonNegativeInteger} N - number of columns of Q (N >= 0)
+* @param {NonNegativeInteger} K - number of elementary reflectors (0 <= K <= M)
+* @param {Float64Array} A - input/output matrix
+* @param {integer} strideA1 - stride of the first dimension of A
+* @param {integer} strideA2 - stride of the second dimension of A
+* @param {NonNegativeInteger} offsetA - starting index for A
+* @param {Float64Array} TAU - scalar factors of reflectors (length K)
+* @param {integer} strideTAU - stride for TAU
+* @param {NonNegativeInteger} offsetTAU - starting index for TAU
+* @param {Float64Array} WORK - workspace (length >= M)
+* @param {integer} strideWORK - stride for WORK
+* @param {NonNegativeInteger} offsetWORK - starting index for WORK
+* @returns {integer} status code (0 = success)
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( 12 );
+* var TAU = new Float64Array( 2 );
+* var WORK = new Float64Array( 3 );
+*
+* var info = dorgl2( 3, 4, 2, A, 4, 1, 0, TAU, 1, 0, WORK, 1, 0 );
+* // returns 0
+* // A => [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0 ]
+* // WORK => [ 0, 0, 0 ]
+*/
+function dorgl2( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK ) {
+ var idx0;
+ var idx1;
+ var idx2;
+ var idx3;
+ var i;
+ var j;
+ var l;
+
+ // Initialize rows K+1..M to rows of the unit matrix
+ if ( K < M ) {
+ if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
+ idx1 = offsetA + ( strideA1*K );
+ for ( l = K; l < M; l++ ) {
+ idx2 = idx1;
+ for ( j = 0; j < N; j++ ) {
+ A[ idx2 ] = 0;
+ idx2 += strideA2;
+ if ( j >= K && j < M ) {
+ A[ offsetA + ( j*( strideA1 + strideA2 ) ) ] = 1;
+ }
+ }
+ idx1 += strideA1;
+ }
+ } else { // column-major
+ idx1 = offsetA;
+ for ( j = 0; j < N; j++ ) {
+ idx2 = idx1 + ( K*strideA1 );
+ for ( l = K; l < M; l++ ) {
+ A[ idx2 ] = 0;
+ idx2 += strideA1;
+ }
+ if ( j >= K && j < M ) {
+ A[ idx1 + ( j*strideA1 ) ] = 1;
+ }
+ idx1 += strideA2;
+ }
+ }
+ }
+
+ idx0 = offsetTAU + ( strideTAU*( K - 1 ) ); // TAU( i )
+ idx1 = offsetA + ( ( K - 1 )*( strideA1 + strideA2 ) ); // A( i,i )
+ idx2 = offsetA + ( ( K - 1 )*strideA1 ); // A( i,0 )
+ for ( i = K - 1; i >= 0; i-- ) {
+ // Apply H(i) to A(i:m,i:n) from the right
+ if ( i < N - 1 ) {
+ if ( i < M - 1 ) {
+ dlarf1f( 'right', M - i - 1, N - i, A, strideA2, idx1, TAU[ idx0 ], A, strideA1, strideA2, idx1 + strideA1, WORK, strideWORK, offsetWORK );
+ }
+ dscal( N - i - 1, -TAU[ idx0 ], A, strideA2, idx1 + strideA2 );
+ }
+
+ A[ idx1 ] = 1 - TAU[ idx0 ];
+
+ // Set A(i,1:i-1) to zero
+ idx3 = idx2; // A( i,l )
+ for ( l = 0; l < i; l++ ) {
+ A[ idx3 ] = 0;
+ idx3 += strideA2;
+ }
+ idx0 -= strideTAU;
+ idx1 -= strideA1 + strideA2;
+ idx2 -= strideA1;
+ }
+ return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dorgl2;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorglq.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorglq.js
new file mode 100644
index 000000000000..019d16c13762
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorglq.js
@@ -0,0 +1,176 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-params */
+
+'use strict';
+
+// MODULES //
+
+var max = require( '@stdlib/math/base/special/max' );
+var min = require( '@stdlib/math/base/special/min' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var dorgl2 = require( './dorgl2.js' );
+var dlarft = require( './dlarft.js' );
+var dlarfb = require( './dlarfb.js' );
+
+
+// MAIN //
+
+/**
+* Generates an `M-by-N` real orthogonal matrix `Q` from the elementary reflectors returned by `DGELQF`.
+*
+* ## Notes
+*
+* - On entry, the i-th row must contain the vector which defines the elementary reflector `H(i)`, for `i = 1,2,...,K`, as returned by `DGELQF` in the first `K` rows of its array argument `A`.
+* - On exit, the `M-by-N` orthogonal matrix `Q`.
+* - `WORK` must have length, `LWORK >= max(1,M)`. For optimum performance `LWORK >= M*NB`.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of `Q`
+* @param {NonNegativeInteger} N - number of columns of `Q`
+* @param {NonNegativeInteger} K - number of elementary reflectors
+* @param {Float64Array} A - input/output matrix
+* @param {integer} strideA1 - stride length of the first dimension of `A`
+* @param {integer} strideA2 - stride length of the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - starting index for `A`
+* @param {Float64Array} TAU - scalar factors of reflectors
+* @param {integer} strideTAU - stride length of `TAU`
+* @param {NonNegativeInteger} offsetTAU - starting index for `TAU`
+* @param {Float64Array} WORK - workspace array
+* @param {integer} strideWORK - stride length of `WORK`
+* @param {NonNegativeInteger} offsetWORK - starting index for `WORK`
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 0, 0, -1, -2, 0 ] );
+* var TAU = new Float64Array( [ 1, 1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* var info = dorglq( 2, 3, 2, A, 1, 2, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+* // A => [ 0, 0, 0, 0, 2, 0 ]
+* // info => 0
+* // WORK[ 0 ] => 2
+*/
+function dorglq( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) {
+ var ldwork;
+ var lquery;
+ var lwkopt;
+ var nbmin;
+ var iws;
+ var nb;
+ var nx;
+ var kk;
+ var ki;
+ var ib;
+ var i;
+ var j;
+ var l;
+
+ nb = 32; // Optimal block size derived from the Fortran LAPACK call `ilaenv( 1, 'DORGLQ', ' ', m, n, k, -1 )`
+ lwkopt = max( 1, M ) * nb;
+ WORK[ offsetWORK ] = lwkopt;
+ lquery = ( LWORK === -1 );
+
+ if ( lquery ) {
+ return 0;
+ }
+
+ // Quick return if possible
+ if ( M === 0 ) {
+ WORK[ offsetWORK ] = 1;
+ return 0;
+ }
+
+ nbmin = 2;
+ nx = 0;
+ iws = M;
+
+ if ( ( nb > 1 ) && ( nb < K ) ) {
+ // Determine when to cross over from blocked to unblocked code.
+ nx = 128; // The crossover point derived from the Fortran LAPACK call `ilaenv( 3, 'DORGLQ', ' ', m, n, k, -1 )`
+
+ if ( nx < K ) {
+ // Determine if workspace is large enough for blocked code.
+ ldwork = M;
+ iws = ldwork * nb;
+ if ( LWORK < iws ) {
+ // Not enough workspace to use optimal NB: reduce NB and determine the minimum value of NB.
+ nb = floor( LWORK / ldwork );
+ nbmin = 2; // The minimum block size derived from the Fortran LAPACK call `ilaenv( 2, 'DORGLQ', ' ', m, n, k, -1 )`
+ }
+ }
+ }
+
+ if ( ( nb >= nbmin ) && ( nb < K ) && ( nx < K ) ) {
+ // Use blocked code after the last block.
+ // The first kk rows are handled by the block method.
+ ki = floor( ( K - nx - 1 ) / nb ) * nb;
+ kk = min( K, ki + nb );
+
+ // Set A(kk+1:m,1:kk) to zero.
+ for ( j = 0; j < kk; j++ ) {
+ for ( i = kk; i < M; i++ ) {
+ A[ offsetA + ( i * strideA1 ) + ( j * strideA2 ) ] = 0;
+ }
+ }
+ } else {
+ kk = 0;
+ }
+
+ // Use unblocked code for the last or only block.
+ if ( kk < M ) {
+ dorgl2( M - kk, N - kk, K - kk, A, strideA1, strideA2, offsetA + ( kk * ( strideA1 + strideA2 ) ), TAU, strideTAU, offsetTAU + ( kk * strideTAU ), WORK, strideWORK, offsetWORK );
+ }
+
+ if ( kk > 0 ) {
+ // Use blocked code
+ for ( i = ki; i >= 0; i -= nb ) {
+ ib = min( nb, K - i );
+
+ if ( i + ib < M ) {
+ // Form the triangular factor of the block reflector, H = H(i) H(i+1) . . . H(i+ib-1)
+ dlarft( 'forward', 'rows', N - i, ib, A, strideA1, strideA2, offsetA + ( i * ( strideA1 + strideA2 ) ), TAU, strideTAU, offsetTAU + ( i * strideTAU ), WORK, 1, ldwork, offsetWORK );
+
+ // Apply H**T to A(i+ib:m,i:n) from the right
+ dlarfb( 'right', 'transpose', 'forward', 'rows', M - i - ib, N - i, ib, A, strideA1, strideA2, offsetA + ( i * ( strideA1 + strideA2 ) ), WORK, 1, ldwork, offsetWORK, A, strideA1, strideA2, offsetA + ( ( i + ib ) * strideA1 ) + ( i * strideA2 ), WORK, 1, ldwork, offsetWORK + ( ib * strideWORK ) );
+ }
+
+ // Apply H**T to columns i:n of current block
+ dorgl2( ib, N - i, ib, A, strideA1, strideA2, offsetA + ( i * ( strideA1 + strideA2 ) ), TAU, strideTAU, offsetTAU + ( i * strideTAU ), WORK, strideWORK, offsetWORK );
+
+ // Set columns 1:i-1 of current block to zero
+ for ( j = 0; j < i; j++ ) {
+ for ( l = i; l < i + ib; l++ ) {
+ A[ offsetA + ( l * strideA1 ) + ( j * strideA2 ) ] = 0.0;
+ }
+ }
+ }
+ }
+
+ WORK[ offsetWORK ] = iws;
+ return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dorglq;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgqr.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgqr.js
new file mode 100644
index 000000000000..82c1830af589
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dorgqr.js
@@ -0,0 +1,176 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+/* eslint-disable max-len, max-params */
+
+// MODULES //
+
+var max = require( '@stdlib/math/base/special/max' );
+var min = require( '@stdlib/math/base/special/min' );
+var dorg2r = require( './dorg2r.js' );
+var dlarfb = require( './dlarfb.js' );
+var dlarft = require( './dlarft.js' );
+
+
+// MAIN //
+
+/**
+* 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`.
+*
+* ## Notes
+*
+* - On entry, the i-th column of A must contain the reflector vector for `H(i)`, as returned by DGEQRF.
+* - On exit, A contains the M-by-N orthogonal matrix Q.
+* - For optimum performance `LWORK >= N*NB`, where `NB` is the optimal blocksize.
+* - If `LWORK = -1`, then 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.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of `Q`
+* @param {NonNegativeInteger} N - number of columns of `Q`
+* @param {NonNegativeInteger} K - number of elementary reflectors whose product defines the matrix `Q`
+* @param {Float64Array} A - input/output matrix
+* @param {integer} strideA1 - stride length for the first dimension of `A`
+* @param {integer} strideA2 - stride length for the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - starting index of `A`
+* @param {Float64Array} TAU - scalar factors of reflectors
+* @param {integer} strideTAU - stride length for `TAU`
+* @param {NonNegativeInteger} offsetTAU - starting index of `TAU`
+* @param {Float64Array} WORK - workspace array
+* @param {integer} strideWORK - stride length for `WORK`
+* @param {NonNegativeInteger} offsetWORK - starting index of `WORK`
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+* var TAU = new Float64Array( [ 2, 2 ] );
+* var WORK = new Float64Array( 10 );
+*
+* var info = dorgqr( 3, 2, 2, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+* // A => [ -1, 0, 0, 0, -1, 0 ]
+* // info => 0
+* // WORK[ 0 ] => 2
+*/
+function dorgqr( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) {
+ var ldwork;
+ var lwkopt;
+ var lquery;
+ var nbmin;
+ var iws;
+ var nb;
+ var nx;
+ var kk;
+ var ki;
+ var ib;
+ var i;
+ var j;
+ var l;
+
+ nb = 32; // The optimal blocksize derived from the Fortran LAPACK call `ilaenv( 1, 'DORGQR', ' ', m, n, k, -1 )`
+ lwkopt = max( 1, N ) * nb;
+ WORK[ offsetWORK ] = lwkopt;
+ lquery = ( LWORK === -1 );
+
+ if ( lquery ) {
+ return 0;
+ }
+
+ // Quick return if possible
+ if ( N === 0 ) {
+ WORK[ offsetWORK ] = 1;
+ return 0;
+ }
+
+ nbmin = 2;
+ nx = 0;
+ iws = N;
+
+ if ( nb > 1 && nb < K ) {
+ // Determine when to cross over from blocked to unblocked code.
+ nx = 128; // The cross-over point derived from the Fortran LAPACK call `ilaenv( 3, 'DORGQR', ' ', m, n, k, -1 )`
+
+ if ( nx < K ) {
+ // Determine if workspace is large enough for blocked code
+ ldwork = N;
+ iws = ldwork * nb;
+ if ( LWORK < iws ) {
+ // Not enough workspace to use optimal NB: reduce NB and determine the minimum value of NB.
+ nb = LWORK / ldwork;
+ nbmin = 2; // The minimum block size derived from the Fortran LAPACK call `ilaenv( 2, 'DORGQR', ' ', m, n, k, -1 )`
+ }
+ }
+ }
+
+ if ( nb >= nbmin && nb < K && nx < K ) {
+ // Use blocked code after the last block. The first kk columns are handled by the block method.
+ ki = ( ( K - nx - 1 ) / nb ) * nb;
+ kk = min( K, ki + nb );
+
+ // Set A(1:kk,kk+1:n) to zero
+ for ( j = kk; j < N; j++ ) {
+ for ( i = 0; i < kk; i++ ) {
+ A[ offsetA + ( i * strideA1 ) + ( j * strideA2 ) ] = 0;
+ }
+ }
+ } else {
+ kk = 0;
+ }
+
+ // Use unblocked code for the last or only block
+ if ( kk < N ) {
+ dorg2r( M - kk, N - kk, K - kk, A, strideA1, strideA2, offsetA + ( kk * strideA1 ) + ( kk * strideA2 ), TAU, strideTAU, offsetTAU + ( kk * strideTAU ), WORK, strideWORK, offsetWORK );
+ }
+
+ if ( kk > 0 ) {
+ // Use blocked code
+ for ( i = ki; i >= 0; i -= nb ) {
+ ib = min( nb, K - i );
+
+ if ( i + ib < N ) {
+ // Form the triangular factor T of the block reflector H = H(i) H(i+1) . . . H(i+ib-1)
+ dlarft( 'forward', 'columns', M - i, ib, A, strideA1, strideA2, offsetA + ( i * ( strideA1 + strideA2 ) ), TAU, strideTAU, offsetTAU + ( i * strideTAU ), WORK, 1, ldwork, offsetWORK );
+
+ // Apply H to A(i:M-1, i+ib:N-1) from the left
+ dlarfb( 'left', 'no-transpose', 'forward', 'columns', M - i, N - i - ib, ib, A, strideA1, strideA2, offsetA + ( i * ( strideA1 + strideA2 ) ), WORK, 1, ldwork, offsetWORK, A, strideA1, strideA2, offsetA + ( i * strideA1 ) + ( ( i + ib ) * strideA2 ), WORK, 1, ldwork, offsetWORK + ( ib * strideWORK ) );
+ }
+
+ // Apply H to rows i:m of current block
+ dorg2r( M - i, ib, ib, A, strideA1, strideA2, offsetA + ( i * ( strideA1 + strideA2 ) ), TAU, strideTAU, offsetTAU + ( i * strideTAU ), WORK, 1, offsetWORK );
+
+ // Set rows 1:i-1 of current block to zero
+ for ( j = i; j < i + ib; j++ ) {
+ for ( l = 0; l < i; l++ ) {
+ A[ offsetA + ( l * strideA1 ) + ( j * strideA2 ) ] = 0;
+ }
+ }
+ }
+ }
+
+ WORK[ offsetWORK ] = iws;
+ return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dorgqr;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dtrmm.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dtrmm.js
new file mode 100644
index 000000000000..f360237c6ef3
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/dtrmm.js
@@ -0,0 +1,362 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-statements, max-lines-per-function */
+
+'use strict';
+
+// MODULES //
+
+var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
+
+
+// FUNCTIONS //
+
+/**
+* Fills a matrix with zeros.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows
+* @param {NonNegativeInteger} N - number of columns
+* @param {Float64Array} X - matrix to fill
+* @param {integer} strideX1 - stride of the first dimension of `X`
+* @param {integer} strideX2 - stride of the second dimension of `X`
+* @param {NonNegativeInteger} offsetX - starting index for `X`
+* @returns {Float64Array} input matrix
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+*
+* zeros( 2, 3, X, 3, 1, 0 );
+* // X => [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+*
+* zeros( 2, 3, X, 1, 2, 0 );
+* // X => [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
+*/
+function zeros( M, N, X, strideX1, strideX2, offsetX ) { // TODO: consider moving to a separate package
+ var dx0;
+ var dx1;
+ var S0;
+ var S1;
+ var i0;
+ var i1;
+ var ix;
+
+ if ( isRowMajor( [ strideX1, strideX2 ] ) ) {
+ // For row-major matrices, the last dimension has the fastest changing index...
+ S0 = N;
+ S1 = M;
+ dx0 = strideX2; // offset increment for innermost loop
+ dx1 = strideX1 - ( S0*strideX2 ); // offset increment for outermost loop
+ } else { // column-major
+ // For column-major matrices, the first dimension has the fastest changing index...
+ S0 = M;
+ S1 = N;
+ dx0 = strideX1; // offset increment for innermost loop
+ dx1 = strideX2 - ( S0*strideX1 ); // offset increment for outermost loop
+ }
+ ix = offsetX;
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ X[ ix ] = 0.0;
+ ix += dx0;
+ }
+ ix += dx1;
+ }
+ return X;
+}
+
+
+// MAIN //
+
+/**
+* Performs one of the matrix-matrix operations `B = α * op(A) * B` or `B = α * B * op(A)` where `α` is a scalar, `B` is an `M` by `N` matrix, `A` is a unit, or non-unit, upper or lower triangular matrix and `op( A )` is one of `op( A ) = A` or `op( A ) = A^T`.
+*
+* @private
+* @param {string} side - specifies whether `op( A )` appears on the left or right side of `B`
+* @param {string} uplo - specifies whether the upper or lower triangular part of the matrix `A` should be referenced
+* @param {string} transa - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
+* @param {string} diag - specifies whether or not `A` is unit triangular
+* @param {NonNegativeInteger} M - number of rows in `B`
+* @param {NonNegativeInteger} N - number of columns in `B`
+* @param {number} alpha - scalar constant
+* @param {Float64Array} A - first input matrix
+* @param {integer} strideA1 - stride of the first dimension of `A`
+* @param {integer} strideA2 - stride of the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - starting index for `A`
+* @param {Float64Array} B - second input matrix
+* @param {integer} strideB1 - stride of the first dimension of `B`
+* @param {integer} strideB2 - stride of the second dimension of `B`
+* @param {NonNegativeInteger} offsetB - starting index for `B`
+* @returns {Float64Array} `B`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 0.0, 0.0, 2.0, 3.0, 0.0, 4.0, 5.0, 6.0 ] );
+* var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
+*
+* dtrmm( 'left', 'lower', 'no-transpose', 'unit', 3, 3, 1.0, A, 3, 1, 0, B, 3, 1, 0 );
+* // B => [ 1.0, 2.0, 3.0, 6.0, 9.0, 12.0, 31.0, 41.0, 51.0 ]
+*/
+function dtrmm( side, uplo, transa, diag, M, N, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB ) { // eslint-disable-line max-params
+ var nonunit;
+ var isrma;
+ var tmp;
+ var oa2;
+ var ob2;
+ var sa0;
+ var sa1;
+ var sb0;
+ var sb1;
+ var oa;
+ var ob;
+ var ia;
+ var ib;
+ var i;
+ var j;
+ var k;
+ var t;
+
+ // Note on variable naming convention: sa#, sb# where # corresponds to the loop number, with `0` being the innermost loop...
+
+ nonunit = ( diag === 'non-unit' );
+
+ if ( M === 0 || N === 0 ) {
+ return B;
+ }
+
+ // Handle alpha = 0 before any layout conversion (zeroing uses original layout)...
+ if ( alpha === 0.0 ) {
+ if ( isRowMajor( [ strideB1, strideB2 ] ) ) {
+ sb0 = strideB2;
+ sb1 = strideB1;
+ } else {
+ sb0 = strideB1;
+ sb1 = strideB2;
+ }
+ zeros( M, N, B, sb0, sb1, offsetB );
+ return B;
+ }
+
+ // Detect layout and convert column-major to an equivalent row-major problem...
+ isrma = isRowMajor( [ strideA1, strideA2 ] );
+ if ( !isrma ) {
+ // Swap strides: effectively view A and B as transposed (row-major)...
+ t = strideA1;
+ strideA1 = strideA2;
+ strideA2 = t;
+
+ t = strideB1;
+ strideB1 = strideB2;
+ strideB2 = t;
+
+ side = ( side === 'left' ) ? 'right' : 'left';
+ uplo = ( uplo === 'upper' ) ? 'lower' : 'upper';
+ t = M;
+ M = N;
+ N = t;
+ }
+
+ // For row-major matrices, the last dimension has the fastest changing index...
+ sa0 = strideA2; // stride for innermost loop
+ sa1 = strideA1; // stride for outermost loop
+ sb0 = strideB2; // stride for innermost loop
+ sb1 = strideB1; // stride for outermost loop
+
+ if ( side === 'left' && uplo === 'upper' && transa === 'no-transpose' ) {
+ for ( j = 0; j < N; j++ ) {
+ ib = offsetB + ( j*sb0 );
+ for ( k = 0; k < M; k++ ) {
+ ob2 = ib + ( k * sb1 );
+ tmp = alpha * B[ ob2 ];
+ ia = offsetA + ( k*sa0 );
+ for ( i = 0; i < k; i++ ) {
+ B[ ib + ( i*sb1 ) ] += ( tmp * A[ ia + ( i*sa1 ) ] );
+ }
+ if ( nonunit ) {
+ tmp *= A[ ia + ( k*sa1 ) ];
+ }
+ B[ ob2 ] = tmp;
+ }
+ }
+ return B;
+ }
+ if ( side === 'left' && uplo === 'lower' && transa === 'no-transpose' ) {
+ for ( j = 0; j < N; j++ ) {
+ ib = offsetB + ( j*sb0 );
+ for ( k = M - 1; k >= 0; k-- ) {
+ ob2 = ib + ( k*sb1 );
+ tmp = alpha * B[ ob2 ];
+ ia = offsetA + ( k*sa0 );
+ for ( i = k + 1; i < M; i++ ) {
+ oa2 = ia + ( i*sa1 );
+ B[ ib + ( i*sb1 ) ] += ( tmp * A[ oa2 ] );
+ }
+ if ( nonunit ) {
+ tmp *= A[ ia + ( k*sa1 ) ];
+ }
+ B[ ob2 ] = tmp;
+ }
+ }
+ return B;
+ }
+ if ( side === 'left' && uplo === 'upper' && transa !== 'no-transpose' ) {
+ for ( j = 0; j < N; j++ ) {
+ ib = offsetB + ( j*sb0 );
+ for ( i = M - 1; i >= 0; i-- ) {
+ ob2 = ib + ( i*sb1 );
+ tmp = 0.0;
+ ia = offsetA + ( i*sa0 );
+ if ( nonunit ) {
+ tmp += ( A[ ia + ( i*sa1 ) ] * B[ ob2 ] );
+ } else {
+ tmp += B[ ob2 ];
+ }
+ for ( k = 0; k < i; k++ ) {
+ oa2 = ia + ( k*sa1 );
+ tmp += A[ oa2 ] * B[ ib + ( k*sb1 ) ];
+ }
+ B[ ob2 ] = alpha * tmp;
+ }
+ }
+ return B;
+ }
+ if ( side === 'left' && uplo === 'lower' && transa !== 'no-transpose' ) {
+ for ( j = 0; j < N; j++ ) {
+ ib = offsetB + ( j * sb0 );
+ for ( i = 0; i < M; i++ ) {
+ ia = offsetA + ( i * sa0 );
+ ob2 = ib + ( i * sb1 );
+ tmp = 0.0;
+ for ( k = i + 1; k < M; k++ ) {
+ tmp += A[ ia + ( k * sa1 ) ] * B[ ib + ( k * sb1 ) ];
+ }
+ if ( nonunit ) {
+ tmp += ( A[ ia + ( i * sa1 ) ] * B[ ob2 ] );
+ } else {
+ tmp += B[ ob2 ];
+ }
+ B[ ob2 ] = alpha * tmp;
+ }
+ }
+ return B;
+ }
+ if ( side === 'right' && uplo === 'upper' && transa === 'no-transpose' ) {
+ for ( j = N - 1; j >= 0; j-- ) {
+ ia = offsetA + ( j*sa0 );
+ ib = offsetB + ( j*sb0 );
+ for ( i = 0; i < M; i++ ) {
+ ob = ib + ( i*sb1 );
+ B[ ob ] *= alpha;
+ if ( nonunit ) {
+ oa2 = ia + ( j*sa1 );
+ tmp = A[ oa2 ];
+ B[ ob ] *= tmp;
+ }
+ for ( k = 0; k < j; k++ ) {
+ oa2 = ia + ( k*sa1 );
+ ob2 = offsetB + ( k*sb0 );
+ if ( A[ oa2 ] !== 0.0 ) {
+ tmp = alpha * A[ oa2 ];
+ B[ ob ] += ( tmp * B[ ob2 + ( i*sb1 ) ] );
+ }
+ }
+ }
+ }
+ return B;
+ }
+ if ( side === 'right' && uplo === 'lower' && transa === 'no-transpose' ) {
+ for ( j = 0; j < N; j++ ) {
+ ia = offsetA + ( j*sa0 );
+ for ( i = 0; i < M; i++ ) {
+ ib = offsetB + ( i*sb1 );
+ ob = ib + ( j*sb0 );
+ B[ ob ] *= alpha;
+ if ( nonunit ) {
+ oa = ia + ( j*sa1 );
+ B[ ob ] *= A[ oa ];
+ }
+ for ( k = j + 1; k < N; k++ ) {
+ oa2 = ia + ( k*sa1 );
+ ob2 = ib + ( k*sb0 );
+ if ( A[ oa2 ] !== 0.0 ) {
+ tmp = alpha * A[ oa2 ];
+ B[ ob ] += ( tmp * B[ ob2 ] );
+ }
+ }
+ }
+ }
+ return B;
+ }
+ if ( side === 'right' && uplo === 'upper' && transa !== 'no-transpose' ) {
+ for ( j = 0; j < N; j++ ) {
+ ia = offsetA + ( j*sa1 );
+ for ( i = 0; i < M; i++ ) {
+ ib = offsetB + ( i*sb1 );
+ oa = ia + ( j*sa0 );
+ ob = ib + ( j*sb0 );
+ if ( nonunit ) {
+ tmp = B[ ob ] * A[ oa ];
+ } else {
+ tmp = B[ ob ];
+ }
+ for ( k = j + 1; k < N; k++ ) {
+ oa2 = ia + ( k*sa0 );
+ ob2 = ib + ( k*sb0 );
+ tmp += ( B[ ob2 ] * A[ oa2 ] );
+ }
+ B[ ob ] = alpha * tmp;
+ }
+ }
+ return B;
+ }
+ // side === 'right', uplo === 'lower', transa !== 'no-transpose'
+ for ( i = 0; i < M; i++ ) {
+ ib = offsetB + ( i*sb1 );
+ for ( j = N - 1; j >= 0; j-- ) {
+ ia = offsetA + ( j*sa1 );
+ oa = ia + ( j*sa0 );
+ ob = ib + ( j*sb0 );
+ if ( nonunit ) {
+ tmp = B[ ob ] * A[ oa ];
+ } else {
+ tmp = B[ ob ];
+ }
+ for ( k = 0; k < j; k++ ) {
+ oa2 = ia + ( k*sa0 );
+ ob2 = ib + ( k*sb0 );
+ tmp += ( B[ ob2 ] * A[ oa2 ] );
+ }
+ B[ ob ] = alpha * tmp;
+ }
+ }
+ return B;
+}
+
+
+// EXPORTS //
+
+module.exports = dtrmm;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/index.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/index.js
new file mode 100644
index 000000000000..1c936e72bd7f
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/index.js
@@ -0,0 +1,63 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+/**
+* LAPACK routine to generate one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`.
+*
+* @module @stdlib/lapack/base/dorgbr
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var dorgbr = require( '@stdlib/lapack/base/dorgbr' );
+*
+* var A = new Float64Array( [ 1, 0.2, -0.1, 0.3, 0, 1, 0.4, -0.2, 0, 0, 1, 0.5 ] );
+* var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* var info = dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
+* // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+* // info => 0
+* // WORK[ 0 ] => 96
+*/
+
+// MODULES //
+
+var join = require( 'path' ).join;
+var tryRequire = require( '@stdlib/utils/try-require' );
+var isError = require( '@stdlib/assert/is-error' );
+var main = require( './main.js' );
+
+
+// MAIN //
+
+var dorgbr;
+var tmp = tryRequire( join( __dirname, './native.js' ) );
+if ( isError( tmp ) ) {
+ dorgbr = main;
+} else {
+ dorgbr = tmp;
+}
+
+
+// EXPORTS //
+
+module.exports = dorgbr;
+
+// exports: { "ndarray": "dorgbr.ndarray" }
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/init_unit_columns.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/init_unit_columns.js
new file mode 100644
index 000000000000..a7aa37422545
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/init_unit_columns.js
@@ -0,0 +1,95 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
+
+
+// MAIN //
+
+/**
+* Initializes columns K+1:N of a matrix to columns of the unit matrix.
+*
+* @private
+* @param {PositiveInteger} M - number of rows in matrix `A`
+* @param {PositiveInteger} N - number of columns in matrix `A`
+* @param {NonNegativeInteger} K - starting column index for initialization
+* @param {Float64Array} A - input matrix
+* @param {integer} strideA1 - stride of the first dimension of `A`
+* @param {integer} strideA2 - stride of the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - index offset for `A`
+* @returns {Float64Array} matrix `A` with columns K+1:N initialized as unit matrix columns
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
+* initUnitColumns( 3, 3, 1, A, 1, 3, 0 );
+* // A => [ 1.0, 2.0, 3.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0 ]
+*/
+function initUnitColumns( M, N, K, A, strideA1, strideA2, offsetA ) {
+ var ia1;
+ var ia2;
+ var del;
+ var da;
+ var i;
+ var j;
+
+ // Initialize columns k+1:n to columns of the unit matrix
+ if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
+ ia2 = offsetA + (K*strideA2);
+ da = strideA1 - ((N-K) * strideA2);
+
+ for ( i = 0; i < M; i++ ) {
+ for ( j = K; j < N; j++ ) {
+ if ( i === j ) {
+ A[ ia2 ] = 1.0;
+ } else {
+ A[ ia2 ] = 0.0;
+ }
+ ia2 += strideA2;
+ }
+ ia2 += da;
+ }
+ } else {
+ ia1 = offsetA + (K*strideA1) + (K*strideA2);
+ ia2 = offsetA + (K*strideA2);
+ da = strideA2 - (M * strideA1);
+ del = strideA1 + strideA2;
+
+ for ( i = K; i < N; i++ ) {
+ for ( j = 0; j < M; j++ ) {
+ A[ ia2 ] = 0.0;
+ ia2 += strideA1;
+ }
+ A[ ia1 ] = 1.0;
+ ia2 += da;
+ ia1 += del;
+ }
+ }
+
+ return A;
+}
+
+
+// EXPORTS //
+
+module.exports = initUnitColumns;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_backward_columns.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_backward_columns.js
new file mode 100644
index 000000000000..5a71b0c9aec0
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_backward_columns.js
@@ -0,0 +1,162 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the left, with backward direction and column storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = leftBackwardColumns( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -557890.0, -592880.0, -627870.0, -596341.0, -632662.0, -668983.0, -7412.0, -7864.0, -8316.0 ]
+*/
+function leftBackwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var transt;
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var i;
+ var j;
+ var o;
+
+ if ( trans === 'no-transpose' ) {
+ transt = 'transpose';
+ } else {
+ transt = 'no-transpose';
+ }
+
+ /* Let V = ( V1 )
+ * ( V2 ) (last K rows)
+ * Where V2 is unit upper triangular.
+ */
+
+ /* Form H * C or H^T * C where C = ( C1 )
+ * ( C2 )
+ * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
+ * W := C2**T
+ */
+ ic = offsetC + ( (M-K) * strideC1 );
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ iw = offsetWork + ( j * strideWork2 );
+ dcopy( N, C, strideC2, ic, work, strideWork1, iw );
+ ic += strideC1;
+ iw += strideWork2;
+ }
+ // W := W * V2
+ iv = offsetV + ( (M-K) * strideV1 );
+ dtrmm( 'right', 'upper', 'no-transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+ if ( M > K ) {
+ // W := W + C1**T * V1
+ dgemm( 'transpose', 'no-transpose', N, K, M-K, 1.0, C, strideC1, strideC2, offsetC, V, strideV1, strideV2, offsetV, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T**T or W * T
+ dtrmm( 'right', 'lower', transt, 'non-unit', N, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - V * W**T
+ if ( M > K ) {
+ // C1 := C1 - V1 * W**T
+ dgemm( 'no-transpose', 'transpose', M-K, N, K, -1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork, 1.0, C, strideC1, strideC2, offsetC );
+ }
+ // W := W * V2**T
+ iv = offsetV + ( (M-K) * strideV1 );
+ dtrmm( 'right', 'upper', 'transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+
+ // C2 := C2 - W**T
+ o = loopOrder( [ K, N ], [ strideC2, strideC1 ], [ strideWork1, strideWork2 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ ia = offsetC + ( (M-K) * strideC1 );
+ ib = offsetWork;
+
+ for ( j = 0; j < S1; j++ ) {
+ for ( i = 0; i < S0; i++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = leftBackwardColumns;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_backward_rows.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_backward_rows.js
new file mode 100644
index 000000000000..89bedab3ecee
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_backward_rows.js
@@ -0,0 +1,165 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the left, with backward direction and row storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = leftBackwardRows( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -155530.0, -164560.0, -173590.0, -292241.0, -308662.0, -325083.0, -4832.0, -5104.0, -5376.0 ]
+*/
+function leftBackwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var transt;
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ if ( trans === 'no-transpose' ) {
+ transt = 'transpose';
+ } else {
+ transt = 'no-transpose';
+ }
+
+ /* Let V = ( V1 V2 ) (V2: last K columns)
+ * Where V2 is unit lower triangular.
+ */
+
+ /* Form H * C or H^T * C where C = ( C1 )
+ * ( C2 )
+ * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
+ * W := C2**T
+ */
+ ic = offsetC;
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( N, C, strideC2, ic, work, strideWork1, iw );
+ ic += strideC1;
+ iw += strideWork2;
+ }
+ // W := W * V2**T
+ iv = offsetV + ( (M-K) * strideV2 );
+ dtrmm( 'right', 'lower', 'transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+ if ( M > K ) {
+ // W := W + C1**T * V1**T
+ dgemm( 'transpose', 'transpose', N, K, M-K, 1.0, C, strideC1, strideC2, offsetC, V, strideV1, strideV2, offsetV, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T**T or W * T
+ dtrmm( 'right', 'lower', transt, 'non-unit', N, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - V**T * W**T
+ if ( M > K ) {
+ // C1 := C1 - V1**T * W**T
+ dgemm( 'transpose', 'transpose', M-K, N, K, -1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork, 1.0, C, strideC1, strideC2, offsetC );
+ }
+ // W := W * V2
+ iv = offsetV + ( (M-K) * strideV2 );
+ dtrmm( 'right', 'lower', 'no-transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+
+ // C2 := C2 - W**T
+ o = loopOrder( [ K, N ], [ strideC1, strideC2 ], [ strideWork2, strideWork1 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC + ( (M-K) * strideC1 );
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = leftBackwardRows;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_forward_columns.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_forward_columns.js
new file mode 100644
index 000000000000..e7b134abf652
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_forward_columns.js
@@ -0,0 +1,168 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the left, with forward direction and column storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = leftForwardColumns( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -1350.0, -1400.0, -1450.0, -30961.0, -32102.0, -33243.0, -266612.0, -275464.0, -284316.0 ]
+*/
+function leftForwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var transt;
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ if ( trans === 'no-transpose' ) {
+ transt = 'transpose';
+ } else {
+ transt = 'no-transpose';
+ }
+
+ /* Let V = ( V1 ) (first K rows)
+ * ( V2 )
+ * Where V1 is unit lower triangular.
+ */
+
+ /* Form H * C or H^T * C where C = ( C1 )
+ * ( C2 )
+ * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
+ * W := C1**T
+ */
+ ic = offsetC;
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( N, C, strideC2, ic, work, strideWork1, iw );
+ ic += strideC1;
+ iw += strideWork2;
+ }
+ // W := W * V1
+ dtrmm( 'right', 'lower', 'no-transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+ if ( M > K ) {
+ // W := W + C2**T * V2
+ ic = offsetC + ( K * strideC1 ); // C( k+1, 1 ) - 0 based index
+ iv = offsetV + ( K * strideV1 ); // V( k+1, 1 ) - 0 based index
+ dgemm( 'transpose', 'no-transpose', N, K, M-K, 1.0, C, strideC1, strideC2, ic, V, strideV1, strideV2, iv, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T**T or W * T
+ dtrmm( 'right', 'upper', transt, 'non-unit', N, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - V * W**T
+ if ( M > K ) {
+ // C2 := C2 - V2 * W**T
+ ic = offsetC + ( K * strideC1 ); // C( k+1, 1 ) - 0 based index
+ iv = offsetV + ( K * strideV1 ); // V( k+1, 1 ) - 0 based index
+ dgemm( 'no-transpose', 'transpose', M-K, N, K, -1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork, 1.0, C, strideC1, strideC2, ic );
+ }
+ // W := W * V1**T
+ dtrmm( 'right', 'lower', 'transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+
+ // C1 := C1 - W**T
+ o = loopOrder( [ K, N ], [ strideC1, strideC2 ], [ strideWork2, strideWork1 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC;
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = leftForwardColumns;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_forward_rows.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_forward_rows.js
new file mode 100644
index 000000000000..d62c3646d67f
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/left_forward_rows.js
@@ -0,0 +1,167 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the left, with forward direction and row storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = leftForwardRows( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -3010.0, -3120.0, -3230.0, -125821.0, -130422.0, -135023.0, -611692.0, -632424.0, -653156.0 ]
+*/
+function leftForwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var transt;
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ if ( trans === 'no-transpose' ) {
+ transt = 'transpose';
+ } else {
+ transt = 'no-transpose';
+ }
+
+ /* Let V = ( V1 V2 ) (V1: first K columns)
+ * Where V1 is unit upper triangular.
+ */
+
+ /* Form H * C or H^T * C where C = ( C1 )
+ * ( C2 )
+ * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in work)
+ * W := C1**T
+ */
+ ic = offsetC;
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( N, C, strideC2, ic, work, strideWork1, iw );
+ ic += strideC1;
+ iw += strideWork2;
+ }
+ // W := W * V1**T
+ dtrmm( 'right', 'upper', 'transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+ if ( M > K ) {
+ // W := W + C2**T * V2**T
+ ic = offsetC + ( K * strideC1 );
+ iv = offsetV + ( K * strideV2 );
+ dgemm( 'transpose', 'transpose', N, K, M-K, 1.0, C, strideC1, strideC2, ic, V, strideV1, strideV2, iv, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T**T or W * T
+ dtrmm( 'right', 'upper', transt, 'non-unit', N, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - V**T * W**T
+ if ( M > K ) {
+ // C2 := C2 - V2**T * W**T
+ ic = offsetC + ( K * strideC1 );
+ iv = offsetV + ( K * strideV2 );
+ dgemm( 'transpose', 'transpose', M-K, N, K, -1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork, 1.0, C, strideC1, strideC2, ic );
+ }
+ // W := W * V1
+ dtrmm( 'right', 'upper', 'no-transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+
+ // C1 := C1 - W**T
+ o = loopOrder( [ K, N ], [ strideC1, strideC2 ], [ strideWork2, strideWork1 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC;
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = leftForwardRows;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/main.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/main.js
new file mode 100644
index 000000000000..e779a74b7b6d
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/main.js
@@ -0,0 +1,35 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+var dorgbr = require( './dorgbr.js' );
+var ndarray = require( './ndarray.js' );
+
+
+// MAIN //
+
+setReadOnly( dorgbr, 'ndarray', ndarray );
+
+
+// EXPORTS //
+
+module.exports = dorgbr;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/ndarray.js
new file mode 100644
index 000000000000..958e9bb34a1d
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/ndarray.js
@@ -0,0 +1,119 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len, max-params */
+
+'use strict';
+
+// MODULES //
+
+var format = require( '@stdlib/string/format' );
+var max = require( '@stdlib/math/base/special/fast/max' );
+var min = require( '@stdlib/math/base/special/min' );
+var base = require( './base.js' );
+
+
+// MAIN //
+
+/**
+* Generates one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`, using alternative indexing semantics.
+*
+* ## Notes
+*
+* - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
+*
+* - If `vect = 'Q'`,
+*
+* - `A` is assumed to have been an `M-by-K` matrix, and `Q` is of order `M`.
+* - if `m >= k`, `Q = H(1) H(2) . . . H(k)` and `dorgbr` returns the first `n` columns of `Q`, where `m >= n >= k`.
+* - if `m < k`, `Q = H(1) H(2) . . . H(m-1)` and `dorgbr` returns `Q` as an `M-by-M` matrix.
+*
+* - If `vect = 'P'`,
+*
+* - `A` is assumed to have been a `K-by-N` matrix, and `P^T` is of order `N`.
+* - if `k < n`, `P^T = G(k) . . . G(2) G(1)` and `dorgbr` returns the first `m` rows of `P^T`, where `n >= m >= k`.
+* - if `k >= n`, `P^T = G(n-1) . . . G(2) G(1)` and `dorgbr` returns `P^T` as an `N-by-N` matrix.
+*
+* - `WORK` must have length, `LWORK >= max(1,min(M,N))`. For optimum performance `LWORK >= min(M,N)*NB`, where `NB` is the optimal blocksize.
+*
+* - If `LWORK = -1`, then 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, and no error message related to `LWORK` is issued.
+*
+* @param {string} vect - specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`
+* @param {NonNegativeInteger} M - number of rows of `Q` or `P^T`
+* @param {NonNegativeInteger} N - number of columns of `Q` or `P^T`
+* @param {NonNegativeInteger} K - number of elementary reflectors
+* @param {Float64Array} A - input/output matrix
+* @param {integer} strideA1 - stride length for the first dimension of `A`
+* @param {integer} strideA2 - stride length for the second dimension of `A`
+* @param {NonNegativeInteger} offsetA - starting index for `A`
+* @param {Float64Array} TAU - scalar factors of elementary reflectors
+* @param {integer} strideTAU - stride length for `TAU`
+* @param {NonNegativeInteger} offsetTAU - starting index for `TAU`
+* @param {Float64Array} WORK - workspace array
+* @param {integer} strideWORK - stride length for `WORK`
+* @param {NonNegativeInteger} offsetWORK - starting index for `WORK`
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @throws {TypeError} first argument must be either `'Q'` or `'P'`
+* @throws {RangeError} second argument must be a non-negative integer
+* @throws {RangeError} third argument must be a non-negative integer satisfying the constraints for the given `vect` argument
+* @throws {RangeError} fourth argument must be a non-negative integer
+* @throws {RangeError} fourteenth argument must be a valid `LWORK` value
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 0.2, -0.1, 0.3, 0, 1, 0.4, -0.2, 0, 0, 1, 0.5 ] );
+* var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+* var WORK = new Float64Array( 10 );
+*
+* var info = dorgbr( 'Q', 4, 3, 3, A, 1, 4, 0, TAU, 1, 0, WORK, 1, 0, 10 );
+* // A => [ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
+* // info => 0
+* // WORK[ 0 ] => 96
+*/
+function dorgbr( vect, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point
+ var wantq;
+
+ if ( vect !== 'Q' && vect !== 'P' ) {
+ throw new TypeError( format( 'invalid argument. First argument must be either `\'Q\'` or `\'P\'`. Value: `%s`.', vect ) );
+ }
+ wantq = ( vect === 'Q' );
+ if ( M < 0 ) {
+ throw new RangeError( format( 'invalid argument. Second argument must be a nonnegative integer. Value: `%d`.', M ) );
+ }
+ if ( wantq ) {
+ if ( N < min( M, K ) || N > M ) {
+ throw new RangeError( format( 'invalid argument. Third argument must be greater than or equal to `min(M,K)` and smaller than or equal to `M`. Value: `%d`.', N ) );
+ }
+ } else if ( N < M || M < min( N, K ) ) {
+ throw new RangeError( format( 'invalid argument. Third argument must be greater than or equal to `M`, and `M` must be greater than or equal to `min(N,K)`. Value: `%d`.', N ) );
+ }
+ if ( K < 0 ) {
+ throw new RangeError( format( 'invalid argument. Fourth argument must be a nonnegative integer. Value: `%d`.', K ) );
+ }
+ if ( LWORK < max( 1, min( M, N ) ) && LWORK !== -1 ) {
+ throw new RangeError( format( 'invalid argument. Fourteenth argument must be greater than or equal to `max(1,min(M,N))` except when equal to -1. Value: `%d`.', LWORK ) );
+ }
+ return base( vect, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
+}
+
+
+// EXPORTS //
+
+module.exports = dorgbr;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_backward_columns.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_backward_columns.js
new file mode 100644
index 000000000000..20f98fd01d52
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_backward_columns.js
@@ -0,0 +1,158 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the right, with backward direction and column storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = rightBackwardColumns( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -402190.0, -419212.0, -5216.0, -752090.0, -782422.0, -9736.0, -1101990.0, -1145632.0, -14256.0 ]
+*/
+function rightBackwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ /* Let V = ( V1 )
+ * ( V2 ) (last K rows)
+ * Where V2 is unit upper triangular.
+ */
+
+ /* Form C * H or C * H^T where C = ( C1 C2 )
+ * W := C * V = (C1*V1 + C2*V2) (stored in WORK)
+ * W := C2
+ */
+ ic = offsetC + ( (N-K) * strideC2 );
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( M, C, strideC1, ic, work, strideWork1, iw );
+ ic += strideC2;
+ iw += strideWork2;
+ }
+ // W := W * V2
+ iv = offsetV + ( (N-K) * strideV1 );
+ dtrmm( 'right', 'upper', 'no-transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+ if ( N > K ) {
+ // W := W + C1 * V1
+ dgemm( 'no-transpose', 'no-transpose', M, K, N-K, 1.0, C, strideC1, strideC2, offsetC, V, strideV1, strideV2, offsetV, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T or W * T**T
+ dtrmm( 'right', 'upper', trans, 'non-unit', M, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - W * V**T
+ if ( N > K ) {
+ // C1 := C1 - W * V1**T
+ dgemm( 'no-transpose', 'transpose', M, N-K, K, -1.0, work, strideWork1, strideWork2, offsetWork, V, strideV1, strideV2, offsetV, 1.0, C, strideC1, strideC2, offsetC );
+ }
+ // W := W * V2**T
+ iv = offsetV + ( (N-K) * strideV1 );
+ dtrmm( 'right', 'upper', 'transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+
+ // C2 := C2 - W
+ o = loopOrder( [ K, M ], [ strideC1, strideC2 ], [ strideWork1, strideWork2 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC + ( (N-K) * strideC2 );
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = rightBackwardColumns;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_backward_rows.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_backward_rows.js
new file mode 100644
index 000000000000..e10b8b011af6
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_backward_rows.js
@@ -0,0 +1,157 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the right, with backward direction and row storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = rightBackwardRows( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -104950.0, -191792.0, -3176.0, -195250.0, -356002.0, -5896.0, -285550.0, -520212.0, -8616.0 ]
+*/
+function rightBackwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ /* Let V = ( V1 V2 ) (V2: last K columns)
+ * Where V2 is unit lower triangular.
+ */
+
+ /* Form C * H or C * H^T where C = ( C1 C2 )
+ * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
+ * W := C2
+ */
+ ic = offsetC + ( (N-K) * strideC2 );
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( M, C, strideC1, ic, work, strideWork1, iw );
+ iw += strideWork2;
+ ic += strideC2;
+ }
+ // W := W * V2**T
+ iv = offsetV + ( (N-K) * strideV2 );
+ dtrmm( 'right', 'lower', 'transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+ if ( N > K ) {
+ // W := W + C1 * V1**T
+ dgemm( 'no-transpose', 'transpose', M, K, N-K, 1.0, C, strideC1, strideC2, offsetC, V, strideV1, strideV2, offsetV, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T or W * T**T
+ dtrmm( 'right', 'lower', trans, 'non-unit', M, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - W * V
+ if ( N > K ) {
+ // C1 := C1 - W * V1
+ dgemm( 'no-transpose', 'no-transpose', M, N-K, K, -1.0, work, strideWork1, strideWork2, offsetWork, V, strideV1, strideV2, offsetV, 1.0, C, strideC1, strideC2, offsetC );
+ }
+ // W := W * V2
+ iv = offsetV + ( (N-K) * strideV2 );
+ dtrmm( 'right', 'lower', 'no-transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
+
+ // C1 := C1 - W
+ o = loopOrder( [ K, M ], [ strideC1, strideC2 ], [ strideWork1, strideWork2 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC;
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = rightBackwardRows;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_forward_columns.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_forward_columns.js
new file mode 100644
index 000000000000..0c7574a3b7b9
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_forward_columns.js
@@ -0,0 +1,160 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the right, with forward direction and column storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = rightForwardColumns( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -630.0, -14392.0, -114296.0, -1130.0, -25802.0, -202816.0, -1630.0, -37212.0, -291336.0 ]
+*/
+function rightForwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ /* Let V = ( V1 ) (first K rows)
+ * ( V2 )
+ * Where V1 is unit lower triangular.
+ */
+
+ /* Form C * H or C * H^T where C = ( C1 C2 )
+ * W := C * V = (C1*V1 + C2*V2) (stored in WORK)
+ * W := C1
+ */
+ ic = offsetC;
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( M, C, strideC1, ic, work, strideWork1, iw );
+ ic += strideC2;
+ iw += strideWork2;
+ }
+ // W := W * V1
+ dtrmm( 'right', 'lower', 'no-transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+ if ( N > K ) {
+ // W := W + C2 * V2
+ ic = offsetC + ( K * strideC2 );
+ iv = offsetV + ( K * strideV1 );
+ dgemm( 'no-transpose', 'no-transpose', M, K, N-K, 1.0, C, strideC1, strideC2, ic, V, strideV1, strideV2, iv, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T or W * T**T
+ dtrmm( 'right', 'upper', trans, 'non-unit', M, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - W * V**T
+ if ( N > K ) {
+ // C2 := C2 - W * V2**T
+ ic = offsetC + ( K * strideC2 );
+ iv = offsetV + ( K * strideV1 );
+ dgemm( 'no-transpose', 'transpose', M, N-K, K, -1.0, work, strideWork1, strideWork2, offsetWork, V, strideV1, strideV2, iv, 1.0, C, strideC1, strideC2, ic );
+ }
+ // W := W * V1**T
+ dtrmm( 'right', 'lower', 'transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+
+ // C1 := C1 - W
+ o = loopOrder( [ K, M ], [ strideC2, strideC1 ], [ strideWork2, strideWork1 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC;
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = rightForwardColumns;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_forward_rows.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_forward_rows.js
new file mode 100644
index 000000000000..830e208c4700
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/lib/right_forward_rows.js
@@ -0,0 +1,159 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
+var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
+var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
+var dtrmm = require( './dtrmm.js' );
+
+
+// MAIN //
+
+/**
+* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the right, with forward direction and row storage.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows of the matrix C
+* @param {NonNegativeInteger} N - number of columns of the matrix C
+* @param {NonNegativeInteger} K - order of the matrix T
+* @param {Float64Array} V - input matrix
+* @param {integer} strideV1 - stride of the first dimension of V
+* @param {integer} strideV2 - stride of the second dimension of V
+* @param {integer} offsetV - index offset for V
+* @param {Float64Array} T - input matrix
+* @param {integer} strideT1 - stride of the first dimension of T
+* @param {integer} strideT2 - stride of the second dimension of T
+* @param {integer} offsetT - index offset for T
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of C
+* @param {integer} strideC2 - stride of the second dimension of C
+* @param {integer} offsetC - index offset for C
+* @param {Float64Array} work - work array
+* @param {integer} strideWork1 - stride of the first dimension of work
+* @param {integer} strideWork2 - stride of the second dimension of work
+* @param {integer} offsetWork - index offset for work
+* @param {string} trans - specifies whether to apply H or H^T
+* @returns {Float64Array} updated matrix C
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
+* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
+* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
+* var work = new Float64Array( 9 );
+*
+* var result = rightForwardRows( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
+* // returns [ -1390.0, -58132.0, -266416.0, -2490.0, -104142.0, -473736.0, -3590.0, -150152.0, -681056.0 ]
+*/
+function rightForwardRows( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
+ var da0;
+ var da1;
+ var db0;
+ var db1;
+ var i0;
+ var i1;
+ var sh;
+ var sa;
+ var sb;
+ var S0;
+ var S1;
+ var ia;
+ var ib;
+ var ic;
+ var iv;
+ var iw;
+ var j;
+ var o;
+
+ /* Let V = ( V1 V2 ) (V1: first K columns)
+ * Where V1 is unit upper triangular.
+ */
+
+ /* Form C * H or C * H^T where C = ( C1 C2 )
+ * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
+ * W := C1
+ */
+ ic = offsetC;
+ iw = offsetWork;
+ for ( j = 0; j < K; j++ ) {
+ dcopy( M, C, strideC1, ic, work, strideWork1, iw );
+ ic += strideC2;
+ iw += strideWork2;
+ }
+ // W := W * V1**T
+ dtrmm( 'right', 'upper', 'transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+ if ( N > K ) {
+ // W := W + C2 * V2**T
+ ic = offsetC + ( K * strideC2 );
+ iv = offsetV + ( K * strideV2 );
+ dgemm( 'no-transpose', 'transpose', M, K, N-K, 1.0, C, strideC1, strideC2, ic, V, strideV1, strideV2, iv, 1.0, work, strideWork1, strideWork2, offsetWork );
+ }
+ // W := W * T or W * T**T
+ dtrmm( 'right', 'upper', trans, 'non-unit', M, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
+
+ // C := C - W * V
+ if ( N > K ) {
+ // C2 := C2 - W * V2
+ ic = offsetC + ( K * strideC2 );
+ iv = offsetV + ( K * strideV2 );
+ dgemm( 'no-transpose', 'no-transpose', M, N-K, K, -1.0, work, strideWork1, strideWork2, offsetWork, V, strideV1, strideV2, iv, 1.0, C, strideC1, strideC2, ic );
+ }
+ // W := W * V1
+ dtrmm( 'right', 'upper', 'no-transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
+
+ // C1 := C1 - W
+ o = loopOrder( [ K, M ], [ strideC1, strideC2 ], [ strideWork1, strideWork2 ] ); // eslint-disable-line max-len
+ sh = o.sh;
+ sa = o.sx;
+ sb = o.sy;
+
+ // Extract loop variables for loop interchange
+ S0 = sh[ 0 ];
+ S1 = sh[ 1 ];
+ da0 = sa[ 0 ];
+ da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
+ db0 = sb[ 0 ];
+ db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
+
+ // Set pointers to first indexed elements
+ ia = offsetC;
+ ib = offsetWork;
+
+ // Iterate over matrix dimensions with optimized loop order
+ for ( i1 = 0; i1 < S1; i1++ ) {
+ for ( i0 = 0; i0 < S0; i0++ ) {
+ C[ ia ] -= work[ ib ];
+ ia += da0;
+ ib += db0;
+ }
+ ia += da1;
+ ib += db1;
+ }
+
+ return C;
+}
+
+
+// EXPORTS //
+
+module.exports = rightForwardRows;
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/package.json b/lib/node_modules/@stdlib/lapack/base/dorgbr/package.json
new file mode 100644
index 000000000000..e31f2533ee92
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/package.json
@@ -0,0 +1,69 @@
+{
+ "name": "@stdlib/lapack/base/dorgbr",
+ "version": "0.0.0",
+ "description": "LAPACK routine to generate one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bidiagonal form: `A = Q*B*P^T`.",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "lib": "./lib",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "mathematics",
+ "math",
+ "lapack",
+ "dorgbr",
+ "reflector",
+ "linear",
+ "algebra",
+ "subroutines",
+ "array",
+ "ndarray",
+ "matrix",
+ "float64",
+ "double",
+ "float64array"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/p_k_ge_n_col_maj.json b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/p_k_ge_n_col_maj.json
new file mode 100644
index 000000000000..b1f863345727
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/p_k_ge_n_col_maj.json
@@ -0,0 +1,123 @@
+{
+ "order": "column-major",
+ "vect": "P",
+ "M": 4,
+ "N": 4,
+ "K": 5,
+ "A": [
+ 1,
+ 0.5,
+ 0.8,
+ 1.1,
+ 0.2,
+ 2,
+ 0.9,
+ 1.2,
+ 0.3,
+ 0.6,
+ 3,
+ 1.3,
+ 0.4,
+ 0.7,
+ 1,
+ 4
+ ],
+ "strideA1": 1,
+ "strideA2": 4,
+ "offsetA": 0,
+ "LDA": 4,
+ "A_mat": [
+ [
+ 1,
+ 0.2,
+ 0.3,
+ 0.4
+ ],
+ [
+ 0.5,
+ 2,
+ 0.6,
+ 0.7
+ ],
+ [
+ 0.8,
+ 0.9,
+ 3,
+ 1
+ ],
+ [
+ 1.1,
+ 1.2,
+ 1.3,
+ 4
+ ]
+ ],
+ "TAU": [
+ 1.5,
+ 0.9,
+ 1.3,
+ 0
+ ],
+ "strideTAU": 1,
+ "offsetTAU": 0,
+ "WORK": [
+ 0,
+ 0,
+ 0,
+ 0
+ ],
+ "strideWORK": 1,
+ "offsetWORK": 0,
+ "LWORK": 4,
+ "A_out": [
+ 1,
+ 0,
+ 0,
+ 0,
+ 0,
+ -0.5,
+ 0.333,
+ 0.015570000000000011,
+ 0,
+ -0.44999999999999996,
+ 0.19989999999999997,
+ 0.19367100000000004,
+ 0,
+ -0.6000000000000001,
+ -0.4968,
+ -0.16147200000000003
+ ],
+ "A_out_mat": [
+ [
+ 1,
+ 0,
+ 0,
+ 0
+ ],
+ [
+ 0,
+ -0.5,
+ -0.44999999999999996,
+ -0.6000000000000001
+ ],
+ [
+ 0,
+ 0.333,
+ 0.19989999999999997,
+ -0.4968
+ ],
+ [
+ 0,
+ 0.015570000000000011,
+ 0.19367100000000004,
+ -0.16147200000000003
+ ]
+ ],
+ "WORK_out": [
+ 96,
+ -0.010380000000000007,
+ 0,
+ 0
+ ],
+ "info": 0
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/p_k_lt_n_col_maj.json b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/p_k_lt_n_col_maj.json
new file mode 100644
index 000000000000..038039002069
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/p_k_lt_n_col_maj.json
@@ -0,0 +1,69 @@
+{
+ "order": "column-major",
+ "vect": "P",
+ "M": 2,
+ "N": 3,
+ "K": 2,
+ "A": [
+ 1,
+ -1,
+ 0,
+ -2,
+ 0,
+ 0
+ ],
+ "strideA1": 1,
+ "strideA2": 2,
+ "offsetA": 0,
+ "LDA": 2,
+ "A_mat": [
+ [
+ 1,
+ 0,
+ 0
+ ],
+ [
+ -1,
+ -2,
+ 0
+ ]
+ ],
+ "TAU": [
+ 1,
+ 1
+ ],
+ "strideTAU": 1,
+ "offsetTAU": 0,
+ "WORK": [
+ 0,
+ 0
+ ],
+ "strideWORK": 1,
+ "offsetWORK": 0,
+ "LWORK": 2,
+ "A_out": [
+ 0,
+ 0,
+ 0,
+ 0,
+ 0,
+ 0
+ ],
+ "A_out_mat": [
+ [
+ 0,
+ 0,
+ 0
+ ],
+ [
+ 0,
+ 0,
+ 0
+ ]
+ ],
+ "WORK_out": [
+ 64,
+ 0
+ ],
+ "info": 0
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/q_m_ge_k_col_maj.json b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/q_m_ge_k_col_maj.json
new file mode 100644
index 000000000000..fbd6706aed17
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/q_m_ge_k_col_maj.json
@@ -0,0 +1,104 @@
+{
+ "order": "column-major",
+ "vect": "Q",
+ "M": 4,
+ "N": 3,
+ "K": 3,
+ "A": [
+ 1,
+ 0.2,
+ -0.1,
+ 0.3,
+ 0,
+ 1,
+ 0.4,
+ -0.2,
+ 0,
+ 0,
+ 1,
+ 0.5
+ ],
+ "strideA1": 1,
+ "strideA2": 4,
+ "offsetA": 0,
+ "LDA": 4,
+ "A_mat": [
+ [
+ 1,
+ 0,
+ 0
+ ],
+ [
+ 0.2,
+ 1,
+ 0
+ ],
+ [
+ -0.1,
+ 0.4,
+ 1
+ ],
+ [
+ 0.3,
+ -0.2,
+ 0.5
+ ]
+ ],
+ "TAU": [
+ 1.3,
+ 0.9,
+ 1.1
+ ],
+ "strideTAU": 1,
+ "offsetTAU": 0,
+ "WORK": [
+ 0,
+ 0,
+ 0
+ ],
+ "strideWORK": 1,
+ "offsetWORK": 0,
+ "LWORK": 3,
+ "A_out": [
+ -0.30000000000000004,
+ -0.26,
+ 0.13,
+ -0.39,
+ -0.14300000000000002,
+ 0.07139999999999998,
+ -0.34570000000000006,
+ 0.13710000000000003,
+ 0.20969000000000004,
+ -0.021061999999999977,
+ -0.1461690000000001,
+ -0.4744930000000001
+ ],
+ "A_out_mat": [
+ [
+ -0.30000000000000004,
+ -0.14300000000000002,
+ 0.20969000000000004
+ ],
+ [
+ -0.26,
+ 0.07139999999999998,
+ -0.021061999999999977
+ ],
+ [
+ 0.13,
+ -0.34570000000000006,
+ -0.1461690000000001
+ ],
+ [
+ -0.39,
+ 0.13710000000000003,
+ -0.4744930000000001
+ ]
+ ],
+ "WORK_out": [
+ 96,
+ -0.16130000000000003,
+ 0
+ ],
+ "info": 0
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/q_m_lt_k_col_maj.json b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/q_m_lt_k_col_maj.json
new file mode 100644
index 000000000000..502f6e7c0503
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/fixtures/q_m_lt_k_col_maj.json
@@ -0,0 +1,88 @@
+{
+ "order": "column-major",
+ "vect": "Q",
+ "M": 3,
+ "N": 3,
+ "K": 5,
+ "A": [
+ 2,
+ 0.1,
+ 0.2,
+ 0.3,
+ 3,
+ 0.4,
+ 0.5,
+ 0.6,
+ 4
+ ],
+ "strideA1": 1,
+ "strideA2": 3,
+ "offsetA": 0,
+ "LDA": 3,
+ "A_mat": [
+ [
+ 2,
+ 0.3,
+ 0.5
+ ],
+ [
+ 0.1,
+ 3,
+ 0.6
+ ],
+ [
+ 0.2,
+ 0.4,
+ 4
+ ]
+ ],
+ "TAU": [
+ 1.5,
+ 0.8,
+ 0
+ ],
+ "strideTAU": 1,
+ "offsetTAU": 0,
+ "WORK": [
+ 0,
+ 0,
+ 0
+ ],
+ "strideWORK": 1,
+ "offsetWORK": 0,
+ "LWORK": 3,
+ "A_out": [
+ 1,
+ 0,
+ 0,
+ 0,
+ -0.5,
+ -0.30000000000000004,
+ 0,
+ -0.05999999999999999,
+ 0.18799999999999994
+ ],
+ "A_out_mat": [
+ [
+ 1,
+ 0,
+ 0
+ ],
+ [
+ 0,
+ -0.5,
+ -0.05999999999999999
+ ],
+ [
+ 0,
+ -0.30000000000000004,
+ 0.18799999999999994
+ ]
+ ],
+ "WORK_out": [
+ 64,
+ 0,
+ 0
+ ],
+ "info": 0
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/test/test.dorgbr.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/test.dorgbr.js
new file mode 100644
index 000000000000..d0e8a644ae72
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/test.dorgbr.js
@@ -0,0 +1,566 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var Float64Array = require( '@stdlib/array/float64' );
+var isAlmostEqual = require( '@stdlib/assert/is-almost-equal-float64array' );
+var dorgbr = require( './../lib/dorgbr.js' );
+
+
+// FIXTURES //
+
+var Q_M_GE_K_COL_MAJ = require( './fixtures/q_m_ge_k_col_maj.json' );
+var Q_M_LT_K_COL_MAJ = require( './fixtures/q_m_lt_k_col_maj.json' );
+var P_K_LT_N_COL_MAJ = require( './fixtures/p_k_lt_n_col_maj.json' );
+var P_K_GE_N_COL_MAJ = require( './fixtures/p_k_ge_n_col_maj.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof dorgbr, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function has an arity of 10', function test( t ) {
+ t.strictEqual( dorgbr.length, 10, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function throws an error if provided a first argument which is not a valid order', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 'foo',
+ 'bar',
+ 'beep',
+ 'boop',
+ -5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( value, 'Q', 3, 2, 2, A, 3, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a second argument which is neither `\'Q\'` nor `\'P\'`', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 'q',
+ 'p',
+ 'foo',
+ 'bar',
+ 'beep',
+ 'boop',
+ -5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', value, 3, 2, 2, A, 3, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a third argument which is smaller than 0', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ -1,
+ -2,
+ -3
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', 'Q', value, 2, 2, A, 3, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided an invalid fourth argument when `vect` is `\'Q\'`', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 5,
+ 2,
+ -1,
+ -2,
+ -3
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', 'Q', 4, value, 3, A, 4, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided an invalid fourth argument when `vect` is `\'P\'`', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 1,
+ -1,
+ -2,
+ -3
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', 'P', 2, value, 2, A, 2, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if `M` is smaller than `min(N,K)` when `vect` is `\'P\'`', function test( t ) {
+ var WORK;
+ var TAU;
+ var A;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ] );
+ TAU = new Float64Array( [ 2, 2, 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ t.throws( badValue, RangeError, 'throws an error when `M` is smaller than `min(N,K)`' );
+ t.end();
+
+ function badValue() {
+ dorgbr( 'column-major', 'P', 2, 3, 4, A, 2, TAU, WORK, 10 );
+ }
+});
+
+tape( 'the function throws an error if provided a fifth argument which is smaller than 0', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ -1,
+ -2,
+ -3
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', 'Q', 3, 2, value, A, 3, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a seventh argument which is not a valid `LDA` (column-major)', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 2,
+ 1,
+ 0
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', 'Q', 3, 2, 2, A, value, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a seventh argument which is not a valid `LDA` (row-major)', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 1,
+ 0,
+ -1
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'row-major', 'Q', 3, 2, 2, A, value, TAU, WORK, 10 );
+ };
+ }
+});
+
+tape( 'the function throws an error when `LWORK` is smaller than `max(1,min(M,N))`', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 0, 0, 0, 1, 0 ] );
+ TAU = new Float64Array( [ 2, 2 ] );
+ WORK = new Float64Array( 10 );
+
+ values = [
+ 2,
+ 1,
+ 0
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, value );
+ };
+ }
+});
+
+tape( 'the function quick returns when `LWORK` is equal to -1', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var WORK;
+ var TAU;
+ var A;
+
+ A = new Float64Array( [ 1, 0.2, -0.1, 0.3, 0, 1, 0.4, -0.2, 0, 0, 1, 0.5 ] );
+ TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
+ WORK = new Float64Array( 10 );
+
+ expectedA = A;
+ expectedWORK = WORK;
+ expectedWORK[ 0 ] = 96;
+
+ info = dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, -1 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( A, expectedA, 'returns expected value' );
+ t.strictEqual( WORK, expectedWORK, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function quick returns when `M` is equal to 0', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var WORK;
+ var TAU;
+ var A;
+
+ A = new Float64Array( 0 );
+ TAU = new Float64Array( 0 );
+ WORK = new Float64Array( 10 );
+
+ expectedA = A;
+ expectedWORK = WORK;
+ expectedWORK[ 0 ] = 1;
+
+ info = dorgbr( 'column-major', 'Q', 0, 0, 0, A, 1, TAU, WORK, 10 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( A, expectedA, 'returns expected value' );
+ t.strictEqual( WORK, expectedWORK, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function quick returns when `N` is equal to 0', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var WORK;
+ var TAU;
+ var A;
+
+ A = new Float64Array( 0 );
+ TAU = new Float64Array( 0 );
+ WORK = new Float64Array( 10 );
+
+ expectedA = A;
+ expectedWORK = WORK;
+ expectedWORK[ 0 ] = 1;
+
+ info = dorgbr( 'column-major', 'Q', 3, 0, 0, A, 3, TAU, WORK, 10 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( A, expectedA, 'returns expected value' );
+ t.strictEqual( WORK, expectedWORK, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function generates the orthogonal matrix `Q` (`m >= k`, column-major)', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = Q_M_GE_K_COL_MAJ;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A_out );
+ expectedWORK = new Float64Array( data.WORK_out );
+
+ info = dorgbr( data.order, data.vect, data.M, data.N, data.K, A, data.LDA, TAU, WORK, data.LWORK );
+ t.strictEqual( info, data.info, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function generates the orthogonal matrix `Q` (`m < k`, column-major)', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = Q_M_LT_K_COL_MAJ;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A_out );
+ expectedWORK = new Float64Array( data.WORK_out );
+
+ info = dorgbr( data.order, data.vect, data.M, data.N, data.K, A, data.LDA, TAU, WORK, data.LWORK );
+ t.strictEqual( info, data.info, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function generates the matrix `P^T` (`k < n`, column-major)', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = P_K_LT_N_COL_MAJ;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A_out );
+ expectedWORK = new Float64Array( data.WORK_out );
+
+ info = dorgbr( data.order, data.vect, data.M, data.N, data.K, A, data.LDA, TAU, WORK, data.LWORK );
+ t.strictEqual( info, data.info, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function generates the matrix `P^T` (`k >= n`, column-major)', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = P_K_GE_N_COL_MAJ;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A_out );
+ expectedWORK = new Float64Array( data.WORK_out );
+
+ info = dorgbr( data.order, data.vect, data.M, data.N, data.K, A, data.LDA, TAU, WORK, data.LWORK );
+ t.strictEqual( info, data.info, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function handles the case where `m < k` and `m <= 1` when `vect` is `\'Q\'`', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var WORK;
+ var TAU;
+ var A;
+
+ A = new Float64Array( [ 0.0 ] );
+ TAU = new Float64Array( [ 2.0 ] );
+ WORK = new Float64Array( 10 );
+
+ expectedA = new Float64Array( [ 1.0 ] );
+ expectedWORK = WORK;
+ expectedWORK[ 0 ] = 1;
+
+ info = dorgbr( 'column-major', 'Q', 1, 1, 2, A, 1, TAU, WORK, 10 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( WORK, expectedWORK, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function handles the case where `k >= n` and `n <= 1` when `vect` is `\'P\'`', function test( t ) {
+ var expectedWORK;
+ var expectedA;
+ var info;
+ var WORK;
+ var TAU;
+ var A;
+
+ A = new Float64Array( [ 0.0 ] );
+ TAU = new Float64Array( [ 2.0 ] );
+ WORK = new Float64Array( 10 );
+
+ expectedA = new Float64Array( [ 1.0 ] );
+ expectedWORK = WORK;
+ expectedWORK[ 0 ] = 1;
+
+ info = dorgbr( 'column-major', 'P', 1, 1, 2, A, 1, TAU, WORK, 10 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( WORK, expectedWORK, 'returns expected value' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/lapack/base/dorgbr/test/test.js b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/test.js
new file mode 100644
index 000000000000..e083a2e6c82f
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dorgbr/test/test.js
@@ -0,0 +1,82 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var proxyquire = require( 'proxyquire' );
+var IS_BROWSER = require( '@stdlib/assert/is-browser' );
+var dorgbr = require( './../lib' );
+
+
+// VARIABLES //
+
+var opts = {
+ 'skip': IS_BROWSER
+};
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof dorgbr, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'attached to the main export is a method providing an ndarray interface', function test( t ) {
+ t.strictEqual( typeof dorgbr.ndarray, 'function', 'method is a function' );
+ t.end();
+});
+
+tape( 'if a native implementation is available, the main export is the native implementation', opts, function test( t ) {
+ var dorgbr = proxyquire( './../lib', {
+ '@stdlib/utils/try-require': tryRequire
+ });
+
+ t.strictEqual( dorgbr, mock, 'returns expected value' );
+ t.end();
+
+ function tryRequire() {
+ return mock;
+ }
+
+ function mock() {
+ // Mock...
+ }
+});
+
+tape( 'if a native implementation is not available, the main export is a JavaScript implementation', opts, function test( t ) {
+ var dorgbr;
+ var main;
+
+ main = require( './../lib/dorgbr.js' );
+
+ dorgbr = proxyquire( './../lib', {
+ '@stdlib/utils/try-require': tryRequire
+ });
+
+ t.strictEqual( dorgbr, main, 'returns expected value' );
+ t.end();
+
+ function tryRequire() {
+ return new Error( 'Cannot find module' );
+ }
+});