diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/README.md b/lib/node_modules/@stdlib/lapack/base/dgeqrf/README.md
new file mode 100644
index 000000000000..927da5f96b22
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/README.md
@@ -0,0 +1,315 @@
+
+
+# dgeqrf
+
+> LAPACK routine to compute a QR factorization of a real `M`-by-`N` matrix `A`.
+
+
+
+`dgeqrf` computes a QR factorization of a real `M`-by-`N` matrix `A`:
+
+```math
+A = Q \cdot \begin{pmatrix} R \\ 0 \end{pmatrix}
+```
+
+where
+
+- **Q** is an `M`-by-`M` orthogonal matrix,
+- **R** is an upper-triangular `N`-by-`N` matrix, and
+- **0** is an `(M-N)`-by-`N` zero matrix if `M > N`.
+
+The matrix `Q` is represented as a product of elementary reflectors
+
+```text
+Q = H(1) H(2) . . . H(k), where k = \min(m,n).
+```
+
+Each `H(i)` has the form
+
+```text
+H(i) = I - \tau \cdot v \cdot v^T
+```
+
+where `\tau` is a real scalar, and `v` is a real vector with `v(1:i-1) = 0` and `v(i) = 1`; `v(i+1:m)` is stored on exit in `A(i+1:m,i)`, and `\tau` in `TAU(i)`.
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var dgeqrf = require( '@stdlib/lapack/base/dgeqrf' );
+```
+
+#### dgeqrf( order, M, N, A, LDA, TAU, WORK, LWORK )
+
+Computes a QR factorization of a real `M`-by-`N` matrix `A`.
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU = new Float64Array( 3 );
+var WORK = new Float64Array( 4 );
+
+dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+// A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+// TAU => [ ~1.097, ~1.084, 0.0 ]
+// WORK => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+```
+
+The function has the following parameters:
+
+- **order**: storage layout.
+- **M**: number of rows in `A`.
+- **N**: number of columns in `A`.
+- **A**: input/output matrix.
+- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+- **TAU**: output array.
+- **WORK**: workspace array.
+- **LWORK**: dimension of the array `WORK`. If `min(M,N) = 0`, `LWORK` must be at least `1`; otherwise, `LWORK` must be at least `max(1,N)`. For optimal performance, `LWORK` should be at least `N * NB` where `NB` is the optimal block size. If `LWORK = -1`, a workspace query is assumed; the routine only calculates the optimal size of the `WORK` array, returns this value as the first entry of the `WORK` array.
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU0 = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+var WORK0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var TAU1 = new Float64Array( TAU0.buffer, TAU0.BYTES_PER_ELEMENT*0 );
+var WORK1 = new Float64Array( WORK0.buffer, WORK0.BYTES_PER_ELEMENT*0 );
+
+dgeqrf( 'column-major', 3, 4, A1, 3, TAU1, WORK1, 4 );
+// A0 => [ 0.0, ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+// TAU0 => [ ~1.097, ~1.084, 0.0 ]
+// WORK0 => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+```
+
+
+
+#### dgeqrf.ndarray( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK )
+
+Computes a QR factorization of a real `M`-by-`N` matrix `A` using alternative indexing semantics.
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU = new Float64Array( 3 );
+var WORK = new Float64Array( 4 );
+
+dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
+// A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+// TAU => [ ~1.097, ~1.084, 0.0 ]
+// WORK => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+```
+
+The function has the following additional parameters:
+
+- **M**: number of rows in `A`.
+- **N**: number of columns in `A`.
+- **A**: input/output matrix as a [`Float64Array`][@stdlib/array/float64].
+- **strideA1**: stride of the first dimension of `A`.
+- **strideA2**: stride of the second dimension of `A`.
+- **offsetA**: starting index for `A`.
+- **TAU**: output array as a [`Float64Array`][@stdlib/array/float64].
+- **strideTAU**: stride for `TAU`.
+- **offsetTAU**: starting index for `TAU`.
+- **WORK**: workspace array as a [`Float64Array`][@stdlib/array/float64].
+- **strideWORK**: stride for `WORK`.
+- **offsetWORK**: starting index for `WORK`.
+- **LWORK**: dimension of the array `WORK`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+var TAU = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+var WORK = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
+
+dgeqrf.ndarray( 3, 4, A, 1, 3, 4, TAU, 1, 0, WORK, 1, 0, 4 );
+// A => [ 0.0, 0.0, 0.0, 0.0, ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+```
+
+
+
+
+
+
+
+## Notes
+
+- `dgeqrf()` corresponds to the [LAPACK][lapack] routine [`dgeqrf`][lapack-dgeqrf].
+
+
+
+
+
+
+
+## Examples
+
+
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var min = require( '@stdlib/math/base/special/min' );
+var dgeqrf = require( '@stdlib/lapack/base/dgeqrf' );
+
+// Specify matrix meta data:
+var shape = [ 3, 4 ];
+var order = 'row-major';
+var strides = shape2strides( shape, order );
+
+// Create a matrix stored in linear memory:
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+// Output arrays:
+var TAU = new Float64Array( min( shape[ 0 ], shape[ 1 ] ) );
+var WORK = new Float64Array( shape[ 1 ] );
+
+// Compute the QR factorization in-place:
+var info = dgeqrf( order, shape[ 0 ], shape[ 1 ], A, strides[ 0 ], TAU, WORK, WORK.length );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+console.log( TAU );
+console.log( WORK );
+```
+
+
+
+
+
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+TODO
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dgeqrf]: https://www.netlib.org/lapack/explore-html/d0/da1/group__geqrf_gade26961283814bb4e62183d9133d8bf5.html
+
+[@stdlib/array/float64]: https://stdlib.io/docs/api/latest/@stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+
+
+
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/benchmark/benchmark.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/benchmark/benchmark.js
new file mode 100644
index 000000000000..9cece0a4c135
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/benchmark/benchmark.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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dgeqrf = require( './../lib/dgeqrf.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+ 'row-major',
+ 'column-major'
+];
+var opts = {
+ 'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {PositiveInteger} N - matrix dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, N ) {
+ var LWORK = N * 32;
+ var work = new Float64Array( N );
+ var TAU = new Float64Array( N );
+ var A = discreteUniform( N*N, 1.0, 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 = dgeqrf( order, N, N, A, N, TAU, work, LWORK );
+ if ( z !== 0 ) {
+ b.fail( 'should return 0' );
+ }
+ }
+ b.toc();
+
+ if ( z !== 0 ) {
+ b.fail( 'should return 0' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var min;
+ var max;
+ var ord;
+ var N;
+ var f;
+ var i;
+ var k;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( k = 0; k < LAYOUTS.length; k++ ) {
+ ord = LAYOUTS[ k ];
+ for ( i = min; i <= max; i++ ) {
+ N = floor( pow( pow( 10, i ), 1.0/3.0 ) );
+ f = createBenchmark( ord, N );
+ bench( format( '%s::square_matrix:order=%s,size=%d', pkg, ord, N*N ), f );
+ }
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/benchmark/benchmark.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/benchmark/benchmark.ndarray.js
new file mode 100644
index 000000000000..40bbdcb6d419
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/benchmark/benchmark.ndarray.js
@@ -0,0 +1,134 @@
+/**
+* @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 floor = require( '@stdlib/math/base/special/floor' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dgeqrf = require( './../lib/ndarray.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+ 'row-major',
+ 'column-major'
+];
+var opts = {
+ 'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {PositiveInteger} N - matrix dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, N ) {
+ var LWORK;
+ var work;
+ var TAU;
+ var sa1;
+ var sa2;
+ var A;
+
+ LWORK = N * 32;
+ work = new Float64Array( N );
+ TAU = new Float64Array( N );
+ A = discreteUniform( N*N, 1.0, 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 = dgeqrf( N, N, A, sa1, sa2, 0, TAU, 1, 0, work, 1, 0, LWORK );
+ if ( z !== 0 ) {
+ b.fail( 'should return 0' );
+ }
+ }
+ b.toc();
+
+ if ( z !== 0 ) {
+ b.fail( 'should return 0' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var min;
+ var max;
+ var ord;
+ var N;
+ var f;
+ var i;
+ var k;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( k = 0; k < LAYOUTS.length; k++ ) {
+ ord = LAYOUTS[ k ];
+ for ( i = min; i <= max; i++ ) {
+ N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+ f = createBenchmark( ord, N );
+ bench( format( '%s::square_matrix:ndarray:order=%s,size=%d', pkg, ord, N*N ), f );
+ }
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/repl.txt b/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/repl.txt
new file mode 100644
index 000000000000..517d461d0e29
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/repl.txt
@@ -0,0 +1,132 @@
+
+{{alias}}( order, M, N, A, LDA, TAU, WORK, LWORK )
+ Computes a QR factorization of a real M-by-N matrix A:
+
+ If LWORK = -1, the routine only calculates the optimal
+ size of the WORK array, returns this value as the first entry of WORK,
+ and exits with info = 0.
+
+ Indexing is relative to the first index. To introduce an offset, use typed
+ array views.
+
+ Parameters
+ ----------
+ order: string
+ Storage layout. Must be either 'row-major' or 'column-major'.
+
+ M: integer
+ Number of rows in the matrix A. Must be a nonnegative integer.
+
+ N: integer
+ Number of columns in the matrix A. Must be a nonnegative integer.
+
+ A: Float64Array
+ Input/output matrix. On input, the M-by-N matrix A. On output, the
+ elements on and above the diagonal contain the min(M,N)-by-N upper
+ trapezoidal matrix R; the elements below the diagonal contain the
+ vectors v defining the elementary reflectors. At least `LDA * max(1,N)`
+ elements for row-major, `LDA * max(1,M)` for column-major.
+
+ LDA: integer
+ Stride of the first dimension of A (a.k.a., leading dimension).
+ For column-major, LDA >= max(1,M). For row-major, LDA >= max(1,N).
+
+ TAU: Float64Array
+ Output array for scalar factors of elementary reflectors.
+ Length must be at least `min(M,N)`.
+
+ WORK: Float64Array
+ Workspace array. For optimal performance, `LWORK >= N*NB` where NB is
+ the optimal block size. If `LWORK = -1`, a workspace query is assumed;
+ the optimal size is returned in `WORK[0]` and no computation is
+ performed.
+
+ LWORK: integer
+ Dimension of the array WORK.
+
+ Returns
+ -------
+ info: integer
+ Status code. 0 indicates success.
+
+ Examples
+ --------
+ > var A = new {{alias:@stdlib/array/float64}}([1,5,9,2,6,10,3,7,11,4,8,12]);
+ > var TAU = new {{alias:@stdlib/array/float64}}( 3 );
+ > var WORK = new {{alias:@stdlib/array/float64}}( 4 );
+ > {{alias}}( 'column-major', 3, 4, A, 3, TAU, WORK, 4 )
+ 0
+ > A
+ [~-10.344,~0.441,~0.793,~-11.794,~0.947,~0.919,~-13.244,~1.894,~0.0,~-14.694,~2.842,~0.0]
+ > TAU
+ [ ~1.097, ~1.084, 0.0 ]
+ > WORK
+ [ 4.0, ~-2.842, ~17.046, 0.0 ]
+
+
+{{alias}}.ndarray( M, N, A,sA1,sA2,oA, TAU,sTAU,oTAU, WORK,sWORK,oWORK, LWORK )
+ Computes a QR factorization of a real M-by-N matrix A using alternative
+ indexing semantics.
+
+ Parameters
+ ----------
+ M: integer
+ Number of rows in the matrix A. Must be a nonnegative integer.
+
+ N: integer
+ Number of columns in the matrix A. Must be a nonnegative integer.
+
+ A: Float64Array
+ Input/output matrix.
+
+ sA1: integer
+ Stride of the first dimension of A.
+
+ sA2: integer
+ Stride of the second dimension of A.
+
+ oA: integer
+ Starting index for A.
+
+ TAU: Float64Array
+ Output array for scalar factors of elementary reflectors.
+
+ sTAU: integer
+ Stride for TAU.
+
+ oTAU: integer
+ Starting index for TAU.
+
+ WORK: Float64Array
+ Workspace array.
+
+ sWORK: integer
+ Stride for WORK array.
+
+ oWORK: integer
+ Starting index for WORK.
+
+ LWORK: integer
+ Dimension of the array WORK.
+
+ Returns
+ -------
+ info: integer
+ Status code. 0 indicates success.
+
+ Examples
+ --------
+ > var A = new {{alias:@stdlib/array/float64}}([1,5,9,2,6,10,3,7,11,4,8,12]);
+ > var TAU = new {{alias:@stdlib/array/float64}}( 3 );
+ > var WORK = new {{alias:@stdlib/array/float64}}( 4 );
+ > {{alias}}.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 )
+ 0
+ > A
+ [~-10.344,~0.441,~0.793,~-11.794,~0.947,~0.919,~-13.244,~1.894,~0.0,~-14.694,~2.842,~0.0]
+ > TAU
+ [ ~1.097, ~1.084, 0.0 ]
+ > WORK
+ [ 4.0, ~-2.842, ~17.046, 0.0 ]
+
+ See Also
+ --------
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/types/index.d.ts b/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/types/index.d.ts
new file mode 100644
index 000000000000..4b7f1e08c22d
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/types/index.d.ts
@@ -0,0 +1,136 @@
+/*
+* @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';
+
+/**
+* Status code.
+*
+* ## Notes
+*
+* The status code indicates the following conditions:
+*
+* - if equal to zero, then the computation was successful.
+* - if less than zero, then the `-i`th argument had an illegal value.
+*/
+type StatusCode = number;
+
+/**
+* Interface describing `dgeqrf`.
+*/
+interface Routine {
+ /**
+ * Computes a QR factorization of a real M-by-N matrix `A`.
+ *
+ * @param order - storage layout
+ * @param M - number of rows in `A`
+ * @param N - number of columns in `A`
+ * @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 - output array of scalar factors (length `min(M,N)`)
+ * @param WORK - workspace array (length >= `M`)
+ * @param LWORK - dimension of the array `WORK`
+ * @returns status code (0 if successful)
+ *
+ * @example
+ * var Float64Array = require( '@stdlib/array/float64' );
+ *
+ * var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ * var TAU = new Float64Array( 3 );
+ * var WORK = new Float64Array( 4 );
+ *
+ * var info = dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+ * // returns 0
+ */
+ ( order: Layout, M: number, N: number, A: Float64Array, LDA: number, TAU: Float64Array, WORK: Float64Array, LWORK: number ): StatusCode;
+
+ /**
+ * Computes a QR factorization of a real M-by-N matrix `A` using alternative indexing semantics.
+ *
+ * @param M - number of rows in `A`
+ * @param N - number of columns in `A`
+ * @param A - input/output matrix
+ * @param strideA1 - stride of the first dimension of `A`
+ * @param strideA2 - stride of the second dimension of `A`
+ * @param offsetA - starting index for `A`
+ * @param TAU - output array of scalar factors (length `min(M,N)`)
+ * @param strideTAU - stride for TAU
+ * @param offsetTAU - starting index for TAU
+ * @param WORK - workspace array (length >= `M`)
+ * @param strideWORK - stride for `WORK`
+ * @param offsetWORK - starting index for `WORK`
+ * @param LWORK - dimension of the array `WORK`
+ * @returns status code
+ *
+ * @example
+ * var Float64Array = require( '@stdlib/array/float64' );
+ *
+ * var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ * var TAU = new Float64Array( 3 );
+ * var WORK = new Float64Array( 4 );
+ *
+ * var info = dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
+ * // returns 0
+ */
+ ndarray( M: number, N: number, A: Float64Array, strideA1: number, strideA2: number, offsetA: number, TAU: Float64Array, strideTAU: number, offsetTAU: number, WORK: Float64Array, strideWORK: number, offsetWORK: number, LWORK: number ): StatusCode;
+}
+
+/**
+* LAPACK routine to compute a QR factorization of a real M-by-N matrix `A`.
+*
+* @param order - storage layout
+* @param M - number of rows in `A`
+* @param N - number of columns in `A`
+* @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 - output array of scalar factors (length `min(M,N)`)
+* @param WORK - workspace array (length >= `M`)
+* @param LWORK - dimension of the array `WORK`
+* @returns status code (0 if successful)
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+* var TAU = new Float64Array( 3 );
+* var WORK = new Float64Array( 4 );
+*
+* var info = dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+* // returns 0
+*
+* @example
+* // ndarray interface:
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+* var TAU = new Float64Array( 3 );
+* var WORK = new Float64Array( 4 );
+*
+* var info = dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
+* // returns 0
+*/
+declare var dgeqrf: Routine;
+
+
+// EXPORTS //
+
+export = dgeqrf;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/types/test.ts b/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/types/test.ts
new file mode 100644
index 000000000000..e56976450e32
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/types/test.ts
@@ -0,0 +1,415 @@
+/*
+* @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.
+*/
+
+import dgeqrf = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 ); // $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, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 5, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( true, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( false, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( null, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( undefined, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( [], 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( {}, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( ( x: number ): number => x, 3, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', '5', 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', true, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', false, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', null, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', undefined, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', [], 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', {}, 4, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', ( x: number ): number => x, 4, A, 3, TAU, WORK, 4 ); // $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, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', 3, '5', A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, true, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, false, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, null, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, undefined, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, [], A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, {}, A, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, ( x: number ): number => x, A, 3, TAU, WORK, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fourth argument which is not a Float64Array...
+{
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', 3, 4, '5', 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, 5, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, true, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, false, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, null, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, undefined, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, [], 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, {}, 3, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, ( x: number ): number => x, 3, TAU, WORK, 4 ); // $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, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', 3, 4, A, '5', TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, true, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, false, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, null, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, undefined, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, [], TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, {}, TAU, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, ( x: number ): number => x, TAU, WORK, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a sixth argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', 3, 4, A, 3, '5', WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, 5, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, true, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, false, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, null, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, undefined, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, [], WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, {}, WORK, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, ( x: number ): number => x, WORK, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a seventh argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, '5', 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, 5, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, true, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, false, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, null, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, undefined, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, [], 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, {}, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, ( x: number ): number => x, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an eighth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, '5' ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, true ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, false ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, null ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, undefined ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, [] ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, {} ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, 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, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf(); // $ExpectError
+ dgeqrf( 'column-major' ); // $ExpectError
+ dgeqrf( 'column-major', 3 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3 ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK ); // $ExpectError
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4, 999 ); // $ExpectError
+}
+
+// Attached to the main export is an `ndarray` method which returns a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectType number
+}
+
+// The compiler throws an error if the `ndarray` method is provided a first argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( '5', 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( true, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( false, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( null, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( undefined, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( [], 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( {}, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( ( x: number ): number => x, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $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, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, '5', A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, true, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, false, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, null, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, undefined, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, [], A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, {}, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, ( x: number ): number => x, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a third argument which is not a Float64Array...
+{
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, '5', 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, 5, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, true, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, false, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, null, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, undefined, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, [], 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, {}, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, ( x: number ): number => x, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a fourth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, '5', 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, true, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, false, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, null, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, undefined, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, [], 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, {}, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, ( x: number ): number => x, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a fifth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, '5', 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, true, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, false, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, null, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, undefined, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, [], 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, {}, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, ( x: number ): number => x, 0, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a sixth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, '5', TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, true, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, false, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, null, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, undefined, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, [], TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, {}, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, ( x: number ): number => x, TAU, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a seventh argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, '5', 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, 5, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, true, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, false, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, null, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, undefined, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, [], 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, {}, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, ( x: number ): number => x, 1, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided an eighth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, '5', 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, true, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, false, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, null, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, undefined, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, [], 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, {}, 0, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, ( x: number ): number => x, 0, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a ninth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, '5', WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, true, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, false, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, null, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, undefined, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, [], WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, {}, WORK, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, ( x: number ): number => x, WORK, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a tenth argument which is not a Float64Array...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, '5', 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, 5, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, true, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, false, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, null, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, undefined, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, [], 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, {}, 1, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, ( x: number ): number => x, 1, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided an eleventh argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, '5', 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, true, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, false, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, null, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, undefined, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, [], 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, {}, 0, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, ( x: number ): number => x, 0, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a twelfth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, '5', 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, true, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, false, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, null, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, undefined, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, [], 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, {}, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, ( x: number ): number => x, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a thirteenth argument which is not a number...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, '5' ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, true ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, false ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, null ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, undefined ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, [] ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, {} ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided an unsupported number of arguments...
+{
+ const A = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
+ const TAU = new Float64Array( 3 );
+ const WORK = new Float64Array( 4 );
+
+ dgeqrf.ndarray(); // $ExpectError
+ dgeqrf.ndarray( 3 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0 ); // $ExpectError
+ dgeqrf.ndarray( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4, 999 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/examples/index.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/examples/index.js
new file mode 100644
index 000000000000..4ad4d90fafad
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/examples/index.js
@@ -0,0 +1,60 @@
+/**
+* @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 min = require( '@stdlib/math/base/special/min' );
+var dgeqrf = require( './../lib' );
+
+// Specify matrix meta data:
+var shape = [ 3, 4 ];
+var order = 'row-major';
+var strides = shape2strides( shape, order );
+
+// Create a matrix stored in linear memory:
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] ); // eslint-disable-line max-len
+
+console.log( 'A (unmodified):', ndarray2array( A, shape, strides, 0, order ) );
+
+// Output arrays:
+var TAU = new Float64Array( min( shape[ 0 ], shape[ 1 ] ) );
+var WORK = new Float64Array( shape[ 1 ] );
+
+// Compute the QR factorization in-place:
+var info = dgeqrf( order, shape[ 0 ], shape[ 1 ], A, strides[ 0 ], TAU, WORK, WORK.length );
+
+console.log( 'Status Code:', info );
+console.log( 'A (R + reflectors):', ndarray2array( A, shape, strides, 0, order ) );
+console.log( 'TAU:', TAU );
+console.log( 'WORK:', WORK );
+
+// Re-initialize arrays for the ndarray interface:
+A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+TAU = new Float64Array( min( shape[ 0 ], shape[ 1 ] ) );
+WORK = new Float64Array( shape[ 1 ] );
+
+// Compute the QR factorization again using the ndarray interface:
+info = dgeqrf.ndarray( shape[ 0 ], shape[ 1 ], A, strides[ 0 ], strides[ 1 ], 0, TAU, 1, 0, WORK, 1, 0, WORK.length );
+
+console.log( 'Status Code:', info );
+console.log( 'A (R + reflectors):', ndarray2array( A, shape, strides, 0, order ) );
+console.log( 'TAU:', TAU );
+console.log( 'WORK:', WORK );
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/base.js
new file mode 100644
index 000000000000..3a16d6aa028b
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/base.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 min = require( '@stdlib/math/base/special/min' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var dgeqr2 = require( './dgeqr2.js' );
+var dlarfb = require( './dlarfb.js' );
+var dlarft = require( './dlarft.js' );
+
+
+// MAIN //
+
+/**
+* Compute a QR factorization of a real M-by-N matrix `A`.
+*
+* ## Notes
+*
+* - On exit, the elements on and above the diagonal of the array contain the `min(M,N)-by-N` upper trapezoidal matrix `R` (`R` is upper triangular if `m >= n`).
+* - On exit, the elements below the diagonal, with the array `TAU`, represent the orthogonal matrix `Q` as a product of `min(m,n)` elementary reflectors.
+* - `LWORK >= 1`, if `MIN(M,N) = 0`, and `LWORK >= N`, otherwise. 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 in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @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 - output array of scalar factors (length `min(M,N)`)
+* @param {integer} strideTAU - stride for TAU
+* @param {NonNegativeInteger} offsetTAU - starting index for TAU
+* @param {Float64Array} WORK - workspace array (length >= `M`)
+* @param {integer} strideWORK - stride for `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, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+* var TAU = new Float64Array( 3 );
+* var WORK = new Float64Array( 4 );
+*
+* dgeqrf( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
+* // A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+* // TAU => [ ~1.097, ~1.084, 0.0 ]
+* // WORK => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+*/
+function dgeqrf( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point, max-len, max-params
+ var ldwork;
+ var lquery;
+ var inctau;
+ var lwkopt;
+ var nbmin;
+ var inca;
+ var taui;
+ var aii;
+ var iws;
+ var ib;
+ var nb;
+ var nx;
+ var i;
+ var k;
+
+ k = min( M, N );
+ nb = 32; // The optimal block size derived from fortran LAPACK call `ilaenv( 1, 'DGEQRF', ' ', m, n, -1, -1 )`
+ lquery = ( LWORK === -1 );
+
+ if ( lquery ) {
+ if ( k === 0 ) {
+ lwkopt = 1;
+ } else {
+ lwkopt = N * nb;
+ }
+ WORK[ offsetWORK ] = lwkopt;
+ return 0;
+ }
+
+ // Quick return if possible
+ if ( k === 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 crossover point derived from fortran LAPACK call `ilaenv( 3, 'DGEQRF', ' ', m, n, -1, -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 = floor( LWORK / ldwork );
+ nbmin = 2; // The minimal block size derived from fortran LAPACK call `ilaenv( 2, 'DGEQRF', ' ', m, n, -1, -1 )`
+ }
+ }
+ }
+
+ inca = nb * ( strideA1 + strideA2 );
+ inctau = nb * strideTAU;
+
+ aii = offsetA; // Index of A(i,i)
+ taui = offsetTAU; // Index of TAU(i)
+
+ if ( nb >= nbmin && nb < k && nx < k ) {
+ // Use blocked code initially
+ for ( i = 0; i < k - nx; i += nb ) {
+ ib = min( k - i, nb );
+
+ // Compute the QR factorization of the current block A(i:m,i:i+ib-1)
+ dgeqr2( M - i, ib, A, strideA1, strideA2, aii, TAU, strideTAU, taui, WORK, strideWORK, offsetWORK );
+
+ if ( i + ib < N ) {
+ // Form the triangular factor of the block reflector: H = H(i) H(i+1) . . . H(i+ib-1)
+ dlarft( 'forward', 'columns', M - i, ib, A, strideA1, strideA2, aii, TAU, strideTAU, taui, WORK, 1, N, offsetWORK );
+
+ // Apply H**T to A(i:m,i+ib:n) from the left
+ dlarfb( 'left', 'transpose', 'forward', 'columns', M - i, N - i - ib, ib, A, strideA1, strideA2, aii, WORK, 1, N, offsetWORK, A, strideA1, strideA2, aii + ( ib * strideA2 ), WORK, 1, ldwork, offsetWORK + ( ib * strideWORK ) );
+ }
+
+ aii += inca;
+ taui += inctau;
+ }
+ } else {
+ i = 0;
+ }
+
+ // Use unblocked code to factor the last or only block
+ if ( i <= k - 1 ) {
+ dgeqr2( M - i, N - i, A, strideA1, strideA2, aii, TAU, strideTAU, taui, WORK, strideWORK, offsetWORK );
+ }
+
+ WORK[ offsetWORK ] = iws;
+
+ return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dgeqrf;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dgeqr2.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dgeqr2.js
new file mode 100644
index 000000000000..6cc46926cd09
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dgeqr2.js
@@ -0,0 +1,99 @@
+/**
+* @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 dlarf1f = require( '@stdlib/lapack/base/dlarf1f' ).ndarray;
+var Float64Array = require( '@stdlib/array/float64' );
+var min = require( '@stdlib/math/base/special/min' );
+var dlarfg = require( './dlarfg.js' );
+
+
+// MAIN //
+
+/**
+* Compute a QR factorization of a general rectangular matrix using an unblocked algorithm.
+*
+* ## Notes
+*
+* - On exit, the elements on and above the diagonal of A contain the min(M,N) by `N` upper trapezoidal matrix R (R is upper triangular if M >= N) matrix `R`.
+* - The elements below the diagonal, with the array `TAU`, represent the orthogonal matrix `Q` as a product of elementary reflectors.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @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 - output array of scalar factors (length min(M,N))
+* @param {integer} strideTAU - stride for TAU
+* @param {NonNegativeInteger} offsetTAU - starting index for TAU
+* @param {Float64Array} WORK - workspace array (length >= M)
+* @param {integer} strideWORK - stride for WORK
+* @param {NonNegativeInteger} offsetWORK - starting index for WORK
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+* var TAU = new Float64Array( 3 );
+* var work = new Float64Array( 4 );
+*
+* dgeqr2( 3, 4, A, 1, 3, 0, TAU, 1, 0, work, 1, 0 );
+* // A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+* // TAU => [ ~1.097, ~1.084, 0.0 ]
+* // work => [ ~-1.894, ~-2.842, ~17.046, 0.0 ]
+*/
+function dgeqr2( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point, max-len, max-params
+ var taui;
+ var aii;
+ var out;
+ var K;
+ var i;
+
+ K = min( M, N );
+ out = new Float64Array( 2 );
+
+ aii = offsetA; // Index of A(i,i)
+ taui = offsetTAU; // Index of TAU(i)
+
+ for ( i = 0; i < K; i++ ) {
+ // Generate elementary reflector H(i) to annihilate A(i+1:m,i)
+ out[ 0 ] = A[ aii ];
+ dlarfg( M - i, A, strideA1, aii + ( min( 1, M - 1 - i ) * strideA1 ), out, 1, 0 );
+ A[ aii ] = out[ 0 ];
+ TAU[ taui ] = out[ 1 ];
+
+ if ( i < N - 1 ) {
+ // Apply H(i) to A(i:m,i+1:n) from the left
+ dlarf1f( 'left', M - i, N - i - 1, A, strideA1, aii, TAU[ taui ], A, strideA1, strideA2, aii + strideA2, WORK, strideWORK, offsetWORK );
+ }
+ aii += strideA1 + strideA2;
+ taui += strideTAU;
+ }
+ return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dgeqr2;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dgeqrf.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dgeqrf.js
new file mode 100644
index 000000000000..0d264edca6f6
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dgeqrf.js
@@ -0,0 +1,105 @@
+/**
+* @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 isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major-string' );
+var max = require( '@stdlib/math/base/special/fast/max' );
+var base = require( './base.js' );
+
+
+// MAIN //
+
+/**
+* Compute a QR factorization of a real M-by-N matrix `A`.
+*
+* ## Notes
+*
+* - On exit, the elements on and above the diagonal of the array contain the `min(M,N)-by-N` upper trapezoidal matrix `R` (`R` is upper triangular if `m >= n`).
+* - On exit, the elements below the diagonal, with the array `TAU`, represent the orthogonal matrix `Q` as a product of `min(m,n)` elementary reflectors.
+* - `LWORK >= 1`, if `MIN(M,N) = 0`, and `LWORK >= N`, otherwise. 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
+*
+* @param {string} order - storage layout
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @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 - output array of scalar factors (length `min(M,N)`)
+* @param {Float64Array} WORK - workspace array (length >= `M`)
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @throws {TypeError} first argument must be a valid order
+* @throws {RangeError} second argument must be a non-negative integer
+* @throws {RangeError} third argument must be a non-negative integer
+* @throws {RangeError} fifth argument must be a valid `LDA` value
+* @throws {RangeError} eight argument must be a valid `LWORK` value
+* @returns {integer} status code (0 if successful)
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+* var TAU = new Float64Array( 3 );
+* var WORK = new Float64Array( 4 );
+*
+* dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+* // A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+* // TAU => [ ~1.097, ~1.084, 0.0 ]
+* // WORK => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+*/
+function dgeqrf( order, M, N, A, LDA, TAU, WORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point
+ var sa1;
+ var sa2;
+
+ if ( !isLayout( order ) ) {
+ throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
+ }
+ if ( M < 0 ) {
+ throw new RangeError( format( 'invalid argument. Second argument must be a nonnegative integer. Value: `%d`.', M ) );
+ }
+ if ( N < 0 ) {
+ throw new RangeError( format( 'invalid argument. Third argument must be a nonnegative integer. Value: `%d`.', N ) );
+ }
+ if ( isRowMajor( order ) ) {
+ if ( LDA < max( 1, N ) ) {
+ throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to `max(1,N)`. Value: `%d`.', LDA ) );
+ }
+ } else if ( LDA < max( 1, M ) ) {
+ throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to `max(1,M)`. Value: `%d`.', LDA ) );
+ }
+ if ( LWORK !== -1 && ( LWORK <= 0 || ( M > 0 && LWORK < max( 1, N ) ) ) ) {
+ throw new RangeError( format( 'invalid argument. Eighth argument must be a valid LWORK value. Value: `%d`.', LWORK ) );
+ }
+ if ( order === 'column-major' ) {
+ sa1 = 1;
+ sa2 = LDA;
+ } else {
+ sa1 = LDA;
+ sa2 = 1;
+ }
+ return base( M, N, A, sa1, sa2, 0, TAU, 1, 0, WORK, 1, 0, LWORK );
+}
+
+
+// EXPORTS //
+
+module.exports = dgeqrf;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dlarfb.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dlarfb.js
new file mode 100644
index 000000000000..96be470af5ea
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/dlarfg.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dlarfg.js
new file mode 100644
index 000000000000..04ab125dc7e7
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dlarfg.js
@@ -0,0 +1,142 @@
+/**
+* @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 dnrm2 = require( '@stdlib/blas/base/dnrm2' ).ndarray;
+var sign = require( '@stdlib/math/base/special/copysign' );
+var dlamch = require( '@stdlib/lapack/base/dlamch' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
+var dlapy2 = require( '@stdlib/lapack/base/dlapy2' );
+
+
+// MAIN //
+
+/**
+* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; X]` zeros out `X`.
+*
+* `H` is a Householder matrix with the form:
+*
+* ```tex
+* H \cdot \begin{bmatrix} \alpha \\ x \end{bmatrix} = \begin{bmatrix} \beta \\ 0 \end{bmatrix}, \quad \text{and} \quad H^T H = I
+* ```
+*
+* where:
+*
+* - `tau` is a scalar
+* - `X` is a vector of length `N-1`
+* - `beta` is a scalar value
+* - `H` is an orthogonal matrix known as a Householder reflector.
+*
+* The reflector `H` is constructed in the form:
+*
+* ```tex
+* H = I - \tau \begin{bmatrix}1 \\ v \end{bmatrix} \begin{bmatrix}1 & v^T \end{bmatrix}
+* ```
+*
+* where:
+*
+* - `tau` is a real scalar
+* - `V` is a real vector of length `N-1` that defines the Householder vector
+* - The vector `[1; V]` is the Householder direction.
+*
+* The values of `tau` and `V` are chosen so that applying `H` to the vector `[alpha; X]` results in a new vector `[beta; 0]`, i.e., only the first component remains nonzero. The reflector matrix `H` is symmetric and orthogonal, satisfying `H^T = H` and `H^T H = I`
+*
+* ## Special cases
+*
+* - If all elements of `X` are zero, then `tau = 0` and `H = I`, the identity matrix.
+* - Otherwise, `tau` satisfies `1 ≤ tau ≤ 2`, ensuring numerical stability in transformations.
+*
+* ## Notes
+*
+* - `X` should have `N-1` indexed elements
+* - The output array contains the following two elements: `alpha` and `tau`
+*
+* @private
+* @param {NonNegativeInteger} N - number of rows/columns of the elementary reflector `H`
+* @param {Float64Array} X - input vector
+* @param {integer} strideX - stride length for `X`
+* @param {NonNegativeInteger} offsetX - starting index of `X`
+* @param {Float64Array} out - output array
+* @param {integer} strideOut - stride length for `out`
+* @param {NonNegativeInteger} offsetOut - starting index of `out`
+* @returns {void}
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var X = new Float64Array( [ 2.0, 3.0, 4.0 ] );
+* var out = new Float64Array( [ 4.0, 0.0 ] );
+*
+* dlarfg( 4, X, 1, 0, out, 1, 0 );
+* // X => [ ~0.19, ~0.28, ~0.37 ]
+* // out => [ ~-6.7, ~1.6 ]
+*/
+function dlarfg( N, X, strideX, offsetX, out, strideOut, offsetOut ) {
+ var safemin;
+ var rsafmin;
+ var xnorm;
+ var alpha;
+ var beta;
+ var tau;
+ var knt;
+ var i;
+
+ if ( N <= 1 ) {
+ out[ offsetOut + strideOut ] = 0.0;
+ return;
+ }
+
+ xnorm = dnrm2( N - 1, X, strideX, offsetX );
+ alpha = out[ offsetOut ];
+
+ if ( xnorm === 0.0 ) {
+ out[ strideOut + offsetOut ] = 0.0;
+ } else {
+ beta = -1.0 * sign( dlapy2( alpha, xnorm ), alpha );
+ safemin = dlamch( 'safemin' ) / dlamch( 'epsilon' );
+ knt = 0;
+ if ( abs( beta ) < safemin ) {
+ rsafmin = 1.0 / safemin;
+ while ( abs( beta ) < safemin && knt < 20 ) {
+ knt += 1;
+ dscal( N-1, rsafmin, X, strideX, offsetX );
+ beta *= rsafmin;
+ alpha *= rsafmin;
+ }
+ xnorm = dnrm2( N - 1, X, strideX, offsetX );
+ beta = -1.0 * sign( dlapy2( alpha, xnorm ), alpha );
+ }
+ tau = ( beta - alpha ) / beta;
+ dscal( N-1, 1.0 / ( alpha - beta ), X, strideX, offsetX );
+ for ( i = 0; i < knt; i++ ) {
+ beta *= safemin;
+ }
+
+ out[ offsetOut ] = beta;
+ out[ strideOut + offsetOut ] = tau;
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = dlarfg;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dlarft.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dlarft.js
new file mode 100644
index 000000000000..e6567023f56f
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/dtrmm.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/dtrmm.js
new file mode 100644
index 000000000000..f360237c6ef3
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/index.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/index.js
new file mode 100644
index 000000000000..bf769bf63fef
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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 compute a QR factorization of a real M-by-N matrix `A`.
+*
+* @module @stdlib/lapack/base/dgeqrf
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var dgeqrf = require( '@stdlib/lapack/base/dgeqrf' );
+*
+* var A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+* var TAU = new Float64Array( 3 );
+* var WORK = new Float64Array( 4 );
+*
+* dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, 4 );
+* // A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+* // TAU => [ ~1.097, ~1.084, 0.0 ]
+* // WORK => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+*/
+
+// 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 dgeqrf;
+var tmp = tryRequire( join( __dirname, './native.js' ) );
+if ( isError( tmp ) ) {
+ dgeqrf = main;
+} else {
+ dgeqrf = tmp;
+}
+
+
+// EXPORTS //
+
+module.exports = dgeqrf;
+
+// exports: { "ndarray": "dgeqrf.ndarray" }
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/left_backward_columns.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/left_backward_columns.js
new file mode 100644
index 000000000000..5a71b0c9aec0
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/left_backward_rows.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/left_backward_rows.js
new file mode 100644
index 000000000000..89bedab3ecee
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/left_forward_columns.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/left_forward_columns.js
new file mode 100644
index 000000000000..e7b134abf652
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/left_forward_rows.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/left_forward_rows.js
new file mode 100644
index 000000000000..d62c3646d67f
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/main.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/main.js
new file mode 100644
index 000000000000..9a9aff4463dd
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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 dgeqrf = require( './dgeqrf.js' );
+var ndarray = require( './ndarray.js' );
+
+
+// MAIN //
+
+setReadOnly( dgeqrf, 'ndarray', ndarray );
+
+
+// EXPORTS //
+
+module.exports = dgeqrf;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/ndarray.js
new file mode 100644
index 000000000000..485240a6a405
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/ndarray.js
@@ -0,0 +1,88 @@
+/**
+* @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 base = require( './base.js' );
+
+
+// MAIN //
+
+/**
+* Compute a QR factorization of a real M-by-N matrix `A` using alternative indexing semantics.
+*
+* ## Notes
+*
+* - On exit, the elements on and above the diagonal of the array contain the `min(M,N)-by-N` upper trapezoidal matrix `R` (`R` is upper triangular if `m >= n`).
+* - On exit, the elements below the diagonal, with the array `TAU`, represent the orthogonal matrix `Q` as a product of `min(m,n)` elementary reflectors.
+* - `LWORK >= 1`, if `MIN(M,N) = 0`, and `LWORK >= N`, otherwise. 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
+*
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @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 - output array of scalar factors (length `min(M,N)`)
+* @param {integer} strideTAU - stride for TAU
+* @param {NonNegativeInteger} offsetTAU - starting index for TAU
+* @param {Float64Array} WORK - workspace array (length >= `M`)
+* @param {integer} strideWORK - stride for `WORK`
+* @param {NonNegativeInteger} offsetWORK - starting index for `WORK`
+* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
+* @throws {RangeError} first argument must be a non-negative integer
+* @throws {RangeError} second argument must be a non-negative integer
+* @throws {RangeError} thirteenth argument must be a valid `LWORK` value
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+* var TAU = new Float64Array( 3 );
+* var WORK = new Float64Array( 4 );
+*
+* dgeqrf( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
+* // A => [ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
+* // TAU => [ ~1.097, ~1.084, 0.0 ]
+* // WORK => [ 4.0, ~-2.842, ~17.046, 0.0 ]
+*/
+function dgeqrf( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point
+ if ( M < 0 ) {
+ throw new RangeError( format( 'invalid argument. Second argument must be a nonnegative integer. Value: `%d`.', M ) );
+ }
+ if ( N < 0 ) {
+ throw new RangeError( format( 'invalid argument. Third argument must be a nonnegative integer. Value: `%d`.', N ) );
+ }
+ if ( LWORK !== -1 && ( LWORK <= 0 || ( M > 0 && LWORK < max( 1, N ) ) ) ) {
+ throw new RangeError( format( 'invalid argument. Eight argument must be a valid LWORK value. Value: `%d`.', LWORK ) );
+ }
+ return base( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
+}
+
+
+// EXPORTS //
+
+module.exports = dgeqrf;
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/right_backward_columns.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/right_backward_columns.js
new file mode 100644
index 000000000000..20f98fd01d52
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/right_backward_rows.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/right_backward_rows.js
new file mode 100644
index 000000000000..e10b8b011af6
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/right_forward_columns.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/right_forward_columns.js
new file mode 100644
index 000000000000..0c7574a3b7b9
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/lib/right_forward_rows.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/lib/right_forward_rows.js
new file mode 100644
index 000000000000..830e208c4700
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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/dgeqrf/package.json b/lib/node_modules/@stdlib/lapack/base/dgeqrf/package.json
new file mode 100644
index 000000000000..9e0f47dfa950
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/package.json
@@ -0,0 +1,69 @@
+{
+ "name": "@stdlib/lapack/base/dgeqrf",
+ "version": "0.0.0",
+ "description": "LAPACK routine to compute a QR factorization of a real `M-by-N` matrix `A`.",
+ "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",
+ "dgelq2",
+ "reflector",
+ "linear",
+ "algebra",
+ "subroutines",
+ "array",
+ "ndarray",
+ "matrix",
+ "float64",
+ "double",
+ "float64array"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/fixtures/blocked.json b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/fixtures/blocked.json
new file mode 100644
index 000000000000..9bbfca89f40a
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/fixtures/blocked.json
@@ -0,0 +1,75625 @@
+{
+ "order": "column-major",
+ "M": 129,
+ "N": 129,
+ "A": [
+ 1,
+ 2,
+ 3,
+ 4,
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+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/fixtures/unblocked.json b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/fixtures/unblocked.json
new file mode 100644
index 000000000000..eb6fb916f907
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/fixtures/unblocked.json
@@ -0,0 +1,40 @@
+{
+ "order": "column-major",
+ "M": 3,
+ "N": 4,
+ "A": [
+ 1, 5, 9,
+ 2, 6, 10,
+ 3, 7, 11,
+ 4, 8, 12
+ ],
+ "strideA1": 1,
+ "strideA2": 3,
+ "offsetA": 0,
+ "LDA": 3,
+ "A_mat": [
+ [ 1, 2, 3, 4 ],
+ [ 5, 6, 7, 8 ],
+ [ 9, 10, 11, 12 ]
+ ],
+ "TAU": [ 0, 0, 0 ],
+ "strideTAU": 1,
+ "offsetTAU": 0,
+ "WORK": [ 0, 0, 0, 0 ],
+ "strideWORK": 1,
+ "offsetWORK": 0,
+ "A_out": [
+ -1.03440804327886031E+001, 4.40758510980594265E-001, 7.93365319765069743E-001,
+ -1.17941851663570922E+001, 9.47204445556625418E-001, 9.18917235137354349E-001,
+ -1.32442898999255867E+001, 1.89440889111325461E+000, 1.55431223447521916E-015,
+ -1.46943946334940847E+001, 2.84161333666988725E+000, 4.44089209850062616E-015
+ ],
+ "A_out_mat": [
+ [ -1.03440804327886031E+001, -1.17941851663570922E+001, -1.32442898999255867E+001, -1.46943946334940847E+001 ],
+ [ 4.40758510980594265E-001, 9.47204445556625418E-001, 1.89440889111325461E+000, 2.84161333666988725E+000 ],
+ [ 7.93365319765069743E-001, 9.18917235137354349E-001, 1.55431223447521916E-015, 4.44089209850062616E-015 ]
+ ],
+ "TAU_out": [ 1.09667364890456631E+000, 1.08435825495645477E+000, 0.00000000000000000E+000 ],
+ "WORK_out": [ 4.00000000000000000E+000, -2.84161333666989080E+000, 1.70464519250255933E+001, 0.00000000000000000E+000 ],
+ "info": 0
+}
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/test.dgeqrf.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/test.dgeqrf.js
new file mode 100644
index 000000000000..72088d26d799
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/test.dgeqrf.js
@@ -0,0 +1,424 @@
+/**
+* @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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var isAlmostEqual = require( '@stdlib/assert/is-almost-equal-float64array' );
+var dlarf1f = require( '@stdlib/lapack/base/dlarf1f' ).ndarray;
+var min = require( '@stdlib/math/base/special/min' );
+var dgeqrf = require( './../lib/dgeqrf.js' );
+
+
+// VARIABLES //
+
+var opts = {
+ 'dtype': 'float64'
+};
+
+
+// FIXTURES //
+
+var UNBLOCKED = require( './fixtures/unblocked.json' );
+var BLOCKED = require( './fixtures/blocked.json' );
+
+
+// FUNCTIONS //
+
+/**
+* Verifies that the orthogonal matrix Q satisfies Q^T * Q = I by checking that a random vector x is recovered after applying Q then Q^T.
+*
+* @private
+* @param {Float64Array} A - matrix after `dgeqrf` (contains R and Householder vectors)
+* @param {Float64Array} TAU - scalar factors of the elementary reflectors
+* @param {NonNegativeInteger} M - number of rows in A
+* @param {NonNegativeInteger} N - number of columns in A
+* @param {NonNegativeInteger} LDA - leading dimension of A
+* @param {NonNegativeInteger} maxULP - maximum allowed ULP difference
+* @returns {boolean} true if the round-trip recovers x within maxULP ULPs
+*/
+function verifyQOrthogonal( A, TAU, M, N, LDA, maxULP ) { // eslint-disable-line stdlib/vars-order
+ var work = new Float64Array( M );
+ var x = discreteUniform( M, 100.0, 200.0, opts );
+ var xOrig = new Float64Array( x );
+ var y = new Float64Array( x );
+ var K = min( M, N );
+ var i;
+
+ // y = Q * x
+ for ( i = 0; i < K; i++ ) {
+ if ( TAU[ i ] !== 0.0 ) {
+ dlarf1f( 'left', M - i, 1, A, 1, ( i * LDA ) + i, TAU[ i ], y, 1, M, i, work, 1, 0 );
+ }
+ }
+
+ // y = Q^T * (Q * x) = x
+ for ( i = K - 1; i >= 0; i-- ) {
+ if ( TAU[ i ] !== 0.0 ) {
+ dlarf1f( 'left', M - i, 1, A, 1, ( i * LDA ) + i, TAU[ i ], y, 1, M, i, work, 1, 0 );
+ }
+ }
+
+ return isAlmostEqual( y, xOrig, maxULP );
+}
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof dgeqrf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function has an arity of 8', function test( t ) {
+ t.strictEqual( dgeqrf.length, 8, '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, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+ TAU = new Float64Array( 3 );
+ WORK = new Float64Array( 4 );
+
+ 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() {
+ dgeqrf( value, 3, 4, A, 3, TAU, WORK, 4 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a second argument which is smaller than 0', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+ TAU = new Float64Array( 3 );
+ WORK = new Float64Array( 4 );
+
+ 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() {
+ dgeqrf( 'column-major', value, 4, A, 3, TAU, WORK, 4 );
+ };
+ }
+});
+
+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, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+ TAU = new Float64Array( 3 );
+ WORK = new Float64Array( 4 );
+
+ 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() {
+ dgeqrf( 'column-major', 3, value, A, 3, TAU, WORK, 4 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided an fifth argument which is not a valid LDA value (column-major)', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+ TAU = new Float64Array( 3 );
+ WORK = new Float64Array( 4 );
+
+ 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() {
+ dgeqrf( 'column-major', 3, 4, A, value, TAU, WORK, 4 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided an fifth argument which is not a valid LDA value (row-major)', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+ TAU = new Float64Array( 3 );
+ WORK = new Float64Array( 4 );
+
+ values = [
+ 3,
+ 2,
+ 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() {
+ dgeqrf( 'row-major', 3, 4, A, value, TAU, WORK, 4 );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided an eighth argument which is not a valid LWORK value', function test( t ) {
+ var values;
+ var WORK;
+ var TAU;
+ var A;
+ var i;
+
+ A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+ TAU = new Float64Array( 3 );
+ WORK = new Float64Array( 4 );
+
+ values = [
+ 3,
+ 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() {
+ dgeqrf( 'column-major', 3, 4, A, 3, TAU, WORK, value );
+ };
+ }
+});
+
+tape( 'the function quick returns when `LWORK` is equal to -1', function test( t ) {
+ var expectedWORK;
+ var expectedTAU;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = UNBLOCKED;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A );
+ expectedTAU = new Float64Array( data.TAU );
+ expectedWORK = new Float64Array( data.WORK );
+ expectedWORK[ 0 ] = 128;
+
+ info = dgeqrf( data.order, data.M, data.N, A, data.LDA, TAU, WORK, -1 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( TAU, expectedTAU, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+
+ expectedWORK[ 0 ] = 1;
+
+ info = dgeqrf( data.order, data.M, 0, A, data.LDA, TAU, WORK, -1 );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( TAU, expectedTAU, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function quick returns when `min(M, N)` is equal to 0', function test( t ) {
+ var expectedWORK;
+ var expectedTAU;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = UNBLOCKED;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A );
+ expectedTAU = new Float64Array( data.TAU );
+ expectedWORK = new Float64Array( data.WORK );
+ expectedWORK[ 0 ] = 1;
+
+ info = dgeqrf( data.order, 0, 0, A, data.LDA, TAU, WORK, data.LWORK );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( TAU, expectedTAU, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function computes a QR factorization (unblocked, column-major)', function test( t ) {
+ var expectedWORK;
+ var expectedTAU;
+ var expectedA;
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = UNBLOCKED;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ expectedA = new Float64Array( data.A_out );
+ expectedTAU = new Float64Array( data.TAU_out );
+ expectedWORK = new Float64Array( data.WORK_out );
+
+ info = dgeqrf( data.order, data.M, data.N, A, data.LDA, TAU, WORK, data.LWORK ); // eslint-disable-line max-len
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( A, expectedA, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( TAU, expectedTAU, 1 ), true, 'returns expected value' );
+ t.strictEqual( isAlmostEqual( WORK, expectedWORK, 1 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function computes a QR factorization (blocked, column-major)', function test( t ) {
+ var info;
+ var data;
+ var WORK;
+ var TAU;
+ var A;
+
+ data = BLOCKED;
+
+ A = new Float64Array( data.A );
+ TAU = new Float64Array( data.TAU );
+ WORK = new Float64Array( data.WORK );
+
+ info = dgeqrf( data.order, data.M, data.N, A, data.LDA, TAU, WORK, data.LWORK ); // eslint-disable-line max-len
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.ok( verifyQOrthogonal( A, TAU, data.M, data.N, data.LDA, 100 ), 'round-trip Q^T * (Q * x) recovers x' );
+ t.end();
+});
+
+tape( 'the function computes a QR factorization (reduced blocksize)', function test( t ) {
+ var LWORK;
+ var info;
+ var WORK;
+ var LDA;
+ var TAU;
+ var A;
+ var i;
+ var M;
+ var N;
+
+ M = 129;
+ N = 129;
+ LDA = 129;
+ LWORK = 516;
+
+ A = new Float64Array( M * N );
+ for ( i = 0; i < M * N; i++ ) {
+ A[ i ] = i + 1;
+ }
+ TAU = new Float64Array( min( M, N ) );
+ WORK = new Float64Array( LWORK );
+
+ info = dgeqrf( 'column-major', M, N, A, LDA, TAU, WORK, LWORK );
+ t.strictEqual( info, 0, 'returns expected value' );
+ t.strictEqual( WORK[ 0 ], 4128, 'first element of WORK is iws' );
+ t.ok( verifyQOrthogonal( A, TAU, M, N, LDA, 100 ), 'round-trip Q^T * (Q * x) recovers x' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/test.js b/lib/node_modules/@stdlib/lapack/base/dgeqrf/test/test.js
new file mode 100644
index 000000000000..5be2a9e10963
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dgeqrf/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 dgeqrf = 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 dgeqrf, '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 dgeqrf.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 dgeqrf = proxyquire( './../lib', {
+ '@stdlib/utils/try-require': tryRequire
+ });
+
+ t.strictEqual( dgeqrf, 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 dgeqrf;
+ var main;
+
+ main = require( './../lib/dgeqrf.js' );
+
+ dgeqrf = proxyquire( './../lib', {
+ '@stdlib/utils/try-require': tryRequire
+ });
+
+ t.strictEqual( dgeqrf, main, 'returns expected value' );
+ t.end();
+
+ function tryRequire() {
+ return new Error( 'Cannot find module' );
+ }
+});