From 1de01c08eb1918f8a253c2dc05d1c6c204f78289 Mon Sep 17 00:00:00 2001 From: Prajjwal Bajpai Date: Fri, 7 Aug 2026 19:46:27 +0530 Subject: [PATCH 1/2] feat: add `lapack/base/dgeqrf` --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: passed - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - 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+ +`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/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 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"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' ); + } +}); From 4505fea127bb2db8c791e42a85abc82ebad428c9 Mon Sep 17 00:00:00 2001 From: Prajjwal Bajpai Date: Fri, 7 Aug 2026 19:50:20 +0530 Subject: [PATCH 2/2] docs: add repl.txt --- .../@stdlib/lapack/base/dgeqrf/docs/repl.txt | 132 ++++++++++++++++++ 1 file changed, 132 insertions(+) create mode 100644 lib/node_modules/@stdlib/lapack/base/dgeqrf/docs/repl.txt 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 + --------