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feat: add blas/ext/base/gtriu2tril
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‎lib/node_modules/@stdlib/blas/ext/base/gtriu2tril/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# gtriu2tril
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> Reflect the upper triangular part of a matrix A into the lower triangular part of another matrix B.
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<section class="usage">
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## Usage
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```javascript
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var gtriu2tril = require( '@stdlib/blas/ext/base/gtriu2tril' );
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```
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#### gtriu2tril( order, M, N, k, A, LDA, B, LDB )
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Reflects the upper triangular part of a matrix `A` into the lower triangular part of another matrix `B`.
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```javascript
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var A = [ 1.0, 2.0, 3.0, 4.0 ];
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var B = [ 0.0, 0.0, 0.0, 0.0 ];
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gtriu2tril( 'row-major', 2, 2, 0, A, 2, B, 2 );
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// B => [ 1.0, 0.0, 2.0, 4.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **M**: number of rows in `A`.
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- **N**: number of columns in `A`.
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- **k**: diagonal below which to ignore. A value of `k = 0` refers to the main diagonal and `k > 0` refers to a diagonal above the main diagonal. When `k > 0`, the function reflects only part of the upper triangle, excluding the main diagonal and the first `k-1` super-diagonals.
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- **A**: input matrix.
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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- **B**: output matrix.
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- **LDB**: stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`).
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Setting the `k` parameter to a value greater than `0` excludes the main diagonal (and, for larger values, additional super-diagonals). For example, to reflect only the elements strictly above the main diagonal,
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```javascript
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var A = [ 1.0, 2.0, 3.0, 4.0 ];
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var B = [ 0.0, 0.0, 0.0, 0.0 ];
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gtriu2tril( 'row-major', 2, 2, 1, A, 2, B, 2 );
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// B => [ 0.0, 0.0, 2.0, 0.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial arrays...
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var A0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var B0 = new Float64Array( 5 );
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// Create offset views...
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var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var B1 = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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gtriu2tril( 'row-major', 2, 2, 0, A1, 2, B1, 2 );
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// B0 => <Float64Array>[ 0.0, 2.0, 0.0, 3.0, 5.0 ]
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```
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#### gtriu2tril.ndarray( M, N, k, A, sa1, sa2, oa, B, sb1, sb2, ob )
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Reflects the upper triangular part of a matrix `A` into the lower triangular part of another matrix `B` using alternative indexing semantics.
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```javascript
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var A = [ 1.0, 2.0, 3.0, 4.0 ];
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var B = [ 0.0, 0.0, 0.0, 0.0 ];
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gtriu2tril.ndarray( 2, 2, 0, A, 2, 1, 0, B, 2, 1, 0 );
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// B => [ 1.0, 0.0, 2.0, 4.0 ]
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```
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The function has the following parameters:
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- **M**: number of rows in `A`.
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- **N**: number of columns in `A`.
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- **k**: diagonal below which to ignore.
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- **A**: input matrix.
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- **sa1**: stride of the first dimension of `A`.
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- **sa2**: stride of the second dimension of `A`.
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- **oa**: starting index for `A`.
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- **B**: output matrix.
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- **sb1**: stride of the first dimension of `B`.
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- **sb2**: stride of the second dimension of `B`.
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- **ob**: starting index for `B`.
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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,
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```javascript
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var A = [ 1.0, 2.0, 3.0, 4.0 ];
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var B = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gtriu2tril.ndarray( 2, 2, 0, A, 2, 1, 0, B, 2, 1, 2 );
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// B => [ 0.0, 0.0, 1.0, 0.0, 2.0, 4.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
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- Elements outside of the reflected region are left unchanged.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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<!-- eslint-disable max-len -->
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```javascript
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var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
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var uniform = require( '@stdlib/random/array/discrete-uniform' );
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var numel = require( '@stdlib/ndarray/base/numel' );
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var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
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var gtriu2tril = require( '@stdlib/blas/ext/base/gtriu2tril' );
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var shape = [ 5, 8 ];
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var order = 'row-major';
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var strides = shape2strides( shape, order );
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var N = numel( shape );
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var A = uniform( N, -10, 10, {
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'dtype': 'generic'
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});
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console.log( ndarray2array( A, shape, strides, 0, order ) );
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var B = uniform( N, -10, 10, {
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'dtype': 'generic'
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});
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var shapeB = [ shape[ 1 ], shape[ 0 ] ];
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var stridesB = shape2strides( shapeB, order );
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console.log( ndarray2array( B, shapeB, stridesB, 0, order ) );
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gtriu2tril( order, shape[ 0 ], shape[ 1 ], 0, A, strides[ 0 ], B, stridesB[ 0 ] );
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console.log( ndarray2array( B, shapeB, stridesB, 0, order ) );
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```
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</section>
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<!-- /.examples -->
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<section class="related">
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</section>
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<!-- /.related -->
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<section class="links">
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/ext/base/gtriu2tril/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2026 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var zeros = require( '@stdlib/array/zeros' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var gtriu2tril = require( './../lib' );
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// VARIABLES //
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var LAYOUTS = [
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'row-major',
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'column-major'
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];
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {string} order - storage layout
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* @param {PositiveInteger} N - number of elements along each dimension
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* @returns {Function} benchmark function
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*/
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function createBenchmark( order, N ) {
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var A = zeros( N*N, 'generic' );
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var B = zeros( N*N, 'generic' );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var z;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = gtriu2tril( order, N, N, 0, A, N, B, N );
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if ( isnan( z[ i%z.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( z[ i%z.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var min;
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var max;
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var ord;
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var N;
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var f;
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var i;
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var k;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( k = 0; k < LAYOUTS.length; k++ ) {
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ord = LAYOUTS[ k ];
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for ( i = min; i <= max; i++ ) {
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N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
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f = createBenchmark( ord, N );
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bench( format( '%s::square_matrix:order=%s,size=%d', pkg, ord, N*N ), f );
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}
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}
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}
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main();

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