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lib/node_modules/@stdlib/blas/base/dsyr2/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# dsyr2
+
+> Perform the symmetric rank 2 operation `A = α*x*y^T + α*y*x^T + A`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dsyr2 = require( '@stdlib/blas/base/dsyr2' );
+```
+
+#### dsyr2( order, uplo, N, α, x, sx, y, sy, A, LDA )
+
+Performs the symmetric rank 2 operation `A = α*x*y^T + α*y*x^T + A`, where `α` is a scalar, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
+var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dsyr2( 'row-major', 'upper', 3, 1.0, x, 1, y, 1, A, 3 );
+// A => <Float64Array>[ 3.0, 6.0, 9.0, 0.0, 9.0, 14.0, 0.0, 0.0, 19.0 ]
+```
+
+The function has the following parameters:
+
+- **order**: storage layout.
+- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced.
+- **N**: number of elements along each dimension of `A`.
+- **α**: scalar constant.
+- **x**: first input [`Float64Array`][mdn-float64array].
+- **sx**: index increment for `x`.
+- **y**: second input [`Float64Array`][mdn-float64array].
+- **sy**: index increment for `y`.
+- **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
+- **lda**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+
+The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over every other element of `x`,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
+var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dsyr2( 'row-major', 'upper', 3, 1.0, x, 2, y, 1, A, 3 );
+// A => <Float64Array>[ 3.0, 7.0, 11.0, 0.0, 13.0, 21.0, 0.0, 0.0, 31.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var x0 = new Float64Array( [ 0.0, 1.0, 1.0, 1.0 ] );
+var y0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
+
+// Create offset views...
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dsyr2( 'row-major', 'upper', 3, 1.0, x1, 1, y1, 1, A, 3 );
+// A => <Float64Array>[ 3.0, 5.0, 7.0, 0.0, 5.0, 7.0, 0.0, 0.0, 7.0 ]
+```
+
+#### dsyr2.ndarray( uplo, N, α, x, sx, ox, y, sy, oy, A, sa1, sa2, oa )
+
+Performs the symmetric rank 2 operation `A = α*x*y^T + α*y*x^T + A`, using alternative indexing semantics and where `α` is a scalar, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
+var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dsyr2.ndarray( 'upper', 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
+// A => <Float64Array>[ 3.0, 6.0, 9.0, 0.0, 9.0, 14.0, 0.0, 0.0, 19.0 ]
+```
+
+The function has the following additional parameters:
+
+- **ox**: starting index for `x`.
+- **oy**: starting index for `y`.
+- **sa1**: stride of the first dimension of `A`.
+- **sa2**: stride of the second dimension of `A`.
+- **oa**: starting index for `A`.
+
+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( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
+var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dsyr2.ndarray( 'upper', 3, 1.0, x, -2, 4, y, 1, 0, A, 3, 1, 0 );
+// A => <Float64Array>[ 11.0, 15.0, 19.0, 0.0, 13.0, 13.0, 0.0, 0.0, 7.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+- `dsyr2()` corresponds to the [BLAS][blas] level 2 function [`dsyr2`][blas-dsyr2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var ones = require( '@stdlib/array/ones' );
+var dsyr2 = require( '@stdlib/blas/base/dsyr2' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+
+var N = 3;
+
+var A = ones( N*N, opts.dtype );
+var x = discreteUniform( N, -10.0, 10.0, opts );
+var y = discreteUniform( N, -10.0, 10.0, opts );
+
+dsyr2( 'row-major', 'upper', 3, 1.0, x, 1, y, 1, A, 3 );
+console.log( A );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[blas]: http://www.netlib.org/blas
+
+[blas-dsyr2]: https://www.netlib.org/lapack/explore-html/dd/de5/group__her2_ga8e576e9319c25b883b11dc1f39366bcc.html#ga8e576e9319c25b883b11dc1f39366bcc
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/base/dsyr2/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var ones = require( '@stdlib/array/ones' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pkg = require( './../package.json' ).name;
+var dsyr2 = require( './../lib/dsyr2.js' );
+
+
+// VARIABLES //
+
+var options = {
+ 'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+ var x = ones( N, options.dtype );
+ var y = ones( N, options.dtype );
+ var A = ones( N*N, options.dtype );
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var z;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ z = dsyr2( 'row-major', 'upper', N, 1.0, x, 1, y, 1, A, N );
+ if ( isnan( z[ i%z.length ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( z[ i%z.length ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var min;
+ var max;
+ var N;
+ var f;
+ var i;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( i = min; i <= max; i++ ) {
+ N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+ f = createBenchmark( N );
+ bench( pkg+':size='+(N*N), f );
+ }
+}
+
+main();