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feat: add blas/base/zher2
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‎lib/node_modules/@stdlib/blas/base/zher2/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2025 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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# zher2
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> Perform the hermitian rank 1 operation `A = alpha*x*x**H + A`, where `alpha` is a real scalar, `X` is an `N` element vector and `A` is an `N` by `N` hermitian matrix.
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<section class="usage">
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## Usage
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```javascript
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var zher2 = require( '@stdlib/blas/base/zher2' );
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```
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#### zher2( order, uplo, N, α, x, strideX, y, strideY, A, LDA )
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Performs the hermitian rank 1 operation `A = alpha*x*x**H + A`, where `alpha` is a real scalar, `X` is an `N` element vector and `A` is an `N` by `N` hermitian matrix.
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var x = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
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var alpha = new Complex128( 1.0, 0.0 );
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zher2( 'row-major', 'lower', x.length, alpha, x, 1, y, 1, A, 2 );
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// A => <Complex128Array>[ 5.0, 0.0, 0.0, 0.0, 6.0, 3.0, 8.0, 0.0 ]
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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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- **uplo**: specifies whether the upper or lower triangular part of the matrix `A` is supplied.
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- **N**: specifies the order of the matrix `A`.
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- **α**: scalar constant.
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- **x**: first input vector [`Complex128Array`][@stdlib/array/complex128].
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- **strideX**: index increment for `x`.
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- **y**: second input vector [`Complex128Array`][@stdlib/array/complex128].
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- **strideY**: index increment for `y`.
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- **A**: input matrix stored in linear memory as [`Complex128Array`][@stdlib/array/complex128].
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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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The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of `x` in reverse order,
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var x = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
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var alpha = new Complex128( 1.0, 0.0 );
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zher2( 'row-major', 'lower', x.length, alpha, x, 1, y, 1, A, 2 );
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// A => <Complex128Array>[ 5.0, 0.0, 0.0, 0.0, 6.0, 3.0, 8.0, 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 Complex128Array = require( '@stdlib/array/complex128' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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// Initial array:
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var x0 = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, 1.0 ] );
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var y0 = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, 1.0 ] );
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var alpha = new Complex128( 1.0, 0.0 );
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// Define a input matrix:
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var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
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// Create an offset view:
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var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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zher2( 'row-major', 'lower', x1.length, alpha, x1, 1, y1, 1, A, 2 );
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// A => <Complex128Array>[ 5.0, 0.0, 0.0, 0.0, 6.0, 3.0, 8.0, 0.0 ]
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```
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<!-- lint disable maximum-heading-length -->
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#### zher2.ndarray( uplo, N, α, x, strideX, offsetX, y, strideY, offsetY, A, strideA1, strideA2, offsetA )
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Performs the hermitian rank 1 operation `A = alpha*x*x**H + A`, where `alpha` is a real scalar, `X` is an `N` element vector and `A` is an `N` by `N` hermitian matrix using alternative indexing semantics.
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var x = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
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var alpha = new Complex128( 1.0, 0.0 );
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zher2.ndarray( 'lower', x.length, alpha, x, 1, 0, y, 1, 0, A, 2, 1, 0 );
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// A => <Complex128Array>[ 5.0, 0.0, 0.0, 0.0, 6.0, 3.0, 8.0, 0.0 ]
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```
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The function has the following additional parameters:
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- **strideA1**: stride of the first dimension of `A`.
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- **strideA2**: stride of the second dimension of `A`.
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- **offsetX**: starting index for `x`.
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- **offsetY**: starting index for `y`.
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- **offsetA**: starting index for `A`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to scale every other value in the input strided array starting from the second element,
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var x = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
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var alpha = new Complex128( 1.0, 0.0 );
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zher2.ndarray( 'lower', x.length, alpha, x, -1, 0, y, -1, 0, A, 2, 1, 0 );
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// A => <Complex128Array>[ 5.0, 0.0, 0.0, 0.0, 6.0, 3.0, 8.0, 0.0 ]
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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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- If `N = 0` or `real( α ) = 0.0` or `imag( α ) = 0.0`, both functions return `x` unchanged.
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- `zher2()` corresponds to the [BLAS][blas] level 2 function [`zher2`][zher2].
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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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```javascript
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var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var logEach = require( '@stdlib/console/log-each' );
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var zher2 = require( '@stdlib/blas/base/zher2' );
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function rand() {
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return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
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}
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var x = filledarrayBy( 3, 'complex128', rand );
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console.log( x.get( 0 ).toString() );
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var y = filledarrayBy( 3, 'complex128', rand );
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console.log( y.get( 0 ).toString() );
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var A = filledarrayBy( 9, 'complex128', rand );
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console.log( A.get( 0 ).toString() );
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var alpha = new Complex128( 2.0, 2.0 );
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console.log( alpha.toString() );
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zher2( 'row-major', 'upper', 3, alpha, x, 1, y, 1, A, 3 );
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// Print the results:
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logEach( '(%s)', A );
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zher2.ndarray( 'upper', 3, alpha, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
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// Print the results:
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logEach( '(%s)', A );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[blas]: http://www.netlib.org/blas
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[zher2]: https://www.netlib.org/lapack/explore-html/dd/de5/group__her2_gaf421f493e6422d08e3acfc6d33bfbf46.html
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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/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
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</section>
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<!-- /.links -->

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