feat: add blas/base/zgbmv

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

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+<!--
+
+@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.
+
+-->
+
+# zgbmv
+
+> Perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var zgbmv = require( '@stdlib/blas/base/zgbmv' );
+```
+
+#### zgbmv( order, trans, M, N, KL, KU, α, A, LDA, x, sx, β, y, sy )
+
+Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL` sub-diagonals and `KU` super-diagonals.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
+var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
+var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
+var alpha = new Complex128( 0.5, 0.5 );
+var beta = new Complex128( 0.5, -0.5 );
+
+zgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, alpha, A, 3, x, 1, beta, y, 1 );
+// y => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
+-   **M**: number of rows in the matrix `A`.
+-   **N**: number of columns in the matrix `A`.
+-   **KL**: number of sub-diagonals in the matrix `A`.
+-   **KU**: number of super-diagonals in the matrix `A`.
+-   **α**: scalar constant.
+-   **A**: input band matrix stored in linear memory as a [`Complex128Array`][@stdlib/array/complex128].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **x**: input [`Complex128Array`][@stdlib/array/complex128].
+-   **sx**: stride length for `x`.
+-   **β**: complex scalar constant.
+-   **y**: output [`Complex128Array`][@stdlib/array/complex128].
+-   **sy**: stride length for `y`.
+
+The stride parameters determine how elements are accessed. For example, to iterate over every other element in `x` and `y`,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
+var x = new Complex128Array( [ 1.0, 1.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 3.0, 3.0 ] );
+var y = new Complex128Array( [ 3.0, 3.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 1.0, 1.0 ] );
+var alpha = new Complex128( 0.5, 0.5 );
+var beta = new Complex128( 0.5, -0.5 );
+
+zgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, alpha, A, 3, x, 2, beta, y, 2 );
+// y => <Complex128Array>[ -4.0, 7.0, 0.0, 0.0, -26.0, 28.0, 0.0, 0.0, -30.0, 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 -->
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+// Initial arrays...
+var x0 = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
+var y0 = new Complex128Array( [ 0.0, 0.0, 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
+var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
+
+var alpha = new Complex128( 0.5, 0.5 );
+var beta = new Complex128( 0.5, -0.5 );
+
+// Create offset views...
+var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd complex element
+var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd complex element
+
+zgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, alpha, A, 3, x1, 1, beta, y1, 1 );
+// y1 => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### zgbmv.ndarray( trans, M, N, KL, KU, α, A, sa1, sa2, oa, x, sx, ox, β, y, sy, oy )
+
+Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y` using alternative indexing semantics, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` band matrix with `KL` sub-diagonals and `KU` super-diagonals.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
+var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
+var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
+
+var alpha = new Complex128( 0.5, 0.5 );
+var beta = new Complex128( 0.5, -0.5 );
+
+zgbmv.ndarray( 'no-transpose', 3, 3, 1, 1, alpha, A, 3, 1, 0, x, 1, 0, beta, y, 1, 0 );
+// y => <Complex128Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+-   **ox**: starting index for `x`.
+-   **oy**: starting index for `y`.
+
+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,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var A = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
+var x = new Complex128Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
+var y = new Complex128Array( [ 1.0, 1.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 3.0, 3.0 ] );
+
+var alpha = new Complex128( 0.5, 0.5 );
+var beta = new Complex128( 0.5, -0.5 );
+
+zgbmv.ndarray( 'no-transpose', 3, 3, 1, 1, alpha, A, 3, 1, 0, x, 1, 1, beta, y, -2, 4 );
+// y => <Complex128Array>[ -30.0, 31.0, 0.0, 0.0, -26.0, 28.0, 0.0, 0.0, -4.0, 7.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `zgbmv()` corresponds to the [BLAS][blas] level 2 function [`zgbmv`][zgbmv].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var filledarrayBy = require( '@stdlib/array/filled-by' );
+var logEach = require( '@stdlib/console/log-each' );
+var zgbmv = require( '@stdlib/blas/base/zgbmv' );
+
+function rand() {
+    return new Complex128( discreteUniform( 0, 255 ), discreteUniform( -128, 127 ) );
+}
+
+var M = 3;
+var N = 3;
+var KL = 1;
+var KU = 1;
+
+var A = filledarrayBy( (KL+KU+1)*N, 'complex128', rand );
+var x = filledarrayBy( N, 'complex128', rand );
+var y = filledarrayBy( M, 'complex128', rand );
+
+var alpha = new Complex128( 0.5, 0.5 );
+var beta = new Complex128( 0.5, -0.5 );
+
+zgbmv( 'row-major', 'no-transpose', M, N, KL, KU, alpha, A, (KL+KU+1), x, 1, beta, y, 1 );
+
+// Print the results:
+logEach( '%s', x );
+
+zgbmv.ndarray( 'no-transpose', M, N, KL, KU, alpha, A, 1, (KL+KU+1), 0, x, 1, 0, beta, y, 1, 0 );
+
+// Print the results:
+logEach( '%s', x );
+```
+
+</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
+
+[zgbmv]: https://www.netlib.org/lapack/explore-html/dd/df4/group__gbmv_ga1e1f6f5b44fb2c1ce48c2f34e293164a.html
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
+
+</section>
+
+<!-- /.links -->