feat: add blas/base/ctbsv

lib/node_modules/@stdlib/blas/base/ctbsv/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.
+
+-->
+
+# ctbsv
+
+> Solve one of the systems of equations `x = A*x` or `x = A^T*x` or `x = A^H*x`.
+
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ctbsv = require( '@stdlib/blas/base/ctbsv' );
+```
+
+#### ctbsv( order, uplo, trans, diag, N, K, A, LDA, x, sx )
+
+Solves one of the systems of equations `A*x = b` or `A^T*x = b` or `x = A^H*x` where `b` and `x` are `N` element vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular band matrix, with ( `K` + 1 ) diagonals.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0 ] );
+var x = new Complex64Array( [ 0.0, 2.0, 0.0, 16.0, 0.0, 46.0 ] );
+
+ctbsv( 'row-major', 'lower', 'no-transpose', 'non-unit', 3, 1, A, 2, x, 1 );
+// x => <Complex64Array>[ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **uplo**: specifies whether `A` is an upper or lower triangular matrix.
+-   **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
+-   **diag**: specifies whether `A` has a unit diagonal.
+-   **N**: number of elements along each dimension of `A`.
+-   **K**: number of super-diagonals or sub-diagonals of the matrix `A`.
+-   **A**: input band matrix stored in linear memory as a [`Complex64Array`][@stdlib/array/complex64].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **x**: input [`Complex64Array`][@stdlib/array/complex64].
+-   **sx**: stride length for `x`.
+
+The stride parameters determine how elements are accessed. For example, to iterate over every other element in `x`,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0 ] );
+var x = new Complex64Array( [ 0.0, 2.0, 0.0, 0.0, 0.0, 16.0, 0.0, 0.0, 0.0, 46.0 ] );
+
+ctbsv( 'row-major', 'lower', 'no-transpose', 'non-unit', 3, 1, A, 2, x, 2 );
+// x => <Complex64Array>[ 1.0, 1.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 3.0, 3.0 ]
+```
+
+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 Complex64Array = require( '@stdlib/array/complex64' );
+
+// Initial arrays...
+var x0 = new Complex64Array( [ 0.0, 0.0, 0.0, 2.0, 0.0, 16.0, 0.0, 46.0 ] );
+var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0 ] );
+
+// Create offset views...
+var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd complex element
+
+ctbsv( 'row-major', 'lower', 'no-transpose', 'non-unit', 3, 1, A, 2, x1, 1 );
+// x1 => <Complex64Array>[ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### ctbsv.ndarray( uplo, trans, diag, N, K, A, sa1, sa2, oa, x, sx, ox )
+
+Solves one of the systems of equations `x = A*x` or `x = A^T*x` or `x = A^H*x`, using alternative indexing semantics and where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular band matrix, with (`K` + 1) diagonals.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0 ] );
+var x = new Complex64Array( [ 0.0, 2.0, 0.0, 16.0, 0.0, 46.0 ] );
+
+ctbsv.ndarray( 'lower', 'no-transpose', 'non-unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
+// x => <Complex64Array>[ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ]
+```
+
+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`.
+
+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 Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0 ] );
+var x = new Complex64Array( [ 0.0, 46.0, 0.0, 16.0, 0.0, 2.0 ] );
+
+ctbsv.ndarray( 'lower', 'no-transpose', 'non-unit', 3, 1, A, 2, 1, 0, x, -1, 2 );
+// x => <Complex64Array>[ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `ctbsv()` corresponds to the [BLAS][blas] level 2 function [`ctbsv`][ctbsv].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var Complex64 = require( '@stdlib/complex/float32/ctor' );
+var filledarrayBy = require( '@stdlib/array/filled-by' );
+var logEach = require( '@stdlib/console/log-each' );
+var ctbsv = require( '@stdlib/blas/base/ctbsv' );
+
+function rand() {
+    return new Complex64( discreteUniform( 0, 255 ), discreteUniform( -128, 127 ) );
+}
+
+var N = 3;
+var K = 1;
+
+var A = filledarrayBy( (K+1)*N, 'complex64', rand );
+var x = filledarrayBy( N, 'complex64', rand );
+
+ctbsv( 'row-major', 'lower', 'no-transpose', 'non-unit', N, 1, A, (K+1), x, 1 );
+
+// Print the results:
+logEach( '%s', x );
+
+ctbsv.ndarray( 'lower', 'no-transpose', 'non-unit', N, 1, A, (K+1), 1, 0, x, 2, 1 );
+
+// 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
+
+[ctbsv]: https://www.netlib.org/lapack/explore-html/d4/dcd/group__tbsv_gaaac28899b66867490cef87edff06f081.html#gaaac28899b66867490cef87edff06f081
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/complex64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex64
+
+</section>
+
+<!-- /.links -->