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docs: adds readme file
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‎lib/node_modules/@stdlib/blas/base/ctrsv/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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# ctrsv
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> Solve one of the systems of equations `x = A*x` or `x = A^T*x` or `x = A^H*x`.
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<section class="usage">
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## Usage
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```javascript
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var ctrsv = require( '@stdlib/blas/base/ctrsv' );
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```
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#### ctrsv( order, uplo, trans, diag, N, A, LDA, x, sx )
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Solves one of the systems of equations `A*x = b` or `A^T*x = b` or `A^H*x = b` where `b` and `x` are `N` element complex vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular complex matrix.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 5.0, 5.0, 6.0, 6.0 ] ); // eslint-disable-line max-params, max-len
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var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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ctrsv( 'row-major', 'lower', 'no-transpose', 'unit', 3, A, 3, x, 1 );
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// x => <Complex64Array>[ 1.0, 1.0, 2.0, -2.0, -17.0, -3.0 ]
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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 `A` is an upper or lower triangular matrix.
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- **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
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- **diag**: specifies whether `A` has a unit diagonal.
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- **N**: number of elements along each dimension of `A`.
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- **A**: input band matrix stored in linear memory as a [`Complex64Array`][@stdlib/array/complex64]. The band matrix is first stored in compact band form, where only the diagonals within the bandwidth are kept, and is then laid out sequentially in linear memory.
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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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- **x**: input [`Complex64Array`][@stdlib/array/complex64].
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- **sx**: stride length for `x`.
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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 Complex64Array = require( '@stdlib/array/complex64' );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 5.0, 5.0, 6.0, 6.0 ] ); // eslint-disable-line max-params, max-len
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var x = new Complex64Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] ); // eslint-disable-line max-params, max-len
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ctrsv( 'row-major', 'lower', 'no-transpose', 'unit', 3, A, 3, x, -1 );
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// x => <Complex64Array>[ -17.0, -3.0, 2.0, -2.0, 1.0, 1.0 ]
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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 Complex64Array = require( '@stdlib/array/complex64' );
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// Initial arrays...
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var x0 = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] ); // eslint-disable-line max-params, max-len
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 5.0, 5.0, 6.0, 6.0 ] ); // eslint-disable-line max-params, max-len
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// Create offset views...
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var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd complex element
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ctrsv( 'row-major', 'lower', 'no-transpose', 'unit', 3, A, 3, x1, 1 );
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// x1 => <Complex64Array>[ 1.0, 1.0, 2.0, -2.0, -17.0, -3.0 ]
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```
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<!-- lint disable maximum-heading-length -->
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#### ctrsv.ndarray( uplo, trans, diag, N, A, sa1, sa2, oa, x, sx, ox )
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Solves one of the systems of equations `A*x = b` or `A^T*x = b` or `A^H*x = b`, using alternative indexing semantics and where `b` and `x` are `N` element complex vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular complex matrix.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 5.0, 5.0, 6.0, 6.0 ] ); // eslint-disable-line max-params, max-len
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var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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ctrsv.ndarray( 'lower', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
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// x => <Complex64Array>[ 1.0, 1.0, 2.0, -2.0, -17.0, -3.0 ]
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```
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The function has the following additional parameters:
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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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- **ox**: starting index for `x`.
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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 Complex64Array = require( '@stdlib/array/complex64' );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 5.0, 5.0, 6.0, 6.0 ] ); // eslint-disable-line max-params, max-len
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var x = new Complex64Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] ); // eslint-disable-line max-params, max-len
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ctrsv.ndarray( 'lower', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, -1, 2 );
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// x => <Complex64Array>[ -17.0, -3.0, 2.0, -2.0, 1.0, 1.0 ]
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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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- `ctrsv()` corresponds to the [BLAS][blas] level 2 function [`ctrsv`][ctrsv].
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- Neither routine tests for singularity or near-singularity. Such tests must be performed before calling the routines.
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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 Complex64 = require( '@stdlib/complex/float32/ctor' );
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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var logEach = require( '@stdlib/console/log-each' );
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var ctrsv = require( '@stdlib/blas/base/ctrsv' );
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function rand() {
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return new Complex64( discreteUniform( 0, 255 ), discreteUniform( -128, 127 ) ); // eslint-disable-line max-params, max-len
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}
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var N = 3;
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var A = filledarrayBy( N*N, 'complex64', rand );
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var x = filledarrayBy( N, 'complex64', rand );
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ctrsv( 'row-major', 'lower', 'no-transpose', 'non-unit', N, A, N, x, 1 );
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// Print the results:
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logEach( '(%s)', x );
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ctrsv.ndarray( 'lower', 'no-transpose', 'non-unit', N, A, N, 1, 0, x, 2, 1 ); // eslint-disable-line max-params, max-len
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// Print the results:
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logEach( '(%s)', x );
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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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[ctrsv]: https://www.netlib.org/lapack/explore-html/dd/dc3/group__trsv_gab8c2d2a6476f67197ba1f92aff4a0b92.html#gab8c2d2a6476f67197ba1f92aff4a0b92
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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/complex64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex64
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</section>
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<!-- /.links -->

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