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feat: add blas/base/ctrmv
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‎lib/node_modules/@stdlib/blas/base/ctrmv/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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# ctrmv
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> Perform one of the matrix-vector operations `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 ctrmv = require( '@stdlib/blas/base/ctrmv' );
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```
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#### ctrmv( order, uplo, trans, diag, N, x, strideX, A, LDA )
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Performs one of the matrix-vector operations `x = A*x`, or `x = A**T*x`, or `x = A**H*x`, where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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ctrmv( 'column-major', 'upper', 'no-transpose', 'non-unit', 3, x, 1, A, 3 );
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// x => <Complex64Array>[ 0.0, 12.0, 0.0, 10.0, 0.0, 6.0 ]
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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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- **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**: specifies the order of the matrix `A`.
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- **x**: input vector [`Complex64Array`][@stdlib/array/complex64].
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- **strideX**: index increment for `x`.
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- **A**: input matrix stored in linear memory as [`Complex64Array`][@stdlib/array/complex64].
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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 Complex64Array = require( '@stdlib/array/complex64' );
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var x = new Complex64Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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ctrmv( 'column-major', 'upper', 'no-transpose', 'non-unit', 3, x, -1, A, 3 );
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// x => <Complex64Array>[ 6.0, 0.0, 10.0, 0.0, 12.0, 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 Complex64Array = require( '@stdlib/array/complex64' );
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// Initial array:
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var x0 = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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// Define a input matrix:
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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// Create an offset view:
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var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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ctrmv( 'column-major', 'upper', 'no-transpose', 'non-unit', 3, x1, 1, A, 3 );
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// x1 => <Complex64Array>[ 0.0, 12.0, 0.0, 10.0, 0.0, 6.0 ]
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```
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#### ctrmv.ndarray( uplo, trans, diag, N, x, strideX, offsetX, A, strideA1, strideA2, offsetA )
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Performs one of the matrix-vector operations `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 matrix.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
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var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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ctrmv.ndarray( 'upper', 'no-transpose', 'non-unit', 3, x, 1, 0, A, 3, 1, 0 );
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// x => <Complex64Array>[ 0.0, 12.0, 0.0, 10.0, 0.0, 6.0 ]
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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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- **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 Complex64Array = require( '@stdlib/array/complex64' );
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var x = new Complex64Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
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var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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ctrmv.ndarray( 'upper', 'no-transpose', 'non-unit', 3, x, -1, 2, A, 3, 1, 1 );
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// x => <Complex64Array>[ 0.0, 6.0, 0.0, 10.0, 0.0, 12.0 ]
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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` both functions return `x` unchanged.
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- `ctrmv()` corresponds to the [BLAS][blas] level 2 function [`ctrmv`][ctrmv].
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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 Complex64 = require( '@stdlib/complex/float32/ctor' );
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var logEach = require( '@stdlib/console/log-each' );
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var ctrmv = require( '@stdlib/blas/base/ctrmv' );
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function rand() {
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return new Complex64( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
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}
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var x = filledarrayBy( 3, 'complex64', rand );
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console.log( x.get( 0 ).toString() );
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var A = filledarrayBy( 9, 'complex64', rand );
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console.log( A.get( 0 ).toString() );
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ctrmv( 'column-major', 'upper', 'no-transpose', 'non-unit', 3, x, 1, A, 3 );
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// Print the results:
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logEach( '(%s)', x );
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ctrmv.ndarray( 'upper', 'no-transpose', 'non-unit', 3, x, 1, 0, A, 1, 3, 0 );
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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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[ctrmv]: https://www.netlib.org/lapack/explore-html/d6/d1c/group__trmv_ga0adaf80ae1dfe117390bd7030fd865f1.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/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 -->

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

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var Complex64Array = require( '@stdlib/array/complex64' );
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var pkg = require( './../package.json' ).name;
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var ctrmv = require( './../lib/ctrmv.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float32'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var xbuf;
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var Abuf;
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var x;
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var A;
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xbuf = uniform( len*2, -100.0, 100.0, options );
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x = new Complex64Array( xbuf.buffer );
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Abuf = uniform( (len*len)*2, -100.0, 100.0, options );
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A = new Complex64Array( Abuf.buffer );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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ctrmv( 'row-major', 'upper', 'no-transpose', 'non-unit', len, x, 1, A, len );
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if ( isnanf( Abuf[ i%(len*2) ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnanf( Abuf[ i%(len*2) ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 4; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

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