feat: add blas/base/ctrsv

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

@@ -0,0 +1,262 @@
+<!--
+
+@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.
+
+-->
+
+# ctrsv
+
+> Solve one of the systems of equations `A*x = b` or `A^T*x = b` or `A^H*x = b`.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ctrsv = require( '@stdlib/blas/base/ctrsv' );
+```
+
+#### ctrsv( order, uplo, trans, diag, N, A, LDA, x, sx )
+
+Solves one of the systems of equations `A*x = b`, `A^T*x = b`, or `A^H*x = b` where `b` and `x` are `N` element vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix.
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 1.0, 0.0, 3.0, 4.0, 0.0, 0.0, 1.0, 0.0 ] );
+var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+ctrsv( 'row-major', 'upper', 'no-transpose', 'unit', 2, A, 2, x, 1 );
+// x => <Complex64Array>[ 8.0, -22.0, 3.0, 4.0 ]
+```
+
+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`.
+-   **A**: input 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 vector [`Complex64Array`][@stdlib/array/complex64].
+-   **sx**: `x` stride length.
+
+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,
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 1.0, 0.0, 3.0, 4.0, 0.0, 0.0, 1.0, 0.0 ] );
+var x = new Complex64Array( [ 3.0, 4.0, 1.0, 2.0 ] );
+
+ctrsv( 'row-major', 'upper', 'no-transpose', 'unit', 2, A, 2, x, -1 );
+// x => <Complex64Array>[ 3.0, 4.0, 8.0, -22.0 ]
+```
+
+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 -->
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+// Initial arrays...
+var x0 = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0 ] );
+var A = new Complex64Array( [ 1.0, 0.0, 3.0, 4.0, 0.0, 0.0, 1.0, 0.0 ] );
+
+// Create offset views...
+var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+ctrsv( 'row-major', 'upper', 'no-transpose', 'unit', 2, A, 2, x1, 1 );
+// x0 => <Complex64Array>[ 1.0, 1.0, 5.0, -19.0, 3.0, 3.0, 4.0, 4.0 ]
+```
+
+#### ctrsv.ndarray( uplo, trans, diag, N, A, sa1, sa2, oa, x, sx, ox )
+
+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 vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix.
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 1.0, 0.0, 3.0, 4.0, 0.0, 0.0, 1.0, 0.0 ] );
+var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+ctrsv.ndarray( 'upper', 'no-transpose', 'unit', 2, A, 2, 1, 0, x, 1, 0 );
+// x => <Complex64Array>[ 8.0, -22.0, 3.0, 4.0 ]
+```
+
+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,
+
+```javascript
+var Complex64Array = require( '@stdlib/array/complex64' );
+
+var A = new Complex64Array( [ 1.0, 0.0, 3.0, 4.0, 0.0, 0.0, 1.0, 0.0 ] );
+var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
+
+ctrsv.ndarray( 'upper', 'no-transpose', 'unit', 2, A, 2, 1, 0, x, 1, 1 );
+// x => <Complex64Array>[ 1.0, 1.0, 5.0, -19.0, 3.0, 3.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `ctrsv()` corresponds to the [BLAS][blas] level 2 function [`ctrsv`][blas-ctrsv].
+-   Neither routine tests for singularity or near-singularity. Such tests must be performed before calling the routines.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var Complex64Array = require( '@stdlib/array/complex64' );
+var ctrsv = require( '@stdlib/blas/base/ctrsv' );
+
+var opts = {
+    'dtype': 'float32'
+};
+
+var N = 5;
+var Abuf = discreteUniform( N * N * 2, -10.0, 10.0, opts );
+var xbuf = discreteUniform( N * 2, -10.0, 10.0, opts );
+
+var A = new Complex64Array( Abuf.buffer );
+var x = new Complex64Array( xbuf.buffer );
+
+ctrsv( 'column-major', 'upper', 'no-transpose', 'unit', N, A, N, x, 1 );
+console.log( x );
+
+ctrsv.ndarray( 'upper', 'no-transpose', 'unit', N, A, 1, N, 0, x, 1, 0 );
+console.log( 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
+
+[blas-ctrsv]: https://www.netlib.org/lapack/explore-html/dd/dc3/group__trsv_gab8c2d2a6476f67197ba1f92aff4a0b92.html
+
+[@stdlib/array/complex64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

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

@@ -0,0 +1,113 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var format = require( '@stdlib/string/format' );
+var Complex64Array = require( '@stdlib/array/complex64' );
+var pkg = require( './../package.json' ).name;
+var ctrsv = require( './../lib/ctrsv.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float32'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var Abuf;
+	var xbuf;
+	var x;
+	var A;
+
+	xbuf = uniform( len*2, -100.0, 100.0, options );
+	Abuf = uniform( len*len*2, -100.0, 100.0, options );
+	x = new Complex64Array( xbuf.buffer );
+	A = new Complex64Array( Abuf.buffer );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			ctrsv( 'row-major', 'upper', 'transpose', 'unit', len, A, len, x, 1 );
+			if ( isnanf( xbuf[ i%(len*2) ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnanf( xbuf[ i%(len*2) ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( len );
+		bench( format( '%s:len=%d', pkg, len ), f );
+	}
+}
+
+main();