feat: add lapack/base/dtrti2

lib/node_modules/@stdlib/lapack/base/dtrti2/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# dtrti2
+
+> Compute the inverse of a triangular matrix.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dtrti2 = require( '@stdlib/lapack/base/dtrti2' );
+```
+
+#### dtrti2( order, uplo, diag, N, A, LDA )
+
+Computes the inverse of a triangular matrix.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 0.0, 4.0 ] );
+dtrti2( 'row-major', 'upper', 'non-unit', 2, A, 2 );
+// A => <Float64Array>[ 1.0, -0.5, 0.0, 0.25 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **uplo**: specifies whether to copy the upper or lower triangular/trapezoidal part of a matrix `A`.
+-   **diag**: specifies whether or not `A` is unit triangular.
+-   **N**: order of matrix `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+
+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 Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 0.0, 4.0 ] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dtrti2( 'row-major', 'upper', 'non-unit', 2, A1, 2 );
+// A0 => <Float64Array>[ 0.0, 1.0, -0.5, 0.0, 0.25 ]
+```
+
+#### dtrti2.ndarray( uplo, diag, N, A, strideA1, strideA2, offsetA )
+
+Computes the inverse of a triangular matrix using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 0.0, 4.0 ] );
+dtrti2.ndarray( 'upper', 'non-unit', 2, A, 2, 1, 0 );
+// A => <Float64Array>[ 1.0, -0.5, 0.0, 0.25 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **uplo**: specifies whether to copy the upper or lower triangular/trapezoidal part of a matrix `A`.
+-   **diag**: specifies whether or not `A` is unit triangular.
+-   **N**: order of matrix `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+
+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 Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 0.0, 0.0, 1.0, 2.0, 0.0, 4.0 ] );
+dtrti2.ndarray( 'upper', 'non-unit', 2, A, 2, 1, 2 );
+// A => <Float64Array>[ 0.0, 0.0, 1.0, -0.5, 0.0, 0.25 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dtrti2()` corresponds to the [LAPACK][lapack] routine [`dtrti2`][lapack-dtrti2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dtrti2 = require( '@stdlib/lapack/base/dtrti2' );
+
+var A = new Float64Array( [ 1.0, 2.0, 0.0, 4.0 ] );
+dtrti2( 'row-major', 'upper', 'non-unit', 2, A, 2 );
+console.log( A );
+```
+
+</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">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dtrti2]: https://www.netlib.org/lapack/explore-html/d3/da3/group__trti2_ga36dcbaa90700a0dc16f835f16b281ac0.html#ga36dcbaa90700a0dc16f835f16b281ac0
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dtrti2/benchmark/benchmark.js

@@ -0,0 +1,97 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var pkg = require( './../package.json' ).name;
+var dtrti2 = require( './../lib/dtrti2.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var x = uniform( len * len, -100.0, 100.0, options );
+	return benchmark;
+
+	function benchmark( b ) {
+		var out;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			out = dtrti2( 'row-major', 'upper', 'non-unit', len, x, len );
+			if ( isnan( out[ i%out.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( out[ i%out.length ] ) ) {
+			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 ), 0.5 ) );
+		f = createBenchmark( len );
+		bench( pkg+':order=row-major,len='+len, f );
+	}
+}
+
+main();