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feat: add lapack/base/dtrti2 #2754

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229 changes: 229 additions & 0 deletions 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 -->
97 changes: 97 additions & 0 deletions lib/node_modules/@stdlib/lapack/base/dtrti2/benchmark/benchmark.js
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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.
*/

'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();
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