npm package: @stdlib/blas-base-dtrsv
Description: Solve one of the systems of equations `A*x = b` or `A^T*x = b`.
Author: The Stdlib Authors
Latest version: 0.1.1

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  <summary>
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# dtrsv

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Solve one of the systems of equations `A*x = b` or `A^T*x = b`.

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-base-dtrsv
```

</section>

<section class="usage">

## Usage

```javascript
var dtrsv = require( '@stdlib/blas-base-dtrsv' );
```

#### dtrsv( order, uplo, trans, diag, N, A, LDA, x, sx )

Solves one of the systems of equations `A*x = b` or `A^T*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 Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dtrsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, 1 );
// x => <Float64Array>[ 0.0, -4.0, 3.0 ]
```

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 [`Float64Array`][mdn-float64array].
-   **lda**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
-   **x**: input vector [`Float64Array`][mdn-float64array].
-   **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 Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );

dtrsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, -1 );
// x => <Float64Array>[ 3.0, -4.0, 0.0 ]
```

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 Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dtrsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x1, 1 );
// x0 => <Float64Array>[ 1.0, 0.0, -1.0, 1.0 ]
```

#### dtrsv.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`, 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 Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dtrsv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
// x => <Float64Array>[ 0.0, -4.0, 3.0 ]
```

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 Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );

dtrsv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, -1, 2 );
// x => <Float64Array>[ 3.0, -4.0, 0.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   `dtrsv()` corresponds to the [BLAS][blas] level 2 function [`dtrsv`][blas-dtrsv].
-   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 dtrsv = require( '@stdlib/blas-base-dtrsv' );

var opts = {
    'dtype': 'float64'
};

var N = 5;

var A = discreteUniform( N*N, -10.0, 10.0, opts );
var x = discreteUniform( N, -10.0, 10.0, opts );

dtrsv( 'column-major', 'upper', 'no-transpose', 'unit', N, A, N, x, 1 );
console.log( x );

dtrsv.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 -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/blas-base-dtrsv/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-base-dtrsv/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-base-dtrsv/tree/umd
[umd-readme]: https://github.com/stdlib-js/blas-base-dtrsv/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/blas-base-dtrsv/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-base-dtrsv/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/blas-base-dtrsv/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-dtrsv/main/LICENSE

[blas]: http://www.netlib.org/blas

[blas-dtrsv]: https://www.netlib.org/lapack/explore-html/dd/dc3/group__trsv_ga7a7dcbb8745b4776ce13063ab031141f.html#ga7a7dcbb8745b4776ce13063ab031141f

[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>

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