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dtrsv

Solve one of the systems of equations A*x = b or A^T*x = b for a triangular matrix A.

Installation

npm install @stdlib/blas-base-ndarray-dtrsv

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

dtrsv( arrays )

Solves one of the systems of equations A*x = b or A^T*x = b, where b and x are one-dimensional ndarrays and A is an N by N unit, or non-unit, upper or lower triangular matrix.

var Float64Matrix = require( '@stdlib/ndarray-matrix-float64' );
var Float64Vector = require( '@stdlib/ndarray-vector-float64' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var resolveTriangle = require( '@stdlib/blas-base-matrix-triangle-resolve-enum' );
var resolveTranspose = require( '@stdlib/blas-base-transpose-operation-resolve-enum' );
var resolveDiagonal = require( '@stdlib/blas-base-diagonal-type-resolve-enum' );

var A = new Float64Matrix( [ [ 1.0, 2.0, 3.0 ], [ 0.0, 4.0, 5.0 ], [ 0.0, 0.0, 6.0 ] ] );
var x = new Float64Vector( [ 1.0, 2.0, 3.0 ] );

var uplo = scalar2ndarray( resolveTriangle( 'upper' ), {
    'dtype': 'int32'
});
var trans = scalar2ndarray( resolveTranspose( 'no-transpose' ), {
    'dtype': 'int32'
});
var diag = scalar2ndarray( resolveDiagonal( 'non-unit' ), {
    'dtype': 'int32'
});

var out = dtrsv( [ A, x, uplo, trans, diag ] );
// x => <ndarray>[ -0.25, -0.125, 0.5 ]

var bool = ( out === x );
// returns true

The function has the following parameters:

• arrays: array-like object containing the following ndarrays:

  • a two-dimensional input ndarray corresponding to A.
  • a one-dimensional input/output ndarray corresponding to x.
  • a zero-dimensional ndarray specifying whether the upper or lower triangular part of A should be referenced.
  • a zero-dimensional ndarray specifying whether A should be transposed, conjugate-transposed, or not transposed.
  • a zero-dimensional ndarray specifying whether A has a unit or non-unit diagonal.

Examples

var discreteUniform = require( '@stdlib/random-discrete-uniform' );
var zeros = require( '@stdlib/ndarray-zeros' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var resolveTriangle = require( '@stdlib/blas-base-matrix-triangle-resolve-enum' );
var resolveTranspose = require( '@stdlib/blas-base-transpose-operation-resolve-enum' );
var resolveDiagonal = require( '@stdlib/blas-base-diagonal-type-resolve-enum' );
var dtriu = require( '@stdlib/blas-ext-base-ndarray-dtriu' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var dtrsv = require( '@stdlib/blas-base-ndarray-dtrsv' );

var opts = {
    'dtype': 'float64'
};
var eopts = {
    'dtype': 'int32'
};

var M = discreteUniform( [ 3, 3 ], 1, 10, opts );
var A = zeros( [ 3, 3 ], opts );
var x = discreteUniform( [ 3 ], 0, 10, opts );

var uplo = scalar2ndarray( resolveTriangle( 'upper' ), eopts );
var trans = scalar2ndarray( resolveTranspose( 'no-transpose' ), eopts );
var diag = scalar2ndarray( resolveDiagonal( 'non-unit' ), eopts );

var k = scalar2ndarray( 0, {
    'dtype': 'generic'
});
dtriu( [ M, A, k ] );

var out = dtrsv( [ A, x, uplo, trans, diag ] );
console.log( ndarray2array( out ) );

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.