strsv

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

Installation

npm install @stdlib/blas-base-strsv

Usage

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

strsv( 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.

var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );

strsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, 1 );
// x => <Float32Array>[ 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 Float32Array.
• LDA: stride of the first dimension of A (a.k.a., leading dimension of the matrix A).
• x: input vector Float32Array.
• 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,

var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 3.0, 2.0, 1.0 ] );

strsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, -1 );
// x => <Float32Array>[ 3.0, -4.0, 0.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float32Array = require( '@stdlib/array-float32' );

// Initial arrays...
var x0 = new Float32Array( [ 1.0, 1.0, 1.0, 1.0 ] );
var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

strsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x1, 1 );
// x0 => <Float32Array>[ 1.0, 0.0, -1.0, 1.0 ]

strsv.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.

var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );

strsv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
// x => <Float32Array>[ 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 views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,

var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 3.0, 2.0, 1.0 ] );

strsv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, -1, 2 );
// x => <Float32Array>[ 3.0, -4.0, 0.0 ]

Notes

• strsv() corresponds to the BLAS level 2 function strsv.
• Neither routine tests for singularity or near-singularity. Such tests must be performed before calling the routines.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var strsv = require( '@stdlib/blas-base-strsv' );

var opts = {
    'dtype': 'float32'
};

var N = 5;

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

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

strsv.ndarray( 'upper', 'no-transpose', 'unit', N, A, 1, N, 0, x, 1, 0 );
console.log( x );

C APIs

Usage

TODO

TODO

TODO.

TODO

TODO

TODO

Examples

TODO

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.