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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

strmv

NPM version Build Status Coverage Status

Perform one of the matrix-vector operations x = A*x or x = A^T*x.

Usage

import strmv from 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-strmv@esm/index.mjs';

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

Performs one of the matrix-vector operations x = A*x or x = A^T*x, where x is an N element vector and A is an N by N unit, or non-unit, upper or lower triangular matrix.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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 ] );

strmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, 1 );
// x => <Float32Array>[ 14.0, 8.0, 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,

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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 ] );

strmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, -1 );
// x => <Float32Array>[ 1.0, 4.0, 10.0 ]

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

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

// 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

strmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x1, 1 );
// x0 => <Float32Array>[ 1.0, 6.0, 3.0, 1.0 ]

strmv.ndarray( uplo, trans, diag, N, A, sa1, sa2, oa, x, sx, ox )

Performs one of the matrix-vector operations x = A*x or x = A^T*x, using alternative indexing semantics and where x is an N element vector and A is an N by N unit, or non-unit, upper or lower triangular matrix.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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 ] );

strmv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
// x => <Float32Array>[ 14.0, 8.0, 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,

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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 ] );

strmv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, -1, 2 );
// x => <Float32Array>[ 1.0, 4.0, 10.0 ]

Notes

  • strmv() corresponds to the BLAS level 2 function strmv.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import discreteUniform from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-array-discrete-uniform@esm/index.mjs';
import strmv from 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-strmv@esm/index.mjs';

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 );

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

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

</script>
</body>
</html>

Notice

This package is part of stdlib, a standard library 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.