dtrmv

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

Installation

npm install @stdlib/blas-base-dtrmv

Usage

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

dtrmv( 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.

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 ] );

dtrmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, 1 );
// x => <Float64Array>[ 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 Float64Array.
• lda: stride of the first dimension of A (a.k.a., leading dimension of the matrix A).
• x: input vector 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,

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 ] );

dtrmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, -1 );
// x => <Float64Array>[ 1.0, 4.0, 10.0 ]

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

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

dtrmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x1, 1 );
// x0 => <Float64Array>[ 1.0, 6.0, 3.0, 1.0 ]

dtrmv.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.

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 ] );

dtrmv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
// x => <Float64Array>[ 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,

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 ] );

dtrmv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, -1, 2 );
// x => <Float64Array>[ 1.0, 4.0, 10.0 ]

Notes

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

Examples

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

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 );

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

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

C APIs

Usage

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Examples

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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.

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License

See LICENSE.

Copyright

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