dtrsv

Usage

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.

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.
• 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( [ 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 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

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.

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 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( [ 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 ]