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dtbsv

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

Usage

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

dtbsv( order, uplo, trans, diag, N, K, 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 band matrix, with ( K + 1 ) diagonals.

var Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dtbsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, 1, A, 2, x, 1 );
// x => <Float64Array>[ 8.0, -7.0, 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.
  • K: number of super-diagonals or sub-diagonals of the matrix 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( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );

dtbsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, 1, A, 2, x, -1 );
// x => <Float64Array>[ 3.0, -7.0, 8.0 ]

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( [ 0.0, 1.0, 2.0, 3.0 ] );
var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dtbsv( 'row-major', 'upper', 'no-transpose', 'unit', 3, 1, A, 2, x1, 1 );
// x1 => <Float64Array>[ 8.0, -7.0, 3.0 ]

dtbsv.ndarray( uplo, trans, diag, N, K, 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 band matrix, with ( K + 1 ) diagonals.

var Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dtbsv.ndarray( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
// x => <Float64Array>[ 8.0, -7.0, 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( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );

dtbsv.ndarray( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, -1, 2 );
// x => <Float64Array>[ 3.0, -7.0, 8.0 ]

Notes

  • dtbsv() corresponds to the BLAS level 2 function dtbsv.
  • 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 dtbsv = require( '@stdlib/blas/base/dtbsv' );

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

var N = 3;

var A = [ 1.0, 2.0, 3.0, 4.0, 5.0, 0.0 ];

var x = discreteUniform( N, -10, 10, opts );

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

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

C APIs

Usage

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Examples

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