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feat: add blas/base/dtbmv
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‎lib/node_modules/@stdlib/blas/base/dtbmv/lib/base.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
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var max = require( '@stdlib/math/base/special/max' );
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var min = require( '@stdlib/math/base/special/min' );
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// MAIN //
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/**
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* 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 band matrix, with ( `K` + 1 ) diagonals.
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*
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* @private
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* @param {string} uplo - specifies whether `A` is an upper or lower triangular matrix
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* @param {string} trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
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* @param {string} diag - specifies whether `A` has a unit diagonal
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* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
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* @param {NonNegativeInteger} K - number of super-diagonals or sub-diagonals of the matrix `A`
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* @param {Float64Array} A - input matrix
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* @param {integer} strideA1 - stride of the first dimension of `A`
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* @param {integer} strideA2 - stride of the second dimension of `A`
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* @param {NonNegativeInteger} offsetA - starting index for `A`
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* @param {Float64Array} x - input vector
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* @param {integer} strideX - `x` stride length
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* @param {NonNegativeInteger} offsetX - starting index for `x`
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* @returns {Float64Array} `x`
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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* var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
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*
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* dtbmv( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
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* // x => <Float64Array>[ 3.0, 11.0, 3.0 ]
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*/
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function dtbmv( uplo, trans, diag, N, K, A, strideA1, strideA2, offsetA, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
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var nonunit;
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var isrm;
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var idx;
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var tmp;
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var sa0;
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var sa1;
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var ix0;
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var ix1;
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var i0;
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var i1;
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var oa;
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var ox;
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// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
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isrm = isRowMajor( [ strideA1, strideA2 ] );
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nonunit = ( diag === 'non-unit' );
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if ( isrm ) {
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// For row-major matrices, the last dimension has the fastest changing index...
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sa0 = strideA2; // stride for innermost loop
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sa1 = strideA1; // stride for outermost loop
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} else { // isColMajor
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// For column-major matrices, the first dimension has the fastest changing index...
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sa0 = strideA1; // stride for innermost loop
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sa1 = strideA2; // stride for outermost loop
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}
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ox = offsetX;
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if (
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( !isrm && trans === 'no-transpose' && uplo === 'upper' ) ||
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( isrm && trans !== 'no-transpose' && uplo === 'lower' )
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) {
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ix1 = ox;
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for ( i1 = 0; i1 < N; i1++ ) {
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oa = offsetA + ( sa1 * i1 );
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tmp = x[ ix1 ];
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if ( nonunit ) {
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tmp = A[ oa + ( sa0 * K ) ] * x[ ix1 ];
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}
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for ( i0 = i1 + 1; i0 <= min( N - 1, i1 + K ); i0++ ) {
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ix0 = ox + ( i0 * strideX );
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idx = oa + ( sa0 * ( K + i0 - i1 ) );
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tmp += A[ idx ] * x[ ix0 ];
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}
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x[ ix1 ] = tmp;
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ix1 += strideX;
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}
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return x;
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}
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if (
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( !isrm && trans === 'no-transpose' && uplo === 'lower' ) ||
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( isrm && trans !== 'no-transpose' && uplo === 'upper' )
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) {
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ix1 = ox + ( (N - 1) * strideX );
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for ( i1 = N - 1; i1 >= 0; i1-- ) {
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oa = offsetA;
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tmp = x[ ix1 ];
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if ( nonunit ) {
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tmp = A[ oa + ( sa1 * i1 ) ] * x[ ix1 ];
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}
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for ( i0 = max( 0, i1 - K ); i0 < i1; i0++ ) {
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idx = oa + ( sa1 * i0 ) + ( sa0 * ( i1 - i0 ) );
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ix0 = ox + ( i0 * strideX );
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tmp += A[ idx ] * x[ ix0 ];
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}
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x[ ix1 ] = tmp;
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ix1 -= strideX;
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}
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return x;
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}
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if (
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( !isrm && trans !== 'no-transpose' && uplo === 'upper' ) ||
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( isrm && trans === 'no-transpose' && uplo === 'lower' )
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) {
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ix1 = x + ( ( N - 1 ) * strideX );
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for ( i1 = N - 1; i1 >= 0; i1-- ) {
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oa = offsetA + ( sa1 * i1 );
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tmp = x[ ix1 ];
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if ( nonunit ) {
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tmp = A[ oa + ( sa0 * K ) ] * x[ ix1 ];
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}
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for ( i0 = max( 0, i1 - K ); i0 < i1; i0++ ) {
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idx = oa + ( sa0 * ( K + i0 - i1 ) );
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ix0 = ox + ( i0 * strideX );
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tmp += A[ idx ] * x[ ix0 ];
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}
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x[ ix1 ] = tmp;
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ix1 -= strideX;
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}
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return x;
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}
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// ( !isrm && trans !== 'no-transpose' && uplo === 'lower' ) || ( isrm && trans === 'no-transpose' && uplo === 'upper' )
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ix1 = ox;
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for ( i1 = 0; i1 < N; i1++ ) {
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oa = offsetA + ( sa1 * i1 );
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tmp = x[ ix1 ];
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if ( nonunit ) {
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tmp = A[ oa ] * x[ ix1 ];
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}
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for ( i0 = i1 + 1; i0 <= min( N - 1, i1 + K ); i0++ ) {
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ix0 = ox + ( i0 * strideX );
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idx = oa + ( sa0 * ( i0 - i1 ) );
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tmp += A[ idx ] * x[ ix0 ];
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}
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x[ ix1 ] = tmp;
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ix1 += strideX;
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}
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return x;
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}
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// EXPORTS //
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module.exports = dtbmv;

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