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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var dfill = require( '@stdlib/blas/ext/base/dfill' ).ndarray;
var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
// MAIN //
/**
* Performs one of the matrix-vector operations `y := α*A*x + β*y, or y := α*A**T*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors and `A` is an `M` by `N` band matrix, with `KL` sub-diagonals and `KU` super-diagonals.
*
* @private
* @param {string} trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
* @param {NonNegativeInteger} M - number of rows in the matrix `A`
* @param {NonNegativeInteger} N - number of columns in the matrix `A`
* @param {NonNegativeInteger} KL - number of sub-diagonals of matrix `A`
* @param {NonNegativeInteger} KU - number of super-diagonals of matrix `A`
* @param {number} alpha - scalar constant
* @param {Float32Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Float32Array} x - first input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {number} beta - scalar constant
* @param {Float32Array} y - second input vector
* @param {integer} strideY - `y` stride length
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @returns {Float32Array} `y`
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var A = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0 ] );
* var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
* var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
*
* dgbmv( 'no-transpose', 3, 3, 1, 1, 1.0, A, 3, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
* // y => <Float32Array>[ 3.0, 12.0, 13.0 ]
*/
function dgbmv( trans, M, N, KL, KU, alpha, A, strideA1, strideA2, offsetA, x, strideX, offsetX, beta, y, strideY, offsetY ) {
var aidx;
var isrm;
var xlen;
var ylen;
var kup1;
var tmp;
var iy1;
var sa0;
var sa1;
var i1;
var i0;
var oa;
// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
isrm = isRowMajor( [ strideA1, strideA2 ] );
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2; // stride for innermost loop
sa1 = strideA1; // stride for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1; // stride for innermost loop
sa1 = strideA2; // stride for outermost loop
}
if ( trans === 'no-transpose' ) {
xlen = N;
ylen = M;
} else {
xlen = M;
ylen = N;
}
// y = beta * y
if ( beta !== 1.0 ) {
if ( beta === 0.0 ) {
dfill( ylen, 0.0, y, strideY, offsetY );
} else {
dscal( ylen, beta, y, strideY, offsetY );
}
}
if ( alpha === 0.0 ) {
return y;
}
// Form: y = α*A*x + y
if (
( !isrm && trans === 'no-transpose' ) ||
( isrm && trans !== 'no-transpose' )
) {
for ( i1 = 0; i1 < xlen; i1++ ) {
tmp = alpha * x[ offsetX + ( i1 * strideX ) ];
oa = offsetA + ( sa1 * i1 );
for ( i0 = max( 0, i1 - KU ); i0 < min( ylen, i1 + KL + 1 ); i0++ ) {
kup1 = i0 - i1;
aidx = oa + ( ( kup1 + KU ) * sa0 );
if ( aidx >= 0 ) {
y[ offsetY + ( i0 * strideY ) ] = y[ offsetY + ( i0 * strideY ) ] + ( A[ aidx ] * tmp );
}
}
}
return y;
}
// Form: y = α*A^T*x + y
// ( !isrm && trans !== 'no-transpose' ) || ( isrm && trans === 'no-transpose' )
kup1 = KU + 1;
iy1 = offsetY;
for ( i1 = 0; i1 < ylen; i1++ ) {
tmp = 0.0;
oa = offsetA + ( sa1 * i1 );
for ( i0 = max( 0, i1 - KU ); i0 < min( xlen, i1 + KL + 1 ); i0++ ) {
kup1 = i0 - i1;
aidx = oa + ( ( kup1 + KU ) * sa0 );
if ( i0 < xlen && aidx >= 0 ) {
tmp += A[ aidx ] * x[ i0 ];
}
}
y[ iy1 ] += alpha * tmp;
iy1 += strideY;
}
return y;
}
// EXPORTS //
module.exports = dgbmv;
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