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* @license Apache-2.0
*
* Copyright (c) 2026 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-params */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var cfill = require( '@stdlib/blas/ext/base/cfill' ).ndarray;
var cscal = require( '@stdlib/blas/base/cscal' ).ndarray;
var realf = require( '@stdlib/complex/float32/real' );
var imagf = require( '@stdlib/complex/float32/imag' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var reinterpret = require( '@stdlib/strided/base/reinterpret-complex64' );
var muladd = require( '@stdlib/complex/float32/base/mul-add' ).assign;
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
// FUNCTIONS //
/**
* Tests whether a provided string indicates to transpose a matrix.
*
* @private
* @param {string} str - input string
* @returns {boolean} boolean indicating whether to transpose a matrix
*
* @example
* var bool = isTransposed( 'transpose' );
* // returns true
*
* @example
* var bool = isTransposed( 'conjugate-transpose' );
* // returns true
*
* @example
* var bool = isTransposed( 'no-transpose' );
* // returns false
*/
function isTransposed( str ) { // NOTE: consider moving to a separate helper utility package
return ( str !== 'no-transpose' );
}
// MAIN //
/**
* Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y` or `y = α*A^H*x + β*y`, where `α` and `β` are complex scalars, `x` and `y` are complex vectors, and `A` is an `M` by `N` complex 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 {Complex64} alpha - complex scalar constant
* @param {Complex64Array} A - input banded complex matrix (compact band storage)
* @param {integer} strideA1 - stride of first dimension of `A`
* @param {integer} strideA2 - stride of second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index into `A`
* @param {Complex64Array} x - first input complex vector `x`
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Complex64} beta - complex scalar constant
* @param {Complex64Array} y - second input complex vector y
* @param {integer} strideY - `y` stride length
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @returns {Complex64Array} `y`
*
* @example
* var Complex64Array = require( '@stdlib/array/complex64' );
* var Complex64 = require( '@stdlib/complex/float32/ctor' );
*
* var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 4.0, 4.0, 6.0, 6.0, 5.0, 5.0, 7.0, 7.0, 0.0, 0.0 ] );
* var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
* var y = new Complex64Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
* var alpha = new Complex64( 0.5, 0.5 );
* var beta = new Complex64( 0.5, -0.5 );
*
* cgbmv( 'no-transpose', 3, 3, 1, 1, alpha, A, 3, 1, 0, x, 1, 0, beta, y, 1, 0 );
* // y => <Complex64Array>[ -4.0, 7.0, -26.0, 28.0, -30.0, 31.0 ]
*/
function cgbmv( trans, M, N, KL, KU, alpha, A, strideA1, strideA2, offsetA, x, strideX, offsetX, beta, y, strideY, offsetY ) { // eslint-disable-line max-len
var realpha;
var imalpha;
var rebeta;
var imbeta;
var viewA;
var viewX;
var viewY;
var retmp;
var imtmp;
var isrm;
var xlen;
var ylen;
var sign;
var sa0;
var sa1;
var rea;
var ima;
var rex;
var imx;
var oa2;
var oa;
var ox;
var oy;
var sx;
var sy;
var i0;
var i1;
var ia;
var ix;
var iy;
var k;
// Layout
isrm = isRowMajor( [ strideA1, strideA2 ] );
// Lengths
if ( isTransposed( trans ) ) {
xlen = M;
ylen = N;
} else {
xlen = N;
ylen = M;
}
// Decompose complex scalars
rebeta = realf( beta );
imbeta = imagf( beta );
realpha = realf( alpha );
imalpha = imagf( alpha );
// y = beta*y
if ( rebeta === 0.0 && imbeta === 0.0 ) {
cfill( ylen, 0.0, y, strideY, offsetY );
} else if ( rebeta !== 1.0 || imbeta !== 0.0 ) {
cscal( ylen, beta, y, strideY, offsetY );
}
// If alpha is zero, early return y
if ( realpha === 0.0 && imalpha === 0.0 ) {
return y;
}
// Reinterpret arrays to raw numeric views
viewA = reinterpret( A, 0 );
viewX = reinterpret( x, 0 );
viewY = reinterpret( y, 0 );
// Set sign to handle conjugation: flip the imaginary part for conjugate-transpose
if ( trans === 'conjugate-transpose' ) {
sign = -1;
} else {
sign = 1;
}
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2 * 2; // offset increment for innermost loop
sa1 = strideA1 * 2; // offset increment for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1 * 2; // offset increment for innermost loop
sa1 = strideA2 * 2; // offset increment for outermost loop
}
// Vector indexing base
oa = offsetA * 2;
ox = offsetX * 2;
oy = offsetY * 2;
// Vector strides
sx = strideX * 2;
sy = strideY * 2;
// Form: y = α*A*x + y
if (
( !isrm && !isTransposed( trans ) ) ||
( isrm && isTransposed( trans ) )
) {
for ( i1 = 0; i1 < xlen; i1++ ) {
ix = ox + ( i1 * sx );
rex = viewX[ ix ];
imx = viewX[ ix + 1 ];
retmp = f32( ( realpha * rex ) - ( imalpha * imx ) );
imtmp = f32( ( realpha * imx ) + ( imalpha * rex ) );
k = KU - i1;
oa2 = oa + ( i1 * sa1 ) + ( k * sa0 );
for ( i0 = max( 0, i1 - KU ); i0 < min( ylen, i1 + KL + 1 ); i0++ ) {
ia = oa2 + ( i0* sa0 );
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
iy = oy + ( i0 * sy );
muladd( rea, ima, retmp, imtmp, viewY[ iy ], viewY[ iy + 1 ], viewY, 1, iy ); // eslint-disable-line max-len
}
}
return y;
}
// Form: y = α*A^T*x + y
// ( !isrm && isTransposed( trans ) ) || ( isrm && !isTransposed( trans ) )
for ( i1 = 0; i1 < ylen; i1++ ) {
retmp = 0.0;
imtmp = 0.0;
k = KL - i1;
oa2 = oa + ( i1 * sa1 ) + ( k * sa0 );
for ( i0 = max( 0, i1 - KL ); i0 < min( xlen, i1 + KU + 1 ); i0++ ) {
ia = oa2 + ( i0 * sa0 );
ix = ox + ( i0 * sx );
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex = viewX[ ix ];
imx = viewX[ ix + 1 ];
retmp = f32( retmp + f32( ( rea * rex ) - ( ima * imx ) ) );
imtmp = f32( imtmp + f32( ( rea * imx ) + ( ima * rex ) ) );
}
iy = oy + ( i1 * sy );
muladd( realpha, imalpha, retmp, imtmp, viewY[ iy ], viewY[ iy + 1 ], viewY, 1, iy ); // eslint-disable-line max-len
}
return y;
}
// EXPORTS //
module.exports = cgbmv;
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