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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.
*/
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var zfill = require( '@stdlib/blas/ext/base/zfill' ).ndarray;
var zscal = require( '@stdlib/blas/base/zscal' ).ndarray;
var realf = require( '@stdlib/complex/float64/real' );
var imagf = require( '@stdlib/complex/float64/imag' );
var reinterpret = require( '@stdlib/strided/base/reinterpret-complex128' );
var muladd = require( '@stdlib/complex/float64/base/mul-add' ).assign;
// MAIN //
/**
* Performs the matrix-vector operation `y = α*A*x + β*y`, where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` Hermitian matrix.
*
* @private
* @param {string} uplo - specifies whether `A` is an upper or lower triangular part of matrix is supplied.
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {Complex128} alpha - scalar constant
* @param {Complex128Array} 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 {Complex128Array} x - first input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Complex128} beta - scalar constant
* @param {Complex128Array} y - second input vector
* @param {integer} strideY - `y` stride length
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @returns {Complex128Array} `y`
*
* @example
* var Complex128Array = require( '@stdlib/array/complex128' );
* var Complex128 = require( '@stdlib/complex/float64/ctor' );
*
* var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, -2.0, 4.0, 0.0, 0.0, 0.0, 3.0, -3.0, 5.0, -5.0, 6.0, 0.0 ] );
* var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
* var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] );
* var alpha = new Complex128( 0.5, 0.5 );
* var beta = new Complex128( 0.5, -0.5 );
*
* zhemv( 'lower', 3, alpha, A, 3, 1, 0, x, 1, 0, beta, y, 1, 0 );
* // y => <Complex128Array>[ -10.0, 14.0, -11.0, 25.0, 14.0, 31.0 ]
*/
function zhemv( uplo, N, alpha, A, strideA1, strideA2, offsetA, x, strideX, offsetX, beta, y, strideY, offsetY ) { // eslint-disable-line max-params, max-len
var realpha;
var imalpha;
var rebeta;
var imbeta;
var retmp1;
var imtmp1;
var retmp2;
var imtmp2;
var viewA;
var viewX;
var viewY;
var isrm;
var cima;
var sign;
var sa0;
var sa1;
var oa2;
var rea;
var ima;
var rex;
var imx;
var ix1;
var ix0;
var iy0;
var iy1;
var oa;
var ox;
var oy;
var sx;
var sy;
var i0;
var i1;
var ia;
// 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 * 2; // stride for innermost loop
sa1 = strideA1 * 2; // stride for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1 * 2; // stride for innermost loop
sa1 = strideA2 * 2; // stride for outermost loop
}
// Decompose scalars into real and imaginary components:
rebeta = realf( beta );
imbeta = imagf( beta );
realpha = realf( alpha );
imalpha = imagf( alpha );
// y = beta*y
if ( rebeta === 0.0 && imbeta === 0.0 ) {
zfill( N, alpha, y, strideY, offsetY );
} else if ( rebeta !== 1.0 || imbeta !== 0.0 ) {
zscal( N, beta, y, strideY, offsetY );
}
if ( realpha === 0.0 && imalpha === 0.0 ) {
return y;
}
// Reinterpret arrays as real-valued views of interleaved real and imaginary components:
viewA = reinterpret( A, 0 );
viewX = reinterpret( x, 0 );
viewY = reinterpret( y, 0 );
if ( isrm ) {
sign = -1;
} else {
sign = 1;
}
oa = offsetA * 2;
ox = offsetX * 2;
oy = offsetY * 2;
sx = strideX * 2;
sy = strideY * 2;
ix1 = ox;
iy1 = oy;
oa2 = oa;
// Form: y = alpha*A*x + y
if ( ( isrm && uplo === 'upper' ) || ( !isrm && uplo === 'lower' ) ) {
for ( i1 = 0; i1 < N; i1++ ) {
rex = viewX[ ix1 ];
imx = viewX[ ix1+1 ];
retmp1 = (realpha*rex) - (imalpha*imx);
imtmp1 = (realpha*imx) + (imalpha*rex);
retmp2 = 0.0;
imtmp2 = 0.0;
ia = oa2 + ((i1+1)*sa0);
ix0 = ix1 + sx;
iy0 = iy1 + sy;
for ( i0 = i1 + 1; i0 < N; i0++ ) {
rea = viewA[ ia ];
ima = viewA[ ia+1 ];
cima = sign * ima;
muladd( retmp1, imtmp1, rea, cima, viewY[ iy0 ], viewY[ iy0+1 ], viewY, 1, iy0 ); // eslint-disable-line max-len
rex = viewX[ ix0 ];
imx = viewX[ ix0+1 ];
retmp2 += (rea*rex) + (cima*imx);
imtmp2 += (rea*imx) - (cima*rex);
ia += sa0;
ix0 += sx;
iy0 += sy;
}
ia = oa2 + (i1*sa0);
rea = viewA[ ia ];
viewY[ iy1 ] += retmp1 * rea;
viewY[ iy1+1 ] += imtmp1 * rea;
muladd( realpha, imalpha, retmp2, imtmp2, viewY[ iy1 ], viewY[ iy1+1 ], viewY, 1, iy1 ); // eslint-disable-line max-len
ix1 += sx;
iy1 += sy;
oa2 += sa1;
}
return y;
}
// ( isrm && uplo === 'lower' ) || ( !isrm && uplo === 'upper' )
for ( i1 = 0; i1 < N; i1++ ) {
rex = viewX[ ix1 ];
imx = viewX[ ix1+1 ];
retmp1 = (realpha*rex) - (imalpha*imx);
imtmp1 = (realpha*imx) + (imalpha*rex);
retmp2 = 0.0;
imtmp2 = 0.0;
ia = oa2;
ix0 = ox;
iy0 = oy;
for ( i0 = 0; i0 < i1; i0++ ) {
rea = viewA[ ia ];
ima = viewA[ ia+1 ];
cima = sign * ima;
muladd( retmp1, imtmp1, rea, cima, viewY[ iy0 ], viewY[ iy0+1 ], viewY, 1, iy0 ); // eslint-disable-line max-len
rex = viewX[ ix0 ];
imx = viewX[ ix0+1 ];
retmp2 += (rea*rex) + (cima*imx);
imtmp2 += (rea*imx) - (cima*rex);
ia += sa0;
ix0 += sx;
iy0 += sy;
}
rea = viewA[ ia ];
viewY[ iy1 ] += retmp1 * rea;
viewY[ iy1+1 ] += imtmp1 * rea;
muladd( realpha, imalpha, retmp2, imtmp2, viewY[ iy1 ], viewY[ iy1+1 ], viewY, 1, iy1 ); // eslint-disable-line max-len
ix1 += sx;
iy1 += sy;
oa2 += sa1;
}
return y;
}
// EXPORTS //
module.exports = zhemv;
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