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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 reinterpret = require( '@stdlib/strided/base/reinterpret-complex128' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );
var mul = require( '@stdlib/complex/float64/base/mul' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
// 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 ) {
return ( str !== 'no-transpose' );
}
/**
* Tests whether to use conjugation when transposing.
*
* @private
* @param {string} str - input string
* @returns {boolean} boolean indicating whether to conjugate
*
* @example
* var bool = isConjugate( 'conjugate-transpose' );
* // returns true
*
* @example
* var bool = isConjugate( 'transpose' );
* // returns false
*/
function isConjugate( str ) {
return ( str === 'conjugate-transpose' );
}
// MAIN //
/**
* Performs one of the matrix-vector operations `y = α*A*x + β*y`, `y = α*A^T*x + β*y`, or `y = α*A^H*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` matrix.
*
* @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 {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, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
* var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
* var y = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0 ] );
*
* zgemv( 'no-transpose', 2, 3, new Complex128( 1.0, 0.0 ), A, 3, 1, 0, x, 1, 0, new Complex128( 1.0, 0.0 ), y, 1, 0 );
*/
function zgemv( trans, M, N, alpha, A, strideA1, strideA2, offsetA, x, strideX, offsetX, beta, y, strideY, offsetY ) { // eslint-disable-line max-params, max-len
var viewA;
var viewX;
var viewY;
var isrm;
var xlen;
var ylen;
var tmp;
var are;
var aim;
var da0;
var da1;
var vre;
var vim;
var tre;
var tim;
var sgn;
var sa;
var ix;
var iy;
var ia;
var i1;
var i0;
// Note on variable naming convention: da#, i# where # corresponds to the loop number, with `0` being the innermost loop...
isrm = isRowMajor( [ strideA1, strideA2 ] );
if ( isTransposed( trans ) ) {
xlen = M;
ylen = N;
} else {
xlen = N;
ylen = M;
}
// y = beta*y
if ( real( beta ) === 0.0 && imag( beta ) === 0.0 ) {
zfill( ylen, new Complex128( 0.0, 0.0 ), y, strideY, offsetY );
} else if ( real( beta ) !== 1.0 || imag( beta ) !== 0.0 ) {
zscal( ylen, beta, y, strideY, offsetY );
}
if ( real( alpha ) === 0.0 && imag( alpha ) === 0.0 ) {
return y;
}
// Reinterpret complex arrays as real arrays:
viewA = reinterpret( A, 0 );
viewX = reinterpret( x, 0 );
viewY = reinterpret( y, 0 );
// Adjust strides and offsets for real arrays (each complex number = 2 doubles):
sa = strideA1 * 2;
strideA2 *= 2;
strideX *= 2;
strideY *= 2;
offsetA *= 2;
offsetX *= 2;
offsetY *= 2;
// Form: y = α*A*x + y
if (
( !isrm && !isTransposed( trans ) ) ||
( isrm && isTransposed( trans ) )
) {
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
da0 = strideA2; // offset increment for innermost loop
da1 = sa - ( ylen * strideA2 ); // offset increment for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
da0 = sa; // offset increment for innermost loop
da1 = strideA2 - ( ylen * sa ); // offset increment for outermost loop
}
sgn = ( isConjugate( trans ) ) ? -1.0 : 1.0;
ia = offsetA;
ix = offsetX;
for ( i1 = 0; i1 < xlen; i1++ ) {
// tmp = alpha * x[ ix ]
tmp = mul( alpha, x.get( ix / 2 ) );
tre = real( tmp );
tim = imag( tmp );
if ( tre !== 0.0 || tim !== 0.0 ) {
iy = offsetY;
for ( i0 = 0; i0 < ylen; i0++ ) {
// y[ iy ] += A[ ia ] * tmp
are = viewA[ ia ];
aim = viewA[ ia + 1 ] * sgn;
vre = viewY[ iy ];
vim = viewY[ iy + 1 ];
// Complex multiply: ( are + aim*i ) * ( tre + tim*i )
viewY[ iy ] = vre + ( ( are * tre ) - ( aim * tim ) );
viewY[ iy + 1 ] = vim + ( ( are * tim ) + ( aim * tre ) );
iy += strideY;
ia += da0;
}
} else {
ia += da0 * ylen;
}
ix += strideX;
ia += da1;
}
return y;
}
// Form: y = α*A^T*x + y or y = α*A^H*x + y
// ( !isrm && isTransposed( trans ) ) || ( isrm && !isTransposed( trans ) )
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
da0 = strideA2; // offset increment for innermost loop
da1 = sa - ( xlen * strideA2 ); // offset increment for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
da0 = sa; // offset increment for innermost loop
da1 = strideA2 - ( xlen * sa ); // offset increment for outermost loop
}
sgn = ( isConjugate( trans ) ) ? -1.0 : 1.0;
ia = offsetA;
iy = offsetY;
for ( i1 = 0; i1 < ylen; i1++ ) {
tre = 0.0;
tim = 0.0;
ix = offsetX;
for ( i0 = 0; i0 < xlen; i0++ ) {
are = viewA[ ia ];
aim = viewA[ ia + 1 ] * sgn;
vre = viewX[ ix ];
vim = viewX[ ix + 1 ];
// tmp += A[ ia ] * x[ ix ] (complex multiply and accumulate)
tre += ( ( are * vre ) - ( aim * vim ) );
tim += ( ( are * vim ) + ( aim * vre ) );
ix += strideX;
ia += da0;
}
// y[ iy ] += alpha * tmp
vre = viewY[ iy ];
vim = viewY[ iy + 1 ];
// alpha * ( tre + tim*i )
are = real( alpha );
aim = imag( alpha );
viewY[ iy ] = vre + ( ( are * tre ) - ( aim * tim ) );
viewY[ iy + 1 ] = vim + ( ( are * tim ) + ( aim * tre ) );
iy += strideY;
ia += da1;
}
return y;
}
// EXPORTS //
module.exports = zgemv;
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