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| 1 | +/** |
| 2 | +* @license Apache-2.0 |
| 3 | +* |
| 4 | +* Copyright (c) 2026 The Stdlib Authors. |
| 5 | +* |
| 6 | +* Licensed under the Apache License, Version 2.0 (the "License"); |
| 7 | +* you may not use this file except in compliance with the License. |
| 8 | +* You may obtain a copy of the License at |
| 9 | +* |
| 10 | +* http://www.apache.org/licenses/LICENSE-2.0 |
| 11 | +* |
| 12 | +* Unless required by applicable law or agreed to in writing, software |
| 13 | +* distributed under the License is distributed on an "AS IS" BASIS, |
| 14 | +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 15 | +* See the License for the specific language governing permissions and |
| 16 | +* limitations under the License. |
| 17 | +*/ |
| 18 | + |
| 19 | +'use strict'; |
| 20 | + |
| 21 | +// MODULES // |
| 22 | + |
| 23 | +var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' ); |
| 24 | +var zfill = require( '@stdlib/blas/ext/base/zfill' ).ndarray; |
| 25 | +var zscal = require( '@stdlib/blas/base/zscal' ).ndarray; |
| 26 | +var realf = require( '@stdlib/complex/float64/real' ); |
| 27 | +var imagf = require( '@stdlib/complex/float64/imag' ); |
| 28 | +var reinterpret = require( '@stdlib/strided/base/reinterpret-complex128' ); |
| 29 | +var muladd = require( '@stdlib/complex/float64/base/mul-add' ).assign; |
| 30 | + |
| 31 | + |
| 32 | +// MAIN // |
| 33 | + |
| 34 | +/** |
| 35 | +* 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. |
| 36 | +* |
| 37 | +* @private |
| 38 | +* @param {string} uplo - specifies whether `A` is an upper or lower triangular part of matrix is supplied. |
| 39 | +* @param {NonNegativeInteger} N - number of elements along each dimension of `A` |
| 40 | +* @param {Complex128} alpha - scalar constant |
| 41 | +* @param {Complex128Array} A - input matrix |
| 42 | +* @param {integer} strideA1 - stride of the first dimension of `A` |
| 43 | +* @param {integer} strideA2 - stride of the second dimension of `A` |
| 44 | +* @param {NonNegativeInteger} offsetA - starting index for `A` |
| 45 | +* @param {Complex128Array} x - first input vector |
| 46 | +* @param {integer} strideX - `x` stride length |
| 47 | +* @param {NonNegativeInteger} offsetX - starting index for `x` |
| 48 | +* @param {Complex128} beta - scalar constant |
| 49 | +* @param {Complex128Array} y - second input vector |
| 50 | +* @param {integer} strideY - `y` stride length |
| 51 | +* @param {NonNegativeInteger} offsetY - starting index for `y` |
| 52 | +* @returns {Complex128Array} `y` |
| 53 | +* |
| 54 | +* @example |
| 55 | +* var Complex128Array = require( '@stdlib/array/complex128' ); |
| 56 | +* var Complex128 = require( '@stdlib/complex/float64/ctor' ); |
| 57 | +* |
| 58 | +* 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 ] ); |
| 59 | +* var x = new Complex128Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] ); |
| 60 | +* var y = new Complex128Array( [ 3.0, 3.0, 2.0, 2.0, 1.0, 1.0 ] ); |
| 61 | +* var alpha = new Complex128( 0.5, 0.5 ); |
| 62 | +* var beta = new Complex128( 0.5, -0.5 ); |
| 63 | +* |
| 64 | +* zhemv( 'lower', 3, alpha, A, 3, 1, 0, x, 1, 0, beta, y, 1, 0 ); |
| 65 | +* // y => <Complex128Array>[ -10.0, 14.0, -11.0, 25.0, 14.0, 31.0 ] |
| 66 | +*/ |
| 67 | +function zhemv( uplo, N, alpha, A, strideA1, strideA2, offsetA, x, strideX, offsetX, beta, y, strideY, offsetY ) { // eslint-disable-line max-params, max-len |
| 68 | + var realpha; |
| 69 | + var imalpha; |
| 70 | + var rebeta; |
| 71 | + var imbeta; |
| 72 | + var retmp1; |
| 73 | + var imtmp1; |
| 74 | + var retmp2; |
| 75 | + var imtmp2; |
| 76 | + var viewA; |
| 77 | + var viewX; |
| 78 | + var viewY; |
| 79 | + var isrm; |
| 80 | + var cima; |
| 81 | + var sign; |
| 82 | + var sa0; |
| 83 | + var sa1; |
| 84 | + var oa2; |
| 85 | + var rea; |
| 86 | + var ima; |
| 87 | + var rex; |
| 88 | + var imx; |
| 89 | + var ix1; |
| 90 | + var ix0; |
| 91 | + var iy0; |
| 92 | + var iy1; |
| 93 | + var oa; |
| 94 | + var ox; |
| 95 | + var oy; |
| 96 | + var sx; |
| 97 | + var sy; |
| 98 | + var i0; |
| 99 | + var i1; |
| 100 | + var ia; |
| 101 | + |
| 102 | + // Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop... |
| 103 | + |
| 104 | + isrm = isRowMajor( [ strideA1, strideA2 ] ); |
| 105 | + if ( isrm ) { |
| 106 | + // For row-major matrices, the last dimension has the fastest changing index... |
| 107 | + sa0 = strideA2 * 2; // stride for innermost loop |
| 108 | + sa1 = strideA1 * 2; // stride for outermost loop |
| 109 | + } else { // isColMajor |
| 110 | + // For column-major matrices, the first dimension has the fastest changing index... |
| 111 | + sa0 = strideA1 * 2; // stride for innermost loop |
| 112 | + sa1 = strideA2 * 2; // stride for outermost loop |
| 113 | + } |
| 114 | + // Decompose scalars into real and imaginary components: |
| 115 | + rebeta = realf( beta ); |
| 116 | + imbeta = imagf( beta ); |
| 117 | + realpha = realf( alpha ); |
| 118 | + imalpha = imagf( alpha ); |
| 119 | + |
| 120 | + // y = beta*y |
| 121 | + if ( rebeta === 0.0 && imbeta === 0.0 ) { |
| 122 | + zfill( N, alpha, y, strideY, offsetY ); |
| 123 | + } else if ( rebeta !== 1.0 || imbeta !== 0.0 ) { |
| 124 | + zscal( N, beta, y, strideY, offsetY ); |
| 125 | + } |
| 126 | + if ( realpha === 0.0 && imalpha === 0.0 ) { |
| 127 | + return y; |
| 128 | + } |
| 129 | + // Reinterpret arrays as real-valued views of interleaved real and imaginary components: |
| 130 | + viewA = reinterpret( A, 0 ); |
| 131 | + viewX = reinterpret( x, 0 ); |
| 132 | + viewY = reinterpret( y, 0 ); |
| 133 | + if ( isrm ) { |
| 134 | + sign = -1; |
| 135 | + } else { |
| 136 | + sign = 1; |
| 137 | + } |
| 138 | + oa = offsetA * 2; |
| 139 | + ox = offsetX * 2; |
| 140 | + oy = offsetY * 2; |
| 141 | + sx = strideX * 2; |
| 142 | + sy = strideY * 2; |
| 143 | + ix1 = ox; |
| 144 | + iy1 = oy; |
| 145 | + oa2 = oa; |
| 146 | + |
| 147 | + // Form: y = alpha*A*x + y |
| 148 | + if ( ( isrm && uplo === 'upper' ) || ( !isrm && uplo === 'lower' ) ) { |
| 149 | + for ( i1 = 0; i1 < N; i1++ ) { |
| 150 | + rex = viewX[ ix1 ]; |
| 151 | + imx = viewX[ ix1+1 ]; |
| 152 | + retmp1 = (realpha*rex) - (imalpha*imx); |
| 153 | + imtmp1 = (realpha*imx) + (imalpha*rex); |
| 154 | + retmp2 = 0.0; |
| 155 | + imtmp2 = 0.0; |
| 156 | + ia = oa2 + ((i1+1)*sa0); |
| 157 | + ix0 = ix1 + sx; |
| 158 | + iy0 = iy1 + sy; |
| 159 | + for ( i0 = i1 + 1; i0 < N; i0++ ) { |
| 160 | + rea = viewA[ ia ]; |
| 161 | + ima = viewA[ ia+1 ]; |
| 162 | + cima = sign * ima; |
| 163 | + muladd( retmp1, imtmp1, rea, cima, viewY[ iy0 ], viewY[ iy0+1 ], viewY, 1, iy0 ); // eslint-disable-line max-len |
| 164 | + rex = viewX[ ix0 ]; |
| 165 | + imx = viewX[ ix0+1 ]; |
| 166 | + retmp2 += (rea*rex) + (cima*imx); |
| 167 | + imtmp2 += (rea*imx) - (cima*rex); |
| 168 | + ia += sa0; |
| 169 | + ix0 += sx; |
| 170 | + iy0 += sy; |
| 171 | + } |
| 172 | + ia = oa2 + (i1*sa0); |
| 173 | + rea = viewA[ ia ]; |
| 174 | + viewY[ iy1 ] += retmp1 * rea; |
| 175 | + viewY[ iy1+1 ] += imtmp1 * rea; |
| 176 | + muladd( realpha, imalpha, retmp2, imtmp2, viewY[ iy1 ], viewY[ iy1+1 ], viewY, 1, iy1 ); // eslint-disable-line max-len |
| 177 | + ix1 += sx; |
| 178 | + iy1 += sy; |
| 179 | + oa2 += sa1; |
| 180 | + } |
| 181 | + return y; |
| 182 | + } |
| 183 | + // ( isrm && uplo === 'lower' ) || ( !isrm && uplo === 'upper' ) |
| 184 | + for ( i1 = 0; i1 < N; i1++ ) { |
| 185 | + rex = viewX[ ix1 ]; |
| 186 | + imx = viewX[ ix1+1 ]; |
| 187 | + retmp1 = (realpha*rex) - (imalpha*imx); |
| 188 | + imtmp1 = (realpha*imx) + (imalpha*rex); |
| 189 | + retmp2 = 0.0; |
| 190 | + imtmp2 = 0.0; |
| 191 | + ia = oa2; |
| 192 | + ix0 = ox; |
| 193 | + iy0 = oy; |
| 194 | + for ( i0 = 0; i0 < i1; i0++ ) { |
| 195 | + rea = viewA[ ia ]; |
| 196 | + ima = viewA[ ia+1 ]; |
| 197 | + cima = sign * ima; |
| 198 | + muladd( retmp1, imtmp1, rea, cima, viewY[ iy0 ], viewY[ iy0+1 ], viewY, 1, iy0 ); // eslint-disable-line max-len |
| 199 | + rex = viewX[ ix0 ]; |
| 200 | + imx = viewX[ ix0+1 ]; |
| 201 | + retmp2 += (rea*rex) + (cima*imx); |
| 202 | + imtmp2 += (rea*imx) - (cima*rex); |
| 203 | + ia += sa0; |
| 204 | + ix0 += sx; |
| 205 | + iy0 += sy; |
| 206 | + } |
| 207 | + rea = viewA[ ia ]; |
| 208 | + viewY[ iy1 ] += retmp1 * rea; |
| 209 | + viewY[ iy1+1 ] += imtmp1 * rea; |
| 210 | + muladd( realpha, imalpha, retmp2, imtmp2, viewY[ iy1 ], viewY[ iy1+1 ], viewY, 1, iy1 ); // eslint-disable-line max-len |
| 211 | + ix1 += sx; |
| 212 | + iy1 += sy; |
| 213 | + oa2 += sa1; |
| 214 | + } |
| 215 | + return y; |
| 216 | +} |
| 217 | + |
| 218 | + |
| 219 | +// EXPORTS // |
| 220 | + |
| 221 | +module.exports = zhemv; |
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