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* @license Apache-2.0
*
* Copyright (c) 2024 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';
// MAIN //
/**
* Performs one of the matrix-vector operations `x = A*x` or `x = A^T*x`, where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix, supplied in packed form.
*
* @private
* @param {string} order - storage layout
* @param {string} uplo - specifies whether `A` is an upper or lower triangular matrix
* @param {string} trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
* @param {string} diag - specifies whether `A` has a unit diagonal
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {Float64Array} AP - packed form of a symmetric matrix `A`
* @param {integer} strideAP - `AP` stride length
* @param {NonNegativeInteger} offsetAP - starting index for `AP`
* @param {Float64Array} x - input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {Float64Array} `x`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] ); // => [ [ 1.0, 2.0, 3.0 ], [ 0.0, 1.0, 2.0 ], [ 0.0, 0.0, 1.0 ] ]
* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
*
* dtpmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, AP, 1, 0, x, 1, 0 );
* // x => <Float64Array>[ 14.0, 8.0, 3.0 ]
*/
function dtpmv( order, uplo, trans, diag, N, AP, strideAP, offsetAP, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
var nonunit;
var isrm;
var tmp;
var iap;
var ix0;
var ix1;
var i0;
var i1;
var kk;
var ox;
isrm = ( order === 'row-major' );
nonunit = ( diag === 'non-unit' );
kk = offsetAP;
ox = offsetX;
if (
( !isrm && uplo === 'upper' && trans === 'no-transpose' ) ||
( isrm && uplo === 'lower' && trans !== 'no-transpose' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
if ( x[ ix1 ] !== 0.0 ) {
tmp = x[ ix1 ];
iap = kk;
ix0 = ox;
for ( i0 = 0; i0 < i1; i0++ ) {
x[ ix0 ] += AP[ iap ] * tmp;
iap += strideAP;
ix0 += strideX;
}
if ( nonunit ) {
x[ix0] *= AP[ iap ];
}
}
ix1 += strideX;
kk += ( i1 + 1 ) * strideAP;
}
return x;
}
if (
( !isrm && uplo === 'lower' && trans === 'no-transpose' ) ||
( isrm && uplo === 'upper' && trans !== 'no-transpose' )
) {
kk += ( ( N * ( N + 1 ) / 2 ) - 1 ) * strideAP;
ox += ( N - 1 ) * strideX;
ix1 = ox;
for ( i1 = N-1; i1 >=0; i1-- ) {
if ( x[ ix1 ] !== 0.0 ) {
tmp = x[ ix1 ];
iap = kk;
ix0 = ox;
for ( i0 = N-1; i0 > i1; i0-- ) {
x[ ix0 ] += AP[ iap ] * tmp;
iap -= strideAP;
ix0 -= strideX;
}
if ( nonunit ) {
x[ ix0 ] *= AP[ iap ];
}
}
ix1 -= strideX;
kk -= ( N - i1 ) * strideAP;
}
return x;
}
if (
( !isrm && uplo === 'upper' && trans !== 'no-transpose' ) ||
( isrm && uplo === 'lower' && trans === 'no-transpose' )
) {
kk += ( ( N * ( N + 1 ) / 2 ) - 1 ) * strideAP;
ix1 = ox + ( ( N - 1 ) * strideX );
for ( i1 = N-1; i1 >= 0; i1-- ) {
tmp = x[ ix1 ];
iap = kk;
ix0 = ix1;
if ( nonunit ) {
tmp *= AP[ iap ];
}
for ( i0 = i1-1; i0 >= 0; i0-- ) {
ix0 -= strideX;
iap -= strideAP;
tmp += AP[ iap ] * x[ ix0 ];
}
x[ ix1 ] = tmp;
ix1 -= strideX;
kk -= ( i1 + 1 ) * strideAP;
}
return x;
}
// ( !isrm && uplo === 'lower' && trans !== 'no-transpose' ) || ( isrm && uplo === 'upper' && trans === 'no-transpose' )
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
tmp = x[ ix1 ];
iap = kk;
ix0 = ix1;
if ( nonunit ) {
tmp *= AP[ iap ];
}
for ( i0 = i1+1; i0 < N; i0++ ) {
ix0 += strideX;
iap += strideAP;
tmp += AP[ iap ] * x[ ix0 ];
}
x[ ix1 ] = tmp;
ix1 += strideX;
kk += ( N - i1 ) * strideAP;
}
return x;
}
// EXPORTS //
module.exports = dtpmv;
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