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* @license Apache-2.0
*
* Copyright (c) 2025 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 sfill = require( '@stdlib/blas/ext/base/sfill' ).ndarray;
var sscal = require( '@stdlib/blas/base/sscal' ).ndarray;
var max = require( '@stdlib/math/base/special/max' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
// MAIN //
/**
* Performs the matrix-vector operation `y = alpha*A*x + beta*y` where `alpha` and `beta` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric band matrix, with `K` super-diagonals.
*
* @param {string} uplo - specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {NonNegativeInteger} K - number of super-diagonals of the matrix `A`
* @param {number} alpha - scalar constant
* @param {Float32Array} A - 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 {Float32Array} x - first input array
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting `x` index
* @param {number} beta - scalar constant
* @param {Float32Array} y - second input array
* @param {integer} strideY - `y` stride length
* @param {NonNegativeInteger} offsetY - starting `y` index
* @returns {Float32Array} `y`
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var A = new Float32Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] );
* var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
* var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
*
* ssbmv( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 0, 0.0, y, 1, 0 );
* // y => <Float32Array>[ 10.0, 25.0, 10.0 ]
*/
function ssbmv( uplo, N, K, alpha, A, strideA1, strideA2, offsetA, x, strideX, offsetX, beta, y, strideY, offsetY ) { // eslint-disable-line max-params, max-len
var temp1;
var temp2;
var isrm;
var jmin;
var sa0;
var sa1;
var ix;
var iy;
var jx;
var jy;
var ox;
var oy;
var oa;
var i;
var j;
isrm = isRowMajor( [ strideA1, strideA2 ] );
if ( isrm ) {
sa0 = strideA2;
sa1 = strideA1;
} else {
sa0 = strideA1;
sa1 = strideA2;
}
// Form: y = beta*y
if ( beta !== 1.0 ) {
if ( beta === 0.0 ) {
sfill( N, 0.0, y, strideY, offsetY );
} else {
sscal( N, beta, y, strideY, offsetY );
}
}
if ( alpha === 0.0 ) {
return y;
}
ox = offsetX;
oy = offsetY;
// Form: y = alpha*A*x + y
if (
( isrm && uplo === 'upper' ) ||
( !isrm && uplo === 'lower' )
) {
ix = ox;
iy = oy;
for ( i = 0; i < N; i++ ) {
temp1 = f32( alpha * x[ ix ] );
temp2 = 0.0;
jmin = max( 0, i - K );
jx = ox + ( jmin * strideX );
jy = oy + ( jmin * strideY );
for ( j = jmin; j < i; j++ ) {
oa = offsetA + ((i - j) * sa0);
y[ jy ] += f32( temp1 * A[ oa + (j * sa1) ] );
temp2 += f32( x[ jx ] * A[ oa + (j * sa1) ] );
jx += strideX;
jy += strideY;
}
y[ iy ] += f32( ( temp1 * A[ offsetA + (i * sa1) ] ) + ( alpha * temp2 ) );
ix += strideX;
iy += strideY;
}
return y;
}
// ( order === 'row-major' && uplo === 'lower') || ( order === 'column-major' && uplo === 'upper' )
if (
( isrm && uplo === 'lower' ) ||
( !isrm && uplo === 'upper' )
) {
ix = ox;
iy = oy;
for ( i = 0; i < N; i++ ) {
temp1 = f32( alpha * x[ ix ] );
temp2 = 0.0;
jmin = max( 0, i - K );
jx = ox + ( jmin * strideX );
jy = oy + ( jmin * strideY );
for ( j = jmin; j < i; j++ ) {
oa = offsetA + +((K + j - i) * sa0);
y[ jy ] += f32( temp1 * A[ oa + (i * sa1) ] );
temp2 += f32( x[ jx ] * A[ oa + (i * sa1) ] );
jx += strideX;
jy += strideY;
}
oa = offsetA + (K * sa0);
y[ iy ] += f32( ( temp1 * A[ oa + (i * sa1) ] ) + ( alpha * temp2 ) );
ix += strideX;
iy += strideY;
}
return y;
}
}
// EXPORTS //
module.exports = ssbmv;
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