feat: add blas/base/dsbmv

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---

Author: ShabiShett07

lib/node_modules/@stdlib/blas/base/dsbmv/lib/ndarray.js

@@ -0,0 +1,174 @@
+/**
+* @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';
+
+// MODULES //
+
+var dfill = require( '@stdlib/blas/ext/base/dfill' ).ndarray;
+var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
+var max = require( '@stdlib/math/base/special/max' );
+var isLayout = require( '@stdlib/blas/base/assert/is-layout' );
+var isMatrixTriangle = require( '@stdlib/blas/base/assert/is-matrix-triangle' );
+
+
+// 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} order - storage layout
+* @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 {Float64Array} A - matrix
+* @param {PositiveInteger} LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
+* @param {Float64Array} x - first input array
+* @param {integer} strideX - `x` stride length
+* @param {NonNegativeInteger} offsetX - starting `x` index
+* @param {number} beta - scalar constant
+* @param {Float64Array} y - second input array
+* @param {integer} strideY - `y` stride length
+* @param {NonNegativeInteger} offsetY - starting `y` index
+* @throws {TypeError} first argument must be a valid order
+* @throws {TypeError} second argument must specify whether to reference the lower or upper triangular matrix
+* @throws {RangeError} third argument must be a nonnegative integer
+* @throws {RangeError} sixth argument must be greater than or equal to max(1,N)
+* @throws {RangeError} eighth argument must be non-zero
+* @throws {RangeError} twelfth argument must be non-zero
+* @returns {Float64Array} `y`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 2.0, 0.0, 4.0, 3.0, 5.0 ] );
+* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+* var y = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+*
+* dsbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0, 0.0, y, 1, 0 );
+* // y => <Float64Array>[ 2.0, 17.0, 21.0 ]
+*/
+function dsbmv( order, uplo, N, K, alpha, A, LDA, x, strideX, offsetX, beta, y, strideY, offsetY ) { // eslint-disable-line max-params, max-len
+	var temp1;
+	var temp2;
+	var jmin;
+	var ix;
+	var iy;
+	var jx;
+	var jy;
+	var ox;
+	var oy;
+	var i;
+	var j;
+
+	if ( !isLayout( order ) ) {
+		throw new TypeError( 'invalid argument. First argument must be a valid order. Value: `%s`.', order );
+	}
+	if ( !isMatrixTriangle( uplo ) ) {
+		throw new TypeError( 'invalid argument. Second argument must specify whether to reference the lower or upper triangular matrix. Value: `%s`.', uplo );
+	}
+	if ( N < 0 ) {
+		throw new RangeError( 'invalid argument. Third argument must be a nonnegative integer. Value: `%d`.', N );
+	}
+	if ( K < 0 ) {
+		throw new RangeError( 'invalid argument. Fourth argument must be a nonnegative integer. Value: `%d`.', K );
+	}
+	if ( LDA < max( K + 1 ) ) {
+		throw new RangeError( 'invalid argument. Seventh argument must be greater than or equal to ( K + 1 ). Value: `%d`.', N, LDA );
+	}
+	if ( strideX === 0 ) {
+		throw new RangeError( 'invalid argument. Ninth argument must be non-zero. Value: `%d`.', strideX );
+	}
+	if ( strideY === 0 ) {
+		throw new RangeError( 'invalid argument. Therteenth argument must be non-zero. Value: `%d`.', strideY );
+	}
+	if ( N === 0 || ( alpha === 0.0 && beta === 1.0 ) ) {
+		return y;
+	}
+	// Form: y = beta*y
+	if ( beta !== 1.0 ) {
+		if ( beta === 0.0 ) {
+			dfill( N, 0.0, y, strideY, offsetY );
+		} else {
+			dscal( N, beta, y, strideY, offsetY );
+		}
+	}
+	if ( alpha === 0.0 ) {
+		return y;
+	}
+	ox = offsetX;
+	oy = offsetY;
+
+	// Form: y = alpha*A*x + y
+	if (
+		( order === 'row-major' && uplo === 'upper' ) ||
+		( order === 'column-major' && uplo === 'lower' )
+	) {
+		ix = ox;
+		iy = oy;
+		for ( i = 0; i < N; i++ ) {
+			temp1 = 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++ ) {
+				y[ jy ] += temp1 * A[ (i - j) + ( j * (K + 1) ) ];
+				temp2 += x[ jx ] * A[ (i - j) + ( j * (K + 1) ) ];
+				jx += strideX;
+				jy += strideY;
+			}
+			y[ iy ] += ( temp1 * A[ 0 + ( i * (K + 1) ) ] ) + ( alpha * temp2 );
+			ix += strideX;
+			iy += strideY;
+		}
+		return y;
+	}
+
+	// ( order === 'row-major' && uplo === 'lower') || ( order === 'column-major' && uplo === 'upper' )
+	if (
+		( order === 'row-major' && uplo === 'lower' ) ||
+		( order === 'column-major' && uplo === 'upper' )
+	) {
+		ix = ox;
+		iy = oy;
+		for ( i = 0; i < N; i++ ) {
+			temp1 = 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++ ) {
+				y[ jy ] += temp1 * ( A[ (K + j - i) + ( i * (K + 1) ) ] );
+				temp2 += x[ jx ] * ( A[ (K + j - i) + ( i * (K + 1) ) ] );
+				jx += strideX;
+				jy += strideY;
+			}
+			y[ iy ] += ( temp1 * ( A[ K + ( i * (K + 1) ) ] ) ) + ( alpha * temp2 );
+			ix += strideX;
+			iy += strideY;
+		}
+		return y;
+	}
+}
+
+
+// EXPORTS //
+
+module.exports = dsbmv;