stdlib-js · ShabiShett07 · Apr 29, 2025
diff --git a/lib/node_modules/@stdlib/blas/base/dtbmv/lib/base.js b/lib/node_modules/@stdlib/blas/base/dtbmv/lib/base.js
@@ -0,0 +1,171 @@
+/**
+* @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 max = require( '@stdlib/math/base/special/max' );
+var min = require( '@stdlib/math/base/special/min' );
+
+
+// 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 band matrix, with ( `K` + 1 ) diagonals.
+*
+* @private
+* @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 {NonNegativeInteger} K - number of super-diagonals or sub-diagonals of the matrix `A`
+* @param {Float64Array} 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 {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 A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+*
+* dtbmv( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
+* // x => <Float64Array>[ 3.0, 11.0, 3.0 ]
+*/
+function dtbmv( uplo, trans, diag, N, K, A, strideA1, strideA2, offsetA, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
+	var nonunit;
+	var isrm;
+	var idx;
+	var tmp;
+	var sa0;
+	var sa1;
+	var ix0;
+	var ix1;
+	var i0;
+	var i1;
+	var oa;
+	var ox;
+
+	// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
+
+	isrm = isRowMajor( [ strideA1, strideA2 ] );
+	nonunit = ( diag === 'non-unit' );
+
+	if ( isrm ) {
+		// For row-major matrices, the last dimension has the fastest changing index...
+		sa0 = strideA2; // stride for innermost loop
+		sa1 = strideA1; // stride for outermost loop
+	} else { // isColMajor
+		// For column-major matrices, the first dimension has the fastest changing index...
+		sa0 = strideA1; // stride for innermost loop
+		sa1 = strideA2; // stride for outermost loop
+	}
+	ox = offsetX;
+	if (
+		( !isrm && trans === 'no-transpose' && uplo === 'upper' ) ||
+		( isrm && trans !== 'no-transpose' && uplo === 'lower' )
+	) {
+		ix1 = ox;
+		for ( i1 = 0; i1 < N; i1++ ) {
+			oa = offsetA + ( sa1 * i1 );
+			tmp = x[ ix1 ];
+			if ( nonunit ) {
+				tmp = A[ oa + ( sa0 * K ) ] * x[ ix1 ];
+			}
+			for ( i0 = i1 + 1; i0 <= min( N - 1, i1 + K ); i0++ ) {
+				ix0 = ox + ( i0 * strideX );
+				idx = oa + ( sa0 * ( K + i0 - i1 ) );
+				tmp += A[ idx ] * x[ ix0 ];
+			}
+			x[ ix1 ] = tmp;
+			ix1 += strideX;
+		}
+		return x;
+	}
+	if (
+		( !isrm && trans === 'no-transpose' && uplo === 'lower' ) ||
+		( isrm && trans !== 'no-transpose' && uplo === 'upper' )
+	) {
+		ix1 = ox + ( (N - 1) * strideX );
+		for ( i1 = N - 1; i1 >= 0; i1-- ) {
+			oa = offsetA;
+			tmp = x[ ix1 ];
+			if ( nonunit ) {
+				tmp = A[ oa + ( sa1 * i1 ) ] * x[ ix1 ];
+			}
+			for ( i0 = max( 0, i1 - K ); i0 < i1; i0++ ) {
+				idx = oa + ( sa1 * i0 ) + ( sa0 * ( i1 - i0 ) );
+				ix0 = ox + ( i0 * strideX );
+				tmp += A[ idx ] * x[ ix0 ];
+			}
+			x[ ix1 ] = tmp;
+			ix1 -= strideX;
+		}
+		return x;
+	}
+	if (
+		( !isrm && trans !== 'no-transpose' && uplo === 'upper' ) ||
+		( isrm && trans === 'no-transpose' && uplo === 'lower' )
+	) {
+		ix1 = x + ( ( N - 1 ) * strideX );
+		for ( i1 = N - 1; i1 >= 0; i1-- ) {
+			oa = offsetA + ( sa1 * i1 );
+			tmp = x[ ix1 ];
+			if ( nonunit ) {
+				tmp = A[ oa + ( sa0 * K ) ] * x[ ix1 ];
+			}
+			for ( i0 = max( 0, i1 - K ); i0 < i1; i0++ ) {
+				idx = oa + ( sa0 * ( K + i0 - i1 ) );
+				ix0 = ox + ( i0 * strideX );
+				tmp += A[ idx ] * x[ ix0 ];
+			}
+			x[ ix1 ] = tmp;
+			ix1 -= strideX;
+		}
+		return x;
+	}
+	// ( !isrm && trans !== 'no-transpose' && uplo === 'lower' ) || ( isrm && trans === 'no-transpose' && uplo === 'upper' )
+	ix1 = ox;
+	for ( i1 = 0; i1 < N; i1++ ) {
+		oa = offsetA + ( sa1 * i1 );
+		tmp = x[ ix1 ];
+		if ( nonunit ) {
+			tmp = A[ oa ] * x[ ix1 ];
+		}
+		for ( i0 = i1 + 1; i0 <= min( N - 1, i1 + K ); i0++ ) {
+			ix0 = ox + ( i0 * strideX );
+			idx = oa + ( sa0 * ( i0 - i1 ) );
+			tmp += A[ idx ] * x[ ix0 ];
+		}
+		x[ ix1 ] = tmp;
+		ix1 += strideX;
+	}
+	return x;
+}
+
+
+// EXPORTS //
+
+module.exports = dtbmv;