Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* @license Apache-2.0
*
* Copyright (c) 2026 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.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var dlassq = require( '@stdlib/lapack/base/dlassq' ).ndarray;
var Float64Array = require( '@stdlib/array/float64' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var max = require( '@stdlib/math/base/special/fast/max' );
var min = require( '@stdlib/math/base/special/fast/min' );
var abs = require( '@stdlib/math/base/special/abs' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
// VARIABLES //
// Reusable scratch array for accumulating the scaled sum-of-squares computed by `dlassq` (single-threaded, so safe to share across invocations and avoids allocating within the implementation):
var ssq = new Float64Array( 2 );
// MAIN //
/**
* Computes the value of the one norm, Frobenius norm, infinity norm, or the element of largest absolute value of a real symmetric band matrix `A`.
*
* @private
* @param {string} norm - specifies the value to be returned
* @param {string} uplo - specifies whether the upper or lower triangular part of the band matrix `A` is supplied
* @param {NonNegativeInteger} N - order of the matrix `A`
* @param {NonNegativeInteger} K - number of super-/sub-diagonals of the band matrix `A`
* @param {Float64Array} AB - input band matrix stored in banded format
* @param {integer} strideAB1 - stride of the first dimension of `AB`
* @param {integer} strideAB2 - stride of the second dimension of `AB`
* @param {NonNegativeInteger} offsetAB - starting index for `AB`
* @param {Float64Array} work - workspace array (only referenced when computing the one or infinity norm)
* @param {integer} strideWork - stride length for `work`
* @param {NonNegativeInteger} offsetWork - starting index for `work`
* @returns {number} norm value
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var AB = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
* var work = new Float64Array( 3 );
*
* var out = dlansb( 'max', 'upper', 3, 1, AB, 1, 2, 0, work, 1, 0 );
* // returns 5.0
*/
function dlansb( norm, uplo, N, K, AB, strideAB1, strideAB2, offsetAB, work, strideWork, offsetWork ) {
var scale;
var value;
var absa;
var diag;
var imax;
var sum;
var l0;
var ia;
var iw;
var i;
var j;
if ( N === 0 ) {
return 0.0;
}
if ( norm === 'max' ) {
// Find max( abs( A( i, j ) ) )...
value = 0.0;
if ( uplo === 'upper' ) {
for ( j = 0; j < N; j++ ) {
ia = offsetAB + ( max( K-j, 0 )*strideAB1 ) + ( j*strideAB2 );
for ( i = max( K-j, 0 ); i <= K; i++ ) {
sum = abs( AB[ ia ] );
if ( value < sum || isnan( sum ) ) {
value = sum;
}
ia += strideAB1;
}
}
} else { // 'lower'
for ( j = 0; j < N; j++ ) {
imax = min( N-1-j, K );
ia = offsetAB + ( j*strideAB2 );
for ( i = 0; i <= imax; i++ ) {
sum = abs( AB[ ia ] );
if ( value < sum || isnan( sum ) ) {
value = sum;
}
ia += strideAB1;
}
}
}
return value;
}
if ( norm === 'one' || norm === 'inf' ) {
// Find normI( A ) ( = norm1( A ), since `A` is symmetric)...
value = 0.0;
if ( uplo === 'upper' ) {
for ( j = 0; j < N; j++ ) {
sum = 0.0;
ia = offsetAB + ( max( K-j, 0 )*strideAB1 ) + ( j*strideAB2 );
iw = offsetWork + ( max( j-K, 0 )*strideWork );
for ( i = max( j-K, 0 ); i < j; i++ ) {
absa = abs( AB[ ia ] );
sum += absa;
work[ iw ] += absa;
ia += strideAB1;
iw += strideWork;
}
diag = offsetAB + ( K*strideAB1 ) + ( j*strideAB2 );
work[ offsetWork + ( j*strideWork ) ] = sum + abs( AB[ diag ] );
}
iw = offsetWork;
for ( i = 0; i < N; i++ ) {
sum = work[ iw ];
if ( value < sum || isnan( sum ) ) {
value = sum;
}
iw += strideWork;
}
} else { // 'lower'
iw = offsetWork;
for ( i = 0; i < N; i++ ) {
work[ iw ] = 0.0;
iw += strideWork;
}
for ( j = 0; j < N; j++ ) {
diag = offsetAB + ( j*strideAB2 );
sum = work[ offsetWork + ( j*strideWork ) ] + abs( AB[ diag ] );
imax = min( N-1, j+K );
ia = offsetAB + strideAB1 + ( j*strideAB2 );
iw = offsetWork + ( ( j+1 )*strideWork );
for ( i = j+1; i <= imax; i++ ) {
absa = abs( AB[ ia ] );
sum += absa;
work[ iw ] += absa;
ia += strideAB1;
iw += strideWork;
}
if ( value < sum || isnan( sum ) ) {
value = sum;
}
}
}
return value;
}
// Find normF( A ), accumulating a scaled sum-of-squares in order to avoid overflow/underflow...
scale = 0.0;
sum = 1.0;
l0 = 0;
if ( K > 0 ) {
if ( uplo === 'upper' ) {
for ( j = 1; j < N; j++ ) {
ia = offsetAB + ( max( K-j, 0 )*strideAB1 ) + ( j*strideAB2 );
dlassq( min( j, K ), AB, strideAB1, ia, scale, sum, ssq, 1, 0 );
scale = ssq[ 0 ];
sum = ssq[ 1 ];
}
l0 = K;
} else { // 'lower'
for ( j = 0; j < N-1; j++ ) {
ia = offsetAB + strideAB1 + ( j*strideAB2 );
dlassq( min( N-1-j, K ), AB, strideAB1, ia, scale, sum, ssq, 1, 0 );
scale = ssq[ 0 ];
sum = ssq[ 1 ];
}
}
sum *= 2.0;
}
diag = offsetAB + ( l0*strideAB1 );
dlassq( N, AB, strideAB2, diag, scale, sum, ssq, 1, 0 );
scale = ssq[ 0 ];
sum = ssq[ 1 ];
return scale * sqrt( sum );
}
// EXPORTS //
module.exports = dlansb;
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