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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 */
'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 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 an upper Hessenberg matrix `A`.
*
* ## Notes
*
* - The part of `A` below the first subdiagonal is not referenced.
*
* @private
* @param {string} norm - specifies the value to be returned
* @param {NonNegativeInteger} N - order 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} work - workspace array (only referenced when computing the 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 A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 0.0, 7.0, 8.0 ] );
* var work = new Float64Array( 3 );
*
* var out = dlanhs( 'max', 3, A, 3, 1, 0, work, 1, 0 );
* // returns 8.0
*/
function dlanhs( norm, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) {
var scale;
var value;
var imax;
var sum;
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;
for ( j = 0; j < N; j++ ) {
imax = min( N-1, j+1 );
ia = offsetA + ( j*strideA2 );
for ( i = 0; i <= imax; i++ ) {
sum = abs( A[ ia ] );
if ( value < sum || isnan( sum ) ) {
value = sum;
}
ia += strideA1;
}
}
return value;
}
if ( norm === 'one' ) {
// Find norm1( A ) (i.e., the maximum column sum)...
value = 0.0;
for ( j = 0; j < N; j++ ) {
imax = min( N-1, j+1 );
ia = offsetA + ( j*strideA2 );
sum = 0.0;
for ( i = 0; i <= imax; i++ ) {
sum += abs( A[ ia ] );
ia += strideA1;
}
if ( value < sum || isnan( sum ) ) {
value = sum;
}
}
return value;
}
if ( norm === 'inf' ) {
// Find normI( A ) (i.e., the maximum row sum)...
iw = offsetWork;
for ( i = 0; i < N; i++ ) {
work[ iw ] = 0.0;
iw += strideWork;
}
for ( j = 0; j < N; j++ ) {
imax = min( N-1, j+1 );
ia = offsetA + ( j*strideA2 );
iw = offsetWork;
for ( i = 0; i <= imax; i++ ) {
work[ iw ] += abs( A[ ia ] );
ia += strideA1;
iw += strideWork;
}
}
value = 0.0;
iw = offsetWork;
for ( i = 0; i < N; i++ ) {
sum = work[ iw ];
if ( value < sum || isnan( sum ) ) {
value = sum;
}
iw += strideWork;
}
return value;
}
// Find normF( A ) (i.e., `norm === 'fro'`), accumulating a scaled sum-of-squares over the columns in order to avoid overflow/underflow...
scale = 0.0;
sum = 1.0;
for ( j = 0; j < N; j++ ) {
ia = offsetA + ( j*strideA2 );
dlassq( min( N, j+2 ), A, strideA1, ia, scale, sum, ssq, 1, 0 );
scale = ssq[ 0 ];
sum = ssq[ 1 ];
}
return scale * sqrt( sum );
}
// EXPORTS //
module.exports = dlanhs;
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