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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.
*/
'use strict';
// MODULES //
var dlassq = require( '@stdlib/lapack/base/dlassq' ).ndarray;
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var Float64Array = require( '@stdlib/array/float64' );
// VARIABLES //
var work = new Float64Array( 2 );
// MAIN //
/**
* Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
*
* ## Notes
*
* - `D` should have `N` indexed elements.
* - `E` should have `N-1` indexed elements.
*
* @private
* @param {string} norm - specifies the norm to be returned
* @param {NonNegativeInteger} N - order of the matrix
* @param {Float64Array} D - array containing the diagonal elements
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index for `D`
* @param {Float64Array} E - array containing the sub-diagonal elements
* @param {integer} strideE - stride length for `E`
* @param {NonNegativeInteger} offsetE - starting index for `E`
* @returns {number} norm value
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var D = new Float64Array( [ 4.0, -2.0, 5.0, -1.0 ] );
* var E = new Float64Array( [ 1.0, -3.0, 2.0 ] );
*
* var out = dlanst( 'max', 4, D, 1, 0, E, 1, 0 );
* // returns 5.0
*/
function dlanst( norm, N, D, strideD, offsetD, E, strideE, offsetE ) {
var anorm;
var scale;
var sum;
var id;
var ie;
var i;
if ( N <= 0 ) {
return 0.0;
}
if ( norm === 'max' ) {
// Find max(abs(A(i,j)))...
id = offsetD + ( ( N - 1 ) * strideD );
anorm = abs( D[ id ] );
id = offsetD;
ie = offsetE;
for ( i = 0; i < N - 1; i++ ) {
sum = abs( D[ id ] );
if ( anorm < sum || isnan( sum ) ) {
anorm = sum;
}
sum = abs( E[ ie ] );
if ( anorm < sum || isnan( sum ) ) {
anorm = sum;
}
id += strideD;
ie += strideE;
}
return anorm;
}
if ( norm === 'one-norm' || norm === 'infinity-norm' ) {
// Find norm1(A) which equals normI(A) for symmetric tridiagonal matrices...
if ( N === 1 ) {
return abs( D[ offsetD ] );
}
anorm = abs( D[ offsetD ] ) + abs( E[ offsetE ] );
id = offsetD + ( ( N - 1 ) * strideD );
ie = offsetE + ( ( N - 2 ) * strideE );
sum = abs( E[ ie ] ) + abs( D[ id ] );
if ( anorm < sum || isnan( sum ) ) {
anorm = sum;
}
id = offsetD + strideD;
ie = offsetE;
for ( i = 1; i < N - 1; i++ ) {
sum = abs( D[ id ] ) + abs( E[ ie + strideE ] ) + abs( E[ ie ] );
if ( anorm < sum || isnan( sum ) ) {
anorm = sum;
}
id += strideD;
ie += strideE;
}
return anorm;
}
// Find normF(A)...
scale = 0.0;
sum = 1.0;
if ( N > 1 ) {
// Seed the workspace with the current scale and sum, as `dlassq` returns the workspace unmodified whenever either value is NaN...
work[ 0 ] = scale;
work[ 1 ] = sum;
dlassq( N - 1, E, strideE, offsetE, scale, sum, work, 1, 0 );
scale = work[ 0 ];
sum = 2.0 * work[ 1 ];
}
// Seed the workspace (see above)...
work[ 0 ] = scale;
work[ 1 ] = sum;
dlassq( N, D, strideD, offsetD, scale, sum, work, 1, 0 );
return work[ 0 ] * sqrt( work[ 1 ] );
}
// EXPORTS //
module.exports = dlanst;
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