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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 abs = require( '@stdlib/math/base/special/abs' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var Float64Array = require( '@stdlib/array/float64' );
var dlassq = require( '@stdlib/lapack/base/dlassq' ).ndarray;
// VARIABLES //
var WORKSPACE = new Float64Array( 2 );
// MAIN //
/**
* Returns the value of the one-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a real tridiagonal matrix `A`.
*
* @private
* @param {string} norm - specifies the norm: 'M' (max abs), '1'/'O' (one-norm), 'I' (infinity-norm), 'F'/'E' (Frobenius)
* @param {NonNegativeInteger} N - order of the matrix
* @param {Float64Array} DL - sub-diagonal elements (length N-1)
* @param {integer} strideDL - stride length for `DL`
* @param {NonNegativeInteger} offsetDL - starting index for `DL`
* @param {Float64Array} D - diagonal elements (length N)
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index for `D`
* @param {Float64Array} DU - super-diagonal elements (length N-1)
* @param {integer} strideDU - stride length for `DU`
* @param {NonNegativeInteger} offsetDU - starting index for `DU`
* @returns {number} matrix norm
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var DL = new Float64Array( [ 1.0, 2.0, 3.0 ] );
* var D = new Float64Array( [ 4.0, 5.0, 6.0, 7.0 ] );
* var DU = new Float64Array( [ 1.0, 1.0, 1.0 ] );
*
* var norm = dlangt( 'M', 4, DL, 1, 0, D, 1, 0, DU, 1, 0 );
* // returns 7.0
*/
function dlangt( norm, N, DL, strideDL, offsetDL, D, strideD, offsetD, DU, strideDU, offsetDU ) {
var anorm;
var scale;
var sumsq;
var temp;
var out;
var odl;
var odu;
var od;
var i;
if ( N <= 0 ) {
return 0.0;
}
odl = offsetDL;
od = offsetD;
odu = offsetDU;
if ( norm === 'M' || norm === 'm' ) {
// Find max(abs(A(i,j)))
anorm = abs( D[ od + ( ( N - 1 ) * strideD ) ] );
for ( i = 0; i < N - 1; i++ ) {
temp = abs( DL[ odl + ( i * strideDL ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
temp = abs( D[ od + ( i * strideD ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
temp = abs( DU[ odu + ( i * strideDU ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
return anorm;
}
if ( norm === 'O' || norm === 'o' || norm === '1' ) {
// Find norm1(A) = max column sum
if ( N === 1 ) {
return abs( D[ od ] );
}
// First column: D[0] + DL[0]
anorm = abs( D[ od ] ) + abs( DL[ odl ] );
// Last column: D[N-1] + DU[N-2]
temp = abs( D[ od + ( ( N - 1 ) * strideD ) ] ) + abs( DU[ odu + ( ( N - 2 ) * strideDU ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
// Middle columns: D[i] + DL[i] + DU[i-1]
for ( i = 1; i < N - 1; i++ ) {
temp = abs( D[ od + ( i * strideD ) ] ) + abs( DL[ odl + ( i * strideDL ) ] ) + abs( DU[ odu + ( ( i - 1 ) * strideDU ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
return anorm;
}
if ( norm === 'I' || norm === 'i' ) {
// Find normI(A) = max row sum
if ( N === 1 ) {
return abs( D[ od ] );
}
// First row: D[0] + DU[0]
anorm = abs( D[ od ] ) + abs( DU[ odu ] );
// Last row: D[N-1] + DL[N-2]
temp = abs( D[ od + ( ( N - 1 ) * strideD ) ] ) + abs( DL[ odl + ( ( N - 2 ) * strideDL ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
// Middle rows: D[i] + DU[i] + DL[i-1]
for ( i = 1; i < N - 1; i++ ) {
temp = abs( D[ od + ( i * strideD ) ] ) + abs( DU[ odu + ( i * strideDU ) ] ) + abs( DL[ odl + ( ( i - 1 ) * strideDL ) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
return anorm;
}
// Find normF(A) = Frobenius norm
out = WORKSPACE;
scale = 0.0;
sumsq = 1.0;
dlassq( N, D, strideD, offsetD, scale, sumsq, out, 1, 0 );
if ( N > 1 ) {
dlassq( N - 1, DL, strideDL, offsetDL, out[ 0 ], out[ 1 ], out, 1, 0 );
dlassq( N - 1, DU, strideDU, offsetDU, out[ 0 ], out[ 1 ], out, 1, 0 );
}
return out[ 0 ] * sqrt( out[ 1 ] );
}
// EXPORTS //
module.exports = dlangt;
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