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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var Float64Array = require( '@stdlib/array/float64' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/abs' );
// VARIABLES //
var out = new Float64Array( 2 );
var work = new Float64Array( 0 );
// MAIN //
/**
* Returns the value of the one-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a real symmetric matrix `A`.
*
* @private
* @param {string} norm - specifies the norm: 'M' (max abs), '1'/'O' (one-norm), 'I' (infinity-norm), 'F'/'E' (Frobenius)
* @param {string} uplo - specifies whether the upper or lower triangular part of `A` is referenced ('upper' or 'lower')
* @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`
* @returns {number} matrix norm
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* // A = [ 1.0, 2.0, 2.0, 5.0 ] (2x2 symmetric, row-major)
* var A = new Float64Array( [ 1.0, 2.0, 2.0, 5.0 ] );
*
* var norm = dlansy( 'M', 'upper', 2, A, 2, 1, 0 );
* // returns 5.0
*/
function dlansy( norm, uplo, N, A, strideA1, strideA2, offsetA ) {
var scale;
var sumsq;
var anorm;
var absa;
var temp;
var i;
var j;
if ( N <= 0 ) {
return 0.0;
}
if ( norm === 'M' || norm === 'm' ) {
// Find max(abs(A(i,j)))
anorm = 0.0;
if ( uplo === 'upper' ) {
for ( j = 0; j < N; j++ ) {
for ( i = 0; i <= j; i++ ) {
temp = abs( A[ offsetA + (i*strideA1) + (j*strideA2) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
}
} else {
for ( j = 0; j < N; j++ ) {
for ( i = j; i < N; i++ ) {
temp = abs( A[ offsetA + (i*strideA1) + (j*strideA2) ] );
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
}
}
return anorm;
}
if ( norm === 'I' || norm === 'i' || norm === 'O' || norm === 'o' || norm === '1' ) {
// Find normI(A) ( = norm1(A), since A is symmetric)
anorm = 0.0;
if ( work.length < N ) {
work = new Float64Array( N );
} else {
for ( i = 0; i < N; i++ ) {
work[ i ] = 0.0;
}
}
if ( uplo === 'upper' ) {
for ( j = 0; j < N; j++ ) {
temp = 0.0;
for ( i = 0; i < j; i++ ) {
absa = abs( A[ offsetA + (i*strideA1) + (j*strideA2) ] );
temp += absa;
work[ i ] += absa;
}
work[ j ] = temp + abs( A[ offsetA + (j*strideA1) + (j*strideA2) ] );
}
for ( i = 0; i < N; i++ ) {
temp = work[ i ];
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
} else {
for ( j = 0; j < N; j++ ) {
temp = work[ j ] + abs( A[ offsetA + (j*strideA1) + (j*strideA2) ] );
for ( i = j + 1; i < N; i++ ) {
absa = abs( A[ offsetA + (i*strideA1) + (j*strideA2) ] );
temp += absa;
work[ i ] += absa;
}
if ( anorm < temp || isnan( temp ) ) {
anorm = temp;
}
}
}
return anorm;
}
if ( norm === 'F' || norm === 'f' || norm === 'E' || norm === 'e' ) {
// Find normF(A) = Frobenius norm
scale = 0.0;
sumsq = 1.0;
if ( uplo === 'upper' ) {
for ( j = 1; j < N; j++ ) {
dlassq( j, A, strideA1, offsetA + (j*strideA2), scale, sumsq, out, 1, 0 );
scale = out[ 0 ];
sumsq = out[ 1 ];
}
} else {
for ( j = 0; j < N - 1; j++ ) {
dlassq( N - j - 1, A, strideA1, offsetA + ((j+1)*strideA1) + (j*strideA2), scale, sumsq, out, 1, 0 );
scale = out[ 0 ];
sumsq = out[ 1 ];
}
}
sumsq *= 2;
dlassq( N, A, strideA1 + strideA2, offsetA, scale, sumsq, out, 1, 0 );
return out[ 0 ] * sqrt( out[ 1 ] );
}
return 0.0;
}
// EXPORTS //
module.exports = dlansy;
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