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* @license Apache-2.0
*
* Copyright (c) 2025 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 sqrt = require( '@stdlib/math/base/special/sqrt' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
// MAIN //
/**
* Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
*
* ## Notes
*
* - the function returns `0` if it sucessfully exits.
* - if the function returns an integer `i` greater then zero then the `i`th diagonal element was non positive.
* - the first indexed element of `out` represents `scond` and the second indexed elements represents `amax`, if it `scond` >= 0.1 and `amax` is not close to overflow/underflow then it is not worth scaling by `S`.
* - if `amax` is too close to overflow/underflow, the matrix should be scaled.
*
* @param {string} order - storage layout
* @param {string} uplo - specifies whether upper or lower triangle of `A` is stored ( `upper` or `lower` )
* @param {NonNegativeInteger} N - number of rows/columns in `A`
* @param {Float64Array} AP - array containing the upper or lower triangle of `A` in packed form, expects `N * ( N + 1 ) / 2` indexed elements
* @param {integer} strideAP - stride length for `AP`
* @param {NonNegativeInteger} offsetAP - starting index for `AP`
* @param {Float64Array} S - array to store the scale factors of `A`, expects `N` indexed elements
* @param {integer} strideS - stride length for `S`
* @param {NonNegativeInteger} offsetS - starting index for `S`
* @param {Float64Array} out - array to store the output
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
* var S = new Float64Array( 3 );
* var out = new Float64Array( 2 );
*
* dppequ( 'row-major', 'lower', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
* // S => <Float64Array>[ 1, ~0.58, ~0.33 ]
* // out => <Float64Array>[ ~0.33, 9 ]
*/
function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, out, strideOut, offsetOut ) { // eslint-disable-line max-len, max-params
var info;
var smin;
var amax;
var iap;
var is;
var i;
if ( N === 0 ) {
out[ offsetOut ] = 1.0; // scond
out[ offsetOut + strideOut ] = 0.0; // amax
return 0; // info
}
is = offsetS;
S[ is ] = AP[ offsetAP ];
smin = S[ is ];
amax = S[ is ];
is = offsetS + strideS;
iap = offsetAP;
if ( uplo === 'upper' ) {
for ( i = 1; i < N; i++ ) {
if ( order === 'row-major' ) {
iap += ( N - i + 1 ) * strideAP;
} else { // order === 'column-major'
iap += ( i + 1 ) * strideAP;
}
S[ is ] = AP[ iap ];
smin = min( smin, S[ is ] );
amax = max( amax, S[ is ] );
is += strideS;
}
} else { // uplo === 'lower'
for ( i = 1; i < N; i++ ) {
if ( order === 'row-major' ) {
iap += ( i + 1 ) * strideAP;
} else { // order === 'column-major'
iap += ( N - i + 1 ) * strideAP;
}
S[ is ] = AP[ iap ];
smin = min( smin, S[ is ] );
amax = max( amax, S[ is ] );
is += strideS;
}
}
is = offsetS;
if ( smin <= 0.0 ) {
for ( i = 0; i < N; i++ ) {
if ( S[ is ] <= 0.0 ) {
// Leave first element of `out` unchanged
out[ offsetOut + strideOut ] = amax; // amax
info = i;
return info;
}
is += strideS;
}
} else {
for ( i = 0; i < N; i++ ) {
S[ is ] = 1.0 / sqrt( S[ is ] );
is += strideS;
}
}
out[ offsetOut ] = sqrt( smin ) / sqrt( amax ); // scond
out[ offsetOut + strideOut ] = amax; // amax
info = 0;
return info;
}
// EXPORTS //
module.exports = dppequ;
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