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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 dlamch = require( '@stdlib/lapack/base/dlamch' );
var abs = require( '@stdlib/math/base/special/abs' );
var pow = require( '@stdlib/math/base/special/pow' );
var ln = require( '@stdlib/math/base/special/ln' );
var trunc = require( '@stdlib/math/base/special/trunc' );
var max = require( '@stdlib/math/base/special/fast/max' );
var min = require( '@stdlib/math/base/special/fast/min' );
// VARIABLES //
var SMLNUM = dlamch( 'S' );
var BIGNUM = 1.0 / SMLNUM;
var RADIX = dlamch( 'B' );
var LOGRDX = ln( RADIX );
// MAIN //
/**
* Computes row and column scale factors intended to equilibrate a matrix `A` and reduce its condition number (using the base of the machine as the scaling restriction).
*
* @private
* @param {NonNegativeInteger} M - number of rows in `A`
* @param {NonNegativeInteger} N - number of columns in `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} R - output vector for the row scale factors
* @param {integer} strideR - stride length for `R`
* @param {NonNegativeInteger} offsetR - starting index for `R`
* @param {Float64Array} C - output vector for the column scale factors
* @param {integer} strideC - stride length for `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @param {Float64Array} out - three element output array whose elements are set to `[ ROWCND, COLCND, AMAX ]`
* @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 A = new Float64Array( [ 1.0, 0.0, 0.0, 4.0 ] );
* var R = new Float64Array( 2 );
* var C = new Float64Array( 2 );
* var out = new Float64Array( 3 );
*
* dgeequb( 2, 2, A, 2, 1, 0, R, 1, 0, C, 1, 0, out, 1, 0 );
* // R => <Float64Array>[ 1.0, 0.25 ]
* // C => <Float64Array>[ 1.0, 1.0 ]
* // out => <Float64Array>[ 0.25, 1.0, 4.0 ]
*/
function dgeequb( M, N, A, strideA1, strideA2, offsetA, R, strideR, offsetR, C, strideC, offsetC, out, strideOut, offsetOut ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point, max-len, max-params
var rcmin;
var rcmax;
var ia;
var ja;
var ir;
var ic;
var i;
var j;
// Quick return if possible...
if ( M === 0 || N === 0 ) {
out[ offsetOut ] = 1.0;
out[ offsetOut + strideOut ] = 1.0;
out[ offsetOut + ( 2*strideOut ) ] = 0.0;
return 0;
}
// Initialize the row scale factors...
ir = offsetR;
for ( i = 0; i < M; i++ ) {
R[ ir ] = 0.0;
ir += strideR;
}
// Find the maximum element in each row...
ja = offsetA;
for ( j = 0; j < N; j++ ) {
ia = ja;
ir = offsetR;
for ( i = 0; i < M; i++ ) {
R[ ir ] = max( R[ ir ], abs( A[ ia ] ) );
ia += strideA1;
ir += strideR;
}
ja += strideA2;
}
// Restrict each row scale factor to a power of the radix...
ir = offsetR;
for ( i = 0; i < M; i++ ) {
if ( R[ ir ] > 0.0 ) {
R[ ir ] = pow( RADIX, trunc( ln( R[ ir ] ) / LOGRDX ) );
}
ir += strideR;
}
// Find the maximum and minimum row scale factors...
rcmin = BIGNUM;
rcmax = 0.0;
ir = offsetR;
for ( i = 0; i < M; i++ ) {
rcmax = max( rcmax, R[ ir ] );
rcmin = min( rcmin, R[ ir ] );
ir += strideR;
}
out[ offsetOut + ( 2*strideOut ) ] = rcmax; // AMAX
if ( rcmin === 0.0 ) {
// Find the first zero scale factor and return an error code...
ir = offsetR;
for ( i = 0; i < M; i++ ) {
if ( R[ ir ] === 0.0 ) {
return i + 1;
}
ir += strideR;
}
} else {
// Invert the row scale factors...
ir = offsetR;
for ( i = 0; i < M; i++ ) {
R[ ir ] = 1.0 / min( max( R[ ir ], SMLNUM ), BIGNUM );
ir += strideR;
}
// Compute `ROWCND = min(R)/max(R)`...
out[ offsetOut ] = max( rcmin, SMLNUM ) / min( rcmax, BIGNUM );
}
// Initialize the column scale factors...
ic = offsetC;
for ( j = 0; j < N; j++ ) {
C[ ic ] = 0.0;
ic += strideC;
}
// Find the largest (row scaled) element in each column...
// Restrict each column scale factor to a power of the radix...
ja = offsetA;
ic = offsetC;
for ( j = 0; j < N; j++ ) {
ia = ja;
ir = offsetR;
for ( i = 0; i < M; i++ ) {
C[ ic ] = max( C[ ic ], abs( A[ ia ] ) * R[ ir ] );
ia += strideA1;
ir += strideR;
}
if ( C[ ic ] > 0.0 ) {
C[ ic ] = pow( RADIX, trunc( ln( C[ ic ] ) / LOGRDX ) );
}
ja += strideA2;
ic += strideC;
}
// Find the maximum and minimum column scale factors...
rcmin = BIGNUM;
rcmax = 0.0;
ic = offsetC;
for ( j = 0; j < N; j++ ) {
rcmin = min( rcmin, C[ ic ] );
rcmax = max( rcmax, C[ ic ] );
ic += strideC;
}
if ( rcmin === 0.0 ) {
// Find the first zero scale factor and return an error code...
ic = offsetC;
for ( j = 0; j < N; j++ ) {
if ( C[ ic ] === 0.0 ) {
return M + j + 1;
}
ic += strideC;
}
} else {
// Invert the column scale factors...
ic = offsetC;
for ( j = 0; j < N; j++ ) {
C[ ic ] = 1.0 / min( max( C[ ic ], SMLNUM ), BIGNUM );
ic += strideC;
}
// Compute `COLCND = min(C)/max(C)`...
rcmin = max( rcmin, SMLNUM );
rcmax = min( rcmax, BIGNUM );
out[ offsetOut + strideOut ] = rcmin / rcmax;
}
return 0;
}
// EXPORTS //
module.exports = dgeequb;
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