All files dlasq2.js

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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';
 
/* eslint-disable max-len, max-statements, max-lines-per-function */
 
// MODULES //
 
var Float64Array = require( '@stdlib/array/float64' );
var dlamch = require( '@stdlib/lapack/base/dlamch' );
var pow = require( '@stdlib/math/base/special/pow' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/abs' );
var floor = require( '@stdlib/math/base/special/floor' );
var dlasq3 = require( './dlasq3.js' );
var dlasrt = require( './dlasrt.js' );
 
 
// VARIABLES //
 
var CBIAS = 1.50;
var EPS = dlamch( 'P' );
var TOL = EPS * 100;
var TOL2 = pow( TOL, 2 );
var SAFMIN = dlamch( 'S' );
var IEEE = true;
 
 
// MAIN //
 
/**
* Computes all the eigenvalues of the symmetric positive definite tri-diagonal matrix associated with the QD Array `Z` to high relative accuracy.
*
* @private
* @param {integer} N - number of rows/columns in `Z`
* @param {Float64Array} Z - qd array
* @param {integer} strideZ - stride length for `Z`
* @param {NonNegativeInteger} offsetZ - starting index of `Z`
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var Z = new Float64Array( [ 100, 4, 81, 3, 64, 2.5, 49, 2, 36, 1.5, 25, 1, 16, 0.5, 9, 0 ] );
*
* var out = dlasq2( 4, Z, 1, 0 );
* // Z => <Float64Array>[ ~115.713, ~83.153, ~62.17, ~42.464, ~83.153, ~20.987, ~0.0, ~0.0, 303.5, ~303.5, 15, 4.0625, 0.0, ~0.0, ~0.172, ~0.096 ]
* // out => 0
*/
function dlasq2( N, Z, strideZ, offsetZ ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point
	var deemin;
	var oldemn;
	var iwhila;
	var iwhilb;
	var desig;
	var dmin1;
	var dmin2;
	var sigma;
	var trace;
	var tempq;
	var tempe;
	var ttype;
	var nfail;
	var emax;
	var emin;
	var iter;
	var nbig;
	var ndiv;
	var ipn4;
	var kmin;
	var dmin;
	var qmax;
	var qmin;
	var temp;
	var zmax;
	var splt;
	var dee;
	var tau;
	var dn1;
	var dn2;
	var out;
	var pp;
	var i0;
	var i1;
	var i4;
	var n0;
	var n1;
	var dn;
	var d;
	var e;
	var g;
	var k;
	var s;
	var t;
 
	out = new Float64Array( 18 );
 
	if ( N === 0 ) {
		return 0;
	}
 
	if ( N === 1 ) {
		// 1-by-1 case
		if ( Z[ offsetZ ] < 0 ) {
			return -201;
		}
		return 0;
	}
 
	if ( N === 2 ) {
		// 2-by-2 case
		if ( Z[ offsetZ ] < 0 ) {
			return -201;
		}

		if ( Z[ offsetZ + strideZ ] < 0 ) {
			return -202;
		}

		if ( Z[ offsetZ + ( 2 * strideZ ) ] < 0 ) {
			return -203;
		}

		if ( Z[ offsetZ + ( 2 * strideZ ) ] > Z[ offsetZ ] ) {
			d = Z[ offsetZ + ( 2 * strideZ ) ];
			Z[ offsetZ + ( 2 * strideZ ) ] = Z[ offsetZ ];
			Z[ offsetZ ] = d;
		}

		Z[ offsetZ + ( 4 * strideZ ) ] = Z[ offsetZ ] + Z[ offsetZ + strideZ ] + Z[ offsetZ + ( 2 * strideZ ) ];

		if ( Z[ offsetZ + strideZ ] > Z[ offsetZ + ( 2 * strideZ ) ] * TOL2 ) {
			t = 0.5 * ( ( Z[ offsetZ ] - Z[ offsetZ + ( 2 * strideZ ) ] ) + Z[ offsetZ + strideZ ] );
			s = Z[ offsetZ + ( 2 * strideZ ) ] * ( Z[ offsetZ + strideZ ] / t );
			if ( s <= t ) {
				s = Z[ offsetZ + ( 2 * strideZ ) ] * ( Z[ offsetZ + strideZ ] / ( t * ( 1 + sqrt( 1 + ( s / t ) ) ) ) );
			} else {
				s = Z[ offsetZ + ( 2 * strideZ ) ] * ( Z[ offsetZ + strideZ ] / ( t + ( sqrt( t ) * sqrt( t + s ) ) ) );
			}
			t = Z[ offsetZ ] + ( s + Z[ offsetZ + strideZ ] );
			Z[ offsetZ + ( 2 * strideZ ) ] = Z[ offsetZ + ( 2 * strideZ ) ] * ( Z[ offsetZ ] / t );
			Z[ offsetZ ] = t;
		}
		Z[ offsetZ + strideZ ] = Z[ offsetZ + ( 2 * strideZ ) ];
		Z[ offsetZ + ( 5 * strideZ ) ] = Z[ offsetZ + strideZ ] + Z[ offsetZ ];
		return 0;
	}
 
	// Check for negative data and compute sums of q's and e's
	Z[ offsetZ + ( ( ( 2 * N ) - 1 ) * strideZ ) ] = 0;
	emin = Z[ offsetZ + strideZ ];
	qmax = 0;
	zmax = 0;
	d = 0;
	e = 0;
 
	for ( k = 0; k < 2 * ( N - 1 ); k += 2 ) {
		if ( Z[ offsetZ + ( k * strideZ ) ] < 0 ) {
			return -( 200 + k );
		}
		if ( Z[ offsetZ + ( k * strideZ ) + strideZ ] < 0 ) {
			return -( 200 + k + 1 );
		}
		d += Z[ offsetZ + ( k * strideZ ) ];
		e += Z[ offsetZ + ( k * strideZ ) + strideZ ];
		qmax = max( qmax, Z[ offsetZ + ( k * strideZ ) ] );
		emin = min( emin, Z[ offsetZ + ( k * strideZ ) + strideZ ] );
		zmax = max( qmax, max( zmax, Z[ offsetZ + ( k * strideZ ) + strideZ ] ) );
	}
	if ( Z[ offsetZ + ( ( ( 2 * N ) - 2 ) * strideZ ) ] < 0 ) {
		return -( 200 + ( 2 * N ) - 1 );
	}
	d += Z[ offsetZ + ( ( ( 2 * N ) - 2 ) * strideZ ) ];
	qmax = max( qmax, Z[ offsetZ + ( ( ( 2 * N ) - 2 ) * strideZ ) ] );
	zmax = max( qmax, zmax );
 
	// Check for diagonality
	if ( e === 0 ) {
		for ( k = 1; k < N; k++ ) {
			Z[ offsetZ + ( k * strideZ ) ] = Z[ offsetZ + ( ( ( 2 * k ) + 1 ) * strideZ ) ];
		}
		dlasrt( 'decreasing', N, Z, strideZ, offsetZ );
		Z[ offsetZ + ( ( ( 2 * N ) - 2 ) * strideZ ) ] = d;
		return 0;
	}
 
	trace = d + e;
 
	// Check for zero data
	if ( trace === 0 ) {
		Z[ offsetZ + ( ( ( 2 * N ) - 2 ) * strideZ ) ] = 0;
		return 0;
	}
 
	// Check whether the machine is IEEE conformable (In JS, always true)
	IEEE = true;
 
	// Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...)
	for ( k = ( 2 * N ) - 1; k >= 1; k -= 2 ) {
		Z[ offsetZ + ( ( ( 2 * k ) + 1 ) * strideZ ) ] = 0;
		Z[ offsetZ + ( ( 2 * k ) * strideZ ) ] = Z[ offsetZ + ( k * strideZ ) ];
		Z[ offsetZ + ( ( ( 2 * k ) - 1 ) * strideZ ) ] = 0;
		Z[ offsetZ + ( ( ( 2 * k ) - 2 ) * strideZ ) ] = Z[ offsetZ + ( k * strideZ ) - strideZ ];
	}
 
	i0 = 0;
	n0 = N-1;
 
	// Reverse the qd-array, if warranted
	if ( CBIAS * Z[ offsetZ + ( ( 4 * i0 ) * strideZ ) ] < Z[ offsetZ + ( ( 4 * n0 ) * strideZ ) ] ) {
		ipn4 = ( 4 * ( i0 + n0 ) ) + 6;
		for ( i4 = ( 4 * i0 ) + 3; i4 <= ( 2 * ( i0 + n0 ) ) + 1; i4 += 4 ) {
			temp = Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ];
			Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ] = Z[ offsetZ + ( ( ipn4 - i4 - 3 ) * strideZ ) ];
			Z[ offsetZ + ( ( ipn4 - i4 - 3 ) * strideZ ) ] = temp;
			temp = Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ];
			Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] = Z[ offsetZ + ( ( ipn4 - i4 - 5 ) * strideZ ) ];
			Z[ offsetZ + ( ( ipn4 - i4 - 5 ) * strideZ ) ] = temp;
		}
	}
 
	// Initial split checking via DQD and Li's test
	pp = 0;
 
	for ( k = 0; k < 2; k++ ) {
		d = Z[ offsetZ + ( ( ( 4 * n0 ) + pp ) * strideZ ) ];
		for ( i4 = ( 4 * n0 ) - 1 + pp; i4 >= ( 4 * i0 ) + pp + 3; i4 -= 4 ) {
			if ( Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] <= TOL2 * d ) {
				Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] = -0;
				d = Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ];
			} else {
				d = Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ] * ( d / ( d + Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] ) );
			}
		}
 
		// DQD maps Z to ZZ plus Li's test
		emin = Z[ offsetZ + ( ( ( 4 * i0 ) + pp + 4 ) * strideZ ) ];
		d = Z[ offsetZ + ( ( ( 4 * i0 ) + pp ) * strideZ ) ];
		for ( i4 = ( 4 * i0 ) + pp + 3; i4 <= ( 4 * n0 ) + pp - 1; i4 += 4 ) {
			Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ] = d + Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ];
			if ( Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] <= TOL2 * d ) {
				Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] = -0;
				Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ] = d;
				Z[ offsetZ + ( ( i4 - ( 2 * pp ) ) * strideZ ) ] = 0;
				d = Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ];
			} else if ( ( SAFMIN * Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ] < Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ] ) && ( SAFMIN * Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ] < Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ] ) ) {
				temp = Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ] / Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ];
				Z[ offsetZ + ( ( i4 - ( 2 * pp ) ) * strideZ ) ] = Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] * temp;
				d *= temp;
			} else {
				Z[ offsetZ + ( ( i4 - ( 2 * pp ) ) * strideZ ) ] = Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ] * ( Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] / Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ] );
				d = Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ] * ( d / Z[ offsetZ + ( ( i4 - ( 2 * pp ) - 2 ) * strideZ ) ] );
			}
			emin = min( emin, Z[ offsetZ + ( ( i4 - ( 2 * pp ) ) * strideZ ) ] );
		}
		Z[ offsetZ + ( ( ( 4 * n0 ) - pp + 1 ) * strideZ ) ] = d;
 
		// Now find qmax
		qmax = Z[ offsetZ + ( ( ( 4 * i0 ) - pp + 1 ) * strideZ ) ];
		for ( i4 = ( 4 * i0 ) - pp + 5; i4 <= ( 4 * n0 ) - pp + 1; i4 += 4 ) {
			qmax = max( qmax, Z[ offsetZ + ( i4 * strideZ ) ] );
		}
 
		// Prepare for the next iteration on K
		pp = 1 - pp;
	}
 
	// Initialize variables to pass to DLASQ3
	ttype = 0;
	dmin1 = 0;
	dmin2 = 0;
	dn = 0;
	dn1 = 0;
	dn2 = 0;
	g = 0;
	tau = 0;
 
	iter = 2;
	nfail = 0;
	ndiv = 2 * ( n0 - i0 );
 
	for ( iwhila = 0; iwhila <= N; iwhila++ ) {
		if ( n0 < 0 ) {
			// Move q's to the front
			for ( k = 1; k < N; k++ ) {
				Z[ offsetZ + ( k * strideZ ) ] = Z[ offsetZ + ( ( 4 * k ) * strideZ ) ];
			}
 
			// Sort and compute sum of eigenvalues
			dlasrt( 'decreasing', N, Z, strideZ, offsetZ );
 
			e = 0;
			for ( k = N - 1; k >= 0; k-- ) {
				e += Z[ offsetZ + ( k * strideZ ) ];
			}
 
			// Store trace, sum(eigenvalues) and information on performance
			Z[ offsetZ + ( ( 2 * N ) * strideZ ) ] = trace;
			Z[ offsetZ + ( ( ( 2 * N ) + 1 ) * strideZ ) ] = e;
			Z[ offsetZ + ( ( ( 2 * N ) + 2 ) * strideZ ) ] = iter;
			Z[ offsetZ + ( ( ( 2 * N ) + 3 ) * strideZ ) ] = ndiv / ( N * N );
			Z[ offsetZ + ( ( ( 2 * N ) + 4 ) * strideZ ) ] = ( 100 * nfail ) / iter;
			return 0;
		}
 
		// E(N0) holds the value of SIGMA when submatrix in I0:N0 splits from the rest of the array, but is negated.
		desig = 0;
		if ( n0 === N - 1 ) {
			sigma = 0;
		} else {
			sigma = -Z[ offsetZ + ( ( ( 4 * n0 ) + 2 ) * strideZ ) ];
		}
		if ( sigma < 0 ) {
			return 1;
		}
 
		// Find last unreduced submatrix's top index I0, find QMAX and EMIN. Find Gershgorin-type bound if Q's much greater than E's.
		emax = 0;
		if ( n0 > i0 ) {
			emin = abs( Z[ offsetZ + ( ( ( 4 * n0 ) - 2 ) * strideZ ) ] );
		} else {
			emin = 0;
		}
		qmin = Z[ offsetZ + ( ( 4 * n0 ) * strideZ ) ];
		qmax = qmin;
 
		for ( i4 = ( 4 * n0 ) + 3; i4 >= 7; i4 -= 4 ) {
			if ( Z[ offsetZ + ( ( i4 - 5 ) * strideZ ) ] <= 0 ) {
				break;
			}
			if ( qmin >= 4 * emax ) {
				qmin = min( qmin, Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ] );
				emax = max( emax, Z[ offsetZ + ( ( i4 - 5 ) * strideZ ) ] );
			}
			qmax = max( qmax, Z[ offsetZ + ( ( i4 - 7 ) * strideZ ) ] + Z[ offsetZ + ( ( i4 - 5 ) * strideZ ) ] );
			emin = min( emin, Z[ offsetZ + ( ( i4 - 5 ) * strideZ ) ] );
		}
 
		// If the loop completed without break, set i4 = 4
		if ( i4 < 7 ) {
			i4 = 3;
		}
 
		i0 = floor( ( ( i4 + 1 ) / 4 ) - 1 );
		pp = 0;
 
		if ( n0 - i0 > 1 ) {
			dee = Z[ offsetZ + ( ( 4 * i0 ) * strideZ ) ];
			deemin = dee;
			kmin = i0;
			for ( i4 = ( 4 * i0 ) + 4; i4 <= 4 * n0; i4 += 4 ) {
				dee = Z[ offsetZ + ( i4 * strideZ ) ] * ( dee / ( dee + Z[ offsetZ + ( ( i4 - 2 ) * strideZ ) ] ) );
				if ( dee <= deemin ) {
					deemin = dee;
					kmin = floor( i4 / 4 );
				}
			}
			if ( ( ( kmin - i0 ) * 2 < n0 - kmin ) && ( deemin <= 0.5 * Z[ offsetZ + ( ( 4 * n0 ) * strideZ ) ] ) ) {
				ipn4 = ( 4 * ( i0 + n0 ) ) + 7;
				pp = 2;
				for ( i4 = ( 4 * i0 ) + 3; i4 <= ( 2 * ( i0 + n0 ) ) + 1; i4 += 4 ) {
					temp = Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ];
					Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ] = Z[ offsetZ + ( ( ipn4 - i4 - 3 ) * strideZ ) ];
					Z[ offsetZ + ( ( ipn4 - i4 - 3 ) * strideZ ) ] = temp;
					temp = Z[ offsetZ + ( ( i4 - 2 ) * strideZ ) ];
					Z[ offsetZ + ( ( i4 - 2 ) * strideZ ) ] = Z[ offsetZ + ( ( ipn4 - i4 - 2 ) * strideZ ) ];
					Z[ offsetZ + ( ( ipn4 - i4 - 2 ) * strideZ ) ] = temp;
					temp = Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ];
					Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] = Z[ offsetZ + ( ( ipn4 - i4 - 5 ) * strideZ ) ];
					Z[ offsetZ + ( ( ipn4 - i4 - 5 ) * strideZ ) ] = temp;
					temp = Z[ offsetZ + ( i4 * strideZ ) ];
					Z[ offsetZ + ( i4 * strideZ ) ] = Z[ offsetZ + ( ( ipn4 - i4 - 4 ) * strideZ ) ];
					Z[ offsetZ + ( ( ipn4 - i4 - 4 ) * strideZ ) ] = temp;
				}
			}
		}
 
		// Put -(initial shift) into DMIN
		dmin = -max( 0, qmin - ( 2 * sqrt( qmin ) * sqrt( emax ) ) );
 
		/*
		Now I0:N0 is unreduced.
		PP = 0 for ping,
		PP = 1 for pong,
		PP = 2 indicates that flipping was applied to the Z array and that the tests for deflation upon entry in DLASQ3 should not be performed.
		*/
		nbig = 100 * ( n0 - i0 + 1 );
		for ( iwhilb = 0; iwhilb < nbig; iwhilb++ ) {
			if ( i0 > n0 ) {
				break;
			}
 
			out[ 0 ] = n0;
			out[ 1 ] = pp;
			out[ 2 ] = dmin;
			out[ 3 ] = sigma;
			out[ 4 ] = desig;
			out[ 5 ] = qmax;
			out[ 6 ] = nfail;
			out[ 7 ] = iter;
			out[ 8 ] = ndiv;
			out[ 9 ] = ttype;
			out[ 10 ] = dmin1;
			out[ 11 ] = dmin2;
			out[ 12 ] = dn;
			out[ 13 ] = dn1;
			out[ 14 ] = dn2;
			out[ 15 ] = g;
			out[ 16 ] = tau;
 
			// Call dlasq3
			dlasq3( i0, Z, strideZ, offsetZ, IEEE, out, 1, 0 );
 
			n0 = out[ 0 ];
			pp = out[ 1 ];
			dmin = out[ 2 ];
			sigma = out[ 3 ];
			desig = out[ 4 ];
			qmax = out[ 5 ];
			nfail = out[ 6 ];
			iter = out[ 7 ];
			ndiv = out[ 8 ];
			ttype = out[ 9 ];
			dmin1 = out[ 10 ];
			dmin2 = out[ 11 ];
			dn = out[ 12 ];
			dn1 = out[ 13 ];
			dn2 = out[ 14 ];
			g = out[ 15 ];
			tau = out[ 16 ];
 
			pp = 1 - pp;
 
			// When EMIN is very small check for splits
			if ( pp === 0 && n0 - i0 >= 3 ) {
				if ( ( Z[ offsetZ + ( ( ( 4 * n0 ) + 3 ) * strideZ ) ] <= TOL2 * qmax ) || ( Z[ offsetZ + ( ( ( 4 * n0 ) + 2 ) * strideZ ) ] <= TOL2 * sigma ) ) {
					splt = i0 - 1;
					qmax = Z[ offsetZ + ( ( 4 * i0 ) * strideZ ) ];
					emin = Z[ offsetZ + ( ( ( 4 * i0 ) + 2 ) * strideZ ) ];
					oldemn = Z[ offsetZ + ( ( ( 4 * i0 ) + 3 ) * strideZ ) ];
					for ( i4 = ( 4 * i0 ) + 3; i4 <= ( 4 * n0 ) - 9; i4 += 4 ) {
						if ( ( Z[ offsetZ + ( i4 * strideZ ) ] <= TOL2 * Z[ offsetZ + ( ( i4 - 3 ) * strideZ ) ] ) || ( Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] <= TOL2 * sigma) ) {
							Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] = -sigma;
							splt = floor( ( i4 + 1 ) / 4 ) - 1;
							qmax = 0;
							emin = Z[ offsetZ + ( ( i4 + 3 ) * strideZ ) ];
							oldemn = Z[ offsetZ + ( ( i4 + 4 ) * strideZ ) ];
						} else {
							qmax = max( qmax, Z[ offsetZ + ( ( i4 + 1 ) * strideZ ) ] );
							emin = min( emin, Z[ offsetZ + ( ( i4 - 1 ) * strideZ ) ] );
							oldemn = min( oldemn, Z[ offsetZ + ( i4 * strideZ ) ] );
						}
					}
					Z[ offsetZ + ( ( ( 4 * n0 ) + 2 ) * strideZ ) ] = emin;
					Z[ offsetZ + ( ( ( 4 * n0 ) + 3 ) * strideZ ) ] = oldemn;
					i0 = splt + 1;
				}
			}
		}
 
		// If inner loop exhausted without breaking, we have INFO = 2
		if ( iwhilb >= nbig ) {
			// Maximum number of iterations exceeded, restore the shift SIGMA and place the new d's and e's in a qd array. This might need to be done for several blocks

			i1 = i0;
			n1 = n0;

			// Label 145 loop
			while ( true ) {
				tempq = Z[ offsetZ + ( ( 4 * i0 ) * strideZ ) ];
				Z[ offsetZ + ( ( 4 * i0 ) * strideZ ) ] += sigma;
				for ( k = i0 + 1; k <= n0; k++ ) {
					tempe = Z[ offsetZ + ( ( ( 4 * k ) - 2 ) * strideZ ) ];
					Z[ offsetZ + ( ( ( 4 * k ) - 2 ) * strideZ ) ] *= tempq / Z[ offsetZ + ( ( ( 4 * k ) - 4 ) * strideZ ) ];
					tempq = Z[ offsetZ + ( ( 4 * k ) * strideZ ) ];
					Z[ offsetZ + ( ( 4 * k ) * strideZ ) ] += sigma + tempe - Z[ offsetZ + ( ( ( 4 * k ) - 2 ) * strideZ ) ];
				}

				// Prepare to do this on the previous block if there is one
				if ( i1 > 0 ) {
					n1 = i1 - 1;
					while ( i1 >= 1 && Z[ offsetZ + ( ( ( 4 * i1 ) - 2 ) * strideZ ) ] >= 0 ) {
						i1 -= 1;
					}
					sigma = -Z[ offsetZ + ( ( ( 4 * n1 ) + 2 ) * strideZ ) ];
				} else {
					break;
				}
			}

			for ( k = 0; k < N; k++ ) {
				Z[ offsetZ + ( ( 2 * k ) * strideZ ) ] = Z[ offsetZ + ( ( 4 * k ) * strideZ ) ];
				if ( k < n0 ) {
					Z[ offsetZ + ( ( ( 2 * k ) + 1 ) * strideZ ) ] = Z[ offsetZ + ( ( ( 4 * k ) + 2 ) * strideZ ) ];
				} else {
					Z[ offsetZ + ( ( ( 2 * k ) + 1 ) * strideZ ) ] = 0;
				}
			}
			return 2;
		}
	}

	return 3;
}
 
 
// EXPORTS //
 
module.exports = dlasq2;