source: trunk/sources/ALGLIB/nsevd.cs @ 2567

/*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee.  All rights reserved.

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
      pseudocode.

See subroutines comments for additional copyrights.

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

using System;

namespace alglib
{
    public class nsevd
    {
        /*************************************************************************
        Finding eigenvalues and eigenvectors of a general matrix

        The algorithm finds eigenvalues and eigenvectors of a general matrix by
        using the QR algorithm with multiple shifts. The algorithm can find
        eigenvalues and both left and right eigenvectors.

        The right eigenvector is a vector x such that A*x = w*x, and the left
        eigenvector is a vector y such that y'*A = w*y' (here y' implies a complex
        conjugate transposition of vector y).

        Input parameters:
            A       -   matrix. Array whose indexes range within [0..N-1, 0..N-1].
            N       -   size of matrix A.
            VNeeded -   flag controlling whether eigenvectors are needed or not.
                        If VNeeded is equal to:
                         * 0, eigenvectors are not returned;
                         * 1, right eigenvectors are returned;
                         * 2, left eigenvectors are returned;
                         * 3, both left and right eigenvectors are returned.

        Output parameters:
            WR      -   real parts of eigenvalues.
                        Array whose index ranges within [0..N-1].
            WR      -   imaginary parts of eigenvalues.
                        Array whose index ranges within [0..N-1].
            VL, VR  -   arrays of left and right eigenvectors (if they are needed).
                        If WI[i]=0, the respective eigenvalue is a real number,
                        and it corresponds to the column number I of matrices VL/VR.
                        If WI[i]>0, we have a pair of complex conjugate numbers with
                        positive and negative imaginary parts:
                            the first eigenvalue WR[i] + sqrt(-1)*WI[i];
                            the second eigenvalue WR[i+1] + sqrt(-1)*WI[i+1];
                            WI[i]>0
                            WI[i+1] = -WI[i] < 0
                        In that case, the eigenvector  corresponding to the first
                        eigenvalue is located in i and i+1 columns of matrices
                        VL/VR (the column number i contains the real part, and the
                        column number i+1 contains the imaginary part), and the vector
                        corresponding to the second eigenvalue is a complex conjugate to
                        the first vector.
                        Arrays whose indexes range within [0..N-1, 0..N-1].

        Result:
            True, if the algorithm has converged.
            False, if the algorithm has not converged.

        Note 1:
            Some users may ask the following question: what if WI[N-1]>0?
            WI[N] must contain an eigenvalue which is complex conjugate to the
            N-th eigenvalue, but the array has only size N?
            The answer is as follows: such a situation cannot occur because the
            algorithm finds a pairs of eigenvalues, therefore, if WI[i]>0, I is
            strictly less than N-1.

        Note 2:
            The algorithm performance depends on the value of the internal parameter
            NS of the InternalSchurDecomposition subroutine which defines the number
            of shifts in the QR algorithm (similarly to the block width in block-matrix
            algorithms of linear algebra). If you require maximum performance
            on your machine, it is recommended to adjust this parameter manually.


        See also the InternalTREVC subroutine.

        The algorithm is based on the LAPACK 3.0 library.
        *************************************************************************/
        public static bool rmatrixevd(double[,] a,
            int n,
            int vneeded,
            ref double[] wr,
            ref double[] wi,
            ref double[,] vl,
            ref double[,] vr)
        {
            bool result = new bool();
            double[,] a1 = new double[0,0];
            double[,] vl1 = new double[0,0];
            double[,] vr1 = new double[0,0];
            double[] wr1 = new double[0];
            double[] wi1 = new double[0];
            int i = 0;
            double mx = 0;
            int i_ = 0;
            int i1_ = 0;

            a = (double[,])a.Clone();

            System.Diagnostics.Debug.Assert(vneeded>=0 & vneeded<=3, "RMatrixEVD: incorrect VNeeded!");
            a1 = new double[n+1, n+1];
            for(i=1; i<=n; i++)
            {
                i1_ = (0) - (1);
                for(i_=1; i_<=n;i_++)
                {
                    a1[i,i_] = a[i-1,i_+i1_];
                }
            }
            result = nonsymmetricevd(a1, n, vneeded, ref wr1, ref wi1, ref vl1, ref vr1);
            if( result )
            {
                wr = new double[n-1+1];
                wi = new double[n-1+1];
                i1_ = (1) - (0);
                for(i_=0; i_<=n-1;i_++)
                {
                    wr[i_] = wr1[i_+i1_];
                }
                i1_ = (1) - (0);
                for(i_=0; i_<=n-1;i_++)
                {
                    wi[i_] = wi1[i_+i1_];
                }
                if( vneeded==2 | vneeded==3 )
                {
                    vl = new double[n-1+1, n-1+1];
                    for(i=0; i<=n-1; i++)
                    {
                        i1_ = (1) - (0);
                        for(i_=0; i_<=n-1;i_++)
                        {
                            vl[i,i_] = vl1[i+1,i_+i1_];
                        }
                    }
                }
                if( vneeded==1 | vneeded==3 )
                {
                    vr = new double[n-1+1, n-1+1];
                    for(i=0; i<=n-1; i++)
                    {
                        i1_ = (1) - (0);
                        for(i_=0; i_<=n-1;i_++)
                        {
                            vr[i,i_] = vr1[i+1,i_+i1_];
                        }
                    }
                }
            }
            return result;
        }


        public static bool nonsymmetricevd(double[,] a,
            int n,
            int vneeded,
            ref double[] wr,
            ref double[] wi,
            ref double[,] vl,
            ref double[,] vr)
        {
            bool result = new bool();
            double[,] s = new double[0,0];
            double[] tau = new double[0];
            bool[] sel = new bool[0];
            int i = 0;
            int info = 0;
            int m = 0;
            int i_ = 0;

            a = (double[,])a.Clone();

            System.Diagnostics.Debug.Assert(vneeded>=0 & vneeded<=3, "NonSymmetricEVD: incorrect VNeeded!");
            if( vneeded==0 )
            {
                
                //
                // Eigen values only
                //
                hessenberg.toupperhessenberg(ref a, n, ref tau);
                hsschur.internalschurdecomposition(ref a, n, 0, 0, ref wr, ref wi, ref s, ref info);
                result = info==0;
                return result;
            }
            
            //
            // Eigen values and vectors
            //
            hessenberg.toupperhessenberg(ref a, n, ref tau);
            hessenberg.unpackqfromupperhessenberg(ref a, n, ref tau, ref s);
            hsschur.internalschurdecomposition(ref a, n, 1, 1, ref wr, ref wi, ref s, ref info);
            result = info==0;
            if( !result )
            {
                return result;
            }
            if( vneeded==1 | vneeded==3 )
            {
                vr = new double[n+1, n+1];
                for(i=1; i<=n; i++)
                {
                    for(i_=1; i_<=n;i_++)
                    {
                        vr[i,i_] = s[i,i_];
                    }
                }
            }
            if( vneeded==2 | vneeded==3 )
            {
                vl = new double[n+1, n+1];
                for(i=1; i<=n; i++)
                {
                    for(i_=1; i_<=n;i_++)
                    {
                        vl[i,i_] = s[i,i_];
                    }
                }
            }
            internaltrevc(ref a, n, vneeded, 1, sel, ref vl, ref vr, ref m, ref info);
            result = info==0;
            return result;
        }


        private static void internaltrevc(ref double[,] t,
            int n,
            int side,
            int howmny,
            bool[] vselect,
            ref double[,] vl,
            ref double[,] vr,
            ref int m,
            ref int info)
        {
            bool allv = new bool();
            bool bothv = new bool();
            bool leftv = new bool();
            bool over = new bool();
            bool pair = new bool();
            bool rightv = new bool();
            bool somev = new bool();
            int i = 0;
            int ierr = 0;
            int ii = 0;
            int ip = 0;
            int iis = 0;
            int j = 0;
            int j1 = 0;
            int j2 = 0;
            int jnxt = 0;
            int k = 0;
            int ki = 0;
            int n2 = 0;
            double beta = 0;
            double bignum = 0;
            double emax = 0;
            double ovfl = 0;
            double rec = 0;
            double remax = 0;
            double scl = 0;
            double smin = 0;
            double smlnum = 0;
            double ulp = 0;
            double unfl = 0;
            double vcrit = 0;
            double vmax = 0;
            double wi = 0;
            double wr = 0;
            double xnorm = 0;
            double[,] x = new double[0,0];
            double[] work = new double[0];
            double[] temp = new double[0];
            double[,] temp11 = new double[0,0];
            double[,] temp22 = new double[0,0];
            double[,] temp11b = new double[0,0];
            double[,] temp21b = new double[0,0];
            double[,] temp12b = new double[0,0];
            double[,] temp22b = new double[0,0];
            bool skipflag = new bool();
            int k1 = 0;
            int k2 = 0;
            int k3 = 0;
            int k4 = 0;
            double vt = 0;
            bool[] rswap4 = new bool[0];
            bool[] zswap4 = new bool[0];
            int[,] ipivot44 = new int[0,0];
            double[] civ4 = new double[0];
            double[] crv4 = new double[0];
            int i_ = 0;
            int i1_ = 0;

            vselect = (bool[])vselect.Clone();

            x = new double[2+1, 2+1];
            temp11 = new double[1+1, 1+1];
            temp11b = new double[1+1, 1+1];
            temp21b = new double[2+1, 1+1];
            temp12b = new double[1+1, 2+1];
            temp22b = new double[2+1, 2+1];
            temp22 = new double[2+1, 2+1];
            work = new double[3*n+1];
            temp = new double[n+1];
            rswap4 = new bool[4+1];
            zswap4 = new bool[4+1];
            ipivot44 = new int[4+1, 4+1];
            civ4 = new double[4+1];
            crv4 = new double[4+1];
            if( howmny!=1 )
            {
                if( side==1 | side==3 )
                {
                    vr = new double[n+1, n+1];
                }
                if( side==2 | side==3 )
                {
                    vl = new double[n+1, n+1];
                }
            }
            
            //
            // Decode and test the input parameters
            //
            bothv = side==3;
            rightv = side==1 | bothv;
            leftv = side==2 | bothv;
            allv = howmny==2;
            over = howmny==1;
            somev = howmny==3;
            info = 0;
            if( n<0 )
            {
                info = -2;
                return;
            }
            if( !rightv & !leftv )
            {
                info = -3;
                return;
            }
            if( !allv & !over & !somev )
            {
                info = -4;
                return;
            }
            
            //
            // Set M to the number of columns required to store the selected
            // eigenvectors, standardize the array SELECT if necessary, and
            // test MM.
            //
            if( somev )
            {
                m = 0;
                pair = false;
                for(j=1; j<=n; j++)
                {
                    if( pair )
                    {
                        pair = false;
                        vselect[j] = false;
                    }
                    else
                    {
                        if( j<n )
                        {
                            if( (double)(t[j+1,j])==(double)(0) )
                            {
                                if( vselect[j] )
                                {
                                    m = m+1;
                                }
                            }
                            else
                            {
                                pair = true;
                                if( vselect[j] | vselect[j+1] )
                                {
                                    vselect[j] = true;
                                    m = m+2;
                                }
                            }
                        }
                        else
                        {
                            if( vselect[n] )
                            {
                                m = m+1;
                            }
                        }
                    }
                }
            }
            else
            {
                m = n;
            }
            
            //
            // Quick return if possible.
            //
            if( n==0 )
            {
                return;
            }
            
            //
            // Set the constants to control overflow.
            //
            unfl = AP.Math.MinRealNumber;
            ovfl = 1/unfl;
            ulp = AP.Math.MachineEpsilon;
            smlnum = unfl*(n/ulp);
            bignum = (1-ulp)/smlnum;
            
            //
            // Compute 1-norm of each column of strictly upper triangular
            // part of T to control overflow in triangular solver.
            //
            work[1] = 0;
            for(j=2; j<=n; j++)
            {
                work[j] = 0;
                for(i=1; i<=j-1; i++)
                {
                    work[j] = work[j]+Math.Abs(t[i,j]);
                }
            }
            
            //
            // Index IP is used to specify the real or complex eigenvalue:
            // IP = 0, real eigenvalue,
            //      1, first of conjugate complex pair: (wr,wi)
            //     -1, second of conjugate complex pair: (wr,wi)
            //
            n2 = 2*n;
            if( rightv )
            {
                
                //
                // Compute right eigenvectors.
                //
                ip = 0;
                iis = m;
                for(ki=n; ki>=1; ki--)
                {
                    skipflag = false;
                    if( ip==1 )
                    {
                        skipflag = true;
                    }
                    else
                    {
                        if( ki!=1 )
                        {
                            if( (double)(t[ki,ki-1])!=(double)(0) )
                            {
                                ip = -1;
                            }
                        }
                        if( somev )
                        {
                            if( ip==0 )
                            {
                                if( !vselect[ki] )
                                {
                                    skipflag = true;
                                }
                            }
                            else
                            {
                                if( !vselect[ki-1] )
                                {
                                    skipflag = true;
                                }
                            }
                        }
                    }
                    if( !skipflag )
                    {
                        
                        //
                        // Compute the KI-th eigenvalue (WR,WI).
                        //
                        wr = t[ki,ki];
                        wi = 0;
                        if( ip!=0 )
                        {
                            wi = Math.Sqrt(Math.Abs(t[ki,ki-1]))*Math.Sqrt(Math.Abs(t[ki-1,ki]));
                        }
                        smin = Math.Max(ulp*(Math.Abs(wr)+Math.Abs(wi)), smlnum);
                        if( ip==0 )
                        {
                            
                            //
                            // Real right eigenvector
                            //
                            work[ki+n] = 1;
                            
                            //
                            // Form right-hand side
                            //
                            for(k=1; k<=ki-1; k++)
                            {
                                work[k+n] = -t[k,ki];
                            }
                            
                            //
                            // Solve the upper quasi-triangular system:
                            //   (T(1:KI-1,1:KI-1) - WR)*X = SCALE*WORK.
                            //
                            jnxt = ki-1;
                            for(j=ki-1; j>=1; j--)
                            {
                                if( j>jnxt )
                                {
                                    continue;
                                }
                                j1 = j;
                                j2 = j;
                                jnxt = j-1;
                                if( j>1 )
                                {
                                    if( (double)(t[j,j-1])!=(double)(0) )
                                    {
                                        j1 = j-1;
                                        jnxt = j-2;
                                    }
                                }
                                if( j1==j2 )
                                {
                                    
                                    //
                                    // 1-by-1 diagonal block
                                    //
                                    temp11[1,1] = t[j,j];
                                    temp11b[1,1] = work[j+n];
                                    internalhsevdlaln2(false, 1, 1, smin, 1, ref temp11, 1.0, 1.0, ref temp11b, wr, 0.0, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale X(1,1) to avoid overflow when updating
                                    // the right-hand side.
                                    //
                                    if( (double)(xnorm)>(double)(1) )
                                    {
                                        if( (double)(work[j])>(double)(bignum/xnorm) )
                                        {
                                            x[1,1] = x[1,1]/xnorm;
                                            scl = scl/xnorm;
                                        }
                                    }
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        k1 = n+1;
                                        k2 = n+ki;
                                        for(i_=k1; i_<=k2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j+n] = x[1,1];
                                    
                                    //
                                    // Update right-hand side
                                    //
                                    k1 = 1+n;
                                    k2 = j-1+n;
                                    k3 = j-1;
                                    vt = -x[1,1];
                                    i1_ = (1) - (k1);
                                    for(i_=k1; i_<=k2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j];
                                    }
                                }
                                else
                                {
                                    
                                    //
                                    // 2-by-2 diagonal block
                                    //
                                    temp22[1,1] = t[j-1,j-1];
                                    temp22[1,2] = t[j-1,j];
                                    temp22[2,1] = t[j,j-1];
                                    temp22[2,2] = t[j,j];
                                    temp21b[1,1] = work[j-1+n];
                                    temp21b[2,1] = work[j+n];
                                    internalhsevdlaln2(false, 2, 1, smin, 1.0, ref temp22, 1.0, 1.0, ref temp21b, wr, 0, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale X(1,1) and X(2,1) to avoid overflow when
                                    // updating the right-hand side.
                                    //
                                    if( (double)(xnorm)>(double)(1) )
                                    {
                                        beta = Math.Max(work[j-1], work[j]);
                                        if( (double)(beta)>(double)(bignum/xnorm) )
                                        {
                                            x[1,1] = x[1,1]/xnorm;
                                            x[2,1] = x[2,1]/xnorm;
                                            scl = scl/xnorm;
                                        }
                                    }
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        k1 = 1+n;
                                        k2 = ki+n;
                                        for(i_=k1; i_<=k2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j-1+n] = x[1,1];
                                    work[j+n] = x[2,1];
                                    
                                    //
                                    // Update right-hand side
                                    //
                                    k1 = 1+n;
                                    k2 = j-2+n;
                                    k3 = j-2;
                                    k4 = j-1;
                                    vt = -x[1,1];
                                    i1_ = (1) - (k1);
                                    for(i_=k1; i_<=k2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,k4];
                                    }
                                    vt = -x[2,1];
                                    i1_ = (1) - (k1);
                                    for(i_=k1; i_<=k2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j];
                                    }
                                }
                            }
                            
                            //
                            // Copy the vector x or Q*x to VR and normalize.
                            //
                            if( !over )
                            {
                                k1 = 1+n;
                                k2 = ki+n;
                                i1_ = (k1) - (1);
                                for(i_=1; i_<=ki;i_++)
                                {
                                    vr[i_,iis] = work[i_+i1_];
                                }
                                ii = blas.columnidxabsmax(ref vr, 1, ki, iis);
                                remax = 1/Math.Abs(vr[ii,iis]);
                                for(i_=1; i_<=ki;i_++)
                                {
                                    vr[i_,iis] = remax*vr[i_,iis];
                                }
                                for(k=ki+1; k<=n; k++)
                                {
                                    vr[k,iis] = 0;
                                }
                            }
                            else
                            {
                                if( ki>1 )
                                {
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        temp[i_] = vr[i_,ki];
                                    }
                                    blas.matrixvectormultiply(ref vr, 1, n, 1, ki-1, false, ref work, 1+n, ki-1+n, 1.0, ref temp, 1, n, work[ki+n]);
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vr[i_,ki] = temp[i_];
                                    }
                                }
                                ii = blas.columnidxabsmax(ref vr, 1, n, ki);
                                remax = 1/Math.Abs(vr[ii,ki]);
                                for(i_=1; i_<=n;i_++)
                                {
                                    vr[i_,ki] = remax*vr[i_,ki];
                                }
                            }
                        }
                        else
                        {
                            
                            //
                            // Complex right eigenvector.
                            //
                            // Initial solve
                            //     [ (T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I* WI)]*X = 0.
                            //     [ (T(KI,KI-1)   T(KI,KI)   )               ]
                            //
                            if( (double)(Math.Abs(t[ki-1,ki]))>=(double)(Math.Abs(t[ki,ki-1])) )
                            {
                                work[ki-1+n] = 1;
                                work[ki+n2] = wi/t[ki-1,ki];
                            }
                            else
                            {
                                work[ki-1+n] = -(wi/t[ki,ki-1]);
                                work[ki+n2] = 1;
                            }
                            work[ki+n] = 0;
                            work[ki-1+n2] = 0;
                            
                            //
                            // Form right-hand side
                            //
                            for(k=1; k<=ki-2; k++)
                            {
                                work[k+n] = -(work[ki-1+n]*t[k,ki-1]);
                                work[k+n2] = -(work[ki+n2]*t[k,ki]);
                            }
                            
                            //
                            // Solve upper quasi-triangular system:
                            // (T(1:KI-2,1:KI-2) - (WR+i*WI))*X = SCALE*(WORK+i*WORK2)
                            //
                            jnxt = ki-2;
                            for(j=ki-2; j>=1; j--)
                            {
                                if( j>jnxt )
                                {
                                    continue;
                                }
                                j1 = j;
                                j2 = j;
                                jnxt = j-1;
                                if( j>1 )
                                {
                                    if( (double)(t[j,j-1])!=(double)(0) )
                                    {
                                        j1 = j-1;
                                        jnxt = j-2;
                                    }
                                }
                                if( j1==j2 )
                                {
                                    
                                    //
                                    // 1-by-1 diagonal block
                                    //
                                    temp11[1,1] = t[j,j];
                                    temp12b[1,1] = work[j+n];
                                    temp12b[1,2] = work[j+n+n];
                                    internalhsevdlaln2(false, 1, 2, smin, 1.0, ref temp11, 1.0, 1.0, ref temp12b, wr, wi, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale X(1,1) and X(1,2) to avoid overflow when
                                    // updating the right-hand side.
                                    //
                                    if( (double)(xnorm)>(double)(1) )
                                    {
                                        if( (double)(work[j])>(double)(bignum/xnorm) )
                                        {
                                            x[1,1] = x[1,1]/xnorm;
                                            x[1,2] = x[1,2]/xnorm;
                                            scl = scl/xnorm;
                                        }
                                    }
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        k1 = 1+n;
                                        k2 = ki+n;
                                        for(i_=k1; i_<=k2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                        k1 = 1+n2;
                                        k2 = ki+n2;
                                        for(i_=k1; i_<=k2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j+n] = x[1,1];
                                    work[j+n2] = x[1,2];
                                    
                                    //
                                    // Update the right-hand side
                                    //
                                    k1 = 1+n;
                                    k2 = j-1+n;
                                    k3 = 1;
                                    k4 = j-1;
                                    vt = -x[1,1];
                                    i1_ = (k3) - (k1);
                                    for(i_=k1; i_<=k2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j];
                                    }
                                    k1 = 1+n2;
                                    k2 = j-1+n2;
                                    k3 = 1;
                                    k4 = j-1;
                                    vt = -x[1,2];
                                    i1_ = (k3) - (k1);
                                    for(i_=k1; i_<=k2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j];
                                    }
                                }
                                else
                                {
                                    
                                    //
                                    // 2-by-2 diagonal block
                                    //
                                    temp22[1,1] = t[j-1,j-1];
                                    temp22[1,2] = t[j-1,j];
                                    temp22[2,1] = t[j,j-1];
                                    temp22[2,2] = t[j,j];
                                    temp22b[1,1] = work[j-1+n];
                                    temp22b[1,2] = work[j-1+n+n];
                                    temp22b[2,1] = work[j+n];
                                    temp22b[2,2] = work[j+n+n];
                                    internalhsevdlaln2(false, 2, 2, smin, 1.0, ref temp22, 1.0, 1.0, ref temp22b, wr, wi, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale X to avoid overflow when updating
                                    // the right-hand side.
                                    //
                                    if( (double)(xnorm)>(double)(1) )
                                    {
                                        beta = Math.Max(work[j-1], work[j]);
                                        if( (double)(beta)>(double)(bignum/xnorm) )
                                        {
                                            rec = 1/xnorm;
                                            x[1,1] = x[1,1]*rec;
                                            x[1,2] = x[1,2]*rec;
                                            x[2,1] = x[2,1]*rec;
                                            x[2,2] = x[2,2]*rec;
                                            scl = scl*rec;
                                        }
                                    }
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        for(i_=1+n; i_<=ki+n;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                        for(i_=1+n2; i_<=ki+n2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j-1+n] = x[1,1];
                                    work[j+n] = x[2,1];
                                    work[j-1+n2] = x[1,2];
                                    work[j+n2] = x[2,2];
                                    
                                    //
                                    // Update the right-hand side
                                    //
                                    vt = -x[1,1];
                                    i1_ = (1) - (n+1);
                                    for(i_=n+1; i_<=n+j-2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j-1];
                                    }
                                    vt = -x[2,1];
                                    i1_ = (1) - (n+1);
                                    for(i_=n+1; i_<=n+j-2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j];
                                    }
                                    vt = -x[1,2];
                                    i1_ = (1) - (n2+1);
                                    for(i_=n2+1; i_<=n2+j-2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j-1];
                                    }
                                    vt = -x[2,2];
                                    i1_ = (1) - (n2+1);
                                    for(i_=n2+1; i_<=n2+j-2;i_++)
                                    {
                                        work[i_] = work[i_] + vt*t[i_+i1_,j];
                                    }
                                }
                            }
                            
                            //
                            // Copy the vector x or Q*x to VR and normalize.
                            //
                            if( !over )
                            {
                                i1_ = (n+1) - (1);
                                for(i_=1; i_<=ki;i_++)
                                {
                                    vr[i_,iis-1] = work[i_+i1_];
                                }
                                i1_ = (n2+1) - (1);
                                for(i_=1; i_<=ki;i_++)
                                {
                                    vr[i_,iis] = work[i_+i1_];
                                }
                                emax = 0;
                                for(k=1; k<=ki; k++)
                                {
                                    emax = Math.Max(emax, Math.Abs(vr[k,iis-1])+Math.Abs(vr[k,iis]));
                                }
                                remax = 1/emax;
                                for(i_=1; i_<=ki;i_++)
                                {
                                    vr[i_,iis-1] = remax*vr[i_,iis-1];
                                }
                                for(i_=1; i_<=ki;i_++)
                                {
                                    vr[i_,iis] = remax*vr[i_,iis];
                                }
                                for(k=ki+1; k<=n; k++)
                                {
                                    vr[k,iis-1] = 0;
                                    vr[k,iis] = 0;
                                }
                            }
                            else
                            {
                                if( ki>2 )
                                {
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        temp[i_] = vr[i_,ki-1];
                                    }
                                    blas.matrixvectormultiply(ref vr, 1, n, 1, ki-2, false, ref work, 1+n, ki-2+n, 1.0, ref temp, 1, n, work[ki-1+n]);
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vr[i_,ki-1] = temp[i_];
                                    }
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        temp[i_] = vr[i_,ki];
                                    }
                                    blas.matrixvectormultiply(ref vr, 1, n, 1, ki-2, false, ref work, 1+n2, ki-2+n2, 1.0, ref temp, 1, n, work[ki+n2]);
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vr[i_,ki] = temp[i_];
                                    }
                                }
                                else
                                {
                                    vt = work[ki-1+n];
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vr[i_,ki-1] = vt*vr[i_,ki-1];
                                    }
                                    vt = work[ki+n2];
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vr[i_,ki] = vt*vr[i_,ki];
                                    }
                                }
                                emax = 0;
                                for(k=1; k<=n; k++)
                                {
                                    emax = Math.Max(emax, Math.Abs(vr[k,ki-1])+Math.Abs(vr[k,ki]));
                                }
                                remax = 1/emax;
                                for(i_=1; i_<=n;i_++)
                                {
                                    vr[i_,ki-1] = remax*vr[i_,ki-1];
                                }
                                for(i_=1; i_<=n;i_++)
                                {
                                    vr[i_,ki] = remax*vr[i_,ki];
                                }
                            }
                        }
                        iis = iis-1;
                        if( ip!=0 )
                        {
                            iis = iis-1;
                        }
                    }
                    if( ip==1 )
                    {
                        ip = 0;
                    }
                    if( ip==-1 )
                    {
                        ip = 1;
                    }
                }
            }
            if( leftv )
            {
                
                //
                // Compute left eigenvectors.
                //
                ip = 0;
                iis = 1;
                for(ki=1; ki<=n; ki++)
                {
                    skipflag = false;
                    if( ip==-1 )
                    {
                        skipflag = true;
                    }
                    else
                    {
                        if( ki!=n )
                        {
                            if( (double)(t[ki+1,ki])!=(double)(0) )
                            {
                                ip = 1;
                            }
                        }
                        if( somev )
                        {
                            if( !vselect[ki] )
                            {
                                skipflag = true;
                            }
                        }
                    }
                    if( !skipflag )
                    {
                        
                        //
                        // Compute the KI-th eigenvalue (WR,WI).
                        //
                        wr = t[ki,ki];
                        wi = 0;
                        if( ip!=0 )
                        {
                            wi = Math.Sqrt(Math.Abs(t[ki,ki+1]))*Math.Sqrt(Math.Abs(t[ki+1,ki]));
                        }
                        smin = Math.Max(ulp*(Math.Abs(wr)+Math.Abs(wi)), smlnum);
                        if( ip==0 )
                        {
                            
                            //
                            // Real left eigenvector.
                            //
                            work[ki+n] = 1;
                            
                            //
                            // Form right-hand side
                            //
                            for(k=ki+1; k<=n; k++)
                            {
                                work[k+n] = -t[ki,k];
                            }
                            
                            //
                            // Solve the quasi-triangular system:
                            // (T(KI+1:N,KI+1:N) - WR)'*X = SCALE*WORK
                            //
                            vmax = 1;
                            vcrit = bignum;
                            jnxt = ki+1;
                            for(j=ki+1; j<=n; j++)
                            {
                                if( j<jnxt )
                                {
                                    continue;
                                }
                                j1 = j;
                                j2 = j;
                                jnxt = j+1;
                                if( j<n )
                                {
                                    if( (double)(t[j+1,j])!=(double)(0) )
                                    {
                                        j2 = j+1;
                                        jnxt = j+2;
                                    }
                                }
                                if( j1==j2 )
                                {
                                    
                                    //
                                    // 1-by-1 diagonal block
                                    //
                                    // Scale if necessary to avoid overflow when forming
                                    // the right-hand side.
                                    //
                                    if( (double)(work[j])>(double)(vcrit) )
                                    {
                                        rec = 1/vmax;
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = rec*work[i_];
                                        }
                                        vmax = 1;
                                        vcrit = bignum;
                                    }
                                    i1_ = (ki+1+n)-(ki+1);
                                    vt = 0.0;
                                    for(i_=ki+1; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j]*work[i_+i1_];
                                    }
                                    work[j+n] = work[j+n]-vt;
                                    
                                    //
                                    // Solve (T(J,J)-WR)'*X = WORK
                                    //
                                    temp11[1,1] = t[j,j];
                                    temp11b[1,1] = work[j+n];
                                    internalhsevdlaln2(false, 1, 1, smin, 1.0, ref temp11, 1.0, 1.0, ref temp11b, wr, 0, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j+n] = x[1,1];
                                    vmax = Math.Max(Math.Abs(work[j+n]), vmax);
                                    vcrit = bignum/vmax;
                                }
                                else
                                {
                                    
                                    //
                                    // 2-by-2 diagonal block
                                    //
                                    // Scale if necessary to avoid overflow when forming
                                    // the right-hand side.
                                    //
                                    beta = Math.Max(work[j], work[j+1]);
                                    if( (double)(beta)>(double)(vcrit) )
                                    {
                                        rec = 1/vmax;
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = rec*work[i_];
                                        }
                                        vmax = 1;
                                        vcrit = bignum;
                                    }
                                    i1_ = (ki+1+n)-(ki+1);
                                    vt = 0.0;
                                    for(i_=ki+1; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j]*work[i_+i1_];
                                    }
                                    work[j+n] = work[j+n]-vt;
                                    i1_ = (ki+1+n)-(ki+1);
                                    vt = 0.0;
                                    for(i_=ki+1; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j+1]*work[i_+i1_];
                                    }
                                    work[j+1+n] = work[j+1+n]-vt;
                                    
                                    //
                                    // Solve
                                    //    [T(J,J)-WR   T(J,J+1)     ]'* X = SCALE*( WORK1 )
                                    //    [T(J+1,J)    T(J+1,J+1)-WR]             ( WORK2 )
                                    //
                                    temp22[1,1] = t[j,j];
                                    temp22[1,2] = t[j,j+1];
                                    temp22[2,1] = t[j+1,j];
                                    temp22[2,2] = t[j+1,j+1];
                                    temp21b[1,1] = work[j+n];
                                    temp21b[2,1] = work[j+1+n];
                                    internalhsevdlaln2(true, 2, 1, smin, 1.0, ref temp22, 1.0, 1.0, ref temp21b, wr, 0, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j+n] = x[1,1];
                                    work[j+1+n] = x[2,1];
                                    vmax = Math.Max(Math.Abs(work[j+n]), Math.Max(Math.Abs(work[j+1+n]), vmax));
                                    vcrit = bignum/vmax;
                                }
                            }
                            
                            //
                            // Copy the vector x or Q*x to VL and normalize.
                            //
                            if( !over )
                            {
                                i1_ = (ki+n) - (ki);
                                for(i_=ki; i_<=n;i_++)
                                {
                                    vl[i_,iis] = work[i_+i1_];
                                }
                                ii = blas.columnidxabsmax(ref vl, ki, n, iis);
                                remax = 1/Math.Abs(vl[ii,iis]);
                                for(i_=ki; i_<=n;i_++)
                                {
                                    vl[i_,iis] = remax*vl[i_,iis];
                                }
                                for(k=1; k<=ki-1; k++)
                                {
                                    vl[k,iis] = 0;
                                }
                            }
                            else
                            {
                                if( ki<n )
                                {
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        temp[i_] = vl[i_,ki];
                                    }
                                    blas.matrixvectormultiply(ref vl, 1, n, ki+1, n, false, ref work, ki+1+n, n+n, 1.0, ref temp, 1, n, work[ki+n]);
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vl[i_,ki] = temp[i_];
                                    }
                                }
                                ii = blas.columnidxabsmax(ref vl, 1, n, ki);
                                remax = 1/Math.Abs(vl[ii,ki]);
                                for(i_=1; i_<=n;i_++)
                                {
                                    vl[i_,ki] = remax*vl[i_,ki];
                                }
                            }
                        }
                        else
                        {
                            
                            //
                            // Complex left eigenvector.
                            //
                            // Initial solve:
                            //   ((T(KI,KI)    T(KI,KI+1) )' - (WR - I* WI))*X = 0.
                            //   ((T(KI+1,KI) T(KI+1,KI+1))                )
                            //
                            if( (double)(Math.Abs(t[ki,ki+1]))>=(double)(Math.Abs(t[ki+1,ki])) )
                            {
                                work[ki+n] = wi/t[ki,ki+1];
                                work[ki+1+n2] = 1;
                            }
                            else
                            {
                                work[ki+n] = 1;
                                work[ki+1+n2] = -(wi/t[ki+1,ki]);
                            }
                            work[ki+1+n] = 0;
                            work[ki+n2] = 0;
                            
                            //
                            // Form right-hand side
                            //
                            for(k=ki+2; k<=n; k++)
                            {
                                work[k+n] = -(work[ki+n]*t[ki,k]);
                                work[k+n2] = -(work[ki+1+n2]*t[ki+1,k]);
                            }
                            
                            //
                            // Solve complex quasi-triangular system:
                            // ( T(KI+2,N:KI+2,N) - (WR-i*WI) )*X = WORK1+i*WORK2
                            //
                            vmax = 1;
                            vcrit = bignum;
                            jnxt = ki+2;
                            for(j=ki+2; j<=n; j++)
                            {
                                if( j<jnxt )
                                {
                                    continue;
                                }
                                j1 = j;
                                j2 = j;
                                jnxt = j+1;
                                if( j<n )
                                {
                                    if( (double)(t[j+1,j])!=(double)(0) )
                                    {
                                        j2 = j+1;
                                        jnxt = j+2;
                                    }
                                }
                                if( j1==j2 )
                                {
                                    
                                    //
                                    // 1-by-1 diagonal block
                                    //
                                    // Scale if necessary to avoid overflow when
                                    // forming the right-hand side elements.
                                    //
                                    if( (double)(work[j])>(double)(vcrit) )
                                    {
                                        rec = 1/vmax;
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = rec*work[i_];
                                        }
                                        for(i_=ki+n2; i_<=n+n2;i_++)
                                        {
                                            work[i_] = rec*work[i_];
                                        }
                                        vmax = 1;
                                        vcrit = bignum;
                                    }
                                    i1_ = (ki+2+n)-(ki+2);
                                    vt = 0.0;
                                    for(i_=ki+2; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j]*work[i_+i1_];
                                    }
                                    work[j+n] = work[j+n]-vt;
                                    i1_ = (ki+2+n2)-(ki+2);
                                    vt = 0.0;
                                    for(i_=ki+2; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j]*work[i_+i1_];
                                    }
                                    work[j+n2] = work[j+n2]-vt;
                                    
                                    //
                                    // Solve (T(J,J)-(WR-i*WI))*(X11+i*X12)= WK+I*WK2
                                    //
                                    temp11[1,1] = t[j,j];
                                    temp12b[1,1] = work[j+n];
                                    temp12b[1,2] = work[j+n+n];
                                    internalhsevdlaln2(false, 1, 2, smin, 1.0, ref temp11, 1.0, 1.0, ref temp12b, wr, -wi, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                        for(i_=ki+n2; i_<=n+n2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j+n] = x[1,1];
                                    work[j+n2] = x[1,2];
                                    vmax = Math.Max(Math.Abs(work[j+n]), Math.Max(Math.Abs(work[j+n2]), vmax));
                                    vcrit = bignum/vmax;
                                }
                                else
                                {
                                    
                                    //
                                    // 2-by-2 diagonal block
                                    //
                                    // Scale if necessary to avoid overflow when forming
                                    // the right-hand side elements.
                                    //
                                    beta = Math.Max(work[j], work[j+1]);
                                    if( (double)(beta)>(double)(vcrit) )
                                    {
                                        rec = 1/vmax;
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = rec*work[i_];
                                        }
                                        for(i_=ki+n2; i_<=n+n2;i_++)
                                        {
                                            work[i_] = rec*work[i_];
                                        }
                                        vmax = 1;
                                        vcrit = bignum;
                                    }
                                    i1_ = (ki+2+n)-(ki+2);
                                    vt = 0.0;
                                    for(i_=ki+2; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j]*work[i_+i1_];
                                    }
                                    work[j+n] = work[j+n]-vt;
                                    i1_ = (ki+2+n2)-(ki+2);
                                    vt = 0.0;
                                    for(i_=ki+2; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j]*work[i_+i1_];
                                    }
                                    work[j+n2] = work[j+n2]-vt;
                                    i1_ = (ki+2+n)-(ki+2);
                                    vt = 0.0;
                                    for(i_=ki+2; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j+1]*work[i_+i1_];
                                    }
                                    work[j+1+n] = work[j+1+n]-vt;
                                    i1_ = (ki+2+n2)-(ki+2);
                                    vt = 0.0;
                                    for(i_=ki+2; i_<=j-1;i_++)
                                    {
                                        vt += t[i_,j+1]*work[i_+i1_];
                                    }
                                    work[j+1+n2] = work[j+1+n2]-vt;
                                    
                                    //
                                    // Solve 2-by-2 complex linear equation
                                    //   ([T(j,j)   T(j,j+1)  ]'-(wr-i*wi)*I)*X = SCALE*B
                                    //   ([T(j+1,j) T(j+1,j+1)]             )
                                    //
                                    temp22[1,1] = t[j,j];
                                    temp22[1,2] = t[j,j+1];
                                    temp22[2,1] = t[j+1,j];
                                    temp22[2,2] = t[j+1,j+1];
                                    temp22b[1,1] = work[j+n];
                                    temp22b[1,2] = work[j+n+n];
                                    temp22b[2,1] = work[j+1+n];
                                    temp22b[2,2] = work[j+1+n+n];
                                    internalhsevdlaln2(true, 2, 2, smin, 1.0, ref temp22, 1.0, 1.0, ref temp22b, wr, -wi, ref rswap4, ref zswap4, ref ipivot44, ref civ4, ref crv4, ref x, ref scl, ref xnorm, ref ierr);
                                    
                                    //
                                    // Scale if necessary
                                    //
                                    if( (double)(scl)!=(double)(1) )
                                    {
                                        for(i_=ki+n; i_<=n+n;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                        for(i_=ki+n2; i_<=n+n2;i_++)
                                        {
                                            work[i_] = scl*work[i_];
                                        }
                                    }
                                    work[j+n] = x[1,1];
                                    work[j+n2] = x[1,2];
                                    work[j+1+n] = x[2,1];
                                    work[j+1+n2] = x[2,2];
                                    vmax = Math.Max(Math.Abs(x[1,1]), vmax);
                                    vmax = Math.Max(Math.Abs(x[1,2]), vmax);
                                    vmax = Math.Max(Math.Abs(x[2,1]), vmax);
                                    vmax = Math.Max(Math.Abs(x[2,2]), vmax);
                                    vcrit = bignum/vmax;
                                }
                            }
                            
                            //
                            // Copy the vector x or Q*x to VL and normalize.
                            //
                            if( !over )
                            {
                                i1_ = (ki+n) - (ki);
                                for(i_=ki; i_<=n;i_++)
                                {
                                    vl[i_,iis] = work[i_+i1_];
                                }
                                i1_ = (ki+n2) - (ki);
                                for(i_=ki; i_<=n;i_++)
                                {
                                    vl[i_,iis+1] = work[i_+i1_];
                                }
                                emax = 0;
                                for(k=ki; k<=n; k++)
                                {
                                    emax = Math.Max(emax, Math.Abs(vl[k,iis])+Math.Abs(vl[k,iis+1]));
                                }
                                remax = 1/emax;
                                for(i_=ki; i_<=n;i_++)
                                {
                                    vl[i_,iis] = remax*vl[i_,iis];
                                }
                                for(i_=ki; i_<=n;i_++)
                                {
                                    vl[i_,iis+1] = remax*vl[i_,iis+1];
                                }
                                for(k=1; k<=ki-1; k++)
                                {
                                    vl[k,iis] = 0;
                                    vl[k,iis+1] = 0;
                                }
                            }
                            else
                            {
                                if( ki<n-1 )
                                {
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        temp[i_] = vl[i_,ki];
                                    }
                                    blas.matrixvectormultiply(ref vl, 1, n, ki+2, n, false, ref work, ki+2+n, n+n, 1.0, ref temp, 1, n, work[ki+n]);
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vl[i_,ki] = temp[i_];
                                    }
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        temp[i_] = vl[i_,ki+1];
                                    }
                                    blas.matrixvectormultiply(ref vl, 1, n, ki+2, n, false, ref work, ki+2+n2, n+n2, 1.0, ref temp, 1, n, work[ki+1+n2]);
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vl[i_,ki+1] = temp[i_];
                                    }
                                }
                                else
                                {
                                    vt = work[ki+n];
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vl[i_,ki] = vt*vl[i_,ki];
                                    }
                                    vt = work[ki+1+n2];
                                    for(i_=1; i_<=n;i_++)
                                    {
                                        vl[i_,ki+1] = vt*vl[i_,ki+1];
                                    }
                                }
                                emax = 0;
                                for(k=1; k<=n; k++)
                                {
                                    emax = Math.Max(emax, Math.Abs(vl[k,ki])+Math.Abs(vl[k,ki+1]));
                                }
                                remax = 1/emax;
                                for(i_=1; i_<=n;i_++)
                                {
                                    vl[i_,ki] = remax*vl[i_,ki];
                                }
                                for(i_=1; i_<=n;i_++)
                                {
                                    vl[i_,ki+1] = remax*vl[i_,ki+1];
                                }
                            }
                        }
                        iis = iis+1;
                        if( ip!=0 )
                        {
                            iis = iis+1;
                        }
                    }
                    if( ip==-1 )
                    {
                        ip = 0;
                    }
                    if( ip==1 )
                    {
                        ip = -1;
                    }
                }
            }
        }


        private static void internalhsevdlaln2(bool ltrans,
            int na,
            int nw,
            double smin,
            double ca,
            ref double[,] a,
            double d1,
            double d2,
            ref double[,] b,
            double wr,
            double wi,
            ref bool[] rswap4,
            ref bool[] zswap4,
            ref int[,] ipivot44,
            ref double[] civ4,
            ref double[] crv4,
            ref double[,] x,
            ref double scl,
            ref double xnorm,
            ref int info)
        {
            int icmax = 0;
            int j = 0;
            double bbnd = 0;
            double bi1 = 0;
            double bi2 = 0;
            double bignum = 0;
            double bnorm = 0;
            double br1 = 0;
            double br2 = 0;
            double ci21 = 0;
            double ci22 = 0;
            double cmax = 0;
            double cnorm = 0;
            double cr21 = 0;
            double cr22 = 0;
            double csi = 0;
            double csr = 0;
            double li21 = 0;
            double lr21 = 0;
            double smini = 0;
            double smlnum = 0;
            double temp = 0;
            double u22abs = 0;
            double ui11 = 0;
            double ui11r = 0;
            double ui12 = 0;
            double ui12s = 0;
            double ui22 = 0;
            double ur11 = 0;
            double ur11r = 0;
            double ur12 = 0;
            double ur12s = 0;
            double ur22 = 0;
            double xi1 = 0;
            double xi2 = 0;
            double xr1 = 0;
            double xr2 = 0;
            double tmp1 = 0;
            double tmp2 = 0;

            zswap4[1] = false;
            zswap4[2] = false;
            zswap4[3] = true;
            zswap4[4] = true;
            rswap4[1] = false;
            rswap4[2] = true;
            rswap4[3] = false;
            rswap4[4] = true;
            ipivot44[1,1] = 1;
            ipivot44[2,1] = 2;
            ipivot44[3,1] = 3;
            ipivot44[4,1] = 4;
            ipivot44[1,2] = 2;
            ipivot44[2,2] = 1;
            ipivot44[3,2] = 4;
            ipivot44[4,2] = 3;
            ipivot44[1,3] = 3;
            ipivot44[2,3] = 4;
            ipivot44[3,3] = 1;
            ipivot44[4,3] = 2;
            ipivot44[1,4] = 4;
            ipivot44[2,4] = 3;
            ipivot44[3,4] = 2;
            ipivot44[4,4] = 1;
            smlnum = 2*AP.Math.MinRealNumber;
            bignum = 1/smlnum;
            smini = Math.Max(smin, smlnum);
            
            //
            // Don't check for input errors
            //
            info = 0;
            
            //
            // Standard Initializations
            //
            scl = 1;
            if( na==1 )
            {
                
                //
                // 1 x 1  (i.e., scalar) system   C X = B
                //
                if( nw==1 )
                {
                    
                    //
                    // Real 1x1 system.
                    //
                    // C = ca A - w D
                    //
                    csr = ca*a[1,1]-wr*d1;
                    cnorm = Math.Abs(csr);
                    
                    //
                    // If | C | < SMINI, use C = SMINI
                    //
                    if( (double)(cnorm)<(double)(smini) )
                    {
                        csr = smini;
                        cnorm = smini;
                        info = 1;
                    }
                    
                    //
                    // Check scaling for  X = B / C
                    //
                    bnorm = Math.Abs(b[1,1]);
                    if( (double)(cnorm)<(double)(1) & (double)(bnorm)>(double)(1) )
                    {
                        if( (double)(bnorm)>(double)(bignum*cnorm) )
                        {
                            scl = 1/bnorm;
                        }
                    }
                    
                    //
                    // Compute X
                    //
                    x[1,1] = b[1,1]*scl/csr;
                    xnorm = Math.Abs(x[1,1]);
                }
                else
                {
                    
                    //
                    // Complex 1x1 system (w is complex)
                    //
                    // C = ca A - w D
                    //
                    csr = ca*a[1,1]-wr*d1;
                    csi = -(wi*d1);
                    cnorm = Math.Abs(csr)+Math.Abs(csi);
                    
                    //
                    // If | C | < SMINI, use C = SMINI
                    //
                    if( (double)(cnorm)<(double)(smini) )
                    {
                        csr = smini;
                        csi = 0;
                        cnorm = smini;
                        info = 1;
                    }
                    
                    //
                    // Check scaling for  X = B / C
                    //
                    bnorm = Math.Abs(b[1,1])+Math.Abs(b[1,2]);
                    if( (double)(cnorm)<(double)(1) & (double)(bnorm)>(double)(1) )
                    {
                        if( (double)(bnorm)>(double)(bignum*cnorm) )
                        {
                            scl = 1/bnorm;
                        }
                    }
                    
                    //
                    // Compute X
                    //
                    internalhsevdladiv(scl*b[1,1], scl*b[1,2], csr, csi, ref tmp1, ref tmp2);
                    x[1,1] = tmp1;
                    x[1,2] = tmp2;
                    xnorm = Math.Abs(x[1,1])+Math.Abs(x[1,2]);
                }
            }
            else
            {
                
                //
                // 2x2 System
                //
                // Compute the real part of  C = ca A - w D  (or  ca A' - w D )
                //
                crv4[1+0] = ca*a[1,1]-wr*d1;
                crv4[2+2] = ca*a[2,2]-wr*d2;
                if( ltrans )
                {
                    crv4[1+2] = ca*a[2,1];
                    crv4[2+0] = ca*a[1,2];
                }
                else
                {
                    crv4[2+0] = ca*a[2,1];
                    crv4[1+2] = ca*a[1,2];
                }
                if( nw==1 )
                {
                    
                    //
                    // Real 2x2 system  (w is real)
                    //
                    // Find the largest element in C
                    //
                    cmax = 0;
                    icmax = 0;
                    for(j=1; j<=4; j++)
                    {
                        if( (double)(Math.Abs(crv4[j]))>(double)(cmax) )
                        {
                            cmax = Math.Abs(crv4[j]);
                            icmax = j;
                        }
                    }
                    
                    //
                    // If norm(C) < SMINI, use SMINI*identity.
                    //
                    if( (double)(cmax)<(double)(smini) )
                    {
                        bnorm = Math.Max(Math.Abs(b[1,1]), Math.Abs(b[2,1]));
                        if( (double)(smini)<(double)(1) & (double)(bnorm)>(double)(1) )
                        {
                            if( (double)(bnorm)>(double)(bignum*smini) )
                            {
                                scl = 1/bnorm;
                            }
                        }
                        temp = scl/smini;
                        x[1,1] = temp*b[1,1];
                        x[2,1] = temp*b[2,1];
                        xnorm = temp*bnorm;
                        info = 1;
                        return;
                    }
                    
                    //
                    // Gaussian elimination with complete pivoting.
                    //
                    ur11 = crv4[icmax];
                    cr21 = crv4[ipivot44[2,icmax]];
                    ur12 = crv4[ipivot44[3,icmax]];
                    cr22 = crv4[ipivot44[4,icmax]];
                    ur11r = 1/ur11;
                    lr21 = ur11r*cr21;
                    ur22 = cr22-ur12*lr21;
                    
                    //
                    // If smaller pivot < SMINI, use SMINI
                    //
                    if( (double)(Math.Abs(ur22))<(double)(smini) )
                    {
                        ur22 = smini;
                        info = 1;
                    }
                    if( rswap4[icmax] )
                    {
                        br1 = b[2,1];
                        br2 = b[1,1];
                    }
                    else
                    {
                        br1 = b[1,1];
                        br2 = b[2,1];
                    }
                    br2 = br2-lr21*br1;
                    bbnd = Math.Max(Math.Abs(br1*(ur22*ur11r)), Math.Abs(br2));
                    if( (double)(bbnd)>(double)(1) & (double)(Math.Abs(ur22))<(double)(1) )
                    {
                        if( (double)(bbnd)>=(double)(bignum*Math.Abs(ur22)) )
                        {
                            scl = 1/bbnd;
                        }
                    }
                    xr2 = br2*scl/ur22;
                    xr1 = scl*br1*ur11r-xr2*(ur11r*ur12);
                    if( zswap4[icmax] )
                    {
                        x[1,1] = xr2;
                        x[2,1] = xr1;
                    }
                    else
                    {
                        x[1,1] = xr1;
                        x[2,1] = xr2;
                    }
                    xnorm = Math.Max(Math.Abs(xr1), Math.Abs(xr2));
                    
                    //
                    // Further scaling if  norm(A) norm(X) > overflow
                    //
                    if( (double)(xnorm)>(double)(1) & (double)(cmax)>(double)(1) )
                    {
                        if( (double)(xnorm)>(double)(bignum/cmax) )
                        {
                            temp = cmax/bignum;
                            x[1,1] = temp*x[1,1];
                            x[2,1] = temp*x[2,1];
                            xnorm = temp*xnorm;
                            scl = temp*scl;
                        }
                    }
                }
                else
                {
                    
                    //
                    // Complex 2x2 system  (w is complex)
                    //
                    // Find the largest element in C
                    //
                    civ4[1+0] = -(wi*d1);
                    civ4[2+0] = 0;
                    civ4[1+2] = 0;
                    civ4[2+2] = -(wi*d2);
                    cmax = 0;
                    icmax = 0;
                    for(j=1; j<=4; j++)
                    {
                        if( (double)(Math.Abs(crv4[j])+Math.Abs(civ4[j]))>(double)(cmax) )
                        {
                            cmax = Math.Abs(crv4[j])+Math.Abs(civ4[j]);
                            icmax = j;
                        }
                    }
                    
                    //
                    // If norm(C) < SMINI, use SMINI*identity.
                    //
                    if( (double)(cmax)<(double)(smini) )
                    {
                        bnorm = Math.Max(Math.Abs(b[1,1])+Math.Abs(b[1,2]), Math.Abs(b[2,1])+Math.Abs(b[2,2]));
                        if( (double)(smini)<(double)(1) & (double)(bnorm)>(double)(1) )
                        {
                            if( (double)(bnorm)>(double)(bignum*smini) )
                            {
                                scl = 1/bnorm;
                            }
                        }
                        temp = scl/smini;
                        x[1,1] = temp*b[1,1];
                        x[2,1] = temp*b[2,1];
                        x[1,2] = temp*b[1,2];
                        x[2,2] = temp*b[2,2];
                        xnorm = temp*bnorm;
                        info = 1;
                        return;
                    }
                    
                    //
                    // Gaussian elimination with complete pivoting.
                    //
                    ur11 = crv4[icmax];
                    ui11 = civ4[icmax];
                    cr21 = crv4[ipivot44[2,icmax]];
                    ci21 = civ4[ipivot44[2,icmax]];
                    ur12 = crv4[ipivot44[3,icmax]];
                    ui12 = civ4[ipivot44[3,icmax]];
                    cr22 = crv4[ipivot44[4,icmax]];
                    ci22 = civ4[ipivot44[4,icmax]];
                    if( icmax==1 | icmax==4 )
                    {
                        
                        //
                        // Code when off-diagonals of pivoted C are real
                        //
                        if( (double)(Math.Abs(ur11))>(double)(Math.Abs(ui11)) )
                        {
                            temp = ui11/ur11;
                            ur11r = 1/(ur11*(1+AP.Math.Sqr(temp)));
                            ui11r = -(temp*ur11r);
                        }
                        else
                        {
                            temp = ur11/ui11;
                            ui11r = -(1/(ui11*(1+AP.Math.Sqr(temp))));
                            ur11r = -(temp*ui11r);
                        }
                        lr21 = cr21*ur11r;
                        li21 = cr21*ui11r;
                        ur12s = ur12*ur11r;
                        ui12s = ur12*ui11r;
                        ur22 = cr22-ur12*lr21;
                        ui22 = ci22-ur12*li21;
                    }
                    else
                    {
                        
                        //
                        // Code when diagonals of pivoted C are real
                        //
                        ur11r = 1/ur11;
                        ui11r = 0;
                        lr21 = cr21*ur11r;
                        li21 = ci21*ur11r;
                        ur12s = ur12*ur11r;
                        ui12s = ui12*ur11r;
                        ur22 = cr22-ur12*lr21+ui12*li21;
                        ui22 = -(ur12*li21)-ui12*lr21;
                    }
                    u22abs = Math.Abs(ur22)+Math.Abs(ui22);
                    
                    //
                    // If smaller pivot < SMINI, use SMINI
                    //
                    if( (double)(u22abs)<(double)(smini) )
                    {
                        ur22 = smini;
                        ui22 = 0;
                        info = 1;
                    }
                    if( rswap4[icmax] )
                    {
                        br2 = b[1,1];
                        br1 = b[2,1];
                        bi2 = b[1,2];
                        bi1 = b[2,2];
                    }
                    else
                    {
                        br1 = b[1,1];
                        br2 = b[2,1];
                        bi1 = b[1,2];
                        bi2 = b[2,2];
                    }
                    br2 = br2-lr21*br1+li21*bi1;
                    bi2 = bi2-li21*br1-lr21*bi1;
                    bbnd = Math.Max((Math.Abs(br1)+Math.Abs(bi1))*(u22abs*(Math.Abs(ur11r)+Math.Abs(ui11r))), Math.Abs(br2)+Math.Abs(bi2));
                    if( (double)(bbnd)>(double)(1) & (double)(u22abs)<(double)(1) )
                    {
                        if( (double)(bbnd)>=(double)(bignum*u22abs) )
                        {
                            scl = 1/bbnd;
                            br1 = scl*br1;
                            bi1 = scl*bi1;
                            br2 = scl*br2;
                            bi2 = scl*bi2;
                        }
                    }
                    internalhsevdladiv(br2, bi2, ur22, ui22, ref xr2, ref xi2);
                    xr1 = ur11r*br1-ui11r*bi1-ur12s*xr2+ui12s*xi2;
                    xi1 = ui11r*br1+ur11r*bi1-ui12s*xr2-ur12s*xi2;
                    if( zswap4[icmax] )
                    {
                        x[1,1] = xr2;
                        x[2,1] = xr1;
                        x[1,2] = xi2;
                        x[2,2] = xi1;
                    }
                    else
                    {
                        x[1,1] = xr1;
                        x[2,1] = xr2;
                        x[1,2] = xi1;
                        x[2,2] = xi2;
                    }
                    xnorm = Math.Max(Math.Abs(xr1)+Math.Abs(xi1), Math.Abs(xr2)+Math.Abs(xi2));
                    
                    //
                    // Further scaling if  norm(A) norm(X) > overflow
                    //
                    if( (double)(xnorm)>(double)(1) & (double)(cmax)>(double)(1) )
                    {
                        if( (double)(xnorm)>(double)(bignum/cmax) )
                        {
                            temp = cmax/bignum;
                            x[1,1] = temp*x[1,1];
                            x[2,1] = temp*x[2,1];
                            x[1,2] = temp*x[1,2];
                            x[2,2] = temp*x[2,2];
                            xnorm = temp*xnorm;
                            scl = temp*scl;
                        }
                    }
                }
            }
        }


        private static void internalhsevdladiv(double a,
            double b,
            double c,
            double d,
            ref double p,
            ref double q)
        {
            double e = 0;
            double f = 0;

            if( (double)(Math.Abs(d))<(double)(Math.Abs(c)) )
            {
                e = d/c;
                f = c+d*e;
                p = (a+b*e)/f;
                q = (b-a*e)/f;
            }
            else
            {
                e = c/d;
                f = d+c*e;
                p = (b+a*e)/f;
                q = (-a+b*e)/f;
            }
        }
    }
}