source: trunk/sources/ALGLIB/rotations.cs @ 2504

/*************************************************************************
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 rotations
    {
        /*************************************************************************
        Application of a sequence of  elementary rotations to a matrix

        The algorithm pre-multiplies the matrix by a sequence of rotation
        transformations which is given by arrays C and S. Depending on the value
        of the IsForward parameter either 1 and 2, 3 and 4 and so on (if IsForward=true)
        rows are rotated, or the rows N and N-1, N-2 and N-3 and so on, are rotated.

        Not the whole matrix but only a part of it is transformed (rows from M1 to
        M2, columns from N1 to N2). Only the elements of this submatrix are changed.

        Input parameters:
            IsForward   -   the sequence of the rotation application.
            M1,M2       -   the range of rows to be transformed.
            N1, N2      -   the range of columns to be transformed.
            C,S         -   transformation coefficients.
                            Array whose index ranges within [1..M2-M1].
            A           -   processed matrix.
            WORK        -   working array whose index ranges within [N1..N2].

        Output parameters:
            A           -   transformed matrix.

        Utility subroutine.
        *************************************************************************/
        public static void applyrotationsfromtheleft(bool isforward,
            int m1,
            int m2,
            int n1,
            int n2,
            ref double[] c,
            ref double[] s,
            ref double[,] a,
            ref double[] work)
        {
            int j = 0;
            int jp1 = 0;
            double ctemp = 0;
            double stemp = 0;
            double temp = 0;
            int i_ = 0;

            if( m1>m2 | n1>n2 )
            {
                return;
            }
            
            //
            // Form  P * A
            //
            if( isforward )
            {
                if( n1!=n2 )
                {
                    
                    //
                    // Common case: N1<>N2
                    //
                    for(j=m1; j<=m2-1; j++)
                    {
                        ctemp = c[j-m1+1];
                        stemp = s[j-m1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            jp1 = j+1;
                            for(i_=n1; i_<=n2;i_++)
                            {
                                work[i_] = ctemp*a[jp1,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                work[i_] = work[i_] - stemp*a[j,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                a[j,i_] = ctemp*a[j,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                a[j,i_] = a[j,i_] + stemp*a[jp1,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                a[jp1,i_] = work[i_];
                            }
                        }
                    }
                }
                else
                {
                    
                    //
                    // Special case: N1=N2
                    //
                    for(j=m1; j<=m2-1; j++)
                    {
                        ctemp = c[j-m1+1];
                        stemp = s[j-m1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            temp = a[j+1,n1];
                            a[j+1,n1] = ctemp*temp-stemp*a[j,n1];
                            a[j,n1] = stemp*temp+ctemp*a[j,n1];
                        }
                    }
                }
            }
            else
            {
                if( n1!=n2 )
                {
                    
                    //
                    // Common case: N1<>N2
                    //
                    for(j=m2-1; j>=m1; j--)
                    {
                        ctemp = c[j-m1+1];
                        stemp = s[j-m1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            jp1 = j+1;
                            for(i_=n1; i_<=n2;i_++)
                            {
                                work[i_] = ctemp*a[jp1,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                work[i_] = work[i_] - stemp*a[j,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                a[j,i_] = ctemp*a[j,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                a[j,i_] = a[j,i_] + stemp*a[jp1,i_];
                            }
                            for(i_=n1; i_<=n2;i_++)
                            {
                                a[jp1,i_] = work[i_];
                            }
                        }
                    }
                }
                else
                {
                    
                    //
                    // Special case: N1=N2
                    //
                    for(j=m2-1; j>=m1; j--)
                    {
                        ctemp = c[j-m1+1];
                        stemp = s[j-m1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            temp = a[j+1,n1];
                            a[j+1,n1] = ctemp*temp-stemp*a[j,n1];
                            a[j,n1] = stemp*temp+ctemp*a[j,n1];
                        }
                    }
                }
            }
        }


        /*************************************************************************
        Application of a sequence of  elementary rotations to a matrix

        The algorithm post-multiplies the matrix by a sequence of rotation
        transformations which is given by arrays C and S. Depending on the value
        of the IsForward parameter either 1 and 2, 3 and 4 and so on (if IsForward=true)
        rows are rotated, or the rows N and N-1, N-2 and N-3 and so on are rotated.

        Not the whole matrix but only a part of it is transformed (rows from M1
        to M2, columns from N1 to N2). Only the elements of this submatrix are changed.

        Input parameters:
            IsForward   -   the sequence of the rotation application.
            M1,M2       -   the range of rows to be transformed.
            N1, N2      -   the range of columns to be transformed.
            C,S         -   transformation coefficients.
                            Array whose index ranges within [1..N2-N1].
            A           -   processed matrix.
            WORK        -   working array whose index ranges within [M1..M2].

        Output parameters:
            A           -   transformed matrix.

        Utility subroutine.
        *************************************************************************/
        public static void applyrotationsfromtheright(bool isforward,
            int m1,
            int m2,
            int n1,
            int n2,
            ref double[] c,
            ref double[] s,
            ref double[,] a,
            ref double[] work)
        {
            int j = 0;
            int jp1 = 0;
            double ctemp = 0;
            double stemp = 0;
            double temp = 0;
            int i_ = 0;

            
            //
            // Form A * P'
            //
            if( isforward )
            {
                if( m1!=m2 )
                {
                    
                    //
                    // Common case: M1<>M2
                    //
                    for(j=n1; j<=n2-1; j++)
                    {
                        ctemp = c[j-n1+1];
                        stemp = s[j-n1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            jp1 = j+1;
                            for(i_=m1; i_<=m2;i_++)
                            {
                                work[i_] = ctemp*a[i_,jp1];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                work[i_] = work[i_] - stemp*a[i_,j];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                a[i_,j] = ctemp*a[i_,j];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                a[i_,j] = a[i_,j] + stemp*a[i_,jp1];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                a[i_,jp1] = work[i_];
                            }
                        }
                    }
                }
                else
                {
                    
                    //
                    // Special case: M1=M2
                    //
                    for(j=n1; j<=n2-1; j++)
                    {
                        ctemp = c[j-n1+1];
                        stemp = s[j-n1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            temp = a[m1,j+1];
                            a[m1,j+1] = ctemp*temp-stemp*a[m1,j];
                            a[m1,j] = stemp*temp+ctemp*a[m1,j];
                        }
                    }
                }
            }
            else
            {
                if( m1!=m2 )
                {
                    
                    //
                    // Common case: M1<>M2
                    //
                    for(j=n2-1; j>=n1; j--)
                    {
                        ctemp = c[j-n1+1];
                        stemp = s[j-n1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            jp1 = j+1;
                            for(i_=m1; i_<=m2;i_++)
                            {
                                work[i_] = ctemp*a[i_,jp1];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                work[i_] = work[i_] - stemp*a[i_,j];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                a[i_,j] = ctemp*a[i_,j];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                a[i_,j] = a[i_,j] + stemp*a[i_,jp1];
                            }
                            for(i_=m1; i_<=m2;i_++)
                            {
                                a[i_,jp1] = work[i_];
                            }
                        }
                    }
                }
                else
                {
                    
                    //
                    // Special case: M1=M2
                    //
                    for(j=n2-1; j>=n1; j--)
                    {
                        ctemp = c[j-n1+1];
                        stemp = s[j-n1+1];
                        if( ctemp!=1 | stemp!=0 )
                        {
                            temp = a[m1,j+1];
                            a[m1,j+1] = ctemp*temp-stemp*a[m1,j];
                            a[m1,j] = stemp*temp+ctemp*a[m1,j];
                        }
                    }
                }
            }
        }


        /*************************************************************************
        The subroutine generates the elementary rotation, so that:

        [  CS  SN  ]  .  [ F ]  =  [ R ]
        [ -SN  CS  ]     [ G ]     [ 0 ]

        CS**2 + SN**2 = 1
        *************************************************************************/
        public static void generaterotation(double f,
            double g,
            ref double cs,
            ref double sn,
            ref double r)
        {
            double f1 = 0;
            double g1 = 0;

            if( g==0 )
            {
                cs = 1;
                sn = 0;
                r = f;
            }
            else
            {
                if( f==0 )
                {
                    cs = 0;
                    sn = 1;
                    r = g;
                }
                else
                {
                    f1 = f;
                    g1 = g;
                    r = Math.Sqrt(AP.Math.Sqr(f1)+AP.Math.Sqr(g1));
                    cs = f1/r;
                    sn = g1/r;
                    if( Math.Abs(f)>Math.Abs(g) & cs<0 )
                    {
                        cs = -cs;
                        sn = -sn;
                        r = -r;
                    }
                }
            }
        }


        private static void testrotations()
        {
            double[,] al1 = new double[0,0];
            double[,] al2 = new double[0,0];
            double[,] ar1 = new double[0,0];
            double[,] ar2 = new double[0,0];
            double[] cl = new double[0];
            double[] sl = new double[0];
            double[] cr = new double[0];
            double[] sr = new double[0];
            double[] w = new double[0];
            int m = 0;
            int n = 0;
            int maxmn = 0;
            double t = 0;
            int pass = 0;
            int passcount = 0;
            int i = 0;
            int j = 0;
            double err = 0;
            double maxerr = 0;
            bool isforward = new bool();

            passcount = 1000;
            maxerr = 0;
            for(pass=1; pass<=passcount; pass++)
            {
                
                //
                // settings
                //
                m = 2+AP.Math.RandomInteger(50);
                n = 2+AP.Math.RandomInteger(50);
                isforward = AP.Math.RandomReal()>0.5;
                maxmn = Math.Max(m, n);
                al1 = new double[m+1, n+1];
                al2 = new double[m+1, n+1];
                ar1 = new double[m+1, n+1];
                ar2 = new double[m+1, n+1];
                cl = new double[m-1+1];
                sl = new double[m-1+1];
                cr = new double[n-1+1];
                sr = new double[n-1+1];
                w = new double[maxmn+1];
                
                //
                // matrices and rotaions
                //
                for(i=1; i<=m; i++)
                {
                    for(j=1; j<=n; j++)
                    {
                        al1[i,j] = 2*AP.Math.RandomReal()-1;
                        al2[i,j] = al1[i,j];
                        ar1[i,j] = al1[i,j];
                        ar2[i,j] = al1[i,j];
                    }
                }
                for(i=1; i<=m-1; i++)
                {
                    t = 2*Math.PI*AP.Math.RandomReal();
                    cl[i] = Math.Cos(t);
                    sl[i] = Math.Sin(t);
                }
                for(j=1; j<=n-1; j++)
                {
                    t = 2*Math.PI*AP.Math.RandomReal();
                    cr[j] = Math.Cos(t);
                    sr[j] = Math.Sin(t);
                }
                
                //
                // Test left
                //
                applyrotationsfromtheleft(isforward, 1, m, 1, n, ref cl, ref sl, ref al1, ref w);
                for(j=1; j<=n; j++)
                {
                    applyrotationsfromtheleft(isforward, 1, m, j, j, ref cl, ref sl, ref al2, ref w);
                }
                err = 0;
                for(i=1; i<=m; i++)
                {
                    for(j=1; j<=n; j++)
                    {
                        err = Math.Max(err, Math.Abs(al1[i,j]-al2[i,j]));
                    }
                }
                maxerr = Math.Max(err, maxerr);
                
                //
                // Test right
                //
                applyrotationsfromtheright(isforward, 1, m, 1, n, ref cr, ref sr, ref ar1, ref w);
                for(i=1; i<=m; i++)
                {
                    applyrotationsfromtheright(isforward, i, i, 1, n, ref cr, ref sr, ref ar2, ref w);
                }
                err = 0;
                for(i=1; i<=m; i++)
                {
                    for(j=1; j<=n; j++)
                    {
                        err = Math.Max(err, Math.Abs(ar1[i,j]-ar2[i,j]));
                    }
                }
                maxerr = Math.Max(err, maxerr);
            }
            System.Console.Write("TESTING ROTATIONS");
            System.Console.WriteLine();
            System.Console.Write("Pass count ");
            System.Console.Write("{0,0:d}",passcount);
            System.Console.WriteLine();
            System.Console.Write("Error is ");
            System.Console.Write("{0,5:E3}",maxerr);
            System.Console.WriteLine();
        }
    }
}