zgivens.c

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#include <../../nrnconf.h>

/**************************************************************************
**
** Copyright (C) 1993 David E. Steward & Zbigniew Leyk, all rights reserved.
**
**               Meschach Library
** 
** This Meschach Library is provided "as is" without any express 
** or implied warranty of any kind with respect to this software. 
** In particular the authors shall not be liable for any direct, 
** indirect, special, incidental or consequential damages arising 
** in any way from use of the software.
** 
** Everyone is granted permission to copy, modify and redistribute this
** Meschach Library, provided:
**  1.  All copies contain this copyright notice.
**  2.  All modified copies shall carry a notice stating who
**      made the last modification and the date of such modification.
**  3.  No charge is made for this software or works derived from it.  
**      This clause shall not be construed as constraining other software
**      distributed on the same medium as this software, nor is a
**      distribution fee considered a charge.
**
***************************************************************************/


/*
    Givens operations file. Contains routines for calculating and
    applying givens rotations for/to vectors and also to matrices by
    row and by column.

    Complex version.
*/

static  char    rcsid[] = "$Id: ";

#include    <stdio.h>
#include    "zmatrix.h"
#include        "zmatrix2.h"
#include    <math.h>

/*
    (Complex) Givens rotation matrix:
        [ c   -s ]
        [ s*   c ]
    Note that c is real and s is complex
*/

/* zgivens -- returns c,s parameters for Givens rotation to
        eliminate y in the **column** vector [ x y ] */
void    zgivens(x,y,c,s)
complex x,y,*s;
Real    *c;
{
    Real    inv_norm, norm;
    complex tmp;

    /* this is a safe way of computing sqrt(|x|^2+|y|^2) */
    tmp.re = zabs(x);   tmp.im = zabs(y);
    norm = zabs(tmp);

    if ( norm == 0.0 )
    {   *c = 1.0;   s->re = s->im = 0.0;    } /* identity */
    else
    {
        inv_norm = 1.0 / tmp.re;    /* inv_norm = 1/|x| */
        x.re *= inv_norm;
        x.im *= inv_norm;       /* normalise x */
        inv_norm = 1.0/norm;        /* inv_norm = 1/||[x,y]||2 */
        *c = tmp.re * inv_norm;
        /* now compute - conj(normalised x).y/||[x,y]||2 */
        s->re = - inv_norm*(x.re*y.re + x.im*y.im);
        s->im =   inv_norm*(x.re*y.im - x.im*y.re);
    }
}

/* rot_zvec -- apply Givens rotation to x's i & k components */
ZVEC    *rot_zvec(x,i,k,c,s,out)
ZVEC    *x,*out;
int i,k;
double  c;
complex s;
{

    complex temp1, temp2;

    if ( x==ZVNULL )
        error(E_NULL,"rot_zvec");
    if ( i < 0 || i >= x->dim || k < 0 || k >= x->dim )
        error(E_RANGE,"rot_zvec");
    if ( x != out )
        out = zv_copy(x,out);

    /* temp1 = c*out->ve[i] - s*out->ve[k]; */
    temp1.re = c*out->ve[i].re
        - s.re*out->ve[k].re + s.im*out->ve[k].im;
    temp1.im = c*out->ve[i].im
        - s.re*out->ve[k].im - s.im*out->ve[k].re;

    /* temp2 = c*out->ve[k] + zconj(s)*out->ve[i]; */
    temp2.re = c*out->ve[k].re
        + s.re*out->ve[i].re + s.im*out->ve[i].im;
    temp2.im = c*out->ve[k].im
        + s.re*out->ve[i].im - s.im*out->ve[i].re;

    out->ve[i] = temp1;
    out->ve[k] = temp2;

    return (out);
}

/* zrot_rows -- premultiply mat by givens rotation described by c,s */
ZMAT    *zrot_rows(mat,i,k,c,s,out)
ZMAT    *mat,*out;
int i,k;
double  c;
complex s;
{
    u_int   j;
    complex temp1, temp2;

    if ( mat==ZMNULL )
        error(E_NULL,"zrot_rows");
    if ( i < 0 || i >= mat->m || k < 0 || k >= mat->m )
        error(E_RANGE,"zrot_rows");

    if ( mat != out )
        out = zm_copy(mat,zm_resize(out,mat->m,mat->n));

    /* temp1 = c*out->me[i][j] - s*out->me[k][j]; */
    for ( j=0; j<mat->n; j++ )
    {
        /* temp1 = c*out->me[i][j] - s*out->me[k][j]; */
        temp1.re = c*out->me[i][j].re
        - s.re*out->me[k][j].re + s.im*out->me[k][j].im;
        temp1.im = c*out->me[i][j].im
        - s.re*out->me[k][j].im - s.im*out->me[k][j].re;
        
        /* temp2 = c*out->me[k][j] + conj(s)*out->me[i][j]; */
        temp2.re = c*out->me[k][j].re
        + s.re*out->me[i][j].re + s.im*out->me[i][j].im;
        temp2.im = c*out->me[k][j].im
        + s.re*out->me[i][j].im - s.im*out->me[i][j].re;
        
        out->me[i][j] = temp1;
        out->me[k][j] = temp2;
    }

    return (out);
}

/* zrot_cols -- postmultiply mat by adjoint Givens rotation described by c,s */
ZMAT    *zrot_cols(mat,i,k,c,s,out)
ZMAT    *mat,*out;
int i,k;
double  c;
complex s;
{
    u_int   j;
    complex x, y;

    if ( mat==ZMNULL )
        error(E_NULL,"zrot_cols");
    if ( i < 0 || i >= mat->n || k < 0 || k >= mat->n )
        error(E_RANGE,"zrot_cols");

    if ( mat != out )
        out = zm_copy(mat,zm_resize(out,mat->m,mat->n));

    for ( j=0; j<mat->m; j++ )
    {
        x = out->me[j][i];  y = out->me[j][k];
        /* out->me[j][i] = c*x - conj(s)*y; */
        out->me[j][i].re = c*x.re - s.re*y.re - s.im*y.im;
        out->me[j][i].im = c*x.im - s.re*y.im + s.im*y.re;
        
        /* out->me[j][k] = c*y + s*x; */
        out->me[j][k].re = c*y.re + s.re*x.re - s.im*x.im;
        out->me[j][k].im = c*y.im + s.re*x.im + s.im*x.re;
    }

    return (out);
}