RISC DISC 1/RISC_DISC_1.iso/pd_share/code/meschach/!Meschach/c/znorm

Text File | 1994-01-12 | 4.5 KB | 209 lines

/**************************************************************************
**
** 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.
**
***************************************************************************/


/*
    A collection of functions for computing norms: scaled and unscaled
    Complex version
*/
static    char    rcsid[] = "$Id: znorm.c,v 1.1 1994/01/13 04:21:31 des Exp $";

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



/* _zv_norm1 -- computes (scaled) 1-norms of vectors */
double    _zv_norm1(x,scale)
ZVEC    *x;
VEC    *scale;
{
    int    i, dim;
    Real    s, sum;

    if ( x == ZVNULL )
    error(E_NULL,"_zv_norm1");
    dim = x->dim;

    sum = 0.0;
    if ( scale == VNULL )
    for ( i = 0; i < dim; i++ )
        sum += zabs(x->ve[i]);
    else if ( scale->dim < dim )
    error(E_SIZES,"_zv_norm1");
    else
    for ( i = 0; i < dim; i++ )
    {
        s = scale->ve[i];
        sum += ( s== 0.0 ) ? zabs(x->ve[i]) : zabs(x->ve[i])/fabs(s);
    }

    return sum;
}

/* square -- returns x^2 */
/******************************
double    square(x)
double    x;
{    return x*x;    }
******************************/

#define    square(x)    ((x)*(x))

/* _zv_norm2 -- computes (scaled) 2-norm (Euclidean norm) of vectors */
double    _zv_norm2(x,scale)
ZVEC    *x;
VEC    *scale;
{
    int    i, dim;
    Real    s, sum;

    if ( x == ZVNULL )
    error(E_NULL,"_zv_norm2");
    dim = x->dim;

    sum = 0.0;
    if ( scale == VNULL )
    for ( i = 0; i < dim; i++ )
        sum += square(x->ve[i].re) + square(x->ve[i].im);
    else if ( scale->dim < dim )
    error(E_SIZES,"_v_norm2");
    else
    for ( i = 0; i < dim; i++ )
    {
        s = scale->ve[i];
        sum += ( s== 0.0 ) ? square(x->ve[i].re) + square(x->ve[i].im) :
        (square(x->ve[i].re) + square(x->ve[i].im))/square(s);
    }

    return sqrt(sum);
}

#define    max(a,b)    ((a) > (b) ? (a) : (b))

/* _zv_norm_inf -- computes (scaled) infinity-norm (supremum norm) of vectors */
double    _zv_norm_inf(x,scale)
ZVEC    *x;
VEC    *scale;
{
    int    i, dim;
    Real    s, maxval, tmp;

    if ( x == ZVNULL )
    error(E_NULL,"_zv_norm_inf");
    dim = x->dim;

    maxval = 0.0;
    if ( scale == VNULL )
    for ( i = 0; i < dim; i++ )
    {
        tmp = zabs(x->ve[i]);
        maxval = max(maxval,tmp);
    }
    else if ( scale->dim < dim )
    error(E_SIZES,"_zv_norm_inf");
    else
    for ( i = 0; i < dim; i++ )
    {
        s = scale->ve[i];
        tmp = ( s == 0.0 ) ? zabs(x->ve[i]) : zabs(x->ve[i])/fabs(s);
        maxval = max(maxval,tmp);
    }

    return maxval;
}

/* zm_norm1 -- compute matrix 1-norm -- unscaled
    -- complex version */
double    zm_norm1(A)
ZMAT    *A;
{
    int    i, j, m, n;
    Real    maxval, sum;

    if ( A == ZMNULL )
    error(E_NULL,"zm_norm1");

    m = A->m;    n = A->n;
    maxval = 0.0;

    for ( j = 0; j < n; j++ )
    {
    sum = 0.0;
    for ( i = 0; i < m; i ++ )
        sum += zabs(A->me[i][j]);
    maxval = max(maxval,sum);
    }

    return maxval;
}

/* zm_norm_inf -- compute matrix infinity-norm -- unscaled
    -- complex version */
double    zm_norm_inf(A)
ZMAT    *A;
{
    int    i, j, m, n;
    Real    maxval, sum;

    if ( A == ZMNULL )
    error(E_NULL,"zm_norm_inf");

    m = A->m;    n = A->n;
    maxval = 0.0;

    for ( i = 0; i < m; i++ )
    {
    sum = 0.0;
    for ( j = 0; j < n; j ++ )
        sum += zabs(A->me[i][j]);
    maxval = max(maxval,sum);
    }

    return maxval;
}

/* zm_norm_frob -- compute matrix frobenius-norm -- unscaled */
double    zm_norm_frob(A)
ZMAT    *A;
{
    int    i, j, m, n;
    Real    sum;

    if ( A == ZMNULL )
    error(E_NULL,"zm_norm_frob");

    m = A->m;    n = A->n;
    sum = 0.0;

    for ( i = 0; i < m; i++ )
    for ( j = 0; j < n; j ++ )
        sum += square(A->me[i][j].re) + square(A->me[i][j].im);

    return sqrt(sum);
}