pxop.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.
**
***************************************************************************/
 
 
/* pxop.c 1.5 12/03/87 */
 
 
#include    <stdio.h>
#include    "matrix.h"
 
static  char    rcsid[] = "pxop.c,v 1.1 1997/12/04 17:55:44 hines Exp";
 
/**********************************************************************
Note: A permutation is often interpreted as a matrix
        (i.e. a permutation matrix).
    A permutation px represents a permutation matrix P where
        P[i][j] == 1 if and only if px->pe[i] == j
**********************************************************************/
 
 
/* px_inv -- invert permutation -- in situ
    -- taken from ACM Collected Algorithms #250 */
PERM    *px_inv(px,out)
PERM    *px, *out;
{
    int i, j, k, n, *p;
    
    out = px_copy(px, out);
    n = out->size;
    p = (int *)(out->pe);
    for ( n--; n>=0; n-- )
    {
    i = p[n];
    if ( i < 0 )    p[n] = -1 - i;
    else if ( i != n )
    {
        k = n;
        while (TRUE)
        {
        if ( i < 0 || i >= out->size )
            error(E_BOUNDS,"px_inv");
        j = p[i];   p[i] = -1 - k;
        if ( j == n )
        {   p[n] = i;   break;      }
        k = i;      i = j;
        }
    }
    }
    return out;
}
 
/* px_mlt -- permutation multiplication (composition) */
PERM    *px_mlt(px1,px2,out)
PERM    *px1,*px2,*out;
{
    u_int   i,size;
    
    if ( px1==(PERM *)NULL || px2==(PERM *)NULL )
    error(E_NULL,"px_mlt");
    if ( px1->size != px2->size )
    error(E_SIZES,"px_mlt");
    if ( px1 == out || px2 == out )
    error(E_INSITU,"px_mlt");
    if ( out==(PERM *)NULL || out->size < px1->size )
    out = px_resize(out,px1->size);
    
    size = px1->size;
    for ( i=0; i<size; i++ )
    if ( px2->pe[i] >= size )
        error(E_BOUNDS,"px_mlt");
    else
        out->pe[i] = px1->pe[px2->pe[i]];
    
    return out;
}
 
/* px_vec -- permute vector */
VEC *px_vec(px,vector,out)
PERM    *px;
VEC *vector,*out;
{
    u_int   old_i, i, size, start;
    Real    tmp;
    
    if ( px==(PERM *)NULL || vector==(VEC *)NULL )
    error(E_NULL,"px_vec");
    if ( px->size > vector->dim )
    error(E_SIZES,"px_vec");
    if ( out==(VEC *)NULL || out->dim < vector->dim )
    out = v_resize(out,vector->dim);
    
    size = px->size;
    if ( size == 0 )
    return v_copy(vector,out);
    if ( out != vector )
    {
    for ( i=0; i<size; i++ )
        if ( px->pe[i] >= size )
        error(E_BOUNDS,"px_vec");
        else
        out->ve[i] = vector->ve[px->pe[i]];
    }
    else
    {   /* in situ algorithm */
    start = 0;
    while ( start < size )
    {
        old_i = start;
        i = px->pe[old_i];
        if ( i >= size )
        {
        start++;
        continue;
        }
        tmp = vector->ve[start];
        while ( TRUE )
        {
        vector->ve[old_i] = vector->ve[i];
        px->pe[old_i] = i+size;
        old_i = i;
        i = px->pe[old_i];
        if ( i >= size )
            break;
        if ( i == start )
        {
            vector->ve[old_i] = tmp;
            px->pe[old_i] = i+size;
            break;
        }
        }
        start++;
    }
 
    for ( i = 0; i < size; i++ )
        if ( px->pe[i] < size )
        error(E_BOUNDS,"px_vec");
        else
        px->pe[i] = px->pe[i]-size;
    }
    
    return out;
}
 
/* pxinv_vec -- apply the inverse of px to x, returning the result in out */
VEC *pxinv_vec(px,x,out)
PERM    *px;
VEC *x, *out;
{
    u_int   i, size;
    
    if ( ! px || ! x )
    error(E_NULL,"pxinv_vec");
    if ( px->size > x->dim )
    error(E_SIZES,"pxinv_vec");
    /* if ( x == out )
    error(E_INSITU,"pxinv_vec"); */
    if ( ! out || out->dim < x->dim )
    out = v_resize(out,x->dim);
    
    size = px->size;
    if ( size == 0 )
    return v_copy(x,out);
    if ( out != x )
    {
    for ( i=0; i<size; i++ )
        if ( px->pe[i] >= size )
        error(E_BOUNDS,"pxinv_vec");
        else
        out->ve[px->pe[i]] = x->ve[i];
    }
    else
    {   /* in situ algorithm --- cheat's way out */
    px_inv(px,px);
    px_vec(px,x,out);
    px_inv(px,px);
    }
 
    return out;
}
 
 
 
/* px_transp -- transpose elements of permutation
        -- Really multiplying a permutation by a transposition */
PERM    *px_transp(px,i1,i2)
PERM    *px;        /* permutation to transpose */
u_int   i1,i2;      /* elements to transpose */
{
    u_int   temp;
 
    if ( px==(PERM *)NULL )
        error(E_NULL,"px_transp");
 
    if ( i1 < px->size && i2 < px->size )
    {
        temp = px->pe[i1];
        px->pe[i1] = px->pe[i2];
        px->pe[i2] = temp;
    }
 
    return px;
}
 
/* myqsort -- a cheap implementation of Quicksort on integers
        -- returns number of swaps */
static int myqsort(a,num)
int *a, num;
{
    int i, j, tmp, v;
    int numswaps;
 
    numswaps = 0;
    if ( num <= 1 )
        return 0;
 
    i = 0;  j = num;    v = a[0];
    for ( ; ; )
    {
        while ( a[++i] < v )
            ;
        while ( a[--j] > v )
            ;
        if ( i >= j )   break;
 
        tmp = a[i];
        a[i] = a[j];
        a[j] = tmp;
        numswaps++;
    }
 
    tmp = a[0];
    a[0] = a[j];
    a[j] = tmp;
    if ( j != 0 )
        numswaps++;
 
    numswaps += myqsort(&a[0],j);
    numswaps += myqsort(&a[j+1],num-(j+1));
 
    return numswaps;
}
 
 
/* px_sign -- compute the ``sign'' of a permutation = +/-1 where
        px is the product of an even/odd # transpositions */
int px_sign(px)
PERM    *px;
{
    int numtransp;
    PERM    *px2;
 
    if ( px==(PERM *)NULL )
        error(E_NULL,"px_sign");
    px2 = px_copy(px,PNULL);
    numtransp = myqsort((int*)px2->pe,px2->size);
    px_free(px2);
 
    return ( numtransp % 2 ) ? -1 : 1;
}
 
 
/* px_cols -- permute columns of matrix A; out = A.px'
    -- May NOT be in situ */
MAT *px_cols(px,A,out)
PERM    *px;
MAT *A, *out;
{
    int i, j, m, n, px_j;
    Real    **A_me, **out_me;
#ifdef ANSI_C
    MAT *m_get(int, int);
#else
    extern MAT  *m_get();
#endif
 
    if ( ! A || ! px )
        error(E_NULL,"px_cols");
    if ( px->size != A->n )
        error(E_SIZES,"px_cols");
    if ( A == out )
        error(E_INSITU,"px_cols");
    m = A->m;   n = A->n;
    if ( ! out || out->m != m || out->n != n )
        out = m_get(m,n);
    A_me = A->me;   out_me = out->me;
 
    for ( j = 0; j < n; j++ )
    {
        px_j = px->pe[j];
        if ( px_j >= n )
            error(E_BOUNDS,"px_cols");
        for ( i = 0; i < m; i++ )
            out_me[i][px_j] = A_me[i][j];
    }
 
    return out;
}
 
/* px_rows -- permute columns of matrix A; out = px.A
    -- May NOT be in situ */
MAT *px_rows(px,A,out)
PERM    *px;
MAT *A, *out;
{
    int i, j, m, n, px_i;
    Real    **A_me, **out_me;
#ifdef ANSI_C
    MAT *m_get(int, int);
#else
    extern MAT  *m_get();
#endif
 
    if ( ! A || ! px )
        error(E_NULL,"px_rows");
    if ( px->size != A->m )
        error(E_SIZES,"px_rows");
    if ( A == out )
        error(E_INSITU,"px_rows");
    m = A->m;   n = A->n;
    if ( ! out || out->m != m || out->n != n )
        out = m_get(m,n);
    A_me = A->me;   out_me = out->me;
 
    for ( i = 0; i < m; i++ )
    {
        px_i = px->pe[i];
        if ( px_i >= m )
            error(E_BOUNDS,"px_rows");
        for ( j = 0; j < n; j++ )
            out_me[i][j] = A_me[px_i][j];
    }
 
    return out;
}