/* $Id: shoot_regularisers.c 7155 2017-08-17 10:55:05Z john $ */
/* (c) John Ashburner (2011) */

#include<mex.h>
#include<math.h>
extern double log(double x);

#include "shoot_boundary.h"
/*
% MATLAB code (requiring Symbolic Toolbox) for computing the
% regulariser for linear elasticity.

syms mu lam
syms v0 v1 v2
N  = 3;
O  = sym(zeros(N));
OO = kron(kron(O,O),O);
I  = sym(eye(N));
G1 = sym(spdiags(repmat([-1 1],N,1),[ 0 1],N,N)); G1(N,1) =  1;
G2 = sym(spdiags(repmat([-1 1],N,1),[-1 0],N,N)); G2(1,N) = -1;
G  = {G1 G2};
LL = sym(zeros(3*N^3,3*N^3));
for i=1:2,
    Di = kron(I,kron(I,G{i}))/v0;
    for j=1:2,
        Dj = kron(I,kron(G{j},I))/v1;
        for k=1:2,
            Dk = kron(G{k},kron(I,I))/v2;
            L1 = [    Di     OO     OO
                      OO     Dj     OO
                      OO     OO     Dk
                  0.5*Dj 0.5*Di     OO
                  0.5*Dk     OO 0.5*Di
                      OO 0.5*Dk 0.5*Dj
                  0.5*Dj 0.5*Di     OO
                  0.5*Dk     OO 0.5*Di
                      OO 0.5*Dk 0.5*Dj]; % Elements of symmetric part of Jacobian

            L2 = [    Di     Dj  Dk];    % Divergence
            LL = LL + mu*(L1.'*L1) + lam*(L2.'*L2);
        end
    end
end
LL = LL/8;
o  = sym(ones(1,27));
LL = LL.*kron([v0*o v1*o v2*o],[o o o].').*kron([v0*o v1*o v2*o].',[o o o]);


L1 = simplify(reshape(LL(:,2+3+9   ),[3 3 3 3]))
L2 = simplify(reshape(LL(:,2+3+9+27),[3 3 3 3]))
L3 = simplify(reshape(LL(:,2+3+9+54),[3 3 3 3]))

*/
/*
% MATLAB code (requiring Symbolic Toolbox) for computing the
% regulariser for bending energy. Note that an additional multiplication
% by the square of the voxel size is needed.

syms s1 s2 s3
syms l1 l2 l3
zz = sym(zeros(3,3));
K1 = cat(3,zz,[0 -1/(v0*v0) 0; 0 2/(v0*v0) 0; 0 -1/(v0*v0) 0],zz);
K2 = cat(3,zz,[0 0 0; -1/(v1*v1) 2/(v1*v1) -1/(v1*v1); 0 0 0],zz);
K3 = sym(zeros(3,3,3));
K3(2,2,1) = -1/(v2*v2);
K3(2,2,2) = 2/(v2*v2);
K3(2,2,3) = -1/(v2*v2);

K  = K1+K2+K3;
K1 = K*l1; K1(2,2,2) = K1(2,2,2)+l2;
K2 = K*l1; K2(2,2,2) = K2(2,2,2)+l3;

% L  = convn(K,K)
L  = sym(zeros(5,5,5));
for i=1:3,
    for j=1:3,
        for k=1:3,
            L(i-1+1:i+1+1,j-1+1:j+1+1,k-1+1:k+1+1) = L(i-1+1:i+1+1,j-1+1:j+1+1,k-1+1:k+1+1) + K1(i,j,k)*K2;
        end;
    end;
end;
disp(simplify(L(3:end,3:end,3:end)))
*/


double trapprox(mwSize dm[], float a[], double s[])
{
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], lam1 = s[4], lam2 = s[5], mu = s[6], lam = s[7];
    double w000, wx000, wy000, wz000;
    double tr = 0.0;
    mwSignedIndex i, j, k;

    w000  =  lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + w000/v0;
    wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + w000/v1;
    wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + w000/v2;

    for(k=0; k<dm[2]; k++)
    {
        for(j=0; j<dm[1]; j++)
        {
           float *paxx, *payy, *pazz, *paxy, *paxz, *payz;

            paxx = a+dm[0]*(j+dm[1]* k);
            payy = a+dm[0]*(j+dm[1]*(k+dm[2]));
            pazz = a+dm[0]*(j+dm[1]*(k+dm[2]*2));
            paxy = a+dm[0]*(j+dm[1]*(k+dm[2]*3));
            paxz = a+dm[0]*(j+dm[1]*(k+dm[2]*4));
            payz = a+dm[0]*(j+dm[1]*(k+dm[2]*5));

            for(i=0; i<dm[0]; i++)
            {
                double axx, ayy, azz, axy, axz, ayz, dt;
                axx  = paxx[i] + wx000;
                ayy  = payy[i] + wy000;
                azz  = pazz[i] + wz000;
                axy  = paxy[i];
                axz  = paxz[i];
                ayz  = payz[i];
                dt   = axx*ayy*azz -axx*ayz*ayz-ayy*axz*axz-azz*axy*axy +2*axy*axz*ayz;
                tr  += (wx000*(ayy*azz - ayz*ayz) 
                       +wy000*(axx*azz - axz*axz)
                       +wz000*(axx*ayy - axy*axy))/dt;

            }
        }
    }
    return(tr);
}


void kernel(mwSize dm[], double s[], float f[])
{
    double w000,w100,w200,
           w010,w110,
           w020,
           w001,w101,
           w011,
           w002;
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], lam1 = s[4], lam2 = s[5], mu = s[6], lam = s[7];
    mwSignedIndex im2,im1,ip1,ip2, jm2,jm1,jp1,jp2, km2,km1,kp1,kp2;

    km2 = (bound((mwSignedIndex)-2,dm[2]))*dm[0]*dm[1];
    km1 = (bound((mwSignedIndex)-1,dm[2]))*dm[0]*dm[1];
    kp1 = (bound((mwSignedIndex) 1,dm[2]))*dm[0]*dm[1];
    kp2 = (bound((mwSignedIndex) 2,dm[2]))*dm[0]*dm[1];

    jm2 = (bound((mwSignedIndex)-2,dm[1]))*dm[0];
    jm1 = (bound((mwSignedIndex)-1,dm[1]))*dm[0];
    jp1 = (bound((mwSignedIndex) 1,dm[1]))*dm[0];
    jp2 = (bound((mwSignedIndex) 2,dm[1]))*dm[0];

    im2 = bound((mwSignedIndex)-2,dm[0]);
    im1 = bound((mwSignedIndex)-1,dm[0]);
    ip1 = bound((mwSignedIndex) 1,dm[0]);
    ip2 = bound((mwSignedIndex) 2,dm[0]);

    w000 = lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    w100 = lam2*(-4*v0*(v0+v1+v2)) -lam1*v0;
    w010 = lam2*(-4*v1*(v0+v1+v2)) -lam1*v1;
    w001 = lam2*(-4*v2*(v0+v1+v2)) -lam1*v2;
    w200 = lam2*v0*v0;
    w020 = lam2*v1*v1;
    w002 = lam2*v2*v2;
    w110 = lam2*2*v0*v1;
    w101 = lam2*2*v0*v2;
    w011 = lam2*2*v1*v2;

    if (mu==0 && lam==0)
    {
        f[0]           += w000;
        f[im1        ] += w100; f[ip1        ] += w100;
        f[    jm1    ] += w010; f[    jp1    ] += w010;
        f[        km1] += w001; f[        kp1] += w001;
        f[im2        ] += w200; f[ip2        ] += w200;
        f[    jm2    ] += w020; f[    jp2    ] += w020;
        f[        km2] += w002; f[        kp2] += w002;
        f[im1+jm1    ] += w110; f[ip1+jm1    ] += w110; f[im1+jp1    ] += w110; f[ip1+jp1    ] += w110;
        f[im1    +km1] += w101; f[ip1    +km1] += w101; f[im1    +kp1] += w101; f[ip1    +kp1] += w101;
        f[    jm1+km1] += w011; f[    jp1+km1] += w011; f[    jm1+kp1] += w011; f[    jp1+kp1] += w011;
    }
    else
    {
        double wx000, wx100, wx010, wx001, wy000, wy100, wy010, wy001, wz000, wz100, wz010, wz001, w2;
        float *pxx, *pxy, *pxz, *pyx, *pyy, *pyz, *pzx, *pzy, *pzz;
        mwSignedIndex m = dm[0]*dm[1]*dm[2];

        wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + w000/v0;
        wx100 = -2*mu-lam + w100/v0;
        wx010 = -mu*v1/v0 + w010/v0;
        wx001 = -mu*v2/v0 + w001/v0;
        wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + w000/v1;
        wy100 = -mu*v0/v1 + w100/v1;
        wy010 = -2*mu-lam + w010/v1;
        wy001 = -mu*v2/v1 + w001/v1;
        wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + w000/v2;
        wz100 = -mu*v0/v2 + w100/v2;
        wz010 = -mu*v1/v2 + w010/v2;
        wz001 = -2*mu-lam + w001/v2;
        w2    = 0.25*mu+0.25*lam;

        pxx = f;
        pyx = f + m;
        pzx = f + m*2;
        pxy = f + m*3;
        pyy = f + m*4;
        pzy = f + m*5;
        pxz = f + m*6;
        pyz = f + m*7;
        pzz = f + m*8;

        pxx[0          ] += wx000;
        pxx[im1        ] += wx100;   pxx[ip1        ] += wx100;
        pxx[    jm1    ] += wx010;   pxx[    jp1    ] += wx010;
        pxx[        km1] += wx001;   pxx[        kp1] += wx001;
        pxy[ip1+jm1    ] += w2;      pxy[ip1+jp1    ] -= w2;      pxy[im1+jm1    ] -= w2;      pxy[im1+jp1    ] += w2;
        pxz[ip1    +km1] += w2;      pxz[ip1    +kp1] -= w2;      pxz[im1    +km1] -= w2;      pxz[im1    +kp1] += w2;
        pxx[im1+jm1    ] += w110/v0; pxx[ip1+jm1    ] += w110/v0; pxx[im1+jp1    ] += w110/v0; pxx[ip1+jp1    ] += w110/v0;
        pxx[im1    +km1] += w101/v0; pxx[ip1    +km1] += w101/v0; pxx[im1    +kp1] += w101/v0; pxx[ip1    +kp1] += w101/v0;
        pxx[    jm1+km1] += w011/v0; pxx[    jp1+km1] += w011/v0; pxx[    jm1+kp1] += w011/v0; pxx[    jp1+kp1] += w011/v0;
        pxx[im2        ] += w200/v0; pxx[ip2        ] += w200/v0;
        pxx[    jm2    ] += w020/v0; pxx[    jp2    ] += w020/v0;
        pxx[        km2] += w002/v0; pxx[        kp2] += w002/v0;

        pyy[0          ] += wy000;
        pyy[im1        ] += wy100;   pyy[ip1        ] += wy100;
        pyy[    jm1    ] += wy010;   pyy[    jp1    ] += wy010;
        pyy[        km1] += wy001;   pyy[        kp1] += wy001;
        pyx[ip1+jm1    ] += w2;      pyx[ip1+jp1    ] -= w2;      pyx[im1+jm1    ] -= w2;      pyx[im1+jp1    ] += w2;
        pyz[    jp1+km1] += w2;      pyz[    jp1+kp1] -= w2;      pyz[    jm1+km1] -= w2;      pyz[    jm1+kp1] += w2;
        pyy[im1+jm1    ] += w110/v1; pyy[ip1+jm1    ] += w110/v1; pyy[im1+jp1    ] += w110/v1; pyy[ip1+jp1    ] += w110/v1;
        pyy[im1    +km1] += w101/v1; pyy[ip1    +km1] += w101/v1; pyy[im1    +kp1] += w101/v1; pyy[ip1    +kp1] += w101/v1;
        pyy[    jm1+km1] += w011/v1; pyy[    jp1+km1] += w011/v1; pyy[    jm1+kp1] += w011/v1; pyy[    jp1+kp1] += w011/v1;
        pyy[im2        ] += w200/v1; pyy[ip2        ] += w200/v1;
        pyy[    jm2    ] += w020/v1; pyy[    jp2    ] += w020/v1;
        pyy[        km2] += w002/v1; pyy[        kp2] += w002/v1;

        pzz[0          ] += wz000;
        pzz[im1        ] += wz100;   pzz[ip1        ] += wz100;
        pzz[    jm1    ] += wz010;   pzz[    jp1    ] += wz010;
        pzz[        km1] += wz001;   pzz[        kp1] += wz001;
        pzx[im1    +kp1] += w2;      pzx[ip1    +kp1] -= w2;      pzx[im1    +km1] -= w2;      pzx[ip1    +km1] += w2;
        pzy[jm1    +kp1] += w2;      pzy[    jp1+kp1] -= w2;      pzy[    jm1+km1] -= w2;      pzy[    jp1+km1] += w2;
        pzz[im1+jm1    ] += w110/v2; pzz[ip1+jm1    ] += w110/v2; pzz[im1+jp1    ] += w110/v2; pzz[ip1+jp1    ] += w110/v2;
        pzz[im1    +km1] += w101/v2; pzz[ip1    +km1] += w101/v2; pzz[im1    +kp1] += w101/v2; pzz[ip1    +kp1] += w101/v2;
        pzz[    jm1+km1] += w011/v2; pzz[    jp1+km1] += w011/v2; pzz[    jm1+kp1] += w011/v2; pzz[    jp1+kp1] += w011/v2;
        pzz[im2        ] += w200/v2; pzz[ip2        ] += w200/v2;
        pzz[    jm2    ] += w020/v2; pzz[    jp2    ] += w020/v2;
        pzz[        km2] += w002/v2; pzz[        kp2] += w002/v2;
    }
}


double sumsq(mwSize dm[], float a[], float b[], double s[], float u[])
{
    double w000,w100,w200,
           w010,w110,
           w020,
           w001,w101,
           w011,
           w002;
    double ss = 0.0;
    mwSignedIndex k;
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], lam1 = s[4], lam2 = s[5], mu = s[6], lam = s[7];
    double wx000, wx100, wx010, wx001, wy000, wy100, wy010, wy001, wz000, wz100, wz010, wz001, w2;

    w000 = lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    w100 = lam2*(-4*v0*(v0+v1+v2)) -lam1*v0;
    w010 = lam2*(-4*v1*(v0+v1+v2)) -lam1*v1;
    w001 = lam2*(-4*v2*(v0+v1+v2)) -lam1*v2;
    w200 = lam2*v0*v0;
    w020 = lam2*v1*v1;
    w002 = lam2*v2*v2;
    w110 = lam2*2*v0*v1;
    w101 = lam2*2*v0*v2;
    w011 = lam2*2*v1*v2;

    wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + w000/v0;
    wx100 = -2*mu-lam + w100/v0;
    wx010 = -mu*v1/v0 + w010/v0;
    wx001 = -mu*v2/v0 + w001/v0;
    wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + w000/v1;
    wy100 = -mu*v0/v1 + w100/v1;
    wy010 = -2*mu-lam + w010/v1;
    wy001 = -mu*v2/v1 + w001/v1;
    wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + w000/v2;
    wz100 = -mu*v0/v2 + w100/v2;
    wz010 = -mu*v1/v2 + w010/v2;
    wz001 = -2*mu-lam + w001/v2;
    w2    = 0.25*mu+0.25*lam;

    for(k=0; k<dm[2]; k++)
    {
        mwSignedIndex j, km2,km1,kp1,kp2;
        km2 = (bound(k-2,dm[2])-k)*dm[0]*dm[1];
        km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
        kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];
        kp2 = (bound(k+2,dm[2])-k)*dm[0]*dm[1];

        for(j=0; j<dm[1]; j++)
        {
            float *pux, *puy, *puz, *pbx, *pby, *pbz, *paxx, *payy, *pazz, *paxy, *paxz, *payz;
            mwSignedIndex i, jm2,jm1,jp1,jp2;

            pux  = u+dm[0]*(j+dm[1]*k);
            puy  = u+dm[0]*(j+dm[1]*(k+dm[2]));
            puz  = u+dm[0]*(j+dm[1]*(k+dm[2]*2));
            pbx  = b+dm[0]*(j+dm[1]*k);
            pby  = b+dm[0]*(j+dm[1]*(k+dm[2]));
            pbz  = b+dm[0]*(j+dm[1]*(k+dm[2]*2));

            if (a)
            {
                paxx = a+dm[0]*(j+dm[1]*k);
                payy = a+dm[0]*(j+dm[1]*(k+dm[2]));
                pazz = a+dm[0]*(j+dm[1]*(k+dm[2]*2));
                paxy = a+dm[0]*(j+dm[1]*(k+dm[2]*3));
                paxz = a+dm[0]*(j+dm[1]*(k+dm[2]*4));
                payz = a+dm[0]*(j+dm[1]*(k+dm[2]*5));
            }

            jm2 = (bound(j-2,dm[1])-j)*dm[0];
            jm1 = (bound(j-1,dm[1])-j)*dm[0];
            jp1 = (bound(j+1,dm[1])-j)*dm[0];
            jp2 = (bound(j+2,dm[1])-j)*dm[0];

            for(i=0; i<dm[0]; i++)
            {
                mwSignedIndex im2,im1,ip1,ip2;
                float *px = pux+i, *py = puy+i, *pz = puz+i;
                double tmp, abx, aby, abz, c;

                im2 = bound(i-2,dm[0])-i;
                im1 = bound(i-1,dm[0])-i;
                ip1 = bound(i+1,dm[0])-i;
                ip2 = bound(i+2,dm[0])-i;

                if (a)
                {
                    abx = paxx[i]*px[0] + paxy[i]*py[0] + paxz[i]*pz[0];
                    aby = paxy[i]*px[0] + payy[i]*py[0] + payz[i]*pz[0];
                    abz = paxz[i]*px[0] + payz[i]*py[0] + pazz[i]*pz[0];
                }
                else
                {
                    abx = aby = abz = 0.0;
                }

                /* Note that a few things have been done here to reduce rounding errors.
                   This may slow things down, but it does lead to more accuracy. */
                c   = px[0];
                tmp = abx - pbx[i]
                        + wx100*((px[im1        ]-c) + (px[ip1        ]-c))
                        + wx010*((px[    jm1    ]-c) + (px[    jp1    ]-c))
                        + wx001*((px[        km1]-c) + (px[        kp1]-c))
                        + w2   *( py[ip1+jm1] - py[ip1+jp1] + py[im1+jp1] - py[im1+jm1] + pz[ip1+km1] - pz[ip1+kp1] + pz[im1+kp1] - pz[im1+km1])
                        + (lam0*c
                        +  w110*((px[im1+jm1    ]-c) + (px[ip1+jm1    ]-c) + (px[im1+jp1    ]-c) + (px[ip1+jp1    ]-c))
                        +  w101*((px[im1    +km1]-c) + (px[ip1    +km1]-c) + (px[im1    +kp1]-c) + (px[ip1    +kp1]-c))
                        +  w011*((px[    jm1+km1]-c) + (px[    jp1+km1]-c) + (px[    jm1+kp1]-c) + (px[    jp1+kp1]-c))
                        +  w200*((px[im2        ]-c) + (px[ip2        ]-c))
                        +  w020*((px[    jm2    ]-c) + (px[    jp2    ]-c))
                        +  w002*((px[        km2]-c) + (px[        kp2]-c)))/v0;
                ss += tmp*tmp;

                c   = py[0];
                tmp = aby - pby[i]
                        + wy100*((py[im1        ]-c) + (py[ip1        ]-c))
                        + wy010*((py[    jm1    ]-c) + (py[    jp1    ]-c))   
                        + wy001*((py[        km1]-c) + (py[        kp1]-c))   
                        + w2   *( px[jp1+im1] - px[jp1+ip1] + px[jm1+ip1] - px[jm1+im1] + pz[jp1+km1] - pz[jp1+kp1] + pz[jm1+kp1] - pz[jm1+km1])
                        + (lam0*c
                        +  w110*((py[im1+jm1    ]-c) + (py[ip1+jm1    ]-c) + (py[im1+jp1    ]-c) + (py[ip1+jp1    ]-c))
                        +  w101*((py[im1    +km1]-c) + (py[ip1    +km1]-c) + (py[im1    +kp1]-c) + (py[ip1    +kp1]-c))
                        +  w011*((py[    jm1+km1]-c) + (py[    jp1+km1]-c) + (py[    jm1+kp1]-c) + (py[    jp1+kp1]-c))
                        +  w200*((py[im2        ]-c) + (py[ip2        ]-c))
                        +  w020*((py[    jm2    ]-c) + (py[    jp2    ]-c))
                        +  w002*((py[        km2]-c) + (py[        kp2]-c)))/v1;
                ss += tmp*tmp;

                c   = pz[0];
                tmp = abz - pbz[i]
                        + wz100*((pz[im1        ]-c) + (pz[ip1        ]-c))
                        + wz010*((pz[    jm1    ]-c) + (pz[    jp1    ]-c))   
                        + wz001*((pz[        km1]-c) + (pz[        kp1]-c))   
                        + w2   *( px[kp1+im1] - px[kp1+ip1] + px[km1+ip1] - px[km1+im1] + py[kp1+jm1] - py[kp1+jp1] + py[km1+jp1] - py[km1+jm1])
                        + (lam0*c
                        +  w110*((pz[im1+jm1    ]-c) + (pz[ip1+jm1    ]-c) + (pz[im1+jp1    ]-c) + (pz[ip1+jp1    ]-c))
                        +  w101*((pz[im1    +km1]-c) + (pz[ip1    +km1]-c) + (pz[im1    +kp1]-c) + (pz[ip1    +kp1]-c))
                        +  w011*((pz[    jm1+km1]-c) + (pz[    jp1+km1]-c) + (pz[    jm1+kp1]-c) + (pz[    jp1+kp1]-c))
                        +  w200*((pz[im2        ]-c) + (pz[ip2        ]-c))
                        +  w020*((pz[    jm2    ]-c) + (pz[    jp2    ]-c))
                        +  w002*((pz[        km2]-c) + (pz[        kp2]-c)))/v2;
                ss += tmp*tmp;
            }
        }
    }
    return(ss);
}


static void Atimesp1(mwSize dm[], float A[], float p[], float Ap[])
{
    mwSignedIndex i, m = dm[0]*dm[1]*dm[2];
    float *pa11 = A ,     *pa22 = A +m,   *pa33 = A +2*m,
          *pa12 = A +3*m, *pa13 = A +4*m, *pa23 = A +5*m;
    float *pap1 = Ap,     *pap2 = Ap+m,   *pap3 = Ap+2*m;
    float *pp1  = p,      *pp2  = p +m,   *pp3  = p +2*m;

    if (A==0) return;

    for(i=0; i<m; i++)
    {
        pap1[i] += pa11[i]*pp1[i] + pa12[i]*pp2[i] + pa13[i]*pp3[i];
        pap2[i] += pa12[i]*pp1[i] + pa22[i]*pp2[i] + pa23[i]*pp3[i];
        pap3[i] += pa13[i]*pp1[i] + pa23[i]*pp2[i] + pa33[i]*pp3[i];
    }
}


void vel2mom_le(mwSize dm[], float f[], double s[], float g[])
{
    mwSignedIndex k;
    double wx000, wx100, wx010, wx001, wy000, wy100, wy010, wy001, wz000, wz100, wz010, wz001, w2;
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], mu = s[6], lam = s[7];

    wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + lam0/v0;
    wx100 = -2*mu-lam;
    wx010 = -mu*v1/v0;
    wx001 = -mu*v2/v0;
    wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + lam0/v1;
    wy100 = -mu*v0/v1;
    wy010 = -2*mu-lam;
    wy001 = -mu*v2/v1;
    wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + lam0/v2;
    wz100 = -mu*v0/v2;
    wz010 = -mu*v1/v2;
    wz001 = -2*mu-lam;
    w2    = 0.25*mu+0.25*lam;

    for(k=0; k<dm[2]; k++)
    {
        mwSignedIndex j, km1,kp1;
        km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
        kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];

        for(j=0; j<dm[1]; j++)
        {
            mwSignedIndex i, jm1,jp1;
            float *pgx, *pgy, *pgz, *pfx, *pfy, *pfz;

            pgx = g+dm[0]*(j+dm[1]*k);
            pgy = g+dm[0]*(j+dm[1]*(k+dm[2]));
            pgz = g+dm[0]*(j+dm[1]*(k+dm[2]*2));

            pfx = f+dm[0]*(j+dm[1]*k);
            pfy = f+dm[0]*(j+dm[1]*(k+dm[2]));
            pfz = f+dm[0]*(j+dm[1]*(k+dm[2]*2));

            jm1 = (bound(j-1,dm[1])-j)*dm[0];
            jp1 = (bound(j+1,dm[1])-j)*dm[0];

            for(i=0; i<dm[0]; i++)
            {
                mwSignedIndex im1,ip1;
                float *px = &pfx[i], *py = &pfy[i], *pz = &pfz[i];
                double c;

                im1 = bound(i-1,dm[0])-i;
                ip1 = bound(i+1,dm[0])-i;

                /* Note that a few things have been done here to reduce rounding errors.
                   This may slow things down, but it does lead to more accuracy. */
                c      = px[0];
                pgx[i] =  lam0/v0*c
                       + wx100*((px[ip1]-c) + (px[im1]-c))
                       + wx010*((px[jp1]-c) + (px[jm1]-c))
                       + wx001*((px[kp1]-c) + (px[km1]-c))
                       + w2   *(py[ip1+jm1] - py[ip1+jp1] + py[im1+jp1] - py[im1+jm1] + pz[ip1+km1] - pz[ip1+kp1] + pz[im1+kp1] - pz[im1+km1]);

                c      = py[0];
                pgy[i] =  lam0/v1*c
                       + wy100*((py[ip1]-c) + (py[im1]-c))
                       + wy010*((py[jp1]-c) + (py[jm1]-c))
                       + wy001*((py[kp1]-c) + (py[km1]-c))
                       + w2   *(px[jp1+im1] - px[jp1+ip1] + px[jm1+ip1] - px[jm1+im1] + pz[jp1+km1] - pz[jp1+kp1] + pz[jm1+kp1] - pz[jm1+km1]);

                c      = pz[0];
                pgz[i] = lam0/v2*c
                       + wz100*((pz[ip1]-c) + (pz[im1]-c))
                       + wz010*((pz[jp1]-c) + (pz[jm1]-c))
                       + wz001*((pz[kp1]-c) + (pz[km1]-c))
                       + w2   *(px[kp1+im1] - px[kp1+ip1] + px[km1+ip1] - px[km1+im1] + py[kp1+jm1] - py[kp1+jp1] + py[km1+jp1] - py[km1+jm1]);
            }
        }
    }
}

void relax_le(mwSize dm[], float a[], float b[], double s[], int nit, float u[])
{
    int it;
    double wx000, wx100, wx010, wx001, wy000, wy100, wy010, wy001, wz000, wz100, wz010, wz001, w2;
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], mu = s[6], lam = s[7];

    wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + lam0/v0;
    wx100 = -2*mu-lam;
    wx010 = -mu*v1/v0;
    wx001 = -mu*v2/v0;
    wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + lam0/v1;
    wy100 = -mu*v0/v1;
    wy010 = -2*mu-lam;
    wy001 = -mu*v2/v1;
    wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + lam0/v2;
    wz100 = -mu*v0/v2;
    wz010 = -mu*v1/v2;
    wz001 = -2*mu-lam;
    w2    = 0.25*mu+0.25*lam;

/*  wx000 = wx000*1.00001 + 1e-6;
    wy000 = wy000*1.00001 + 1e-6;
    wz000 = wz000*1.00001 + 1e-6; */

    if (dm[0]==1)
    {
        wx000 += 2*wx100 + 2*wy100 + 2*wz100;
        wx100  = 0.0;
        wy100  = 0.0;
        wz100  = 0.0;
    }
    if (dm[1]==1)
    {
        wx000 += 2*wx010 + 2*wy010 + 2*wz010;
        wx010  = 0.0;
        wy010  = 0.0;
        wz010  = 0.0;
    }
    if (dm[2]==1)
    {
        wx000 += 2*wx001 + 2*wy001 + 2*wz001;
        wx001  = 0.0;
        wy001  = 0.0;
        wz001  = 0.0;
    }

#   ifdef VERBOSE
        for(it=0; it< 10-(int)ceil(1.44269504088896*log((double)dm[0])); it++) printf("  ");
        printf("L%dx%dx%d: %g ", dm[0],dm[1],dm[2], sumsq(dm, a, b, s, u));
#   endif

    for(it=0; it<8*nit; it++)
    {
        mwSignedIndex k;
        for(k=it&1; k<dm[2]; k+=2)
        {
            mwSignedIndex j, km1, kp1;
            km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
            kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];

            for(j=(it>>1)&1; j<dm[1]; j+=2)
            {
                float *pux, *puy, *puz, *pbx, *pby, *pbz, *paxx, *payy, *pazz, *paxy, *paxz, *payz;
                mwSignedIndex i, jm1,jp1;

                pux  = u+dm[0]*(j+dm[1]* k);
                puy  = u+dm[0]*(j+dm[1]*(k+dm[2]));
                puz  = u+dm[0]*(j+dm[1]*(k+dm[2]*2));
                pbx  = b+dm[0]*(j+dm[1]* k);
                pby  = b+dm[0]*(j+dm[1]*(k+dm[2]));
                pbz  = b+dm[0]*(j+dm[1]*(k+dm[2]*2));

                if (a)
                {
                    paxx = a+dm[0]*(j+dm[1]* k);
                    payy = a+dm[0]*(j+dm[1]*(k+dm[2]));
                    pazz = a+dm[0]*(j+dm[1]*(k+dm[2]*2));
                    paxy = a+dm[0]*(j+dm[1]*(k+dm[2]*3));
                    paxz = a+dm[0]*(j+dm[1]*(k+dm[2]*4));
                    payz = a+dm[0]*(j+dm[1]*(k+dm[2]*5));
                }

                jm1 = (bound(j-1,dm[1])-j)*dm[0];
                jp1 = (bound(j+1,dm[1])-j)*dm[0];

                for(i=(it>>2)&1; i<dm[0]; i+=2)
                {
                    mwSignedIndex im1,ip1;
                    double sux, suy, suz;
                    float *px = pux+i, *py = puy+i, *pz = puz+i;

                    im1 = bound(i-1,dm[0])-i;
                    ip1 = bound(i+1,dm[0])-i;

                    sux = pbx[i] - ( wx100*(px[im1] + px[ip1])
                                   + wx010*(px[jm1] + px[jp1])
                                   + wx001*(px[km1] + px[kp1])
                                   + w2   *(py[ip1+jm1] - py[ip1+jp1] + py[im1+jp1] - py[im1+jm1] + pz[ip1+km1] - pz[ip1+kp1] + pz[im1+kp1] - pz[im1+km1]));

                    suy = pby[i] - ( wy100*(py[im1] + py[ip1])
                                   + wy010*(py[jm1] + py[jp1])
                                   + wy001*(py[km1] + py[kp1])
                                   + w2   *(px[jp1+im1] - px[jp1+ip1] + px[jm1+ip1] - px[jm1+im1] + pz[jp1+km1] - pz[jp1+kp1] + pz[jm1+kp1] - pz[jm1+km1]));

                    suz = pbz[i] - ( wz100*(pz[im1] + pz[ip1])
                                   + wz010*(pz[jm1] + pz[jp1])
                                   + wz001*(pz[km1] + pz[kp1])
                                   + w2   *(px[kp1+im1] - px[kp1+ip1] + px[km1+ip1] - px[km1+im1] + py[kp1+jm1] - py[kp1+jp1] + py[km1+jp1] - py[km1+jm1]));

                    if (a)
                    {
                        double axx, ayy, azz, axy, axz, ayz, idt;

                        axx  = paxx[i] + wx000;
                        ayy  = payy[i] + wy000;
                        azz  = pazz[i] + wz000;
                        axy  = paxy[i];
                        axz  = paxz[i];
                        ayz  = payz[i];
                        idt  = 1.0/(axx*ayy*azz -axx*ayz*ayz-ayy*axz*axz-azz*axy*axy +2*axy*axz*ayz);

                        *px = idt*(sux*(ayy*azz-ayz*ayz)+suy*(axz*ayz-axy*azz)+suz*(axy*ayz-axz*ayy));
                        *py = idt*(sux*(axz*ayz-axy*azz)+suy*(axx*azz-axz*axz)+suz*(axy*axz-axx*ayz));
                        *pz = idt*(sux*(axy*ayz-axz*ayy)+suy*(axy*axz-axx*ayz)+suz*(axx*ayy-axy*axy));
                    }
                    else
                    {
                        *px = sux/wx000;
                        *py = suy/wy000;
                        *pz = suz/wz000;
                    }
                }
            }
        } 
#       ifdef VERBOSE
            if ((it%8)==7) printf(" %g", sumsq(dm, a, b, s, u));
#       endif
    }
#   ifdef VERBOSE
        printf("\n");
#   endif
}


void Atimesp_le(mwSize dm[], float A[], double param[], float p[], float Ap[])
{
    vel2mom_le(dm, p, param, Ap);
    Atimesp1(dm, A, p, Ap);
}

void vel2mom_me(mwSize dm[], float f[], double s[], float g[])
{
    mwSignedIndex i, j, k, km1,kp1, jm1,jp1, im1,ip1;
    float *pgx, *pgy, *pgz, *pfx, *pfy, *pfz;
    double w000,w001,w010,w100;
    double lam0 = s[3], lam1 = s[4];

    w000 = lam1*(2*s[0]*s[0]+2*s[1]*s[1]+2*s[2]*s[2]) + lam0;
    w001 = lam1*(-s[2]*s[2]);
    w010 = lam1*(-s[1]*s[1]);
    w100 = lam1*(-s[0]*s[0]);

    for(k=0; k<dm[2]; k++)
    {
        km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
        kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];

        for(j=0; j<dm[1]; j++)
        {
            pgx = g+dm[0]*(j+dm[1]*k);
            pgy = g+dm[0]*(j+dm[1]*(k+dm[2]));
            pgz = g+dm[0]*(j+dm[1]*(k+dm[2]*2));

            pfx = f+dm[0]*(j+dm[1]*k);
            pfy = f+dm[0]*(j+dm[1]*(k+dm[2]));
            pfz = f+dm[0]*(j+dm[1]*(k+dm[2]*2));

            jm1 = (bound(j-1,dm[1])-j)*dm[0];
            jp1 = (bound(j+1,dm[1])-j)*dm[0];

            for(i=0; i<dm[0]; i++)
            {
                float *px = &pfx[i], *py = &pfy[i], *pz = &pfz[i];

                im1 = bound(i-1,dm[0])-i;
                ip1 = bound(i+1,dm[0])-i;

                pgx[i] = (w000*px[0] + w001*(px[km1] + px[kp1]) + w010*(px[jm1] + px[jp1]) + w100*(px[im1] + px[ip1]))/(s[0]*s[0]);
                pgy[i] = (w000*py[0] + w001*(py[km1] + py[kp1]) + w010*(py[jm1] + py[jp1]) + w100*(py[im1] + py[ip1]))/(s[1]*s[1]);
                pgz[i] = (w000*pz[0] + w001*(pz[km1] + pz[kp1]) + w010*(pz[jm1] + pz[jp1]) + w100*(pz[im1] + pz[ip1]))/(s[2]*s[2]);
            }
        }
    }
}

void relax_me(mwSize dm[], float a[], float b[], double s[], int nit, float u[])
{
    int it;
    double w000,w001,w010,w100;
    double lam0 = s[3], lam1 = s[4];

    w000 = lam1*(2*s[0]*s[0]+2*s[1]*s[1]+2*s[2]*s[2]) + lam0;
    w001 = lam1*(-s[2]*s[2]);
    w010 = lam1*(-s[1]*s[1]);
    w100 = lam1*(-s[0]*s[0]);

    w000 = w000*1.00001 + 1e-6;

    if (dm[0]==1)
    {
        w000 += 2*w100;
        w100  = 0.0;
    }
    if (dm[1]==1)
    {
        w000 += 2*w010;
        w010  = 0.0;
    }
    if (dm[2]==1)
    {
        w000 += 2*w001;
        w001  = 0.0;
    }

#   ifdef VERBOSE
        for(it=0; it< 10-(int)ceil(1.44269504088896*log((double)dm[0])); it++) printf("  ");
        printf("M%dx%dx%d: %g ", dm[0],dm[1],dm[2], sumsq(dm, a, b, s, u));
#   endif

    for(it=0; it<2*nit; it++)
    {
        mwSignedIndex k, kstart;
        mwSignedIndex j, jstart;
        mwSignedIndex i, istart;

        kstart = it%2;
        for(k=0; k<dm[2]; k++)
        {
            mwSignedIndex km1, kp1;
            km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
            kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];

            jstart = (kstart == (k%2));
            for(j=0; j<dm[1]; j++)
            {
                float *pux, *puy, *puz, *pbx, *pby, *pbz, *paxx, *paxy, *payy, *paxz, *payz, *pazz;
                mwSignedIndex jm1,jp1, im1,ip1;

                pux  = u+dm[0]*(j+dm[1]*k);
                puy  = u+dm[0]*(j+dm[1]*(k+dm[2]));
                puz  = u+dm[0]*(j+dm[1]*(k+dm[2]*2));
                pbx  = b+dm[0]*(j+dm[1]*k);
                pby  = b+dm[0]*(j+dm[1]*(k+dm[2]));
                pbz  = b+dm[0]*(j+dm[1]*(k+dm[2]*2));

                if (a)
                {
                    paxx = a+dm[0]*(j+dm[1]*k);
                    payy = a+dm[0]*(j+dm[1]*(k+dm[2]));
                    pazz = a+dm[0]*(j+dm[1]*(k+dm[2]*2));
                    paxy = a+dm[0]*(j+dm[1]*(k+dm[2]*3));
                    paxz = a+dm[0]*(j+dm[1]*(k+dm[2]*4));
                    payz = a+dm[0]*(j+dm[1]*(k+dm[2]*5));
                }

                jm1 = (bound(j-1,dm[1])-j)*dm[0];
                jp1 = (bound(j+1,dm[1])-j)*dm[0];

                istart = (jstart == (j%2));

                for(i=istart; i<dm[0]; i+=2)
                {
                    double sux, suy, suz;
                    float *px = pux+i, *py = puy+i, *pz = puz+i;

                    im1 = bound(i-1,dm[0])-i;
                    ip1 = bound(i+1,dm[0])-i;

                    sux = pbx[i]-(w001*(px[km1] + px[kp1]) + w010*(px[jm1] + px[jp1]) + w100*(px[im1] + px[ip1]))/(s[0]*s[0]);
                    suy = pby[i]-(w001*(py[km1] + py[kp1]) + w010*(py[jm1] + py[jp1]) + w100*(py[im1] + py[ip1]))/(s[1]*s[1]);
                    suz = pbz[i]-(w001*(pz[km1] + pz[kp1]) + w010*(pz[jm1] + pz[jp1]) + w100*(pz[im1] + pz[ip1]))/(s[2]*s[2]);

                    if (a)
                    {
                        double axx, ayy, azz, axy, axz, ayz, idt;
                        /*
                           syms axx ayy azz axy axz ayz sux suy suz
                           A = [axx axy axz; axy ayy ayz; axz ayz azz];
                           su = [sux ; suy; suz]
                           simplify(inv(A)*su)
                        */
                        axx = paxx[i] + w000/(s[0]*s[0]);
                        ayy = payy[i] + w000/(s[1]*s[1]);
                        azz = pazz[i] + w000/(s[2]*s[2]);
                        axy = paxy[i];
                        axz = paxz[i];
                        ayz = payz[i];
                        idt = 1.0/(axx*ayy*azz -axx*ayz*ayz-ayy*axz*axz-azz*axy*axy +2*axy*axz*ayz);
                        *px = idt*(sux*(ayy*azz-ayz*ayz)+suy*(axz*ayz-axy*azz)+suz*(axy*ayz-axz*ayy));
                        *py = idt*(sux*(axz*ayz-axy*azz)+suy*(axx*azz-axz*axz)+suz*(axy*axz-axx*ayz));
                        *pz = idt*(sux*(axy*ayz-axz*ayy)+suy*(axy*axz-axx*ayz)+suz*(axx*ayy-axy*axy));
                    }
                    else
                    {
                        *px = (s[0]*s[0])*sux/w000;
                        *py = (s[1]*s[1])*suy/w000;
                        *pz = (s[2]*s[2])*suz/w000;
                    }
                }
            }
        }
#   ifdef VERBOSE
        if ((it%2)==1) printf(" %g", sumsq(dm, a, b, s, u));
#   endif
    }
#ifdef VERBOSE
    printf("\n");
#endif

}

void Atimesp_me(mwSize dm[], float A[], double param[], float p[], float Ap[])
{
    vel2mom_me(dm, p, param, Ap);
    Atimesp1(dm, A, p, Ap);
}

void vel2mom_be(mwSize dm[], float f[], double s[], float g[])
{
    mwSignedIndex k;
    double w000,w100,w200,
           w010,w110,
           w020,
           w001,w101,
           w011,
           w002;
    double lam0 = s[3], lam1 = s[4], lam2 = s[5];
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];

    w000 = lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    w100 = lam2*(-4*v0*(v0+v1+v2)) -lam1*v0;
    w010 = lam2*(-4*v1*(v0+v1+v2)) -lam1*v1;
    w001 = lam2*(-4*v2*(v0+v1+v2)) -lam1*v2;
    w200 = lam2*v0*v0;
    w020 = lam2*v1*v1;
    w002 = lam2*v2*v2;
    w110 = lam2*2*v0*v1;
    w101 = lam2*2*v0*v2;
    w011 = lam2*2*v1*v2;

    /*
        syms s1 s2 s3
        syms l1 l2 l3
        zz = sym(zeros(3,3));
        K1 = cat(3,zz,[0 -s1*s1 0; 0 2*s1*s1 0; 0 -s1*s1 0],zz);
        K2 = cat(3,zz,[0 0 0; -s2*s2 2*s2*s2 -s2*s2; 0 0 0],zz);
        K3 = sym(zeros(3,3,3));
        K3(2,2,1) = -s3*s3;
        K3(2,2,2) = 2*s3*s3;
        K3(2,2,3) = -s3*s3;

        K  = K1+K2+K3;
        K1 = K*l1; K1(2,2,2) = K1(2,2,2)+l2;
        K2 = K*l1; K2(2,2,2) = K2(2,2,2)+l3;

        % L  = convn(K,K)
        L  = sym(zeros(5,5,5));
        for i=1:3,
            for j=1:3,
                for k=1:3,
                    L(i-1+1:i+1+1,j-1+1:j+1+1,k-1+1:k+1+1) = L(i-1+1:i+1+1,j-1+1:j+1+1,k-1+1:k+1+1) + K1(i,j,k)*K2;
                end;
            end;
        end;
        disp(simplify(L(3:end,3:end,3:end)))
    */

    for(k=0; k<dm[2]; k++)
    {
        mwSignedIndex j, km2,km1,kp1,kp2;
        km2 = (bound(k-2,dm[2])-k)*dm[0]*dm[1];
        km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
        kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];
        kp2 = (bound(k+2,dm[2])-k)*dm[0]*dm[1];

        for(j=0; j<dm[1]; j++)
        {
            mwSignedIndex i, jm2,jm1,jp1,jp2;
            float *pgx, *pgy, *pgz, *pfx, *pfy, *pfz;

            pgx = g+dm[0]*(j+dm[1]*k);
            pgy = g+dm[0]*(j+dm[1]*(k+dm[2]));
            pgz = g+dm[0]*(j+dm[1]*(k+dm[2]*2));

            pfx = f+dm[0]*(j+dm[1]*k);
            pfy = f+dm[0]*(j+dm[1]*(k+dm[2]));
            pfz = f+dm[0]*(j+dm[1]*(k+dm[2]*2));

            jm2 = (bound(j-2,dm[1])-j)*dm[0];
            jm1 = (bound(j-1,dm[1])-j)*dm[0];
            jp1 = (bound(j+1,dm[1])-j)*dm[0];
            jp2 = (bound(j+2,dm[1])-j)*dm[0];

            for(i=0; i<dm[0]; i++)
            {
                mwSignedIndex im2,im1,ip1,ip2;
                float *px = &pfx[i], *py = &pfy[i], *pz = &pfz[i];
                double c;

                im2 = bound(i-2,dm[0])-i;
                im1 = bound(i-1,dm[0])-i;
                ip1 = bound(i+1,dm[0])-i;
                ip2 = bound(i+2,dm[0])-i;

                /* Note that a few things have been done here to reduce rounding errors.
                   This may slow things down, but it does lead to more accuracy. */
                c      = px[0];
                pgx[i] =(lam0*c
                       + w100*((px[im1        ]-c) + (px[ip1        ]-c))
                       + w010*((px[    jm1    ]-c) + (px[    jp1    ]-c))
                       + w001*((px[        km1]-c) + (px[        kp1]-c))
                       + w200*((px[im2        ]-c) + (px[ip2        ]-c))
                       + w020*((px[    jm2    ]-c) + (px[    jp2    ]-c))
                       + w002*((px[        km2]-c) + (px[        kp2]-c))
                       + w110*((px[im1+jm1    ]-c) + (px[ip1+jm1    ]-c) + (px[im1+jp1    ]-c) + (px[ip1+jp1    ]-c))
                       + w101*((px[im1    +km1]-c) + (px[ip1    +km1]-c) + (px[im1    +kp1]-c) + (px[ip1    +kp1]-c))
                       + w011*((px[    jm1+km1]-c) + (px[    jp1+km1]-c) + (px[    jm1+kp1]-c) + (px[    jp1+kp1]-c)))/v0;

                c      = py[0];
                pgy[i] =(lam0*c
                       + w100*((py[im1        ]-c) + (py[ip1        ]-c))
                       + w010*((py[    jm1    ]-c) + (py[    jp1    ]-c))
                       + w001*((py[        km1]-c) + (py[        kp1]-c))
                       + w200*((py[im2        ]-c) + (py[ip2        ]-c))
                       + w020*((py[    jm2    ]-c) + (py[    jp2    ]-c))
                       + w002*((py[        km2]-c) + (py[        kp2]-c))
                       + w110*((py[im1+jm1    ]-c) + (py[ip1+jm1    ]-c) + (py[im1+jp1    ]-c) + (py[ip1+jp1    ]-c))
                       + w101*((py[im1    +km1]-c) + (py[ip1    +km1]-c) + (py[im1    +kp1]-c) + (py[ip1    +kp1]-c))
                       + w011*((py[    jm1+km1]-c) + (py[    jp1+km1]-c) + (py[    jm1+kp1]-c) + (py[    jp1+kp1]-c)))/v1;

                c      = pz[0];
                pgz[i] =(lam0*c
                       + w100*((pz[im1        ]-c) + (pz[ip1        ]-c))
                       + w010*((pz[    jm1    ]-c) + (pz[    jp1    ]-c))
                       + w001*((pz[        km1]-c) + (pz[        kp1]-c))
                       + w200*((pz[im2        ]-c) + (pz[ip2        ]-c))
                       + w020*((pz[    jm2    ]-c) + (pz[    jp2    ]-c))
                       + w002*((pz[        km2]-c) + (pz[        kp2]-c))
                       + w110*((pz[im1+jm1    ]-c) + (pz[ip1+jm1    ]-c) + (pz[im1+jp1    ]-c) + (pz[ip1+jp1    ]-c))
                       + w200*((pz[im2        ]-c) + (pz[ip2        ]-c))
                       + w101*((pz[im1    +km1]-c) + (pz[ip1    +km1]-c) + (pz[im1    +kp1]-c) + (pz[ip1    +kp1]-c))
                       + w011*((pz[    jm1+km1]-c) + (pz[    jp1+km1]-c) + (pz[    jm1+kp1]-c) + (pz[    jp1+kp1]-c)))/v2;
            }
        }
    }
}

void relax_be(mwSize dm[], float a[], float b[], double s[], int nit, float u[])
{
    int it;
    double w000,w100,w200,
           w010,w110,
           w020,
           w001,w101,
           w011,
           w002;
    double lam0 = s[3], lam1 = s[4], lam2 = s[5];
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];

    w000 = lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    w100 = lam2*(-4*v0*(v0+v1+v2)) -lam1*v0;
    w010 = lam2*(-4*v1*(v0+v1+v2)) -lam1*v1;
    w001 = lam2*(-4*v2*(v0+v1+v2)) -lam1*v2;
    w200 = lam2*v0*v0;
    w020 = lam2*v1*v1;
    w002 = lam2*v2*v2;
    w110 = lam2*2*v0*v1;
    w101 = lam2*2*v0*v2;
    w011 = lam2*2*v1*v2;

    w000 = w000*1.00001 + 1e-6;

    if (dm[0]<=2)
    {
        w000 += 2*w200;
        w200  = 0.0;
    }
    if (dm[1]<=2)
    {
        w000 += 2*w020;
        w020  = 0.0;
    }
    if (dm[2]<=2)
    {
        w000 += 2*w002;
        w002  = 0.0;
    }

    if (dm[0]==1)
    {
        w000 += 2*w100;
        w100  = 0.0;
        if (dm[1]==1)
        {
            w000 += 4*w110;
            w110  = 0.0;
        }
        if (dm[2]==1)
        {
            w000 += 4*w101;
            w101  = 0.0;
        }
    }
    if (dm[1]==1)
    {
        w000 += 2*w010;
        w010  = 0.0;
        if (dm[2]==1)
        {
            w000 += 4*w011;
            w011  = 0.0;
        }
    }
    if (dm[2]==1)
    {
        w000 += 2*w001;
        w001  = 0.0;
    }

#   ifdef VERBOSE
        for(it=0; it< 10-(int)ceil(1.44269504088896*log((double)dm[0])); it++) printf("  ");
        printf("B%dx%dx%d: %g ", dm[0],dm[1],dm[2],sumsq(dm, a, b, s, u));
#   endif

    for(it=0; it<27*nit; it++)
    {
        mwSignedIndex i, j, k;
        for(k=(it/9)%3; k<dm[2]; k+=3)
        {
            mwSignedIndex km2, km1, kp1, kp2;
            km2 = (bound(k-2,dm[2])-k)*dm[0]*dm[1];
            km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
            kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];
            kp2 = (bound(k+2,dm[2])-k)*dm[0]*dm[1];

            for(j=(it/3)%3; j<dm[1]; j+=3)
            {
                float *pux, *puy, *puz, *pbx, *pby, *pbz, *paxx, *payy, *pazz, *paxy, *paxz, *payz;
                mwSignedIndex jm2,jm1,jp1,jp2;

                pux  = u+dm[0]*(j+dm[1]* k);
                puy  = u+dm[0]*(j+dm[1]*(k+dm[2]));
                puz  = u+dm[0]*(j+dm[1]*(k+dm[2]*2));
                pbx  = b+dm[0]*(j+dm[1]* k);
                pby  = b+dm[0]*(j+dm[1]*(k+dm[2]));
                pbz  = b+dm[0]*(j+dm[1]*(k+dm[2]*2));

                if (a)
                {
                    paxx = a+dm[0]*(j+dm[1]* k);
                    payy = a+dm[0]*(j+dm[1]*(k+dm[2]));
                    pazz = a+dm[0]*(j+dm[1]*(k+dm[2]*2));
                    paxy = a+dm[0]*(j+dm[1]*(k+dm[2]*3));
                    paxz = a+dm[0]*(j+dm[1]*(k+dm[2]*4));
                    payz = a+dm[0]*(j+dm[1]*(k+dm[2]*5));
                }

                jm2 = (bound(j-2,dm[1])-j)*dm[0];
                jm1 = (bound(j-1,dm[1])-j)*dm[0];
                jp1 = (bound(j+1,dm[1])-j)*dm[0];
                jp2 = (bound(j+2,dm[1])-j)*dm[0];

                for(i=it%3; i<dm[0]; i+=3)
                {
                    mwSignedIndex im2,im1,ip1,ip2;
                    double sux, suy, suz, c;
                    float *px = pux+i, *py = puy+i, *pz = puz+i;

                    im2 = bound(i-2,dm[0])-i;
                    im1 = bound(i-1,dm[0])-i;
                    ip1 = bound(i+1,dm[0])-i;
                    ip2 = bound(i+2,dm[0])-i;

                    /* Note that a few things have been done here to reduce rounding errors.
                       This may slow things down, but it does lead to more accuracy. */
                    c   = px[0];
                    sux = pbx[i] - (lam0*c
                                  + w100*((px[im1        ]-c) + (px[ip1        ]-c))
                                  + w010*((px[    jm1    ]-c) + (px[    jp1    ]-c))
                                  + w001*((px[        km1]-c) + (px[        kp1]-c))
                                  + w200*((px[im2        ]-c) + (px[ip2        ]-c))
                                  + w020*((px[    jm2    ]-c) + (px[    jp2    ]-c))
                                  + w002*((px[        km2]-c) + (px[        kp2]-c))
                                  + w110*((px[im1+jm1    ]-c) + (px[ip1+jm1    ]-c) + (px[im1+jp1    ]-c) + (px[ip1+jp1    ]-c))
                                  + w101*((px[im1    +km1]-c) + (px[ip1    +km1]-c) + (px[im1    +kp1]-c) + (px[ip1    +kp1]-c))
                                  + w011*((px[    jm1+km1]-c) + (px[    jp1+km1]-c) + (px[    jm1+kp1]-c) + (px[    jp1+kp1]-c)))/v0;

                    c   = py[0];
                    suy = pby[i] - (lam0*c
                                  + w100*((py[im1        ]-c) + (py[ip1        ]-c))
                                  + w010*((py[    jm1    ]-c) + (py[    jp1    ]-c))
                                  + w001*((py[        km1]-c) + (py[        kp1]-c))
                                  + w200*((py[im2        ]-c) + (py[ip2        ]-c))
                                  + w020*((py[    jm2    ]-c) + (py[    jp2    ]-c))
                                  + w002*((py[        km2]-c) + (py[        kp2]-c))
                                  + w110*((py[im1+jm1    ]-c) + (py[ip1+jm1    ]-c) + (py[im1+jp1    ]-c) + (py[ip1+jp1    ]-c))
                                  + w101*((py[im1    +km1]-c) + (py[ip1    +km1]-c) + (py[im1    +kp1]-c) + (py[ip1    +kp1]-c))
                                  + w011*((py[    jm1+km1]-c) + (py[    jp1+km1]-c) + (py[    jm1+kp1]-c) + (py[    jp1+kp1]-c)))/v1;

                    c   = pz[0];
                    suz = pbz[i] - (lam0*c
                                  + w100*((pz[im1        ]-c) + (pz[ip1        ]-c))
                                  + w010*((pz[    jm1    ]-c) + (pz[    jp1    ]-c))
                                  + w001*((pz[        km1]-c) + (pz[        kp1]-c))
                                  + w200*((pz[im2        ]-c) + (pz[ip2        ]-c))
                                  + w020*((pz[    jm2    ]-c) + (pz[    jp2    ]-c))
                                  + w002*((pz[        km2]-c) + (pz[        kp2]-c))
                                  + w110*((pz[im1+jm1    ]-c) + (pz[ip1+jm1    ]-c) + (pz[im1+jp1    ]-c) + (pz[ip1+jp1    ]-c))
                                  + w101*((pz[im1    +km1]-c) + (pz[ip1    +km1]-c) + (pz[im1    +kp1]-c) + (pz[ip1    +kp1]-c))
                                  + w011*((pz[    jm1+km1]-c) + (pz[    jp1+km1]-c) + (pz[    jm1+kp1]-c) + (pz[    jp1+kp1]-c)))/v2;

                    if (a)
                    {
                        double axx, ayy, azz, axy, axz, ayz, idt;

                        sux -= (paxx[i]*px[0] + paxy[i]*py[0] + paxz[i]*pz[0]);
                        suy -= (paxy[i]*px[0] + payy[i]*py[0] + payz[i]*pz[0]);
                        suz -= (paxz[i]*px[0] + payz[i]*py[0] + pazz[i]*pz[0]);

                        axx  = paxx[i] + w000/v0;
                        ayy  = payy[i] + w000/v1;
                        azz  = pazz[i] + w000/v2;
                        axy  = paxy[i];
                        axz  = paxz[i];
                        ayz  = payz[i];
                        idt  = 1.0/(axx*ayy*azz -axx*ayz*ayz-ayy*axz*axz-azz*axy*axy +2*axy*axz*ayz);
                        *px += idt*(sux*(ayy*azz-ayz*ayz)+suy*(axz*ayz-axy*azz)+suz*(axy*ayz-axz*ayy));
                        *py += idt*(sux*(axz*ayz-axy*azz)+suy*(axx*azz-axz*axz)+suz*(axy*axz-axx*ayz));
                        *pz += idt*(sux*(axy*ayz-axz*ayy)+suy*(axy*axz-axx*ayz)+suz*(axx*ayy-axy*axy));
                    }
                    else
                    {
                        *px += v0*sux/w000;
                        *py += v1*suy/w000;
                        *pz += v2*suz/w000;
                    }
                }
            }
        }
#       ifdef VERBOSE
        if ((it%27) == 26)
            printf(" %g", sumsq(dm, a, b, s, u));
#       endif
    }
#   ifdef VERBOSE
        printf("\n");
#   endif
}


void Atimesp_be(mwSize dm[], float A[], double param[], float p[], float Ap[])
{
    vel2mom_be(dm, p, param, Ap);
    Atimesp1(dm, A, p, Ap);
}






/************************************************************************************************/


void vel2mom_all(mwSize dm[], float f[], double s[], float g[])
{
    mwSignedIndex k;
    double w000,w100,w200,
           w010,w110,
           w020,
           w001,w101,
           w011,
           w002;
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], lam1 = s[4], lam2 = s[5], mu = s[6], lam = s[7];
    double wx000, wx100, wx010, wx001, wy000, wy100, wy010, wy001, wz000, wz100, wz010, wz001, w2;

    w000 = lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    w100 = lam2*(-4*v0*(v0+v1+v2)) -lam1*v0;
    w010 = lam2*(-4*v1*(v0+v1+v2)) -lam1*v1;
    w001 = lam2*(-4*v2*(v0+v1+v2)) -lam1*v2;
    w200 = lam2*v0*v0;
    w020 = lam2*v1*v1;
    w002 = lam2*v2*v2;
    w110 = lam2*2*v0*v1;
    w101 = lam2*2*v0*v2;
    w011 = lam2*2*v1*v2;

    wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + w000/v0;
    wx100 = -2*mu-lam + w100/v0;
    wx010 = -mu*v1/v0 + w010/v0;
    wx001 = -mu*v2/v0 + w001/v0;
    wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + w000/v1;
    wy100 = -mu*v0/v1 + w100/v1;
    wy010 = -2*mu-lam + w010/v1;
    wy001 = -mu*v2/v1 + w001/v1;
    wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + w000/v2;
    wz100 = -mu*v0/v2 + w100/v2;
    wz010 = -mu*v1/v2 + w010/v2;
    wz001 = -2*mu-lam + w001/v2;
    w2    = 0.25*mu+0.25*lam;

    for(k=0; k<dm[2]; k++)
    {
        mwSignedIndex j, km2,km1,kp1,kp2;
        km2 = (bound(k-2,dm[2])-k)*dm[0]*dm[1];
        km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
        kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];
        kp2 = (bound(k+2,dm[2])-k)*dm[0]*dm[1];

        for(j=0; j<dm[1]; j++)
        {
            mwSignedIndex i, jm2,jm1,jp1,jp2;
            float *pgx, *pgy, *pgz, *pfx, *pfy, *pfz;

            pgx = g+dm[0]*(j+dm[1]*k);
            pgy = g+dm[0]*(j+dm[1]*(k+dm[2]));
            pgz = g+dm[0]*(j+dm[1]*(k+dm[2]*2));

            pfx = f+dm[0]*(j+dm[1]*k);
            pfy = f+dm[0]*(j+dm[1]*(k+dm[2]));
            pfz = f+dm[0]*(j+dm[1]*(k+dm[2]*2));

            jm2 = (bound(j-2,dm[1])-j)*dm[0];
            jm1 = (bound(j-1,dm[1])-j)*dm[0];
            jp1 = (bound(j+1,dm[1])-j)*dm[0];
            jp2 = (bound(j+2,dm[1])-j)*dm[0];

            for(i=0; i<dm[0]; i++)
            {
                mwSignedIndex im2,im1,ip1,ip2;
                float *px = &pfx[i], *py = &pfy[i], *pz = &pfz[i];
                double c;

                im2 = bound(i-2,dm[0])-i;
                im1 = bound(i-1,dm[0])-i;
                ip1 = bound(i+1,dm[0])-i;
                ip2 = bound(i+2,dm[0])-i;

                /* Note that a few things have been done here to reduce rounding errors.
                   This may slow things down, but it does lead to more accuracy. */
                c      = px[0];
                pgx[i] = (wx100*((px[im1        ]-c) + (px[ip1        ]-c))
                        + wx010*((px[    jm1    ]-c) + (px[    jp1    ]-c))
                        + wx001*((px[        km1]-c) + (px[        kp1]-c))
                        + w2   *( py[ip1+jm1] - py[ip1+jp1] + py[im1+jp1] - py[im1+jm1] + pz[ip1+km1] - pz[ip1+kp1] + pz[im1+kp1] - pz[im1+km1])
                        + (lam0*c
                        +  w110*((px[im1+jm1    ]-c) + (px[ip1+jm1    ]-c) + (px[im1+jp1    ]-c) + (px[ip1+jp1    ]-c))
                        +  w101*((px[im1    +km1]-c) + (px[ip1    +km1]-c) + (px[im1    +kp1]-c) + (px[ip1    +kp1]-c))
                        +  w011*((px[    jm1+km1]-c) + (px[    jp1+km1]-c) + (px[    jm1+kp1]-c) + (px[    jp1+kp1]-c))
                        +  w200*((px[im2        ]-c) + (px[ip2        ]-c))
                        +  w020*((px[    jm2    ]-c) + (px[    jp2    ]-c))
                        +  w002*((px[        km2]-c) + (px[        kp2]-c)))/v0);

                c      = py[0];
                pgy[i] = (wy100*((py[im1        ]-c) + (py[ip1        ]-c))
                        + wy010*((py[    jm1    ]-c) + (py[    jp1    ]-c))
                        + wy001*((py[        km1]-c) + (py[        kp1]-c))
                        + w2   *( px[jp1+im1] - px[jp1+ip1] + px[jm1+ip1] - px[jm1+im1] + pz[jp1+km1] - pz[jp1+kp1] + pz[jm1+kp1] - pz[jm1+km1])
                        + (lam0*c
                        +  w110*((py[im1+jm1    ]-c) + (py[ip1+jm1    ]-c) + (py[im1+jp1    ]-c) + (py[ip1+jp1    ]-c))
                        +  w101*((py[im1    +km1]-c) + (py[ip1    +km1]-c) + (py[im1    +kp1]-c) + (py[ip1    +kp1]-c))
                        +  w011*((py[    jm1+km1]-c) + (py[    jp1+km1]-c) + (py[    jm1+kp1]-c) + (py[    jp1+kp1]-c))
                        +  w200*((py[im2        ]-c) + (py[ip2        ]-c))
                        +  w020*((py[    jm2    ]-c) + (py[    jp2    ]-c))
                        +  w002*((py[        km2]-c) + (py[        kp2]-c)))/v1);

                c      = pz[0];
                pgz[i] = (wz100*((pz[im1        ]-c) + (pz[ip1        ]-c))
                        + wz010*((pz[    jm1    ]-c) + (pz[    jp1    ]-c))
                        + wz001*((pz[        km1]-c) + (pz[        kp1]-c))
                        + w2   *( px[kp1+im1] - px[kp1+ip1] + px[km1+ip1] - px[km1+im1] + py[kp1+jm1] - py[kp1+jp1] + py[km1+jp1] - py[km1+jm1])
                        + (lam0*c
                        +  w110*((pz[im1+jm1    ]-c) + (pz[ip1+jm1    ]-c) + (pz[im1+jp1    ]-c) + (pz[ip1+jp1    ]-c))
                        +  w101*((pz[im1    +km1]-c) + (pz[ip1    +km1]-c) + (pz[im1    +kp1]-c) + (pz[ip1    +kp1]-c))
                        +  w011*((pz[    jm1+km1]-c) + (pz[    jp1+km1]-c) + (pz[    jm1+kp1]-c) + (pz[    jp1+kp1]-c))
                        +  w200*((pz[im2        ]-c) + (pz[ip2        ]-c))
                        +  w020*((pz[    jm2    ]-c) + (pz[    jp2    ]-c))
                        +  w002*((pz[        km2]-c) + (pz[        kp2]-c)))/v2);
            }
        }
    }
}

void relax_all(mwSize dm[], float a[], float b[], double s[], int nit, float u[])
{
    int it;
    double w000,w100,w200,
           w010,w110,
           w020,
           w001,w101,
           w011,
           w002;
    double v0 = s[0]*s[0], v1 = s[1]*s[1], v2 = s[2]*s[2];
    double lam0 = s[3], lam1 = s[4], lam2 = s[5], mu = s[6], lam = s[7];
    double wx000, wx100, wx010, wx001, wy000, wy100, wy010, wy001, wz000, wz100, wz010, wz001, w2;

    w000 = lam2*(6*(v0*v0+v1*v1+v2*v2) +8*(v0*v1+v0*v2+v1*v2)) +lam1*2*(v0+v1+v2) + lam0;
    w100 = lam2*(-4*v0*(v0+v1+v2)) -lam1*v0;
    w010 = lam2*(-4*v1*(v0+v1+v2)) -lam1*v1;
    w001 = lam2*(-4*v2*(v0+v1+v2)) -lam1*v2;
    w200 = lam2*v0*v0;
    w020 = lam2*v1*v1;
    w002 = lam2*v2*v2;
    w110 = lam2*2*v0*v1;
    w101 = lam2*2*v0*v2;
    w011 = lam2*2*v1*v2;

    wx000 =  2*mu*(2*v0+v1+v2)/v0+2*lam + w000/v0;
    wx100 = -2*mu-lam + w100/v0;
    wx010 = -mu*v1/v0 + w010/v0;
    wx001 = -mu*v2/v0 + w001/v0;
    wy000 =  2*mu*(v0+2*v1+v2)/v1+2*lam + w000/v1;
    wy100 = -mu*v0/v1 + w100/v1;
    wy010 = -2*mu-lam + w010/v1;
    wy001 = -mu*v2/v1 + w001/v1;
    wz000 =  2*mu*(v0+v1+2*v2)/v2+2*lam + w000/v2;
    wz100 = -mu*v0/v2 + w100/v2;
    wz010 = -mu*v1/v2 + w010/v2;
    wz001 = -2*mu-lam + w001/v2;
    w2    = 0.25*mu+0.25*lam;

/*  wx000 = wx000*1.00001 + 1e-6;
    wy000 = wy000*1.00001 + 1e-6;
    wz000 = wz000*1.00001 + 1e-6; */

    if (dm[0]<=2)
    {
        wx000 += 2*w200/v0;
        wy000 += 2*w200/v1;
        wz000 += 2*w200/v2;
        w200   = 0.0;
    }
    if (dm[1]<=2)
    {
        wx000 += 2*w020/v0;
        wy000 += 2*w020/v1;
        wz000 += 2*w020/v2;
        w020   = 0.0;
    }
    if (dm[2]<=2)
    {
        wx000 += 2*w002/v0;
        wy000 += 2*w002/v1;
        wz000 += 2*w002/v2; 
        w002   = 0.0;
    }

    if (dm[0]==1)
    {
        wx000 += 2*wx100; wx100  = 0.0;
        wy000 += 2*wy100; wy100  = 0.0;
        wz000 += 2*wz100; wz100  = 0.0;
        if (dm[1]==1)
        {
            wx000 += 4*w110/v0;
            wy000 += 4*w110/v1;
            wz000 += 4*w110/v2;
            w110   = 0.0;
        }
        if (dm[2]==1)
        {
            wx000 += 4*w101/v0;
            wy000 += 4*w101/v1;
            wz000 += 4*w101/v2;
            w101   = 0.0;
        }

    }
    if (dm[1]==1)
    {
        wx000 += 2*wx010; wx010  = 0.0;
        wy000 += 2*wy010; wy010  = 0.0;
        wz000 += 2*wz010; wz010  = 0.0;
        if (dm[2]==1)
        {
            wx000 += 4*w011/v0;
            wy000 += 4*w011/v1;
            wz000 += 4*w011/v2;
            w011   = 0.0;
        }
    }
    if (dm[2]==1)
    {
        wx000 += 2*wx001; wx001  = 0.0;
        wy000 += 2*wy001; wy001  = 0.0;
        wz000 += 2*wz001; wz001  = 0.0;
    }
    if (wx000<0.0) wx000;
    if (wy000<0.0) wy000;
    if (wz000<0.0) wz000;

#   ifdef VERBOSE
        for(it=0; it< 10-(int)ceil(1.44269504088896*log((double)dm[0])); it++) printf("  ");
        printf("A%dx%dx%d: %g ", dm[0],dm[1],dm[2],sumsq(dm, a, b, s, u));
#   endif

    for(it=0; it<27*nit; it++)
    {
        mwSignedIndex i, j, k;
        for(k=(it/9)%3; k<dm[2]; k+=3)
        {
            mwSignedIndex km2, km1, kp1, kp2;
            km2 = (bound(k-2,dm[2])-k)*dm[0]*dm[1];
            km1 = (bound(k-1,dm[2])-k)*dm[0]*dm[1];
            kp1 = (bound(k+1,dm[2])-k)*dm[0]*dm[1];
            kp2 = (bound(k+2,dm[2])-k)*dm[0]*dm[1];

            for(j=(it/3)%3; j<dm[1]; j+=3)
            {
                float *pux, *puy, *puz, *pbx, *pby, *pbz, *paxx, *payy, *pazz, *paxy, *paxz, *payz;
                mwSignedIndex jm2,jm1,jp1,jp2;

                pux  = u+dm[0]*(j+dm[1]* k);
                puy  = u+dm[0]*(j+dm[1]*(k+dm[2]));
                puz  = u+dm[0]*(j+dm[1]*(k+dm[2]*2));
                pbx  = b+dm[0]*(j+dm[1]* k);
                pby  = b+dm[0]*(j+dm[1]*(k+dm[2]));
                pbz  = b+dm[0]*(j+dm[1]*(k+dm[2]*2));

                if (a)
                {
                    paxx = a+dm[0]*(j+dm[1]* k);
                    payy = a+dm[0]*(j+dm[1]*(k+dm[2]));
                    pazz = a+dm[0]*(j+dm[1]*(k+dm[2]*2));
                    paxy = a+dm[0]*(j+dm[1]*(k+dm[2]*3));
                    paxz = a+dm[0]*(j+dm[1]*(k+dm[2]*4));
                    payz = a+dm[0]*(j+dm[1]*(k+dm[2]*5));
                }

                jm2 = (bound(j-2,dm[1])-j)*dm[0];
                jm1 = (bound(j-1,dm[1])-j)*dm[0];
                jp1 = (bound(j+1,dm[1])-j)*dm[0];
                jp2 = (bound(j+2,dm[1])-j)*dm[0];

                for(i=it%3; i<dm[0]; i+=3)
                {
                    mwSignedIndex im2,im1,ip1,ip2;
                    double sux, suy, suz, c;
                    float *px = pux+i, *py = puy+i, *pz = puz+i;

                    im2 = bound(i-2,dm[0])-i;
                    im1 = bound(i-1,dm[0])-i;
                    ip1 = bound(i+1,dm[0])-i;
                    ip2 = bound(i+2,dm[0])-i;

                    /* Note that a few things have been done here to reduce rounding errors.
                       This may slow things down, but it does lead to more accuracy. */
                    c   = px[0];
                    sux = pbx[i]
                          - ( wx100*((px[im1        ]-c) + (px[ip1        ]-c))
                            + wx010*((px[    jm1    ]-c) + (px[    jp1    ]-c))
                            + wx001*((px[        km1]-c) + (px[        kp1]-c))
                            + w2   *( py[ip1+jm1] - py[ip1+jp1] + py[im1+jp1] - py[im1+jm1] + pz[ip1+km1] - pz[ip1+kp1] + pz[im1+kp1] - pz[im1+km1])
                            + (lam0*c
                            +  w110*((px[im1+jm1    ]-c) + (px[ip1+jm1    ]-c) + (px[im1+jp1    ]-c) + (px[ip1+jp1    ]-c))
                            +  w101*((px[im1    +km1]-c) + (px[ip1    +km1]-c) + (px[im1    +kp1]-c) + (px[ip1    +kp1]-c))
                            +  w011*((px[    jm1+km1]-c) + (px[    jp1+km1]-c) + (px[    jm1+kp1]-c) + (px[    jp1+kp1]-c))
                            +  w200*((px[im2        ]-c) + (px[ip2        ]-c))
                            +  w020*((px[    jm2    ]-c) + (px[    jp2    ]-c))
                            +  w002*((px[        km2]-c) + (px[        kp2]-c)))/v0);

                    c   = py[0];
                    suy = pby[i]
                          - ( wy100*((py[im1        ]-c) + (py[ip1        ]-c))
                            + wy010*((py[    jm1    ]-c) + (py[    jp1    ]-c))
                            + wy001*((py[        km1]-c) + (py[        kp1]-c))
                            + w2   *( px[jp1+im1] - px[jp1+ip1] + px[jm1+ip1] - px[jm1+im1] + pz[jp1+km1] - pz[jp1+kp1] + pz[jm1+kp1] - pz[jm1+km1])
                            + (lam0*c
                            +  w110*((py[im1+jm1    ]-c) + (py[ip1+jm1    ]-c) + (py[im1+jp1    ]-c) + (py[ip1+jp1    ]-c))
                            +  w101*((py[im1    +km1]-c) + (py[ip1    +km1]-c) + (py[im1    +kp1]-c) + (py[ip1    +kp1]-c))
                            +  w011*((py[    jm1+km1]-c) + (py[    jp1+km1]-c) + (py[    jm1+kp1]-c) + (py[    jp1+kp1]-c))
                            +  w200*((py[im2        ]-c) + (py[ip2        ]-c))
                            +  w020*((py[    jm2    ]-c) + (py[    jp2    ]-c))
                            +  w002*((py[        km2]-c) + (py[        kp2]-c)))/v1);

                    c   = pz[0];
                    suz = pbz[i]
                          - ( wz100*((pz[im1        ]-c) + (pz[ip1        ]-c))
                            + wz010*((pz[    jm1    ]-c) + (pz[    jp1    ]-c))
                            + wz001*((pz[        km1]-c) + (pz[        kp1]-c))
                            + w2   *(px[kp1+im1] - px[kp1+ip1] + px[km1+ip1] - px[km1+im1] + py[kp1+jm1] - py[kp1+jp1] + py[km1+jp1] - py[km1+jm1])
                            + (lam0*c
                            +  w110*((pz[im1+jm1    ]-c) + (pz[ip1+jm1    ]-c) + (pz[im1+jp1    ]-c) + (pz[ip1+jp1    ]-c))
                            +  w101*((pz[im1    +km1]-c) + (pz[ip1    +km1]-c) + (pz[im1    +kp1]-c) + (pz[ip1    +kp1]-c))
                            +  w011*((pz[    jm1+km1]-c) + (pz[    jp1+km1]-c) + (pz[    jm1+kp1]-c) + (pz[    jp1+kp1]-c))
                            +  w200*((pz[im2        ]-c) + (pz[ip2        ]-c))
                            +  w020*((pz[    jm2    ]-c) + (pz[    jp2    ]-c))
                            +  w002*((pz[        km2]-c) + (pz[        kp2]-c)))/v2);

                    if (a)
                    {
                        double axx, ayy, azz, axy, axz, ayz, idt;

                        sux -= (paxx[i]*px[0] + paxy[i]*py[0] + paxz[i]*pz[0]);
                        suy -= (paxy[i]*px[0] + payy[i]*py[0] + payz[i]*pz[0]);
                        suz -= (paxz[i]*px[0] + payz[i]*py[0] + pazz[i]*pz[0]);

                        axx  = paxx[i] + wx000;
                        ayy  = payy[i] + wy000;
                        azz  = pazz[i] + wz000;
                        axy  = paxy[i];
                        axz  = paxz[i];
                        ayz  = payz[i];
                        idt  = 1.0/(axx*ayy*azz -axx*ayz*ayz-ayy*axz*axz-azz*axy*axy +2*axy*axz*ayz);
                        *px += idt*(sux*(ayy*azz-ayz*ayz)+suy*(axz*ayz-axy*azz)+suz*(axy*ayz-axz*ayy));
                        *py += idt*(sux*(axz*ayz-axy*azz)+suy*(axx*azz-axz*axz)+suz*(axy*axz-axx*ayz));
                        *pz += idt*(sux*(axy*ayz-axz*ayy)+suy*(axy*axz-axx*ayz)+suz*(axx*ayy-axy*axy));
                    }
                    else
                    {
                        *px += sux/wx000;
                        *py += suy/wy000;
                        *pz += suz/wz000;
                    }
                }
            }
        }
#       ifdef VERBOSE
        if ((it%27) == 26)
            printf(" %g", sumsq(dm, a, b, s, u));
#       endif
    }
#   ifdef VERBOSE
        printf("\n");
#   endif
}

void relax(mwSize dm[], float a[], float b[], double s[], int nit, float u[])
{
    if (s[5]==0 && s[6]==0 && s[7]==0)
        relax_me(dm, a, b, s, nit, u);
    else if (s[6]==0 && s[7]==0)
        relax_be(dm, a, b, s, nit, u);
    else if (s[4]==0 && s[5]==0)
        relax_le(dm, a, b, s, nit, u);
    else
        relax_all(dm, a, b, s, nit, u);
}

void vel2mom(mwSize dm[], float f[], double s[], float g[])
{
    if (s[5]==0 && s[6]==0 && s[7]==0)
        vel2mom_me(dm, f, s, g);
    else if (s[6]==0 && s[7]==0)
        vel2mom_be(dm, f, s, g);
    else if (s[4]==0 && s[5]==0)
        vel2mom_le(dm, f, s, g);
    else
        vel2mom_all(dm, f, s, g);
}

void Atimesp(mwSize dm[], float A[], double param[], float p[], float Ap[])
{
    vel2mom(dm, p, param, Ap);
    Atimesp1(dm, A, p, Ap);
}