Function Kabsch

evaluation/TMscore.cpp:3162–3482

Implemetation of Kabsch algoritm for finding the best rotation matrix --------------------------------------------------------------------------- x - x(i,m) are coordinates of atom m in set x (input) y - y(i,m) are coordinates of atom m in set y (input) n - n is number of atom pairs (input) mode - 0:calculate rms only

t    - t(i)   is translation vector for best superposition  (output)
**************************************************************************/
bool Kabsch(double **x, double **y, int n, int mode, double *rms,
    double t[3], double u[3][3])
{
    int i, j, m, m1, l, k;
    double e0, rms1, d, h, g;
    double cth, sth, sqrth, p, det, sigma;
    double xc[3], yc[3];
    double a[3][3], b[3][3], r[3][3], e[3], rr[6], ss[6];
    double sqrt3 = 1.73205080756888, tol = 0.01;
    int ip[] = { 0, 1, 3, 1, 2, 4, 3, 4, 5 };
    int ip2312[] = { 1, 2, 0, 1 };

    int a_failed = 0, b_failed = 0;
    double epsilon = 0.00000001;

    //initialization
    *rms = 0;
    rms1 = 0;
    e0 = 0;
    double c1[3], c2[3];
    double s1[3], s2[3];
    double sx[3], sy[3], sz[3];
    for (i = 0; i < 3; i++)
    {
        s1[i] = 0.0;
        s2[i] = 0.0;

        sx[i] = 0.0;
        sy[i] = 0.0;
        sz[i] = 0.0;
    }

    for (i = 0; i<3; i++)
    {
        xc[i] = 0.0;
        yc[i] = 0.0;
        t[i] = 0.0;
        for (j = 0; j<3; j++)
        {
            u[i][j] = 0.0;
            r[i][j] = 0.0;
            a[i][j] = 0.0;
            if (i == j)
            {
                u[i][j] = 1.0;
                a[i][j] = 1.0;
            }
        }
    }

    if (n<1) return false;

    //compute centers for vector sets x, y
    for (i = 0; i<n; i++)
    {
        for (j = 0; j < 3; j++)
        {
            c1[j] = x[i][j];