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cmn_fncs.c
executable file
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cmn_fncs.c
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/*<<<
* ------------------------------------------------------------------------
* This file is part of the SCHNAarP software package for the analysis and
* rebuilding of double helical nucleic acid structures. Detailed description
* of the underlying algorithms can be found in the following three papers:
*
* (1) Xiang-Jun Lu, M. A. El Hassan and C. A. Hunter (1997), "Structure
* and Conformation of Helical Nucleic Acids: Analysis Program
* (SCHNAaP)", J. Mol. Biol. 273, 668--680.
*
* (2) Xiang-Jun Lu, M. A. El Hassan and C. A. Hunter (1997), "Structure
* and Conformation of Helical Nucleic Acids: Rebuilding Program
* (SCHNArP)", J. Mol. Biol. 273, 681--691.
*
* (3) M. A. El Hassan and C. R. Calladine (1995), "The Assessment of the
* Geometry of Dinucleotide Steps in Double-Helical DNA; a New Local
* Calculation Scheme", J. Mol. Biol. 251, 648--664.
*
* Copyright (C) 1996-2002 Xiang-Jun Lu. Permission to use, copy, and modify
* this software is hereby granted to all academic and not-for-profit
* institutions without fee, provided that the above papers (or part of) are
* properly cited in related publications. However, the right to use this
* software in conjunction with for profit activities, and the right to
* distribute the software or modified or extended versions thereof for profit
* are *NOT* granted except by prior arrangement and written consent of the
* copyright holders.
*
* The software is provided "AS-IS" and without warranty of any kind, express,
* implied or otherwise, including without limitation, any warranty of
* merchantability or fitness for a particular purpose.
*
* The software was written by Xiang-Jun Lu ([email protected]). It started
* off his PhD thesis work at Dr. Chris Hunter Laboratory at University of
* Sheffield, U.K. The source code should be valuable for understanding the
* elegant CEHS algorithm, and many other aspects of nucleic acid structures.
* For real world applications, however, you are strongly recommended to
* switch to 3DNA (http://3dna.rutgers.edu).
*
* Revision history -- please see file 'Change.log'
*
* $LastChangedDate: 2009-06-01 18:34:25 -0400 (Mon, 01 Jun 2009) $
* $LastChangedRevision: 1556 $
* $LastChangedBy: xiangjun $
* ------------------------------------------------------------------------
>>>*/
#include "schna_ar_p.h"
/* >>>adapt the following 4 functions from NR in C (2nd Edition) <<< */
#define ROTATE(a,i,j,k,l) g=a[i][j];h=a[k][l];a[i][j]=g-s*(h+g*tau);a[k][l]=h+s*(g-h*tau);
void jacobi(double **a, long n, double *d, double **v, long *nrot)
{
long j, iq, ip, i;
double tresh, theta, tau, t, sm, s, h, g, c, *b, *z;
/* BEGIN INSERT jacobi.c HERE */
/* the first two lines would be:
b = dvector(1, n);
z = dvector(1, n);
*/
/* (float) ----> (double)
if (i > 4 && (double) (fabs(d[ip]) + g) == (double) fabs(d[ip])
^^^^^^
*/
/* end with
nrerror("Too many iterations.");
*/
b=dvector(1,n);
z=dvector(1,n);
for (ip=1;ip<=n;ip++) {
for (iq=1;iq<=n;iq++) v[ip][iq]=0.0;
v[ip][ip]=1.0;
}
for (ip=1;ip<=n;ip++) {
b[ip]=d[ip]=a[ip][ip];
z[ip]=0.0;
}
*nrot=0;
for (i=1;i<=50;i++) {
sm=0.0;
for (ip=1;ip<=n-1;ip++) {
for (iq=ip+1;iq<=n;iq++)
sm += fabs(a[ip][iq]);
}
if (sm == 0.0) {
free_dvector(z,1,n);
free_dvector(b,1,n);
return;
}
if (i < 4)
tresh=0.2*sm/(n*n);
else
tresh=0.0;
for (ip=1;ip<=n-1;ip++) {
for (iq=ip+1;iq<=n;iq++) {
g=100.0*fabs(a[ip][iq]);
if (i > 4 && (double)(fabs(d[ip])+g) == (double)fabs(d[ip])
&& (double)(fabs(d[iq])+g) == (double)fabs(d[iq]))
a[ip][iq]=0.0;
else if (fabs(a[ip][iq]) > tresh) {
h=d[iq]-d[ip];
if ((double)(fabs(h)+g) == (double)fabs(h))
t=(a[ip][iq])/h;
else {
theta=0.5*h/(a[ip][iq]);
t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
if (theta < 0.0) t = -t;
}
c=1.0/sqrt(1+t*t);
s=t*c;
tau=s/(1.0+c);
h=t*a[ip][iq];
z[ip] -= h;
z[iq] += h;
d[ip] -= h;
d[iq] += h;
a[ip][iq]=0.0;
for (j=1;j<=ip-1;j++) {
ROTATE(a,j,ip,j,iq)
}
for (j=ip+1;j<=iq-1;j++) {
ROTATE(a,ip,j,j,iq)
}
for (j=iq+1;j<=n;j++) {
ROTATE(a,ip,j,iq,j)
}
for (j=1;j<=n;j++) {
ROTATE(v,j,ip,j,iq)
}
++(*nrot);
}
}
}
for (ip=1;ip<=n;ip++) {
b[ip] += z[ip];
d[ip]=b[ip];
z[ip]=0.0;
}
}
nrerror("Too many iterations in routine jacobi");
/* END INSERT jacobi.c HERE */
}
#undef ROTATE
void eigsrt(double *d, double **v, long n)
{
long k, j, i;
double p;
/* BEGIN INSERT eigsrt.c HERE */
for (i=1;i<n;i++) {
p=d[k=i];
for (j=i+1;j<=n;j++)
if (d[j] >= p) p=d[k=j];
if (k != i) {
d[k]=d[i];
d[i]=p;
for (j=1;j<=n;j++) {
p=v[j][i];
v[j][i]=v[j][k];
v[j][k]=p;
}
}
}
/* END INSERT eigsrt.c HERE */
}
#define TINY 1.0e-20
void dludcmp(double **a, long n, long *indx, double *d)
{
long i, imax, j, k;
double big, dum, sum, temp;
double *vv;
/* BEGIN INSERT ludcmp.c HERE */
/* start with
vv = dvector(1, n);
*d = 1.0;
*/
/* ends with
free_dvector(vv, 1, n);
*/
vv=dvector(1,n);
*d=1.0;
for (i=1;i<=n;i++) {
big=0.0;
for (j=1;j<=n;j++)
if ((temp=fabs(a[i][j])) > big) big=temp;
if (big == 0.0) nrerror("Singular matrix in routine ludcmp");
vv[i]=1.0/big;
}
for (j=1;j<=n;j++) {
for (i=1;i<j;i++) {
sum=a[i][j];
for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];
a[i][j]=sum;
}
big=0.0;
for (i=j;i<=n;i++) {
sum=a[i][j];
for (k=1;k<j;k++)
sum -= a[i][k]*a[k][j];
a[i][j]=sum;
if ( (dum=vv[i]*fabs(sum)) >= big) {
big=dum;
imax=i;
}
}
if (j != imax) {
for (k=1;k<=n;k++) {
dum=a[imax][k];
a[imax][k]=a[j][k];
a[j][k]=dum;
}
*d = -(*d);
vv[imax]=vv[j];
}
indx[j]=imax;
if (a[j][j] == 0.0) a[j][j]=TINY;
if (j != n) {
dum=1.0/(a[j][j]);
for (i=j+1;i<=n;i++) a[i][j] *= dum;
}
}
free_dvector(vv,1,n);
/* END INSERT ludcmp.c HERE */
}
#undef TINY
void dlubksb(double **a, long n, long *indx, double *b)
{
long i, ii = 0, ip, j;
double sum;
/* BEGIN INSERT lubksb.c HERE */
for (i=1;i<=n;i++) {
ip=indx[i];
sum=b[ip];
b[ip]=b[i];
if (ii)
for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];
else if (sum) ii=i;
b[i]=sum;
}
for (i=n;i>=1;i--) {
sum=b[i];
for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];
b[i]=sum/a[i][i];
}
/* END INSERT lubksb.c HERE */
}
/* >>> END of 4 functions from NR in C (2nd Edition) <<< */
double dist_ab(double a, double b)
{
return (sqrt(a * a + b * b));
}
void zero_dmatrix(double **a, long nr, long nc)
{
long i, j;
for (i = 1; i <= nr; i++) {
for (j = 1; j <= nc; j++)
a[i][j] = 0.0;
}
}
void one_dmatrix(double **a, long nr, long nc)
{
long i, j;
for (i = 1; i <= nr; i++) {
for (j = 1; j <= nc; j++)
a[i][j] = 1.0;
}
}
void zero_dvector(double *a, long n)
{
long i;
for (i = 1; i <= n; i++)
a[i] = 0.0;
}
void zero_lvector(long *a, long n)
{
long i;
for (i = 1; i <= n; i++)
a[i] = 0;
}
void identity_dmatrix(double **a, long n)
{
long i, j;
for (i = 1; i <= n; i++) {
for (j = 1; j <= n; j++)
a[i][j] = 0.0;
a[i][i] = 1.0;
}
}
double deg2rad(double theta)
{
return (theta * PI / 180.0);
}
double rad2deg(double theta)
{
return (theta * 180.0 / PI);
}
void rotx(double **rotmat, double theta)
/* "theta" MUST be in degree */
{
double c, s, ang;
ang = deg2rad(theta);
c = cos(ang);
s = sin(ang);
rotmat[1][1] = 1.0;
rotmat[1][2] = 0.0;
rotmat[1][3] = 0.0;
rotmat[2][1] = 0.0;
rotmat[2][2] = c;
rotmat[2][3] = -s;
rotmat[3][1] = 0.0;
rotmat[3][2] = s;
rotmat[3][3] = c;
}
void roty(double **rotmat, double theta)
/* "theta" MUST be in degree */
{
double c, s, ang;
ang = deg2rad(theta);
c = cos(ang);
s = sin(ang);
rotmat[1][1] = c;
rotmat[1][2] = 0.0;
rotmat[1][3] = s;
rotmat[2][1] = 0.0;
rotmat[2][2] = 1.0;
rotmat[2][3] = 0.0;
rotmat[3][1] = -s;
rotmat[3][2] = 0.0;
rotmat[3][3] = c;
}
void rotz(double **rotmat, double theta)
/* "theta" MUST be in degree */
{
double c, s, ang;
ang = deg2rad(theta);
c = cos(ang);
s = sin(ang);
rotmat[1][1] = c;
rotmat[1][2] = -s;
rotmat[1][3] = 0.0;
rotmat[2][1] = s;
rotmat[2][2] = c;
rotmat[2][3] = 0.0;
rotmat[3][1] = 0.0;
rotmat[3][2] = 0.0;
rotmat[3][3] = 1.0;
}
void mul_dmatrix(double **o, double **a, double **b,
long nr_a, long nc_a, long nr_b, long nc_b)
{
double tmp;
long i, j, k;
if (nc_a != nr_b)
nrerror("Matrices a and b do NOT conform!");
for (i = 1; i <= nr_a; i++) {
for (j = 1; j <= nc_b; j++) {
tmp = 0.0;
for (k = 1; k <= nc_a; k++)
tmp += a[i][k] * b[k][j];
o[i][j] = tmp;
}
}
}
void tr_dmatrix(double **o, double **a, long nr, long nc)
/* Matrix transpose */
{
long i, j;
for (i = 1; i <= nc; i++) {
for (j = 1; j <= nr; j++)
o[i][j] = a[j][i];
}
}
void cov_dmatrix(double **cov_mtx, double **xyz, long nr, long nc)
/* Get the covariance matrix of XYZ */
{
long i, j;
double **xyzT, **o, **oT, **tmp1, **tmp2, **tmp3, **tmp4;
xyzT = dmatrix(1, nc, 1, nr);
o = dmatrix(1, nr, 1, 1);
oT = dmatrix(1, 1, 1, nr);
tmp1 = dmatrix(1, nc, 1, nc);
tmp2 = dmatrix(1, nc, 1, 1);
tmp3 = dmatrix(1, 1, 1, nc);
tmp4 = dmatrix(1, nc, 1, nc);
one_dmatrix(o, nr, 1);
tr_dmatrix(oT, o, nr, 1);
tr_dmatrix(xyzT, xyz, nr, nc);
mul_dmatrix(tmp1, xyzT, xyz, nc, nr, nr, nc);
mul_dmatrix(tmp2, xyzT, o, nc, nr, nr, 1);
mul_dmatrix(tmp3, oT, xyz, 1, nr, nr, nc);
mul_dmatrix(tmp4, tmp2, tmp3, nc, 1, 1, nc);
for (i = 1; i <= nc; i++) {
for (j = 1; j <= nc; j++)
tmp4[i][j] = tmp4[i][j] / nr;
}
for (i = 1; i <= nc; i++) {
for (j = 1; j <= nc; j++)
cov_mtx[i][j] = (tmp1[i][j] - tmp4[i][j]) / (nr - 1);
}
free_dmatrix(o, 1, nr, 1, 1);
free_dmatrix(oT, 1, 1, 1, nr);
free_dmatrix(tmp2, 1, nc, 1, 1);
free_dmatrix(tmp3, 1, 1, 1, nc);
free_dmatrix(xyzT, 1, nc, 1, nr);
free_dmatrix(tmp1, 1, nc, 1, nc);
free_dmatrix(tmp4, 1, nc, 1, nc);
}
void mean_dmatrix(double *o, double **a, long nr, long nc)
/* Columnwise mean of matrix a */
{
long i, j;
double dsum;
for (i = 1; i <= nc; i++) {
dsum = 0;
for (j = 1; j <= nr; j++)
dsum += a[j][i];
o[i] = dsum / nr;
}
}
void std_dmatrix(double *o, double **a, long nr, long nc)
/* Columnwise std of matrix a */
{
long i, j;
double tmp, dsum, *ave_a;
if (nr < 1)
nrerror("Number of samples < 1");
ave_a = dvector(1, nc);
mean_dmatrix(ave_a, a, nr, nc);
for (i = 1; i <= nc; i++) {
dsum = 0;
for (j = 1; j <= nr; j++) {
tmp = a[j][i] - ave_a[i];
dsum += DSQR(tmp);
}
o[i] = sqrt(dsum / (nr - 1));
}
free_dvector(ave_a, 1, nc);
}
double mean_dvector(double *a, long n)
{
long i;
double dsum = 0;
for (i = 1; i <= n; i++)
dsum += a[i];
return (dsum / n);
}
double std_dvector(double *a, long n)
{
long i;
double mean_a, dsum = 0, tmp;
if (n < 1)
nrerror("Number of samples < 1");
mean_a = mean_dvector(a, n);
for (i = 1; i <= n; i++) {
tmp = a[i] - mean_a;
dsum += DSQR(tmp);
}
return (sqrt(dsum / (n - 1)));
}
double dot_dvector(double *a, double *b, long n)
{
long i;
double dsum = 0;
for (i = 1; i <= n; i++)
dsum += a[i] * b[i];
return dsum;
}
void cross_dvector(double *o, double *a, double *b)
{
o[1] = a[2] * b[3] - a[3] * b[2];
o[2] = a[3] * b[1] - a[1] * b[3];
o[3] = a[1] * b[2] - a[2] * b[1];
}
double mag_dvector(double *a, long n)
/* Get the magnitude of a vector */
{
return (sqrt(dot_dvector(a, a, n)));
}
void norm_dvector(double *o, double *a, long n)
/* Normalize a vector */
{
long i;
double mag;
mag = mag_dvector(a, n);
if (mag <= EPS)
zero_dvector(o, n); /* a must be a zero vector */
else {
for (i = 1; i <= n; i++)
o[i] = a[i] / mag;
}
}
void lsplane(double *vec_normal, double *org_dist, double *pnts_dist,
double **xyz, long nr)
/* Get the LS plane */
{
long i, j, nrot, nc = 3;
double *d, **v, **cov_mtx;
d = dvector(1, nc);
v = dmatrix(1, nc, 1, nc);
cov_mtx = dmatrix(1, nc, 1, nc);
cov_dmatrix(cov_mtx, xyz, nr, nc);
jacobi(cov_mtx, nc, d, v, &nrot);
eigsrt(d, v, nc);
for (i = 1; i <= nc; i++)
vec_normal[i] = v[i][nc];
if ((d[1] - d[nc]) <= EPS) {
vec_normal[1] = 0;
vec_normal[2] = 0;
vec_normal[3] = 1;
}
if (vec_normal[nc] < 0) {
for (i = 1; i <= nc; i++)
vec_normal[i] = -vec_normal[i];
}
mean_dmatrix(d, xyz, nr, nc);
*org_dist = dot_dvector(d, vec_normal, nc);
for (i = 1; i <= nr; i++) {
for (j = 1; j <= nc; j++)
pnts_dist[i] += xyz[i][j] * vec_normal[j];
pnts_dist[i] -= *org_dist;
}
free_dvector(d, 1, nc);
free_dmatrix(v, 1, nc, 1, nc);
free_dmatrix(cov_mtx, 1, nc, 1, nc);
}
void lsline(double *vec_line, double *xyzpoint, double *pnts_dist, double **xyz, long nr)
/* Get the LS line */
{
long i, j, nrot, nc = 3;
double *d, **v, **cov_mtx, *o;
d = dvector(1, nc);
v = dmatrix(1, nc, 1, nc);
cov_mtx = dmatrix(1, nc, 1, nc);
o = dvector(1, nc);
cov_dmatrix(cov_mtx, xyz, nr, nc);
jacobi(cov_mtx, nc, d, v, &nrot);
eigsrt(d, v, nc);
for (i = 1; i <= nc; i++)
vec_line[i] = v[i][1];
if ((d[1] - d[nc]) <= EPS) {
vec_line[1] = 0;
vec_line[2] = 0;
vec_line[3] = 1;
}
if (vec_line[nc] < 0) {
for (i = 1; i <= nc; i++)
vec_line[i] = -vec_line[i];
}
mean_dmatrix(xyzpoint, xyz, nr, nc);
for (i = 1; i <= nr; i++) {
for (j = 1; j <= nc; j++)
d[j] = xyz[i][j] - xyzpoint[j];
cross_dvector(o, d, vec_line);
pnts_dist[i] = mag_dvector(o, nc);
}
free_dvector(d, 1, nc);
free_dmatrix(v, 1, nc, 1, nc);
free_dmatrix(cov_mtx, 1, nc, 1, nc);
free_dvector(o, 1, nc);
}
void alignz(double **rotmat, double *rot_axis)
{
double mag, v12, c, s, *dircos, **Rz, **Rx;
dircos = dvector(1, 3);
Rz = dmatrix(1, 3, 1, 3);
Rx = dmatrix(1, 3, 1, 3);
mag = mag_dvector(rot_axis, 3);
if (mag <= EPS) {
identity_dmatrix(rotmat, 3);
return;
} else
norm_dvector(dircos, rot_axis, 3);
/* Rotate about z-axis to make <dircos> in yz-plane */
v12 = dist_ab(dircos[1], dircos[2]);
if (v12 <= EPS)
identity_dmatrix(Rz, 3);
else {
c = dircos[2] / v12;
s = dircos[1] / v12;
Rz[1][1] = c;
Rz[1][2] = -s;
Rz[1][3] = 0.0;
Rz[2][1] = s;
Rz[2][2] = c;
Rz[2][3] = 0.0;
Rz[3][1] = 0.0;
Rz[3][2] = 0.0;
Rz[3][3] = 1.0;
}
/* Rotate about x-axis to make <dircos> align with +z-axis */
Rx[1][1] = 1.0;
Rx[1][2] = 0.0;
Rx[1][3] = 0.0;
Rx[2][1] = 0.0;
Rx[2][2] = dircos[3];
Rx[2][3] = -v12;
Rx[3][1] = 0.0;
Rx[3][2] = v12;
Rx[3][3] = dircos[3];
/* Final rotation matrix */
mul_dmatrix(rotmat, Rx, Rz, 3, 3, 3, 3);
free_dvector(dircos, 1, 3);
free_dmatrix(Rz, 1, 3, 1, 3);
free_dmatrix(Rx, 1, 3, 1, 3);
}
void arbrot(double **rotmat, double *rot_axis, double theta)
{
double mag, v12, c, s, ang;
double *dircos, **Rz, **Rx, **R, **tmp, **tmpT;
ang = deg2rad(theta);
dircos = dvector(1, 3);
Rz = dmatrix(1, 3, 1, 3);
Rx = dmatrix(1, 3, 1, 3);
R = dmatrix(1, 3, 1, 3);
tmp = dmatrix(1, 3, 1, 3);
tmpT = dmatrix(1, 3, 1, 3);
mag = mag_dvector(rot_axis, 3);
if (mag <= EPS) {
identity_dmatrix(rotmat, 3);
return;
} else
norm_dvector(dircos, rot_axis, 3);
/* Rotate about z-axis to make <dircos> in yz-plane */
v12 = dist_ab(dircos[1], dircos[2]);
if (v12 <= EPS)
identity_dmatrix(Rz, 3);
else {
c = dircos[2] / v12;
s = dircos[1] / v12;
Rz[1][1] = c;
Rz[1][2] = -s;
Rz[1][3] = 0.0;
Rz[2][1] = s;
Rz[2][2] = c;
Rz[2][3] = 0.0;
Rz[3][1] = 0.0;
Rz[3][2] = 0.0;
Rz[3][3] = 1.0;
}
/* Rotate about x-axis to make <dircos> align with +z-axis */
Rx[1][1] = 1.0;
Rx[1][2] = 0.0;
Rx[1][3] = 0.0;
Rx[2][1] = 0.0;
Rx[2][2] = dircos[3];
Rx[2][3] = -v12;
Rx[3][1] = 0.0;
Rx[3][2] = v12;
Rx[3][3] = dircos[3];
/* Real rotation is about z-axis by <ang> */
c = cos(ang);
s = sin(ang);
R[1][1] = c;
R[1][2] = -s;
R[1][3] = 0.0;
R[2][1] = s;
R[2][2] = c;
R[2][3] = 0.0;
R[3][1] = 0.0;
R[3][2] = 0.0;
R[3][3] = 1.0;
/* Final rotation matrix */
mul_dmatrix(tmp, Rx, Rz, 3, 3, 3, 3);
mul_dmatrix(rotmat, R, tmp, 3, 3, 3, 3);
tr_dmatrix(tmpT, Rx, 3, 3);
mul_dmatrix(tmp, tmpT, rotmat, 3, 3, 3, 3);
tr_dmatrix(tmpT, Rz, 3, 3);
mul_dmatrix(rotmat, tmpT, tmp, 3, 3, 3, 3);
free_dvector(dircos, 1, 3);
free_dmatrix(Rz, 1, 3, 1, 3);
free_dmatrix(Rx, 1, 3, 1, 3);
free_dmatrix(R, 1, 3, 1, 3);
free_dmatrix(tmp, 1, 3, 1, 3);
free_dmatrix(tmpT, 1, 3, 1, 3);
}
double magang(double *veca, double *vecb)
/* Get the magnitude of angle in degrees between two vectors */
{
double *na, *nb, dval, ang;
na = dvector(1, 3);
nb = dvector(1, 3);
/* Get the normalized vectors */
norm_dvector(na, veca, 3);
norm_dvector(nb, vecb, 3);
/* Get the angle in degrees */
dval = dot_dvector(na, nb, 3);
/* Special case: due to round off error, abs(dval) could > 1.0!!! */
if (dval > 1.0)
dval = 1.0;
if (dval < -1.0)
dval = -1.0;
ang = rad2deg(acos(dval));
free_dvector(na, 1, 3);
free_dvector(nb, 1, 3);
return ang;
}
double vec_ang(double *veca, double *vecb, double *vec_ref)
/* <veca> & <vecb> will be normalized in "magang"
<vec_ref> is used for sign control and does NOT need to be normalized
ang_deg> in the range of [-180, +180] */
{
double ang, *aXb;
aXb = dvector(1, 3);
ang = magang(veca, vecb);
cross_dvector(aXb, veca, vecb);
if (dot_dvector(aXb, vec_ref, 3) < 0)
ang = -ang;
free_dvector(aXb, 1, 3);
return ang;
}
void bpfunc(double **orien, double *pos, double *param)
/* The order of the 6 base-pair parameters should be:
% x y z x y z
% SHEAR STRETCH STAGGER BUCKLE PROPELLER OPENING
*/
{
long i, j;
double propeller, opening, buckle, stretch, stagger, shear;
double buckleopening, phi, dsum;
double *a, *b, *r, **tmp1, **tmp2, **mbp_orien;
a = dvector(1, 3);
b = dvector(1, 3);
r = dvector(1, 3);
tmp1 = dmatrix(1, 3, 1, 3);
tmp2 = dmatrix(1, 3, 1, 3);
mbp_orien = dmatrix(1, 3, 1, 3);
shear = param[1];
stretch = param[2];
stagger = param[3];
buckle = param[4];
propeller = param[5];
opening = param[6];
buckleopening = dist_ab(opening, buckle);
a[1] = buckle;
a[2] = 0;
a[3] = opening;
b[1] = 1.0;
b[2] = 0.0;
b[3] = 0.0;
r[1] = 0.0;
r[2] = 1.0;
r[3] = 0.0;
phi = vec_ang(a, b, r);
roty(orien, 0.5 * propeller - phi);
rotx(tmp1, buckleopening);
mul_dmatrix(tmp2, orien, tmp1, 3, 3, 3, 3);
roty(tmp1, 0.5 * propeller + phi);
mul_dmatrix(orien, tmp2, tmp1, 3, 3, 3, 3);
roty(mbp_orien, 0.5 * propeller - phi);
rotx(tmp1, 0.5 * buckleopening);
mul_dmatrix(tmp2, mbp_orien, tmp1, 3, 3, 3, 3);
roty(tmp1, phi);
mul_dmatrix(mbp_orien, tmp2, tmp1, 3, 3, 3, 3);
a[1] = shear;
a[2] = stretch;
a[3] = stagger;
tr_dmatrix(tmp1, mbp_orien, 3, 3);
for (i = 1; i <= 3; i++) {
dsum = 0;
for (j = 1; j <= 3; j++)
dsum += a[j] * tmp1[j][i];
pos[i] = dsum;
}
free_dvector(a, 1, 3);
free_dvector(b, 1, 3);
free_dvector(r, 1, 3);
free_dmatrix(tmp1, 1, 3, 1, 3);
free_dmatrix(tmp2, 1, 3, 1, 3);
free_dmatrix(mbp_orien, 1, 3, 1, 3);
}
void stepfunc(double **orien, double **mst, double *pos, double *param)
/* The order of the 6 step parameters should be:
% x y z x y z
% SHIFT SLIDE RISE TILT ROLL TWIST
*/
{
long i, j;
double twist, roll, tilt, rise, slide, shift;
double rolltilt, phi, dsum;
double *a, *b, *r, **tmp1, **tmp2;
a = dvector(1, 3);
b = dvector(1, 3);
r = dvector(1, 3);
tmp1 = dmatrix(1, 3, 1, 3);
tmp2 = dmatrix(1, 3, 1, 3);
shift = param[1];
slide = param[2];
rise = param[3];
tilt = param[4];
roll = param[5];
twist = param[6];
rolltilt = dist_ab(tilt, roll);
a[1] = tilt;
a[2] = roll;
a[3] = 0.0;
b[1] = 0.0;
b[2] = 1.0;
b[3] = 0.0;
r[1] = 0.0;
r[2] = 0.0;
r[3] = 1.0;
phi = vec_ang(a, b, r);
rotz(orien, 0.5 * twist - phi);
roty(tmp1, rolltilt);
mul_dmatrix(tmp2, orien, tmp1, 3, 3, 3, 3);
rotz(tmp1, 0.5 * twist + phi);
mul_dmatrix(orien, tmp2, tmp1, 3, 3, 3, 3);
rotz(mst, 0.5 * twist - phi);
roty(tmp1, 0.5 * rolltilt);
mul_dmatrix(tmp2, mst, tmp1, 3, 3, 3, 3);
rotz(tmp1, phi);
mul_dmatrix(mst, tmp2, tmp1, 3, 3, 3, 3);
a[1] = shift;
a[2] = slide;
a[3] = rise;
tr_dmatrix(tmp1, mst, 3, 3);
for (i = 1; i <= 3; i++) {
dsum = 0;
for (j = 1; j <= 3; j++)
dsum += a[j] * tmp1[j][i];
pos[i] = dsum;
}
free_dvector(a, 1, 3);
free_dvector(b, 1, 3);
free_dvector(r, 1, 3);
free_dmatrix(tmp1, 1, 3, 1, 3);
free_dmatrix(tmp2, 1, 3, 1, 3);
}
void cirshift(long *o, long *a, long n, long m)
{
long i, j, ipm;
for (i = 1; i <= n; i++) {
ipm = i + m;
if (ipm <= 0)
ipm = ipm + n;
if (ipm <= n)
o[ipm] = a[i];
else {
j = ipm % n;
o[j] = a[i];
}
}
}
void vec_orth(double *o, double *veca, double *vecb)
{
long n = 3;
double *nb, *tmp1, *tmp2;
nb = dvector(1, n);
tmp1 = dvector(1, n);
tmp2 = dvector(1, n);