/* "dblock_projections2" CALCULATES THE PROJECTION
FROM FULL RESIDUE SPACE TO RIGID BLOCK SPACE */
int dblock_projections2(dSparse_Matrix *PP,PDB_File *PDB,
int nres,int nblx,int bmx)
{
double **X,**I,**IC,*CM,*W,**A,**ISQT;
double x,tr,dd,df;
int *IDX,nbp,b,i,j,k,ii,jj,aa,bb,elm;
/* INITIALIZE BLOCK ARRAYS */
elm=0;
X=dmatrix(1,bmx,1,3);
IDX=ivector(1,bmx);
CM=dvector(1,3);
I=dmatrix(1,3,1,3);
IC=dmatrix(1,3,1,3);
W=dvector(1,3);
A=dmatrix(1,3,1,3);
ISQT=dmatrix(1,3,1,3);
/* CYCLE THROUGH BLOCKS */
for(b=1;b<=nblx;b++){
/* CLEAR MATRICES */
for(j=1;j<=3;j++){
CM[j]=0.0;
for(i=1;i<=3;i++) I[i][j]=0.0;
for(i=1;i<=bmx;i++) X[i][j]=0.0;
}
/* STORE VALUES FOR CURRENT BLOCK */
nbp=0;
for(i=1;i<=nres;i++){
if(PDB->atom[i].model==b){
IDX[++nbp]=i;
for(j=1;j<=3;j++){
x=(double)PDB->atom[i].X[j-1];
X[nbp][j]=x;
CM[j]+=x;
}
}
}
/* TRANSLATE BLOCK CENTER OF MASS TO ORIGIN */
for(j=1;j<=3;j++) CM[j]/=(double)nbp;
for(i=1;i<=nbp;i++)
for(j=1;j<=3;j++)
X[i][j]-=CM[j];
/* CALCULATE INERTIA TENSOR */
for(k=1;k<=nbp;k++){
dd=0.0;
for(j=1;j<=3;j++){
df=X[k][j];
dd+=df*df;
}
for(i=1;i<=3;i++){
I[i][i]+=(dd-X[k][i]*X[k][i]);
for(j=i+1;j<=3;j++){
I[i][j]-=X[k][i]*X[k][j];
I[j][i]=I[i][j];
}
}
}
/* DIAGONALIZE INERTIA TENSOR */
for(i=1;i<=3;i++)
for(j=1;j<=3;j++)
IC[i][j]=I[i][j];
dsvdcmp(IC,3,3,W,A);
deigsrt(W,A,3);
righthand2(W,A,3);
/* FIND ITS SQUARE ROOT */
for(i=1;i<=3;i++)
for(j=1;j<=3;j++){
dd=0.0;
for(k=1;k<=3;k++)
dd+=A[i][k]*A[j][k]/sqrt(W[k]);
ISQT[i][j]=dd;
}
/* UPDATE PP WITH THE RIGID MOTIONS OF THE BLOCK */
tr=1.0/sqrt((double)nbp);
for(i=1;i<=nbp;i++){
/* TRANSLATIONS: 3*(IDX[i]-1)+1 = x-COORDINATE OF RESIDUE IDX[i];
6*(b-1)+1 = x-COORDINATE OF BLOCK b */
for(j=1;j<=3;j++){
elm++;
PP->IDX[elm][1] = 3*(IDX[i]-1)+j;
PP->IDX[elm][2] = 6*(b-1)+j;
PP->X[elm] = tr;
}
/* ROTATIONS */
if(nbp>1){
for(ii=1;ii<=3;ii++){
for(jj=1;jj<=3;jj++){
if(jj==1) {aa=2; bb=3;}
else if(jj==2) {aa=3; bb=1;}
else {aa=1; bb=2;}
dd=ISQT[ii][aa]*X[i][bb]-ISQT[ii][bb]*X[i][aa];
elm++;
PP->IDX[elm][1] = 3*(IDX[i]-1)+jj;
PP->IDX[elm][2] = 6*(b-1)+3+ii;
PP->X[elm] = dd;
}
}
}
}
}
free_dmatrix(X,1,bmx,1,3);
free_ivector(IDX,1,bmx);
free_dvector(CM,1,3);
free_dmatrix(I,1,3,1,3);
free_dmatrix(IC,1,3,1,3);
free_dvector(W,1,3);
free_dmatrix(A,1,3,1,3);
free_dmatrix(ISQT,1,3,1,3);
return elm;
}
void rotation(double *vo, double *vt, int n, symatrix &R)
{ int i,j,k;
symatrix A(4),AT(4),C(4),W(3),W2(3),RS(3);
double **B,**U,eval[5],gamma;
// char s[100];
B = dmatrix(1,4,1,4);
U = dmatrix(1,4,1,4);
for (i = 1; i <= 4; i++)
for (j = 1; j <= 4; j++)
B[i][j] = 0.0;
for (i = 0; i < 4; i++) A.el(i,i) = 0.0;
for (k = 0; k < n; k++)
{
A.el(0,1) = vo[3*k+2] + vt[3*k+2];
A.el(0,2) = -vo[3*k+1] - vt[3*k+1];
A.el(1,2) = vo[3*k] + vt[3*k];
for (i = 0; i < 3; i++) A.el(i,3) = vo[3*k+i] - vt[3*k+i];
for (i = 1; i < 4; i++)
for (j = 0; j < i; j++)
A.el(i,j) = -A.el(j,i);
AT = A.transpose();
C = A * AT;
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
{ B[i+1][j+1] += C.el(i,j);
}
}
djacobi(B,4,eval,U,&i);
deigsrt(eval,U,4);
R.identity();
RS.identity();
gamma = 2 * acos(U[4][4]);
for (i = 0; i < 3; i++) W.el(i,i) = 0.0;
W.el(0,1) = U[3][4] / sin(gamma/2);
W.el(0,2) = -U[2][4] / sin(gamma/2);
W.el(1,2) = U[1][4] / sin(gamma/2);
for (i = 1; i < 3; i++)
for (j = 0; j < i; j++)
W.el(i,j) = - W.el(j,i);
W2 = W * W;
for (i = 0; i < 3; i++)
{ W.multiply_col(i,sin(gamma));
W2.multiply_col(i,1-cos(gamma));
}
RS += (W + W2);
RS = RS.transpose();
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
R.el(i,j) = RS.el(i,j);
free_dmatrix(B,1,4,1,4);
free_dmatrix(U,1,4,1,4);
}
