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// $Id: mmdb_math.cpp $
// =================================================================
//
// CCP4 Coordinate Library: support of coordinate-related
// functionality in protein crystallography applications.
//
// Copyright (C) Eugene Krissinel 2000-2013.
//
// This library is free software: you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License version 3, modified in accordance with the provisions
// of the license to address the requirements of UK law.
//
// You should have received a copy of the modified GNU Lesser
// General Public License along with this library. If not, copies
// may be downloaded from http://www.ccp4.ac.uk/ccp4license.php
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// =================================================================
//
// 11.09.13 <-- Date of Last Modification.
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// -----------------------------------------------------------------
//
// **** Module : Math <implementation>
// ~~~~~~~~~
// **** Functions : mmdb::math::GetTorsion
// ~~~~~~~~~~~ mmdb::math::GetAngle
//
// (C) E. Krissinel 2000-2013
//
// =================================================================
//
#include <math.h>
#include "mmdb_math_.h"
namespace mmdb {
namespace math {
// --------------------------------------------------------------
realtype GetTorsion ( rvector U, rvector W, rvector V ) {
// U W V
// o<----o----->o----->o
//
realtype A[3],B[3],C[3],Wmag,S,T;
A[0] = U[1]*W[2] - W[1]*U[2];
A[1] = U[2]*W[0] - W[2]*U[0];
A[2] = U[0]*W[1] - W[0]*U[1];
B[0] = V[1]*W[2] - W[1]*V[2];
B[1] = V[2]*W[0] - W[2]*V[0];
B[2] = V[0]*W[1] - W[0]*V[1];
C[0] = A[1]*B[2] - B[1]*A[2];
C[1] = A[2]*B[0] - B[2]*A[0];
C[2] = A[0]*B[1] - B[0]*A[1];
Wmag = sqrt(W[0]*W[0]+W[1]*W[1]+W[2]*W[2]);
S = C[0]*W[0] + C[1]*W[1] + C[2]*W[2];
T = A[0]*B[0] + A[1]*B[1] + A[2]*B[2];
T *= Wmag;
if ((S==0.0) && (T==0.0)) return NO_TORSION;
else return atan2(S,T);
}
realtype GetAngle ( rvector v1, rvector v2 ) {
realtype l1,l2;
l1 = v1[0]*v1[0] + v1[1]*v1[1] + v1[2]*v1[2];
if (l1==0.0) l1 = 1.0;
l2 = v2[0]*v2[0] + v2[1]*v2[1] + v2[2]*v2[2];
if (l2==0.0) l2 = 1.0;
return acos((v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])/sqrt(l1*l2));
}
#define nCombMax 500
realtype Combinations ( int n, int m ) {
// 0<=n<=nCombMax, 0<=m<=n
realtype P[nCombMax+1];
int i,j;
if ((m<0) || (m>n)) return 0.0;
if ((m==0) || (m==n)) return 1.0;
if ((m==1) || (m==n-1)) return realtype(n);
P[0] = 1.0;
P[1] = 3.0;
P[2] = 3.0;
P[3] = 1.0;
for (i=4;i<=n;i++) {
P[i] = 1.0;
for (j=i-1;j>0;j--)
P[j] += P[j-1];
}
return P[m];
}
realtype log1mx ( realtype x ) {
// Calculates precisely log(1-x) for x<1, including
// very small x
realtype z,z1,z2,n;
if (x>=1.0-10.0*MachEps) z = -MaxReal;
else if (fabs(x)>1.0e-8) z = log(1.0-x);
else {
z1 = x;
z = 0.0;
n = 1.0;
do {
z2 = z;
z -= z1/n;
z1 *= x;
n += 1.0;
} while (z!=z2);
}
return z;
}
realtype expc ( realtype x ) {
// Calculates precisely 1 - exp(x) for any x including
// very small values
realtype z,z1,z2,n;
if (x>LnMaxReal) z = -MaxReal;
else if (x<-LnMaxReal) z = 1.0;
else if (fabs(x)>1.0e-8) z = 1.0 - Exp(x);
else {
z1 = x;
z = x;
n = 1.0;
do {
z2 = z;
n += 1.0;
z1 *= x/n;
z += z1;
} while (z!=z2);
z = -z;
}
return z;
}
realtype expc1mx ( realtype x, realtype y ) {
// Calculates precisely 1-(1-x)**y including very small x and
// very large y
realtype z,z1,z2,n,s;
// Calculate (1-x)**y as exp(y*log(1-x)). Get log(1-x) first:
if (x>1.0e-8) z = log(1.0-x);
else {
z1 = x;
z = 0.0;
n = 1.0;
do {
z2 = z;
z -= z1/n;
z1 *= x;
n += 1.0;
} while (z!=z2);
}
// Now calculate 1 - exp(y*log(1-x)) :
z *= y;
if (fabs(z)>1.0e-8) s = 1.0 - exp(z);
else {
z1 = z;
s = z;
n = 1.0;
do {
z2 = s;
n += 1.0;
z1 *= z/n;
s += z1;
} while (s!=z2);
s = -s;
}
return s;
}
}
}
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