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/*
* BioJava development code
*
* This code may be freely distributed and modified under the
* terms of the GNU Lesser General Public Licence. This should
* be distributed with the code. If you do not have a copy,
* see:
*
* http://www.gnu.org/copyleft/lesser.html
*
* Copyright for this code is held jointly by the individual
* authors. These should be listed in @author doc comments.
*
* For more information on the BioJava project and its aims,
* or to join the biojava-l mailing list, visit the home page
* at:
*
* http://www.biojava.org/
*
* Created on 08.05.2004
*
*/
package org.biojava.nbio.structure ;
import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import javax.vecmath.Matrix3d;
import javax.vecmath.Matrix4d;
import javax.vecmath.Point3d;
import javax.vecmath.Vector3d;
import org.biojava.nbio.structure.geometry.CalcPoint;
import org.biojava.nbio.structure.geometry.Matrices;
import org.biojava.nbio.structure.geometry.SuperPositionSVD;
import org.biojava.nbio.structure.jama.Matrix;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
/**
* Utility operations on Atoms, AminoAcids, Matrices, Point3d, etc.
*
* Currently the coordinates of an Atom are stored as an array of size 3
* (double[3]). It would be more powerful to use Point3d from javax.vecmath.
* Overloaded methods for Point3d operations exist in the {@link CalcPoint}
* Class.
*
* @author Andreas Prlic
* @author Aleix Lafita
* @since 1.4
* @version %I% %G%
*/
public class Calc {
private final static Logger logger = LoggerFactory.getLogger(Calc.class);
/**
* calculate distance between two atoms.
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return a double
*/
public static final double getDistance(Atom a, Atom b) {
double x = a.getX() - b.getX();
double y = a.getY() - b.getY();
double z = a.getZ() - b.getZ();
double s = x * x + y * y + z * z;
return Math.sqrt(s);
}
/**
* Will calculate the square of distances between two atoms. This will be
* faster as it will not perform the final square root to get the actual
* distance. Use this if doing large numbers of distance comparisons - it is
* marginally faster than getDistance().
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return a double
*/
public static double getDistanceFast(Atom a, Atom b) {
double x = a.getX() - b.getX();
double y = a.getY() - b.getY();
double z = a.getZ() - b.getZ();
return x * x + y * y + z * z;
}
public static final Atom invert(Atom a) {
double[] coords = new double[]{0.0,0.0,0.0} ;
Atom zero = new AtomImpl();
zero.setCoords(coords);
return subtract(zero, a);
}
/**
* add two atoms ( a + b).
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return an Atom object
*/
public static final Atom add(Atom a, Atom b){
Atom c = new AtomImpl();
c.setX( a.getX() + b.getX() );
c.setY( a.getY() + b.getY() );
c.setZ( a.getZ() + b.getZ() );
return c ;
}
/**
* subtract two atoms ( a - b).
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return n new Atom object representing the difference
*/
public static final Atom subtract(Atom a, Atom b) {
Atom c = new AtomImpl();
c.setX( a.getX() - b.getX() );
c.setY( a.getY() - b.getY() );
c.setZ( a.getZ() - b.getZ() );
return c ;
}
/**
* Vector product (cross product).
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return an Atom object
*/
public static final Atom vectorProduct(Atom a , Atom b){
Atom c = new AtomImpl();
c.setX( a.getY() * b.getZ() - a.getZ() * b.getY() ) ;
c.setY( a.getZ() * b.getX() - a.getX() * b.getZ() ) ;
c.setZ( a.getX() * b.getY() - a.getY() * b.getX() ) ;
return c ;
}
/**
* Scalar product (dot product).
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return a double
*/
public static final double scalarProduct(Atom a, Atom b) {
return a.getX() * b.getX() + a.getY() * b.getY() + a.getZ() * b.getZ();
}
/**
* Gets the length of the vector (2-norm)
*
* @param a
* an Atom object
* @return Square root of the sum of the squared elements
*/
public static final double amount(Atom a){
return Math.sqrt(scalarProduct(a,a));
}
/**
* Gets the angle between two vectors
*
* @param a
* an Atom object
* @param b
* an Atom object
* @return Angle between a and b in degrees, in range [0,180]. If either
* vector has length 0 then angle is not defined and NaN is returned
*/
public static final double angle(Atom a, Atom b){
Vector3d va = new Vector3d(a.getCoordsAsPoint3d());
Vector3d vb = new Vector3d(b.getCoordsAsPoint3d());
return Math.toDegrees(va.angle(vb));
}
/**
* Returns the unit vector of vector a .
*
* @param a
* an Atom object
* @return an Atom object
*/
public static final Atom unitVector(Atom a) {
double amount = amount(a) ;
double[] coords = new double[3];
coords[0] = a.getX() / amount ;
coords[1] = a.getY() / amount ;
coords[2] = a.getZ() / amount ;
a.setCoords(coords);
return a;
}
/**
* Calculate the torsion angle, i.e. the angle between the normal vectors of
* the two plains a-b-c and b-c-d. See
* http://en.wikipedia.org/wiki/Dihedral_angle
*
* @param a
* an Atom object
* @param b
* an Atom object
* @param c
* an Atom object
* @param d
* an Atom object
* @return the torsion angle in degrees, in range +-[0,180]. If either first
* 3 or last 3 atoms are colinear then torsion angle is not defined
* and NaN is returned
*/
public static final double torsionAngle(Atom a, Atom b, Atom c, Atom d) {
Atom ab = subtract(a,b);
Atom cb = subtract(c,b);
Atom bc = subtract(b,c);
Atom dc = subtract(d,c);
Atom abc = vectorProduct(ab,cb);
Atom bcd = vectorProduct(bc,dc);
double angl = angle(abc,bcd) ;
/* calc the sign: */
Atom vecprod = vectorProduct(abc,bcd);
double val = scalarProduct(cb,vecprod);
if (val < 0.0)
angl = -angl;
return angl;
}
/**
* Calculate the phi angle.
*
* @param a
* an AminoAcid object
* @param b
* an AminoAcid object
* @return a double
* @throws StructureException
* if aminoacids not connected or if any of the 4 needed atoms
* missing
*/
public static final double getPhi(AminoAcid a, AminoAcid b)
throws StructureException {
if ( ! isConnected(a,b)){
throw new StructureException(
"can not calc Phi - AminoAcids are not connected!");
}
Atom a_C = a.getC();
Atom b_N = b.getN();
Atom b_CA = b.getCA();
Atom b_C = b.getC();
// C and N were checked in isConnected already
if (b_CA == null)
throw new StructureException(
"Can not calculate Phi, CA atom is missing");
return torsionAngle(a_C,b_N,b_CA,b_C);
}
/**
* Calculate the psi angle.
*
* @param a
* an AminoAcid object
* @param b
* an AminoAcid object
* @return a double
* @throws StructureException
* if aminoacids not connected or if any of the 4 needed atoms
* missing
*/
public static final double getPsi(AminoAcid a, AminoAcid b)
throws StructureException {
if ( ! isConnected(a,b)) {
throw new StructureException(
"can not calc Psi - AminoAcids are not connected!");
}
Atom a_N = a.getN();
Atom a_CA = a.getCA();
Atom a_C = a.getC();
Atom b_N = b.getN();
// C and N were checked in isConnected already
if (a_CA == null)
throw new StructureException(
"Can not calculate Psi, CA atom is missing");
return torsionAngle(a_N,a_CA,a_C,b_N);
}
/**
* Test if two amino acids are connected, i.e. if the distance from C to N <
* 2.5 Angstrom.
*
* If one of the AminoAcids has an atom missing, returns false.
*
* @param a
* an AminoAcid object
* @param b
* an AminoAcid object
* @return true if ...
*/
public static final boolean isConnected(AminoAcid a, AminoAcid b) {
Atom C = null ;
Atom N = null;
C = a.getC();
N = b.getN();
if ( C == null || N == null)
return false;
// one could also check if the CA atoms are < 4 A...
double distance = getDistance(C,N);
return distance < 2.5;
}
/**
* Rotate a single Atom aroud a rotation matrix. The rotation Matrix must be
* a pre-multiplication 3x3 Matrix.
*
* If the matrix is indexed m[row][col], then the matrix will be
* pre-multiplied (y=atom*M)
*
* @param atom
* atom to be rotated
* @param m
* a rotation matrix represented as a double[3][3] array
*/
public static final void rotate(Atom atom, double[][] m){
double x = atom.getX();
double y = atom.getY() ;
double z = atom.getZ();
double nx = m[0][0] * x + m[0][1] * y + m[0][2] * z ;
double ny = m[1][0] * x + m[1][1] * y + m[1][2] * z ;
double nz = m[2][0] * x + m[2][1] * y + m[2][2] * z ;
atom.setX(nx);
atom.setY(ny);
atom.setZ(nz);
}
/**
* Rotate a structure. The rotation Matrix must be a pre-multiplication
* Matrix.
*
* @param structure
* a Structure object
* @param rotationmatrix
* an array (3x3) of double representing the rotation matrix.
* @throws StructureException
* ...
*/
public static final void rotate(Structure structure,
double[][] rotationmatrix) throws StructureException {
if ( rotationmatrix.length != 3 ) {
throw new StructureException ("matrix does not have size 3x3 !");
}
AtomIterator iter = new AtomIterator(structure) ;
while (iter.hasNext()) {
Atom atom = iter.next() ;
Calc.rotate(atom,rotationmatrix);
}
}
/**
* Rotate a Group. The rotation Matrix must be a pre-multiplication Matrix.
*
* @param group
* a group object
* @param rotationmatrix
* an array (3x3) of double representing the rotation matrix.
* @throws StructureException
* ...
*/
public static final void rotate(Group group, double[][] rotationmatrix)
throws StructureException {
if ( rotationmatrix.length != 3 ) {
throw new StructureException ("matrix does not have size 3x3 !");
}
AtomIterator iter = new AtomIterator(group) ;
while (iter.hasNext()) {
Atom atom = null ;
atom = iter.next() ;
rotate(atom,rotationmatrix);
}
}
/**
* Rotate an Atom around a Matrix object. The rotation Matrix must be a
* pre-multiplication Matrix.
*
* @param atom
* atom to be rotated
* @param m
* rotation matrix to be applied to the atom
*/
public static final void rotate(Atom atom, Matrix m){
double x = atom.getX();
double y = atom.getY();
double z = atom.getZ();
double[][] ad = new double[][]{{x,y,z}};
Matrix am = new Matrix(ad);
Matrix na = am.times(m);
atom.setX(na.get(0,0));
atom.setY(na.get(0,1));
atom.setZ(na.get(0,2));
}
/**
* Rotate a group object. The rotation Matrix must be a pre-multiplication
* Matrix.
*
* @param group
* a group to be rotated
* @param m
* a Matrix object representing the rotation matrix
*/
public static final void rotate(Group group, Matrix m){
AtomIterator iter = new AtomIterator(group) ;
while (iter.hasNext()) {
Atom atom = iter.next() ;
rotate(atom,m);
}
}
/**
* Rotate a structure object. The rotation Matrix must be a
* pre-multiplication Matrix.
*
* @param structure
* the structure to be rotated
* @param m
* rotation matrix to be applied
*/
public static final void rotate(Structure structure, Matrix m){
AtomIterator iter = new AtomIterator(structure) ;
while (iter.hasNext()) {
Atom atom = iter.next() ;
rotate(atom,m);
}
}
/**
* Transform an array of atoms at once. The transformation Matrix must be a
* post-multiplication Matrix.
*
* @param ca
* array of Atoms to shift
* @param t
* transformation Matrix4d
*/
public static void transform(Atom[] ca, Matrix4d t) {
for (Atom atom : ca)
Calc.transform(atom, t);
}
/**
* Transforms an atom object, given a Matrix4d (i.e. the vecmath library
* double-precision 4x4 rotation+translation matrix). The transformation
* Matrix must be a post-multiplication Matrix.
*
* @param atom
* @param m
*/
public static final void transform (Atom atom, Matrix4d m) {
Point3d p = new Point3d(atom.getX(),atom.getY(),atom.getZ());
m.transform(p);
atom.setX(p.x);
atom.setY(p.y);
atom.setZ(p.z);
}
/**
* Transforms a group object, given a Matrix4d (i.e. the vecmath library
* double-precision 4x4 rotation+translation matrix). The transformation
* Matrix must be a post-multiplication Matrix.
*
* @param group
* @param m
*/
public static final void transform(Group group, Matrix4d m) {
for (Atom atom : group.getAtoms()) {
transform(atom, m);
}
for (Group altG : group.getAltLocs()) {
transform(altG, m);
}
}
/**
* Transforms a structure object, given a Matrix4d (i.e. the vecmath library
* double-precision 4x4 rotation+translation matrix). The transformation
* Matrix must be a post-multiplication Matrix.
*
* @param structure
* @param m
*/
public static final void transform(Structure structure, Matrix4d m) {
for (int n=0; n .999d || m22 < -.999d) {
rZ1 = Math.toDegrees(Math.atan2(m.get(1,0), m.get(1,1)));
rZ2 = 0;
} else {
rZ1 = Math.toDegrees(Math.atan2(m.get(2,1), -m.get(2,0)));
rZ2 = Math.toDegrees(Math.atan2(m.get(1,2), m.get(0,2)));
}
return new double[] {rZ1,rY,rZ2};
}
/**
* Convert a rotation Matrix to Euler angles. This conversion uses
* conventions as described on page:
* http://www.euclideanspace.com/maths/geometry/rotations/euler/index.htm
* Coordinate System: right hand Positive angle: right hand Order of euler
* angles: heading first, then attitude, then bank
*
* @param m
* the rotation matrix
* @return a array of three doubles containing the three euler angles in
* radians
*/
public static final double[] getXYZEuler(Matrix m){
double heading, attitude, bank;
// Assuming the angles are in radians.
if (m.get(1,0) > 0.998) { // singularity at north pole
heading = Math.atan2(m.get(0,2),m.get(2,2));
attitude = Math.PI/2;
bank = 0;
} else if (m.get(1,0) < -0.998) { // singularity at south pole
heading = Math.atan2(m.get(0,2),m.get(2,2));
attitude = -Math.PI/2;
bank = 0;
} else {
heading = Math.atan2(-m.get(2,0),m.get(0,0));
bank = Math.atan2(-m.get(1,2),m.get(1,1));
attitude = Math.asin(m.get(1,0));
}
return new double[] { heading, attitude, bank };
}
/**
* This conversion uses NASA standard aeroplane conventions as described on
* page:
* http://www.euclideanspace.com/maths/geometry/rotations/euler/index.htm
* Coordinate System: right hand Positive angle: right hand Order of euler
* angles: heading first, then attitude, then bank. matrix row column
* ordering: [m00 m01 m02] [m10 m11 m12] [m20 m21 m22]
*
* @param heading
* in radians
* @param attitude
* in radians
* @param bank
* in radians
* @return the rotation matrix
*/
public static final Matrix matrixFromEuler(double heading, double attitude,
double bank) {
// Assuming the angles are in radians.
double ch = Math.cos(heading);
double sh = Math.sin(heading);
double ca = Math.cos(attitude);
double sa = Math.sin(attitude);
double cb = Math.cos(bank);
double sb = Math.sin(bank);
Matrix m = new Matrix(3,3);
m.set(0,0, ch * ca);
m.set(0,1, sh*sb - ch*sa*cb);
m.set(0,2, ch*sa*sb + sh*cb);
m.set(1,0, sa);
m.set(1,1, ca*cb);
m.set(1,2, -ca*sb);
m.set(2,0, -sh*ca);
m.set(2,1, sh*sa*cb + ch*sb);
m.set(2,2, -sh*sa*sb + ch*cb);
return m;
}
/**
* Calculates the angle from centerPt to targetPt in degrees. The return
* should range from [0,360), rotating CLOCKWISE, 0 and 360 degrees
* represents NORTH, 90 degrees represents EAST, etc...
*
* Assumes all points are in the same coordinate space. If they are not, you
* will need to call SwingUtilities.convertPointToScreen or equivalent on
* all arguments before passing them to this function.
*
* @param centerPt
* Point we are rotating around.
* @param targetPt
* Point we want to calculate the angle to.
* @return angle in degrees. This is the angle from centerPt to targetPt.
*/
public static double calcRotationAngleInDegrees(Atom centerPt, Atom targetPt) {
// calculate the angle theta from the deltaY and deltaX values
// (atan2 returns radians values from [-PI,PI])
// 0 currently points EAST.
// NOTE: By preserving Y and X param order to atan2, we are expecting
// a CLOCKWISE angle direction.
double theta = Math.atan2(targetPt.getY() - centerPt.getY(),
targetPt.getX() - centerPt.getX());
// rotate the theta angle clockwise by 90 degrees
// (this makes 0 point NORTH)
// NOTE: adding to an angle rotates it clockwise.
// subtracting would rotate it counter-clockwise
theta += Math.PI/2.0;
// convert from radians to degrees
// this will give you an angle from [0->270],[-180,0]
double angle = Math.toDegrees(theta);
// convert to positive range [0-360)
// since we want to prevent negative angles, adjust them now.
// we can assume that atan2 will not return a negative value
// greater than one partial rotation
if (angle < 0) {
angle += 360;
}
return angle;
}
public static void main(String[] args){
Atom a =new AtomImpl();
a.setX(0);
a.setY(0);
a.setZ(0);
Atom b = new AtomImpl();
b.setX(1);
b.setY(1);
b.setZ(0);
logger.info("Angle between atoms: ", calcRotationAngleInDegrees(a, b));
}
public static void rotate(Atom[] ca, Matrix matrix) {
for (Atom atom : ca)
Calc.rotate(atom, matrix);
}
/**
* Shift an array of atoms at once.
*
* @param ca
* array of Atoms to shift
* @param b
* reference Atom vector
*/
public static void shift(Atom[] ca, Atom b) {
for (Atom atom : ca)
Calc.shift(atom, b);
}
/**
* Convert JAMA rotation and translation to a Vecmath transformation matrix.
* Because the JAMA matrix is a pre-multiplication matrix and the Vecmath
* matrix is a post-multiplication one, the rotation matrix is transposed to
* ensure that the transformation they produce is the same.
*
* @param rot
* 3x3 Rotation matrix
* @param trans
* 3x1 translation vector in Atom coordinates
* @return 4x4 transformation matrix
*/
public static Matrix4d getTransformation(Matrix rot, Atom trans) {
return new Matrix4d(new Matrix3d(rot.getColumnPackedCopy()),
new Vector3d(trans.getCoordsAsPoint3d()), 1.0);
}
/**
* Extract the translational vector as an Atom of a transformation matrix.
*
* @param transform
* Matrix4d
* @return Atom shift vector
*/
public static Atom getTranslationVector(Matrix4d transform){
Atom transl = new AtomImpl();
double[] coords = {transform.m03, transform.m13, transform.m23};
transl.setCoords(coords);
return transl;
}
/**
* Convert an array of atoms into an array of vecmath points
*
* @param atoms
* list of atoms
* @return list of Point3ds storing the x,y,z coordinates of each atom
*/
public static Point3d[] atomsToPoints(Atom[] atoms) {
Point3d[] points = new Point3d[atoms.length];
for(int i = 0; i< atoms.length;i++) {
points[i] = atoms[i].getCoordsAsPoint3d();
}
return points;
}
/**
* Convert an array of atoms into an array of vecmath points
*
* @param atoms
* list of atoms
* @return list of Point3ds storing the x,y,z coordinates of each atom
*/
public static List atomsToPoints(Collection atoms) {
ArrayList points = new ArrayList<>(atoms.size());
for (Atom atom : atoms) {
points.add(atom.getCoordsAsPoint3d());
}
return points;
}
/**
* Calculate the RMSD of two Atom arrays, already superposed.
*
* @param x
* array of Atoms superposed to y
* @param y
* array of Atoms superposed to x
* @return RMSD
*/
public static double rmsd(Atom[] x, Atom[] y) {
return CalcPoint.rmsd(atomsToPoints(x), atomsToPoints(y));
}
/**
* Calculate the TM-Score for the superposition.
*
* Normalizes by the minimum-length structure (that is, {@code min\{len1,len2\}}).
*
* Atom sets must be pre-rotated.
*
*
* Citation:
* Zhang Y and Skolnick J (2004). "Scoring function for automated
* assessment of protein structure template quality". Proteins 57: 702 -
* 710.
*
* @param atomSet1
* atom array 1
* @param atomSet2
* atom array 2
* @param len1
* The full length of the protein supplying atomSet1
* @param len2
* The full length of the protein supplying atomSet2
* @return The TM-Score
* @throws StructureException
*/
public static double getTMScore(Atom[] atomSet1, Atom[] atomSet2, int len1, int len2) throws StructureException {
return getTMScore(atomSet1, atomSet2, len1, len2,true);
}
/**
* Calculate the TM-Score for the superposition.
*
* Atom sets must be pre-rotated.
*
*
* Citation:
* Zhang Y and Skolnick J (2004). "Scoring function for automated
* assessment of protein structure template quality". Proteins 57: 702 -
* 710.
*
* @param atomSet1
* atom array 1
* @param atomSet2
* atom array 2
* @param len1
* The full length of the protein supplying atomSet1
* @param len2
* The full length of the protein supplying atomSet2
* @param normalizeMin
* Whether to normalize by the minimum-length structure,
* that is, {@code min\{len1,len2\}}. If false, normalized by the {@code max\{len1,len2\}}).
*
* @return The TM-Score
* @throws StructureException
*/
public static double getTMScore(Atom[] atomSet1, Atom[] atomSet2, int len1,
int len2, boolean normalizeMin) throws StructureException {
if (atomSet1.length != atomSet2.length) {
throw new StructureException(
"The two atom sets are not of same length!");
}
if (atomSet1.length > len1) {
throw new StructureException(
"len1 must be greater or equal to the alignment length!");
}
if (atomSet2.length > len2) {
throw new StructureException(
"len2 must be greater or equal to the alignment length!");
}
int Lnorm;
if (normalizeMin) {
Lnorm = Math.min(len1, len2);
} else {
Lnorm = Math.max(len1, len2);
}
int Laln = atomSet1.length;
double d0 = 1.24 * Math.cbrt(Lnorm - 15.) - 1.8;
double d0sq = d0 * d0;
double sum = 0;
for (int i = 0; i < Laln; i++) {
double d = Calc.getDistance(atomSet1[i], atomSet2[i]);
sum += 1. / (1 + d * d / d0sq);
}
return sum / Lnorm;
}
}