/*
 *                    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 org.biojava.nbio.structure.jama.Matrix;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;

import javax.vecmath.Matrix3d;
import javax.vecmath.Matrix4d;
import javax.vecmath.Point3d;
import javax.vecmath.Vector3d;

/**
 * Utility operations on Atoms, AminoAcids, etc.
 * <p>
 * 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, but unfortunately this is not a part of standard
 * java installations, since it comes with java3d. So to keep things
 * simple at the moment biojava does not depend on java3d.
 *
 * @author Andreas Prlic
 * @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.getCoords());
                Vector3d vb = new Vector3d(b.getCoords());

                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) {
                AtomIterator iter = new AtomIterator(group) ;

                while (iter.hasNext()) {
                        Atom atom = iter.next() ;
                        transform(atom,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) {
                AtomIterator iter = new AtomIterator(structure) ;

                while (iter.hasNext()) {
                        Atom atom = iter.next() ;
                        transform(atom,m);

                }
        }

        /**
         * Transforms a chain 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 chain
         * @param m
         */
        public static final void transform (Chain chain, Matrix4d m) {

                for (Group g:chain.getAtomGroups()) {
                        for (Atom atom: g.getAtoms()) {
                                transform(atom,m);
                        }
                }
        }

        /**
         * Translates an atom object, given a Vector3d (i.e. the vecmath library
         * double-precision 3-d vector)
         * @param atom
         * @param v
         */
        public static final void translate (Atom atom, Vector3d v) {

                atom.setX(atom.getX()+v.x);
                atom.setY(atom.getY()+v.y);
                atom.setZ(atom.getZ()+v.z);
        }

        /**
         * Translates a group object, given a Vector3d (i.e. the vecmath library
         * double-precision 3-d vector)
         * @param group
         * @param v
         */
        public static final void translate (Group group, Vector3d v) {
                AtomIterator iter = new AtomIterator(group) ;

                while (iter.hasNext()) {
                        Atom atom = iter.next() ;
                        translate(atom,v);

                }
        }

        /**
         * Translates a chain object, given a Vector3d (i.e. the vecmath library
         * double-precision 3-d vector)
         * @param chain
         * @param v
         */
        public static final void translate (Chain chain, Vector3d v) {

                for (Group g:chain.getAtomGroups()) {
                        for (Atom atom: g.getAtoms()) {
                                translate(atom,v);
                        }
                }
        }

        /**
         * Translates a Structure object, given a Vector3d (i.e. the vecmath library
         * double-precision 3-d vector)
         * @param structure
         * @param v
         */
        public static final void translate (Structure structure, Vector3d v) {
                AtomIterator iter = new AtomIterator(structure) ;

                while (iter.hasNext()) {
                        Atom atom = iter.next() ;
                        translate(atom,v);

                }
        }

        /** calculate structure + Matrix coodinates ...
         *
         * @param s the structure to operate on
         * @param matrix a Matrix object
         */
        public static final void plus(Structure s, Matrix matrix){
                AtomIterator iter = new AtomIterator(s) ;
                Atom oldAtom = null;
                Atom rotOldAtom = null;
                while (iter.hasNext()) {
                        Atom atom = null ;

                        atom = iter.next() ;
                        try {
                                if ( oldAtom != null){
                                        logger.debug("before {}", getDistance(oldAtom,atom));
                                }
                        } catch (Exception e){
                                logger.error("Exception: ", e);
                        }
                        oldAtom = (Atom)atom.clone();

                        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.plus(matrix);

                        double[] coords = new double[3] ;
                        coords[0] = na.get(0,0);
                        coords[1] = na.get(0,1);
                        coords[2] = na.get(0,2);
                        atom.setCoords(coords);
                        try {
                                if ( rotOldAtom != null){
                                        logger.debug("after {}", getDistance(rotOldAtom,atom));
                                }
                        } catch (Exception e){
                                logger.error("Exception: ", e);
                        }
                        rotOldAtom  = (Atom) atom.clone();
                }

        }



        /** shift a structure with a vector.
         *
         * @param structure  a Structure object
         * @param a          an Atom object representing a shift vector
         */
        public static final void shift(Structure structure, Atom a ){

                AtomIterator iter = new AtomIterator(structure) ;
                while (iter.hasNext() ) {
                        Atom atom = null ;

                        atom = iter.next()  ;

                        Atom natom = add(atom,a);
                        double x = natom.getX();
                        double y = natom.getY() ;
                        double z = natom.getZ();
                        atom.setX(x);
                        atom.setY(y);
                        atom.setZ(z);

                }
        }

        /** Shift a vector.
         *
         * @param a vector a
         * @param b vector b
         */
        public static final void shift(Atom a, Atom b){

                Atom natom = add(a,b);
                double x = natom.getX();
                double y = natom.getY() ;
                double z = natom.getZ();
                a.setX(x);
                a.setY(y);
                a.setZ(z);
        }

        /** Shift a Group with a vector.
         *
         * @param group   a group object
         * @param a          an Atom object representing a shift vector
         */
        public static final void shift(Group group , Atom a ){

                AtomIterator iter = new AtomIterator(group) ;
                while (iter.hasNext() ) {
                        Atom atom = null ;

                        atom = iter.next()  ;

                        Atom natom = add(atom,a);
                        double x = natom.getX();
                        double y = natom.getY() ;
                        double z = natom.getZ();
                        atom.setX(x);
                        atom.setY(y);
                        atom.setZ(z);

                }
        }



        /** 
         * Returns the center  of mass of the set of atoms.
         * @param atomSet a set of Atoms
         * @return an Atom representing the Centroid of the set of atoms
         */
        public static final Atom getCentroid(Atom[] atomSet){

                // if we don't catch this case, the centroid returned is (NaN,NaN,NaN), which can cause lots of problems down the line
                if (atomSet.length==0) 
                        throw new IllegalArgumentException("Atom array has length 0, can't calculate centroid!");
                
                double[] coords = new double[3];

                coords[0] = 0;
                coords[1] = 0;
                coords[2] = 0 ;

                for (Atom a : atomSet) {
                        coords[0] += a.getX();
                        coords[1] += a.getY();
                        coords[2] += a.getZ();
                }

                int n = atomSet.length;
                coords[0] = coords[0] / n;
                coords[1] = coords[1] / n;
                coords[2] = coords[2] / n;

                Atom vec = new AtomImpl();
                vec.setCoords(coords);
                return vec;

        }

        public static  Atom centerOfMass(Atom[] points) {
                Atom center = new AtomImpl();

                float totalMass = 0.0f;
                for (Atom a : points) {
                        float mass = a.getElement().getAtomicMass();
                        totalMass += mass;
                        center = scaleAdd(mass, a, center);
                }

                center = scaleEquals(center, 1.0f/totalMass);
                return center;
        }

        /**
         * Multiply elements of a by s (in place)
         * @param a
         * @param s
         * @return the modified a
         */
        public static Atom scaleEquals(Atom a, double s) {
                double x = a.getX();
                double y = a.getY();
                double z = a.getZ();

                x *= s;
                y *= s;
                z *= s;

                //Atom b = new AtomImpl();
                a.setX(x);
                a.setY(y);
                a.setZ(z);

                return a;
        }

        /**
         * Multiply elements of a by s
         * @param a
         * @param s
         * @return A new Atom with s*a
         */
        public static Atom scale(Atom a, double s) {
                double x = a.getX();
                double y = a.getY();
                double z = a.getZ();

                Atom b = new AtomImpl();
                b.setX(x*s);
                b.setY(y*s);
                b.setZ(z*s);

                return b;
        }


        /**
         * Perform linear transformation s*X+B, and store the result in b
         * @param s Amount to scale x
         * @param x Input coordinate
         * @param b Vector to translate (will be modified)
         * @return b, after modification
         */
        public static Atom scaleAdd(double s, Atom x, Atom b){

                double xc = s*x.getX() + b.getX();
                double yc = s*x.getY() + b.getY();
                double zc = s*x.getZ() + b.getZ();

                //Atom a = new AtomImpl();
                b.setX(xc);
                b.setY(yc);
                b.setZ(zc);

                return b;
        }

        /** Returns the Vector that needs to be applied to shift a set of atoms
         * to the Centroid.
         * @param atomSet array of Atoms
         * @return the vector needed to shift the set of atoms to its geometric center
         */
        public static final Atom getCenterVector(Atom[] atomSet){
                Atom centroid = getCentroid(atomSet);

                return getCenterVector(atomSet,centroid);

        }

        /** Returns the Vector that needs to be applied to shift a set of atoms
         * to the Centroid, if the centroid is already known
         * @param atomSet array of Atoms
         * @return the vector needed to shift the set of atoms to its geometric center
         */
        public static final Atom getCenterVector(Atom[] atomSet, Atom centroid){


                double[] coords = new double[3];
                coords[0] = 0 - centroid.getX();
                coords[1] = 0 - centroid.getY();
                coords[2] = 0 - centroid.getZ();

                Atom shiftVec = new AtomImpl();
                shiftVec.setCoords(coords);
                return shiftVec;

        }


        /** Center the atoms at the Centroid.
         * @param atomSet a set of Atoms
         * @return an Atom representing the Centroid of the set of atoms
         * @throws StructureException
         * */
        public static final Atom[] centerAtoms(Atom[] atomSet) throws StructureException {

                Atom centroid = getCentroid(atomSet);
                return centerAtoms(atomSet, centroid);
        }

        /** Center the atoms at the Centroid, if the centroid is already know.
         * @param atomSet a set of Atoms
         * @return an Atom representing the Centroid of the set of atoms
         * @throws StructureException
         * */
        public static final Atom[] centerAtoms(Atom[] atomSet, Atom centroid) throws StructureException {

                Atom shiftVector = getCenterVector(atomSet, centroid);

                Atom[] newAtoms = new AtomImpl[atomSet.length];

                for (int i =0 ; i < atomSet.length; i++){
                        Atom a = atomSet[i];
                        Atom n = add(a,shiftVector);
                        newAtoms[i] = n ;
                }
                return newAtoms;
        }




        /** creates a virtual C-beta atom. this might be needed when working with GLY
         *
         * thanks to Peter Lackner for a python template of this method.
         * @param amino the amino acid for which a "virtual" CB atom should be calculated
         * @return a "virtual" CB atom
         * @throws StructureException
         */
        public static final Atom createVirtualCBAtom(AminoAcid amino)
                        throws StructureException{

                AminoAcid  ala = StandardAminoAcid.getAminoAcid("ALA");
                Atom aN  = ala.getN();
                Atom aCA = ala.getCA();
                Atom aC  = ala.getC();
                Atom aCB = ala.getCB();


                Atom[] arr1 = new Atom[3];
                arr1[0] = aN;
                arr1[1] = aCA;
                arr1[2] = aC;

                Atom[] arr2 = new Atom[3];
                arr2[0] = amino.getN();
                arr2[1] = amino.getCA();
                arr2[2] = amino.getC();

                // ok now we got the two arrays, do a SVD:

                SVDSuperimposer svd = new SVDSuperimposer(arr2,arr1);

                Matrix rotMatrix = svd.getRotation();
                Atom tranMatrix = svd.getTranslation();

                Calc.rotate(aCB,rotMatrix);

                Atom virtualCB = Calc.add(aCB,tranMatrix);
                virtualCB.setName("CB");

                return virtualCB;
        }


        /**
         * Gets euler angles for a matrix given in ZYZ convention.
         * (as e.g. used by Jmol)
         *
         * @param m the rotation matrix
         * @return the euler values for a rotation around Z, Y, Z in degrees...
         */
        public static final double[] getZYZEuler(Matrix m) {
                double m22 = m.get(2,2);
                double rY = Math.toDegrees(Math.acos(m22));
                double rZ1, rZ2;
                if (m22 > .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 matrix
         * @return 4x4 transformation matrix
         */
        public static Matrix4d getTransformation(Matrix rot, Matrix trans) {
                return new Matrix4d( new Matrix3d(rot.getColumnPackedCopy()),
                                new Vector3d(trans.getColumnPackedCopy()),
                                1.0);
        }

        /**
         * 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.getCoords()),
                                1.0);
        }

        /**
         * Convert Vecmath transformation into a JAMA rotation 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 transform Matrix4d with transposed rotation matrix
         * @return
         */
        public static Matrix getRotationMatrix(Matrix4d transform){

                Matrix rot = new Matrix(3,3);
                for (int i=0;i<3;i++) {
                        for (int j=0;j<3;j++) {
                                rot.set(j, i, transform.getElement(i, j)); //transposed
                        }
                }
                return rot;
        }

        /**
         * Extract the translational vector of a Vecmath transformation.
         *
         * @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] = new Point3d(atoms[i].getCoords());
                }
                return points;
        }
}