Package org.biojava.nbio.structure

Class Calc

  • public class Calc
extends Object
    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 CalcPoint Class.

    Since:
    1.4
    Version:
    %I% %G%
    Author:
    Andreas Prlic, Aleix Lafita

    • Constructor Summary

      Constructors 
      Constructor Description
      Calc()  

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static Atom add​(Atom a, Atom b)
      add two atoms ( a + b).
      static double amount​(Atom a)
      Gets the length of the vector (2-norm)
      static double angle​(Atom a, Atom b)
      Gets the angle between two vectors
      static List<javax.vecmath.Point3d> atomsToPoints​(Collection<Atom> atoms)
      Convert an array of atoms into an array of vecmath points
      static javax.vecmath.Point3d[] atomsToPoints​(Atom[] atoms)
      Convert an array of atoms into an array of vecmath points
      static double calcRotationAngleInDegrees​(Atom centerPt, Atom targetPt)
      Calculates the angle from centerPt to targetPt in degrees.
      static Atom[] centerAtoms​(Atom[] atomSet)
      Center the atoms at the Centroid.
      static Atom[] centerAtoms​(Atom[] atomSet, Atom centroid)
      Center the atoms at the Centroid, if the centroid is already know.
      static Atom centerOfMass​(Atom[] points)
      Returns the center of mass of the set of atoms.
      static Atom createVirtualCBAtom​(AminoAcid amino)
      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.
      static Atom getCenterVector​(Atom[] atomSet)
      Returns the Vector that needs to be applied to shift a set of atoms to the Centroid.
      static Atom getCenterVector​(Atom[] atomSet, Atom centroid)
      Returns the Vector that needs to be applied to shift a set of atoms to the Centroid, if the centroid is already known
      static Atom getCentroid​(Atom[] atomSet)
      Returns the centroid of the set of atoms.
      static double getDistance​(Atom a, Atom b)
      calculate distance between two atoms.
      static double getDistanceFast​(Atom a, Atom b)
      Will calculate the square of distances between two atoms.
      static double getPhi​(AminoAcid a, AminoAcid b)
      Calculate the phi angle.
      static double getPsi​(AminoAcid a, AminoAcid b)
      Calculate the psi angle.
      static double getTMScore​(Atom[] atomSet1, Atom[] atomSet2, int len1, int len2)
      Calculate the TM-Score for the superposition.
      static double getTMScore​(Atom[] atomSet1, Atom[] atomSet2, int len1, int len2, boolean normalizeMin)
      Calculate the TM-Score for the superposition.
      static javax.vecmath.Matrix4d getTransformation​(Matrix rot, Atom trans)
      Convert JAMA rotation and translation to a Vecmath transformation matrix.
      static Atom getTranslationVector​(javax.vecmath.Matrix4d transform)
      Extract the translational vector as an Atom of a transformation matrix.
      static double[] getXYZEuler​(Matrix m)
      Convert a rotation Matrix to Euler angles.
      static double[] getZYZEuler​(Matrix m)
      Gets euler angles for a matrix given in ZYZ convention.
      static Atom invert​(Atom a)  
      static boolean isConnected​(AminoAcid a, AminoAcid b)
      Test if two amino acids are connected, i.e. if the distance from C to N < 2.5 Angstrom.
      static void main​(String[] args)  
      static Matrix matrixFromEuler​(double heading, double attitude, double 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]
      static void plus​(Structure s, Matrix matrix)
      calculate structure + Matrix coodinates ...
      static double rmsd​(Atom[] x, Atom[] y)
      Calculate the RMSD of two Atom arrays, already superposed.
      static void rotate​(Atom[] ca, Matrix matrix)  
      static void rotate​(Atom atom, double[][] m)
      Rotate a single Atom aroud a rotation matrix.
      static void rotate​(Atom atom, Matrix m)
      Rotate an Atom around a Matrix object.
      static void rotate​(Group group, double[][] rotationmatrix)
      Rotate a Group.
      static void rotate​(Group group, Matrix m)
      Rotate a group object.
      static void rotate​(Structure structure, double[][] rotationmatrix)
      Rotate a structure.
      static void rotate​(Structure structure, Matrix m)
      Rotate a structure object.
      static double scalarProduct​(Atom a, Atom b)
      Scalar product (dot product).
      static Atom scale​(Atom a, double s)
      Multiply elements of a by s
      static Atom scaleAdd​(double s, Atom x, Atom b)
      Perform linear transformation s*X+B, and store the result in b
      static Atom scaleEquals​(Atom a, double s)
      Multiply elements of a by s (in place)
      static void shift​(Atom[] ca, Atom b)
      Shift an array of atoms at once.
      static void shift​(Atom a, Atom b)
      Shift a vector.
      static void shift​(Group group, Atom a)
      Shift a Group with a vector.
      static void shift​(Structure structure, Atom a)
      shift a structure with a vector.
      static Atom subtract​(Atom a, Atom b)
      subtract two atoms ( a - b).
      static double torsionAngle​(Atom a, Atom b, Atom c, Atom d)
      Calculate the torsion angle, i.e. the angle between the normal vectors of the two plains a-b-c and b-c-d.
      static void transform​(Atom[] ca, javax.vecmath.Matrix4d t)
      Transform an array of atoms at once.
      static void transform​(Atom atom, javax.vecmath.Matrix4d m)
      Transforms an atom object, given a Matrix4d (i.e. the vecmath library double-precision 4x4 rotation+translation matrix).
      static void transform​(Chain chain, javax.vecmath.Matrix4d m)
      Transforms a chain object, given a Matrix4d (i.e. the vecmath library double-precision 4x4 rotation+translation matrix).
      static void transform​(Group group, javax.vecmath.Matrix4d m)
      Transforms a group object, given a Matrix4d (i.e. the vecmath library double-precision 4x4 rotation+translation matrix).
      static void transform​(Structure structure, javax.vecmath.Matrix4d m)
      Transforms a structure object, given a Matrix4d (i.e. the vecmath library double-precision 4x4 rotation+translation matrix).
      static void translate​(Atom atom, javax.vecmath.Vector3d v)
      Translates an atom object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
      static void translate​(Chain chain, javax.vecmath.Vector3d v)
      Translates a chain object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
      static void translate​(Group group, javax.vecmath.Vector3d v)
      Translates a group object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
      static void translate​(Structure structure, javax.vecmath.Vector3d v)
      Translates a Structure object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
      static Atom unitVector​(Atom a)
      Returns the unit vector of vector a .
      static Atom vectorProduct​(Atom a, Atom b)
      Vector product (cross product).

    • Constructor Detail

      • Calc

        public Calc()

    • Method Detail

      • getDistance

        public static final double getDistance​(Atom a,
                                       Atom b)
        calculate distance between two atoms.
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        a double

      • getDistanceFast

        public static double getDistanceFast​(Atom a,
                                     Atom b)
        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().
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        a double

      • add

        public static final Atom add​(Atom a,
                             Atom b)
        add two atoms ( a + b).
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        an Atom object

      • subtract

        public static final Atom subtract​(Atom a,
                                  Atom b)
        subtract two atoms ( a - b).
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        n new Atom object representing the difference

      • vectorProduct

        public static final Atom vectorProduct​(Atom a,
                                       Atom b)
        Vector product (cross product).
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        an Atom object

      • scalarProduct

        public static final double scalarProduct​(Atom a,
                                         Atom b)
        Scalar product (dot product).
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        a double

      • amount

        public static final double amount​(Atom a)
        Gets the length of the vector (2-norm)
        Parameters:
        a - an Atom object
        Returns:
        Square root of the sum of the squared elements

      • angle

        public static final double angle​(Atom a,
                                 Atom b)
        Gets the angle between two vectors
        Parameters:
        a - an Atom object
        b - an Atom object
        Returns:
        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

      • unitVector

        public static final Atom unitVector​(Atom a)
        Returns the unit vector of vector a .
        Parameters:
        a - an Atom object
        Returns:
        an Atom object

      • torsionAngle

        public static final double torsionAngle​(Atom a,
                                        Atom b,
                                        Atom c,
                                        Atom d)
        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
        Parameters:
        a - an Atom object
        b - an Atom object
        c - an Atom object
        d - an Atom object
        Returns:
        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

      • getPhi

        public static final double getPhi​(AminoAcid a,
                                  AminoAcid b)
                           throws StructureException
        Calculate the phi angle.
        Parameters:
        a - an AminoAcid object
        b - an AminoAcid object
        Returns:
        a double
        Throws:
        StructureException - if aminoacids not connected or if any of the 4 needed atoms missing

      • getPsi

        public static final double getPsi​(AminoAcid a,
                                  AminoAcid b)
                           throws StructureException
        Calculate the psi angle.
        Parameters:
        a - an AminoAcid object
        b - an AminoAcid object
        Returns:
        a double
        Throws:
        StructureException - if aminoacids not connected or if any of the 4 needed atoms missing

      • isConnected

        public static final boolean isConnected​(AminoAcid a,
                                        AminoAcid b)
        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.
        Parameters:
        a - an AminoAcid object
        b - an AminoAcid object
        Returns:
        true if ...

      • rotate

        public static final void rotate​(Atom atom,
                                double[][] m)
        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)
        Parameters:
        atom - atom to be rotated
        m - a rotation matrix represented as a double[3][3] array

      • rotate

        public static final void rotate​(Structure structure,
                                double[][] rotationmatrix)
                         throws StructureException
        Rotate a structure. The rotation Matrix must be a pre-multiplication Matrix.
        Parameters:
        structure - a Structure object
        rotationmatrix - an array (3x3) of double representing the rotation matrix.
        Throws:
        StructureException - ...

      • rotate

        public static final void rotate​(Group group,
                                double[][] rotationmatrix)
                         throws StructureException
        Rotate a Group. The rotation Matrix must be a pre-multiplication Matrix.
        Parameters:
        group - a group object
        rotationmatrix - an array (3x3) of double representing the rotation matrix.
        Throws:
        StructureException - ...

      • rotate

        public static final void rotate​(Atom atom,
                                Matrix m)
        Rotate an Atom around a Matrix object. The rotation Matrix must be a pre-multiplication Matrix.
        Parameters:
        atom - atom to be rotated
        m - rotation matrix to be applied to the atom

      • rotate

        public static final void rotate​(Group group,
                                Matrix m)
        Rotate a group object. The rotation Matrix must be a pre-multiplication Matrix.
        Parameters:
        group - a group to be rotated
        m - a Matrix object representing the rotation matrix

      • rotate

        public static final void rotate​(Structure structure,
                                Matrix m)
        Rotate a structure object. The rotation Matrix must be a pre-multiplication Matrix.
        Parameters:
        structure - the structure to be rotated
        m - rotation matrix to be applied

      • transform

        public static void transform​(Atom[] ca,
                             javax.vecmath.Matrix4d t)
        Transform an array of atoms at once. The transformation Matrix must be a post-multiplication Matrix.
        Parameters:
        ca - array of Atoms to shift
        t - transformation Matrix4d

      • transform

        public static final void transform​(Atom atom,
                                   javax.vecmath.Matrix4d m)
        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.
        Parameters:
        atom -
        m -

      • transform

        public static final void transform​(Group group,
                                   javax.vecmath.Matrix4d m)
        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.
        Parameters:
        group -
        m -

      • transform

        public static final void transform​(Structure structure,
                                   javax.vecmath.Matrix4d 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.
        Parameters:
        structure -
        m -

      • transform

        public static final void transform​(Chain chain,
                                   javax.vecmath.Matrix4d 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.
        Parameters:
        chain -
        m -

      • translate

        public static final void translate​(Atom atom,
                                   javax.vecmath.Vector3d v)
        Translates an atom object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
        Parameters:
        atom -
        v -

      • translate

        public static final void translate​(Group group,
                                   javax.vecmath.Vector3d v)
        Translates a group object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
        Parameters:
        group -
        v -

      • translate

        public static final void translate​(Chain chain,
                                   javax.vecmath.Vector3d v)
        Translates a chain object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
        Parameters:
        chain -
        v -

      • translate

        public static final void translate​(Structure structure,
                                   javax.vecmath.Vector3d v)
        Translates a Structure object, given a Vector3d (i.e. the vecmath library double-precision 3-d vector)
        Parameters:
        structure -
        v -

      • plus

        public static final void plus​(Structure s,
                              Matrix matrix)
        calculate structure + Matrix coodinates ...
        Parameters:
        s - the structure to operate on
        matrix - a Matrix object

      • shift

        public static final void shift​(Structure structure,
                               Atom a)
        shift a structure with a vector.
        Parameters:
        structure - a Structure object
        a - an Atom object representing a shift vector

      • shift

        public static final void shift​(Atom a,
                               Atom b)
        Shift a vector.
        Parameters:
        a - vector a
        b - vector b

      • shift

        public static final void shift​(Group group,
                               Atom a)
        Shift a Group with a vector.
        Parameters:
        group - a group object
        a - an Atom object representing a shift vector

      • getCentroid

        public static final Atom getCentroid​(Atom[] atomSet)
        Returns the centroid of the set of atoms.
        Parameters:
        atomSet - a set of Atoms
        Returns:
        an Atom representing the Centroid of the set of atoms

      • centerOfMass

        public static Atom centerOfMass​(Atom[] points)
        Returns the center of mass of the set of atoms. Atomic masses of the Atoms are used.
        Parameters:
        points - a set of Atoms
        Returns:
        an Atom representing the center of mass

      • scaleEquals

        public static Atom scaleEquals​(Atom a,
                               double s)
        Multiply elements of a by s (in place)
        Parameters:
        a -
        s -
        Returns:
        the modified a

      • scale

        public static Atom scale​(Atom a,
                         double s)
        Multiply elements of a by s
        Parameters:
        a -
        s -
        Returns:
        A new Atom with s*a

      • scaleAdd

        public static Atom scaleAdd​(double s,
                            Atom x,
                            Atom b)
        Perform linear transformation s*X+B, and store the result in b
        Parameters:
        s - Amount to scale x
        x - Input coordinate
        b - Vector to translate (will be modified)
        Returns:
        b, after modification

      • getCenterVector

        public static final Atom getCenterVector​(Atom[] atomSet)
        Returns the Vector that needs to be applied to shift a set of atoms to the Centroid.
        Parameters:
        atomSet - array of Atoms
        Returns:
        the vector needed to shift the set of atoms to its geometric center

      • getCenterVector

        public static final Atom getCenterVector​(Atom[] atomSet,
                                         Atom centroid)
        Returns the Vector that needs to be applied to shift a set of atoms to the Centroid, if the centroid is already known
        Parameters:
        atomSet - array of Atoms
        Returns:
        the vector needed to shift the set of atoms to its geometric center

      • centerAtoms

        public static final Atom[] centerAtoms​(Atom[] atomSet,
                                       Atom centroid)
                                throws StructureException
        Center the atoms at the Centroid, if the centroid is already know.
        Parameters:
        atomSet - a set of Atoms
        Returns:
        an Atom representing the Centroid of the set of atoms
        Throws:
        StructureException

      • createVirtualCBAtom

        public static final Atom createVirtualCBAtom​(AminoAcid amino)
                                      throws StructureException
        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.
        Parameters:
        amino - the amino acid for which a "virtual" CB atom should be calculated
        Returns:
        a "virtual" CB atom
        Throws:
        StructureException

      • getZYZEuler

        public static final double[] getZYZEuler​(Matrix m)
        Gets euler angles for a matrix given in ZYZ convention. (as e.g. used by Jmol)
        Parameters:
        m - the rotation matrix
        Returns:
        the euler values for a rotation around Z, Y, Z in degrees...

      • getXYZEuler

        public static final double[] getXYZEuler​(Matrix m)
        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
        Parameters:
        m - the rotation matrix
        Returns:
        a array of three doubles containing the three euler angles in radians

      • matrixFromEuler

        public static final Matrix matrixFromEuler​(double heading,
                                           double attitude,
                                           double 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]
        Parameters:
        heading - in radians
        attitude - in radians
        bank - in radians
        Returns:
        the rotation matrix

      • calcRotationAngleInDegrees

        public static double calcRotationAngleInDegrees​(Atom centerPt,
                                                Atom targetPt)
        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.
        Parameters:
        centerPt - Point we are rotating around.
        targetPt - Point we want to calculate the angle to.
        Returns:
        angle in degrees. This is the angle from centerPt to targetPt.

      • main

        public static void main​(String[] args)

      • shift

        public static void shift​(Atom[] ca,
                         Atom b)
        Shift an array of atoms at once.
        Parameters:
        ca - array of Atoms to shift
        b - reference Atom vector

      • getTransformation

        public static javax.vecmath.Matrix4d getTransformation​(Matrix rot,
                                                       Atom trans)
        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.
        Parameters:
        rot - 3x3 Rotation matrix
        trans - 3x1 translation vector in Atom coordinates
        Returns:
        4x4 transformation matrix

      • getTranslationVector

        public static Atom getTranslationVector​(javax.vecmath.Matrix4d transform)
        Extract the translational vector as an Atom of a transformation matrix.
        Parameters:
        transform - Matrix4d
        Returns:
        Atom shift vector

      • atomsToPoints

        public static javax.vecmath.Point3d[] atomsToPoints​(Atom[] atoms)
        Convert an array of atoms into an array of vecmath points
        Parameters:
        atoms - list of atoms
        Returns:
        list of Point3ds storing the x,y,z coordinates of each atom

      • atomsToPoints

        public static List<javax.vecmath.Point3d> atomsToPoints​(Collection<Atom> atoms)
        Convert an array of atoms into an array of vecmath points
        Parameters:
        atoms - list of atoms
        Returns:
        list of Point3ds storing the x,y,z coordinates of each atom

      • rmsd

        public static double rmsd​(Atom[] x,
                          Atom[] y)
        Calculate the RMSD of two Atom arrays, already superposed.
        Parameters:
        x - array of Atoms superposed to y
        y - array of Atoms superposed to x
        Returns:
        RMSD

      • getTMScore

        public static double getTMScore​(Atom[] atomSet1,
                                Atom[] atomSet2,
                                int len1,
                                int len2)
                         throws StructureException
        Calculate the TM-Score for the superposition. Normalizes by the minimum-length structure (that is, 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.

        Parameters:
        atomSet1 - atom array 1
        atomSet2 - atom array 2
        len1 - The full length of the protein supplying atomSet1
        len2 - The full length of the protein supplying atomSet2
        Returns:
        The TM-Score
        Throws:
        StructureException

      • getTMScore

        public static double getTMScore​(Atom[] atomSet1,
                                Atom[] atomSet2,
                                int len1,
                                int len2,
                                boolean normalizeMin)
                         throws StructureException
        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.

        Parameters:
        atomSet1 - atom array 1
        atomSet2 - atom array 2
        len1 - The full length of the protein supplying atomSet1
        len2 - The full length of the protein supplying atomSet2
        normalizeMin - Whether to normalize by the minimum-length structure, that is, min\{len1,len2\}. If false, normalized by the max\{len1,len2\}).
        Returns:
        The TM-Score
        Throws:
        StructureException