/*
* 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/
*
*/
package org.biojava.nbio.structure.xtal;
import javax.vecmath.*;
import java.io.Serializable;
import java.util.ArrayList;
import java.util.Collections;
//import org.slf4j.Logger;
//import org.slf4j.LoggerFactory;
/**
* A crystal cell's parameters.
*
* @author duarte_j
*
*/
public class CrystalCell implements Serializable {
private static final long serialVersionUID = 1L;
//private static final Logger logger = LoggerFactory.getLogger(CrystalCell.class);
public static final double MIN_VALID_CELL_SIZE = 10.0; // the minimum admitted for a crystal cell
private double a;
private double b;
private double c;
private double alpha;
private double beta;
private double gamma;
private double alphaRad;
private double betaRad;
private double gammaRad;
private double volume; // cached volume
private double maxDimension; // cached max dimension
private Matrix3d M; // cached basis change transformation matrix
private Matrix3d Minv; // cached basis change transformation matrix
private Matrix3d Mtransp;
private Matrix3d MtranspInv;
public CrystalCell() {
}
public CrystalCell(double a, double b, double c, double alpha, double beta, double gamma){
this.a = a;
this.b = b;
this.c = c;
this.setAlpha(alpha); // initialises both alpha and alphaRad
this.setBeta(beta);
this.setGamma(gamma);
}
public double getA() {
return a;
}
public void setA(double a) {
this.a = a;
}
public double getB() {
return b;
}
public void setB(double b) {
this.b = b;
}
public double getC() {
return c;
}
public void setC(double c) {
this.c = c;
}
public double getAlpha() {
return alpha;
}
public void setAlpha(double alpha) {
this.alpha = alpha;
this.alphaRad = Math.toRadians(alpha);
}
public double getBeta() {
return beta;
}
public void setBeta(double beta) {
this.beta = beta;
this.betaRad = Math.toRadians(beta);
}
public double getGamma() {
return gamma;
}
public void setGamma(double gamma) {
this.gamma = gamma;
this.gammaRad = Math.toRadians(gamma);
}
/**
* Returns the volume of this unit cell.
* See http://en.wikipedia.org/wiki/Parallelepiped
* @return
*/
public double getVolume() {
if (volume!=0) {
return volume;
}
volume = a*b*c*
Math.sqrt(1-Math.cos(alphaRad)*Math.cos(alphaRad)-Math.cos(betaRad)*Math.cos(betaRad)-Math.cos(gammaRad)*Math.cos(gammaRad)
+2.0*Math.cos(alphaRad)*Math.cos(betaRad)*Math.cos(gammaRad));
return volume;
}
/**
* Get the index of a unit cell to which the query point belongs.
*
* <p>For instance, all points in the unit cell at the origin will return (0,0,0);
* Points in the unit cell one unit further along the `a` axis will return (1,0,0),
* etc.
* @param pt Input point (in orthonormal coordinates)
* @return A new point with the three indices of the cell containing pt
*/
public Point3i getCellIndices(Tuple3d pt) {
Point3d p = new Point3d(pt);
this.transfToCrystal(p);
int x = (int)Math.floor(p.x);
int y = (int)Math.floor(p.y);
int z = (int)Math.floor(p.z);
return new Point3i(x,y,z);
}
/**
* Converts the coordinates in pt so that they occur within the (0,0,0) unit cell
* @param pt
*/
public void transfToOriginCell(Tuple3d pt) {
transfToCrystal(pt);
// convert all coordinates to [0,1) interval
pt.x = pt.x<0 ? (pt.x%1.0 + 1.0)%1.0 : pt.x%1.0;
pt.y = pt.y<0 ? (pt.y%1.0 + 1.0)%1.0 : pt.y%1.0;
pt.z = pt.z<0 ? (pt.z%1.0 + 1.0)%1.0 : pt.z%1.0;
transfToOrthonormal(pt);
}
/**
* Converts a set of points so that the reference point falls in the unit cell.
*
* This is useful to transform a whole chain at once, allowing some of the
* atoms to be outside the unit cell, but forcing the centroid to be within it.
*
* @param points A set of points to transform (in orthonormal coordinates)
* @param reference The reference point, which is unmodified but which would
* be in the unit cell were it to have been transformed. It is safe to
* use a member of the points array here.
*/
public void transfToOriginCell(Tuple3d[] points, Tuple3d reference) {
reference = new Point3d(reference);//clone
transfToCrystal(reference);
int x = (int)Math.floor(reference.x);
int y = (int)Math.floor(reference.y);
int z = (int)Math.floor(reference.z);
for( Tuple3d point: points ) {
transfToCrystal(point);
point.x -= x;
point.y -= y;
point.z -= z;
transfToOrthonormal(point);
}
}
/**
*
* @param ops Set of operations in orthonormal coordinates
* @param reference Reference point, which should be in the unit cell after
* each operation (also in orthonormal coordinates)
* @return A set of orthonormal operators with equivalent rotation to the
* inputs, but with translation such that the reference point would fall
* within the unit cell
*/
public Matrix4d[] transfToOriginCellOrthonormal(Matrix4d[] ops, Tuple3d reference) {
// reference in crystal coords
Point3d refXtal = new Point3d(reference);
transfToCrystal(refXtal);
// Convert to crystal coords
Matrix4d[] opsXtal = new Matrix4d[ops.length];
for(int i=0;i<ops.length;i++) {
opsXtal[i] = transfToCrystal(ops[i]);
}
Matrix4d[] transformed = transfToOriginCellCrystal(opsXtal, refXtal);
// Convert back to orthonormal
for(int i=0;i<ops.length;i++) {
transformed[i] = transfToOrthonormal(transformed[i]);
}
return transformed;
}
/**
*
* @param ops Set of operations in crystal coordinates
* @param reference Reference point, which should be in the unit cell after
* each operation (also in crystal coordinates)
* @return A set of crystal operators with equivalent rotation to the
* inputs, but with translation such that the reference point would fall
* within the unit cell
*/
public Matrix4d[] transfToOriginCellCrystal(Matrix4d[] ops, Tuple3d reference) {
Matrix4d[] transformed = new Matrix4d[ops.length];
for(int j=0;j<ops.length;j++) {
Matrix4d op = ops[j];
// transform the reference point
Point3d xXtal = new Point3d(reference);
op.transform(xXtal);
// Calculate unit cell of transformed reference
int x = (int)Math.floor(xXtal.x);
int y = (int)Math.floor(xXtal.y);
int z = (int)Math.floor(xXtal.z);
Matrix4d translation = new Matrix4d();
translation.set(new Vector3d(-x,-y,-z));
// Compose op with an additional translation operator
translation.mul(op);
Point3d ref2 = new Point3d(reference);
translation.transform(ref2);
transformed[j] = translation;
}
return transformed;
}
/**
* Transform given Matrix4d in crystal basis to the orthonormal basis using
* the PDB axes convention (NCODE=1)
* @param m
* @return
*/
public Matrix4d transfToOrthonormal(Matrix4d m) {
Vector3d trans = new Vector3d(m.m03,m.m13,m.m23);
transfToOrthonormal(trans);
Matrix3d rot = new Matrix3d();
m.getRotationScale(rot);
// see Giacovazzo section 2.E, eq. 2.E.1
// Rprime = MT-1 * R * MT
rot.mul(this.getMTranspose());
rot.mul(this.getMTransposeInv(),rot);
return new Matrix4d(rot,trans,1.0);
}
/**
* Transforms the given crystal basis coordinates into orthonormal coordinates.
* e.g. transfToOrthonormal(new Point3d(1,1,1)) returns the orthonormal coordinates of the
* vertex of the unit cell.
* See Giacovazzo section 2.E, eq. 2.E.1 (or any linear algebra manual)
* @param v
*/
public void transfToOrthonormal(Tuple3d v) {
// see Giacovazzo section 2.E, eq. 2.E.1
getMTransposeInv().transform(v);
}
/**
* Transform given Matrix4d in orthonormal basis to the crystal basis using
* the PDB axes convention (NCODE=1)
* @param m
* @return
*/
public Matrix4d transfToCrystal(Matrix4d m) {
Vector3d trans = new Vector3d(m.m03,m.m13,m.m23);
transfToCrystal(trans);
Matrix3d rot = new Matrix3d();
m.getRotationScale(rot);
// see Giacovazzo section 2.E, eq. 2.E.1 (the inverse equation)
// R = MT * Rprime * MT-1
rot.mul(this.getMTransposeInv());
rot.mul(this.getMTranspose(),rot);
return new Matrix4d(rot,trans,1.0);
}
/**
* Transforms the given orthonormal basis coordinates into crystal coordinates.
* See Giacovazzo eq 2.20 (or any linear algebra manual)
* @param v
*/
public void transfToCrystal(Tuple3d v) {
getMTranspose().transform(v);
}
/**
* Returns the change of basis (crystal to orthonormal) transform matrix, that is
* M inverse in the notation of Giacovazzo.
* Using the PDB axes convention
* (CCP4 uses NCODE identifiers to distinguish the different conventions, the PDB one is called NCODE=1)
* The matrix is only calculated upon first call of this method, thereafter it is cached.
* See "Fundamentals of Crystallography" C. Giacovazzo, section 2.5 (eq 2.30)
*
* The non-standard orthogonalisation codes (NCODE for ccp4) are flagged in REMARK 285 after 2011's remediation
* with text: "THE ENTRY COORDINATES ARE NOT PRESENTED IN THE STANDARD CRYSTAL FRAME". There were only 148 PDB
* entries with non-standard code in 2011. See:
* http://www.wwpdb.org/documentation/2011remediation_overview-061711.pdf
* The SCALE1,2,3 records contain the correct transformation matrix (what Giacovazzo calls M matrix).
* In those cases if we calculate the M matrix following Giacovazzo's equations here, we get an entirely wrong one.
* Examples of PDB with non-standard orthogonalisation are 1bab and 1bbb.
* @return
*/
private Matrix3d getMInv() {
if (Minv!=null) {
return Minv;
}
// see eq. 2.30 Giacovazzo
Minv = new Matrix3d( this.a, 0, 0,
this.b*Math.cos(gammaRad), this.b*Math.sin(gammaRad), 0,
this.c*Math.cos(betaRad) , -this.c*Math.sin(betaRad)*getCosAlphaStar(), 1.0/getCstar());
return Minv;
}
// another axes convention (from Giacovazzo) eq. 2.31b, not sure what would be the NCODE of this
// private Matrix3d getMInv() {
// if (Minv!=null) {
// return Minv;
// }
// Minv = new Matrix3d( 1/getAstar(), -(getCosGammaStar()/getSinGammaStar())/getAstar(), this.a*Math.cos(betaRad),
// 0, 1/(getBstar()*getSinGammaStar()), this.b*Math.sin(alphaRad),
// 0, 0, this.c);
// return Minv;
// }
// and yet another axes convention (from Giacovazzo) eq. 2.31c, not sure what would be the NCODE of this
// private Matrix3d getMInv() {
// if (Minv!=null) {
// return Minv;
// }
// Minv = new Matrix3d( alphaRad*Math.sin(gammaRad)*getSinBetaStar(), this.a*Math.cos(gammaRad), this.a*Math.sin(gammaRad)*getCosBetaStar(),
// 0, this.b, 0,
// 0, this.c*Math.cos(alphaRad), this.c*Math.sin(alphaRad));
// return Minv;
// }
// relationships among direct and reciprocal lattice parameters
// see Table 2.1 of chapter 2 of Giacovazzo
@SuppressWarnings("unused")
private double getAstar() {
return (this.b*this.c*Math.sin(alphaRad))/getVolume();
}
@SuppressWarnings("unused")
private double getBstar() {
return (this.a*this.c*Math.sin(betaRad))/getVolume();
}
private double getCstar() {
return (this.a*this.b*Math.sin(gammaRad))/getVolume();
}
private double getCosAlphaStar() {
return (Math.cos(betaRad)*Math.cos(gammaRad)-Math.cos(alphaRad))/(Math.sin(betaRad)*Math.sin(gammaRad));
}
@SuppressWarnings("unused")
private double getCosBetaStar() {
return (Math.cos(alphaRad)*Math.cos(gammaRad)-Math.cos(betaRad))/(Math.sin(alphaRad)*Math.sin(gammaRad));
}
@SuppressWarnings("unused")
private double getCosGammaStar() {
return (Math.cos(alphaRad)*Math.cos(betaRad)-Math.cos(gammaRad))/(Math.sin(alphaRad)*Math.sin(betaRad));
}
@SuppressWarnings("unused")
private double getSinAlphaStar() {
return getVolume()/(this.a*this.b*this.c*Math.sin(betaRad)*Math.sin(gammaRad));
}
@SuppressWarnings("unused")
private double getSinBetaStar() {
return getVolume()/(this.a*this.b*this.c*Math.sin(alphaRad)*Math.sin(gammaRad));
}
@SuppressWarnings("unused")
private double getSinGammaStar() {
return getVolume()/(this.a*this.b*this.c*Math.sin(alphaRad)*Math.sin(betaRad));
}
/**
* Returns the change of basis (orthonormal to crystal) transform matrix, that is
* M in the notation of Giacovazzo.
* Using the PDB convention (NCODE=1).
* The matrix is only calculated upon first call of this method, thereafter it is cached.
* See "Fundamentals of Crystallography" C. Giacovazzo, section 2.5
* @return
*/
private Matrix3d getM() {
if (M!=null){
return M;
}
M = new Matrix3d();
M.invert(getMInv());
return M;
}
public Matrix3d getMTranspose() {
if (Mtransp!=null){
return Mtransp;
}
Matrix3d M = getM();
Mtransp = new Matrix3d();
Mtransp.transpose(M);
return Mtransp;
}
private Matrix3d getMTransposeInv() {
if (MtranspInv!=null){
return MtranspInv;
}
MtranspInv = new Matrix3d();
MtranspInv.invert(getMTranspose());
return MtranspInv;
}
/**
* Gets the maximum dimension of the unit cell.
* @return
*/
public double getMaxDimension() {
if (maxDimension!=0) {
return maxDimension;
}
Point3d vert0 = new Point3d(0,0,0);
Point3d vert1 = new Point3d(1,0,0);
transfToOrthonormal(vert1);
Point3d vert2 = new Point3d(0,1,0);
transfToOrthonormal(vert2);
Point3d vert3 = new Point3d(0,0,1);
transfToOrthonormal(vert3);
Point3d vert4 = new Point3d(1,1,0);
transfToOrthonormal(vert4);
Point3d vert5 = new Point3d(1,0,1);
transfToOrthonormal(vert5);
Point3d vert6 = new Point3d(0,1,1);
transfToOrthonormal(vert6);
Point3d vert7 = new Point3d(1,1,1);
transfToOrthonormal(vert7);
ArrayList<Double> vertDists = new ArrayList<Double>();
vertDists.add(vert0.distance(vert7));
vertDists.add(vert3.distance(vert4));
vertDists.add(vert1.distance(vert6));
vertDists.add(vert2.distance(vert5));
maxDimension = Collections.max(vertDists);
return maxDimension;
}
/**
* Given a scale matrix parsed from the PDB entry (SCALE1,2,3 records),
* checks that the matrix is a consistent scale matrix by comparing the
* cell volume to the inverse of the scale matrix determinant (tolerance of 1/100).
* If they don't match false is returned.
* See the PDB documentation for the SCALE record.
* See also last equation of section 2.5 of "Fundamentals of Crystallography" C. Giacovazzo
* @param scaleMatrix
* @return
*/
public boolean checkScaleMatrixConsistency(Matrix4d scaleMatrix) {
double vol = getVolume();
Matrix3d m = new Matrix3d();
scaleMatrix.getRotationScale(m);
// note we need to have a relaxed tolerance here as the PDB scale matrix is given with not such high precision
// plus we don't want to have false positives, so we stay conservative
double tolerance = vol/100.0;
if ((Math.abs(vol - 1.0/m.determinant() )>tolerance)) {
//System.err.println("Warning! SCALE matrix from PDB does not match 1/determinat == cell volume: "+
// String.format("vol=%6.3f 1/det=%6.3f",vol,1.0/m.determinant()));
return false;
}
// this would be to check our own matrix, must always match!
//if (!deltaComp(vol,1.0/getMTranspose().determinant())) {
// System.err.println("Our calculated SCALE matrix does not match 1/det=cell volume");
//}
return true;
}
/**
* Given a scale matrix parsed from a PDB entry (SCALE1,2,3 records),
* compares it to our calculated Mtranspose matrix to see if they coincide and
* returns true if they do.
* If they don't that means that the PDB entry is not in the standard
* orthogonalisation (NCODE=1 in ccp4).
* In 2011's remediation only 148 PDB entries were found not to be in
* a non-standard orthogonalisation. See:
* http://www.wwpdb.org/documentation/2011remediation_overview-061711.pdf
* For normal cases the scale matrix is diagonal without a translation component.
* Additionally the translation component of the SCALE matrix is also checked to
* make sure it is (0,0,0), if not false is return
* @param scaleMatrix
* @return
*/
public boolean checkScaleMatrix(Matrix4d scaleMatrix) {
Matrix3d mtranspose = getMTranspose();
for (int i=0;i<3;i++) {
for (int j=0;j<3;j++) {
if (!deltaComp(mtranspose.getElement(i, j),scaleMatrix.getElement(i, j))) {
//System.out.println("Our value ("+i+","+j+"): "+getM().getElement(i,j));
//System.out.println("Their value ("+i+","+j+"): "+scaleMatrix.getElement(i,j));
return false;
}
}
}
for (int i=0;i<3;i++) {
if (!deltaComp(scaleMatrix.getElement(i, 3),0)) {
return false;
}
}
return true;
}
private boolean deltaComp(double d1, double d2) {
if (Math.abs(d1-d2)<0.0001) return true;
return false;
}
/**
* Checks whether the dimensions of this crystal cell are reasonable for protein
* crystallography: if all 3 dimensions are below {@value #MIN_VALID_CELL_SIZE} the cell
* is considered unrealistic and false returned
* @return
*/
public boolean isCellReasonable() {
// this check is necessary mostly when reading PDB files that can contain the default 1 1 1 crystal cell
// if we use that further things can go wrong, for instance for interface calculation
// For instance programs like coot produce by default a 1 1 1 cell
if (this.getA()<MIN_VALID_CELL_SIZE &&
this.getB()<MIN_VALID_CELL_SIZE &&
this.getC()<MIN_VALID_CELL_SIZE) {
return false;
}
return true;
}
@Override
public String toString() {
return String.format("a%7.2f b%7.2f c%7.2f alpha%6.2f beta%6.2f gamma%6.2f", a, b, c, alpha, beta, gamma);
}
}