/
xtalcomp.cpp
2195 lines (2000 loc) · 70.5 KB
/
xtalcomp.cpp
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/**********************************************************************
XtalComp - Determine if two crystal descriptions represent the same
structure
Copyright (C) 2011 by David C. Lonie
This source code is released under the New BSD License, (the "License").
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
***********************************************************************/
#include "xtalcomp.h"
#include "stablecomparison.h"
extern "C" {
#include "spglib.h"
}
#include <algorithm>
#include <assert.h>
#include <iostream>
#include <limits.h>
#include <stddef.h>
#include <stdio.h>
// Save some keystrokes...
typedef XtalComp::DuplicateMap DuplicateMap;
#define RAD_TO_DEG 57.2957795131
#define DEG_TO_RAD 0.0174532925199
#define PRECISION 1e-8
#undef XTALCOMP_DEBUG
//#define XTALCOMP_DEBUG 1
#ifdef XTALCOMP_DEBUG
#define DEBUG_BREAK printf("\n");
#define DEBUG_DIV printf("\
--------------------------------------------------------------------------------\n")
#define DEBUG_ATOM(t,c) printf("%2d: | %9.5f %9.5f %9.5f |\n", t, (c).x(), (c).y(), (c).z())
#define DEBUG_ATOMCF(t,c,f) printf("%2d: | %9.5f %9.5f %9.5f | %9.5f %9.5f %9.5f |\n", \
t, (c).x(), (c).y(), (c).z(), \
(f).x(), (f).y(), (f).z())
#define DEBUG_VECTOR(v) printf("| %9.5f %9.5f %9.5f |\n", (v).x(), (v).y(), (v).z())
#define DEBUG_MATRIX(m) printf("| %9.5f %9.5f %9.5f |\n" \
"| %9.5f %9.5f %9.5f |\n" \
"| %9.5f %9.5f %9.5f |\n", \
(m)(0,0), (m)(0,1), (m)(0,2), \
(m)(1,0), (m)(1,1), (m)(1,2), \
(m)(2,0), (m)(2,1), (m)(2,2))
#define DEBUG_STRING_VECTOR(s,v) printf("%s: | %9.5f %9.5f %9.5f |\n", \
s, (v).x(), (v).y(), (v).z())
#define DEBUG_MATRIX4(m) printf("| %9.5f %9.5f %9.5f %9.5f |\n" \
"| %9.5f %9.5f %9.5f %9.5f |\n" \
"| %9.5f %9.5f %9.5f %9.5f |\n" \
"| %9.5f %9.5f %9.5f %9.5f |\n", \
(m)(0,0), (m)(0,1), (m)(0,2), (m)(0,3), \
(m)(1,0), (m)(1,1), (m)(1,2), (m)(1,3), \
(m)(2,0), (m)(2,1), (m)(2,2), (m)(2,3), \
(m)(3,0), (m)(3,1), (m)(3,2), (m)(3,3))
#define DEBUG_STRING(str) printf("%s\n", str)
#define DEBUG_STRING_INT(str, i) printf("%s %d\n", str, i)
#endif
// vecs += trans
inline void translateVectorsInPlace(std::vector<XcVector> *vecs,
const XcVector &trans)
{
for (std::vector<XcVector>::iterator it = vecs->begin(),
it_end = vecs->end(); it != it_end; ++it) {
*it += trans;
}
}
// Calculate a standardized angle between v1 and v2 -- if the
// vectors are mirrored (e.g. an enantiomorphic pair of crystals),
// the angles will vary in a non-obvious way:
//
// v1 y v2
// ^ ^ ^
// \ | /
// \ | /
// \ | /
// \|/
// -----|--------> x
//
// v1 and v2 are simply mirrored around the y axis. Define:
// a1 = fabs(angle(x, v1))
// a2 = fabs(angle(x, v2))
// b = fabs(angle(y, v1)) = fabs(angle(y, v2)
//
// In this case, a2 = a1 - 2b.
//
// So check if any of the angles are greater than 90. If so
// correct by calculating b = a-90, then correct with a -= 2b.
static inline double compAngle(const XcVector &v1,
const XcVector &v2)
{
const double angle = fabs( acos( v1.dot(v2) /
sqrt(v1.squaredNorm() *
v2.squaredNorm()))
* RAD_TO_DEG);
if (angle <= 90.0)
return angle;
else
return 180.0 - angle;
}
class XtalComp::ReducedXtal
{
private:
unsigned int m_numAtoms;
std::vector<unsigned int> m_types;
std::vector<XcVector> m_ccoords;
std::vector<XcVector> m_fcoords;
// Fractionation and cell matrices -- ready to use:
// ccoord = cmat * fcoord
// fcoord = fmat * ccoord
XcMatrix m_cmat;
XcMatrix m_fmat;
public:
ReducedXtal(const XcMatrix cellMatrix,
const std::vector<unsigned int> types,
const std::vector<XcVector> positions) :
m_numAtoms(types.size()),
m_types(types),
m_ccoords(),
m_fcoords(positions),
m_cmat(cellMatrix.transpose()),
m_fmat(m_cmat.inverse())
{
// Fill ccoords
m_ccoords.reserve(m_fcoords.size());
for (std::vector<XcVector>::const_iterator it = m_fcoords.begin(),
it_end = m_fcoords.end(); it != it_end; ++it) {
m_ccoords.push_back(m_cmat * (*it));
}
}
virtual ~ReducedXtal() {}
unsigned int numAtoms() const {return m_numAtoms;}
const std::vector<unsigned int> & types() const {return m_types;}
const std::vector<XcVector> & ccoords() const {return m_ccoords;}
const std::vector<XcVector> & fcoords() const {return m_fcoords;}
const XcMatrix & cmat() const {return m_cmat;}
const XcMatrix & fmat() const {return m_fmat;}
double volume() const {return fabs(m_cmat.determinant());}
XcVector v1() const {return m_cmat.col(0);}
XcVector v2() const {return m_cmat.col(1);}
XcVector v3() const {return m_cmat.col(2);}
// Defined at end of file:
// Niggli reduce, rotate to std orientation, wrap atoms to cell:
bool canonicalizeLattice();
bool isNiggliReduced() const;
XcMatrix getCellMatrixInStandardOrientation() const;
void frac2Cart(const XcVector &fcoord, XcVector *ccoord) const
{
*ccoord = m_cmat * fcoord;
}
void cart2Frac(const XcVector &ccoord, XcVector *fcoord) const
{
*fcoord = m_fmat * ccoord;
}
// Translate member coords by the fractional translation vector fracTrans
void translateAndExpandCoords(const XcVector & fracTrans,
const float cartLengthTol,
DuplicateMap *duplicateAtoms)
{
// Translate coords
for(std::vector<XcVector>::iterator it = m_fcoords.begin(),
it_end = m_fcoords.end(); it != it_end; ++it) {
*it += fracTrans;
}
// Expand / wrap fcoords
XtalComp::expandFractionalCoordinates(&m_types, &m_fcoords,
duplicateAtoms,
m_cmat, cartLengthTol);
// update ccoords:
m_ccoords.resize(m_fcoords.size());
m_numAtoms = m_fcoords.size();
for (size_t i = 0; i < m_numAtoms; ++i) {
frac2Cart(m_fcoords[i], &m_ccoords[i]);
}
}
};
bool XtalComp::compare(const XcMatrix &_cellMatrix1,
const std::vector<unsigned int> &_types1,
const std::vector<XcVector> &_positions1,
const XcMatrix &_cellMatrix2,
const std::vector<unsigned int> &_types2,
const std::vector<XcVector> &_positions2,
float transform[16],
const double cartTol,
const double angleTol,
const bool reduceXtalsToPrimitive)
{
// Make a non-const copy of these variables so we may edit them if
// reduceToPrimitive is true
XcMatrix cellMatrix1 = _cellMatrix1;
std::vector<unsigned int> types1 = _types1;
std::vector<XcVector> positions1 = _positions1;
XcMatrix cellMatrix2 = _cellMatrix2;
std::vector<unsigned int> types2 = _types2;
std::vector<XcVector> positions2 = _positions2;
// First, reduce the xtals to their primitive form if needed
if (reduceXtalsToPrimitive) {
// Perhaps we'll use these later
//unsigned int numAtoms1 = types1.size();
//unsigned int numAtoms2 = types2.size();
// We'll use the same cartesian tolerance for the spglib calls, too
unsigned int spg1 = reduceToPrimitive(positions1, types1,
cellMatrix1, cartTol);
unsigned int spg2 = reduceToPrimitive(positions2, types2,
cellMatrix2, cartTol);
// bool cellReduced1 = false, cellReduced2 = false;
//if (numAtoms1 != types1.size()) cellReduced1 = true;
//if (numAtoms2 != types2.size()) cellReduced2 = true;
if (spg1 < 1 || spg1 > 230) {
std::cerr << "An invalid spg was detected by spglib for cell 1\n";
return false;
}
if (spg2 < 1 || spg2 > 230) {
std::cerr << "An invalid spg was detected by spglib for cell 2\n";
return false;
}
}
// Next, check that types and positions are of the same size
if (types1.size() != positions1.size() ||
types2.size() != positions2.size() ){
fprintf(stderr, "XtalComp::compare was given a structure description with"
" differing numbers of types and positions:\n\ttypes1: %d "
"positions1: %d\n\ttypes2: %d positions2: %d\n", types1.size(),
positions1.size(),types2.size(), positions2.size());
return false;
}
// Next ensure that the two descriptions have the same number of atoms
if (types1.size() != types2.size()) {
return false;
}
// Check that compositions match
// Make copy of types, sort, and compare
std::vector<unsigned int> types1Comp (types1);
std::vector<unsigned int> types2Comp (types2);
std::sort(types1Comp.begin(), types1Comp.end());
std::sort(types2Comp.begin(), types2Comp.end());
// Compare
for (size_t i = 0; i < types1Comp.size(); ++i) {
if (types1Comp[i] != types2Comp[i]) {
return false;
}
}
// Build ReducedXtals
ReducedXtal x1 (cellMatrix1, types1, positions1);
ReducedXtal x2 (cellMatrix2, types2, positions2);
// Standardize the lattices
if (!x1.canonicalizeLattice() ||
!x2.canonicalizeLattice() ){
std::cerr << "XtalComp warning: Failed to canonicalize one of the "
"lattices. Returning false without finishing comparison.\n";
return false;
}
// Check params here. Do not just compare the matrices, as this may
// not catch certain enantiomorphs:
// Compare volumes. Tolerance is 1% of this->getVolume()
const double vol1 = fabs(cellMatrix1.determinant());
const double vol2 = fabs(cellMatrix2.determinant());
// Match volumes to within 1%
const double voltol = 0.01 * 0.5 * (vol1 + vol2);
if (fabs(vol1 - vol2) > voltol) return false;
// Normalize and compare lattice params
const double a1 = x1.v1().squaredNorm();
const double b1 = x1.v2().squaredNorm();
const double c1 = x1.v3().squaredNorm();
const double a2 = x2.v1().squaredNorm();
const double b2 = x2.v2().squaredNorm();
const double c2 = x2.v3().squaredNorm();
// Estimate scaled error, 4 * x * \Delta x
const double cart2Tol ( 4.0 * sqrt((a1 + b1 + c1 + a2 + b2 + c2)
* 0.166666666667) * cartTol);
if (fabs(a1 - a2) > cart2Tol) return false;
if (fabs(b1 - b2) > cart2Tol) return false;
if (fabs(c1 - c2) > cart2Tol) return false;
// Angles -- see comment above definition of compAngle for
// explanation
const double alpha1 = compAngle(x1.v2(), x1.v3());
const double beta1 = compAngle(x1.v1(), x1.v3());
const double gamma1 = compAngle(x1.v1(), x1.v2());
const double alpha2 = compAngle(x2.v2(), x2.v3());
const double beta2 = compAngle(x2.v1(), x2.v3());
const double gamma2 = compAngle(x2.v1(), x2.v2());
if (fabs(alpha1 - alpha2) > angleTol) return false;
if (fabs(beta1 - beta2) > angleTol) return false;
if (fabs(gamma1 - gamma2) > angleTol) return false;
// Run the XtalComp algorithm
XtalComp xc (&x1, &x2, cartTol, angleTol);
// iterate through comparisons
while (xc.hasMoreTransforms()) {
xc.applyNextTransform();
if (xc.compareCurrent()) {
if (transform != NULL) {
xc.getCurrentTransform(transform);
}
// Found a match!
return true;
}
}
// No match
return false;
}
XtalComp::~XtalComp()
{
// ReducedXtals are cleaned up in compare(...)
}
XtalComp::XtalComp(ReducedXtal *x1, ReducedXtal *x2,
const double cartTol, const double angleTol) :
m_rx1(x1),
m_rx2(x2),
m_lengthtol(cartTol),
m_angletol(angleTol),
m_lfAtomType(UINT_MAX),
m_lfAtomCount(UINT_MAX),
m_transformsIndex(0)
{
setLeastFrequentAtomInfo();
setReferenceBasis();
prepareRx1();
buildSuperLfCCoordList2();
#ifdef XTALCOMP_DEBUG
DEBUG_BREAK;
DEBUG_DIV;
printf("Number of atoms: %d and %d\n", x1->numAtoms(), x2->numAtoms());
printf("There are %d atoms of type %d\n", m_lfAtomCount, m_lfAtomType);
DEBUG_DIV;
DEBUG_STRING("Reference Xtal 1 cmat:");
DEBUG_MATRIX(m_rx1->cmat());
DEBUG_STRING("Reference Xtal 1 fmat:");
DEBUG_MATRIX(m_rx1->fmat());
DEBUG_STRING("Reference Xtal 1 atoms (cart|frac):");
for (int i = 0; i < m_rx1->ccoords().size(); ++i) {
DEBUG_ATOMCF(m_rx1->types()[i], m_rx1->ccoords()[i],
m_rx1->fcoords()[i]);
}
DEBUG_DIV;
DEBUG_STRING("Reference Xtal 2 cmat:");
DEBUG_MATRIX(m_rx2->cmat());
DEBUG_STRING("Reference Xtal 2 fmat:");
DEBUG_MATRIX(m_rx2->fmat());
DEBUG_STRING("Original Xtal 2 atoms (cart|frac):");
for (int i = 0; i < m_rx2->ccoords().size(); ++i) {
DEBUG_ATOMCF(m_rx2->types()[i], m_rx2->ccoords()[i],
m_rx2->fcoords()[i]);
}
DEBUG_DIV;
#endif
findCandidateTransforms();
#ifdef XTALCOMP_DEBUG
printf("Number of transforms: %d\n", m_transforms.size());
DEBUG_DIV;
#endif
}
void XtalComp::setLeastFrequentAtomInfo()
{
// Get list of unique types
const std::vector<unsigned int> &rx1_types = m_rx1->types();
const std::vector<unsigned int> &rx2_types = m_rx2->types();
// Copy
std::vector<unsigned int> uniqueTypes (rx1_types);
// Sort before unique'ing
sort(uniqueTypes.begin(), uniqueTypes.end());
// Remove consecutive duplicates
const std::vector<unsigned int>::const_iterator uniqueTypes_end =
unique_copy(rx1_types.begin(), rx1_types.end(), uniqueTypes.begin());
// Now the range [uniqueTypes.begin(), uniqueTypes.end()) is
// sorted and unique.
// determine least frequent atom type
for (std::vector<unsigned int>::iterator it = uniqueTypes.begin();
it != uniqueTypes_end; ++it) {
ptrdiff_t cur = count(rx1_types.begin(), rx1_types.end(), *it);
unsigned int ucur = static_cast<unsigned int>(cur);
if (ucur < m_lfAtomCount) {
m_lfAtomCount = ucur;
m_lfAtomType = *it;
}
}
}
void XtalComp::setReferenceBasis()
{
// Just use the cell vectors of rx1
m_refVec1 = m_rx1->cmat().col(0);
m_refVec2 = m_rx1->cmat().col(1);
m_refVec3 = m_rx1->cmat().col(2);
}
void XtalComp::prepareRx1()
{
// Find a translation vector that moves an lfAtom in rx1 to the
// origin (e.g., the negative of an lfAtom's coordinates)
assert (m_rx1->fcoords().size() == m_rx1->types().size());
size_t refTransIndex = 0;
std::vector<unsigned int>::const_iterator refTransTypeIterator
= m_rx1->types().begin();
// Assert that there is at least one atom of type lfAtomType
assert (find(m_rx1->types().begin(), m_rx1->types().end(), m_lfAtomType)
!= m_rx1->types().end());
while (*refTransTypeIterator != m_lfAtomType) {
++refTransIndex;
++refTransTypeIterator;
}
XcVector rx1_ftrans = - (m_rx1->fcoords()[refTransIndex]);
// Translate rx1 by the above vector. This places an lfAtom at the origin.
m_rx1->translateAndExpandCoords(rx1_ftrans, m_lengthtol, &m_duplicatedAtoms);
}
void XtalComp::getCurrentTransform(float ret[16])
{
// Fill ret with the 4x4 matrix of the current transform.
const XcVector &trans = m_transform.translation();
const XcMatrix &rot = m_transform.rotation();
ret[0*4+0] = rot(0,0);
ret[0*4+1] = rot(0,1);
ret[0*4+2] = rot(0,2);
ret[0*4+3] = trans(0);
ret[1*4+0] = rot(1,0);
ret[1*4+1] = rot(1,1);
ret[1*4+2] = rot(1,2);
ret[1*4+3] = trans(1);
ret[2*4+0] = rot(2,0);
ret[2*4+1] = rot(2,1);
ret[2*4+2] = rot(2,2);
ret[2*4+3] = trans(2);
ret[3*4+0] = 0.0;
ret[3*4+1] = 0.0;
ret[3*4+2] = 0.0;
ret[3*4+3] = 1.0;
}
void XtalComp::buildSuperLfCCoordList2()
{
// Find all lfAtoms in rx2 and build a supercell of them
const std::vector<unsigned int> &types = m_rx2->types();
const std::vector<XcVector> &ccoords = m_rx2->ccoords();
m_superLfCCoordList2.clear();
m_superLfCCoordList2.reserve(8 * m_lfAtomCount);
assert (ccoords.size() == types.size());
// Determine the length of the cell diagonal. If it is the same as
// any vector length, we need to build a 3x3x3
// supercell. Otherwise, a (faster) 2x2x2 will suffice.
const XcVector v1 (m_rx2->cmat().col(0)); // 1 0 0
const XcVector v2 (m_rx2->cmat().col(1)); // 0 1 0
const XcVector v3 (m_rx2->cmat().col(2)); // 0 0 1
const double v1SqNorm = v1.squaredNorm();
const double v2SqNorm = v2.squaredNorm();
const double v3SqNorm = v3.squaredNorm();
const double diagSqNorm = (v1+v2+v3).squaredNorm();
const double normTol = 1e-4;
bool diagonalSameLengthAsVector =
(fabs(diagSqNorm - v1SqNorm) < normTol ||
fabs(diagSqNorm - v2SqNorm) < normTol ||
fabs(diagSqNorm - v3SqNorm) < normTol );
// We also need to build 3x3x3 for hexagonal cells
bool cellIsHexagonal =
((fabs(v1SqNorm - v2SqNorm) < normTol &&
fabs(compAngle(v1, v2) - 60.0) < m_angletol) ||
(fabs(v1SqNorm - v3SqNorm) < normTol &&
fabs(compAngle(v1, v3) - 60.0) < m_angletol) ||
(fabs(v2SqNorm - v3SqNorm) < normTol &&
fabs(compAngle(v2, v3) - 60.0) < m_angletol));
#ifdef XTALCOMP_DEBUG
if (cellIsHexagonal)
DEBUG_STRING("Cell is hexagonal");
#endif
// 3x3x3 case:
if (diagonalSameLengthAsVector || cellIsHexagonal) {
const XcVector v4 (v1 + v2); // 1 1 0
const XcVector v5 (v4 + v2); // 1 2 0
const XcVector v6 (v1 + v3); // 1 0 1
const XcVector v7 (v6 + v3); // 1 0 2
const XcVector v8 (v4 + v3); // 1 1 1
const XcVector v9 (v8 + v3); // 1 1 2
const XcVector v10(v8 + v2); // 1 2 1
const XcVector v11(v10 + v3); // 1 2 2
const XcVector v12(v1 + v1); // 2 0 0
const XcVector v13(v12 + v2); // 2 1 0
const XcVector v14(v13 + v2); // 2 2 0
const XcVector v15(v12 + v3); // 2 0 1
const XcVector v16(v15 + v3); // 2 0 2
const XcVector v17(v13 + v3); // 2 1 1
const XcVector v18(v17 + v3); // 2 1 2
const XcVector v19(v17 + v2); // 2 2 1
const XcVector v20(v19 + v3); // 2 2 2
const XcVector v21(v2 + v3); // 0 1 1
const XcVector v22(v21 + v3); // 0 1 2
const XcVector v23(v2 + v2); // 0 2 0
const XcVector v24(v23 + v3); // 0 2 1
const XcVector v25(v24 + v3); // 0 2 2
const XcVector v26(v3 + v3); // 0 0 2
for (size_t i = 0; i < types.size(); ++i) {
if (types[i] == m_lfAtomType) {
const XcVector &tmpVec = ccoords[i];
// Add to cell
m_superLfCCoordList2.push_back(tmpVec);
// Replicate to supercell
m_superLfCCoordList2.push_back(tmpVec + v1 );
m_superLfCCoordList2.push_back(tmpVec + v2 );
m_superLfCCoordList2.push_back(tmpVec + v3 );
m_superLfCCoordList2.push_back(tmpVec + v4 );
m_superLfCCoordList2.push_back(tmpVec + v5 );
m_superLfCCoordList2.push_back(tmpVec + v6 );
m_superLfCCoordList2.push_back(tmpVec + v7 );
m_superLfCCoordList2.push_back(tmpVec + v8 );
m_superLfCCoordList2.push_back(tmpVec + v9 );
m_superLfCCoordList2.push_back(tmpVec + v10);
m_superLfCCoordList2.push_back(tmpVec + v11);
m_superLfCCoordList2.push_back(tmpVec + v12);
m_superLfCCoordList2.push_back(tmpVec + v13);
m_superLfCCoordList2.push_back(tmpVec + v14);
m_superLfCCoordList2.push_back(tmpVec + v15);
m_superLfCCoordList2.push_back(tmpVec + v16);
m_superLfCCoordList2.push_back(tmpVec + v17);
m_superLfCCoordList2.push_back(tmpVec + v18);
m_superLfCCoordList2.push_back(tmpVec + v19);
m_superLfCCoordList2.push_back(tmpVec + v20);
m_superLfCCoordList2.push_back(tmpVec + v21);
m_superLfCCoordList2.push_back(tmpVec + v22);
m_superLfCCoordList2.push_back(tmpVec + v23);
m_superLfCCoordList2.push_back(tmpVec + v24);
m_superLfCCoordList2.push_back(tmpVec + v25);
m_superLfCCoordList2.push_back(tmpVec + v26);
}
}
}
// 2x2x2 case:
else {
const XcVector v4 (v1 + v2); // 1 1 0
const XcVector v5 (v1 + v3); // 1 0 1
const XcVector v6 (v4 + v3); // 1 1 1
const XcVector v7 (v2 + v3); // 0 1 1
for (size_t i = 0; i < types.size(); ++i) {
if (types[i] == m_lfAtomType) {
const XcVector &tmpVec = ccoords[i];
// Add to cell
m_superLfCCoordList2.push_back(tmpVec);
// Replicate to supercell
m_superLfCCoordList2.push_back(tmpVec + v1 );
m_superLfCCoordList2.push_back(tmpVec + v2 );
m_superLfCCoordList2.push_back(tmpVec + v3 );
m_superLfCCoordList2.push_back(tmpVec + v4 );
m_superLfCCoordList2.push_back(tmpVec + v5 );
m_superLfCCoordList2.push_back(tmpVec + v6 );
m_superLfCCoordList2.push_back(tmpVec + v7 );
}
}
}
}
void XtalComp::findCandidateTransforms()
{
// Find all sets of 4 coordinates that correspond to the reference
// translation vectors
//
// a
// | c
// | /
// |/
// o------b
//
// o, a, b, and c are cartesian coordinates in
// m_superLfCCoordList. Define:
//
// t1 = a-o
// t2 = b-o
// t3 = c-o
//
// If:
//
// t1.squaredNorm() == m_refVec1.squaredNorm() &&
// t2.squaredNorm() == m_refVec2.squaredNorm() &&
// t3.squaredNorm() == m_refVec3.squaredNorm() &&
// angle(t1,t2) == angle(m_refVec1,refVec2) (== gamma) &&
// angle(t1,t3) == angle(m_refVec1,refVec3) (== beta) &&
// angle(t2,t3) == angle(m_refVec2,refVec3) (== alpha)
//
// Then we have a valid candidate reference frame. Store -o as the
// translation and calculate a rotation/reflection matrix that
// will transform t1, t2, t3 into the refVecs. Use the XcTransform
// class to store these operations for later retrieval.
// Set tolerance for vector checks:
const double tol = m_lengthtol;
const double squaredTol = tol*tol;
// Allocate room for all lfAtoms in the translations list, (this
// is the maximum)
m_transforms.clear();
m_transforms.reserve(m_lfAtomCount);
// Lists to store candidate tX vectors
std::vector<XcVector> t1_candidates;
std::vector<XcVector> t2_candidates;
std::vector<XcVector> t3_candidates;
// Search for candidate tX vectors:
//
// Cache some values:
const double v1Norm2 = m_refVec1.squaredNorm();
const double v2Norm2 = m_refVec2.squaredNorm();
const double v3Norm2 = m_refVec3.squaredNorm();
const double vAlpha = compAngle(m_refVec2, m_refVec3);
const double vBeta = compAngle(m_refVec1, m_refVec3);
const double vGamma = compAngle(m_refVec1, m_refVec2);
XcMatrix V;
V.fillCols(m_refVec1, m_refVec2, m_refVec3);
//
// iterate over all "o" atoms.
for (std::vector<XcVector>::const_iterator
atm1 = m_superLfCCoordList2.begin(),
super_end = m_superLfCCoordList2.end();
atm1 != super_end; ++atm1) {
//
// Reset candidate tX lists
t1_candidates.clear();
t2_candidates.clear();
t3_candidates.clear();
// Search for all a, b, c atoms
for (std::vector<XcVector>::const_iterator
atm2 = m_superLfCCoordList2.begin();
atm2 != super_end; ++atm2) {
//
// Get trial vector:
XcVector t ((*atm2) - (*atm1));
const double tNorm2 = t.squaredNorm();
//
// Compare against reference vectors. Check the norm of their
// differences to a tolerance.
if (fabs(tNorm2 - v1Norm2) < squaredTol) t1_candidates.push_back(t);
if (fabs(tNorm2 - v2Norm2) < squaredTol) t2_candidates.push_back(t);
if (fabs(tNorm2 - v3Norm2) < squaredTol) t3_candidates.push_back(t);
}
// Move to next candidate origin if any candidates are missing:
if (!t1_candidates.size() ||
!t2_candidates.size() ||
!t3_candidates.size()) {
continue;
}
#ifdef XTALCOMP_DEBUG
DEBUG_DIV;
DEBUG_STRING("Candidate transforms for offset:");
DEBUG_VECTOR(*atm1);
DEBUG_DIV;
DEBUG_STRING("Candidates for t1");
for (std::vector<XcVector>::const_iterator
it = t1_candidates.begin(),
it_end = t1_candidates.end();
it != it_end; ++it) {
DEBUG_VECTOR(*it);
}
DEBUG_STRING("Candidates for t2");
for (std::vector<XcVector>::const_iterator
it = t2_candidates.begin(),
it_end = t2_candidates.end();
it != it_end; ++it) {
DEBUG_VECTOR(*it);
}
DEBUG_STRING("Candidates for t3");
for (std::vector<XcVector>::const_iterator
it = t3_candidates.begin(),
it_end = t3_candidates.end();
it != it_end; ++it) {
DEBUG_VECTOR(*it);
}
#endif
// Search for transforms by comparing angles:
//
// Iterate over all t1 candidates
for (std::vector<XcVector>::const_iterator
t1 = t1_candidates.begin(),
t1_end = t1_candidates.end();
t1 != t1_end; ++t1) {
#ifdef XTALCOMP_DEBUG
DEBUG_STRING_VECTOR("Using t1", *t1);
#endif
// Iterate over all t2 candidates
for (std::vector<XcVector>::const_iterator
t2 = t2_candidates.begin(),
t2_end = t2_candidates.end();
t2 != t2_end; ++t2) {
#ifdef XTALCOMP_DEBUG
DEBUG_STRING_VECTOR("Using t2", *t2);
printf("Comparing angles: t1,t2= %f v1,v2= %f\n", compAngle(*t1,*t2), vGamma);
#endif
// Compare t1.t2 with v1.v2
if (fabs(compAngle(*t1,*t2) - vGamma) < m_angletol) {
// They match, so now search for a valid t3
for (std::vector<XcVector>::const_iterator
t3 = t3_candidates.begin(),
t3_end = t3_candidates.end();
t3 != t3_end; ++t3) {
#ifdef XTALCOMP_DEBUG
DEBUG_STRING_VECTOR("Using t3", *t3);
printf("Comparing angles: t1,t3= %f v1,v2= %f\n", compAngle(*t1,*t3), vBeta);
printf("Comparing angles: t2,t3= %f v1,v2= %f\n", compAngle(*t2,*t3), vAlpha);
#endif
// Compare t1.t3 with v1.v3 and t2.t3 with v2.v3
if (fabs(compAngle(*t1,*t3) - vBeta) < m_angletol &&
fabs(compAngle(*t2,*t3) - vAlpha) < m_angletol) {
// t1, t2, and t3 correspond to v1, v2, and v3
//
// Find rotation matrix that converts matrix T = (t1,
// t2, t3) into matrix V = (v1, v2, v3). In other
// words, let's find a matrix R such that:
//
// V = R T
//
// Thus, R = V T^-1
XcMatrix T;
T.fillCols(*t1, *t2, *t3);
const XcMatrix R (V * T.inverse());
// Build and store XcTransform:
XcTransform transform;
transform.setIdentity();
transform.rotate(R);
transform.translate(-(*atm1));
m_transforms.push_back(transform);
#ifdef XTALCOMP_DEBUG
DEBUG_STRING("Found transform:");
DEBUG_STRING("Translation:");
DEBUG_VECTOR(-(*atm1));
DEBUG_STRING("Rotation");
DEBUG_MATRIX(R);
DEBUG_STRING("transform: rot, trans");
DEBUG_MATRIX(transform.rotation());
DEBUG_VECTOR(transform.translation());
#endif
// Verify that this is a pure rot/ref matrix (allow a rather
// large fudge factor here -- the vectors may not match exactly)
//assert(fabs(fabs(R.determinant()) - 1.0) < .1);
// DL 20120119 Removed assertion: This is not worth dying over.
}
}
}
}
}
}
}
bool XtalComp::hasMoreTransforms() const
{
// Are there any more transforms?
if (m_transformsIndex < m_transforms.size()) {
return true;
}
#ifdef XTALCOMP_DEBUG
DEBUG_DIV;
DEBUG_STRING("No more transforms");
DEBUG_DIV;
#endif
return false;
}
void XtalComp::applyNextTransform()
{
#ifdef XTALCOMP_DEBUG
DEBUG_DIV;
printf("Applying transform %d of %d\n", m_transformsIndex+1, m_transforms.size());
#endif
// Get current transformation
assert (m_transformsIndex < m_transforms.size());
m_transform = m_transforms[m_transformsIndex];
#ifdef XTALCOMP_DEBUG
DEBUG_STRING("m_transform: rot, trans");
DEBUG_MATRIX(m_transform.rotation());
DEBUG_VECTOR(m_transform.translation());
#endif
buildTransformedXtal2();
// Update transform index
++m_transformsIndex;
#ifdef XTALCOMP_DEBUG
DEBUG_DIV;
DEBUG_STRING("Transform applied");
DEBUG_STRING("Transformed cmat:");
DEBUG_MATRIX(m_transformedCMat);
DEBUG_STRING("Transformed fmat:");
DEBUG_MATRIX(m_transformedFMat);
DEBUG_STRING("Transformed atoms (cart|frac):");
for (int i = 0; i < m_transformedTypes.size(); ++i) {
DEBUG_ATOMCF(m_transformedTypes.at(i), m_transformedCCoords.at(i),
m_transformedFCoords.at(i));
}
DEBUG_DIV;
#endif
}
void XtalComp::buildTransformedXtal2()
{
// Transform matrices
m_transformedCMat = m_transform.rotation() * m_rx2->cmat();
m_transformedFMat = m_transformedCMat.inverse();
// TODO isUnitary
//assert((m_transformedFMat * m_transformedCMat).isUnitary(1e-4));
// Reset transformed types to the original types
m_transformedTypes.resize(m_rx2->types().size());
copy(m_rx2->types().begin(), m_rx2->types().end(),
m_transformedTypes.begin());
// Set transformed coordinates:
//
// First we need to adjust the transformation matrix. The
// translation in m_transform is in cartesian units, but we want
// to transform the fractional coordinates, since we will need to
// expand them before converting to the final cartesian set. So we
// first make a copy of the current transform:
XcTransform fracTransform (m_transform);
// We will be multiplying fractional coords from the right, so
// append a frac -> cart conversion to the right hand side of the
// transform:
fracTransform.rotate(m_rx2->cmat());
// We then need to convert back into fractional coordinates after the translation
fracTransform.prerotate(m_transformedFMat);
#ifdef XTALCOMP_DEBUG
DEBUG_STRING("FracTransform: rot, trans");
DEBUG_MATRIX(fracTransform.rotation());
DEBUG_VECTOR(fracTransform.translation());
#endif
// Now to perform the transformations
m_transformedFCoords.clear();
m_transformedFCoords.reserve(m_rx2->fcoords().size());
for (std::vector<XcVector>::const_iterator
it = m_rx2->fcoords().begin(),
it_end = m_rx2->fcoords().end();
it != it_end; ++it) {
// Transform each fractional coordinate
m_transformedFCoords.push_back(fracTransform * (*it));
}
// Don't bother wrapping these into the new unit cell -- they will be
// translated in rx1's cell during the comparison.
// Convert to cartesian
m_transformedCCoords.clear();
m_transformedCCoords.reserve(m_transformedFCoords.size());
for (std::vector<XcVector>::iterator
it = m_transformedFCoords.begin(),
it_end = m_transformedFCoords.end();
it != it_end; ++it) {
m_transformedCCoords.push_back(m_transformedCMat * (*it));
}
}
void XtalComp::expandFractionalCoordinates(std::vector<unsigned int> *types,
std::vector<XcVector> *fcoords,
DuplicateMap *duplicateAtoms,
const XcMatrix &cmat,
const double tol)
{
// Wrap translated coordinates and expand translated coordinates
// (if an atom is very close to a cell boundary, place another
// atom at the opposite boundary for numerical stability)
//
// Definitions using fractional basis:
//
// 5------8
// /: /|
// / : / |
// / 2.../..7
// 3--/---6 /
// | / | /
// |/ |/
// 1------4
//
// Points:
// p1 = (0 0 0) | p5 = (1 1 0)
// p2 = (1 0 0) | p6 = (0 1 1)
// p3 = (0 1 0) | p7 = (1 0 1)
// p4 = (0 0 1) | p8 = (1 1 1)
//
// Vectors:
// v1 (a) = p2 - p1 = (1 0 0)
// v2 (b) = p3 - p1 = (0 1 0)
// v3 (c) = p4 - p1 = (0 0 1)
//
// Planes:
// #: normal point | points
// 1: v1 p1 | 1,3,4,6
// 2: v2 p1 | 1,2,4,7
// 3: v3 p1 | 1,2,3,5
// 4: v1 p8 | 2,5,7,8
// 5: v2 p8 | 3,5,6,8
// 6: v3 p8 | 4,6,7,8
//
// Edges:
// # | pts | planes ## | pts | planes
// 1 | 1,2 | 2,3 7 | 3,6 | 1,5
// 2 | 1,3 | 1,3 8 | 4,6 | 1,6
// 3 | 1,4 | 1,2 9 | 4,7 | 2,6
// 4 | 2,5 | 3,4 10 | 5,8 | 4,5
// 5 | 2,7 | 2,4 11 | 6,8 | 5,6
// 6 | 3,5 | 3,5 12 | 7.8 | 4,6
//
// Defining cell boundaries as planes, n ( r - r0 ) = 0,
// n = normal vector
// r0 = point in plane
// r = coordinate
//
// There are 6 planes, defined using v1, v2, v3 as possible n, and
// p1, p8 as possible r0:
//
// Plane 1:
// n = v1; r0 = p1
// Plane equ: v1 ( r - p1 ) = 0 = v1[0] * r[0]
// r[0] = 0
//
// Plane 2:
// n = v2; r0 = p1
// Plane equ: v2 ( r - p1 ) = 0 = v2[1] * r[1]
// r[1] = 0
//
// Plane 3:
// n = v3; r0 = p1
// Plane equ: v3 ( r - p1 ) = 0 = v3[2] * r[2]
// r[2] = 0
//
// Plane 4:
// n = v1; r0 = p8
// Plane equ: v1 ( r - p8 ) = 0 = v1[0] * r[0] - v1[1] * r0[0] or
// Plane equ: v1 ( r - p8 ) = 0 = v1[0] * r[0] - v1[0] * r0[0] ??
// r[0] - 1 = 0
//
// Plane 5:
// n = v2; r0 = p8
// Plane equ: v2 ( r - p8 ) = 0 = v2[1] * r[1] - v2[1] * r0[1]
// r[1] - 1 = 0
//
// Plane 6: