diff --git a/src/USER-UEF/fix_nh_uef.cpp b/src/USER-UEF/fix_nh_uef.cpp
index cd0b2ba2683742ab1140ce3a41e0e7c506a40a33..bfa45492864ff4708fb0e22167b04b69ca95cbc1 100644
--- a/src/USER-UEF/fix_nh_uef.cpp
+++ b/src/USER-UEF/fix_nh_uef.cpp
@@ -536,10 +536,26 @@ void FixNHUef::pre_exchange()
rotate_x(rot);
rotate_f(rot);
- // put all atoms in the new box
- double **x = atom->x;
+ // this is a generalization of what is done in domain->image_flip(...)
+ int ri[3][3];
+ uefbox->get_inverse_cob(ri);
imageint *image = atom->image;
int nlocal = atom->nlocal;
+ for (int i=0; i<nlocal; i++) {
+ int iold[3],inew[3];
+ iold[0] = (image[i] & IMGMASK) - IMGMAX;
+ iold[1] = (image[i] >> IMGBITS & IMGMASK) - IMGMAX;
+ iold[2] = (image[i] >> IMG2BITS) - IMGMAX;
+ inew[0] = ri[0][0]*iold[0] + ri[0][1]*iold[1] + ri[0][2]*iold[2];
+ inew[1] = ri[1][0]*iold[0] + ri[1][1]*iold[1] + ri[1][2]*iold[2];
+ inew[2] = ri[2][0]*iold[0] + ri[2][1]*iold[1] + ri[2][2]*iold[2];
+ image[i] = ((imageint) (inew[0] + IMGMAX) & IMGMASK) |
+ (((imageint) (inew[1] + IMGMAX) & IMGMASK) << IMGBITS) |
+ (((imageint) (inew[2] + IMGMAX) & IMGMASK) << IMG2BITS);
+ }
+
+ // put all atoms in the new box
+ double **x = atom->x;
for (int i=0; i<nlocal; i++) domain->remap(x[i],image[i]);
// move atoms to the right processors
diff --git a/src/USER-UEF/uef_utils.cpp b/src/USER-UEF/uef_utils.cpp
index a5498d605f3d28291d91dcc320a4cd41dd999ce2..a2e6cb291e0cb4c7b4ff48e9d1d181d0b7f65e4a 100644
--- a/src/USER-UEF/uef_utils.cpp
+++ b/src/USER-UEF/uef_utils.cpp
@@ -30,47 +30,54 @@ namespace LAMMPS_NS {
UEFBox::UEFBox()
{
+
// initial box (also an inverse eigenvector matrix of automorphisms)
+
double x = 0.327985277605681;
double y = 0.591009048506103;
double z = 0.736976229099578;
l0[0][0]= z; l0[0][1]= y; l0[0][2]= x;
l0[1][0]=-x; l0[1][1]= z; l0[1][2]=-y;
l0[2][0]=-y; l0[2][1]= x; l0[2][2]= z;
+
// spectra of the two automorpisms (log of eigenvalues)
+
w1[0]=-1.177725211523360;
w1[1]=-0.441448620566067;
w1[2]= 1.619173832089425;
w2[0]= w1[1];
w2[1]= w1[2];
w2[2]= w1[0];
+
// initialize theta
// strain = w1 * theta1 + w2 * theta2
- theta[0]=theta[1]=0;
+ theta[0]=theta[1]=0;
//set up the initial box l and change of basis matrix r
+
for (int k=0;k<3;k++)
- for (int j=0;j<3;j++)
- {
+ for (int j=0;j<3;j++) {
l[k][j] = l0[k][j];
r[j][k]=(j==k);
+ ri[j][k]=(j==k);
}
// get the initial rotation and upper triangular matrix
+
rotation_matrix(rot, lrot ,l);
// this is just a way to calculate the automorphisms
// themselves, which play a minor role in the calculations
// it's overkill, but only called once
+
double t1[3][3];
double t1i[3][3];
double t2[3][3];
double t2i[3][3];
double l0t[3][3];
for (int k=0; k<3; ++k)
- for (int j=0; j<3; ++j)
- {
+ for (int j=0; j<3; ++j) {
t1[k][j] = exp(w1[k])*l0[k][j];
t1i[k][j] = exp(-w1[k])*l0[k][j];
t2[k][j] = exp(w2[k])*l0[k][j];
@@ -82,8 +89,7 @@ UEFBox::UEFBox()
mul_m2(l0t,t2);
mul_m2(l0t,t2i);
for (int k=0; k<3; ++k)
- for (int j=0; j<3; ++j)
- {
+ for (int j=0; j<3; ++j) {
a1[k][j] = round(t1[k][j]);
a1i[k][j] = round(t1i[k][j]);
a2[k][j] = round(t2[k][j]);
@@ -92,6 +98,7 @@ UEFBox::UEFBox()
// winv used to transform between
// strain increments and theta increments
+
winv[0][0] = w2[1];
winv[0][1] = -w2[0];
winv[1][0] = -w1[1];
@@ -102,7 +109,9 @@ UEFBox::UEFBox()
winv[k][j] /= d;
}
-// get volume-correct r basis in: basis*cbrt(vol) = q*r
+/* ----------------------------------------------------------------------
+ get volume-correct r basis in: basis*cbrt(vol) = q*r
+------------------------------------------------------------------------- */
void UEFBox::get_box(double x[3][3], double v)
{
v = cbrtf(v);
@@ -111,7 +120,9 @@ void UEFBox::get_box(double x[3][3], double v)
x[k][j] = lrot[k][j]*v;
}
-// get rotation matrix q in: basis = q*r
+/* ----------------------------------------------------------------------
+ get rotation matrix q in: basis = q*r
+------------------------------------------------------------------------- */
void UEFBox::get_rot(double x[3][3])
{
for (int k=0;k<3;k++)
@@ -119,20 +130,32 @@ void UEFBox::get_rot(double x[3][3])
x[k][j]=rot[k][j];
}
-// diagonal, incompressible deformation
+/* ----------------------------------------------------------------------
+ get inverse change of basis matrix
+------------------------------------------------------------------------- */
+void UEFBox::get_inverse_cob(int x[3][3])
+{
+ for (int k=0;k<3;k++)
+ for (int j=0;j<3;j++)
+ x[k][j]=ri[k][j];
+}
+
+/* ----------------------------------------------------------------------
+ apply diagonal, incompressible deformation
+------------------------------------------------------------------------- */
void UEFBox::step_deform(const double ex, const double ey)
{
// increment theta values used in the reduction
+
theta[0] +=winv[0][0]*ex + winv[0][1]*ey;
theta[1] +=winv[1][0]*ex + winv[1][1]*ey;
- // deformation of the box. reduce() needs to
- // be called regularly or calculation will become
- // unstable
+ // deformation of the box. reduce() needs to be called regularly or
+ // calculation will become unstable
+
double eps[3];
eps[0]=ex; eps[1] = ey; eps[2] = -ex-ey;
- for (int k=0;k<3;k++)
- {
+ for (int k=0;k<3;k++) {
eps[k] = exp(eps[k]);
l[k][0] = eps[k]*l[k][0];
l[k][1] = eps[k]*l[k][1];
@@ -140,68 +163,84 @@ void UEFBox::step_deform(const double ex, const double ey)
}
rotation_matrix(rot,lrot, l);
}
-// reuduce the current basis
+
+/* ----------------------------------------------------------------------
+ reduce the current basis
+------------------------------------------------------------------------- */
bool UEFBox::reduce()
{
- // determine how many times to apply the automorphisms
- // and find new theta values
+ // determine how many times to apply the automorphisms and find new theta
+ // values
+
int f1 = round(theta[0]);
int f2 = round(theta[1]);
theta[0] -= f1;
theta[1] -= f2;
- // store old change or basis matrix to determine if it
- // changes
+ // store old change or basis matrix to determine if it changes
+
int r0[3][3];
for (int k=0;k<3;k++)
for (int j=0;j<3;j++)
r0[k][j]=r[k][j];
- // this modifies the old change basis matrix to
- // handle the case where the automorphism transforms
- // the box but the reduced basis doesn't change
+ // this modifies the old change basis matrix to handle the case where the
+ // automorphism transforms the box but the reduced basis doesn't change
// (r0 should still equal r at the end)
+
if (f1 > 0) for (int k=0;k<f1;k++) mul_m2 (a1,r0);
if (f1 < 0) for (int k=0;k<-f1;k++) mul_m2 (a1i,r0);
if (f2 > 0) for (int k=0;k<f2;k++) mul_m2 (a2,r0);
if (f2 < 0) for (int k=0;k<-f2;k++) mul_m2 (a2i,r0);
// robust reduction to the box defined by Dobson
- for (int k=0;k<3;k++)
- {
+
+ for (int k=0;k<3;k++) {
double eps = exp(theta[0]*w1[k]+theta[1]*w2[k]);
l[k][0] = eps*l0[k][0];
l[k][1] = eps*l0[k][1];
l[k][2] = eps*l0[k][2];
}
+
// further reduce the box using greedy reduction and check
// if it changed from the last step using the change of basis
// matrices r and r0
- greedy(l,r);
+
+ greedy(l,r,ri);
+
+ // multiplying the inverse by the old change of basis matrix gives
+ // the inverse of the transformation itself (should be identity if
+ // no reduction takes place). This is used for image flags only.
+
+ mul_m1(ri,r0);
rotation_matrix(rot,lrot, l);
return !mat_same(r,r0);
}
+
+/* ----------------------------------------------------------------------
+ set the strain to a specific value
+------------------------------------------------------------------------- */
void UEFBox::set_strain(const double ex, const double ey)
{
- theta[0] =winv[0][0]*ex + winv[0][1]*ey;
- theta[1] =winv[1][0]*ex + winv[1][1]*ey;
+ theta[0] = winv[0][0]*ex + winv[0][1]*ey;
+ theta[1] = winv[1][0]*ex + winv[1][1]*ey;
theta[0] -= round(theta[0]);
theta[1] -= round(theta[1]);
- for (int k=0;k<3;k++)
- {
+ for (int k=0;k<3;k++) {
double eps = exp(theta[0]*w1[k]+theta[1]*w2[k]);
l[k][0] = eps*l0[k][0];
l[k][1] = eps*l0[k][1];
l[k][2] = eps*l0[k][2];
}
- greedy(l,r);
+ greedy(l,r,ri);
rotation_matrix(rot,lrot, l);
}
-// this is just qr reduction using householder reflections
-// m is input matrix, q is a rotation, r is upper triangular
-// q*m = r
+/* ----------------------------------------------------------------------
+ qr reduction using householder reflections
+ q*m = r. q is orthogonal. m is input matrix. r is upper triangular
+------------------------------------------------------------------------- */
void rotation_matrix(double q[3][3], double r[3][3], const double m[3][3])
{
for (int k=0;k<3;k++)
@@ -217,8 +256,7 @@ void rotation_matrix(double q[3][3], double r[3][3], const double m[3][3])
v[0] /= a; v[1] /= a; v[2] /= a;
double qt[3][3];
for (int k=0;k<3;k++)
- for (int j=0;j<3;j++)
- {
+ for (int j=0;j<3;j++) {
qt[k][j] = (k==j) - 2*v[k]*v[j];
q[k][j]= qt[k][j];
}
@@ -235,38 +273,42 @@ void rotation_matrix(double q[3][3], double r[3][3], const double m[3][3])
qt[k][j] = (k==j) - 2*v[k]*v[j];
mul_m2(qt,r);
mul_m2(qt,q);
+
// this makes r have positive diagonals
// q*m = r <==> (-q)*m = (-r) will hold row-wise
+
if (r[0][0] < 0){ neg_row(q,0); neg_row(r,0); }
if (r[1][1] < 0){ neg_row(q,1); neg_row(r,1); }
if (r[2][2] < 0){ neg_row(q,2); neg_row(r,2); }
}
-
-
-//sort columns in order of increasing length
-void col_sort(double b[3][3],int r[3][3])
+/* ----------------------------------------------------------------------
+ sort columns of b in order of increasing length
+ mimic column operations on ri and r
+------------------------------------------------------------------------- */
+void col_sort(double b[3][3],int r[3][3],int ri[3][3])
{
- if (col_prod(b,0,0)>col_prod(b,1,1))
- {
+ if (col_prod(b,0,0)>col_prod(b,1,1)) {
col_swap(b,0,1);
col_swap(r,0,1);
+ col_swap(ri,0,1);
}
- if (col_prod(b,0,0)>col_prod(b,2,2))
- {
+ if (col_prod(b,0,0)>col_prod(b,2,2)) {
col_swap(b,0,2);
col_swap(r,0,2);
+ col_swap(ri,0,2);
}
- if (col_prod(b,1,1)>col_prod(b,2,2))
- {
+ if (col_prod(b,1,1)>col_prod(b,2,2)) {
col_swap(b,1,2);
col_swap(r,1,2);
+ col_swap(ri,1,2);
}
}
-
-// 1-2 reduction (Graham-Schmidt)
-void red12(double b[3][3],int r[3][3])
+/* ----------------------------------------------------------------------
+ 1-2 reduction (Graham-Schmidt)
+------------------------------------------------------------------------- */
+void red12(double b[3][3],int r[3][3],int ri[3][3])
{
int y = round(col_prod(b,0,1)/col_prod(b,0,0));
b[0][1] -= y*b[0][0];
@@ -276,16 +318,23 @@ void red12(double b[3][3],int r[3][3])
r[0][1] -= y*r[0][0];
r[1][1] -= y*r[1][0];
r[2][1] -= y*r[2][0];
- if (col_prod(b,1,1) < col_prod(b,0,0))
- {
+
+ ri[0][0] += y*ri[0][1];
+ ri[1][0] += y*ri[1][1];
+ ri[2][0] += y*ri[2][1];
+
+ if (col_prod(b,1,1) < col_prod(b,0,0)) {
col_swap(b,0,1);
col_swap(r,0,1);
- red12(b,r);
+ col_swap(ri,0,1);
+ red12(b,r,ri);
}
}
-// The Semaev condition for a 3-reduced basis
-void red3(double b[3][3], int r[3][3])
+/* ----------------------------------------------------------------------
+ Apply the Semaev condition for a 3-reduced basis
+------------------------------------------------------------------------- */
+void red3(double b[3][3], int r[3][3], int ri[3][3])
{
double b11 = col_prod(b,0,0);
double b22 = col_prod(b,1,1);
@@ -304,63 +353,97 @@ void red3(double b[3][3], int r[3][3])
x1v[0] = floor(y1); x1v[1] = x1v[0]+1;
x2v[0] = floor(y2); x2v[1] = x2v[0]+1;
for (int k=0;k<2;k++)
- for (int j=0;j<2;j++)
- {
+ for (int j=0;j<2;j++) {
double a[3];
a[0] = b[0][2] + x1v[k]*b[0][0] + x2v[j]*b[0][1];
a[1] = b[1][2] + x1v[k]*b[1][0] + x2v[j]*b[1][1];
a[2] = b[2][2] + x1v[k]*b[2][0] + x2v[j]*b[2][1];
double val=a[0]*a[0]+a[1]*a[1]+a[2]*a[2];
- if (val<min)
- {
+ if (val<min) {
min = val;
x1 = x1v[k];
x2 = x2v[j];
}
}
- if (x1 || x2)
- {
+ if (x1 || x2) {
b[0][2] += x1*b[0][0] + x2*b[0][1];
b[1][2] += x1*b[1][0] + x2*b[1][1];
b[2][2] += x1*b[2][0] + x2*b[2][1];
r[0][2] += x1*r[0][0] + x2*r[0][1];
r[1][2] += x1*r[1][0] + x2*r[1][1];
r[2][2] += x1*r[2][0] + x2*r[2][1];
- greedy_recurse(b,r); // note the recursion step is here
+ ri[0][0] += -x1*ri[0][2];
+ ri[1][0] += -x1*ri[1][2];
+ ri[2][0] += -x1*ri[2][2];
+ ri[0][1] += -x2*ri[0][2];
+ ri[1][1] += -x2*ri[1][2];
+ ri[2][1] += -x2*ri[2][2];
+ greedy_recurse(b,r,ri); // note the recursion step is here
}
}
-// the meat of the greedy reduction algorithm
-void greedy_recurse(double b[3][3], int r[3][3])
+/* ----------------------------------------------------------------------
+ the meat of the greedy reduction algorithm
+------------------------------------------------------------------------- */
+void greedy_recurse(double b[3][3], int r[3][3], int ri[3][3])
{
- col_sort(b,r);
- red12(b,r);
- red3(b,r); // recursive caller
+ col_sort(b,r,ri);
+ red12(b,r,ri);
+ red3(b,r,ri); // recursive caller
}
-// set r (change of basis) to be identity then reduce basis and make it unique
-void greedy(double b[3][3],int r[3][3])
+/* ----------------------------------------------------------------------
+ reduce the basis b. also output the change of basis matrix r and its
+ inverse ri
+------------------------------------------------------------------------- */
+void greedy(double b[3][3],int r[3][3],int ri[3][3])
{
r[0][1]=r[0][2]=r[1][0]=r[1][2]=r[2][0]=r[2][1]=0;
r[0][0]=r[1][1]=r[2][2]=1;
- greedy_recurse(b,r);
- make_unique(b,r);
+ ri[0][1]=ri[0][2]=ri[1][0]=ri[1][2]=ri[2][0]=ri[2][1]=0;
+ ri[0][0]=ri[1][1]=ri[2][2]=1;
+ greedy_recurse(b,r,ri);
+ make_unique(b,r,ri);
+ transpose(ri);
}
-// A reduced basis isn't unique. This procedure will make it
-// "more" unique. Degenerate cases are possible, but unlikely
-// with floating point math.
-void make_unique(double b[3][3], int r[3][3])
+/* ----------------------------------------------------------------------
+ A reduced basis isn't unique. This procedure will make it
+ "more" unique. Degenerate cases are possible, but unlikely
+ with floating point math.
+------------------------------------------------------------------------- */
+void make_unique(double b[3][3], int r[3][3], int ri[3][3])
{
- if (fabs(b[0][0]) < fabs(b[0][1]))
- { col_swap(b,0,1); col_swap(r,0,1); }
- if (fabs(b[0][0]) < fabs(b[0][2]))
- { col_swap(b,0,2); col_swap(r,0,2); }
- if (fabs(b[1][1]) < fabs(b[1][2]))
- { col_swap(b,1,2); col_swap(r,1,2); }
-
- if (b[0][0] < 0){ neg_col(b,0); neg_col(r,0); }
- if (b[1][1] < 0){ neg_col(b,1); neg_col(r,1); }
- if (det(b) < 0){ neg_col(b,2); neg_col(r,2); }
+ if (fabs(b[0][0]) < fabs(b[0][1])) {
+ col_swap(b,0,1);
+ col_swap(r,0,1);
+ col_swap(ri,0,1);
+ }
+ if (fabs(b[0][0]) < fabs(b[0][2])) {
+ col_swap(b,0,2);
+ col_swap(r,0,2);
+ col_swap(ri,0,2);
+ }
+ if (fabs(b[1][1]) < fabs(b[1][2])) {
+ col_swap(b,1,2);
+ col_swap(r,1,2);
+ col_swap(ri,1,2);
+ }
+
+ if (b[0][0] < 0) {
+ neg_col(b,0);
+ neg_col(r,0);
+ neg_col(ri,0);
+ }
+ if (b[1][1] < 0) {
+ neg_col(b,1);
+ neg_col(r,1);
+ neg_col(ri,1);
+ }
+ if (det(b) < 0) {
+ neg_col(b,2);
+ neg_col(r,2);
+ neg_col(ri,2);
+ }
}
}}
diff --git a/src/USER-UEF/uef_utils.h b/src/USER-UEF/uef_utils.h
index a16f6fff1a70f1e5e15b3f993efc702deaaf034f..0a1cfcc9b2ca9f897d9bf4caed142644d24cf3fe 100644
--- a/src/USER-UEF/uef_utils.h
+++ b/src/USER-UEF/uef_utils.h
@@ -27,26 +27,27 @@ class UEFBox
bool reduce();
void get_box(double[3][3], double);
void get_rot(double[3][3]);
+ void get_inverse_cob(int[3][3]);
private:
double l0[3][3]; // initial basis
- double w1[3],w2[3], winv[3][3]; // omega1 and omega2 (spectra of automorphisms)
- //double edot[3], delta[2];
+ double w1[3],w2[3],winv[3][3];//omega1 and omega2 (spectra of automorphisms)
double theta[2];
double l[3][3], rot[3][3], lrot[3][3];
- int r[3][3],a1[3][3],a2[3][3],a1i[3][3],a2i[3][3];
+ int r[3][3],ri[3][3],a1[3][3],a2[3][3],a1i[3][3],a2i[3][3];
};
-
// lattice reduction routines
-void greedy(double[3][3],int[3][3]);
-void col_sort(double[3][3],int[3][3]);
-void red12(double[3][3],int[3][3]);
-void greedy_recurse(double[3][3],int[3][3]);
-void red3(double [3][3],int r[3][3]);
-void make_unique(double[3][3],int[3][3]);
+
+void greedy(double[3][3],int[3][3],int[3][3]);
+void col_sort(double[3][3],int[3][3],int[3][3]);
+void red12(double[3][3],int[3][3],int[3][3]);
+void greedy_recurse(double[3][3],int[3][3],int[3][3]);
+void red3(double [3][3],int r[3][3],int[3][3]);
+void make_unique(double[3][3],int[3][3],int[3][3]);
void rotation_matrix(double[3][3],double[3][3],const double [3][3]);
// A few utility functions for 3x3 arrays
+
template<typename T>
T col_prod(T x[3][3], int c1, int c2)
{
@@ -56,8 +57,7 @@ T col_prod(T x[3][3], int c1, int c2)
template<typename T>
void col_swap(T x[3][3], int c1, int c2)
{
- for (int k=0;k<3;k++)
- {
+ for (int k=0;k<3;k++) {
T t = x[k][c2];
x[k][c2]=x[k][c1];
x[k][c1]=t;
@@ -101,9 +101,21 @@ bool mat_same(T x1[3][3], T x2[3][3])
}
template<typename T>
-void mul_m1(T m1[3][3], const T m2[3][3])
+void transpose(T m[3][3])
{
T t[3][3];
+ for (int k=0;k<3;k++)
+ for (int j=k+1;j<3;j++) {
+ T x = m[k][j];
+ m[k][j] = m[j][k];
+ m[j][k] = x;
+ }
+}
+
+template<typename T1,typename T2>
+void mul_m1(T1 m1[3][3], const T2 m2[3][3])
+{
+ T1 t[3][3];
for (int k=0;k<3;k++)
for (int j=0;j<3;j++)
t[k][j]=m1[k][j];
@@ -113,10 +125,10 @@ void mul_m1(T m1[3][3], const T m2[3][3])
m1[k][j] = t[k][0]*m2[0][j] + t[k][1]*m2[1][j] + t[k][2]*m2[2][j];
}
-template<typename T>
-void mul_m2(const T m1[3][3], T m2[3][3])
+template<typename T1, typename T2>
+void mul_m2(const T1 m1[3][3], T2 m2[3][3])
{
- T t[3][3];
+ T2 t[3][3];
for (int k=0;k<3;k++)
for (int j=0;j<3;j++)
t[k][j]=m2[k][j];