void build_graph(double *x,VTYPE &y,double (*fun)(double,double*),double x0,double x1,int nx,VTYPE &par)
{
double dx=(x1-x0)/nx;
#ifdef JACK
VTYPE xj(nx+1,par.njack);
y=VTYPE(nx+1,par.njack);
#else
VTYPE xj(nx+1,par.nboot,par.njack);
y=VTYPE(nx+1,par.nboot,par.njack);
#endif
for(int i=0;i<=nx;i++) xj.data[i]=x[i]=x0+dx*i;
y=par_single_fun(fun,xj,par);
}
void cnbint(
int i,
const double pos[][3],
const double vel[][3],
const double mass[],
int nnb,
int list[],
double f[3],
double fdot[3]){
const int NBMAX = 512;
assert(nnb <= NBMAX);
double xbuf[NBMAX] __attribute__ ((aligned(16)));
double ybuf[NBMAX] __attribute__ ((aligned(16)));
double zbuf[NBMAX] __attribute__ ((aligned(16)));
float vxbuf[NBMAX] __attribute__ ((aligned(16)));
float vybuf[NBMAX] __attribute__ ((aligned(16)));
float vzbuf[NBMAX] __attribute__ ((aligned(16)));
float mbuf[NBMAX] __attribute__ ((aligned(16)));
for(int k=0; k<nnb; k++){
int j = list[k];
xbuf[k] = pos[j][0];
ybuf[k] = pos[j][1];
zbuf[k] = pos[j][2];
vxbuf[k] = vel[j][0];
vybuf[k] = vel[j][1];
vzbuf[k] = vel[j][2];
mbuf[k] = mass[j];
}
for(int k=nnb; k%4; k++){
xbuf[k] = 16.0;
ybuf[k] = 16.0;
zbuf[k] = 16.0;
vxbuf[k] = 0.0f;
vybuf[k] = 0.0f;
vzbuf[k] = 0.0f;
mbuf[k] = 0.0f;
}
v4df xi(pos[i][0]);
v4df yi(pos[i][1]);
v4df zi(pos[i][2]);
v4sf vxi(vel[i][0]);
v4sf vyi(vel[i][1]);
v4sf vzi(vel[i][2]);
v4df ax(0.0), ay(0.0), az(0.0);
v4sf jx(0.0), jy(0.0), jz(0.0);
for(int k=0; k<nnb; k+=4){
v4df xj(xbuf + k);
v4df yj(ybuf + k);
v4df zj(zbuf + k);
v4sf vxj(vxbuf + k);
v4sf vyj(vybuf + k);
v4sf vzj(vzbuf + k);
v4sf mj(mbuf + k);
v4sf dx = v4sf::_v4sf(xj - xi);
v4sf dy = v4sf::_v4sf(yj - yi);
v4sf dz = v4sf::_v4sf(zj - zi);
v4sf dvx = vxj - vxi;
v4sf dvy = vyj - vyi;
v4sf dvz = vzj - vzi;
v4sf r2 = dx*dx + dy*dy + dz*dz;
v4sf rv = dx*dvx + dy*dvy + dz*dvz;
rv *= v4sf(-3.0f);
// v4sf rinv1 = r2.rsqrt() & v4sf(mask);
v4sf rinv1 = r2.rsqrt();
v4sf rinv2 = rinv1 * rinv1;
rv *= rinv2;
v4sf rinv3 = mj * rinv1 * rinv2;
dx *= rinv3; ax += v4df(dx);
dy *= rinv3; ay += v4df(dy);
dz *= rinv3; az += v4df(dz);
dvx *= rinv3; jx += dvx;
dvy *= rinv3; jy += dvy;
dvz *= rinv3; jz += dvz;
dx *= rv; jx += dx;
dy *= rv; jy += dy;
dz *= rv; jz += dz;
}
f[0] = ax.sum();
f[1] = ay.sum();
f[2] = az.sum();
fdot[0] = (v4df(jx)).sum();
fdot[1] = (v4df(jy)).sum();
fdot[2] = (v4df(jz)).sum();
assert(f[0] == f[0]);
assert(f[1] == f[1]);
assert(f[2] == f[2]);
assert(fdot[0] == fdot[0]);
assert(fdot[1] == fdot[1]);
assert(fdot[2] == fdot[2]);
}
//--------------------------------------------------------
// apply local coulomb forces
// -- due to image charges
//--------------------------------------------------------
void ChargeRegulatorMethodImageCharge::apply_local_forces()
{
int inum = lammpsInterface_->neighbor_list_inum();
int * ilist = lammpsInterface_->neighbor_list_ilist();
int * numneigh = lammpsInterface_->neighbor_list_numneigh();
int ** firstneigh = lammpsInterface_->neighbor_list_firstneigh();
const int *mask = lammpsInterface_->atom_mask();
///..............................................
double ** x = lammpsInterface_->xatom();
double ** f = lammpsInterface_->fatom();
double * q = lammpsInterface_->atom_charge();
// loop over neighbor list
for (int ii = 0; ii < inum; ii++) {
int i = ilist[ii];
double qi = q[i];
if ((mask[i] & atomGroupBit_) && qi != 0.) {
double* fi = f[i];
DENS_VEC xi(x[i],nsd_);
// distance to surface
double dn = reflect(xi);
// all ions near the interface/wall
// (a) self image
if (dn < rC_) { // close enough to wall to have explicit image charges
double factor_coul = 1;
double dx = 2.*dn; // distance to image charge
double fn = factor_coul*qi*qi*permittivityRatio_/dx;
fi[0] += fn*normal_[0];
fi[1] += fn*normal_[1];
fi[2] += fn*normal_[2];
sum_ += fn*normal_;
// (b) neighbor images
int * jlist = firstneigh[i];
int jnum = numneigh[i];
for (int jj = 0; jj < jnum; jj++) {
int j = jlist[jj];
// this changes j
double factor_coul = lammpsInterface_->coulomb_factor(j);
double qj = q[j];
if (qj != 0.) { // all charged neighbors
DENS_VEC xj(x[j],nsd_);
dn = reflect(xj);
DENS_VEC dx = xi-xj;
double r2 = dx.norm_sq();
// neighbor image j' inside cutoff from i
if (r2 < rCsq_) {
double fm = factor_coul*qi*qj*permittivityRatio_/r2;
fi[0] += fm*dx(0);
fi[1] += fm*dx(1);
fi[2] += fm*dx(2);
sum_ += fm*dx;
}
}
}
} // end i < rC if
}
}
// update managed data
(interscaleManager_->fundamental_atom_quantity(LammpsInterface::ATOM_FORCE))->force_reset();
}
void Matrix::test(void)
{
int i,j;
//Matrix *A,*B,*C,*AT,*K;
/*test matrix mult*/
// A = new Matrix(3,2);
// B = new Matrix(2,3);
// C = new Matrix(3,3);
// AT = new Matrix(2,3);
// K = new Matrix(2*3,3*2);
Matrix A(3,2),B(2,3),C(3,3),AT(2,3),K(2*3,3*2);
Matrix M(3,3),x(3,1),b(3,1);
A[0][0] = 0;
A[0][1] = 1;
A[1][0] = 3;
A[1][1] = 1;
A[2][0] = 2;
A[2][1] = 0;
B[0][0] = 4;
B[0][1] = 1;
B[0][2] = 0;
B[1][0] = 2;
B[1][1] = 1;
B[1][2] = 2;
std::cout << A.mat[1][0] << std::endl;
C = Matrix::matrix_mult(A,B);
for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
std::cout << C[i][j] << " ";
std::cout << std::endl;
}
std::cout << "now A transposed" << std::endl;
A.transpose(AT);
for(i=0;i<2;i++)
{
for(j=0;j<3;j++)
std::cout << AT[i][j] << " ";
std::cout << std::endl;
}
std::cout << "now Kronecker product" << std::endl;
K = Matrix::kron_(A,B);
std::cout << "product calced " << K.getM() << " " << K.getN() << std::endl;
for(i=0;i<2*3;i++)
{
for(j=0;j<3*2;j++)
std::cout << K.mat[i][j] << " ";
std::cout << std::endl;
}
cv::Mat_<double> a(3,2), l(2,3);
a(0,0) = 0;
a(0,1) = 1;
a(1,0) = 3;
a(1,1) = 1;
a(2,0) = 2;
a(2,1) = 0;
l(0,0) = 4;
l(0,1) = 1;
l(0,2) = 0;
l(1,0) = 2;
l(1,1) = 1;
l(1,2) = 2;
cv::Mat_<double> k = Matrix::kronecker(a,l);
std::cout << "mat cv Kronecker" << std::endl << Matrix(k);
Matrix sub(3,6);
sub = submatrix_(K,2,4);
std::cout << "Submatix of K rows 2 to 4 is : \n" << sub;
std::cout << "now test solving a linear system using SVD: " << std::endl;
std::cout << "A*x = b; A = U*D*V', inv(A) = V*inv(D)*U', x = V*inv(D)*U'*b" << std::endl;
//if element in diagonal of D is 0 set element in inv(D) to 0 proof in numerical recipies
M[0][0] = 4;
M[0][1] = 1.5;
M[0][2] = 2;
M[1][0] = 3;
M[1][1] = 3;
M[1][2] = 1;
M[2][0] = 2;
M[2][1] = 1;
M[2][2] = 5;
b[0][0] = 10.6;
b[1][0] = 11.3;
b[2][0] = 9;
//x should be 1.5, 2, 0.8
Matrix result = solveLinSysSvd(M,b);
std::cout << " The result of the linear system is : " << std::endl;
std::cout << result;
A = Matrix::matrix_mult(Matrix::eye(2),Matrix::matrix_mult(Matrix::eye(2),Matrix::eye(2)));
cv::Mat_<double> aj(2,2);
cv::Mat_<double> bj(2,1);
aj(0,0) = 2;
aj(0,1) = 1;
aj(1,0) = 5;
aj(1,1) = 7;
bj(0,0) = 11;
bj(1,0) = 13;
cv::Mat_<double> xj(2,1);
Matrix::jacobi(aj,bj,xj);
std::cout << "jacobi " << Matrix(xj);
}