std::shared_ptr<Matrix> MultiExcitonHamiltonian<VecType>::compute_diagonal_1e(const DSubSpace& AB, const double* hAA, const double* hBB, const double diag) const {
std::shared_ptr<const VecType> ccvecA = AB.template ci<0>();
std::shared_ptr<const VecType> ccvecB = AB.template ci<1>();
std::shared_ptr<const VecType> sigmavecA = form_sigma_1e(ccvecA, hAA);
std::shared_ptr<const VecType> sigmavecB = form_sigma_1e(ccvecB, hBB);
const int nstatesA = AB.template nstates<0>();
const int nstatesB = AB.template nstates<1>();
const int dimerstates = AB.dimerstates();
auto out = std::make_shared<Matrix>(dimerstates, dimerstates);
// first H^{AA}_{AA}
for(int stateA = 0; stateA < nstatesA; ++stateA) {
std::shared_ptr<const CiType> isigma = sigmavecA->data(stateA);
for(int stateAp = 0; stateAp < stateA; ++stateAp) {
std::shared_ptr<const CiType> icc = ccvecA->data(stateAp);
const double dotproduct = isigma->dot_product(*icc);
for(int stateB = 0; stateB < nstatesB; ++stateB) {
const int stateApB = AB.dimerindex(stateAp, stateB);
const int stateAB = AB.dimerindex(stateA, stateB);
out->element(stateAB, stateApB) += dotproduct;
out->element(stateApB, stateAB) += dotproduct;
}
}
const double dotproduct = isigma->dot_product(*ccvecA->data(stateA));
for(int stateB = 0; stateB < nstatesB; ++stateB) {
const int stateAB = AB.dimerindex(stateA, stateB);
out->element(stateAB,stateAB) += dotproduct;
}
}
// H^{BB}_{BB}
for(int stateB = 0; stateB < nstatesB; ++stateB) {
std::shared_ptr<const CiType> isigma = sigmavecB->data(stateB);
for(int stateBp = 0; stateBp < stateB; ++stateBp) {
std::shared_ptr<const CiType> icc = ccvecB->data(stateBp);
const double dotproduct = isigma->dot_product(*icc);
for(int stateA = 0; stateA < nstatesA; ++stateA) {
const int stateAB = AB.dimerindex(stateA, stateB);
const int stateABp = AB.dimerindex(stateA, stateBp);
out->element(stateAB, stateABp) += dotproduct;
out->element(stateABp, stateAB) += dotproduct;
}
}
const double dotproduct = ccvecB->data(stateB)->dot_product(*isigma);
for(int stateA = 0; stateA < nstatesA; ++stateA) {
const int stateAB = AB.dimerindex(stateA, stateB);
out->element(stateAB,stateAB) += dotproduct;
}
}
out->add_diag(diag);
return out;
}
std::shared_ptr<Matrix> MultiExcitonHamiltonian<VecType>::compute_intra(const DSubSpace& AB, std::shared_ptr<const DimerJop> jop, const double diag) {
const int nstatesA = AB.template nstates<0>();
const int nstatesB = AB.template nstates<1>();
const int dimerstates = AB.dimerstates();
auto out = std::make_shared<Matrix>(dimerstates, dimerstates);
// first H^{AA}_{AA}
for(int stateA = 0; stateA < nstatesA; ++stateA) {
for(int stateAp = 0; stateAp < stateA; ++stateAp) {
const double value = AB.template sigma<0>()->element(stateAp, stateA);
for(int stateB = 0; stateB < nstatesB; ++stateB) {
const int stateApB = AB.dimerindex(stateAp, stateB);
const int stateAB = AB.dimerindex(stateA, stateB);
out->element(stateAB, stateApB) += value;
out->element(stateApB, stateAB) += value;
}
}
const double value = AB.template sigma<0>()->element(stateA, stateA);
for(int stateB = 0; stateB < nstatesB; ++stateB) {
const int stateAB = AB.dimerindex(stateA, stateB);
out->element(stateAB,stateAB) += value;
}
}
// H^{BB}_{BB}
for(int stateB = 0; stateB < nstatesB; ++stateB) {
for(int stateBp = 0; stateBp < stateB; ++stateBp) {
const double value = AB.template sigma<1>()->element(stateBp, stateB);
for(int stateA = 0; stateA < nstatesA; ++stateA) {
const int stateAB = AB.dimerindex(stateA, stateB);
const int stateABp = AB.dimerindex(stateA, stateBp);
out->element(stateAB, stateABp) += value;
out->element(stateABp, stateAB) += value;
}
}
const double value = AB.template sigma<1>()->element(stateB, stateB);
for(int stateA = 0; stateA < nstatesA; ++stateA) {
const int stateAB = AB.dimerindex(stateA, stateB);
out->element(stateAB,stateAB) += value;
}
}
out->add_diag(diag);
return out;
}
int hFcn(double *obj, const Mesh *m)
{
const int e = m->ne;
double *v = m->v;
double *g_obj = m->g;
double *h_obj = m->dat;
double *w;
int *t = m->e;
int *p = m->p;
int *inst = m->inst;
double x[12];
double d[12];
double h[78];
double A[9];
double o, f;
int v1, v2, v3, v4;
int i;
*obj = 0.0;
memset(g_obj, 0, 3*sizeof(double)*m->nn);
memset(h_obj, 0, 1*sizeof(double)*m->nz);
o = 0.0;
for (i = 0; i < e; ++i) {
v1 = t[0];
v2 = t[1];
v3 = t[2];
v4 = t[3];
t += 4;
w = v + 3*v1;
x[0] = w[0];
x[4] = w[1];
x[8] = w[2];
w = v + 3*v2;
x[1] = w[0];
x[5] = w[1];
x[9] = w[2];
w = v + 3*v3;
x[2] = w[0];
x[6] = w[1];
x[10]= w[2];
w = v + 3*v4;
x[3] = w[0];
x[7] = w[1];
x[11]= w[2];
if (h_fcn(&f, d, h, x)) return 1;
v1 = p[v1];
v2 = p[v2];
v3 = p[v3];
v4 = p[v4];
if (v1 >= 0) {
/* Add the gradient information */
w = g_obj + v1;
w[0] += d[0];
w[1] += d[4];
w[2] += d[8];
/* Add diagonal block */
A[0] = h[0];
A[1] = h[10];
A[2] = h[26];
A[3] = h[42];
A[4] = h[52];
A[5] = h[68];
add_diag(h_obj + *inst++, A);
if (v2 >= 0) {
A[0] = h[1];
A[1] = h[11];
A[2] = h[27];
A[3] = h[14];
A[4] = h[43];
A[5] = h[53];
A[6] = h[30];
A[7] = h[56];
A[8] = h[69];
/* Add first off diagonal block */
if (v1 < v2) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
if (v3 >= 0) {
A[0] = h[2];
A[1] = h[12];
A[2] = h[28];
A[3] = h[18];
A[4] = h[44];
A[5] = h[54];
A[6] = h[34];
A[7] = h[60];
A[8] = h[70];
/* Add second off diagonal block */
if (v1 < v3) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
if (v4 >= 0) {
A[0] = h[3];
A[1] = h[13];
A[2] = h[29];
A[3] = h[22];
A[4] = h[45];
A[5] = h[55];
A[6] = h[38];
A[7] = h[64];
A[8] = h[71];
/* Add third off diagonal block */
if (v1 < v4) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
}
if (v2 >= 0) {
/* Add the gradient information */
w = g_obj + v2;
w[0] += d[1];
w[1] += d[5];
w[2] += d[9];
/* Add diagonal block */
A[0] = h[4];
A[1] = h[15];
A[2] = h[31];
A[3] = h[46];
A[4] = h[57];
A[5] = h[72];
add_diag(h_obj + *inst++, A);
if (v3 >= 0) {
A[0] = h[5];
A[1] = h[16];
A[2] = h[32];
A[3] = h[19];
A[4] = h[47];
A[5] = h[58];
A[6] = h[35];
A[7] = h[61];
A[8] = h[73];
/* Add first off diagonal block */
if (v2 < v3) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
if (v4 >= 0) {
A[0] = h[6];
A[1] = h[17];
A[2] = h[33];
A[3] = h[23];
A[4] = h[48];
A[5] = h[59];
A[6] = h[39];
A[7] = h[65];
A[8] = h[74];
/* Add second off diagonal block */
if (v2 < v4) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
}
if (v3 >= 0) {
/* Add the gradient information */
w = g_obj + v3;
w[0] += d[2];
w[1] += d[6];
w[2] += d[10];
/* Add diagonal block */
A[0] = h[7];
A[1] = h[20];
A[2] = h[36];
A[3] = h[49];
A[4] = h[62];
A[5] = h[75];
add_diag(h_obj + *inst++, A);
if (v4 >= 0) {
A[0] = h[8];
A[1] = h[21];
A[2] = h[37];
A[3] = h[24];
A[4] = h[50];
A[5] = h[63];
A[6] = h[40];
A[7] = h[66];
A[8] = h[76];
/* Add first off diagonal block */
if (v3 < v4) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
}
if (v4 >= 0) {
/* Add the gradient information */
w = g_obj + v4;
w[0] += d[3];
w[1] += d[7];
w[2] += d[11];
/* Add diagonal block */
A[0] = h[9];
A[1] = h[25];
A[2] = h[41];
A[3] = h[51];
A[4] = h[67];
A[5] = h[77];
add_diag(h_obj + *inst++, A);
}
o += f;
}
*obj = o;
return 0;
}
void hOnly(const Mesh *m)
{
const int e = m->ne;
double *v = m->v;
double *h_obj = m->dat;
double *w;
int *t = m->e;
int *p = m->p;
int *inst = m->inst;
double x[12];
double h[78];
double A[9];
int v1, v2, v3, v4;
int i;
memset(h_obj, 0, 1*sizeof(double)*m->nz);
for (i = 0; i < e; ++i) {
v1 = t[0];
v2 = t[1];
v3 = t[2];
v4 = t[3];
t += 4;
w = v + 3*v1;
x[0] = w[0];
x[4] = w[1];
x[8] = w[2];
w = v + 3*v2;
x[1] = w[0];
x[5] = w[1];
x[9] = w[2];
w = v + 3*v3;
x[2] = w[0];
x[6] = w[1];
x[10]= w[2];
w = v + 3*v4;
x[3] = w[0];
x[7] = w[1];
x[11]= w[2];
h_only(h, x);
v1 = p[v1];
v2 = p[v2];
v3 = p[v3];
v4 = p[v4];
if (v1 >= 0) {
/* Add diagonal block */
A[0] = h[0];
A[1] = h[10];
A[2] = h[26];
A[3] = h[42];
A[4] = h[52];
A[5] = h[68];
add_diag(h_obj + *inst++, A);
if (v2 >= 0) {
A[0] = h[1];
A[1] = h[11];
A[2] = h[27];
A[3] = h[14];
A[4] = h[43];
A[5] = h[53];
A[6] = h[30];
A[7] = h[56];
A[8] = h[69];
/* Add first off diagonal block */
if (v1 < v2) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
if (v3 >= 0) {
A[0] = h[2];
A[1] = h[12];
A[2] = h[28];
A[3] = h[18];
A[4] = h[44];
A[5] = h[54];
A[6] = h[34];
A[7] = h[60];
A[8] = h[70];
/* Add second off diagonal block */
if (v1 < v3) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
if (v4 >= 0) {
A[0] = h[3];
A[1] = h[13];
A[2] = h[29];
A[3] = h[22];
A[4] = h[45];
A[5] = h[55];
A[6] = h[38];
A[7] = h[64];
A[8] = h[71];
/* Add third off diagonal block */
if (v1 < v4) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
}
if (v2 >= 0) {
/* Add diagonal block */
A[0] = h[4];
A[1] = h[15];
A[2] = h[31];
A[3] = h[46];
A[4] = h[57];
A[5] = h[72];
add_diag(h_obj + *inst++, A);
if (v3 >= 0) {
A[0] = h[5];
A[1] = h[16];
A[2] = h[32];
A[3] = h[19];
A[4] = h[47];
A[5] = h[58];
A[6] = h[35];
A[7] = h[61];
A[8] = h[73];
/* Add first off diagonal block */
if (v2 < v3) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
if (v4 >= 0) {
A[0] = h[6];
A[1] = h[17];
A[2] = h[33];
A[3] = h[23];
A[4] = h[48];
A[5] = h[59];
A[6] = h[39];
A[7] = h[65];
A[8] = h[74];
/* Add second off diagonal block */
if (v2 < v4) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
}
if (v3 >= 0) {
/* Add diagonal block */
A[0] = h[7];
A[1] = h[20];
A[2] = h[36];
A[3] = h[49];
A[4] = h[62];
A[5] = h[75];
add_diag(h_obj + *inst++, A);
if (v4 >= 0) {
A[0] = h[8];
A[1] = h[21];
A[2] = h[37];
A[3] = h[24];
A[4] = h[50];
A[5] = h[63];
A[6] = h[40];
A[7] = h[66];
A[8] = h[76];
/* Add first off diagonal block */
if (v3 < v4) {
add_block(h_obj + *inst++, A);
}
else {
add_blockT(h_obj + *inst++, A);
}
}
}
if (v4 >= 0) {
/* Add diagonal block */
A[0] = h[9];
A[1] = h[25];
A[2] = h[41];
A[3] = h[51];
A[4] = h[67];
A[5] = h[77];
add_diag(h_obj + *inst++, A);
}
}
return;
}
int hFcn_d(double *obj, const Mesh *m)
{
const int e = m->ne;
double *v = m->v;
double *g_obj = m->g;
double *h_obj = m->dat;
double *w;
int *t = m->e;
int *p = m->p;
double x[12];
double d[12];
double h[78];
double A[9];
double o, f;
int v1, v2, v3, v4;
int i;
*obj = 0.0;
memset(g_obj, 0, 3*sizeof(double)*m->nn);
memset(h_obj, 0, 6*sizeof(double)*m->nn);
o = 0.0;
for (i = 0; i < e; ++i) {
v1 = t[0];
v2 = t[1];
v3 = t[2];
v4 = t[3];
t += 4;
w = v + 3*v1;
x[0] = w[0];
x[4] = w[1];
x[8] = w[2];
w = v + 3*v2;
x[1] = w[0];
x[5] = w[1];
x[9] = w[2];
w = v + 3*v3;
x[2] = w[0];
x[6] = w[1];
x[10]= w[2];
w = v + 3*v4;
x[3] = w[0];
x[7] = w[1];
x[11]= w[2];
if (h_fcn(&f, d, h, x)) return 1;
v1 = p[v1];
v2 = p[v2];
v3 = p[v3];
v4 = p[v4];
if (v1 >= 0) {
/* Add the gradient information */
w = g_obj + v1;
w[0] += d[0];
w[1] += d[4];
w[2] += d[8];
/* Add diagonal block */
A[0] = h[0];
A[1] = h[10];
A[2] = h[26];
A[3] = h[42];
A[4] = h[52];
A[5] = h[68];
add_diag(h_obj + 2*v1, A);
}
if (v2 >= 0) {
/* Add the gradient information */
w = g_obj + v2;
w[0] += d[1];
w[1] += d[5];
w[2] += d[9];
/* Add diagonal block */
A[0] = h[4];
A[1] = h[15];
A[2] = h[31];
A[3] = h[46];
A[4] = h[57];
A[5] = h[72];
add_diag(h_obj + 2*v2, A);
}
if (v3 >= 0) {
/* Add the gradient information */
w = g_obj + v3;
w[0] += d[2];
w[1] += d[6];
w[2] += d[10];
/* Add diagonal block */
A[0] = h[7];
A[1] = h[20];
A[2] = h[36];
A[3] = h[49];
A[4] = h[62];
A[5] = h[75];
add_diag(h_obj + 2*v3, A);
}
if (v4 >= 0) {
/* Add the gradient information */
w = g_obj + v4;
w[0] += d[3];
w[1] += d[7];
w[2] += d[11];
/* Add diagonal block */
A[0] = h[9];
A[1] = h[25];
A[2] = h[41];
A[3] = h[51];
A[4] = h[67];
A[5] = h[77];
add_diag(h_obj + 2*v4, A);
}
o += f;
}
*obj = o;
return 0;
}
