/*
* Use DIIS to help SCF
*/
void calculateSCFDIIS(molecule_t *molecule) {
#define EPS 0.0000000000001
#define DEL 0.0000000000001
double **fs[6], **es[6], **b, *c;
int **piv;
hamiltonian(molecule);
sqrtMolecule(molecule);
int n = molecule->orbitals; //So that the same thing does not need to be typed repeatedly.
int count = 0;
double elec, energy = 0, elast, rms;
double **f0, **f1, **f2, **c0, **c1, **d0, **d1, **work1, **work2, **work3,
**ham, **shalf, **s;
double **sort;
f0 = calloc_contiguous(2, sizeof(double), n, n);
f1 = calloc_contiguous(2, sizeof(double), n, n);
f2 = calloc_contiguous(2, sizeof(double), n, n);
c0 = calloc_contiguous(2, sizeof(double), n, n);
c1 = calloc_contiguous(2, sizeof(double), n, n);
d0 = calloc_contiguous(2, sizeof(double), n, n);
d1 = calloc_contiguous(2, sizeof(double), n, n);
work1 = calloc_contiguous(2, sizeof(double), n, n);
work2 = calloc_contiguous(2, sizeof(double), n, n);
work3 = calloc_contiguous(2, sizeof(double), n, n);
ham = calloc_contiguous(2, sizeof(double), n, n);
shalf = calloc_contiguous(2, sizeof(double), n, n);
sort = calloc_contiguous(2, sizeof(double), n, n);
b = calloc_contiguous(2, sizeof(double), 7, 7);
c = calloc(7, sizeof(double));
s = calloc_contiguous(2, sizeof(double), n, n);
piv = calloc_contiguous(2, sizeof(double), 7, 7);
for(int i = 0; i < 6; i++) {
fs[i] = calloc_contiguous(2, sizeof(double), n, n);
es[i] = calloc_contiguous(2, sizeof(double), n, n);
}
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
s[i][j] = molecule->overlap[i][j];
shalf[i][j] = molecule->symmetric[i][j];
}
}
printf("\nElec\t\tEnergy\t\tDiff\t\tRMS\n");
do {
elast = energy;
if(count == 0) {
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
//Find the initial Fock guess.
f0[i][j] = ham[i][j] = molecule->hamiltonian[i][j];
}
}
} else {
memcpy(*d1, *d0, n * n * sizeof(double));
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
f0[i][j] = ham[i][j];
for(int k = 0; k < n; k++) {
for(int l = 0; l < n; l++) {
f0[i][j] += d0[k][l]
* (2 * molecule->two_electron[TEI(i, j, k, l)]
- molecule->two_electron[TEI(i, k, j, l)]);
}
}
}
}
}
//DIIS extrapolation.
memcpy(*(fs[count % 6]), *f0, n * n * sizeof(double));
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0, *s,
n, *d0, n, 0, *work1, n);
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
*work1, n, *f0, n, 0, *work2, n);
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
*f0, n, *d0, n, 0, *work1, n);
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
*work1, n, *s, n, 0, *work3, n);
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
es[count % 6][i][j] = work3[i][j] - work2[i][j];
}
}
if(count >= 6) {
for(int i = 0; i < ((count > 6)? 6: count); i++) {
for(int j = 0; j < ((count > 6)? 6: count); j++) {
b[i][j] = 0;
for(int k = 0; k < n; k++) {
for(int l = 0; l < n; l++) {
b[i][j] += es[i][k][l] * es[j][k][l];
}
}
}
}
if(count < 6) {
for(int i = 0; i < 6; i++) {
for(int j = 0; j < 6; j++) {
if(i < count && j < count) {
continue;
}
if(i == j) {
b[i][j] = 1;
} else {
b[i][j] = 0;
}
}
}
}
for(int i = 0; i < 6; i++) {
b[6][i] = -1;
b[i][6] = -1;
c[i] = 0;
}
b[6][6] = 0;
c[6] = -1;
LAPACKE_dgesv(LAPACK_ROW_MAJOR, 7, 1, *b, 7, *piv, c, 1);
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
f2[i][j] = 0;
for(int m = 0; m < 6; m++) {
f2[i][j] += c[m] * fs[m][i][j];
}
}
}
cblas_dgemm(CblasRowMajor, CblasTrans, CblasNoTrans, n, n, n, 1.0,
*shalf, n, *f2, n, 0, *work1, n);
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
*work1, n, *shalf, n, 0, *f1, n);
} else {
cblas_dgemm(CblasRowMajor, CblasTrans, CblasNoTrans, n, n, n, 1.0,
*shalf, n, *f0, n, 0, *work1, n);
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
*work1, n, *shalf, n, 0, *f1, n);
}
memset(work1[0], 0, n * n * sizeof(double));
memset(work2[0], 0, n * n * sizeof(double));
memset(work3[0], 0, n * n * sizeof(double));
LAPACKE_dgeev(LAPACK_ROW_MAJOR, 'N', 'V', n, *f1, n, *work1, *work2,
*work3, n, *c1, n);
//Prepare for sorting.
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
work2[i][j] = c1[i][j];
}
}
//Sort
for(int i = 0; i < n; i++) {
sort[i] = work1[0] + i;
}
qsort(sort, n, sizeof(double *), comparedd);
//Sift through data.
for(int i = 0; i < n; i++) {
unsigned long off = ((unsigned long) sort[i]
- (unsigned long) work1[0]);
off /= sizeof(double);
for(int j = 0; j < n; j++) {
c1[j][i] = work2[j][off];
}
}
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0,
*shalf, n, *c1, n, 0, *c0, n);
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
d0[i][j] = 0;
for(int k = 0; k < molecule->electrons / 2; k++) {
d0[i][j] += c0[i][k] * c0[j][k];
}
}
}
elec = 0;
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
elec += d0[i][j] * (ham[i][j] + f0[i][j]);
}
}
energy = elec + molecule->enuc;
rms = 0;
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
rms += (d0[i][j] - d1[i][j]) * (d0[i][j] - d1[i][j]);
}
}
rms = sqrt(rms);
count++;
printf("%d\t%.15f\t%.15f\t%.15f\t%.15f\n", count, elec, energy, fabs(elast - energy), rms);
} while(count < 100 && (fabs(elast - energy) > EPS && rms > DEL));
molecule->scf_energy = energy;
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
molecule->density[i][j] = d0[i][j];
molecule->fock[i][j] = f0[i][j];
molecule->molecular_orbitals[i][j] = c0[i][j];
molecule->molecular_eigs[i][j] = ((i == j)? sort[i][0]: 0);
}
}
free_mult_contig(16, c0, c1, d0, d1, f0, f1, f2, ham, shalf, work1, work2,
work3, sort, b, c, s);
for(int i = 0; i < 6; i++) {
free(fs[i]);
free(es[i]);
}
}
template <> inline
int geev(const char order, const char jobVL, const char jobVR, const int N, double *A, const int LDA, double *WR, double *WI, double *VL, const int LDVL, double *VR, const int LDVR)
{
return LAPACKE_dgeev(order, jobVL, jobVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR);
}
