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spinsys.c
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spinsys.c
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/*
Spinsystem routines
Copyright (C) 1999 Mads Bak
2010 Zdenek Tosner
This file is part of the SIMPSON General NMR Simulation Package
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
Routines for calculation of spin-tensors for the spin-system.
Used by readsys.c that creates the spinsystem, and
sim.c to create the start and detect operators.
*/
#include <stdio.h>
#include <ctype.h>
#include <stdlib.h>
#include <string.h>
#include <tcl.h>
#include <math.h>
#include <assert.h>
#include "matrix.h"
#include "cm.h"
#include "blockdiag.h"
#include "spinsys.h"
#include "tclutil.h"
#include "ham.h"
#include "defs.h"
double ss_gamma1H()
{
if (isotopes[0].number != 1) {
fprintf(stderr,"error: isotope list does not have 1H as first entry\n");
exit(1);
}
return isotopes[0].gamma;
}
void ss_showspins(SpinSys* S)
{
int i;
for (i=1;i<=S->nspins;i++) {
printf("Spin[%d] : I = %g\n",i,S->iso[i]->spin);
}
}
ISOTOPE* ss_findisotope(char* name)
{
char buf[256],*src,*dst;
int number,niso, gotnumber=0;
if (!name) {
fprintf(stderr,"ss_findisotope: argument must not be NULL\n");
exit(1);
}
if (*name == 'e') {
static ISOTOPE e = {0, "e", 0.5, 17608.59707877};
return &e;
}
src=name;
dst=buf;
while (isdigit(*src) && *src != 0) {
*dst++ = *src++;
}
if (src == name) {
fprintf(stderr,"error: name of isotope '%s' is wrong, '23Na' is a correct example\n",name);
exit(1);
}
*dst=0;
number=atoi(buf);
niso=0;
while (isotopes[niso].number) {
if (isotopes[niso].number == number) {
gotnumber=1;
sprintf(buf,"%d%s",isotopes[niso].number,isotopes[niso].name);
if (!strcmp(name,buf)) {
/*
fprintf(stderr,"error: name of isotope '%s' is wrong, maybe '%s' is correct ?\n",name,buf);
exit(1);
*/
return &isotopes[niso];
}
}
niso++;
}
fprintf(stderr,"error: unable to find name '%s' in the internal isotope table.\n", name);
if (gotnumber==1) {
niso=0;
fprintf(stderr, " My suggestions are ");
while (isotopes[niso].number) {
if (isotopes[niso].number == number)
fprintf(stderr, "'%d%s' ", number, isotopes[niso].name);
if (!strcmp(isotopes[niso].name, src))
fprintf(stderr, "'%d%s' ", isotopes[niso].number, isotopes[niso].name);
niso++;
}
fprintf(stderr, "\n");
}
exit(1);
}
double ss_qn(SpinSys* S,int spin)
{
if (spin < 1 || spin > S->nspins) {
fprintf(stderr,"error: invalid range of spin (was %d)\n",spin);
exit(1);
}
return S->iso[spin]->spin;
}
double ss_gamma(SpinSys* S,int spin)
{
if (spin < 1 || spin > S->nspins) {
fprintf(stderr,"error: invalid range of spin (was %d)\n",spin);
exit(1);
}
return S->iso[spin]->gamma;
}
ISOTOPE* ss_isotope(SpinSys* S,int spin)
{
if (spin < 1 || spin > S->nspins) {
fprintf(stderr,"error: invalid range of spin (was %d)\n",spin);
exit(1);
}
return S->iso[spin];
}
int ss_matdim(SpinSys* S)
{
int i;
double N;
if (S->nspins < 1) return 0;
N = 1.0;
for (i=1;i<=S->nspins;i++)
N *= (double)(2.0*(S->iso[i]->spin)+1.0);
return (int)N;
}
void ss_addspin(SpinSys* S,char* name)
{
S->nspins++;
if (S->nspins >= MAXSPINS) {
fprintf(stderr,"error: max number of spins reached, increase MAXSPINS\n");
exit(1);
}
S->iso[S->nspins]=ss_findisotope(name);
S->matdim=ss_matdim(S);
}
void ss_initialize(SpinSys* S)
{
S->nspins=0;
S->nchan=0;
}
int ss_issame(SpinSys* S,int spin1,int spin2)
{
if (spin1 < 1 || spin1 > S->nspins) {
fprintf(stderr,"error: invalid range of spin (was %d)\n",spin1);
exit(1);
}
if (spin2 < 1 || spin2 > S->nspins) {
fprintf(stderr,"error: invalid range of spin (was %d)\n",spin2);
exit(1);
}
return (S->iso[spin1] == S->iso[spin2]);
}
mat_complx * _Ip(double I)
{
int i,j,S;
double mm,m;
mat_complx * M;
S= (int)(2*I+1);
M=complx_matrix(S,S,MAT_DENSE,0,0);
for (i=0;i<S;i++) {
mm= I-i;
for (j=0;j<S;j++) {
m= I-j;
if (mm == m + 1)
M->data[i+j*S]=Complx(sqrt(I*(I+1.0)-m*(m+1.0)),0.0);
else
M->data[i+j*S]=Complx(0.0,0.0);
}
}
return M;
}
mat_complx * _Im(double I)
{
int i,j,S;
double mm,m;
mat_complx * M;
S= (int)(2*I+1);
M=complx_matrix(S,S,MAT_DENSE,0,0);
for (i=0;i<S;i++) {
mm= I-i;
for (j=0;j<S;j++) {
m= I-j;
if (mm == m - 1)
M->data[i+j*S]=Complx(sqrt(I*(I+1.0)-m*(m-1.0)),0.0);
else
M->data[i+j*S]=Complx(0.0,0.0);
}
}
return M;
}
/***** moved to Iz directly *****
mat_complx * _Iz(double I)
{
int i,j,S;
double mm,m;
mat_complx * M;
S= (int)(2*I+1);
M=complx_matrix(S,S,MAT_DENSE,0);
for (i=0;i<S;i++) {
mm= I-i;
for (j=0;j<S;j++) {
m= I-j;
if (mm == m)
M->data[i+j*S]=Complx(m,0.0);
else
M->data[i+j*S]=Complx(0.0,0.0);
}
}
return M;
}
*/
mat_complx * _Iq(double I)
{
int i,j,S;
double mm,m;
mat_complx * M;
S= (int)(2*I+1);
M=complx_matrix(S,S,MAT_DENSE,0,0);
for (i=0;i<S;i++) {
mm= I-i;
for (j=0;j<S;j++) {
m= I-j;
M->data[i+j*S]=Complx(m,mm);
}
}
return M;
}
/* this probably wont work in multi-spin cases. */
mat_complx * _Ic(double I)
{
int S;
mat_complx * M;
/* ZT: adding test for I>1 and half-integer spin */
if ( (I<1.4) || ( fabs(I-floor(I)-0.5)>0.01 ) ) {
fprintf(stderr,"error in central transition operator, spin=%f is not allowed\n",I);
exit(1);
}
S= (int)(2*I+1);
M = complx_matrix(S,S,MAT_DENSE,0,0);
cm_zero(M);
M->data[S/2-1+(S/2)*S]=Complx(sqrt(I*(I+1)+0.25),0.0);
return M;
}
mat_complx * _Ix(double I)
{
/* return (Ip(I)+Im(I))*complx(0.5,0); */
mat_complx *ip,*im;
ip=_Ip(I);
im=_Im(I);
cm_addto(ip,im);
cm_muld(ip,0.5);
free_complx_matrix(im);
return ip;
}
mat_complx * _Iy(double I)
{
/* return (Ip(I)-Im(I))*complx(0.0,-5.0); */
mat_complx *ip,*im;
ip=_Ip(I);
im=_Im(I);
cm_subfrom(ip,im);
cm_mulc(ip,Complx(0.0,-0.5));
free_complx_matrix(im);
return ip;
}
/* creates the direct product, for example creates
for a four spin-system with spin=3 the matrix:
1 (x) 1 (x) m (x) 1
****
* ZT: new and faster version of In (not using direct product)
****/
mat_complx * In(Sim_info* sim, mat_complx * m,int spin)
{
int k,l,i,j,r,c,K,L,N,matdim;
complx z;
SpinSys * S;
mat_complx *res;
assert(m->row == m->col);
S = sim->ss;
/*printf("spin = %d\n",spin);
cm_print(m,"matrix is");*/
N = m->row;
matdim = S->matdim;
K = 1;
for (i=1;i<spin;i++) {
K *= (int)(2.0*ss_qn(S,i)+1.0);
}
L = 1;
for (i=spin+1; i<=S->nspins; i++) {
L *= (int)(2.0*ss_qn(S,i)+1.0);
}
/*printf("sp_In report: K = %d; N = %d; L = %d; matdim = %d\n",K,N,L,matdim);*/
if (K*N*L != matdim) {
fprintf(stderr,"In error: mismatch in dimensions (%d * %d * %d != %d)\n",K,N,L,matdim);
exit(1);
}
if (sim->sparse) {
const int nnz = cm_nnz(m)*K*L;
res = complx_matrix(matdim,matdim,MAT_SPARSE,nnz,0);
complx *zz = res->data;
int *ic = res->icol;
res->irow[0] = 1;
r = 0;
for (k=0; k<K; k++) {
for (i=0; i<N; i++) {
for (l=0; l<L; l++) {
res->irow[r+1] = res->irow[r];
for (j=0; j<N; j++) {
z = m->data[i+j*N];
if ( fabs(z.re) < SPARSE_TOL && fabs(z.im) < SPARSE_TOL) continue;
*zz = z;
*ic = j*L + l + 1 + k*N*L;
(res->irow[r+1])++;
zz++;
ic++;
}
r++;
}
}
}
assert(res->irow[matdim] == nnz+1);
} else {
res = complx_matrix(matdim,matdim,MAT_DENSE,0,0);
cm_zero(res);
for (i=0; i<N; i++) {
for (j=0; j<N; j++) {
z = m->data[i+j*N];
if ( fabs(z.re) < SPARSE_TOL && fabs(z.im) < SPARSE_TOL) continue;
for (k=0; k<K; k++) {
for (l=0; l<L; l++) {
r = i*L +l + k*L*N;
c = j*L +l + k*L*N;
res->data[r+c*matdim] = z;
}
}
}
}
}
return res;
}
mat_double * In_real(Sim_info* sim, mat_double * m,int spin)
{
int k,l,i,j,r,c,K,L,N,matdim;
double z;
SpinSys * S;
mat_double *res;
assert(m->row == m->col);
S = sim->ss;
/*printf("spin = %d\n",spin);
cm_print(m,"matrix is");*/
N = m->row;
matdim = S->matdim;
K = 1;
for (i=1;i<spin;i++) {
K *= (int)(2.0*ss_qn(S,i)+1.0);
}
L = 1;
for (i=spin+1; i<=S->nspins; i++) {
L *= (int)(2.0*ss_qn(S,i)+1.0);
}
/*printf("sp_In report: K = %d; N = %d; L = %d; matdim = %d\n",K,N,L,matdim);*/
if (K*N*L != matdim) {
fprintf(stderr,"In_real error: mismatch in dimensions (%d * %d * %d != %d)\n",K,N,L,matdim);
exit(1);
}
if (sim->sparse) {
const int nnz = dm_nnz(m)*K*L;
res = double_matrix(matdim,matdim,MAT_SPARSE,nnz,0);
double *zz = res->data;
int *ic = res->icol;
res->irow[0] = 1;
r = 0;
for (k=0; k<K; k++) {
for (i=0; i<N; i++) {
for (l=0; l<L; l++) {
res->irow[r+1] = res->irow[r];
for (j=0; j<N; j++) {
z = m->data[i+j*N];
if ( fabs(z) < SPARSE_TOL ) continue;
*zz = z;
*ic = j*L + l + 1 + k*N*L;
(res->irow[r+1])++;
zz++;
ic++;
}
r++;
}
}
}
assert(res->irow[matdim] == nnz+1);
} else {
res = double_matrix(matdim,matdim,MAT_DENSE,0,0);
dm_zero(res);
for (i=0; i<N; i++) {
for (j=0; j<N; j++) {
z = m->data[i+j*N];
if ( fabs(z) < SPARSE_TOL ) continue;
for (k=0; k<K; k++) {
for (l=0; l<L; l++) {
r = i*L +l + k*L*N;
c = j*L +l + k*L*N;
res->data[r+c*matdim] = z;
}
}
}
}
}
return res;
}
mat_complx * Icoherence(Sim_info* sim, double* coh)
{
SpinSys *S=sim->ss;
int i,j,k,N;
mat_complx *m=NULL,*curr=NULL,*tmp=NULL;
for (k=1;k <= S->nspins;k++) {
m = _Iq(ss_qn(S,k));
N = m->row;
for (i=0;i<N;i++) {
for (j=0;j<N;j++) {
double ok = 0;
int pp = i+j*N;
if ( (m->data[pp].im - m->data[pp].re) == coh[k] ) ok=1;
m->data[pp]=Complx(ok,0.0);
//DEBUGPRINT("Icoherence: k=%d: element [%d, %d] = %f\n",k,i,j,ok);
}
}
if (k == 1) {
curr=m;
} else {
tmp=cm_direct(curr,m);
free_complx_matrix(curr);
free_complx_matrix(m);
curr=tmp;
}
}
if (sim->sparse) cm_sparse(curr, SPARSE_TOL);
return curr;
}
/* this returns full matrix */
mat_complx * Iq(SpinSys *S)
{
int i;
mat_complx *curr=NULL,*tmp,*tmp2;
for (i=1;i <= S->nspins;i++) {
if (i == 1) {
curr=_Iq(ss_qn(S,i));
} else {
tmp2=_Iq(ss_qn(S,i));
tmp=cm_directadd(curr,tmp2);
free_complx_matrix(curr);
free_complx_matrix(tmp2);
curr=tmp;
}
}
return curr;
}
mat_complx* Iqdelta(Sim_info* sim)
{
SpinSys* S = sim->ss;
int i,j,N;
mat_complx * M;
N=S->matdim;
M=Iq(S);
for (i=0;i<N;i++) {
for (j=0;j<N;j++) {
int pp = i+j*N;
M->data[pp] = Complx( M->data[pp].im - M->data[pp].re, 0.0);
}
}
if (sim->sparse) cm_sparse(M, SPARSE_TOL);
return M;
}
mat_complx * Ie(Sim_info* sim)
{
mat_complx *a;
if (sim->sparse)
a = complx_matrix(sim->matdim,sim->matdim,MAT_SPARSE_DIAG,sim->matdim,0);
else
a = complx_matrix(sim->matdim,sim->matdim,MAT_DENSE_DIAG,1,0);
cm_unit(a);
return a;
}
mat_complx * _Ia(double I)
{
mat_complx * M;
if ( fabs(I-0.5)>0.01 ) {
fprintf(stderr,"error in alpha-state operator, it is undefined for spin=%f\n",I);
exit(1);
}
M = complx_matrix(2,2,MAT_DENSE,0,0);
cm_zero(M);
M->data[0].re = 1.0;
return M;
}
mat_complx * _Ib(double I)
{
mat_complx * M;
if ( fabs(I-0.5)>0.01 ) {
fprintf(stderr,"error in beta-state operator, it is undefined for spin=%f\n",I);
exit(1);
}
M = complx_matrix(2,2,MAT_DENSE,0,0);
cm_zero(M);
M->data[3].re = 1.0;
return M;
}
/****
* ZT: adding I_alpha operator for spin=1/2
****/
mat_complx * Ia(Sim_info* sim, int spin) {
SpinSys* S = sim->ss;
mat_complx *a, *b;
a = _Ia( ss_qn(S,spin) );
b = In(sim,a,spin);
free_complx_matrix(a);
return b;
}
/****
* ZT: adding I_beta operator for spin=1/2
****/
mat_complx * Ib(Sim_info *sim, int spin) {
mat_complx *a, *b;
a = _Ib(ss_qn(sim->ss,spin));
b = In(sim,a,spin);
free_complx_matrix(a);
return b;
}
#define DECLARE_SIFUNC(TYPE) \
mat_complx * TYPE(Sim_info* sim,int spin)\
{\
mat_complx *a,*b;\
a= _##TYPE(ss_qn(sim->ss,spin));\
b=In(sim,a,spin);\
free_complx_matrix(a);\
return b;\
}
DECLARE_SIFUNC(Ic)
DECLARE_SIFUNC(Ip)
DECLARE_SIFUNC(Im)
DECLARE_SIFUNC(Ix)
DECLARE_SIFUNC(Iy)
/* Iz is diagonal matrix */
mat_complx * Iz(Sim_info* sim, int nuc)
{
mat_complx *res;
int i, ii, iii, dim, K, L, N, cnt;
double I;
I = ss_qn(sim->ss,nuc);
N = (int)(2*I+1);
dim = sim->matdim;
K = 1;
for (i=1;i<nuc;i++) {
K *= (int)(2.0*ss_qn(sim->ss,i)+1.0);
}
L = 1;
for (i=nuc+1; i<=sim->ss->nspins; i++) {
L *= (int)(2.0*ss_qn(sim->ss,i)+1.0);
}
assert(K*N*L == dim);
res = complx_matrix(dim,dim,MAT_DENSE_DIAG,0,0);
cnt = 0;
for (i=0; i<K; i++) {
for (ii=0; ii<N; ii++) {
for (iii=0; iii<L; iii++) {
res->data[cnt] = Complx(I - ii,0.0);
cnt++;
}
}
}
return res;
}
/* moved here from readsys */
mat_double * Iz_ham(Sim_info* sim, int nuc)
{
mat_double *res;
int i, ii, iii, dim, K, L, N, cnt;
double I;
I = ss_qn(sim->ss,nuc);
N = (int)(2*I+1);
dim = sim->matdim;
K = 1;
for (i=1;i<nuc;i++) {
K *= (int)(2.0*ss_qn(sim->ss,i)+1.0);
}
L = 1;
for (i=nuc+1; i<=sim->ss->nspins; i++) {
L *= (int)(2.0*ss_qn(sim->ss,i)+1.0);
}
assert(K*N*L == dim);
res = double_matrix(dim,dim,MAT_DENSE_DIAG,0,sim->basis);
cnt = 0;
for (i=0; i<K; i++) {
for (ii=0; ii<N; ii++) {
for (iii=0; iii<L; iii++) {
res->data[cnt] = I - ii;
cnt++;
}
}
}
if (sim->basis != 0) {
double* ddum = (double*)malloc(dim*sizeof(double));
int *permvec = sim->perm_table[0+sim->basis*sim->Nbasis];
for (i=0; i<dim; i++) ddum[i] = res->data[permvec[i+1]-1];
free(res->data);
res->data = ddum;
}
return res;
}
blk_mat_double * IzIz_sqrt2by3(Sim_info *sim, int n1, int n2)
{
blk_mat_double *res;
mat_double *Iz1, *Iz2;
int i, j;
double *d1, *d2, *d3;
Iz1 = Iz_ham(sim,n1);
Iz2 = Iz_ham(sim,n2);
if (sim->basis == 0)
res = create_blk_mat_double(sim->matdim,1,NULL,MAT_DENSE_DIAG,sim->basis);
else
res = create_blk_mat_double(sim->matdim,LEN(sim->dims_table[sim->basis]),sim->dims_table[sim->basis],MAT_DENSE_DIAG,sim->basis);
d1 = Iz1->data;
d2 = Iz2->data;
for (i=0; i<res->Nblocks; i++) {
d3 = res->m[i].data;
assert(res->m[i].type == MAT_DENSE_DIAG);
for (j=0; j<res->blk_dims[i]; j++) {
*d3 = (*d1)*(*d2)*SQRT2BY3;
d1++;
d2++;
d3++;
}
}
free_double_matrix(Iz1);
free_double_matrix(Iz2);
return res;
}
mat_double * Ip_real(Sim_info *sim, int nuc)
{
mat_double *res, *pom;
int i,j,S;
double I, mm,m;
I = ss_qn(sim->ss,nuc);
S= (int)(2*I+1);
pom = double_matrix(S,S,MAT_DENSE,0,0);
for (i=0;i<S;i++) {
mm = I-i;
for (j=0;j<S;j++) {
m = I-j;
if (mm == m + 1)
pom->data[i+j*S] = sqrt(I*(I+1.0)-m*(m+1.0));
else
pom->data[i+j*S] = 0.0;
}
}
res = In_real(sim,pom,nuc);
free_double_matrix(pom);
return res;
}
mat_double * Im_real(Sim_info *sim, int nuc)
{
mat_double *res, *pom;
int i,j,S;
double I, mm,m;
I = ss_qn(sim->ss,nuc);
S= (int)(2*I+1);
pom = double_matrix(S,S,MAT_DENSE,0,0);
for (i=0;i<S;i++) {
mm = I-i;
for (j=0;j<S;j++) {
m = I-j;
if (mm == m - 1)
pom->data[i+j*S] = sqrt(I*(I+1.0)-m*(m-1.0));
else
pom->data[i+j*S] = 0.0;
}
}
res = In_real(sim,pom,nuc);
free_double_matrix(pom);
return res;
}
mat_double * Ix_real(Sim_info *sim, int nuc)
{
mat_double *res, *pom;
int i,j,S;
double I, mm,m;
I = ss_qn(sim->ss,nuc);
S= (int)(2*I+1);
pom = double_matrix(S,S,MAT_DENSE,0,0);
dm_zero(pom);
for (i=0;i<S;i++) {
mm = I-i;
for (j=0;j<S;j++) {
m = I-j;
/* this is for Im */
if (mm == m - 1) pom->data[i+j*S] += 0.5*sqrt(I*(I+1.0)-m*(m-1.0));
/* this is for Ip */
if (mm == m + 1) pom->data[i+j*S] += 0.5*sqrt(I*(I+1.0)-m*(m+1.0));
}
}
res = In_real(sim,pom,nuc);
free_double_matrix(pom);
return res;
}
mat_double * Iy_real(Sim_info *sim, int nuc)
{
mat_double *res, *pom;
int i,j,S;
double I, mm,m;
I = ss_qn(sim->ss,nuc);
S= (int)(2*I+1);
pom = double_matrix(S,S,MAT_DENSE,0,0);
dm_zero(pom);
for (i=0;i<S;i++) {
mm = I-i;
for (j=0;j<S;j++) {
m = I-j;
/* this is for Im */
if (mm == m - 1) pom->data[i+j*S] += 0.5*sqrt(I*(I+1.0)-m*(m-1.0));
/* this is for Ip */
if (mm == m + 1) pom->data[i+j*S] -= 0.5*sqrt(I*(I+1.0)-m*(m+1.0));
}
}
res = In_real(sim,pom,nuc);
free_double_matrix(pom);
return res;
}
/* ( I+ S- + I- S+ )/2 = IxSx + IySy */
blk_mat_double * zq_ham(Sim_info *sim, int n1, int n2)
{
blk_mat_double *res;
mat_double *a, *b;
int nb,dim,i,j;
assert(n1 != n2); // this code hold for this ONLY!!!
a = Ip_real(sim,n1);
b = Im_real(sim,n2);
dm_multo(a,b);
free_double_matrix(b);
if (sim->basis == 0) {
res = create_blk_mat_double(sim->matdim,1,NULL,sim->sparse ? MAT_SPARSE : MAT_DENSE,sim->basis);
dm_zero(res->m);
dm_multod(res->m,a,0.5);
dm_transposei(a);
dm_multod(res->m,a,0.5);
free_double_matrix(a);
return res;
}
// when blocking is active:
//printf("a is %s\n",matrix_type(a->type));
res = create_blk_mat_double(sim->matdim,LEN(sim->dims_table[sim->basis]),sim->dims_table[sim->basis],sim->sparse ? MAT_SPARSE : MAT_DENSE,sim->basis);
int sft = 1;
int *permvec = sim->perm_table[0+sim->basis*sim->Nbasis];
for (nb=0; nb<res->Nblocks; nb++) {
dim = res->blk_dims[nb];
//printf("nb = %d, dim = %d, %s\n",nb,dim,matrix_type(res->m[nb].type));
if (dim == 1) {
res->m[nb].data[0] = dm_getelem(a,permvec[sft],permvec[sft]);
} else if (res->m[nb].type == MAT_DENSE) {
for (i=0; i<dim; i++) {
res->m[nb].data[i+i*dim] = dm_getelem(a,permvec[i+sft],permvec[i+sft]);
for (j=i+1; j<dim; j++) {
res->m[nb].data[i+j*dim] = 0.5*dm_getelem(a,permvec[i+sft],permvec[j+sft]);
res->m[nb].data[i+j*dim] += 0.5*dm_getelem(a,permvec[j+sft],permvec[i+sft]);
res->m[nb].data[j+i*dim] = res->m[nb].data[i+j*dim];
}
}
} else {
assert(res->m[nb].type == MAT_SPARSE);
b = dm_get_diagblock_permute(a,permvec,sft,dim);
b->basis = sim->basis;
dm_zero(&(res->m[nb]));
dm_multod(&(res->m[nb]),b,0.5);
dm_transposei(b);
dm_multod(&(res->m[nb]),b,0.5);
free_double_matrix(b);
}
sft += dim;
}
free_double_matrix(a);
return res;
}
blk_mat_double * zq_ham_permuted(Sim_info *sim, int n1, int n2)
{
blk_mat_double *res;
mat_double *a, *b;
int nb,dim,i,j;
assert(n1 != n2); // this code hold for this ONLY!!!
if (sim->basis == 0) {
a = Ip_real(sim,n1);
b = Im_real(sim,n2);
dm_multo(a,b);
free_double_matrix(b);
res = create_blk_mat_double(sim->matdim,1,NULL,sim->sparse ? MAT_SPARSE : MAT_DENSE,sim->basis);
dm_zero(res->m);
dm_multod(res->m,a,0.5);
dm_transposei(a);
dm_multod(res->m,a,0.5);
free_double_matrix(a);
} else {
// when blocking is active:
a = Ip_real(sim,n1);
b = Im_real(sim,n2);
dm_multo(a,b);
free_double_matrix(b);
dm_permute(a,sim->perm_table[0+sim->basis*sim->Nbasis]);
res = create_blk_mat_double(sim->matdim,LEN(sim->dims_table[sim->basis]),sim->dims_table[sim->basis],sim->sparse ? MAT_SPARSE : MAT_DENSE,sim->basis);
int sft = 0;
for (nb=0; nb<res->Nblocks; nb++) {
dim = res->blk_dims[nb];
if (dim == 1) {
res->m[nb].data[0] = dm_getelem(a,sft+1,sft+1);
} else {
b = dm_extract_block(a,sft,sft,dim,dim);
dm_zero(&(res->m[nb]));
if (b != NULL) {
b->basis = sim->basis;
dm_multod(&(res->m[nb]),b,0.5);
dm_transposei(b);
dm_multod(&(res->m[nb]),b,0.5);
free_double_matrix(b);
}
}
sft += dim;
}
free_double_matrix(a);
}
return res;
}
blk_mat_double * II(Sim_info* sim, int n1, int n2)
{
blk_mat_double *a, *b;
a = IzIz_sqrt2by3(sim,n1,n2);
b = zq_ham(sim,n1,n2);
blk_dm_multod(b,a,1.0/SQRT2BY3);
free_blk_mat_double(a);
return b;
}
blk_mat_double * T20(Sim_info* sim, int n1, int n2)
{
blk_mat_double *a, *b;
a = IzIz_sqrt2by3(sim,n1,n2);
//b = zq_ham(sim,n1,n2);
b = zq_ham_permuted(sim,n1,n2);
//blk_dm_print(b,"zq_ham");
blk_dm_multod(a,b,-1.0/sqrt(6.0));
free_blk_mat_double(b);
return a;
}
mat_double * T20II(Sim_info *sim, int nuc)
{
mat_double *res;
int i, ii, iii, dim, K, L, N, cnt;
double I, val;
I = ss_qn(sim->ss,nuc);
N = (int)(2*I+1);
dim = sim->matdim;
K = 1;
for (i=1;i<nuc;i++) {
K *= (int)(2.0*ss_qn(sim->ss,i)+1.0);
}
L = 1;
for (i=nuc+1; i<=sim->ss->nspins; i++) {
L *= (int)(2.0*ss_qn(sim->ss,i)+1.0);
}
assert(K*N*L == dim);
res = double_matrix(dim,dim,MAT_DENSE_DIAG,0,sim->basis);
cnt = 0;
for (i=0; i<K; i++) {
for (ii=0; ii<N; ii++) {
val = (I - ii)*(I - ii)*SQRT2BY3;
if (ii < N-1) val -= (I*(I+1)-(I-ii-1)*(I-ii))*(0.5/sqrt(6.0));
if (ii>0) val -= (I*(I+1)-(I-ii+1)*(I-ii))*(0.5/sqrt(6.0));
for (iii=0; iii<L; iii++) {
res->data[cnt] = val;
cnt++;
}
}
}
if (sim->basis != 0) {
double* ddum = (double*)malloc(dim*sizeof(double));
int *permvec = sim->perm_table[0+sim->basis*sim->Nbasis];
for (i=0; i<dim; i++) ddum[i] = res->data[permvec[i+1]-1];
free(res->data);