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Former-commit-id: a91bbb883f6e9fdee34ac9568ec92070c4c095b7
This commit is contained in:
Marek Nečada 2017-03-21 06:18:17 +00:00
parent ae4065d30d
commit 70dcb594c2
1 changed files with 170 additions and 73 deletions
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243
qpms/gaunt.c
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@ -49,7 +49,7 @@ double f_a0 (int m, int n, int mu, int nu) {
} }
// coefficient Ap(m,n,mu,nu,p) (from vec_trans.f90) // coefficient Ap(m,n,mu,nu,p) (from vec_trans.f90)
int Ap(int m, int n, int mu, int nu, int p) { int f_Ap(int m, int n, int mu, int nu, int p) {
return p*(p-1)*(m-mu)-(m+mu)*(n-nu)*(n+nu+1); return p*(p-1)*(m-mu)-(m+mu)*(n-nu)*(n+nu+1);
} }
@ -58,7 +58,7 @@ int Ap(int m, int n, int mu, int nu, int p) {
double f_a1norm(int m, int n, int mu, int nu) { double f_a1norm(int m, int n, int mu, int nu) {
int n4 = n + nu - m - mu; int n4 = n + nu - m - mu;
return ((2.*n + 2.*nu - 3.) / 2.) * (1. - ((2.*n + 2.*nu - 1.) / (n4 * (n4-1.))) return ((2.*n + 2.*nu - 3.) / 2.) * (1. - ((2.*n + 2.*nu - 1.) / (n4 * (n4-1.)))
* ((m - n) * (m - n + 1.) / (2.*n - 1.) + (mu-nu) * (mu-nu+1.)/(2.nu-1.))); * ((m - n) * (m - n + 1.) / (2.*n - 1.) + (mu-nu) * (mu-nu+1.)/(2.*nu-1.)));
} }
// coefficient a(m,n,mu,nu,2) normalized by the backward recursion (From vec_trans.f90) // coefficient a(m,n,mu,nu,2) normalized by the backward recursion (From vec_trans.f90)
@ -85,7 +85,6 @@ double f_alpha(int n, int nu, int p) {
return (isq(p) - isq(n-nu))*(isq(p)-isq(n+nu+1)) / (double)(4*isq(p)-1); return (isq(p) - isq(n-nu))*(isq(p)-isq(n+nu+1)) / (double)(4*isq(p)-1);
} }
static inline int min1pow(int pow) { return (pow % 2) ? -1 : 1; } static inline int min1pow(int pow) { return (pow % 2) ? -1 : 1; }
// starting value of coefficient a(m,n,mu,nu,qmax) for the forward recursion // starting value of coefficient a(m,n,mu,nu,qmax) for the forward recursion
@ -111,7 +110,7 @@ double f_aqmax(int m, int n, int mu, int nu, int qmax) {
} else if (pmin==m+mu+1) { } else if (pmin==m+mu+1) {
int Apmin = f_Ap(m,n,mu,nu,pmin); int Apmin = f_Ap(m,n,mu,nu,pmin);
double logw = lpoch(qmax+1,qmax)+lnf(n+nu-qmax)+lnf(n+m)+lnf(nu+mu) \ double logw = lpoch(qmax+1,qmax)+lnf(n+nu-qmax)+lnf(n+m)+lnf(nu+mu) \
-lnf(n+nu+pmin+1)-lnf(n-qmax)-lnf(nu-qmax)-lnf(n-m)-lnf(nu-mu) -lnf(n+nu+pmin+1)-lnf(n-qmax)-lnf(nu-qmax)-lnf(n-m)-lnf(nu-mu);
return min1pow(n+m-qmax)*Apmin*(2*pmin+1)*exp(logw)/(double)(pmin-1); return min1pow(n+m-qmax)*Apmin*(2*pmin+1)*exp(logw)/(double)(pmin-1);
} else if (pmin==-m-mu+1) { } else if (pmin==-m-mu+1) {
int Apmin=f_Ap(m,n,mu,nu,pmin); int Apmin=f_Ap(m,n,mu,nu,pmin);
@ -168,17 +167,166 @@ double f_a2normr(int m, int n, int mu, int nu, double a1norm) {
} }
} }
#define MAX(x,y) (((x) > (y)) ? (x) : (y))
int j3minimum(int j1, int j2, int m1, int m2) {
return MAX(abs(j1-j2), abs(m1+m2));
}
int nw(int j1, int j2, int m1, int m2) {
return j1+j2+1-MAX(abs(j1-j2),abs(m1+m2));
}
double wdown(int j1, int j2, int m1, int m2) {
double logw = .5*(lnf(2.*j1,
TODO TODO TODO ZDE JSEM SKONČIL
//******************************************************************************
//7) subroutine Wigner3jm: calcolo il vettore di simboli 3jm
//******************************************************************************
void wigner3jm(int j1, int j2, int m1, int m2, int j3min, int j3max, double *v_w3jm){
// in the original code, the dimension of v_w3jm is (j3min:j3max).
// In C, this means it has length j3max-j3min+1, and we must
// always deduct j3min from the indices
// Inizializzo gli indici per la downward recursion
int j3 = j3max; // we don't use separate j3int as gevero does.
// In questo if separo i casi in cui ho un vettore di lunghezza uno da quelli che
// necessitano dell'uso della ricorsione
if (j3min==j3max) // big_if
v_w3jm[j3max-j3min]=wdown0(j1,j2,m1,m2); // Unico termine da calcolare
else {
// Si inizializza la ricorsione
v_w3jm[j3max-j3min]=wdown0(j1,j2,m1,m2);
v_w3jm[j3max-1-j3min]=-(dr(j1,j2,j1+j2,m1,m2,-m1-m2)/( (j1+j2+1)*cr(j1,j2,j1+j2,m1,m2,-m1-m2) ))*v_w3jm[j3max-j3min];
// Ciclo per il calcolo ricorsivo
while(j3-2>=j3min){ // down_do
//Primo coeff della ricorsione
cd1=dr(j1,j2,j3-1,m1,m2,-m1-m2)/(j3*cr(j1,j2,j3-1,m1,m2,-m1-m2))
cd2=((j3-1)*cr(j1,j2,j3,m1,m2,-m1-m2))/(j3*cr(j1,j2,j3-1,m1,m2,-m1-m2))
//Ricorsione
v_w3jm[j3int-2-j3min]=-cd1*v_w3jm[j3int-1-j3min]-cd2*v_w3jm[j3int-j3min]
//Aggiorno gli indici
--j3;
} //END DO down_do
// Inizializzo gli indici per la upward recursion
j3int=j3min
j3=REAL(j3min,dbl)
// Calcolo del primo termine di wigner dal basso
v_w3jm[j3int-j3min]=wup0(j1,j2,m1,m2)
// Calcolo del secondo termine di wigner dal basso
// Pongo anche la condizione sul coefficienti nel caso ci sia signolarita'
cu3_if: IF (j3min==0) THEN
cu3=0
ELSE
cu3=dr(j1,j2,j3,m1,m2,-m1-m2)/(j3*cr(j1,j2,j3+1,m1,m2,-m1-m2))
END IF cu3_if
w3jm_temp=-cu3*v_w3jm[j3int-j3min]
// If legato alla monotonia della successione
up_if: IF (ABS(w3jm_temp)>ABS(v_w3jm[j3min-j3min])) THEN
// Aggiorno gli indici e metto nell'array il secondo valore
// in questo modo sono pronto per iniziale la upward recursion
// a tre termini
j3int=j3int+1
v_w3jm[j3int-j3min]=w3jm_temp
up_do: DO
//Aggiorno gli indici
j3int=j3int+1
j3=REAL(j3int,dbl)
IF (j3int-1==j3max) EXIT
// IF ((INT(-m1)==-1).AND.(INT(j1)==1).AND.(INT(m2)==1).AND.(INT(j2)==2)) THEN
// WRITE(*,*) "j3-1,cr1,cr2",j3-1,cr(j1,j2,j3,m1,m2,-m1-m2),cr(j1,j2,j3,m1,m2,-m1-m2)
// END IF
//Primo e secondo coeff della ricorsione
cu1=dr(j1,j2,j3-1,m1,m2,-m1-m2)/((j3-1)*cr(j1,j2,j3,m1,m2,-m1-m2))
cu2=(j3*cr(j1,j2,j3-1,m1,m2,-m1-m2))/((j3-1)*cr(j1,j2,j3,m1,m2,-m1-m2))
//Assegnazione temporanea della ricorsione
w3jm_temp=-cu1*v_w3jm[j3int-1-j3min]-cu2*v_w3jm[j3int-2-j3min]
IF ((ABS(w3jm_temp)<ABS(v_w3jm[j3int-1-j3min])) .OR. ((j3int-1)==j3max) ) EXIT // Cond. di uscita
v_w3jm[j3int-j3min]=w3jm_temp //Assegno perche' e' ok
END DO up_do
END IF up_if
} // big_if
END SUBROUTINE wigner3jm
void gaunt_cz(int m, int n, int mu, int n, int qmaxa, double *v_aq, int *error) {
*error = 0;
if (abs(m) > n || abs(mu) > nu) { // error_if
*error=1;
assert(0);
return;
}
// calcolo i bounds dei vettori di wigner
int pmin = j3minimum(n,nu,m,mu);
int pmax = n+nu;
int pmin0 = j3minimum(n,nu,0,0);
// Alloco i vettori di wigner e li calcolo
ALLOCATE(v_w3jm(pmin:pmax),v_w3jm0(pmin0:pmax),STAT=stat_a)
CALL wigner3jm(n,nu,m,mu,pmin,pmax,v_w3jm)
CALL wigner3jm(n,nu,0.0D0,0.0D0,pmin0,pmax,v_w3jm0)
// Entro nel ciclo per il calcolo dei coefficienti di gaunt
gaunt_do: DO q=0,qmaxa
// Calcolo dell'indice p, sia reale che intero
p=INT(n+nu,lo)-2*q
pr=REAL(p,dbl)
//Calcolo del fattoriale
logw = 0.5D0* (lnf(n+m,r)+lnf(nu+mu,r)+lnf(pr-m-mu,r) - &
lnf(n-m,r)-lnf(nu-mu,r)-lnf(pr+m+mu,r))
fac= EXP(logw)
// Calcolo del coefficiente di gaunt
v_aq(q)=((-1.0D0)**INT(m+mu,lo))*(2.0D0*pr+1.0D0)*fac*v_w3jm(p)*v_w3jm0(p)
END DO gaunt_do
// Disalloco i vettori di wigner a lavoro finito
DEALLOCATE(v_w3jm,v_w3jm0)
END SUBROUTINE gaunt_cz
// gaunt_xu from vec_trans.f90 // gaunt_xu from vec_trans.f90
// FIXME set some sensible return value // FIXME set some sensible return value
double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error) { void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error) {
int v_zero[qmax] = {0}; // FIXME FAKT TO MÁ BÝT INITIALISOVÁNO NA 0???? KDYŽ SE TOMU NÍŽE PŘIŘAZUJÍ NULY??!!!
*error = 0; *error = 0;
int v_zero[qmax];
for (int i = 0; i < qmax; i++) v_zero[i] = 1;
double v_aq_cz[qmax];
for (int i = 0; i < qmax; i++) v_aq_cz[i] = 0.;
int qi = 0;
if(abs(m)>n || abs(mu)=nu) { if(abs(m)>n || abs(mu)>nu) {
*error = 1; *error = 1;
fprintf(stderr, "invalid values for m, n, mu or nu\n") fprintf(stderr, "invalid values for m, n, mu or nu\n");
return NAN; return; // FIXME vyřešit chyby
} }
switch(qmax) { //qmax_case switch(qmax) { //qmax_case
@ -305,7 +453,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
// forward recursion // forward recursion
// Primo valore per la forward recursion,errore relativo e suo swap // Primo valore per la forward recursion,errore relativo e suo swap
double aq_fwd=f_aqmax(m,n,mu,nu,qmax) double aq_fwd=f_aqmax(m,n,mu,nu,qmax);
double res=fabs(aq_fwd-v_aq[qmax])/fabs(aq_fwd); double res=fabs(aq_fwd-v_aq[qmax])/fabs(aq_fwd);
//Se non ho precisione, sostituisco i valori //Se non ho precisione, sostituisco i valori
@ -314,13 +462,13 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
int qi=1; int qi=1;
int zeroswitch = 0; // black magic (gevero's "switch") int zeroswitch = 0; // black magic (gevero's "switch")
//Entro nel ciclo della sostituzione valori //Entro nel ciclo della sostituzione valori
for( int q=qmax-1,q>=0,--q) { // tre_f_do for( int q=qmax-1;q>=0;--q) { // tre_f_do
switch(qmax-q) {// tre_q_case // FIXME switch -> if/else switch(qmax-q) {// tre_q_case // FIXME switch -> if/else
case 1: {// q==qmax-1 case 1: {// q==qmax-1
//Calcolo v_aq[qmax-1] //Calcolo v_aq[qmax-1]
int p=n+nu-2*(q+2); int p=n+nu-2*(q+2);
double c1=4*isq(m)+f_alpha(n,nu,p+2)+f_alpha(n,nu,p+3); double c1=4*isq(m)+f_alpha(n,nu,p+2)+f_alpha(n,nu,p+3);
double c2=-f_alpha(n,nu,p+4) double c2=-f_alpha(n,nu,p+4);
double aq_fwd=-(c1/c2)*v_aq[qmax]; double aq_fwd=-(c1/c2)*v_aq[qmax];
switch(v_zero[q]) { // z_3_1_case switch(v_zero[q]) { // z_3_1_case
@ -339,7 +487,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
//Calcolo v_aq[qmax-1] //Calcolo v_aq[qmax-1]
int p=n+nu-2*(q+2); int p=n+nu-2*(q+2);
double c0=f_alpha(n,nu,p+1); double c0=f_alpha(n,nu,p+1);
double c1=4*(m**2)+f_alpha(n,nu,p+2)+f_alpha(n,nu,p+3); double c1=4*isq(m)+f_alpha(n,nu,p+2)+f_alpha(n,nu,p+3);
double c2=-f_alpha(n,nu,p+4); double c2=-f_alpha(n,nu,p+4);
aq_fwd=-(c1/c2)*v_aq[q+1]+(c0/c2)*v_aq[q+2]; aq_fwd=-(c1/c2)*v_aq[q+1]+(c0/c2)*v_aq[q+2];
@ -362,9 +510,10 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
//Sono nel ciclo, allora sostituisco eaggiorno indice e residuo //Sono nel ciclo, allora sostituisco eaggiorno indice e residuo
v_aq[q]=aq_fwd; v_aq[q]=aq_fwd;
qi=q; qi=q;
assert(q); // assert níže přesunut sem
} // tre_f_do } // tre_f_do
// Check sul ciclo di sostituzione // Check sul ciclo di sostituzione
assert(q); //assert(q);
/* /*
error_if1: IF (q==0) THEN error_if1: IF (q==0) THEN
WRITE(*,*) WRITE(*,*)
@ -505,7 +654,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
v_aq[q]=0.; v_aq[q]=0.;
v_zero[q]=0; v_zero[q]=0;
} }
} else if ((v_zero[q-1]==0) && (v_zero[q-2]/=0)) { } else if ((v_zero[q-1]==0) && (v_zero[q-2] !=0)) {
if (fabs(v_aq[q]/v_aq[q-2])<ZERO_THRESHOLD) {//zgq_if1: if (fabs(v_aq[q]/v_aq[q-2])<ZERO_THRESHOLD) {//zgq_if1:
v_aq[q]=0.; v_aq[q]=0.;
v_zero[q]=0; v_zero[q]=0;
@ -534,7 +683,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
//Calcolo il secondo valore, e se la precisione e' raggiunta esco //Calcolo il secondo valore, e se la precisione e' raggiunta esco
double aq_fwd=f_aqmax_1(m,n,mu,nu,qmax); double aq_fwd=f_aqmax_1(m,n,mu,nu,qmax);
res=fabs(aq_fwd-v_aq[qmax-1])/fabs(aq_fwd); double res=fabs(aq_fwd-v_aq[qmax-1])/fabs(aq_fwd);
if (res<BF_PREC) if (res<BF_PREC)
return; return;
@ -542,7 +691,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
v_aq[qmax-1]=aq_fwd; v_aq[qmax-1]=aq_fwd;
qi=1; //FIXME nepoužitá proměnná qi=1; //FIXME nepoužitá proměnná
for (q = qmax; q >= 2; --q) { //Apmin_do: DO q=qmax,2,-1 for (int q = qmax; q >= 2; --q) { //Apmin_do: DO q=qmax,2,-1
//Calcolo pre-coefficienti //Calcolo pre-coefficienti
int p=n+nu-2*(q); int p=n+nu-2*(q);
@ -666,8 +815,8 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
continue; //CYCLE gen_f_do continue; //CYCLE gen_f_do
break; break;
case 1: case 1:
gaunt_cz(m,n,mu,nu,qmax,v_aq_cz(qi),error); // FIXME implementace gaunt_cz gaunt_cz(m,n,mu,nu,qmax,&(v_aq_cz[qi]),error); // FIXME implementace gaunt_cz
aq_fwd=v_aq_cz(qi); aq_fwd=(v_aq_cz[qi]);
res=fabs(aq_fwd-v_aq[qi])/fabs(aq_fwd); res=fabs(aq_fwd-v_aq[qi])/fabs(aq_fwd);
break; break;
default: default:
@ -748,7 +897,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
break; break;
case 1: case 1:
res=fabs(aq_fwd-v_aq[qi])/fabs(aq_fwd); res=fabs(aq_fwd-v_aq[qi])/fabs(aq_fwd);
if (res<PREC_BF) { // EXIT gen_f_do if (res<BF_PREC) { // EXIT gen_f_do
assert(qi); assert(qi);
return; return;
} }
@ -872,7 +1021,7 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
continue; // CYCLE gen_f_do continue; // CYCLE gen_f_do
break; break;
case 1: case 1:
gaunt_cz(m,n,mu,nu,qmax,&(v_aq_cz[qi]),error); gaunt_cz(m,n,mu,nu,qmax,&(v_aq_cz[qi]),error); // FIXME je potřeba mít v_aq_cz jako pole?
aq_fwd=v_aq_cz[qi]; aq_fwd=v_aq_cz[qi];
res=fabs(aq_fwd-v_aq[qi])/fabs(aq_fwd); res=fabs(aq_fwd-v_aq[qi])/fabs(aq_fwd);
break; break;
@ -952,55 +1101,3 @@ double gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error
/*
// gaunt_xu2 from vec_trans.f90
// btw, what is the difference from gaunt_xu?
double gaunt_xu2(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error) {
int v_zero[qmax] = {0};
*error = 0;
if(abs(m)>n || abs(mu)=nu) {
*error = 1;
fprintf(stderr, "invalid values for m, n, mu or nu\n")
return NAN;
}
switch(qmax) {
case 0:
v_aq[0] = f_a0(m,n,mu,nu);
break;
case 1:
v_aq[0] = f_a0(m,n,mu,nu);
v_aq[1] = v_aq[0] + f_a1norm(m,n,mu,nu);
// Check for zeros
if (fabs(v_aq[1]/v_aq[0]) < ZERO_THRESHOLD) {
v_aq[1] = 0.;
v_zero[1] = 0.;
}
break;
case 2:
v_aq[0] = f_a0(m,n,mu,nu);
v_aq[1] = v_aq[0] + f_a1norm(m,n,mu,nu);
// Check for zeros
if (fabs(v_aq[1]/v_aq[0]) < ZERO_THRESHOLD) {
v_aq[1] = 0.;
v_zero[1] = 0.;
}
v_aq[2] = v_aq[0] * f_a2norm_
break;
!!!!!!!!!TODO CONTINUE HERE
*/