static void
Qs(float_DD_put)(char *buf, size_t index, int count, void *v_arg)
{
Qs(USQCDArgs) *arg = v_arg;
#if QNc == 'N'
typedef QLA_DN_DiracPropagator(arg->nc, Ptype);
#else
typedef Qx(QLA_D,_DiracPropagator) Ptype;
#endif
Ptype *P = arg->P;
Ptype *dst = &P[index];
QLA_F_Complex *src = (void *)buf;
int js = arg->js;
int jc = arg->jc;
int is, ic;
if (count != 1)
luaL_error(arg->L, "qcd.ddpairs.read(): count != 1");
for (is = 0; is < QDP_Ns; is++) {
for (ic = 0; ic < arg->nc; ic++, src++) {
QLA_c_eq_r_plus_ir(QLA_elem_P(*dst, ic, is, jc, js),
QLA_real(*src), QLA_imag(*src));
}
}
}
void
set_H(QLA_HalfFermion *h, int i)
{
for(int j=0; j<QLA_Nc; j++) {
for(int k=0; k<(QLA_Ns/2); k++) {
QLA_c_eq_r_plus_ir(QLA_elem_H(*h,j,k), (j+4)*(k+1)+cos(i), (j+4)*(k+1)+sin(i));
}
}
}
void
set_D(QLA_DiracFermion *d, int i)
{
for(int j=0; j<QLA_Nc; j++) {
for(int k=0; k<QLA_Ns; k++) {
QLA_c_eq_r_plus_ir(QLA_elem_D(*d,j,k), (j+4)*(k+1)+cos(i), (j+4)*(k+1)+sin(i));
}
}
}
QLA_D_Complex
QLA_D_cexpi(QLA_D_Real theta)
{
QLA_D_Real s, c;
sincos(theta, &s, &c);
QLA_D_Complex z;
QLA_c_eq_r_plus_ir(z, c, s);
return z;
}
void
set_V(QLA_ColorVector *v, int i)
{
for(int j=0; j<QLA_Nc; j++) {
QLA_c_eq_r_plus_ir(QLA_elem_V(*v,j), j+1+cos(i), j+1+sin(i));
//QLA_real(QLA_elem_V(*v,j)) = 1;
//QLA_imag(QLA_elem_V(*v,j)) = 0;
}
}
int
main(void)
{
QLA_ColorMatrix x, y, c, f, f2, yt;
for(int i=0; i<QLA_Nc; i++) {
for(int j=0; j<QLA_Nc; j++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(x,i,j), i+1, QLA_Nc*(j+1));
QLA_c_eq_r_plus_ir(QLA_elem_M(c,i,j), QLA_Nc*(j+1), i-1);
//QLA_c_eq_r(QLA_elem_M(x,i,j), 0);
//QLA_c_eq_r(QLA_elem_M(c,i,j), 0);
}
QLA_c_eq_r_plus_ir(QLA_elem_M(x,i,i), 2+1, 1);
QLA_c_eq_r_plus_ir(QLA_elem_M(c,i,i), 0.1, 0.5);
}
QLA_M_eq_sqrt_M(&y, &x);
QLA_M_eq_Ma(&yt, &y);
//sqrt_deriv_site(&f, &y, &x, &c);
sylsolve_site(&f, &y, &y, &c);
printm(&x);
printm(&y);
printm(&c);
printm(&f);
QLA_ColorMatrix dx, dy;
for(int i=0; i<QLA_Nc; i++) {
for(int j=0; j<QLA_Nc; j++) {
QLA_Real eps = 1e-6;
QLA_M_eq_M(&dx, &x);
QLA_c_peq_r(QLA_elem_M(dx,i,j), eps);
QLA_M_eq_sqrt_M(&dy, &dx);
QLA_M_meq_M(&dy, &y);
QLA_Real ieps = 1/eps;
QLA_M_eq_r_times_M(&dy, &ieps, &dy);
//printm(&dy);
QLA_M_eq_M_times_Ma(&f2, &dy, &c);
QLA_Real r;
QLA_R_eq_re_trace_M(&r, &f2);
printf("%g\n", r);
}
}
// printm(&f2);
return 0;
}
void
set_M(QLA_ColorMatrix *m, int i)
{
for(int j=0; j<QLA_Nc; j++) {
for(int k=0; k<QLA_Nc; k++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,j,k),
(((j-k+QLA_Nc+1)*(j+k+1))%19)+cos(i),
(((j+4)*(k+1))%17)+sin(i));
}
}
}
static void
su2_fill(NCPROT QLA_ColorMatrix(*m), QLA_Real r[4], int i, int j)
{
QLA_Complex z;
QLA_c_eq_r(z, 1);
QLA_M_eq_c(m, &z);
QLA_c_eq_r_plus_ir(z, r[0], r[3]);
QLA_M_eq_elem_C(m, &z, i, i);
QLA_c_eq_r_plus_ir(z, r[2], r[1]);
QLA_M_eq_elem_C(m, &z, i, j);
r[2] = -r[2];
QLA_c_eq_r_plus_ir(z, r[2], r[1]);
QLA_M_eq_elem_C(m, &z, j, i);
r[3] = -r[3];
QLA_c_eq_r_plus_ir(z, r[0], r[3]);
QLA_M_eq_elem_C(m, &z, j, j);
}
static void
randforce(NCPROT QLA_ColorMatrix(*m), int i, void *args)
{
QLA_RandomState *s = (QLA_RandomState*)args + i;
QLA_Real s2 = 0.70710678118654752440; // sqrt(1/2)
QLA_Real s3 = 0.57735026918962576450; // sqrt(1/3)
QLA_Real r3 = s2*QLA_gaussian(s);
QLA_Real r8 = s2*s3*QLA_gaussian(s);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,0,0), 0, r3+r8);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,1,1), 0, -r3+r8);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,2,2), 0, -2*r8);
QLA_Real r01 = s2*QLA_gaussian(s);
QLA_Real r02 = s2*QLA_gaussian(s);
QLA_Real r12 = s2*QLA_gaussian(s);
QLA_Real i01 = s2*QLA_gaussian(s);
QLA_Real i02 = s2*QLA_gaussian(s);
QLA_Real i12 = s2*QLA_gaussian(s);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,0,1), r01, i01);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,1,0), -r01, i01);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,0,2), r02, i02);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,2,0), -r02, i02);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,1,2), r12, i12);
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,2,1), -r12, i12);
}
static void
qlamakegroup(QLA_Complex *x, int g)
{
switch(g&GROUP_TYPE) {
case GROUP_GL: break;
case GROUP_U: {
QLA_Real n = QLA_norm2_c(*x);
if(n==0) { QLA_c_eq_r(*x, 1); }
else {
n = 1/sqrt(n);
QLA_c_eq_r_times_c(*x, n, *x);
}
} break;
case GROUP_H: QLA_c_eq_r(*x, QLA_real(*x)); break;
case GROUP_AH: QLA_c_eq_r_plus_ir(*x, 0, QLA_imag(*x)); break;
}
if(g&GROUP_S) QLA_c_eq_r(*x, 1);
if(g&GROUP_T) QLA_c_eq_r(*x, 0);
}
/*
* qcd.Clover(U, -- 1, {U0,U1,U2,U3}, a table of color matrices
* kappa, -- 2, double, the hopping parameter
* c_sw, -- 3, double, the clover term
* boundary) -- 4, {r/c, ...}, a table of boundary phases
*/
static int
q_clover(lua_State *L)
{
int i;
luaL_checktype(L, 1, LUA_TTABLE);
lua_pushnumber(L, 1);
lua_gettable(L, 1);
qlua_checkLatColMat3(L, -1, NULL, 3);
mLattice *S = qlua_ObjLattice(L, -1);
int Sidx = lua_gettop(L);
mClover *c = qlua_newClover(L, Sidx);
if (S->rank != QOP_CLOVER_DIM)
return luaL_error(L, "clover is not implemented for #L=%d", S->rank);
if (QDP_Ns != QOP_CLOVER_FERMION_DIM)
return luaL_error(L, "clover does not support Ns=%d", QDP_Ns);
QCArgs args;
luaL_checktype(L, 4, LUA_TTABLE);
for (i = 0; i < QOP_CLOVER_DIM; i++) {
lua_pushnumber(L, i + 1);
lua_gettable(L, 4);
switch (qlua_qtype(L, -1)) {
case qReal:
QLA_c_eq_r_plus_ir(args.bf[i], lua_tonumber(L, -1), 0);
break;
case qComplex:
QLA_c_eq_c(args.bf[i], *qlua_checkComplex(L, -1));
break;
default:
luaL_error(L, "bad clover boundary condition type");
}
lua_pop(L, 1);
}
double kappa = luaL_checknumber(L, 2);
double c_sw = luaL_checknumber(L, 3);
c->kappa = kappa;
c->c_sw = c_sw;
QDP_D3_ColorMatrix *UF[Nz];
luaL_checktype(L, 1, LUA_TTABLE);
CALL_QDP(L);
/* create a temporary F, and temp M */
for (i = QOP_CLOVER_DIM; i < Nz; i++)
UF[i] = QDP_D3_create_M_L(S->lat);
/* extract U from the arguments */
for (i = 0; i < QOP_CLOVER_DIM; i++) {
lua_pushnumber(L, i + 1); /* [sic] lua indexing */
lua_gettable(L, 1);
UF[i] = qlua_checkLatColMat3(L, -1, S, 3)->ptr;
lua_pop(L, 1);
}
int mu, nu;
QDP_Shift *neighbor = QDP_neighbor_L(S->lat);
CALL_QDP(L); /* just in case, because we touched LUA state above */
/* compute 8i*F[mu,nu] in UF[Nf...] */
for (i = 0, mu = 0; mu < QOP_CLOVER_DIM; mu++) {
for (nu = mu + 1; nu < QOP_CLOVER_DIM; nu++, i++) {
/* clover in [mu, nu] --> UF[Nu + i] */
QDP_D3_M_eq_sM(UF[Nt], UF[nu], neighbor[mu], QDP_forward,
S->all);
QDP_D3_M_eq_Ma_times_M(UF[Nt+1], UF[nu], UF[mu], S->all);
QDP_D3_M_eq_M_times_M(UF[Nt+2], UF[Nt+1], UF[Nt], S->all);
QDP_D3_M_eq_sM(UF[Nt+3], UF[Nt+2], neighbor[nu], QDP_backward,
S->all);
QDP_D3_M_eq_M_times_Ma(UF[Nt+4], UF[Nt+3], UF[mu], S->all);
QDP_D3_M_eq_sM(UF[Nt+1], UF[mu], neighbor[nu], QDP_forward,
S->all);
QDP_D3_M_eq_Ma_times_M(UF[Nt+5], UF[mu], UF[Nt+3], S->all);
QDP_D3_M_eq_M_times_Ma(UF[Nt+2], UF[Nt], UF[Nt+1], S->all);
QDP_D3_M_eq_M_times_Ma(UF[Nt+3], UF[Nt+2], UF[nu], S->all);
QDP_D3_M_peq_M_times_M(UF[Nt+4], UF[mu], UF[Nt+3], S->all);
QDP_D3_M_peq_M_times_M(UF[Nt+5], UF[Nt+3], UF[mu], S->all);
QDP_D3_M_eq_sM(UF[Nt+2], UF[Nt+5], neighbor[mu], QDP_backward,
S->all);
QDP_D3_M_peq_M(UF[Nt+4], UF[Nt+2], S->all);
QDP_D3_M_eq_M(UF[Nu+i], UF[Nt+4], S->all);
QDP_D3_M_meq_Ma(UF[Nu+i], UF[Nt+4], S->all);
}
}
args.lat = S->lat;
/* create the clover state */
QDP_latsize_L(S->lat, args.lattice);
struct QOP_CLOVER_Config cc;
cc.self = S->node;
cc.master_p = QMP_is_primary_node();
cc.rank = S->rank;
cc.lat = S->dim;
cc.net = S->net;
cc.neighbor_up = S->neighbor_up;
cc.neighbor_down = S->neighbor_down;
cc.sublattice = qlua_sublattice;
cc.env = S;
if (QOP_CLOVER_init(&c->state, &cc))
return luaL_error(L, "CLOVER_init() failed");
/* import the gauge field */
for (i = 0; i < Nt; i++) {
args.uf[i] = QDP_D3_expose_M(UF[i]);
}
if (QOP_CLOVER_import_gauge(&c->gauge, c->state, kappa, c_sw,
q_CL_u_reader, q_CL_f_reader, &args)) {
return luaL_error(L, "CLOVER_import_gauge() failed");
}
for (i = 0; i < Nt; i++)
QDP_D3_reset_M(UF[i]);
/* clean up temporaries */
for (i = QOP_CLOVER_DIM; i < Nz; i++)
QDP_D3_destroy_M(UF[i]);
return 1;
}
/*
void
traceless_herm_M_evalues(QLA_ColorMatrix *Q, double *u, double *w,
double *q1, double *q2, double *q3) {
QLA_Complex c0, c1;
QLA_ColorMatrix Q2;
QLA_M_eq_M_times_M(&Q2, Q, Q);
printf("Q^2 = \n"); printm(&Q2);
QLA_C_eq_det_M (&c0, Q); // c0 = det(Q)
QLA_C_eq_trace_M (&c1, &Q2); // c1 = tr(Q^2)
double athird = 1.0/3.0;
double cc0, cc1, cc0max;
cc0 = QLA_real(c0);
cc1 = 0.5 * QLA_real(c1);
cc0max = 2*sqrt(cc1 * athird)*(cc1 * athird); //c_0^max = 2 * (c1/3)^{3/2}
printf("c0 = %f\n", cc0);
printf("c1 = %f\n", cc1);
printf("c0_max = %f\n", cc0max);
double theta;
theta =acos(cc0/cc0max);
*u = sqrt(athird * cc1) * cos(athird * theta);
*w = sqrt(cc1) * sin(athird * theta);
*q1 = 2 * *u;
*q2 = -*u + *w;
*q3 = -*u - *w;
printf("u = %f, w = %f, q1 = %f, q2 = %f, q3 = %f\n", *u, *w, *q1, *q2, *q3);
}
void
get_f_coeffs(QLA_ColorMatrix *Q, double _Complex *f0, double _Complex *f1, double _Complex *f2){
double u, w, q1, q2, q3;
traceless_herm_M_evalues(Q, &u, &w, &q1, &q2, &q3);
printf("q1=\n"); printc99(&q1);
double _Complex e2iu, e_iu;
e2iu = cexp(2 * _Complex_I * u);
e_iu = cexp(-1.0 * _Complex_I * u);
double u2 = u*u;
double w2 = w*w;
double _Complex zeta0w;
if (fabs(w) > 0.05) {
zeta0w = sin(w)/w;
}
else {
zeta0w = 1 - w2/6. * (1-w2/20. * (1 - w2/42.));
}
double _Complex h0, h1, h2;
h0 = (u2 - w2) * e2iu + e_iu * ( 8 * u2 *cos(w) + 2*_Complex_I*u * (3*u2+w2)*zeta0w);
h1 = 2*u*e2iu - e_iu * (2 * u * cos(w) - _Complex_I * (3*u2-w2)*zeta0w);
h2 = e2iu - e_iu * ( cos(w) + 3*_Complex_I*u * zeta0w);
double fac = 1.0/(9*u2-w2);
*f0 = h0 * fac;
*f1 = h1 * fac;
*f2 = h2 * fac;
}
void
get_Bs(QLA_ColorMatrix *Q, QLA_ColorMatrix *Q2, QLA_ColorMatrix *B1, QLA_ColorMatrix *B2, double _Complex *f0, double _Complex *f1, double _Complex *f2) {
double u, w, q1, q2, q3;
traceless_herm_M_evalues(Q, &u, &w, &q1, &q2, &q3);
printf("q1=\n"); printc99(&q1);
double _Complex e2iu, e_iu;
e2iu = cexp(2 * _Complex_I * u);
e_iu = cexp(-1.0 * _Complex_I * u);
double u2 = u*u;
double w2 = w*w;
double _Complex zeta0w, zeta1w;
if (fabs(w) > 0.05) {
zeta0w = sin(w)/w;
zeta1w = (cos(w)-zeta0w)/w2;
}
else {
zeta0w = 1 - w2/6. * (1-w2/20. * (1 - w2/42.));
zeta1w = -(1 - w2/10. * (1 - w2/28.*(1 - w2/54.)))/3.0;
}
double _Complex h0, h1, h2;
h0 = (u2 - w2) * e2iu + e_iu * ( 8 * u2 *cos(w) + 2*_Complex_I*u * (3*u2+w2)*zeta0w);
h1 = 2*u*e2iu - e_iu * (2 * u * cos(w) - _Complex_I * (3*u2-w2)*zeta0w);
h2 = e2iu - e_iu * ( cos(w) + 3*_Complex_I*u * zeta0w);
double fac = 1.0/(9*u2-w2);
*f0 = h0 * fac;
*f1 = h1 * fac;
*f2 = h2 * fac;
double _Complex r01, r11, r21, r02, r12, r22, iu;
double cosw = cos(w);
iu = _Complex_I * u;
r01 = 2*(u + _Complex_I * (u2 - w2)) * e2iu
+ 2 * e_iu * ( 4*u*(2 - iu) * cosw + _Complex_I * (9 * u2 + w2 - iu * (3*u2 + w2))*zeta0w);
r11 = 2*(1 + 2*iu) * e2iu
+ e_iu * ( -2 * (1-iu) * cosw + _Complex_I * (6*u + _Complex_I * (w2 - 3*u2)) * zeta0w);
r21 = 2 * _Complex_I * e2iu + _Complex_I * e_iu * (cosw - 3*(1-iu)*zeta0w);
r02 = -2 * e2iu + 2 * iu * e_iu * (cosw + (1+4*iu) * zeta0w + 3 * u2 * zeta1w);
r12 = -_Complex_I * e_iu * ( cosw + (1+2*iu) * zeta0w - 3*u2 * zeta1w);
r22 = e_iu * (zeta0w - 3 * iu * zeta1w);
double _Complex b10, b11, b12, b20, b21, b22;
double fac1, fac2, fac3;
double mult = 0.5 * fac * fac;
fac1 = 2 * u;
fac2 = 3*u2 - w2;
fac3 = 2*(15*u2+w2);
b10 = fac1 * r01 + fac2 * r02 - fac3 * (*f0);
b10 *= mult;
b11 = fac1 * r11 + fac2 * r12 - fac3 * (*f1);
b11 *= mult;
b12 = fac1 * r21 + fac2 * r22 - fac3 * (*f2);
b12 *= mult;
fac2 = 3*u;
fac3 = 24*u;
b20 = r01 - fac2 * r02 - fac3 * (*f0);
b20 *= mult;
b21 = r11 - fac2 * r12 - fac3 * (*f1);
b21 *= mult;
b22 = r21 - fac2 * r22 - fac3 * (*f2);
b22 *= mult;
QLA_Complex qb10, qb11, qb12, qb20, qb21, qb22;
QLA_c_eq_c99(qb10, b10);
QLA_c_eq_c99(qb11, b11);
QLA_c_eq_c99(qb12, b12);
QLA_c_eq_c99(qb20, b20);
QLA_c_eq_c99(qb21, b21);
QLA_c_eq_c99(qb22, b22);
QLA_M_eq_c(B1, &qb10);
QLA_M_peq_c_times_M(B1, &qb11, Q);
QLA_M_peq_c_times_M(B1, &qb12, Q2);
QLA_M_eq_c(B2, &qb20);
QLA_M_peq_c_times_M(B2, &qb21, Q);
QLA_M_peq_c_times_M(B2, &qb22, Q2);
}
*/
int
main(void) {
QLA_ColorMatrix O, iQ, matI;
QLA_M_eq_zero(&matI);
for(int i=0; i<QLA_Nc; i++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(matI,i,i), 1.0, 0.0);
}
printm(&matI);
//QLA_Complex tr;
//QLA_Real half = 0.5;
for(int i=0; i<QLA_Nc; i++) {
for(int j=0; j<QLA_Nc; j++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,j), i+1, QLA_Nc*(j+1));
}
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,i), 2+1, 1);
}
printm(&O);
#if QDP_Colors == 3
QLA_ColorMatrix A;
QLA_M_eq_zero(&A);
for ( int m = 0; m < QLA_Nc; m++) {
for ( int n = 0; n < QLA_Nc; n++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(A, m, n), 3+m, 2-n);
}
QLA_c_eq_r_plus_ir(QLA_elem_M(A,m,m), 2+1, 1);
}
QLA_M_eq_antiherm_M(&A, &A);
printm(&A);
QLA_M_eq_zero(&A);
QLA_c_eq_r_plus_ir(QLA_elem_M(A,0,0),0,-1);
QLA_c_eq_r_plus_ir(QLA_elem_M(A,1,1),0,0.4);
QLA_c_eq_r_plus_ir(QLA_elem_M(A,2,2),0,0.6);
printm(&A);
QLA_Complex minus_i;
QLA_c_eq_r_plus_ir(minus_i, 0, -1);
QLA_ColorMatrix Q, Q2, expiQ, qla_expA;
QLA_M_eq_C_times_M(&Q, &minus_i, &matI);
QLA_M_eq_M_times_M(&Q2, &Q, &Q);
printf("Q=\n"); printm(&Q);
double _Complex f0, f1, f2;
QLA_ColorMatrix B1, B2;
get_Bs(&Q, &Q2, &B1, &B2, &f0, &f1, &f2);
printf("f0, f1, f2=\n");
printc99(&f0);
printc99(&f1);
printc99(&f2);
QLA_Complex qf0, qf1, qf2;
QLA_c_eq_c99(qf0, f0);
QLA_c_eq_c99(qf1, f1);
QLA_c_eq_c99(qf2, f2);
QLA_M_eq_c(&expiQ, &qf0);
QLA_M_peq_c_times_M(&expiQ, &qf1, &Q);
QLA_M_peq_c_times_M(&expiQ, &qf2, &Q2);
QLA_M_eq_exp_M(&qla_expA, &matI);
printf("my expiQ = \n");
printm(&expiQ);
printf("qla expA = \n");
printm(&qla_expA);
// derivative
QLA_Complex trB1M, trB2M;
QLA_ColorMatrix prod, deriv;
//tr(B_1 M)
QLA_M_eq_M_times_M (&prod, &B1, &matI); //B_1 M
QLA_C_eq_trace_M (&trB1M, &prod);
//tr(B_2 M);
QLA_M_eq_M_times_M (&prod, &B2, &matI); //B_2 M
QLA_C_eq_trace_M (&trB2M, &prod);
// deriv = Tr(B_1 M) Q
QLA_M_eq_c_times_M (&deriv, &trB1M, &Q);
// deriv += Tr(B_2 M) Q^2
QLA_M_peq_c_times_M (&deriv, &trB2M, &Q2);
// deriv += f1 M
QLA_M_peq_c_times_M (&deriv, &qf1, &matI);
// deriv += f2 Q M
QLA_M_eq_M_times_M (&prod, &Q, &matI); // Q M
QLA_M_peq_c_times_M (&deriv, &qf2, &prod);
// deriv += f2 M Q
QLA_M_eq_M_times_M (&prod, &matI, &Q); // M Q
QLA_M_peq_c_times_M (&deriv, &qf2, &prod);
QLA_M_eq_c_times_M (&deriv, &minus_i, &deriv);
printf("M = \n");
printm(&matI);
printf("deriv = \n");
printm(&deriv);
QLA_M_meq_M(&deriv, &expiQ);
printf("diff = \n");
printm(&deriv);
/*
printf("2/3f0 = \n");
f0 *= 2.0/3;
printc99(&f0);
printc(&qf0);
printc(&qf1);
printc(&qf2);
*/
#endif
#if QDP_Colors == 2
QLA_ColorMatrix expO;
QLA_Complex Tr, det;
QLA_c_eq_c_times_c(det, QLA_elem_M(O,0,0),QLA_elem_M(O,1,1));
QLA_c_meq_c_times_c(det, QLA_elem_M(O,0,1), QLA_elem_M(O,1,0));
QLA_C_eq_trace_M(&Tr, &O);
QLA_Complex qs, qt;
QLA_c_eq_r_times_c(qs, 0.5, Tr); // s=TrA/2
QLA_Complex qs2;
QLA_c_eq_c_times_c(qs2, qs, qs); //s2 = s^2
QLA_c_meq_c(qs2, det); //s2 = s^2 - detA
double _Complex t = QLA_real(qs2) + QLA_imag(qs2) * _Complex_I;
t = csqrt(t); // sqrt(s^2 - det A)
QLA_c_eq_r_plus_ir(qt, creal(t), cimag(t)); // t = sqrt(s^2 - det A)
printf(" Matrix O = \n"); printm(&O);
printf("TrO = "); printc(&Tr);
printf("detO = "); printc(&det);
printf("s = "); printc(&qs);
printf("t^2 = "); printc(&qs2);
printf("t = "); printc(&qt);
//use the QLA exp function
QLA_ColorMatrix qla_exp;
QLA_M_eq_exp_M(&qla_exp, &O); //exp(O)
double _Complex exps, cosht, sinht, sinht_t;
double _Complex s = QLA_real(qs) + QLA_imag(qs) * _Complex_I;
exps = cexp(s);
if(creal(t) == 0 && cimag(t) == 0) {
cosht = 1;
sinht = 0;
sinht_t = 1;
} else {
cosht = ccosh(t);
sinht = csinh(t);
sinht_t = sinht/t;
}
double _Complex f0, f1;
f1 = exps * sinht_t;
f0 = exps * cosht - s * f1;;
//derivative of the exponential
double _Complex f0s, f1s, f1t, f0t2, f1t2, t2;
t2 = t*t;
f0s = f0 - f1;
f1s = f1;
if (cabs(t) > 0.05) {
f1t = ((f0-f1) + s*f1)/t;
f1t2 = f1t/t;
}
else { //when |t| < 0.05, the error is O(10^{-14})
f1t = exps * t/3 * (1+t2/10*(1+t2/28));
f1t2 = exps / 3 * (1+t2/10*(1+t2/28));
}
// f0t = t * f1 - s * f1t;
f0t2 = f1 - s * f1t2;
printf("f0 = \n"); printc99(&f0);
printf("f1 = \n"); printc99(&f1);
printf("f0s = \n"); printc99(&f0s);
printf("f1s = \n"); printc99(&f1s);
printf("f1t = \n"); printc99(&f1t);
printf("f0t2 = \n"); printc99(&f0t2);
printf("f1t2 = \n"); printc99(&f1t2);
QLA_Complex qf0, qf1;
QLA_c_eq_r_plus_ir(qf0, creal(f0), cimag(f0));
QLA_c_eq_r_plus_ir(qf1, creal(f1), cimag(f1));
QLA_M_eq_c_times_M(&expO, &qf1, &O);
QLA_M_peq_c(&expO, &qf0);
printf("QLA exp = \n"); printm(&qla_exp);
printf("my expO = \n"); printm(&expO);
/*
QLA_Complex qf0s, qf0t, qf1s, qf1t;
QLA_c_eq_r_plus_ir(qf0s, creal(f0s), cimag(f0s));
QLA_c_eq_r_plus_ir(qf0t, creal(f0t), cimag(f0t));
QLA_c_eq_r_plus_ir(qf1s, creal(f1s), cimag(f1s));
QLA_c_eq_r_plus_ir(qf1t, creal(f1t), cimag(f1t));
*/
QLA_ColorMatrix deriv;
QLA_M_eq_zero(&deriv);
QLA_ColorMatrix B, AB;
QLA_M_eq_M(&B, &matI);
//QLA_c_eq_r_plus_ir(QLA_elem_M(B,1,0), 0.1, 0.2);
//QLA_c_eq_r_plus_ir(QLA_elem_M(B,0,1), 0.2, 0.1);
printf("B=\n"); printm(&B);
QLA_M_eq_M_times_M(&AB, &O, &B);
printf("AB=\n"); printm(&AB);
QLA_M_eq_c_times_M(&deriv, &qf1, &B); //f1 * B
printf("f1 B = \n"); printm(&deriv);
QLA_Complex trB, trAB;
QLA_C_eq_trace_M(&trB, &B);
QLA_C_eq_trace_M(&trAB, &AB);
double _Complex ctrB = QLA_real(trB) + _Complex_I * QLA_imag(trB);
double _Complex ctrAB = QLA_real(trAB) + _Complex_I * QLA_imag(trAB);
double _Complex coeff;
coeff = (f0s - f0t2 * s) * ctrB;
coeff += (f1s - f1t2 * s) * ctrAB;
coeff *= 0.5;
printf("coeff = "); printc99(&coeff);
QLA_Complex qc;
QLA_D_c_eq_c99(qc, coeff);
printc(&qc);
QLA_M_peq_c_times_M(&deriv, &qc, &matI); // f1 * B + () I
printf("f1B+()I=\n"); printm(&deriv);
coeff = 0.5 * (f0t2 * ctrB + f1t2 * ctrAB);
QLA_D_c_eq_c99(qc, coeff);
printc(&qc);
QLA_M_peq_c_times_M(&deriv, &qc, &O);
printm(&deriv);
exp_deriv_site(&deriv, &expO, &O, &B);
printm(&deriv);
#endif
return 0;
}
void
set_C(QLA_Complex *c, int i)
{
QLA_c_eq_r_plus_ir(*c, 1+cos(i), 1+sin(i));
}
int
main(void) {
QLA_ColorMatrix O, iQ, tmp, matI;
QLA_M_eq_zero(&matI);
for(int i=0; i<QLA_Nc; i++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(matI,i,i), 1.0, 0.0);
}
printm(&matI);
QLA_Complex tr;
QLA_Real half = 0.5;
for(int i=0; i<QLA_Nc; i++) {
for(int j=0; j<QLA_Nc; j++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,j), i+1, QLA_Nc*(j+1));
}
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,i), 2+1, 1);
}
#if QDP_Colors == 3
QLA_Complex ci;
QLA_c_eq_r_plus_ir(ci, 0, 1);
//use my own implementation
QLA_ColorMatrix expiQ;
QLA_ColorMatrix QQ;
QLA_ColorMatrix QQQ;
QLA_M_eq_M_times_M(&QQ, &iQ, &iQ); //-Q^2
QLA_M_eq_M_times_M(&QQQ, &QQ, &iQ); //-iQ^3
QLA_M_eq_c_times_M(&QQQ, &ci, &QQQ); //Q^3
QLA_Complex c0, c1;
QLA_C_eq_trace_M(&c0, &QQQ);
QLA_c_eq_r_times_c(c0, 0.3333333, c0);
QLA_C_eq_trace_M(&c1, &QQ);
QLA_c_eq_r_times_c(c1, -0.5, c1);
double _Complex tf0, tf1, tf2;
getfs(&tf0, &tf1, &tf2, QLA_real(c0), QLA_real(c1));
QLA_Complex f0, f1, f2;
f0 = tf0;
f1 = tf1;
f2 = tf2;
printm(&O);
printf("iQ = \n");
printm(&iQ);
printf("QLA: exp(iQ) = \n");
printm(&qla_exp);
printf("Q^3 = \n");
printm(&QQQ);
printf("c0 = "); printc(&c0);
printf("c1 = "); printc(&c1);
#endif
#if QDP_Colors == 2
QLA_ColorMatrix expO;
QLA_Complex Tr, det;
QLA_c_eq_c_times_c(det, QLA_elem_M(O,0,0),QLA_elem_M(O,1,1));
QLA_c_meq_c_times_c(det, QLA_elem_M(O,0,1), QLA_elem_M(O,1,0));
QLA_C_eq_trace_M(&Tr, &O);
QLA_Complex s, t;
QLA_c_eq_r_times_c(s, 0.5, Tr); // s=TrA/2
QLA_Complex s2;
QLA_c_eq_c_times_c(s2, s, s); //s2 = s^2
QLA_c_meq_c(s2, det); //s2 = s^2 - detA
double _Complex dc_t = QLA_real(s2) + QLA_imag(s2) * _Complex_I;
dc_t = csqrt(dc_t); // sqrt(s^2 - det A)
QLA_c_eq_r_plus_ir(t, creal(dc_t), cimag(dc_t)); // t = sqrt(s^2 - det A)
printf(" Matrix O = \n"); printm(&O);
printf("TrO = "); printc(&Tr);
printf("detO = "); printc(&det);
printf("s = "); printc(&s);
printf("t^2 = "); printc(&s2);
printf("t = "); printc(&t);
//use the QLA exp function
QLA_ColorMatrix qla_exp;
QLA_M_eq_exp_M(&qla_exp, &O); //exp(O)
double _Complex cosht, sinht, sinht_t;
if(QLA_real(t) == 0 && QLA_imag(t) == 0) {
cosht = 1;
sinht = 0;
sinht_t = 1;
} else {
cosht = ccosh(dc_t);
sinht = csinh(dc_t);
sinht_t = sinht/dc_t;
}
double _Complex dc_s = QLA_real(s) + QLA_imag(s) * _Complex_I;
double _Complex dc_f0, dc_f1;
dc_f0 = cexp(dc_s) * (cosht - dc_s * sinht_t);
dc_f1 = cexp(dc_s) * sinht_t;
QLA_Complex f0, f1;
QLA_c_eq_r_plus_ir(f0, creal(dc_f0), cimag(dc_f0));
QLA_c_eq_r_plus_ir(f1, creal(dc_f1), cimag(dc_f1));
QLA_M_eq_c_times_M(&expO, &f1, &O);
QLA_M_peq_c(&expO, &f0);
printf("QLA exp = \n"); printm(&qla_exp);
printf("my expO = \n"); printm(&expO);
#endif
return 0;
}
void
set_M(QLA_ColorMatrix *m, int i)
{
#if 0
static QLA_ColorMatrix t;
for(int j=0; j<QLA_Nc; j++) {
for(int k=0; k<QLA_Nc; k++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(*m,j,k),
(((j-k+QLA_Nc+1)*(j+k+1))%19)+cos(i),
(((j+4)*(k+1))%17)+sin(i));
//QLA_real(QLA_elem_M(*m,j,k)) = 1;
//QLA_imag(QLA_elem_M(*m,j,k)) = 0;
}
}
#endif
for(int j=0; j<QLA_Nc; j++) {
for(int k=0; k<QLA_Nc; k++) {
QLA_c_eq_r(QLA_elem_M(*m,j,k), 0);
}
}
QLA_Real step = 1e-5;
if(Mtype&MtypeNZ) {
for(int j=0; j<QLA_Nc; j++) {
QLA_c_peq_r_plus_ir(QLA_elem_M(*m,j,j), step, -step);
}
}
int ii=i;
if((Mtype&MtypeNN)==0) ii>>=QLA_Nc;
for(int j=0,k=1; ii; ii>>=1,j++) {
if(j>=QLA_Nc) { j=0; k*=2; }
if(ii&1) QLA_c_peq_r_plus_ir(QLA_elem_M(*m,j,j), k*step, -k*step);
}
ii = i;
if((Mtype&MtypeNN)==0) {
for(int j=0; j<QLA_Nc; j++) {
if(ii&1) QLA_c_eqm_c(QLA_elem_M(*m,j,j), QLA_elem_M(*m,j,j));
ii >>= 1;
}
}
if(Mtype&MtypeH) { // make Hermitian
QLA_ColorMatrix m2;
QLA_M_eq_M(&m2, m);
QLA_M_peq_Ma(&m2, m);
QLA_M_eq_M(m, &m2);
}
if((Mtype&MtypeP)&&(Mtype&MtypeH)) { // make positive Hermitian
QLA_ColorMatrix m2;
QLA_M_eq_M_times_Ma(&m2, m, m);
QLA_M_eq_M(m, &m2);
}
if(Mtype&MtypeA) { // make anti-Hermitian
QLA_ColorMatrix m2;
QLA_M_eq_M(&m2, m);
QLA_M_meq_Ma(&m2, m);
QLA_M_eq_M(m, &m2);
}
if((Mtype&MtypeT)&&(Mtype&MtypeA)) { // make traceless anti-Hermitian
QLA_ColorMatrix m2;
QLA_M_eq_antiherm_M(&m2, m);
QLA_M_eq_M(m, &m2);
}
//QLA_Real n2;
//QLA_r_eq_norm2_M(&n2, m);
//printf("%i\t%g\n", i, n2);
}
