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expo.c
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expo.c
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/***********************************************************************
* Copyright (C) 2001 Martin Hasenbusch
* Modified by Bartosz Kostrzewa (2012 void versions)
*
* This file is part of tmLQCD.
*
* tmLQCD 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 3 of the License, or
* (at your option) any later version.
*
* tmLQCD 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 tmLQCD. If not, see <http://www.gnu.org/licenses/>.
*
* File expo.c
*
*
* The externally accessible functions are
*
* void exposu3(su3* const vr, const su3adj* const p);
* extern void exposu3_check(su3* const vr, const su3adj* const p, int im);
* extern void restoresu3(su3* const vr,const su3* const u);
* extern void restoresu3_in_place(su3* const u);
* extern void exposu3_in_place(su3* const u);
*
* Author: Martin Hasenbusch <martin.hasenbusch@desy.de>
* Tue Aug 28 10:06:56 MEST 2001
*
************************************************************************/
#ifdef HAVE_CONFIG_H
# include<config.h>
#endif
#ifdef SSE
# undef SSE
#endif
#ifdef SSE2
# undef SSE2
#endif
#ifdef SSE3
# undef SSE3
#endif
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "sse.h"
#include "su3.h"
#include "su3adj.h"
#include "expo.h"
void exposu3(su3* const vr, const su3adj* const p) {
int i;
su3 ALIGN v,v2;
double ALIGN fac,r;
double ALIGN a,b;
_Complex double ALIGN a0,a1,a2,a1p;
/* it writes 'p=vec(h_{j,mu})' in matrix form 'v' */
_make_su3(v,*p);
/* calculates v^2 */
_su3_times_su3(v2,v,v);
/* */
a = 0.5 * (creal(v2.c00) + creal(v2.c11) + creal(v2.c22));
/* 1/3 imaginary part of tr v*v2 */
b = 0.33333333333333333 * cimag(v.c00 * v2.c00 + v.c01 * v2.c10 + v.c02 * v2.c20 +
v.c10 * v2.c01 + v.c11 * v2.c11 + v.c12 * v2.c21 +
v.c20 * v2.c02 + v.c21 * v2.c12 + v.c22 * v2.c22 );
a0 = 0.16059043836821615e-9;
a1 = 0.11470745597729725e-10;
a2 = 0.76471637318198165e-12;
fac = 0.20876756987868099e-8; /* 1/12! */
r = 12.0;
for(i = 3; i <= 15; ++i)
{
a1p = a0 + a * a2;
a0 = fac + b * I * a2;
a2 = a1;
a1 = a1p;
fac *= r;
r -= 1.0;
}
/* vr = a0 + a1*v + a2*v2 */
vr->c00 = a0 + a1 * v.c00 + a2 * v2.c00;
vr->c01 = a1 * v.c01 + a2 * v2.c01;
vr->c02 = a1 * v.c02 + a2 * v2.c02;
vr->c10 = a1 * v.c10 + a2 * v2.c10;
vr->c11 = a0 + a1 * v.c11 + a2 * v2.c11;
vr->c12 = a1 * v.c12 + a2 * v2.c12;
vr->c20 = a1 * v.c20 + a2 * v2.c20;
vr->c21 = a1 * v.c21 + a2 * v2.c21;
vr->c22 = a0 + a1 * v.c22 + a2 * v2.c22;
}
void exposu3_check(su3* const vr, const su3adj* const p, int im) {
/* compute the result by taylor series */
su3 ALIGN v,v2,v3;
double ALIGN fac;
int i;
_make_su3(v, *p);
_su3_one(*vr);
_su3_acc(*vr, v);
_su3_times_su3(v2, v, v);
_su3_refac_acc(*vr, 0.5, v2);
fac = 0.5;
for(i = 3; i <= im; i++) {
fac = fac/i;
_su3_times_su3(v3, v2, v);
_su3_refac_acc(*vr, fac, v3);
_su3_assign(v2, v3);
}
}
void restoresu3(su3* const vr, const su3* const u) {
double ALIGN n0,n1;
/* normalize rows 1 and 2 */
n0 = 1.0 / sqrt(conj(u->c00) * u->c00 + conj(u->c01) * u->c01 + conj(u->c02) * u->c02);
n1 = 1.0 / sqrt(conj(u->c10) * u->c10 + conj(u->c11) * u->c11 + conj(u->c12) * u->c12);
vr->c00 = n0 * u->c00;
vr->c01 = n0 * u->c01;
vr->c02 = n0 * u->c02;
vr->c10 = n1 * u->c10;
vr->c11 = n1 * u->c11;
vr->c12 = n1 * u->c12;
/* compute row 3 as the conjugate of the cross-product of 1 and 2 */
vr->c20 = conj(vr->c01 * vr->c12 - vr->c02 * vr->c11);
vr->c21 = conj(vr->c02 * vr->c10 - vr->c00 * vr->c12);
vr->c22 = conj(vr->c00 * vr->c11 - vr->c01 * vr->c10);
}
void restoresu3_in_place(su3* const u) {
double ALIGN n0,n1;
/* normalize rows 1 and 2 */
n0 = 1.0 / sqrt(conj(u->c00) * u->c00 + conj(u->c01) * u->c01 + conj(u->c02) * u->c02);
n1 = 1.0 / sqrt(conj(u->c10) * u->c10 + conj(u->c11) * u->c11 + conj(u->c12) * u->c12);
u->c00 = n0 * u->c00;
u->c01 = n0 * u->c01;
u->c02 = n0 * u->c02;
u->c10 = n1 * u->c10;
u->c11 = n1 * u->c11;
u->c12 = n1 * u->c12;
/* compute row 3 as the conjugate of the cross-product of 1 and 2 */
u->c20 = conj(u->c01 * u->c12 - u->c02 * u->c11);
u->c21 = conj(u->c02 * u->c10 - u->c00 * u->c12);
u->c22 = conj(u->c00 * u->c11 - u->c01 * u->c10);
}
/* Exponentiates a hermitian 3x3 matrix Q */
/* Convenience function -- wrapper around Hasenbusch's implementation */
void exposu3_in_place(su3* const u) {
su3adj ALIGN p;
_trace_lambda(p, *u); /* Projects onto the Gell-Mann matrices */
/* -2.0 to get su3 to su3adjoint consistency ****/
p.d1 *= -0.5; p.d2 *= -0.5; p.d3 *= -0.5; p.d4 *= -0.5;
p.d5 *= -0.5; p.d6 *= -0.5; p.d7 *= -0.5; p.d8 *= -0.5;
exposu3(u,&p);
}