void print_error(char *type, char *what, double diff, xc_func_type *func, double *p)
{
static char *red="\033[31;1m", *norm="\033[0m";
char *color;
color = (diff > 5e-4) ? red : norm;
printf("%s error %s: %s%g%s\n", type, what, color, diff, norm);
if(func == NULL) return;
printf(" point (% 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e)\n",
p[0], p[1], p[2], p[3], p[4]);
if(strcmp(what, "vrho")==0 || strcmp(what, "vsig")==0){
double e, v_an[5], v_fd[5];
int j;
for(j=0; j<5; j++)
v_fd[j] = v_an[j] = 0.0;
get_vxc(func, p, &e, v_an);
first_derivative(func, p, v_fd, 0);
if(strcmp(what, "vrho") == 0){
printf(" analyt (% 8.2e, % 8.2e)\n", v_an[0], v_an[1]);
printf(" fd (% 8.2e, % 8.2e)\n", v_fd[0], v_fd[1]);
}
if(strcmp(what, "vsig") == 0){
printf(" analyt (% 8.2e, % 8.2e, % 8.2e)\n", v_an[2], v_an[3], v_an[4]);
printf(" fd (% 8.2e, % 8.2e, % 8.2e)\n", v_fd[2], v_fd[3], v_fd[4]);
}
}
if(strcmp(what, "v2rho2")==0 || strcmp(what, "v2rhosig")==0 || strcmp(what, "v2sig2")==0){
double f_an[5][5], f_fd[5][5];
int i, j;
get_fxc(func, p, f_an);
second_derivatives(func, p, f_fd);
if(strcmp(what, "v2rho2") == 0){
printf(" analyt (% 8.2e, % 8.2e, % 8.2e)\n", f_an[0][0], f_an[0][1], f_an[1][1]);
printf(" fd (% 8.2e, % 8.2e, % 8.2e)\n", f_fd[0][0], f_fd[0][1], f_fd[1][1]);
}
if(strcmp(what, "v2rhosig") == 0){
printf(" analyt (% 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e)\n",
f_an[2][0], f_an[3][0], f_an[4][0], f_an[2][1], f_an[3][1], f_an[4][1]);
printf(" fd (% 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e)\n",
f_fd[2][0], f_fd[3][0], f_fd[4][0], f_fd[2][1], f_fd[3][1], f_fd[4][1]);
}
if(strcmp(what, "v2sig2") == 0){
printf(" analyt (% 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e)\n",
f_an[2][2], f_an[3][2], f_an[4][2], f_an[3][3], f_an[4][3], f_an[4][4]);
printf(" fd (% 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e, % 8.2e)\n",
f_fd[2][2], f_fd[3][2], f_fd[4][2], f_fd[3][3], f_fd[4][3], f_fd[4][4]);
}
}
}
void test_functional(int functional)
{
xc_func_type func;
const xc_func_info_type *info;
int i, j, k, p_max[6][5];
double max_diff[6][5], avg_diff[6][5], val[5];
#if defined(HAVE_FEENABLEEXCEPT)
feenableexcept(FE_INVALID | FE_OVERFLOW);
#endif
/* initialize functional */
if(xc_func_init(&func, functional, nspin) != 0){
fprintf(stderr, "Functional '%d' not found\n", functional);
exit(1);
}
info = func.info;
if(functional == XC_LDA_C_2D_PRM)
xc_lda_c_2d_prm_set_params(&func, 10.0);
for(k=0; k<6; k++)
for(j=0; j<5; j++){
avg_diff[k][j] = 0.0;
p_max[k][j] = 0;
max_diff[k][j] = -1.0;
}
for(i=0; xc_trial_points[i][0]!=0.0; i++){
double e, v_fd[5], f_fd[5][5], v_an[5], f_an[5][5];
for(j=0; j<5; j++)
v_fd[j] = v_an[j] = 0.0;
get_val(xc_trial_points[i], val);
/* first, get the analytic gradients */
get_vxc(&func, val, &e, v_an);
/* now get the numerical gradients */
first_derivative(&func, val, v_fd, 0);
if(info->flags & XC_FLAGS_HAVE_FXC){
int i, j;
/* initialize */
for(i=0; i<5; i++)
for(j=0; j<5; j++)
f_an[i][j] = f_fd[i][j] = 0.0;
/* now get the second derivatives */
second_derivatives(&func, val, f_fd);
get_fxc(&func, val, f_an);
}
/* make statistics */
for(j=0; j<5; j++){
double diff = fabs(v_an[j] - v_fd[j]);
/* do not test in case of spin unpolarized or if spin down is zero */
if((nspin==1 || val[1]==0.0) && (j!=0 && j!=2))
continue;
avg_diff[0][j] += diff;
if(diff > max_diff[0][j]){
max_diff[0][j] = diff;
p_max[0][j] = i;
}
if(info->flags & XC_FLAGS_HAVE_FXC){
for(k=0; k<5; k++){
/* do not test in case of spin unpolarized or if spin down is zero */
if((nspin==1 || val[1]==0.0) && (k!=0 && k!=2))
continue;
diff = fabs(f_an[k][j] - f_fd[k][j]);
avg_diff[k+1][j] += diff;
if(diff > max_diff[k+1][j]){
max_diff[k+1][j] = diff;
p_max[k+1][j] = i;
}
}
}
}
}
for(k=0; k<6; k++)
for(j=0; j<5; j++){
avg_diff[k][j] /= i;
}
/* print statistics */
{
double diff;
int i, j;
printf("Functional: %s\n", info->name);
print_error("Avg.", "vrho", (avg_diff[0][0] + avg_diff[0][1])/2.0, NULL, NULL);
j = (max_diff[0][0] > max_diff[0][1]) ? 0 : 1;
get_val(xc_trial_points[p_max[0][j]], val);
print_error("Max.", "vrho", max_diff[0][j], &func, val);
if(info->family > XC_FAMILY_LDA){
print_error("Avg.", "vsig", (avg_diff[0][2] + avg_diff[0][3] + avg_diff[0][4])/3.0, NULL, NULL);
j = (max_diff[0][2] > max_diff[0][3]) ? 2 : 3;
j = (max_diff[0][j] > max_diff[0][4]) ? j : 4;
get_val(xc_trial_points[p_max[0][j]], val);
print_error("Max.", "vsig", max_diff[0][j], &func, val);
}
if(info->flags & XC_FLAGS_HAVE_FXC){
diff = avg_diff[1][0] + avg_diff[1][1] + avg_diff[2][1];
diff = diff/3.0;
print_error("Avg.", "v2rho2", diff, NULL, NULL);
if(max_diff[1][0] > max_diff[1][1]) {i=1; j=0;} else {i=1; j=1;}
if(max_diff[2][1] > max_diff[i][j]) {i=2; j=1;}
get_val(xc_trial_points[p_max[i][j]], val);
print_error("Max.", "v2rho2", max_diff[i][j], &func, val);
if(info->family > XC_FAMILY_LDA){
diff = avg_diff[3][0] + avg_diff[4][0] + avg_diff[5][0] + avg_diff[3][1] + avg_diff[4][1] + avg_diff[5][1];
diff = diff/6.0;
print_error("Avg.", "v2rhosig", diff, NULL, NULL);
if(max_diff[3][0] > max_diff[4][0]) {i=3; j=0;} else {i=4; j=0;}
if(max_diff[5][0] > max_diff[i][j]) {i=5; j=0;}
if(max_diff[3][1] > max_diff[i][j]) {i=3; j=1;}
if(max_diff[4][1] > max_diff[i][j]) {i=4; j=1;}
if(max_diff[5][1] > max_diff[i][j]) {i=5; j=1;}
get_val(xc_trial_points[p_max[i][j]], val);
print_error("Max.", "v2rhosig", max_diff[i][j], &func, val);
diff = avg_diff[3][2] + avg_diff[4][2] + avg_diff[5][2] + avg_diff[4][3] + avg_diff[5][3] + avg_diff[5][4];
diff = diff/6.0;
print_error("Avg.", "v2sig2", diff, NULL, NULL);
if(max_diff[3][2] > max_diff[4][2]) {i=3; j=2;} else {i=4; j=2;}
if(max_diff[5][2] > max_diff[i][j]) {i=5; j=2;}
if(max_diff[4][3] > max_diff[i][j]) {i=4; j=3;}
if(max_diff[5][3] > max_diff[i][j]) {i=5; j=3;}
if(max_diff[5][4] > max_diff[i][j]) {i=5; j=4;}
get_val(xc_trial_points[p_max[i][j]], val);
print_error("Max.", "v2sig2", max_diff[i][j], &func, val);
}
}
}
xc_func_end(&func);
}
void test_functional(int functional)
{
functionals_type func;
const xc_func_info_type *info;
int i, j, k, p_max[6][5];
double max_diff[6][5], avg_diff[6][5], val[5];
/* initialize functional */
func.family = xc_family_from_id(functional);
switch(func.family)
{
case XC_FAMILY_LDA:
if(functional == XC_LDA_X)
xc_lda_x_init(&(func.lda_func), nspin, 3, 0);
else
xc_lda_init(&(func.lda_func), functional, nspin);
info = func.lda_func.info;
break;
case XC_FAMILY_GGA:
xc_gga_init(&(func.gga_func), functional, nspin);
info = func.gga_func.info;
break;
case XC_FAMILY_HYB_GGA:
xc_hyb_gga_init(&(func.hyb_gga_func), functional, nspin);
info = func.hyb_gga_func.info;
break;
default:
fprintf(stderr, "Functional '%d' not found\n", functional);
exit(1);
}
for(k=0; k<6; k++)
for(j=0; j<5; j++) {
avg_diff[k][j] = 0.0;
p_max[k][j] = 0;
max_diff[k][j] = -1.0;
}
for(i=0; xc_trial_points[i][0]!=0.0; i++) {
double e, v_fd[5], f_fd[5][5], v_an[5], f_an[5][5];
for(j=0; j<5; j++)
v_fd[j] = v_an[j] = 0.0;
get_val(xc_trial_points[i], val);
/* first, get the analitic gradients */
get_vxc(&func, val, &e, v_an);
/* now get the numerical gradients */
first_derivative(&func, val, v_fd, 0);
if(info->provides & XC_PROVIDES_FXC) {
int i, j;
/* initialize */
for(i=0; i<5; i++)
for(j=0; j<5; j++)
f_an[i][j] = f_fd[i][j] = 0.0;
/* now get the second derivatives */
second_derivatives(&func, val, f_fd);
get_fxc(&func, val, f_an);
}
/* make statistics */
for(j=0; j<5; j++) {
double diff = fabs(v_an[j] - v_fd[j]);
/* do not test in case of spin unpolarized or if spin down is zero */
if((nspin==1 || val[1]==0.0) && (j!=0 && j!=2))
continue;
avg_diff[0][j] += diff;
if(diff > max_diff[0][j]) {
max_diff[0][j] = diff;
p_max[0][j] = i;
}
if(info->provides & XC_PROVIDES_FXC) {
for(k=0; k<5; k++) {
/* do not test in case of spin unpolarized or if spin down is zero */
if((nspin==1 || val[1]==0.0) && (k!=0 && k!=2))
continue;
diff = fabs(f_an[k][j] - f_fd[k][j]);
avg_diff[k+1][j] += diff;
if(diff > max_diff[k+1][j]) {
max_diff[k+1][j] = diff;
p_max[k+1][j] = i;
}
}
}
}
}
for(k=0; k<6; k++)
for(j=0; j<5; j++) {
avg_diff[k][j] /= i;
}
/* print statistics */
{
double diff;
int i, j;
printf("Functional: %s\n", info->name);
print_error("Avg.", "vrho", (avg_diff[0][0] + avg_diff[0][1])/2.0, NULL, NULL);
j = (max_diff[0][0] > max_diff[0][1]) ? 0 : 1;
get_val(xc_trial_points[p_max[0][j]], val);
print_error("Max.", "vrho", max_diff[0][j], &func, val);
if(func.family > XC_FAMILY_LDA) {
print_error("Avg.", "vsig", (avg_diff[0][2] + avg_diff[0][3] + avg_diff[0][4])/3.0, NULL, NULL);
j = (max_diff[0][2] > max_diff[0][3]) ? 2 : 3;
j = (max_diff[0][j] > max_diff[0][4]) ? j : 4;
get_val(xc_trial_points[p_max[0][j]], val);
print_error("Max.", "vsig", max_diff[0][j], &func, val);
}
if(info->provides & XC_PROVIDES_FXC) {
diff = avg_diff[1][0] + avg_diff[1][1] + avg_diff[2][1];
diff = diff/3.0;
print_error("Avg.", "v2rho2", diff, NULL, NULL);
if(max_diff[1][0] > max_diff[1][1]) {
i=1;
j=0;
}
else {
i=1;
j=1;
}
if(max_diff[2][1] > max_diff[i][j]) {
i=2;
j=1;
}
get_val(xc_trial_points[p_max[i][j]], val);
print_error("Max.", "v2rho2", max_diff[i][j], &func, val);
if(func.family > XC_FAMILY_LDA) {
diff = avg_diff[3][0] + avg_diff[4][0] + avg_diff[5][0] + avg_diff[3][1] + avg_diff[4][1] + avg_diff[5][1];
diff = diff/6.0;
print_error("Avg.", "v2rhosig", diff, NULL, NULL);
if(max_diff[3][0] > max_diff[4][0]) {
i=3;
j=0;
}
else {
i=4;
j=0;
}
if(max_diff[5][0] > max_diff[i][j]) {
i=5;
j=0;
}
if(max_diff[3][1] > max_diff[i][j]) {
i=3;
j=1;
}
if(max_diff[4][1] > max_diff[i][j]) {
i=4;
j=1;
}
if(max_diff[5][1] > max_diff[i][j]) {
i=5;
j=1;
}
get_val(xc_trial_points[p_max[i][j]], val);
print_error("Max.", "v2rhosig", max_diff[i][j], &func, val);
diff = avg_diff[3][2] + avg_diff[4][2] + avg_diff[5][2] + avg_diff[4][3] + avg_diff[5][3] + avg_diff[5][4];
diff = diff/6.0;
print_error("Avg.", "v2sig2", diff, NULL, NULL);
if(max_diff[3][2] > max_diff[4][2]) {
i=3;
j=2;
}
else {
i=4;
j=2;
}
if(max_diff[5][2] > max_diff[i][j]) {
i=5;
j=2;
}
if(max_diff[4][3] > max_diff[i][j]) {
i=4;
j=3;
}
if(max_diff[5][3] > max_diff[i][j]) {
i=5;
j=3;
}
if(max_diff[5][4] > max_diff[i][j]) {
i=5;
j=4;
}
get_val(xc_trial_points[p_max[i][j]], val);
print_error("Max.", "v2sig2", max_diff[i][j], &func, val);
}
}
}
}
