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paschen.c
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paschen.c
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/* ------- file: -------------------------- paschen.c ---------------
Version: rh2.0
Author: Han Uitenbroek ([email protected])
Last modified: Wed Aug 5 09:57:21 2009 --
-------------------------- ----------RH-- */
/* --- Routines for implementing the incomplete Paschen-Back effect.
See: E. Landi Degl'Innocenti & M. Landolfi, 2004
"Polarization in Spectral Lines", Kluwer
Section 3.4
-- -------------- */
#include <stdlib.h>
#include <math.h>
#include "rh.h"
#include "atom.h"
#include "error.h"
#include "constant.h"
#define N_MAX_ITER_TQLI 30
#define SIGN(a, b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
/* --- Function prototypes -- -------------- */
double Pythag(double a, double b);
void tqli(double *d, double *e, int N, double **z);
void Paschen(double L, double S, double *E0, double B,
Paschenstruct *ps);
/* --- Global variables -- -------------- */
extern char messageStr[];
/* ------- begin -------------------------- Paschen_Back.c ---------- */
void Paschen_Back()
{
}
/* ------- end ---------------------------- Paschen_Back.c ---------- */
/* ------- begin -------------------------- Paschen.c --------------- */
void Paschen(double L, double S, double *E0, double B, Paschenstruct *ps)
{
register int M, j, jp;
int Mindex;
double Larmor, *ud, J, Jp, Jmin, Jmax, Ja, Jb;
/* --- See: E. Landi Degl'Innocenti & M. Landolfi, 2004
"Polarization in Spectral Lines", Kluwer
Eqs. 3.57 and 3.58
-- -------------- */
/* --- Larmor frequency in energy units (J) -- -------------- */
Larmor = (HPLANCK * Q_ELECTRON / (4.0 * PI *M_ELECTRON)) * B;
Jmin = fabs(L - S);
Jmax = L + S;
Mindex = 0;
for (M = -Jmax; M <=Jmax; M++) {
Ja = MAX(fabs(M), Jmin);
Jb = Jmax;
ps[Mindex].Nj = (int)(Jb - Ja) + 1;
ps[Mindex].eigenval = (double *) malloc(ps[Mindex].Nj * sizeof(double));
ps[Mindex].C = matrix_double(ps[Mindex].Nj, ps[Mindex].Nj);
ud = (double *) malloc(ps[Mindex].Nj * sizeof(double));
for (j = 0; j < ps[Mindex].Nj; j++) {
J = Ja + j;
ps[Mindex].eigenval[j] += E0[j] +
Larmor * (M + (((int) (2*J + L + S + M)) % 2 ? -1.0 : 1.0) *
(2.0*J + 1.0) * sqrt(S * (S + 1.0) * (2.0*S + 1.0)) *
w3js(J, J, 1.0, -M, M, 0.0) * w6js(J, J, 1.0, S, S, L));
}
if (ps[Mindex].Nj > 1) {
for (jp = 1; jp < ps[Mindex].Nj; jp++) {
Jp = Ja + jp;
J = Jp - 1.0;
ud[jp] = Larmor * (((int) (J + Jp + L + S + M)) % 2 ? -1.0 : 1.0) *
sqrt((2.0*J +1.0) * (2.0*Jp + 1.0) * S * (S + 1.0) * (2.0*S + 1.0)) *
w3js(J, Jp, 2.0, -M, M, 0.0) * w6js(J, Jp, 1.0, S, S, L);
}
}
for (j = 0; j < ps[Mindex].Nj; j++) ps[Mindex].C[j][j] = 1.0;
tqli(ps[Mindex].eigenval, ud, ps[Mindex].Nj, ps[Mindex].C);
free(ud);
Mindex++;
}
}
/* ------- end ---------------------------- Paschen.c --------------- */
/* ------- begin -------------------------- Pythag.c ---------------- */
double Pythag(double a, double b)
{
double absa, absb;
/* --- Returns sqrt(a^2 + b^2) without destructive
under- or overflow.
See: Press, Flannery, Teukolsky and Vetterling, 1992
Numerical Recipes in C,
The art of scientific computing, p. 70
-- -------------- */
absa = fabs(a);
absb = fabs(b);
if (absa > absb)
return absa * sqrt(1.0 + SQ(absb / absa));
else
return ((absb == 0.0) ? 0.0 : absb * sqrt(1.0 + SQ(absa / absb)));
}
/* ------- end ---------------------------- Pythag.c ---------------- */
/* ------- begin -------------------------- tqli.c ------------------ */
void tqli(double *d, double *e, int N, double **z)
{
const char routineName[] = "tqli";
register int m, l, iter, i, k;
double s, r, p, g, f, dd, c, b;
/* --- Tridiagonal QL implicit eigenvector decomposition (tqli.c).
See: Press, Flannery, Teukolsky and Vetterling, 1992
Numerical Recipes in C,
The art of scientific computing, p. 480
Note: Modified for proper C indexing starting at 0.
-- -------------- */
if (N == 1) return;
for (i = 1; i < N; i++) e[i - 1] = e[i];
e[N-1] = 0.0;
for (l = 0; l < N; l++) {
iter = 0;
do {
for (m = l; m < N - 1; m++) {
dd = fabs(d[m]) + fabs(d[m + 1]);
if ((double)(fabs(e[m]) + dd) == dd) break;
}
if (m != l) {
if (iter++ == N_MAX_ITER_TQLI) {
sprintf(messageStr,
" Too many iterations in tqli: %d\n", iter-1);
Error(ERROR_LEVEL_2, routineName, messageStr);
}
g = (d[l + 1] - d[l]) / (2.0 * e[l]);
r = Pythag(g, 1.0);
g = d[m] - d[l] + e[l] / (g + SIGN(r, g));
c = 1.0;
s = 1.0;
p = 0.0;
for (i = m-1; i >= l; i--) {
f = s * e[i];
b = c * e[i];
r = Pythag(f, g);
e[i + 1] = r;
if (r == 0.0) {
d[i + 1] -= p;
e[m] = 0.0;
break;
}
s = f / r;
c = g / r;
g = d[i + 1] - p;
r = (d[i] - g) * s + 2.0 * c * b;
p = s * r;
d[i + 1] = g + p;
g = c * r - b;
for (k = 0; k < N; k++) {
f = z[k][i + 1];
z[k][i + 1] = s * z[k][i] + c * f;
z[k][i] = c * z[k][i] - s * f;
}
}
if (r == 0.0 && i >= l) continue;
d[l] -= p;
e[l] = g;
e[m] = 0.0;
}
} while (m != l);
}
}
/* ------- end ---------------------------- tqli.c ------------------ */