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modify igrf
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@seki-hiro
seki-hiro committed Feb 5, 2025
1 parent a413790 commit 358f164
Showing 1 changed file with 68 additions and 43 deletions.
111 changes: 68 additions & 43 deletions src/math_physics/geomagnetic/igrf.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -91,56 +91,72 @@ void set_file_path(const char *fname) { strcpy(coeff_file, fname); }

static void fcalc(void) /* This is an internal function */
{
double t, pn1m, tx, ty, tz;
double t, tx, ty, tz;
int n, m;
if (kr != 0) {
kr = 0;
t = ra / r;
rar[0] = t * t;
for (n = 0; n < maxod; n++) rar[n + 1] = rar[n] * t;
rar[0] = t * t; /*** (ra/r)**(n+2): rar[n] ***/
for (n = 1; n <= maxod; n++) rar[n] = rar[n - 1] * t;
}
if (kth != 0) {
kth = 0;
kth = 0; /*** Pnm: p[m][n] Qnm: p[n+1][m] ***/
p[0][0] = 1.;
p[1][0] = 0.;
p[1][0] = 0.; /*** n=m=0 ***/
p[0][1] = cth;
p[2][0] = -sth; /*** n=1 m=0 ***/
p[1][1] = sth;
p[2][0] = -sth;
p[2][1] = cth;
for (n = 1; n < maxod; n++) {
p[0][n + 1] = (p[0][n] * cth * (n + n + 1) - p[0][n - 1] * n) / (n + 1);
p[n + 2][0] = (p[0][n + 1] * cth - p[0][n]) * (n + 1) / sth;
for (m = 0; m <= n; m++) {
pn1m = p[m][n + 1];
p[m + 1][n + 1] = (p[m][n] * (n + m + 1) - pn1m * cth * (n - m + 1)) / sth;
p[n + 2][m + 1] = pn1m * (n + m + 2) * (n - m + 1) - p[m + 1][n + 1] * cth * (m + 1) / sth;
p[2][1] = cth; /*** n=1 m=1 ***/
for (n = 2; n <= maxod; n++) { /*** n=2..maxod ***/
/*** m=0 (P) ***/
/*** P(n,0) <== P(n-1,0), P(n-2,0) ***/
p[0][n] = (p[0][n - 1] * cth * (n + n - 1) - p[0][n - 2] * (n - 1)) / n;
for (m = 1; m < n; m++) { /*** m=1..(n-1) (P) ***/
/*** 0.175 ~= cos(80deg.) ***/
if (sth > 0.175) { /*** Low-Middle Lat. ***/
/*** P(n,m) <== P(n-1,m-1), P(n,m-1) ***/
p[m][n] = (p[m - 1][n - 1] * (n + m - 1) - p[m - 1][n] * cth * (n - m + 1)) / sth;
} else { /*** Polar region ***/
/*** P(n,m) <== P(n-1,m), P(n,m-1) ***/
p[m][n] = (p[m][n - 1] + p[m - 1][n] * sth * (n - m + 1)) / cth;
}
}
/*** P(n,n) <== P(n-1,n-1) ***/ /*** m=n (P) ***/
p[n][n] = p[n - 1][n - 1] * sth * (n + n - 1);
/*** Q(n,0) <== P(n,1) ***/ /*** m=0 (Q) ***/
p[n + 1][0] = -p[1][n];
for (m = 1; m < n; m++) { /*** m=1..(n-1) (Q) ***/
/*** Q(n,m) <== P(n,m-1), Q(n,m) ***/
p[n + 1][m] = (p[m - 1][n] * (n + m) * (n - m + 1) - p[m + 1][n]) / 2.;
} /*** m=n (Q) ***/
/*** Q(n,n) <== P(n-1,n-1), Q(n-1,n-1) ***/
p[n + 1][n] = (p[n - 1][n - 1] * cth + p[n][n - 1] * sth) * (n + n - 1);
}
}
if (kph != 0) {
kph = 0;
kph = 0; /*** cos(m*phi): csp[m] sin(m*phi): snp[m] ***/
csp[0] = 1.;
snp[0] = 0.;
for (m = 0; m < maxod; m++) {
csp[m + 1] = csp[m] * cph - snp[m] * sph;
snp[m + 1] = snp[m] * cph + csp[m] * sph;
for (m = 1; m <= maxod; m++) {
csp[m] = csp[m - 1] * cph - snp[m - 1] * sph;
snp[m] = snp[m - 1] * cph + csp[m - 1] * sph;
}
}
x = 0.;
y = 0.;
z = 0.;
for (n = 0; n < maxod; n++) {
tx = g[0][n + 1] * p[n + 2][0];
z = 0.; /*** Calc. X,Y,Z and F ***/
for (n = 1; n <= maxod; n++) { /*** n=1..maxod ***/
tx = g[0][n] * p[n + 1][0];
ty = 0.;
tz = g[0][n + 1] * p[0][n + 1];
for (m = 0; m <= n; m++) {
tx += (g[m + 1][n + 1] * csp[m + 1] + g[n + 1][m] * snp[m + 1]) * p[n + 2][m + 1];
ty += (g[m + 1][n + 1] * snp[m + 1] - g[n + 1][m] * csp[m + 1]) * p[m + 1][n + 1] * (m + 1);
tz += (g[m + 1][n + 1] * csp[m + 1] + g[n + 1][m] * snp[m + 1]) * p[m + 1][n + 1];
tz = g[0][n] * p[0][n]; /*** m=0 ***/
for (m = 1; m <= n; m++) { /*** m=1..n ***/
tx += (g[m][n] * csp[m] + g[n][m - 1] * snp[m]) * p[n + 1][m];
ty += (g[m][n] * snp[m] - g[n][m - 1] * csp[m]) * p[m][n] * m;
tz += (g[m][n] * csp[m] + g[n][m - 1] * snp[m]) * p[m][n];
}
x += rar[n + 1] * tx;
y += rar[n + 1] * ty;
z -= rar[n + 1] * tz * (n + 2);
x += rar[n] * tx;
y += rar[n] * ty;
z -= rar[n] * tz * (n + 1);
}
y /= sth;
if (kext != 0) {
Expand Down Expand Up @@ -168,22 +184,22 @@ void field(double are, double aflat, double ara, int maxoda) {
}

void tcoef(double agh[MxOD + 1][MxOD + 1], double aght[MxOD + 1][MxOD + 1], double atzero, int kexta, double aext[3]) {
int nn, mm;
int n, m;
double fac;
tzero = atzero;
kext = kexta;
gh[0][0] = 0.;
ght[0][0] = 0.;
for (nn = 1; nn <= maxod; nn++) {
gh[0][nn] = agh[0][nn];
ght[0][nn] = aght[0][nn];
for (n = 1; n <= maxod; n++) { /*** n=1..maxod ***/
gh[0][n] = agh[0][n];
ght[0][n] = aght[0][n]; /*** m=0 ***/
fac = sqrt(2.);
for (mm = 1; mm <= nn; mm++) {
fac /= sqrt((double)((nn + mm) * (nn - mm + 1)));
gh[mm][nn] = agh[mm][nn] * fac;
gh[nn][mm - 1] = agh[nn][mm - 1] * fac;
ght[mm][nn] = aght[mm][nn] * fac;
ght[nn][mm - 1] = aght[nn][mm - 1] * fac;
for (m = 1; m <= n; m++) { /*** m=1..n ***/
fac /= sqrt((double)((n + m) * (n - m + 1)));
gh[m][n] = agh[m][n] * fac;
gh[n][m - 1] = agh[n][m - 1] * fac;
ght[m][n] = aght[m][n] * fac;
ght[n][m - 1] = aght[n][m - 1] * fac;
}
}
if (kext == 0) {
Expand All @@ -199,11 +215,14 @@ void tcoef(double agh[MxOD + 1][MxOD + 1], double aght[MxOD + 1][MxOD + 1], doub

void tyear(double ayear) {
double dyear;
int nn, mm;
int n, m;
dyear = ayear - tzero;
for (nn = 0; nn <= maxod; nn++) {
for (mm = 0; mm <= maxod; mm++) {
g[mm][nn] = gh[mm][nn] + ght[mm][nn] * dyear;
g[0][0] = 0.;
for (n = 1; n <= maxod; n++) { /*** n=1..maxod ***/
g[0][n] = gh[0][n] + ght[0][n] * dyear; /*** m=0 ***/
for (m = 1; m <= n; m++) { /*** m=1..n ***/
g[m][n] = gh[m][n] + ght[m][n] * dyear;
g[n][m - 1] = gh[n][m - 1] + ght[n][m - 1] * dyear;
}
}
}
Expand All @@ -216,6 +235,8 @@ void mfldg(double alat, double alon, double ahi, double *ax, double *ay, double
kth = 1;
blat = alat;
bhi = ahi;
/*** calculate geocentric distance (r) ***/
/*** and sine/cosine of colatitude (sth/cth) ***/
rlat = alat / URAD;
hi = ahi;
slat = sin(rlat);
Expand All @@ -227,6 +248,8 @@ void mfldg(double alat, double alon, double ahi, double *ax, double *ay, double
r = sqrt(rrm + 2. * hi * rm + hi * hi);
cth = slat * (hi + rp2 / rm) / r;
sth = sqrt(1. - cth * cth);
/*** force sin(colat) non-zero to avoid DIV-by-0 error ***/
if (sth < 0.00000015) sth = 0.00000015;
}
if (blon != alon) kph = 1;
if (kph != 0) {
Expand Down Expand Up @@ -260,6 +283,8 @@ void mfldc(double athe, double alon, double ar, double *ax, double *ay, double *
the = athe / URAD;
cth = cos(the);
sth = sin(the);
/*** force sin(colat) non-zero to avoid DIV-by-0 error ***/
if (sth < 0.00000015) sth = 0.00000015;
}
if (blon != alon) kph = 1;
if (kph != 0) {
Expand Down

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