/*
* Compute Gradient of I
*/
int Lgm_Grad_I( Lgm_Vector *v0, Lgm_Vector *GradI, Lgm_MagModelInfo *mInfo ) {
Lgm_Vector u, Pa, Pb;
double rat, H, h, a, b, SS, Sa, Sb, I, f[6], r;
int i, N;
/*
* We want to compute the gradient of I at the point v0.
* This requires 3 derivatives: one each in x, y and z directions.
* We will try a fairly acurate difference scehme:
*
* f_0^(1) = 1/(60h) ( f_3 - 9f_2 + 45f_1 - 45f_-1 + 9f_-2 - f_-3 )
* See page 450 of CRC standard Math tables 28th edition.
*/
/*
* Set h to a smallish value
*/
// h = 5e-2;
h = 0.1;
// h = 0.2;
switch ( DIFF_SCHEME ) {
case USE_SIX_POINT:
N = 3;
break;
case USE_FOUR_POINT:
N = 2;
break;
case USE_TWO_POINT:
N = 1;
break;
}
// User should set these?
mInfo->Lgm_I_Integrator = DQAGS;
mInfo->Lgm_I_Integrator_epsabs = 0.0;
mInfo->Lgm_I_Integrator_epsrel = 1e-5;
/* X-component */
mInfo->UseInterpRoutines = 1;
if (mInfo->VerbosityLevel > 0) printf("\t\tComputing dIdx: h = %g\n", h);
for (i=-N; i<=N; ++i){
if (i!=0) { // dont need the center value in our difference scheme
u = *v0; H = (double)i*h; u.x += H;
/*
* Trace to southern mirror point
*/
if ( Lgm_TraceToMirrorPoint( &u, &Pa, &Sa, mInfo->Bm, -1.0, mInfo->Lgm_TraceToMirrorPoint_Tol, mInfo ) > 0 ) {
/*
* Trace to northern mirror point
*/
if ( Lgm_TraceToMirrorPoint( &Pa, &Pb, &SS, mInfo->Bm, 1.0, mInfo->Lgm_TraceToMirrorPoint_Tol, mInfo ) > 0 ) {
r = Lgm_Magnitude( &Pb );
//mInfo->Hmax = SS/200.0;
mInfo->Hmax = SS/(double)mInfo->nDivs;
Lgm_TraceLine2( &Pa, &Pb, (r-1.0)*Re, 0.5*SS-mInfo->Hmax, 1.0, 1e-7, FALSE, mInfo );
ReplaceFirstPoint( 0.0, mInfo->Bm, &Pa, mInfo );
AddNewPoint( SS, mInfo->Bm, &Pb, mInfo );
InitSpline( mInfo );
mInfo->Lgm_I_integrand_S = 0.0;
mInfo->Lgm_I_integrand_FirstCall = TRUE;
mInfo->Lgm_n_I_integrand_Calls = 0;
mInfo->Sm_South = 0.0;
mInfo->Sm_North = SS;
if ( SS <= 1e-5 ) {
// if FL length is small, use an approx expression for I
rat = mInfo->Bmin/mInfo->Bm;
if ((1.0-rat) < 0.0) {
I = 0.0;
} else {
// Eqn 2.66b in Roederer
I = SS*sqrt(1.0 - rat);
printf("HEREEEEEEEEEEEEEEEEEEEEEEe\n");
}
} else {
I = Iinv_interped( mInfo );
}
if (mInfo->VerbosityLevel > 2) printf("I = %g Lgm_n_I_integrand_Calls = %d\n", I, mInfo->Lgm_n_I_integrand_Calls );
FreeSpline( mInfo );
} else {
printf("\t\tMirror point below %g km in Southern Hemisphere\n", mInfo->Lgm_LossConeHeight);
exit(0);
}
} else {
printf("\t\tMirror point below %g km in Northern Hemisphere\n", mInfo->Lgm_LossConeHeight);
exit(0);
}
f[i+N] = I;
}
}
if (DIFF_SCHEME == USE_SIX_POINT){
GradI->x = (f[6] - 9.0*f[5] + 45.0*f[4] - 45.0*f[2] + 9.0*f[1] - f[0])/(60.0*h);
} else if (DIFF_SCHEME == USE_FOUR_POINT){
GradI->x = (-f[4] + 8.0*f[3] - 8.0*f[1] + f[0])/(12.0*h);
} else if (DIFF_SCHEME == USE_TWO_POINT){
GradI->x = (f[2] - f[0])/(2.0*h);
}
/* Y-component */
if (mInfo->VerbosityLevel > 0) printf("\t\tComputing dIdy: h = %g\n", h);
for (i=-N; i<=N; ++i){
if (i!=0) { // dont need the center value in our difference scheme
u = *v0; H = (double)i*h; u.y += H;
/*
* Trace to southern mirror point
*/
if ( Lgm_TraceToMirrorPoint( &u, &Pa, &Sa, mInfo->Bm, -1.0, mInfo->Lgm_TraceToMirrorPoint_Tol, mInfo ) > 0 ) {
/*
* Trace to northern mirror point
*/
if ( Lgm_TraceToMirrorPoint( &Pa, &Pb, &SS, mInfo->Bm, 1.0, mInfo->Lgm_TraceToMirrorPoint_Tol, mInfo ) > 0 ) {
r = Lgm_Magnitude( &Pb );
//mInfo->Hmax = SS/200.0;
mInfo->Hmax = SS/(double)mInfo->nDivs;
Lgm_TraceLine2( &Pa, &Pb, (r-1.0)*Re, 0.5*SS-mInfo->Hmax, 1.0, 1e-7, FALSE, mInfo );
ReplaceFirstPoint( 0.0, mInfo->Bm, &Pa, mInfo );
AddNewPoint( SS, mInfo->Bm, &Pb, mInfo );
InitSpline( mInfo );
mInfo->Lgm_I_integrand_S = 0.0;
mInfo->Lgm_I_integrand_FirstCall = TRUE;
mInfo->Lgm_n_I_integrand_Calls = 0;
mInfo->Sm_South = 0.0;
mInfo->Sm_North = SS;
if ( SS <= 1e-5 ) {
// if FL length is small, use an approx expression for I
rat = mInfo->Bmin/mInfo->Bm;
if ((1.0-rat) < 0.0) {
I = 0.0;
} else {
// Eqn 2.66b in Roederer
I = SS*sqrt(1.0 - rat);
}
} else {
I = Iinv_interped( mInfo );
}
if (mInfo->VerbosityLevel > 2) printf("I = %g Lgm_n_I_integrand_Calls = %d\n", I, mInfo->Lgm_n_I_integrand_Calls );
FreeSpline( mInfo );
} else {
printf("\t\tMirror point below %g km in Southern Hemisphere\n", mInfo->Lgm_LossConeHeight);
exit(0);
}
} else {
printf("\t\tMirror point below %g km in Northern Hemisphere\n", mInfo->Lgm_LossConeHeight);
exit(0);
}
f[i+N] = I;
}
}
if (DIFF_SCHEME == USE_SIX_POINT){
GradI->y = (f[6] - 9.0*f[5] + 45.0*f[4] - 45.0*f[2] + 9.0*f[1] - f[0])/(60.0*h);
} else if (DIFF_SCHEME == USE_FOUR_POINT){
GradI->y = (-f[4] + 8.0*f[3] - 8.0*f[1] + f[0])/(12.0*h);
} else if (DIFF_SCHEME == USE_TWO_POINT){
GradI->y = (f[2] - f[0])/(2.0*h);
}
/* Z-component */
if (mInfo->VerbosityLevel > 0) printf("\t\tComputing dIdz: h = %g\n", h);
for (i=-N; i<=N; ++i){
if (i!=0) { // dont need the center value in our difference scheme
u = *v0; H = (double)i*h; u.z += H;
/*
* Trace to southern mirror point
*/
if ( Lgm_TraceToMirrorPoint( &u, &Pa, &Sa, mInfo->Bm, -1.0, mInfo->Lgm_TraceToMirrorPoint_Tol, mInfo ) > 0 ) {
/*
* Trace to northern mirror point
*/
if ( Lgm_TraceToMirrorPoint( &Pa, &Pb, &SS, mInfo->Bm, 1.0, mInfo->Lgm_TraceToMirrorPoint_Tol, mInfo ) > 0 ) {
r = Lgm_Magnitude( &Pb );
//mInfo->Hmax = SS/200.0;
mInfo->Hmax = SS/(double)mInfo->nDivs;
Lgm_TraceLine2( &Pa, &Pb, (r-1.0)*Re, 0.5*SS-mInfo->Hmax, 1.0, 1e-7, FALSE, mInfo );
ReplaceFirstPoint( 0.0, mInfo->Bm, &Pa, mInfo );
AddNewPoint( SS, mInfo->Bm, &Pb, mInfo );
InitSpline( mInfo );
mInfo->Lgm_I_integrand_S = 0.0;
mInfo->Lgm_I_integrand_FirstCall = TRUE;
mInfo->Lgm_n_I_integrand_Calls = 0;
mInfo->Sm_South = 0.0;
mInfo->Sm_North = SS;
if ( SS <= 1e-5 ) {
// if FL length is small, use an approx expression for I
rat = mInfo->Bmin/mInfo->Bm;
if ((1.0-rat) < 0.0) {
I = 0.0;
} else {
// Eqn 2.66b in Roederer
I = SS*sqrt(1.0 - rat);
}
} else {
I = Iinv_interped( mInfo );
}
if (mInfo->VerbosityLevel > 2) printf("I = %g Lgm_n_I_integrand_Calls = %d\n", I, mInfo->Lgm_n_I_integrand_Calls );
FreeSpline( mInfo );
} else {
printf("\t\tMirror point below %g km in Southern Hemisphere\n", mInfo->Lgm_LossConeHeight);
exit(0);
}
} else {
printf("\t\tMirror point below %g km in Northern Hemisphere\n", mInfo->Lgm_LossConeHeight);
exit(0);
}
f[i+N] = I;
}
}
if (DIFF_SCHEME == USE_SIX_POINT){
GradI->z = (f[6] - 9.0*f[5] + 45.0*f[4] - 45.0*f[2] + 9.0*f[1] - f[0])/(60.0*h);
} else if (DIFF_SCHEME == USE_FOUR_POINT){
GradI->z = (-f[4] + 8.0*f[3] - 8.0*f[1] + f[0])/(12.0*h);
} else if (DIFF_SCHEME == USE_TWO_POINT){
GradI->z = (f[2] - f[0])/(2.0*h);
}
return(0);
}
void InitSplineModule()
{
InitSpline();
}
/*
* This version traces FLs from the Earth at the given MLT/mlat instead of trying to find the Bm radially out first.
*/
double ComputeI_FromMltMlat2( double Bm, double MLT, double mlat, double *r, double I0, Lgm_LstarInfo *LstarInfo ) {
int reset=1, reset2, TraceFlag;
double Bmin, I, Phi, cl, sl, rat, SS1, SS2, SS, Sn, Ss, Htry, Hdid, Hnext, Bs, Be, s, sgn;
Lgm_Vector w, u, Pmirror1, Pmirror2, v1, v2, v3, Bvec, P, Ps, u_scale, Bvectmp, Ptmp;
double stmp, Btmp;
/*
* First do a trace to identify the FL type and some of its critical points.
*/
*r = 1.0 + 100.0/Re;
Phi = 15.0*(MLT-12.0)*RadPerDeg;
cl = cos( mlat * RadPerDeg ); sl = sin( mlat * RadPerDeg );
w.x = (*r)*cl*cos(Phi); w.y = (*r)*cl*sin(Phi); w.z = (*r)*sl;
Lgm_Convert_Coords( &w, &u, SM_TO_GSM, LstarInfo->mInfo->c );
printf("w = %g %g %g\n", w.x, w.y, w.z);
TraceFlag = Lgm_Trace( &u, &v1, &v2, &v3, LstarInfo->mInfo->Lgm_LossConeHeight, 1e-6, 1e-8, LstarInfo->mInfo );
LstarInfo->mInfo->Bfield( &v3, &Bvec, LstarInfo->mInfo );
Bmin = Lgm_Magnitude( &Bvec );
printf("Got here\n");
if ( TraceFlag != LGM_CLOSED ) {
if (LstarInfo->VerbosityLevel > 1){ printf( "\t\t\t> Field Line not closed\n" ); }
return( 9e99 );
} else if ( Bmin <= Bm ) {
/*
* From the minimum B point, attempt to trace along the field to get the northern mirror point.
*/
P = v3;
SS1 = 0.0;
if ( Lgm_TraceToMirrorPoint( &P, &Pmirror1, &SS1, LstarInfo->mInfo->Bm, 1.0, LstarInfo->mInfo->Lgm_TraceToMirrorPoint_Tol, LstarInfo->mInfo ) > 0 ) {
SS2 = 0.0;
if ( Lgm_TraceToMirrorPoint( &P, &Pmirror2, &SS2, LstarInfo->mInfo->Bm, -1.0, LstarInfo->mInfo->Lgm_TraceToMirrorPoint_Tol, LstarInfo->mInfo ) > 0 ) {
} else {
if (LstarInfo->VerbosityLevel > 3){ printf( "\t\t\t> Unable to find southern mirror point\n" ); }
return( 9e99 );
}
// total distance between mirror point.
SS = SS1 + SS2;
// If its really small, just return 0.0 for I
if ( fabs(SS) < 1e-7) {
if (LstarInfo->VerbosityLevel > 3){ printf( "\t\t\t> Distance between mirror points is < 1e-7Re, Assuming I=0\n" ); }
return( 0.0 );
}
} else {
if (LstarInfo->VerbosityLevel > 3){ printf( "\t\t\t> Unable to find northern mirror point\n" ); }
return( 9e99 );
}
/*
* OK, we have both mirror points. LEts compute I
*/
I = 9e99;
LstarInfo->mInfo->Hmax = 0.1;
LstarInfo->mInfo->Hmax = SS/(double)LstarInfo->mInfo->nDivs;
/*
* This little section is attempting to solve an annoying
* precision issue. If the distance over which we are trying
* to trace is too small, too many sub-divisions (i.e. total
* steps) will lead to a step size that is too small. We can
* end up with the gridded FL points computed in
* Lgm_TraceLine3() such that the distance, s of the final
* point is very slightly less than we expect. This tries to
* reduce the number of divisions to avoid this in cases where
* the total distance to trace is very small.
*/
int nDivs;
if ( SS/LstarInfo->mInfo->nDivs < 1e-6 ) {
nDivs = SS/1e-6;
if (nDivs < 10) nDivs = 10;
} else {
nDivs = LstarInfo->mInfo->nDivs;
}
if ( Lgm_TraceLine3( &(LstarInfo->mInfo->Pm_South), SS, nDivs, 1.0, 1e-7, FALSE, LstarInfo->mInfo ) < 0 ) return( 9e99 );
/*
* Set the limits of integration.
*/
LstarInfo->mInfo->Sm_South = 0.0;
LstarInfo->mInfo->Sm_North = SS;
if ( InitSpline( LstarInfo->mInfo ) ) {
/*
* Do I integral with interped integrand.
*/
I = Iinv_interped( LstarInfo->mInfo );
if (LstarInfo->VerbosityLevel > 1) {
printf("\t\t%s mlat: %13.6g I: %13.6g I0: %13.6g I-I0: %13.6g [Sa,Sb]: %.8g %.8g (nCalls = %d)%s\n", LstarInfo->PreStr, mlat, I, I0, I-I0, LstarInfo->mInfo->Sm_South, LstarInfo->mInfo->Sm_North, LstarInfo->mInfo->Lgm_n_I_integrand_Calls, LstarInfo->PostStr );
}
FreeSpline( LstarInfo->mInfo );
} else {
I = 9e99;
}
} else {
if (LstarInfo->VerbosityLevel > 1){ printf( "\t\t\t> Field line min-B is greater than Bm. Bm = %g Bmin = %g\n", Bm, Bmin ); }
return( 9e99 );
}
return( I );
}
