WorldMagModel.c

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/*
 * This program 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.
 *
 * This program 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 this program; if not, see <http://www.gnu.org/licenses/>
 */

#include "openpilot.h"
#include "physical_constants.h"

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include <stdint.h>

#include "WorldMagModel.h"
#include "WMMInternal.h"

// const should hopefully keep them in the flash region
static const float CoeffFile[91][6] = COEFFS_FROM_NASA;

static WMMtype_Ellipsoid        Ellip;
static WMMtype_MagneticModel    MagneticModel;
static float                    decimal_date;

/**************************************************************************************
*   Example use - very simple - only two exposed functions
*
*       WMM_Initialize(); // Set default values and constants
*
*       WMM_GetMagVector(float Lat, float Lon, float Alt, uint16_t Month, uint16_t Day, uint16_t Year, float B[3]);
*       e.g. Iceland in may of 2012 = WMM_GetMagVector(65.0, -20.0, 0.0, 5, 5, 2012, B);
*       Alt is above the WGS-84 Ellipsoid
*       B is the NED (XYZ) magnetic vector in nTesla
**************************************************************************************/

int WMM_Initialize()
//      Sets default values for WMM subroutines.
//      UPDATES : Ellip and MagneticModel
{               
        // Sets WGS-84 parameters
        Ellip.a     = WGS84_A;               // semi-major axis of the ellipsoid in km
        Ellip.b     = WGS84_B;               // semi-minor axis of the ellipsoid in km
        Ellip.fla   = WGS84_FLATTENING;      // flattening
        Ellip.eps   = WGS84_EPS;             // first eccentricity
        Ellip.epssq = WGS84_EPS2;            // first eccentricity squared
        Ellip.re    = WGS84_RADIUS_EARTH_KM; // Earth's radius in km

        // Sets Magnetic Model parameters
        MagneticModel.nMax = WMM_MAX_MODEL_DEGREES;
        MagneticModel.nMaxSecVar = WMM_MAX_SECULAR_VARIATION_MODEL_DEGREES;
        MagneticModel.SecularVariationUsed = 0;
        MagneticModel.epoch       = MAGNETIC_MODEL_EPOCH;

        // Must be updated periodically. Last update expires in 2020

        return 0;                       // OK
}

int WMM_GetMagVector(float Lat, float Lon, float AltEllipsoid, uint16_t Month, uint16_t Day, uint16_t Year, float B[3])
{       
    // return '0' if all appears to be OK
    // return < 0 if error

    int returned = 0;   // default to OK

    // ***********
    // range check supplied params

    if (Lat <  -90) return -1;  // error
    if (Lat >   90) return -2;  // error

    if (Lon < -180) return -3;  // error
    if (Lon >  180) return -4;  // error


    WMMtype_CoordSpherical CoordSpherical;
    WMMtype_CoordGeodetic CoordGeodetic;
    WMMtype_GeoMagneticElements GeoMagneticElements;


    // ***********

    if (returned >= 0)
    {
        if (WMM_Initialize() < 0)
            returned = -6;  // error
    }

    if (returned >= 0)
    {
        CoordGeodetic.lambda = Lon;
        CoordGeodetic.phi = Lat;
        CoordGeodetic.HeightAboveEllipsoid = AltEllipsoid/1000.0f; // convert to km

        // Convert from geodeitic to Spherical Equations: 17-18, WMM Technical report
        if (WMM_GeodeticToSpherical(&CoordGeodetic, &CoordSpherical) < 0)
            returned = -7;  // error
    }


    if (returned >= 0)
    {
        if (WMM_DateToYear(Month, Day, Year) < 0)
            returned = -8;  // error
    }

    if (returned >= 0)
    {
        // Compute the geoMagnetic field elements and their time change
        if (WMM_Geomag(&CoordSpherical, &CoordGeodetic, &GeoMagneticElements) < 0)
            returned = -9;  // error
        else
        {   // set the returned values
                B[0] = GeoMagneticElements.X * 1e-2f;
                B[1] = GeoMagneticElements.Y * 1e-2f;
                B[2] = GeoMagneticElements.Z * 1e-2f;
        }
    }


    return returned;
}

int WMM_Geomag(WMMtype_CoordSpherical * CoordSpherical, WMMtype_CoordGeodetic * CoordGeodetic, WMMtype_GeoMagneticElements * GeoMagneticElements)
   /*
      The main subroutine that calls a sequence of WMM sub-functions to calculate the magnetic field elements for a single point.
      The function expects the model coefficients and point coordinates as input and returns the magnetic field elements and
      their rate of change. Though, this subroutine can be called successively to calculate a time series, profile or grid
      of magnetic field, these are better achieved by the subroutine WMM_Grid.

      INPUT: Ellip
      CoordSpherical
      CoordGeodetic
      TimedMagneticModel

      OUTPUT : GeoMagneticElements

      CALLS:    WMM_ComputeSphericalHarmonicVariables( Ellip, CoordSpherical, TimedMagneticModel->nMax, &SphVariables); (Compute Spherical Harmonic variables  )
      WMM_AssociatedLegendreFunction(CoordSpherical, TimedMagneticModel->nMax, LegendreFunction);       Compute ALF
      WMM_Summation(LegendreFunction, TimedMagneticModel, SphVariables, CoordSpherical, &MagneticResultsSph);  Accumulate the spherical harmonic coefficients
      WMM_SecVarSummation(LegendreFunction, TimedMagneticModel, SphVariables, CoordSpherical, &MagneticResultsSphVar); Sum the Secular Variation Coefficients
      WMM_RotateMagneticVector(CoordSpherical, CoordGeodetic, MagneticResultsSph, &MagneticResultsGeo); Map the computed Magnetic fields to Geodeitic coordinates
      WMM_RotateMagneticVector(CoordSpherical, CoordGeodetic, MagneticResultsSphVar, &MagneticResultsGeoVar);  Map the secular variation field components to Geodetic coordinates
      WMM_CalculateGeoMagneticElements(&MagneticResultsGeo, GeoMagneticElements);   Calculate the Geomagnetic elements
      WMM_CalculateSecularVariation(MagneticResultsGeoVar, GeoMagneticElements); Calculate the secular variation of each of the Geomagnetic elements

    */
{
    int returned = 0;   // default to OK

    WMMtype_MagneticResults             MagneticResultsSph;
    WMMtype_MagneticResults             MagneticResultsGeo;
    WMMtype_MagneticResults             MagneticResultsSphVar;
    WMMtype_MagneticResults             MagneticResultsGeoVar;

    WMMtype_LegendreFunction            LegendreFunction;
    WMMtype_SphericalHarmonicVariables  SphVariables;

    // ********

    if (returned >= 0)
    {   // Compute Spherical Harmonic variables
        if (WMM_ComputeSphericalHarmonicVariables(CoordSpherical, MagneticModel.nMax, &SphVariables) < 0)
            returned = -2;  // error
    }

    if (returned >= 0)
    {   // Compute ALF
        if (WMM_AssociatedLegendreFunction(CoordSpherical, MagneticModel.nMax, &LegendreFunction) < 0)
            returned = -3;  // error
    }

    if (returned >= 0)
    {   // Accumulate the spherical harmonic coefficients
        if (WMM_Summation(&LegendreFunction, &SphVariables, CoordSpherical, &MagneticResultsSph) < 0)
            returned = -4;  // error
    }

    if (returned >= 0)
    {   // Sum the Secular Variation Coefficients
        if (WMM_SecVarSummation(&LegendreFunction, &SphVariables, CoordSpherical, &MagneticResultsSphVar) < 0)
            returned = -5;  // error
    }

    if (returned >= 0)
    {   // Map the computed Magnetic fields to Geodeitic coordinates
        if (WMM_RotateMagneticVector(CoordSpherical, CoordGeodetic, &MagneticResultsSph, &MagneticResultsGeo) < 0)
            returned = -6;  // error
    }

    if (returned >= 0)
    {   // Map the secular variation field components to Geodetic coordinates
        if (WMM_RotateMagneticVector(CoordSpherical, CoordGeodetic, &MagneticResultsSphVar, &MagneticResultsGeoVar) < 0)
            returned = -7;  // error
    }

    if (returned >= 0)
    {   // Calculate the Geomagnetic elements, Equation 18 , WMM Technical report
        if (WMM_CalculateGeoMagneticElements(&MagneticResultsGeo, GeoMagneticElements) < 0)
            returned = -8;  // error
    }

    if (returned >= 0)
    {   // Calculate the secular variation of each of the Geomagnetic elements
        if (WMM_CalculateSecularVariation(&MagneticResultsGeoVar, GeoMagneticElements) < 0)
            returned = -9;  // error
    }

    return returned;
}

int WMM_ComputeSphericalHarmonicVariables(WMMtype_CoordSpherical *CoordSpherical, uint16_t nMax, WMMtype_SphericalHarmonicVariables *SphVariables)

   /* Computes Spherical variables
      Variables computed are (a/r)^(n+2), cos_m(lamda) and sin_m(lambda) for spherical harmonic
      summations. (Equations 10-12 in the WMM Technical Report)
      INPUT   Ellip  data  structure with the following elements
      float a; semi-major axis of the ellipsoid
      float b; semi-minor axis of the ellipsoid
      float fla;  flattening
      float epssq; first eccentricity squared
      float eps;  first eccentricity
      float re; mean radius of  ellipsoid
      CoordSpherical    A data structure with the following elements
      float lambda; ( longitude)
      float phig; ( geocentric latitude )
      float r;            ( distance from the center of the ellipsoid)
      nMax   integer     ( Maxumum degree of spherical harmonic secular model)\

      OUTPUT  SphVariables  Pointer to the   data structure with the following elements
      float RelativeRadiusPower[WMM_MAX_MODEL_DEGREES+1];   [earth_reference_radius_km  sph. radius ]^n
      float cos_mlambda[WMM_MAX_MODEL_DEGREES+1]; cp(m)  - cosine of (mspherical coord. longitude)
      float sin_mlambda[WMM_MAX_MODEL_DEGREES+1];  sp(m)  - sine of (mspherical coord. longitude)
      CALLS : none
    */
{
        float cos_lambda, sin_lambda;
        uint16_t m, n;

        cos_lambda = cosf(CoordSpherical->lambda * DEG2RAD);
        sin_lambda = sinf(CoordSpherical->lambda * DEG2RAD);

        /* for n = 0 ... model_order, compute (Radius of Earth / Spherica radius r)^(n+2)
           for n  1..nMax-1 (this is much faster than calling pow MAX_N+1 times).      */

        SphVariables->RelativeRadiusPower[0] = (Ellip.re / CoordSpherical->r) * (Ellip.re / CoordSpherical->r);
        for (n = 1; n <= nMax; n++)
                SphVariables->RelativeRadiusPower[n] = SphVariables->RelativeRadiusPower[n - 1] * (Ellip.re / CoordSpherical->r);

        /*
           Compute cos(m*lambda), sin(m*lambda) for m = 0 ... nMax
           cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
           sin(a + b) = cos(a)*sin(b) + sin(a)*cos(b)
         */
        SphVariables->cos_mlambda[0] = 1.0;
        SphVariables->sin_mlambda[0] = 0.0;

        SphVariables->cos_mlambda[1] = cos_lambda;
        SphVariables->sin_mlambda[1] = sin_lambda;
        for (m = 2; m <= nMax; m++)
        {
                SphVariables->cos_mlambda[m] = SphVariables->cos_mlambda[m - 1] * cos_lambda - SphVariables->sin_mlambda[m - 1] * sin_lambda;
                SphVariables->sin_mlambda[m] = SphVariables->cos_mlambda[m - 1] * sin_lambda + SphVariables->sin_mlambda[m - 1] * cos_lambda;
        }

        return 0;   // OK
}

int WMM_AssociatedLegendreFunction(WMMtype_CoordSpherical * CoordSpherical, uint16_t nMax, WMMtype_LegendreFunction * LegendreFunction)

        /* Computes  all of the Schmidt-semi normalized associated Legendre
           functions up to degree nMax. If nMax <= 16, function WMM_PcupLow is used.
           Otherwise WMM_PcupHigh is called.
           INPUT  CoordSpherical        A data structure with the following elements
           float lambda; ( longitude)
           float phig; ( geocentric latitude )
           float r;       ( distance from the center of the ellipsoid)
           nMax         integer          ( Maxumum degree of spherical harmonic secular model)
           LegendreFunction Pointer to data structure with the following elements
           float *Pcup;  (  pointer to store Legendre Function  )
           float *dPcup; ( pointer to store  Derivative of Lagendre function )

           OUTPUT  LegendreFunction  Calculated Legendre variables in the data structure

         */
{
        float sin_phi = sinf(CoordSpherical->phig * DEG2RAD);   /* sin  (geocentric latitude) */

        if (nMax <= 16 || (1 - fabsf(sin_phi)) < 1.0e-10f)      /* If nMax is less tha 16 or at the poles */
        {
                if (WMM_PcupLow(LegendreFunction->Pcup, LegendreFunction->dPcup, sin_phi, nMax) < 0)
                    return -1;  // error
        }
        else
        {
                if (WMM_PcupHigh(LegendreFunction->Pcup, LegendreFunction->dPcup, sin_phi, nMax) < 0)
                    return -2;  // error
        }

        return 0;   // OK
}

int WMM_Summation(WMMtype_LegendreFunction * LegendreFunction,
                       WMMtype_SphericalHarmonicVariables * SphVariables,
                       WMMtype_CoordSpherical * CoordSpherical, WMMtype_MagneticResults * MagneticResults)
{
        /* Computes Geomagnetic Field Elements X, Y and Z in Spherical coordinate system using
           spherical harmonic summation.

           The vector Magnetic field is given by -grad V, where V is Geomagnetic scalar potential
           The gradient in spherical coordinates is given by:

           dV ^     1 dV ^        1     dV ^
           grad V = -- r  +  - -- t  +  -------- -- p
           dr       r dt       r sin(t) dp

           INPUT :  LegendreFunction
           MagneticModel
           SphVariables
           CoordSpherical
           OUTPUT : MagneticResults

           CALLS : WMM_SummationSpecial

           Manoj Nair, June, 2009 Manoj.C.Nair@Noaa.Gov
         */

    uint16_t m, n, index;
        float cos_phi;

        MagneticResults->Bz = 0.0;
        MagneticResults->By = 0.0;
        MagneticResults->Bx = 0.0;

        for (n = 1; n <= MagneticModel.nMax; n++)
        {
                for (m = 0; m <= n; m++)
                {
                        index = (n * (n + 1) / 2 + m);

/*                  nMax        (n+2)     n     m            m           m
        Bz =   -SUM (a/r)   (n+1) SUM  [g cos(m p) + h sin(m p)] P (sin(phi))
                        n=1                   m=0   n            n           n  */
/* Equation 12 in the WMM Technical report.  Derivative with respect to radius.*/
                        MagneticResults->Bz -=
                            SphVariables->RelativeRadiusPower[n] *
                            (WMM_get_main_field_coeff_g(index) *
                             SphVariables->cos_mlambda[m] + WMM_get_main_field_coeff_h(index) * SphVariables->sin_mlambda[m])
                            * (float)(n + 1) * LegendreFunction->Pcup[index];

/*                1 nMax  (n+2)    n     m            m           m
        By =    SUM (a/r) (m)  SUM  [g cos(m p) + h sin(m p)] dP (sin(phi))
                   n=1             m=0   n            n           n  */
/* Equation 11 in the WMM Technical report. Derivative with respect to longitude, divided by radius. */
                        MagneticResults->By +=
                            SphVariables->RelativeRadiusPower[n] *
                            (WMM_get_main_field_coeff_g(index) *
                             SphVariables->sin_mlambda[m] - WMM_get_main_field_coeff_h(index) * SphVariables->cos_mlambda[m])
                            * (float)(m) * LegendreFunction->Pcup[index];
/*                 nMax  (n+2) n     m            m           m
        Bx = - SUM (a/r)   SUM  [g cos(m p) + h sin(m p)] dP (sin(phi))
                   n=1         m=0   n            n           n  */
/* Equation 10  in the WMM Technical report. Derivative with respect to latitude, divided by radius. */

                        MagneticResults->Bx -=
                            SphVariables->RelativeRadiusPower[n] *
                            (WMM_get_main_field_coeff_g(index) *
                             SphVariables->cos_mlambda[m] + WMM_get_main_field_coeff_h(index) * SphVariables->sin_mlambda[m])
                            * LegendreFunction->dPcup[index];

                }
        }

        cos_phi = cosf(CoordSpherical->phig * DEG2RAD);
        if (fabsf(cos_phi) > 1.0e-10f)
        {
                MagneticResults->By = MagneticResults->By / cos_phi;
        }
        else
        {
        /* Special calculation for component - By - at Geographic poles.
         * If the user wants to avoid using this function,  please make sure that
         * the latitude is not exactly +/-90. An option is to make use the function
         * WMM_CheckGeographicPoles.
         */
                if (WMM_SummationSpecial(SphVariables, CoordSpherical, MagneticResults) < 0)
                    return -1;  // error
        }

        return 0;   // OK
}

int WMM_SecVarSummation(WMMtype_LegendreFunction * LegendreFunction,
                             WMMtype_SphericalHarmonicVariables *
                             SphVariables, WMMtype_CoordSpherical * CoordSpherical, WMMtype_MagneticResults * MagneticResults)
{
        /*This Function sums the secular variation coefficients to get the secular variation of the Magnetic vector.
           INPUT :  LegendreFunction
           MagneticModel
           SphVariables
           CoordSpherical
           OUTPUT : MagneticResults

           CALLS : WMM_SecVarSummationSpecial

         */

    uint16_t m, n, index;
        float cos_phi;

        MagneticModel.SecularVariationUsed = TRUE;

        MagneticResults->Bz = 0.0;
        MagneticResults->By = 0.0;
        MagneticResults->Bx = 0.0;

        for (n = 1; n <= MagneticModel.nMaxSecVar; n++)
        {
                for (m = 0; m <= n; m++)
                {
                        index = (n * (n + 1) / 2 + m);

/*                  nMax        (n+2)     n     m            m           m
        Bz =   -SUM (a/r)   (n+1) SUM  [g cos(m p) + h sin(m p)] P (sin(phi))
                        n=1                   m=0   n            n           n  */
/*  Derivative with respect to radius.*/
                        MagneticResults->Bz -=
                            SphVariables->RelativeRadiusPower[n] *
                            (WMM_get_secular_var_coeff_g(index) *
                             SphVariables->cos_mlambda[m] + WMM_get_secular_var_coeff_h(index) * SphVariables->sin_mlambda[m])
                            * (float)(n + 1) * LegendreFunction->Pcup[index];

/*                1 nMax  (n+2)    n     m            m           m
        By =    SUM (a/r) (m)  SUM  [g cos(m p) + h sin(m p)] dP (sin(phi))
                   n=1             m=0   n            n           n  */
/* Derivative with respect to longitude, divided by radius. */
                        MagneticResults->By +=
                            SphVariables->RelativeRadiusPower[n] *
                            (WMM_get_secular_var_coeff_g(index) *
                             SphVariables->sin_mlambda[m] - WMM_get_secular_var_coeff_h(index) * SphVariables->cos_mlambda[m])
                            * (float)(m) * LegendreFunction->Pcup[index];
/*                 nMax  (n+2) n     m            m           m
        Bx = - SUM (a/r)   SUM  [g cos(m p) + h sin(m p)] dP (sin(phi))
                   n=1         m=0   n            n           n  */
/* Derivative with respect to latitude, divided by radius. */

                        MagneticResults->Bx -=
                            SphVariables->RelativeRadiusPower[n] *
                            (WMM_get_secular_var_coeff_g(index) *
                             SphVariables->cos_mlambda[m] + WMM_get_secular_var_coeff_h(index) * SphVariables->sin_mlambda[m])
                            * LegendreFunction->dPcup[index];
                }
        }
        cos_phi = cosf(CoordSpherical->phig * DEG2RAD);
        if (fabsf(cos_phi) > 1.0e-10f)
        {
                MagneticResults->By = MagneticResults->By / cos_phi;
        }
        else
                /* Special calculation for component By at Geographic poles */
        {
                if (WMM_SecVarSummationSpecial(SphVariables, CoordSpherical, MagneticResults) < 0)
                    return -1;  // error
        }

    return 0;   // OK
}

int WMM_RotateMagneticVector(WMMtype_CoordSpherical * CoordSpherical,
                                  WMMtype_CoordGeodetic * CoordGeodetic,
                                  WMMtype_MagneticResults * MagneticResultsSph, WMMtype_MagneticResults * MagneticResultsGeo)
        /* Rotate the Magnetic Vectors to Geodetic Coordinates
           Manoj Nair, June, 2009 Manoj.C.Nair@Noaa.Gov
           Equation 16, WMM Technical report

           INPUT : CoordSpherical : Data structure WMMtype_CoordSpherical with the following elements
           float lambda; ( longitude)
           float phig; ( geocentric latitude )
           float r;       ( distance from the center of the ellipsoid)

           CoordGeodetic : Data structure WMMtype_CoordGeodetic with the following elements
           float lambda; (longitude)
           float phi; ( geodetic latitude)
           float HeightAboveEllipsoid; (height above the ellipsoid (HaE) )
           float HeightAboveGeoid;(height above the Geoid )

           MagneticResultsSph : Data structure WMMtype_MagneticResults with the following elements
           float Bx;     North
           float By;       East
           float Bz;    Down

           OUTPUT: MagneticResultsGeo Pointer to the data structure WMMtype_MagneticResults, with the following elements
           float Bx;     North
           float By;       East
           float Bz;    Down

           CALLS : none

         */
{
        /* Difference between the spherical and Geodetic latitudes */
        float Psi = (CoordSpherical->phig - CoordGeodetic->phi) * DEG2RAD;

        /* Rotate spherical field components to the Geodeitic system */
        MagneticResultsGeo->Bz = MagneticResultsSph->Bx * sinf(Psi) + MagneticResultsSph->Bz * cosf(Psi);
        MagneticResultsGeo->Bx = MagneticResultsSph->Bx * cosf(Psi) - MagneticResultsSph->Bz * sinf(Psi);
        MagneticResultsGeo->By = MagneticResultsSph->By;

    return 0;
}

int WMM_CalculateGeoMagneticElements(WMMtype_MagneticResults * MagneticResultsGeo, WMMtype_GeoMagneticElements * GeoMagneticElements)

        /* Calculate all the Geomagnetic elements from X,Y and Z components
           INPUT     MagneticResultsGeo   Pointer to data structure with the following elements
           float Bx;    ( North )
           float By;      ( East )
           float Bz;    ( Down )
           OUTPUT    GeoMagneticElements    Pointer to data structure with the following elements
           float Decl; (Angle between the magnetic field vector and true north, positive east)
           float Incl; Angle between the magnetic field vector and the horizontal plane, positive down
           float F; Magnetic Field Strength
           float H; Horizontal Magnetic Field Strength
           float X; Northern component of the magnetic field vector
           float Y; Eastern component of the magnetic field vector
           float Z; Downward component of the magnetic field vector
           CALLS : none
         */
{
        GeoMagneticElements->X = MagneticResultsGeo->Bx;
        GeoMagneticElements->Y = MagneticResultsGeo->By;
        GeoMagneticElements->Z = MagneticResultsGeo->Bz;

        GeoMagneticElements->H = sqrtf(MagneticResultsGeo->Bx * MagneticResultsGeo->Bx + MagneticResultsGeo->By * MagneticResultsGeo->By);
        GeoMagneticElements->F = sqrtf(GeoMagneticElements->H * GeoMagneticElements->H + MagneticResultsGeo->Bz * MagneticResultsGeo->Bz);
        GeoMagneticElements->Decl = atan2f(GeoMagneticElements->Y, GeoMagneticElements->X) * RAD2DEG;
        GeoMagneticElements->Incl = atan2f(GeoMagneticElements->Z, GeoMagneticElements->H) * RAD2DEG;

    return 0;   // OK
}

int WMM_CalculateSecularVariation(WMMtype_MagneticResults * MagneticVariation, WMMtype_GeoMagneticElements * MagneticElements)
/*This takes the Magnetic Variation in x, y, and z and uses it to calculate the secular variation of each of the Geomagnetic elements.
        INPUT     MagneticVariation   Data structure with the following elements
                                float Bx;    ( North )
                                float By;         ( East )
                                float Bz;    ( Down )
        OUTPUT   MagneticElements   Pointer to the data  structure with the following elements updated
                        float Decldot; Yearly Rate of change in declination
                        float Incldot; Yearly Rate of change in inclination
                        float Fdot; Yearly rate of change in Magnetic field strength
                        float Hdot; Yearly rate of change in horizontal field strength
                        float Xdot; Yearly rate of change in the northern component
                        float Ydot; Yearly rate of change in the eastern component
                        float Zdot; Yearly rate of change in the downward component
                        float GVdot;Yearly rate of chnage in grid variation
        CALLS : none

*/
{
        MagneticElements->Xdot = MagneticVariation->Bx;
        MagneticElements->Ydot = MagneticVariation->By;
        MagneticElements->Zdot = MagneticVariation->Bz;
        MagneticElements->Hdot = (MagneticElements->X * MagneticElements->Xdot + MagneticElements->Y * MagneticElements->Ydot) / MagneticElements->H;   //See equation 19 in the WMM technical report
        MagneticElements->Fdot =
            (MagneticElements->X * MagneticElements->Xdot +
             MagneticElements->Y * MagneticElements->Ydot + MagneticElements->Z * MagneticElements->Zdot) / MagneticElements->F;
        MagneticElements->Decldot =
            RAD2DEG * (MagneticElements->X * MagneticElements->Ydot -
                            MagneticElements->Y * MagneticElements->Xdot) / (MagneticElements->H * MagneticElements->H);
        MagneticElements->Incldot =
            RAD2DEG * (MagneticElements->H * MagneticElements->Zdot -
                            MagneticElements->Z * MagneticElements->Hdot) / (MagneticElements->F * MagneticElements->F);
        MagneticElements->GVdot = MagneticElements->Decldot;

    return 0;   // OK
}

int WMM_PcupHigh(float *Pcup, float *dPcup, float x, uint16_t nMax)

/*      This function evaluates all of the Schmidt-semi normalized associated Legendre
        functions up to degree nMax. The functions are initially scaled by
        10^280 sin^m in order to minimize the effects of underflow at large m
        near the poles (see Holmes and Featherstone 2002, J. Geodesy, 76, 279-299).
        Note that this function performs the same operation as WMM_PcupLow.
        However this function also can be used for high degree (large nMax) models.

        Calling Parameters:
                INPUT
                        nMax:    Maximum spherical harmonic degree to compute.
                        x:              cos(colatitude) or sin(latitude).

                OUTPUT
                        Pcup:   A vector of all associated Legendgre polynomials evaluated at
                                        x up to nMax. The lenght must by greater or equal to (nMax+1)*(nMax+2)/2.
                  dPcup:   Derivative of Pcup(x) with respect to latitude

                CALLS : none
        Notes:

  Adopted from the FORTRAN code written by Mark Wieczorek September 25, 2005.

  Manoj Nair, Nov, 2009 Manoj.C.Nair@Noaa.Gov

  Change from the previous version
  The prevous version computes the derivatives as
  dP(n,m)(x)/dx, where x = sin(latitude) (or cos(colatitude) ).
  However, the WMM Geomagnetic routines requires dP(n,m)(x)/dlatitude.
  Hence the derivatives are multiplied by sin(latitude).
  Removed the options for CS phase and normalizations.

  Note: In geomagnetism, the derivatives of ALF are usually found with
  respect to the colatitudes. Here the derivatives are found with respect
  to the latitude. The difference is a sign reversal for the derivative of
  the Associated Legendre Functions.

  The derivates can't be computed for latitude = |90| degrees.
        */
{
    uint16_t    k, kstart, m, n;
    float       pm2, pm1, pmm, plm, rescalem, z, scalef;

    float f1_s[NUMPCUP];
    float f2_s[NUMPCUP];
    float pre_sqr[NUMPCUP];

        float       *f1 = f1_s;
        float       *f2 = f2_s;
        float       *PreSqr = pre_sqr;
  

        if (fabsf(x) == 1.0f)
        {
                // Error in PcupHigh: derivative cannot be calculated at poles
                return -2;
        }

        scalef = 1.0e-280;

        for (n = 0; n <= 2 * nMax + 1; ++n)
                PreSqr[n] = sqrtf((float)(n));

        k = 2;

        for (n = 2; n <= nMax; n++)
        {
                k = k + 1;
                f1[k] = (float)(2 * n - 1) / (float)(n);
                f2[k] = (float)(n - 1) / (float)(n);
                for (m = 1; m <= n - 2; m++)
                {
                        k = k + 1;
                        f1[k] = (float)(2 * n - 1) / PreSqr[n + m] / PreSqr[n - m];
                        f2[k] = PreSqr[n - m - 1] * PreSqr[n + m - 1] / PreSqr[n + m] / PreSqr[n - m];
                }
                k = k + 2;
        }

        /*z = sin (geocentric latitude) */
        z = sqrtf((1.0f - x) * (1.0f + x));
        pm2 = 1.0;
        Pcup[0] = 1.0;
        dPcup[0] = 0.0;
        if (nMax == 0)
    {
        return -3;
    }
        pm1 = x;
        Pcup[1] = pm1;
        dPcup[1] = z;
        k = 1;

        for (n = 2; n <= nMax; n++)
        {
                k = k + n;
                plm = f1[k] * x * pm1 - f2[k] * pm2;
                Pcup[k] = plm;
                dPcup[k] = (float)(n) * (pm1 - x * plm) / z;
                pm2 = pm1;
                pm1 = plm;
        }

        pmm = PreSqr[2] * scalef;
        rescalem = 1.0f / scalef;
        kstart = 0;

        for (m = 1; m <= nMax - 1; ++m)
        {
                rescalem = rescalem * z;

                /* Calculate Pcup(m,m) */
                kstart = kstart + m + 1;
                pmm = pmm * PreSqr[2 * m + 1] / PreSqr[2 * m];
                Pcup[kstart] = pmm * rescalem / PreSqr[2 * m + 1];
                dPcup[kstart] = -((float)(m) * x * Pcup[kstart] / z);
                pm2 = pmm / PreSqr[2 * m + 1];
                /* Calculate Pcup(m+1,m) */
                k = kstart + m + 1;
                pm1 = x * PreSqr[2 * m + 1] * pm2;
                Pcup[k] = pm1 * rescalem;
                dPcup[k] = ((pm2 * rescalem) * PreSqr[2 * m + 1] - x * (float)(m + 1) * Pcup[k]) / z;
                /* Calculate Pcup(n,m) */
                for (n = m + 2; n <= nMax; ++n)
                {
                        k = k + n;
                        plm = x * f1[k] * pm1 - f2[k] * pm2;
                        Pcup[k] = plm * rescalem;
                        dPcup[k] = (PreSqr[n + m] * PreSqr[n - m] * (pm1 * rescalem) - (float)(n) * x * Pcup[k]) / z;
                        pm2 = pm1;
                        pm1 = plm;
                }
        }

        /* Calculate Pcup(nMax,nMax) */
        rescalem = rescalem * z;
        kstart = kstart + m + 1;
        pmm = pmm / PreSqr[2 * nMax];
        Pcup[kstart] = pmm * rescalem;
        dPcup[kstart] = -(float)(nMax) * x * Pcup[kstart] / z;

        return 0;   // OK
}

int WMM_PcupLow(float *Pcup, float *dPcup, float x, uint16_t nMax)

/*   This function evaluates all of the Schmidt-semi normalized associated Legendre
        functions up to degree nMax.

        Calling Parameters:
                INPUT
                        nMax:    Maximum spherical harmonic degree to compute.
                        x:              cos(colatitude) or sin(latitude).

                OUTPUT
                        Pcup:   A vector of all associated Legendgre polynomials evaluated at
                                        x up to nMax.
                   dPcup: Derivative of Pcup(x) with respect to latitude

        Notes: Overflow may occur if nMax > 20 , especially for high-latitudes.
        Use WMM_PcupHigh for large nMax.

   Writted by Manoj Nair, June, 2009 . Manoj.C.Nair@Noaa.Gov.

  Note: In geomagnetism, the derivatives of ALF are usually found with
  respect to the colatitudes. Here the derivatives are found with respect
  to the latitude. The difference is a sign reversal for the derivative of
  the Associated Legendre Functions.
*/
{
    uint16_t    n, m, index, index1, index2;
    float       k, z;
    float schmidtQuasiNorm_s[NUMPCUP];
    float       *schmidtQuasiNorm = schmidtQuasiNorm_s;

    if (!schmidtQuasiNorm)
    {
        return -1;
    }

        Pcup[0] = 1.0;
        dPcup[0] = 0.0;

        /*sin (geocentric latitude) - sin_phi */
        z = sqrtf((1.0f - x) * (1.0f + x));

        /*       First, Compute the Gauss-normalized associated Legendre  functions */
        for (n = 1; n <= nMax; n++)
        {
                for (m = 0; m <= n; m++)
                {
                        index = (n * (n + 1) / 2 + m);
                        if (n == m)
                        {
                                index1 = (n - 1) * n / 2 + m - 1;
                                Pcup[index] = z * Pcup[index1];
                                dPcup[index] = z * dPcup[index1] + x * Pcup[index1];
                        }
                        else
                        if (n == 1 && m == 0)
                        {
                                index1 = (n - 1) * n / 2 + m;
                                Pcup[index] = x * Pcup[index1];
                                dPcup[index] = x * dPcup[index1] - z * Pcup[index1];
                        }
                        else
                        if (n > 1 && n != m)
                        {
                                index1 = (n - 2) * (n - 1) / 2 + m;
                                index2 = (n - 1) * n / 2 + m;
                                if (m > n - 2)
                                {
                                        Pcup[index] = x * Pcup[index2];
                                        dPcup[index] = x * dPcup[index2] - z * Pcup[index2];
                                }
                                else
                                {
                                        k = (float)(((n - 1) * (n - 1)) - (m * m)) / (float)((2 * n - 1)
                                                                                             * (2 * n - 3));
                                        Pcup[index] = x * Pcup[index2] - k * Pcup[index1];
                                        dPcup[index] = x * dPcup[index2] - z * Pcup[index2] - k * dPcup[index1];
                                }
                        }
                }
        }
/*Compute the ration between the Gauss-normalized associated Legendre
  functions and the Schmidt quasi-normalized version. This is equivalent to
  sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)!  */

        schmidtQuasiNorm[0] = 1.0;
        for (n = 1; n <= nMax; n++)
        {
                index = (n * (n + 1) / 2);
                index1 = (n - 1) * n / 2;
                /* for m = 0 */
                schmidtQuasiNorm[index] = schmidtQuasiNorm[index1] * (float)(2 * n - 1) / (float)n;

                for (m = 1; m <= n; m++)
                {
                        index = (n * (n + 1) / 2 + m);
                        index1 = (n * (n + 1) / 2 + m - 1);
                        schmidtQuasiNorm[index] = schmidtQuasiNorm[index1] * sqrtf((float)((n - m + 1) * (m == 1 ? 2 : 1)) / (float)(n + m));
                }

        }

/* Converts the  Gauss-normalized associated Legendre
          functions to the Schmidt quasi-normalized version using pre-computed
          relation stored in the variable schmidtQuasiNorm */

        for (n = 1; n <= nMax; n++)
        {
                for (m = 0; m <= n; m++)
                {
                        index = (n * (n + 1) / 2 + m);
                        Pcup[index] = Pcup[index] * schmidtQuasiNorm[index];
                        dPcup[index] = -dPcup[index] * schmidtQuasiNorm[index];
                        /* The sign is changed since the new WMM routines use derivative with respect to latitude
                           insted of co-latitude */
                }
        }

        return 0;   // OK
}

int WMM_SummationSpecial(WMMtype_SphericalHarmonicVariables *
                              SphVariables, WMMtype_CoordSpherical * CoordSpherical, WMMtype_MagneticResults * MagneticResults)
        /* Special calculation for the component By at Geographic poles.
           Manoj Nair, June, 2009 manoj.c.nair@noaa.gov
           INPUT: MagneticModel
           SphVariables
           CoordSpherical
           OUTPUT: MagneticResults
           CALLS : none
           See Section 1.4, "SINGULARITIES AT THE GEOGRAPHIC POLES", WMM Technical report

         */
{
    uint16_t    n, index;
    float       k, sin_phi;
    float       schmidtQuasiNorm1;
    float       schmidtQuasiNorm2;
    float       schmidtQuasiNorm3;

    float PcupsS_s[NUMPCUPS];
    float       *PcupS = PcupsS_s;
        if (!PcupS)
                return -1;

        PcupS[0] = 1;
        schmidtQuasiNorm1 = 1.0;

        MagneticResults->By = 0.0;
        sin_phi = sinf(CoordSpherical->phig * DEG2RAD);

        for (n = 1; n <= MagneticModel.nMax; n++)
        {

                /*Compute the ration between the Gauss-normalized associated Legendre
                   functions and the Schmidt quasi-normalized version. This is equivalent to
                   sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)!  */

                index = (n * (n + 1) / 2 + 1);
                schmidtQuasiNorm2 = schmidtQuasiNorm1 * (float)(2 * n - 1) / (float)n;
                schmidtQuasiNorm3 = schmidtQuasiNorm2 * sqrtf((float)(n * 2) / (float)(n + 1));
                schmidtQuasiNorm1 = schmidtQuasiNorm2;
                if (n == 1)
                {
                        PcupS[n] = PcupS[n - 1];
                }
                else
                {
                        k = (float)(((n - 1) * (n - 1)) - 1) / (float)((2 * n - 1) * (2 * n - 3));
                        PcupS[n] = sin_phi * PcupS[n - 1] - k * PcupS[n - 2];
                }

/*                1 nMax  (n+2)    n     m            m           m
        By =    SUM (a/r) (m)  SUM  [g cos(m p) + h sin(m p)] dP (sin(phi))
                   n=1             m=0   n            n           n  */
/* Equation 11 in the WMM Technical report. Derivative with respect to longitude, divided by radius. */

                MagneticResults->By +=
                    SphVariables->RelativeRadiusPower[n] *
                    (WMM_get_main_field_coeff_g(index) *
                     SphVariables->sin_mlambda[1] - WMM_get_main_field_coeff_h(index) * SphVariables->cos_mlambda[1])
                    * PcupS[n] * schmidtQuasiNorm3;
        }

        return 0;   // OK
}

int WMM_SecVarSummationSpecial(WMMtype_SphericalHarmonicVariables *
                                    SphVariables, WMMtype_CoordSpherical * CoordSpherical, WMMtype_MagneticResults * MagneticResults)
{
        /*Special calculation for the secular variation summation at the poles.

           INPUT: MagneticModel
           SphVariables
           CoordSpherical
           OUTPUT: MagneticResults
           CALLS : none

         */
    uint16_t    n, index;
    float       k, sin_phi;
    float       schmidtQuasiNorm1;
    float       schmidtQuasiNorm2;
    float       schmidtQuasiNorm3;

    float PcupsS_s[NUMPCUPS];
    float       *PcupS = PcupsS_s;
        if (!PcupS)
                return -1;

        PcupS[0] = 1;
        schmidtQuasiNorm1 = 1.0;

        MagneticResults->By = 0.0;
        sin_phi = sinf(CoordSpherical->phig * DEG2RAD);

        for (n = 1; n <= MagneticModel.nMaxSecVar; n++)
        {
                index = (n * (n + 1) / 2 + 1);
                schmidtQuasiNorm2 = schmidtQuasiNorm1 * (float)(2 * n - 1) / (float)n;
                schmidtQuasiNorm3 = schmidtQuasiNorm2 * sqrtf((float)(n * 2) / (float)(n + 1));
                schmidtQuasiNorm1 = schmidtQuasiNorm2;
                if (n == 1)
                {
                        PcupS[n] = PcupS[n - 1];
                }
                else
                {
                        k = (float)(((n - 1) * (n - 1)) - 1) / (float)((2 * n - 1) * (2 * n - 3));
                        PcupS[n] = sin_phi * PcupS[n - 1] - k * PcupS[n - 2];
                }

/*                1 nMax  (n+2)    n     m            m           m
        By =    SUM (a/r) (m)  SUM  [g cos(m p) + h sin(m p)] dP (sin(phi))
                   n=1             m=0   n            n           n  */
/* Derivative with respect to longitude, divided by radius. */

                MagneticResults->By +=
                    SphVariables->RelativeRadiusPower[n] *
                    (WMM_get_secular_var_coeff_g(index) *
                     SphVariables->sin_mlambda[1] - WMM_get_secular_var_coeff_h(index) * SphVariables->cos_mlambda[1])
                    * PcupS[n] * schmidtQuasiNorm3;
        }

        return 0;   // OK
}

float WMM_get_main_field_coeff_g(uint16_t index) 
{       
        if (index >= NUMTERMS)
                return 0;

    uint16_t n, m, sum_index, a, b;

    float coeff = CoeffFile[index][2];
        
        a = MagneticModel.nMaxSecVar;
        b = (a * (a + 1) / 2 + a);
        for (n = 1; n <= MagneticModel.nMax; n++)
        {
                for (m = 0; m <= n; m++)
                {
                        
                        sum_index = (n * (n + 1) / 2 + m);
                        
                        /* Hacky for now, will solve for which conditions need summing analytically */
                        if (sum_index != index)
                                continue;
                        
                        if (index <= b) 
                                coeff += (decimal_date - MagneticModel.epoch) * WMM_get_secular_var_coeff_g(sum_index);
                        
                }
        }
        
        return coeff;
}

float WMM_get_main_field_coeff_h(uint16_t index) 
{       
        if (index >= NUMTERMS)
                return 0;
        
    uint16_t n, m, sum_index, a, b;
        float coeff = CoeffFile[index][3];
        
        a = MagneticModel.nMaxSecVar;
        b = (a * (a + 1) / 2 + a);
        for (n = 1; n <= MagneticModel.nMax; n++)
        {
                for (m = 0; m <= n; m++)
                {
                        
                        sum_index = (n * (n + 1) / 2 + m);
                        
                        /* Hacky for now, will solve for which conditions need summing analytically */
                        if (sum_index != index)
                                continue;
                        
                        if (index <= b) 
                                coeff += (decimal_date - MagneticModel.epoch) * WMM_get_secular_var_coeff_h(sum_index);
                }
        }
        
        return coeff;   
}

float WMM_get_secular_var_coeff_g(uint16_t index) 
{               
        if (index >= NUMTERMS)
                return 0;
        
        return CoeffFile[index][4];
}

float WMM_get_secular_var_coeff_h(uint16_t index) 
{               
        if (index >= NUMTERMS)
                return 0;
        
        return CoeffFile[index][5];
}

int WMM_DateToYear(uint16_t month, uint16_t day, uint16_t year)
// Converts a given calendar date into a decimal year
{
        uint16_t temp = 0;      // Total number of days
        uint16_t MonthDays[13] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
        uint16_t ExtraDay = 0;
        uint16_t i;

        if ((year % 4 == 0 && year % 100 != 0) || (year % 400 == 0))
                ExtraDay = 1;
        MonthDays[2] += ExtraDay;

        /******************Validation********************************/

        if (month <= 0 || month > 12)
                return -1;  // error

        if (day <= 0 || day > MonthDays[month])
                return -2;  // error

        /****************Calculation of t***************************/
        for (i = 1; i <= month; i++)
                temp += MonthDays[i - 1];
        temp += day;
        
        decimal_date = year + (temp - 1) / (365.0f + ExtraDay);

        return 0;   // OK
}

int WMM_GeodeticToSpherical(WMMtype_CoordGeodetic * CoordGeodetic, WMMtype_CoordSpherical * CoordSpherical)
// Converts Geodetic coordinates to Spherical coordinates
// Convert geodetic coordinates, (defined by the WGS-84
// reference ellipsoid), to Earth Centered Earth Fixed Cartesian
// coordinates, and then to spherical coordinates.
{
        float CosLat, SinLat, rc, xp, zp;       // all local variables

        CosLat = cosf(CoordGeodetic->phi * DEG2RAD);
        SinLat = sinf(CoordGeodetic->phi * DEG2RAD);

        // compute the local radius of curvature on the WGS-84 reference ellipsoid
        rc = Ellip.a / sqrtf(1.0f - Ellip.epssq * SinLat * SinLat);

        // compute ECEF Cartesian coordinates of specified point (for longitude=0)

        xp = (rc + CoordGeodetic->HeightAboveEllipsoid) * CosLat;
        zp = (rc * (1.0f - Ellip.epssq) + CoordGeodetic->HeightAboveEllipsoid) * SinLat;

        // compute spherical radius and angle lambda and phi of specified point

        CoordSpherical->r = sqrtf(xp * xp + zp * zp);
        CoordSpherical->phig = asinf(zp / CoordSpherical->r) * RAD2DEG; // geocentric latitude
        CoordSpherical->lambda = CoordGeodetic->lambda; // longitude

        return 0;   // OK
}