Merged in f5soh/librepilot/LP-607_world_mag_model_2015v2 (pull request #526)

[librepilot.git] / flight / libraries / WorldMagModel.c

/**
 ******************************************************************************
 *
 * @file       WorldMagModel.c
 * @author     The LibrePilot Project, http://www.librepilot.org Copyright (C) 2015-2019.
 *             The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
 * @brief      Source file for the World Magnetic Model
 *             This is a port of code available from the US NOAA.
 *
 *             The hard coded coefficients should be valid until 2020.
 *
 *             Updated coeffs from ..
 *             http://www.ngdc.noaa.gov/geomag/WMM/wmm_ddownload.shtml
 *
 *             NASA C source code ..
 *             http://www.ngdc.noaa.gov/geomag/WMM/wmm_wdownload.shtml
 *
 *             Major changes include:
 *                - No geoid model (altitude must be geodetic WGS-84)
 *                - Floating point calculation (not double precision)
 *                - Hard coded coefficients for model
 *                - Elimination of user interface
 *                - Elimination of dynamic memory allocation
 *
 * @see        The GNU Public License (GPL) Version 3
 *
 *****************************************************************************/
/*
 * 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, write to the Free Software Foundation, Inc.,
 * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 */

#include "openpilot.h"

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

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

#define MALLOC(x) pios_malloc(x)
#define FREE(x)   vPortFree(x)
// #define MALLOC(x) malloc(x)
// #define FREE(x) free(x)

// http://reviews.openpilot.org/cru/OPReview-436#c6476 :
// first column not used but it will be optimized out by compiler
static const float CoeffFile[91][6] = {
    { 0.0f,  0.0f,  0.0f,      0.0f,     0.0f,   0.0f   },
    { 1.0f,  0.0f,  -29438.2f, 0.0f,     7.0f,   0.0f   },
    { 1.0f,  1.0f,  -1493.5f,  4796.3f,  9.0f,   -30.2f },
    { 2.0f,  0.0f,  -2444.5f,  0.0f,     -11.0f, 0.0f   },
    { 2.0f,  1.0f,  3014.7f,   -2842.4f, -6.2f,  -29.6f },
    { 2.0f,  2.0f,  1679.0f,   -638.8f,  0.3f,   -17.3f },
    { 3.0f,  0.0f,  1351.8f,   0.0f,     2.4f,   0.0f   },
    { 3.0f,  1.0f,  -2351.6f,  -113.7f,  -5.7f,  6.5f   },
    { 3.0f,  2.0f,  1223.6f,   246.5f,   2.0f,   -0.8f  },
    { 3.0f,  3.0f,  582.3f,    -537.4f,  -11.0f, -2.0f  },
    { 4.0f,  0.0f,  907.5f,    0.0f,     -0.8f,  0.0f   },
    { 4.0f,  1.0f,  814.8f,    283.3f,   -0.9f,  -0.4f  },
    { 4.0f,  2.0f,  117.8f,    -188.6f,  -6.5f,  5.8f   },
    { 4.0f,  3.0f,  -335.6f,   180.7f,   5.2f,   3.8f   },
    { 4.0f,  4.0f,  69.7f,     -330.0f,  -4.0f,  -3.5f  },
    { 5.0f,  0.0f,  -232.9f,   0.0f,     -0.3f,  0.0f   },
    { 5.0f,  1.0f,  360.1f,    46.9f,    0.6f,   0.2f   },
    { 5.0f,  2.0f,  191.7f,    196.5f,   -0.8f,  2.3f   },
    { 5.0f,  3.0f,  -141.3f,   -119.9f,  0.1f,   -0.0f  },
    { 5.0f,  4.0f,  -157.2f,   16.0f,    1.2f,   3.3f   },
    { 5.0f,  5.0f,  7.7f,      100.6f,   1.4f,   -0.6f  },
    { 6.0f,  0.0f,  69.4f,     0.0f,     -0.8f,  0.0f   },
    { 6.0f,  1.0f,  67.7f,     -20.1f,   -0.5f,  0.3f   },
    { 6.0f,  2.0f,  72.3f,     32.8f,    -0.1f,  -1.5f  },
    { 6.0f,  3.0f,  -129.1f,   59.1f,    1.6f,   -1.2f  },
    { 6.0f,  4.0f,  -28.4f,    -67.1f,   -1.6f,  0.4f   },
    { 6.0f,  5.0f,  13.6f,     8.1f,     0.0f,   0.2f   },
    { 6.0f,  6.0f,  -70.3f,    61.9f,    1.2f,   1.3f   },
    { 7.0f,  0.0f,  81.7f,     0.0f,     -0.3f,  0.0f   },
    { 7.0f,  1.0f,  -75.9f,    -54.3f,   -0.2f,  0.6f   },
    { 7.0f,  2.0f,  -7.1f,     -19.5f,   -0.3f,  0.5f   },
    { 7.0f,  3.0f,  52.2f,     6.0f,     0.9f,   -0.8f  },
    { 7.0f,  4.0f,  15.0f,     24.5f,    0.1f,   -0.2f  },
    { 7.0f,  5.0f,  9.1f,      3.5f,     -0.6f,  -1.1f  },
    { 7.0f,  6.0f,  -3.0f,     -27.7f,   -0.9f,  0.1f   },
    { 7.0f,  7.0f,  5.9f,      -2.9f,    0.7f,   0.2f   },
    { 8.0f,  0.0f,  24.2f,     0.0f,     -0.1f,  0.0f   },
    { 8.0f,  1.0f,  8.9f,      10.1f,    0.2f,   -0.4f  },
    { 8.0f,  2.0f,  -16.9f,    -18.3f,   -0.2f,  0.6f   },
    { 8.0f,  3.0f,  -3.1f,     13.3f,    0.5f,   -0.1f  },
    { 8.0f,  4.0f,  -20.7f,    -14.5f,   -0.1f,  0.6f   },
    { 8.0f,  5.0f,  13.3f,     16.2f,    0.4f,   -0.2f  },
    { 8.0f,  6.0f,  11.6f,     6.0f,     0.4f,   -0.5f  },
    { 8.0f,  7.0f,  -16.3f,    -9.2f,    -0.1f,  0.5f   },
    { 8.0f,  8.0f,  -2.1f,     2.4f,     0.4f,   0.1f   },
    { 9.0f,  0.0f,  5.5f,      0.0f,     -0.1f,  0.0f   },
    { 9.0f,  1.0f,  8.8f,      -21.8f,   -0.1f,  -0.3f  },
    { 9.0f,  2.0f,  3.0f,      10.7f,    -0.0f,  0.1f   },
    { 9.0f,  3.0f,  -3.2f,     11.8f,    0.4f,   -0.4f  },
    { 9.0f,  4.0f,  0.6f,      -6.8f,    -0.4f,  0.3f   },
    { 9.0f,  5.0f,  -13.2f,    -6.9f,    0.0f,   0.1f   },
    { 9.0f,  6.0f,  -0.1f,     7.9f,     0.3f,   -0.0f  },
    { 9.0f,  7.0f,  8.7f,      1.0f,     0.0f,   -0.1f  },
    { 9.0f,  8.0f,  -9.1f,     -3.9f,    -0.0f,  0.5f   },
    { 9.0f,  9.0f,  -10.4f,    8.5f,     -0.3f,  0.2f   },
    { 10.0f, 0.0f,  -2.0f,     0.0f,     0.0f,   0.0f   },
    { 10.0f, 1.0f,  -6.1f,     3.3f,     -0.0f,  0.0f   },
    { 10.0f, 2.0f,  0.2f,      -0.4f,    -0.1f,  0.1f   },
    { 10.0f, 3.0f,  0.6f,      4.6f,     0.2f,   -0.2f  },
    { 10.0f, 4.0f,  -0.5f,     4.4f,     -0.1f,  0.1f   },
    { 10.0f, 5.0f,  1.8f,      -7.9f,    -0.2f,  -0.1f  },
    { 10.0f, 6.0f,  -0.7f,     -0.6f,    -0.0f,  0.1f   },
    { 10.0f, 7.0f,  2.2f,      -4.2f,    -0.1f,  -0.0f  },
    { 10.0f, 8.0f,  2.4f,      -2.9f,    -0.2f,  -0.1f  },
    { 10.0f, 9.0f,  -1.8f,     -1.1f,    -0.1f,  0.2f   },
    { 10.0f, 10.0f, -3.6f,     -8.8f,    -0.0f,  -0.0f  },
    { 11.0f, 0.0f,  3.0f,      0.0f,     -0.0f,  0.0f   },
    { 11.0f, 1.0f,  -1.4f,     -0.0f,    0.0f,   0.0f   },
    { 11.0f, 2.0f,  -2.3f,     2.1f,     -0.0f,  0.1f   },
    { 11.0f, 3.0f,  2.1f,      -0.6f,    0.0f,   0.0f   },
    { 11.0f, 4.0f,  -0.8f,     -1.1f,    -0.0f,  0.1f   },
    { 11.0f, 5.0f,  0.6f,      0.7f,     -0.1f,  -0.0f  },
    { 11.0f, 6.0f,  -0.7f,     -0.2f,    0.0f,   -0.0f  },
    { 11.0f, 7.0f,  0.1f,      -2.1f,    -0.0f,  0.1f   },
    { 11.0f, 8.0f,  1.7f,      -1.5f,    -0.0f,  -0.0f  },
    { 11.0f, 9.0f,  -0.2f,     -2.6f,    -0.1f,  -0.1f  },
    { 11.0f, 10.0f, 0.4f,      -2.0f,    -0.0f,  -0.0f  },
    { 11.0f, 11.0f, 3.5f,      -2.3f,    -0.1f,  -0.1f  },
    { 12.0f, 0.0f,  -2.0f,     0.0f,     0.0f,   0.0f   },
    { 12.0f, 1.0f,  -0.1f,     -1.0f,    0.0f,   -0.0f  },
    { 12.0f, 2.0f,  0.5f,      0.3f,     -0.0f,  0.0f   },
    { 12.0f, 3.0f,  1.2f,      1.8f,     0.0f,   -0.1f  },
    { 12.0f, 4.0f,  -0.9f,     -2.2f,    -0.1f,  0.1f   },
    { 12.0f, 5.0f,  0.9f,      0.3f,     -0.0f,  -0.0f  },
    { 12.0f, 6.0f,  0.1f,      0.7f,     0.0f,   0.0f   },
    { 12.0f, 7.0f,  0.6f,      -0.1f,    -0.0f,  -0.0f  },
    { 12.0f, 8.0f,  -0.4f,     0.3f,     0.0f,   0.0f   },
    { 12.0f, 9.0f,  -0.5f,     0.2f,     -0.0f,  0.0f   },
    { 12.0f, 10.0f, 0.2f,      -0.9f,    -0.0f,  -0.0f  },
    { 12.0f, 11.0f, -0.9f,     -0.2f,    -0.0f,  0.0f   },
    { 12.0f, 12.0f, -0.0f,     0.8f,     -0.1f,  -0.1f  }
};

static WMMtype_Ellipsoid *Ellip = NULL;
static WMMtype_MagneticModel *MagneticModel = NULL;
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
{
    if (!Ellip) {
        return -1; // invalid pointer
    }
    if (!MagneticModel) {
        return -2; // invalid pointer
    }
    // Sets WGS-84 parameters
    Ellip->a     = 6378.137f;   // semi-major axis of the ellipsoid in km
    Ellip->b     = 6356.7523142f;       // semi-minor axis of the ellipsoid in km
    Ellip->fla   = 1.0f / 298.257223563f;     // flattening
    Ellip->eps   = sqrt(1 - (Ellip->b * Ellip->b) / (Ellip->a * Ellip->a));   // first eccentricity
    Ellip->epssq = (Ellip->eps * Ellip->eps); // first eccentricity squared
    Ellip->re    = 6371.2f;    // 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;

    // Really, Really needs to be read from a file - out of date in 2020 at latest
    MagneticModel->EditionDate = 0.0f; /* OP change. Originally 5.7863328170559505e-307, truncates to 0.0f */
    MagneticModel->epoch = 2015.0f;
    sprintf(MagneticModel->ModelName, "WMM-2015v2");

    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 < -90.0f) {
        return -1; // error
    }
    if (Lat > 90.0f) {
        return -2; // error
    }
    if (Lon < -180.0f) {
        return -3; // error
    }
    if (Lon > 180.0f) {
        return -4; // error
    }
    // ***********
    // allocated required memory

// Ellip = NULL;
// MagneticModel = NULL;

// MagneticModel = NULL;
// CoordGeodetic = NULL;
// GeoMagneticElements = NULL;

    Ellip = (WMMtype_Ellipsoid *)MALLOC(sizeof(WMMtype_Ellipsoid));
    MagneticModel = (WMMtype_MagneticModel *)MALLOC(sizeof(WMMtype_MagneticModel));

    WMMtype_CoordSpherical *CoordSpherical = (WMMtype_CoordSpherical *)MALLOC(sizeof(WMMtype_CoordSpherical));
    WMMtype_CoordGeodetic *CoordGeodetic   = (WMMtype_CoordGeodetic *)MALLOC(sizeof(WMMtype_CoordGeodetic));
    WMMtype_GeoMagneticElements *GeoMagneticElements = (WMMtype_GeoMagneticElements *)MALLOC(sizeof(WMMtype_GeoMagneticElements));

    if (!Ellip || !MagneticModel || !CoordSpherical || !CoordGeodetic || !GeoMagneticElements) {
        returned = -5; // error
    }
    // ***********

    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 geodetic 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;
            B[1] = GeoMagneticElements->Y;
            B[2] = GeoMagneticElements->Z;
        }
    }

    // ***********
    // free allocated memory

    if (GeoMagneticElements) {
        FREE(GeoMagneticElements);
    }

    if (CoordGeodetic) {
        FREE(CoordGeodetic);
    }

    if (CoordSpherical) {
        FREE(CoordSpherical);
    }

    if (MagneticModel) {
        FREE(MagneticModel);
        MagneticModel = NULL;
    }

    if (Ellip) {
        FREE(Ellip);
        Ellip = NULL;
    }

    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;

    // ********
    // allocate required memory

    WMMtype_LegendreFunction *LegendreFunction = (WMMtype_LegendreFunction *)MALLOC(sizeof(WMMtype_LegendreFunction));
    WMMtype_SphericalHarmonicVariables *SphVariables = (WMMtype_SphericalHarmonicVariables *)MALLOC(sizeof(WMMtype_SphericalHarmonicVariables));

    if (!LegendreFunction || !SphVariables) {
        returned = -1; // memory allocation error
    }
    // ********

    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
        }
    }

    // ********
    // free allocated memory

    if (SphVariables) {
        FREE(SphVariables);
    }

    if (LegendreFunction) {
        FREE(LegendreFunction);
    }

    // ********

    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(DEG2RAD(CoordSpherical->lambda));
    sin_lambda = sinf(DEG2RAD(CoordSpherical->lambda));

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

    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(DEG2RAD(CoordSpherical->phig)); /* sinf  (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 sinf(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 = 0.0f;
    MagneticResults->By = 0.0f;
    MagneticResults->Bx = 0.0f;

    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 cosf(m p) + h sinf(m p)] P (sinf(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 cosf(m p) + h sinf(m p)] dP (sinf(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 cosf(m p) + h sinf(m p)] dP (sinf(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(DEG2RAD(CoordSpherical->phig));
    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 = 0.0f;
    MagneticResults->By = 0.0f;
    MagneticResults->Bx = 0.0f;

    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 cosf(m p) + h sinf(m p)] P (sinf(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 cosf(m p) + h sinf(m p)] dP (sinf(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 cosf(m p) + h sinf(m p)] dP (sinf(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(DEG2RAD(CoordSpherical->phig));
    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 = DEG2RAD(CoordSpherical->phig - CoordGeodetic->phi);

    /* 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 = RAD2DEG(atan2f(GeoMagneticElements->Y, GeoMagneticElements->X));
    GeoMagneticElements->Incl = RAD2DEG(atan2f(GeoMagneticElements->Z, GeoMagneticElements->H));

    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 =
        180.0f / M_PI_F * (MagneticElements->X * MagneticElements->Ydot -
                           MagneticElements->Y * MagneticElements->Xdot) / (MagneticElements->H * MagneticElements->H);
    MagneticElements->Incldot =
        180.0f / M_PI_F * (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 sinf^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:              cosf(colatitude) or sinf(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 = sinf(latitude) (or cosf(colatitude) ).
   However, the WMM Geomagnetic routines requires dP(n,m)(x)/dlatitude.
   Hence the derivatives are multiplied by sinf(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     = (float *)MALLOC(sizeof(float) * NUMPCUP);
    float *f2     = (float *)MALLOC(sizeof(float) * NUMPCUP);
    float *PreSqr = (float *)MALLOC(sizeof(float) * NUMPCUP);

    if (!PreSqr || !f2 || !f1) { // memory allocation error
        if (PreSqr) {
            FREE(PreSqr);
        }
        if (f2) {
            FREE(f2);
        }
        if (f1) {
            FREE(f1);
        }

        return -1;
    }

    /*
     * Note: OP code change to avoid floating point equality test.
     * Was: if (fabs(x) == 1.0)
     */
    if (fabsf(x) - 1.0f < 1e-9f) {
        FREE(PreSqr);
        FREE(f2);
        FREE(f1);

        // printf("Error in PcupHigh: derivative cannot be calculated at poles\n");
        return -2;
    }

    /* OP Change: 1.0e-280 is too small to store in a float - the compiler truncates
     * it to 0.0f, which is bad as the code below divides by scalef. */
    scalef = 1.0e-20f;

    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 = sinf (geocentric latitude) */
    z        = sqrtf((1.0f - x) * (1.0f + x));
    pm2      = 1.0f;
    Pcup[0]  = 1.0f;
    dPcup[0] = 0.0f;
    if (nMax == 0) {
        FREE(PreSqr);
        FREE(f2);
        FREE(f1);
        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;

    // *********
    // free allocated memory

    FREE(PreSqr);
    FREE(f2);
    FREE(f1);

    // *********

    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:              cosf(colatitude) or sinf(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 = (float *)MALLOC(sizeof(float) * NUMPCUP);

    if (!schmidtQuasiNorm) { // memory allocation error
        return -1;
    }

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

    /*sinf (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] = 1.0f;
    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 */
        }
    }

    FREE(schmidtQuasiNorm);

    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 *PcupS = (float *)MALLOC(sizeof(float) * NUMPCUPS);

    if (!PcupS) {
        return -1; // memory allocation error
    }
    PcupS[0] = 1;
    schmidtQuasiNorm1   = 1.0f;

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

    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 cosf(m p) + h sinf(m p)] dP (sinf(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;
    }

    FREE(PcupS);

    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 *PcupS = (float *)MALLOC(sizeof(float) * NUMPCUPS);

    if (!PcupS) {
        return -1; // memory allocation error
    }
    PcupS[0] = 1;
    schmidtQuasiNorm1   = 1.0f;

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

    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 cosf(m p) + h sinf(m p)] dP (sinf(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;
    }

    FREE(PcupS);

    return 0; // OK
}

/**
 * @brief Comput the MainFieldCoeffH accounting for the date
 */
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(DEG2RAD(CoordGeodetic->phi));
    SinLat = sinf(DEG2RAD(CoordGeodetic->phi));

    // 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   = RAD2DEG(asinf(zp / CoordSpherical->r));  // geocentric latitude
    CoordSpherical->lambda = CoordGeodetic->lambda; // longitude

    return 0; // OK
}