android/hardware/GeomagneticField.java - platform/prebuilts/fullsdk/sources/android-29 - Git at Google

 /*
  * Copyright (C) 2009 The Android Open Source Project
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
  *
  *      http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  * See the License for the specific language governing permissions and
  * limitations under the License.
  */

 package android.hardware;

 import java.util.GregorianCalendar;

 /**
  * Estimates magnetic field at a given point on
  * Earth, and in particular, to compute the magnetic declination from true
  * north.
  *
  * <p>This uses the World Magnetic Model produced by the United States National
  * Geospatial-Intelligence Agency.  More details about the model can be found at
  * <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>.
  * This class currently uses WMM-2015 which is valid until 2020, but should
  * produce acceptable results for several years after that. Future versions of
  * Android may use a newer version of the model.
  */
 public class GeomagneticField {
     // The magnetic field at a given point, in nanoteslas in geodetic
     // coordinates.
     private float mX;
     private float mY;
     private float mZ;

     // Geocentric coordinates -- set by computeGeocentricCoordinates.
     private float mGcLatitudeRad;
     private float mGcLongitudeRad;
     private float mGcRadiusKm;

     // Constants from WGS84 (the coordinate system used by GPS)
     static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f;
     static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523142f;
     static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f;

     // These coefficients and the formulae used below are from:
     // NOAA Technical Report: The US/UK World Magnetic Model for 2015-2020
     static private final float[][] G_COEFF = new float[][] {
         { 0.0f },
         { -29438.5f, -1501.1f },
         { -2445.3f, 3012.5f, 1676.6f },
         { 1351.1f, -2352.3f, 1225.6f, 581.9f },
         { 907.2f, 813.7f, 120.3f, -335.0f, 70.3f },
         { -232.6f, 360.1f, 192.4f, -141.0f, -157.4f, 4.3f },
         { 69.5f, 67.4f, 72.8f, -129.8f, -29.0f, 13.2f, -70.9f },
         { 81.6f, -76.1f, -6.8f, 51.9f, 15.0f, 9.3f, -2.8f, 6.7f },
         { 24.0f, 8.6f, -16.9f, -3.2f, -20.6f, 13.3f, 11.7f, -16.0f, -2.0f },
         { 5.4f, 8.8f, 3.1f, -3.1f, 0.6f, -13.3f, -0.1f, 8.7f, -9.1f, -10.5f },
         { -1.9f, -6.5f, 0.2f, 0.6f, -0.6f, 1.7f, -0.7f, 2.1f, 2.3f, -1.8f, -3.6f },
         { 3.1f, -1.5f, -2.3f, 2.1f, -0.9f, 0.6f, -0.7f, 0.2f, 1.7f, -0.2f, 0.4f, 3.5f },
         { -2.0f, -0.3f, 0.4f, 1.3f, -0.9f, 0.9f, 0.1f, 0.5f, -0.4f, -0.4f, 0.2f, -0.9f, 0.0f } };

     static private final float[][] H_COEFF = new float[][] {
         { 0.0f },
         { 0.0f, 4796.2f },
         { 0.0f, -2845.6f, -642.0f },
         { 0.0f, -115.3f, 245.0f, -538.3f },
         { 0.0f, 283.4f, -188.6f, 180.9f, -329.5f },
         { 0.0f, 47.4f, 196.9f, -119.4f, 16.1f, 100.1f },
         { 0.0f, -20.7f, 33.2f, 58.8f, -66.5f, 7.3f, 62.5f },
         { 0.0f, -54.1f, -19.4f, 5.6f, 24.4f, 3.3f, -27.5f, -2.3f },
         { 0.0f, 10.2f, -18.1f, 13.2f, -14.6f, 16.2f, 5.7f, -9.1f, 2.2f },
         { 0.0f, -21.6f, 10.8f, 11.7f, -6.8f, -6.9f, 7.8f, 1.0f, -3.9f, 8.5f },
         { 0.0f, 3.3f, -0.3f, 4.6f, 4.4f, -7.9f, -0.6f, -4.1f, -2.8f, -1.1f, -8.7f },
         { 0.0f, -0.1f, 2.1f, -0.7f, -1.1f, 0.7f, -0.2f, -2.1f, -1.5f, -2.5f, -2.0f, -2.3f },
         { 0.0f, -1.0f, 0.5f, 1.8f, -2.2f, 0.3f, 0.7f, -0.1f, 0.3f, 0.2f, -0.9f, -0.2f, 0.7f } };

     static private final float[][] DELTA_G = new float[][] {
         { 0.0f },
         { 10.7f, 17.9f },
         { -8.6f, -3.3f, 2.4f },
         { 3.1f, -6.2f, -0.4f, -10.4f },
         { -0.4f, 0.8f, -9.2f, 4.0f, -4.2f },
         { -0.2f, 0.1f, -1.4f, 0.0f, 1.3f, 3.8f },
         { -0.5f, -0.2f, -0.6f, 2.4f, -1.1f, 0.3f, 1.5f },
         { 0.2f, -0.2f, -0.4f, 1.3f, 0.2f, -0.4f, -0.9f, 0.3f },
         { 0.0f, 0.1f, -0.5f, 0.5f, -0.2f, 0.4f, 0.2f, -0.4f, 0.3f },
         { 0.0f, -0.1f, -0.1f, 0.4f, -0.5f, -0.2f, 0.1f, 0.0f, -0.2f, -0.1f },
         { 0.0f, 0.0f, -0.1f, 0.3f, -0.1f, -0.1f, -0.1f, 0.0f, -0.2f, -0.1f, -0.2f },
         { 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, -0.1f },
         { 0.1f, 0.0f, 0.0f, 0.1f, -0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };

     static private final float[][] DELTA_H = new float[][] {
         { 0.0f },
         { 0.0f, -26.8f },
         { 0.0f, -27.1f, -13.3f },
         { 0.0f, 8.4f, -0.4f, 2.3f },
         { 0.0f, -0.6f, 5.3f, 3.0f, -5.3f },
         { 0.0f, 0.4f, 1.6f, -1.1f, 3.3f, 0.1f },
         { 0.0f, 0.0f, -2.2f, -0.7f, 0.1f, 1.0f, 1.3f },
         { 0.0f, 0.7f, 0.5f, -0.2f, -0.1f, -0.7f, 0.1f, 0.1f },
         { 0.0f, -0.3f, 0.3f, 0.3f, 0.6f, -0.1f, -0.2f, 0.3f, 0.0f },
         { 0.0f, -0.2f, -0.1f, -0.2f, 0.1f, 0.1f, 0.0f, -0.2f, 0.4f, 0.3f },
         { 0.0f, 0.1f, -0.1f, 0.0f, 0.0f, -0.2f, 0.1f, -0.1f, -0.2f, 0.1f, -0.1f },
         { 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, -0.1f },
         { 0.0f, 0.0f, 0.0f, -0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };

     static private final long BASE_TIME =
             new GregorianCalendar(2015, 1, 1).getTimeInMillis();

     // The ratio between the Gauss-normalized associated Legendre functions and
     // the Schmid quasi-normalized ones. Compute these once staticly since they
     // don't depend on input variables at all.
     static private final float[][] SCHMIDT_QUASI_NORM_FACTORS =
         computeSchmidtQuasiNormFactors(G_COEFF.length);

     /**
      * Estimate the magnetic field at a given point and time.
      *
      * @param gdLatitudeDeg
      *            Latitude in WGS84 geodetic coordinates -- positive is east.
      * @param gdLongitudeDeg
      *            Longitude in WGS84 geodetic coordinates -- positive is north.
      * @param altitudeMeters
      *            Altitude in WGS84 geodetic coordinates, in meters.
      * @param timeMillis
      *            Time at which to evaluate the declination, in milliseconds
      *            since January 1, 1970. (approximate is fine -- the declination
      *            changes very slowly).
      */
     public GeomagneticField(float gdLatitudeDeg,
                             float gdLongitudeDeg,
                             float altitudeMeters,
                             long timeMillis) {
         final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients.

         // We don't handle the north and south poles correctly -- pretend that
         // we're not quite at them to avoid crashing.
         gdLatitudeDeg = Math.min(90.0f - 1e-5f,
                                  Math.max(-90.0f + 1e-5f, gdLatitudeDeg));
         computeGeocentricCoordinates(gdLatitudeDeg,
                                      gdLongitudeDeg,
                                      altitudeMeters);

         assert G_COEFF.length == H_COEFF.length;

         // Note: LegendreTable computes associated Legendre functions for
         // cos(theta).  We want the associated Legendre functions for
         // sin(latitude), which is the same as cos(PI/2 - latitude), except the
         // derivate will be negated.
         LegendreTable legendre =
             new LegendreTable(MAX_N - 1,
                               (float) (Math.PI / 2.0 - mGcLatitudeRad));

         // Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in
         // 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times).
         float[] relativeRadiusPower = new float[MAX_N + 2];
         relativeRadiusPower[0] = 1.0f;
         relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm;
         for (int i = 2; i < relativeRadiusPower.length; ++i) {
             relativeRadiusPower[i] = relativeRadiusPower[i - 1] *
                 relativeRadiusPower[1];
         }

         // Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N --
         // this is much faster than calling Math.sin and Math.com MAX_N+1 times.
         float[] sinMLon = new float[MAX_N];
         float[] cosMLon = new float[MAX_N];
         sinMLon[0] = 0.0f;
         cosMLon[0] = 1.0f;
         sinMLon[1] = (float) Math.sin(mGcLongitudeRad);
         cosMLon[1] = (float) Math.cos(mGcLongitudeRad);

         for (int m = 2; m < MAX_N; ++m) {
             // Standard expansions for sin((m-x)*theta + x*theta) and
             // cos((m-x)*theta + x*theta).
             int x = m >> 1;
             sinMLon[m] = sinMLon[m-x] * cosMLon[x] + cosMLon[m-x] * sinMLon[x];
             cosMLon[m] = cosMLon[m-x] * cosMLon[x] - sinMLon[m-x] * sinMLon[x];
         }

         float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad);
         float yearsSinceBase =
             (timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f);

         // We now compute the magnetic field strength given the geocentric
         // location. The magnetic field is the derivative of the potential
         // function defined by the model. See NOAA Technical Report: The US/UK
         // World Magnetic Model for 2015-2020 for the derivation.
         float gcX = 0.0f;  // Geocentric northwards component.
         float gcY = 0.0f;  // Geocentric eastwards component.
         float gcZ = 0.0f;  // Geocentric downwards component.

         for (int n = 1; n < MAX_N; n++) {
             for (int m = 0; m <= n; m++) {
                 // Adjust the coefficients for the current date.
                 float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m];
                 float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m];

                 // Negative derivative with respect to latitude, divided by
                 // radius.  This looks like the negation of the version in the
                 // NOAA Techincal report because that report used
                 // P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the
                 // derivative with respect to theta is negated.
                 gcX += relativeRadiusPower[n+2]
                     * (g * cosMLon[m] + h * sinMLon[m])
                     * legendre.mPDeriv[n][m]
                     * SCHMIDT_QUASI_NORM_FACTORS[n][m];

                 // Negative derivative with respect to longitude, divided by
                 // radius.
                 gcY += relativeRadiusPower[n+2] * m
                     * (g * sinMLon[m] - h * cosMLon[m])
                     * legendre.mP[n][m]
                     * SCHMIDT_QUASI_NORM_FACTORS[n][m]
                     * inverseCosLatitude;

                 // Negative derivative with respect to radius.
                 gcZ -= (n + 1) * relativeRadiusPower[n+2]
                     * (g * cosMLon[m] + h * sinMLon[m])
                     * legendre.mP[n][m]
                     * SCHMIDT_QUASI_NORM_FACTORS[n][m];
             }
         }

         // Convert back to geodetic coordinates.  This is basically just a
         // rotation around the Y-axis by the difference in latitudes between the
         // geocentric frame and the geodetic frame.
         double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad;
         mX = (float) (gcX * Math.cos(latDiffRad)
                       + gcZ * Math.sin(latDiffRad));
         mY = gcY;
         mZ = (float) (- gcX * Math.sin(latDiffRad)
                       + gcZ * Math.cos(latDiffRad));
     }

     /**
      * @return The X (northward) component of the magnetic field in nanoteslas.
      */
     public float getX() {
         return mX;
     }

     /**
      * @return The Y (eastward) component of the magnetic field in nanoteslas.
      */
     public float getY() {
         return mY;
     }

     /**
      * @return The Z (downward) component of the magnetic field in nanoteslas.
      */
     public float getZ() {
         return mZ;
     }

     /**
      * @return The declination of the horizontal component of the magnetic
      *         field from true north, in degrees (i.e. positive means the
      *         magnetic field is rotated east that much from true north).
      */
     public float getDeclination() {
         return (float) Math.toDegrees(Math.atan2(mY, mX));
     }

     /**
      * @return The inclination of the magnetic field in degrees -- positive
      *         means the magnetic field is rotated downwards.
      */
     public float getInclination() {
         return (float) Math.toDegrees(Math.atan2(mZ,
                                                  getHorizontalStrength()));
     }

     /**
      * @return  Horizontal component of the field strength in nanoteslas.
      */
     public float getHorizontalStrength() {
         return (float) Math.hypot(mX, mY);
     }

     /**
      * @return  Total field strength in nanoteslas.
      */
     public float getFieldStrength() {
         return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ);
     }

     /**
      * @param gdLatitudeDeg
      *            Latitude in WGS84 geodetic coordinates.
      * @param gdLongitudeDeg
      *            Longitude in WGS84 geodetic coordinates.
      * @param altitudeMeters
      *            Altitude above sea level in WGS84 geodetic coordinates.
      * @return Geocentric latitude (i.e. angle between closest point on the
      *         equator and this point, at the center of the earth.
      */
     private void computeGeocentricCoordinates(float gdLatitudeDeg,
                                               float gdLongitudeDeg,
                                               float altitudeMeters) {
         float altitudeKm = altitudeMeters / 1000.0f;
         float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM;
         float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM;
         double gdLatRad = Math.toRadians(gdLatitudeDeg);
         float clat = (float) Math.cos(gdLatRad);
         float slat = (float) Math.sin(gdLatRad);
         float tlat = slat / clat;
         float latRad =
             (float) Math.sqrt(a2 * clat * clat + b2 * slat * slat);

         mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2)
                                            / (latRad * altitudeKm + a2));

         mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg);

         float radSq = altitudeKm * altitudeKm
             + 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat +
                                                  b2 * slat * slat)
             + (a2 * a2 * clat * clat + b2 * b2 * slat * slat)
             / (a2 * clat * clat + b2 * slat * slat);
         mGcRadiusKm = (float) Math.sqrt(radSq);
     }


     /**
      * Utility class to compute a table of Gauss-normalized associated Legendre
      * functions P_n^m(cos(theta))
      */
     static private class LegendreTable {
         // These are the Gauss-normalized associated Legendre functions -- that
         // is, they are normal Legendre functions multiplied by
         // (n-m)!/(2n-1)!! (where (2n-1)!! = 1*3*5*...*2n-1)
         public final float[][] mP;

         // Derivative of mP, with respect to theta.
         public final float[][] mPDeriv;

         /**
          * @param maxN
          *            The maximum n- and m-values to support
          * @param thetaRad
          *            Returned functions will be Gauss-normalized
          *            P_n^m(cos(thetaRad)), with thetaRad in radians.
          */
         public LegendreTable(int maxN, float thetaRad) {
             // Compute the table of Gauss-normalized associated Legendre
             // functions using standard recursion relations. Also compute the
             // table of derivatives using the derivative of the recursion
             // relations.
             float cos = (float) Math.cos(thetaRad);
             float sin = (float) Math.sin(thetaRad);

             mP = new float[maxN + 1][];
             mPDeriv = new float[maxN + 1][];
             mP[0] = new float[] { 1.0f };
             mPDeriv[0] = new float[] { 0.0f };
             for (int n = 1; n <= maxN; n++) {
                 mP[n] = new float[n + 1];
                 mPDeriv[n] = new float[n + 1];
                 for (int m = 0; m <= n; m++) {
                     if (n == m) {
                         mP[n][m] = sin * mP[n - 1][m - 1];
                         mPDeriv[n][m] = cos * mP[n - 1][m - 1]
                             + sin * mPDeriv[n - 1][m - 1];
                     } else if (n == 1 || m == n - 1) {
                         mP[n][m] = cos * mP[n - 1][m];
                         mPDeriv[n][m] = -sin * mP[n - 1][m]
                             + cos * mPDeriv[n - 1][m];
                     } else {
                         assert n > 1 && m < n - 1;
                         float k = ((n - 1) * (n - 1) - m * m)
                             / (float) ((2 * n - 1) * (2 * n - 3));
                         mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m];
                         mPDeriv[n][m] = -sin * mP[n - 1][m]
                             + cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m];
                     }
                 }
             }
         }
     }

     /**
      * 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)!
      */
     private static float[][] computeSchmidtQuasiNormFactors(int maxN) {
         float[][] schmidtQuasiNorm = new float[maxN + 1][];
         schmidtQuasiNorm[0] = new float[] { 1.0f };
         for (int n = 1; n <= maxN; n++) {
             schmidtQuasiNorm[n] = new float[n + 1];
             schmidtQuasiNorm[n][0] =
                 schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n;
             for (int m = 1; m <= n; m++) {
                 schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1]
                     * (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1)
                                 / (float) (n + m));
             }
         }
         return schmidtQuasiNorm;
     }
 }
	/*
	* Copyright (C) 2009 The Android Open Source Project
	*
	* Licensed under the Apache License, Version 2.0 (the "License");
	* you may not use this file except in compliance with the License.
	* You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/

	package android.hardware;

	import java.util.GregorianCalendar;

	/**
	* Estimates magnetic field at a given point on
	* Earth, and in particular, to compute the magnetic declination from true
	* north.
	*
	* <p>This uses the World Magnetic Model produced by the United States National
	* Geospatial-Intelligence Agency. More details about the model can be found at
	* <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>.
	* This class currently uses WMM-2015 which is valid until 2020, but should
	* produce acceptable results for several years after that. Future versions of
	* Android may use a newer version of the model.
	*/
	public class GeomagneticField {
	// The magnetic field at a given point, in nanoteslas in geodetic
	// coordinates.
	private float mX;
	private float mY;
	private float mZ;

	// Geocentric coordinates -- set by computeGeocentricCoordinates.
	private float mGcLatitudeRad;
	private float mGcLongitudeRad;
	private float mGcRadiusKm;

	// Constants from WGS84 (the coordinate system used by GPS)
	static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f;
	static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523142f;
	static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f;

	// These coefficients and the formulae used below are from:
	// NOAA Technical Report: The US/UK World Magnetic Model for 2015-2020
	static private final float[][] G_COEFF = new float[][] {
	{ 0.0f },
	{ -29438.5f, -1501.1f },
	{ -2445.3f, 3012.5f, 1676.6f },
	{ 1351.1f, -2352.3f, 1225.6f, 581.9f },
	{ 907.2f, 813.7f, 120.3f, -335.0f, 70.3f },
	{ -232.6f, 360.1f, 192.4f, -141.0f, -157.4f, 4.3f },
	{ 69.5f, 67.4f, 72.8f, -129.8f, -29.0f, 13.2f, -70.9f },
	{ 81.6f, -76.1f, -6.8f, 51.9f, 15.0f, 9.3f, -2.8f, 6.7f },
	{ 24.0f, 8.6f, -16.9f, -3.2f, -20.6f, 13.3f, 11.7f, -16.0f, -2.0f },
	{ 5.4f, 8.8f, 3.1f, -3.1f, 0.6f, -13.3f, -0.1f, 8.7f, -9.1f, -10.5f },
	{ -1.9f, -6.5f, 0.2f, 0.6f, -0.6f, 1.7f, -0.7f, 2.1f, 2.3f, -1.8f, -3.6f },
	{ 3.1f, -1.5f, -2.3f, 2.1f, -0.9f, 0.6f, -0.7f, 0.2f, 1.7f, -0.2f, 0.4f, 3.5f },
	{ -2.0f, -0.3f, 0.4f, 1.3f, -0.9f, 0.9f, 0.1f, 0.5f, -0.4f, -0.4f, 0.2f, -0.9f, 0.0f } };

	static private final float[][] H_COEFF = new float[][] {
	{ 0.0f },
	{ 0.0f, 4796.2f },
	{ 0.0f, -2845.6f, -642.0f },
	{ 0.0f, -115.3f, 245.0f, -538.3f },
	{ 0.0f, 283.4f, -188.6f, 180.9f, -329.5f },
	{ 0.0f, 47.4f, 196.9f, -119.4f, 16.1f, 100.1f },
	{ 0.0f, -20.7f, 33.2f, 58.8f, -66.5f, 7.3f, 62.5f },
	{ 0.0f, -54.1f, -19.4f, 5.6f, 24.4f, 3.3f, -27.5f, -2.3f },
	{ 0.0f, 10.2f, -18.1f, 13.2f, -14.6f, 16.2f, 5.7f, -9.1f, 2.2f },
	{ 0.0f, -21.6f, 10.8f, 11.7f, -6.8f, -6.9f, 7.8f, 1.0f, -3.9f, 8.5f },
	{ 0.0f, 3.3f, -0.3f, 4.6f, 4.4f, -7.9f, -0.6f, -4.1f, -2.8f, -1.1f, -8.7f },
	{ 0.0f, -0.1f, 2.1f, -0.7f, -1.1f, 0.7f, -0.2f, -2.1f, -1.5f, -2.5f, -2.0f, -2.3f },
	{ 0.0f, -1.0f, 0.5f, 1.8f, -2.2f, 0.3f, 0.7f, -0.1f, 0.3f, 0.2f, -0.9f, -0.2f, 0.7f } };

	static private final float[][] DELTA_G = new float[][] {
	{ 0.0f },
	{ 10.7f, 17.9f },
	{ -8.6f, -3.3f, 2.4f },
	{ 3.1f, -6.2f, -0.4f, -10.4f },
	{ -0.4f, 0.8f, -9.2f, 4.0f, -4.2f },
	{ -0.2f, 0.1f, -1.4f, 0.0f, 1.3f, 3.8f },
	{ -0.5f, -0.2f, -0.6f, 2.4f, -1.1f, 0.3f, 1.5f },
	{ 0.2f, -0.2f, -0.4f, 1.3f, 0.2f, -0.4f, -0.9f, 0.3f },
	{ 0.0f, 0.1f, -0.5f, 0.5f, -0.2f, 0.4f, 0.2f, -0.4f, 0.3f },
	{ 0.0f, -0.1f, -0.1f, 0.4f, -0.5f, -0.2f, 0.1f, 0.0f, -0.2f, -0.1f },
	{ 0.0f, 0.0f, -0.1f, 0.3f, -0.1f, -0.1f, -0.1f, 0.0f, -0.2f, -0.1f, -0.2f },
	{ 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, -0.1f },
	{ 0.1f, 0.0f, 0.0f, 0.1f, -0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };

	static private final float[][] DELTA_H = new float[][] {
	{ 0.0f },
	{ 0.0f, -26.8f },
	{ 0.0f, -27.1f, -13.3f },
	{ 0.0f, 8.4f, -0.4f, 2.3f },
	{ 0.0f, -0.6f, 5.3f, 3.0f, -5.3f },
	{ 0.0f, 0.4f, 1.6f, -1.1f, 3.3f, 0.1f },
	{ 0.0f, 0.0f, -2.2f, -0.7f, 0.1f, 1.0f, 1.3f },
	{ 0.0f, 0.7f, 0.5f, -0.2f, -0.1f, -0.7f, 0.1f, 0.1f },
	{ 0.0f, -0.3f, 0.3f, 0.3f, 0.6f, -0.1f, -0.2f, 0.3f, 0.0f },
	{ 0.0f, -0.2f, -0.1f, -0.2f, 0.1f, 0.1f, 0.0f, -0.2f, 0.4f, 0.3f },
	{ 0.0f, 0.1f, -0.1f, 0.0f, 0.0f, -0.2f, 0.1f, -0.1f, -0.2f, 0.1f, -0.1f },
	{ 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, -0.1f },
	{ 0.0f, 0.0f, 0.0f, -0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } };

	static private final long BASE_TIME =
	new GregorianCalendar(2015, 1, 1).getTimeInMillis();

	// The ratio between the Gauss-normalized associated Legendre functions and
	// the Schmid quasi-normalized ones. Compute these once staticly since they
	// don't depend on input variables at all.
	static private final float[][] SCHMIDT_QUASI_NORM_FACTORS =
	computeSchmidtQuasiNormFactors(G_COEFF.length);

	/**
	* Estimate the magnetic field at a given point and time.
	*
	* @param gdLatitudeDeg
	* Latitude in WGS84 geodetic coordinates -- positive is east.
	* @param gdLongitudeDeg
	* Longitude in WGS84 geodetic coordinates -- positive is north.
	* @param altitudeMeters
	* Altitude in WGS84 geodetic coordinates, in meters.
	* @param timeMillis
	* Time at which to evaluate the declination, in milliseconds
	* since January 1, 1970. (approximate is fine -- the declination
	* changes very slowly).
	*/
	public GeomagneticField(float gdLatitudeDeg,
	float gdLongitudeDeg,
	float altitudeMeters,
	long timeMillis) {
	final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients.

	// We don't handle the north and south poles correctly -- pretend that
	// we're not quite at them to avoid crashing.
	gdLatitudeDeg = Math.min(90.0f - 1e-5f,
	Math.max(-90.0f + 1e-5f, gdLatitudeDeg));
	computeGeocentricCoordinates(gdLatitudeDeg,
	gdLongitudeDeg,
	altitudeMeters);

	assert G_COEFF.length == H_COEFF.length;

	// Note: LegendreTable computes associated Legendre functions for
	// cos(theta). We want the associated Legendre functions for
	// sin(latitude), which is the same as cos(PI/2 - latitude), except the
	// derivate will be negated.
	LegendreTable legendre =
	new LegendreTable(MAX_N - 1,
	(float) (Math.PI / 2.0 - mGcLatitudeRad));

	// Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in
	// 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times).
	float[] relativeRadiusPower = new float[MAX_N + 2];
	relativeRadiusPower[0] = 1.0f;
	relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm;
	for (int i = 2; i < relativeRadiusPower.length; ++i) {
	relativeRadiusPower[i] = relativeRadiusPower[i - 1] *
	relativeRadiusPower[1];
	}

	// Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N --
	// this is much faster than calling Math.sin and Math.com MAX_N+1 times.
	float[] sinMLon = new float[MAX_N];
	float[] cosMLon = new float[MAX_N];
	sinMLon[0] = 0.0f;
	cosMLon[0] = 1.0f;
	sinMLon[1] = (float) Math.sin(mGcLongitudeRad);
	cosMLon[1] = (float) Math.cos(mGcLongitudeRad);

	for (int m = 2; m < MAX_N; ++m) {
	// Standard expansions for sin((m-x)theta + xtheta) and
	// cos((m-x)theta + xtheta).
	int x = m >> 1;
	sinMLon[m] = sinMLon[m-x] * cosMLon[x] + cosMLon[m-x] * sinMLon[x];
	cosMLon[m] = cosMLon[m-x] * cosMLon[x] - sinMLon[m-x] * sinMLon[x];
	}

	float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad);
	float yearsSinceBase =
	(timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f);

	// We now compute the magnetic field strength given the geocentric
	// location. The magnetic field is the derivative of the potential
	// function defined by the model. See NOAA Technical Report: The US/UK
	// World Magnetic Model for 2015-2020 for the derivation.
	float gcX = 0.0f; // Geocentric northwards component.
	float gcY = 0.0f; // Geocentric eastwards component.
	float gcZ = 0.0f; // Geocentric downwards component.

	for (int n = 1; n < MAX_N; n++) {
	for (int m = 0; m <= n; m++) {
	// Adjust the coefficients for the current date.
	float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m];
	float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m];

	// Negative derivative with respect to latitude, divided by
	// radius. This looks like the negation of the version in the
	// NOAA Techincal report because that report used
	// P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the
	// derivative with respect to theta is negated.
	gcX += relativeRadiusPower[n+2]
	* (g * cosMLon[m] + h * sinMLon[m])
	* legendre.mPDeriv[n][m]
	* SCHMIDT_QUASI_NORM_FACTORS[n][m];

	// Negative derivative with respect to longitude, divided by
	// radius.
	gcY += relativeRadiusPower[n+2] * m
	* (g * sinMLon[m] - h * cosMLon[m])
	* legendre.mP[n][m]
	* SCHMIDT_QUASI_NORM_FACTORS[n][m]
	* inverseCosLatitude;

	// Negative derivative with respect to radius.
	gcZ -= (n + 1) * relativeRadiusPower[n+2]
	* (g * cosMLon[m] + h * sinMLon[m])
	* legendre.mP[n][m]
	* SCHMIDT_QUASI_NORM_FACTORS[n][m];
	}
	}

	// Convert back to geodetic coordinates. This is basically just a
	// rotation around the Y-axis by the difference in latitudes between the
	// geocentric frame and the geodetic frame.
	double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad;
	mX = (float) (gcX * Math.cos(latDiffRad)
	+ gcZ * Math.sin(latDiffRad));
	mY = gcY;
	mZ = (float) (- gcX * Math.sin(latDiffRad)
	+ gcZ * Math.cos(latDiffRad));
	}

	/**
	* @return The X (northward) component of the magnetic field in nanoteslas.
	*/
	public float getX() {
	return mX;
	}

	/**
	* @return The Y (eastward) component of the magnetic field in nanoteslas.
	*/
	public float getY() {
	return mY;
	}

	/**
	* @return The Z (downward) component of the magnetic field in nanoteslas.
	*/
	public float getZ() {
	return mZ;
	}

	/**
	* @return The declination of the horizontal component of the magnetic
	* field from true north, in degrees (i.e. positive means the
	* magnetic field is rotated east that much from true north).
	*/
	public float getDeclination() {
	return (float) Math.toDegrees(Math.atan2(mY, mX));
	}

	/**
	* @return The inclination of the magnetic field in degrees -- positive
	* means the magnetic field is rotated downwards.
	*/
	public float getInclination() {
	return (float) Math.toDegrees(Math.atan2(mZ,
	getHorizontalStrength()));
	}

	/**
	* @return Horizontal component of the field strength in nanoteslas.
	*/
	public float getHorizontalStrength() {
	return (float) Math.hypot(mX, mY);
	}

	/**
	* @return Total field strength in nanoteslas.
	*/
	public float getFieldStrength() {
	return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ);
	}

	/**
	* @param gdLatitudeDeg
	* Latitude in WGS84 geodetic coordinates.
	* @param gdLongitudeDeg
	* Longitude in WGS84 geodetic coordinates.
	* @param altitudeMeters
	* Altitude above sea level in WGS84 geodetic coordinates.
	* @return Geocentric latitude (i.e. angle between closest point on the
	* equator and this point, at the center of the earth.
	*/
	private void computeGeocentricCoordinates(float gdLatitudeDeg,
	float gdLongitudeDeg,
	float altitudeMeters) {
	float altitudeKm = altitudeMeters / 1000.0f;
	float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM;
	float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM;
	double gdLatRad = Math.toRadians(gdLatitudeDeg);
	float clat = (float) Math.cos(gdLatRad);
	float slat = (float) Math.sin(gdLatRad);
	float tlat = slat / clat;
	float latRad =
	(float) Math.sqrt(a2 * clat * clat + b2 * slat * slat);

	mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2)
	/ (latRad * altitudeKm + a2));

	mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg);

	float radSq = altitudeKm * altitudeKm
	+ 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat +
	b2 * slat * slat)
	+ (a2 * a2 * clat * clat + b2 * b2 * slat * slat)
	/ (a2 * clat * clat + b2 * slat * slat);
	mGcRadiusKm = (float) Math.sqrt(radSq);
	}


	/**
	* Utility class to compute a table of Gauss-normalized associated Legendre
	* functions P_n^m(cos(theta))
	*/
	static private class LegendreTable {
	// These are the Gauss-normalized associated Legendre functions -- that
	// is, they are normal Legendre functions multiplied by
	// (n-m)!/(2n-1)!! (where (2n-1)!! = 135...2n-1)
	public final float[][] mP;

	// Derivative of mP, with respect to theta.
	public final float[][] mPDeriv;

	/**
	* @param maxN
	* The maximum n- and m-values to support
	* @param thetaRad
	* Returned functions will be Gauss-normalized
	* P_n^m(cos(thetaRad)), with thetaRad in radians.
	*/
	public LegendreTable(int maxN, float thetaRad) {
	// Compute the table of Gauss-normalized associated Legendre
	// functions using standard recursion relations. Also compute the
	// table of derivatives using the derivative of the recursion
	// relations.
	float cos = (float) Math.cos(thetaRad);
	float sin = (float) Math.sin(thetaRad);

	mP = new float[maxN + 1][];
	mPDeriv = new float[maxN + 1][];
	mP[0] = new float[] { 1.0f };
	mPDeriv[0] = new float[] { 0.0f };
	for (int n = 1; n <= maxN; n++) {
	mP[n] = new float[n + 1];
	mPDeriv[n] = new float[n + 1];
	for (int m = 0; m <= n; m++) {
	if (n == m) {
	mP[n][m] = sin * mP[n - 1][m - 1];
	mPDeriv[n][m] = cos * mP[n - 1][m - 1]
	+ sin * mPDeriv[n - 1][m - 1];
	} else if (n == 1 \|\| m == n - 1) {
	mP[n][m] = cos * mP[n - 1][m];
	mPDeriv[n][m] = -sin * mP[n - 1][m]
	+ cos * mPDeriv[n - 1][m];
	} else {
	assert n > 1 && m < n - 1;
	float k = ((n - 1) * (n - 1) - m * m)
	/ (float) ((2 * n - 1) * (2 * n - 3));
	mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m];
	mPDeriv[n][m] = -sin * mP[n - 1][m]
	+ cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m];
	}
	}
	}
	}
	}

	/**
	* 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)!
	*/
	private static float[][] computeSchmidtQuasiNormFactors(int maxN) {
	float[][] schmidtQuasiNorm = new float[maxN + 1][];
	schmidtQuasiNorm[0] = new float[] { 1.0f };
	for (int n = 1; n <= maxN; n++) {
	schmidtQuasiNorm[n] = new float[n + 1];
	schmidtQuasiNorm[n][0] =
	schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n;
	for (int m = 1; m <= n; m++) {
	schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1]
	* (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1)
	/ (float) (n + m));
	}
	}
	return schmidtQuasiNorm;
	}
	}