content: /*
   * 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   * Android may use a newer version of the model.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;
      }
  }
  