/*
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* Copyright (C) 2009 The Android Open Source Project
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package android.hardware;
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import java.util.GregorianCalendar;
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/**
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* Estimates magnetic field at a given point on
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* Earth, and in particular, to compute the magnetic declination from true
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* north.
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*
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* <p>This uses the World Magnetic Model produced by the United States National
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* Geospatial-Intelligence Agency. More details about the model can be found at
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* <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>.
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* This class currently uses WMM-2015 which is valid until 2020, but should
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* produce acceptable results for several years after that. Future versions of
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* Android may use a newer version of the model.
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*/
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public class GeomagneticField {
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// The magnetic field at a given point, in nanoteslas in geodetic
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// coordinates.
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private float mX;
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private float mY;
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private float mZ;
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// Geocentric coordinates -- set by computeGeocentricCoordinates.
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private float mGcLatitudeRad;
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private float mGcLongitudeRad;
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private float mGcRadiusKm;
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// Constants from WGS84 (the coordinate system used by GPS)
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static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f;
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static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523142f;
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static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f;
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// These coefficients and the formulae used below are from:
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// NOAA Technical Report: The US/UK World Magnetic Model for 2015-2020
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static private final float[][] G_COEFF = new float[][] {
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{ 0.0f },
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{ -29438.5f, -1501.1f },
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{ -2445.3f, 3012.5f, 1676.6f },
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{ 1351.1f, -2352.3f, 1225.6f, 581.9f },
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{ 907.2f, 813.7f, 120.3f, -335.0f, 70.3f },
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{ -232.6f, 360.1f, 192.4f, -141.0f, -157.4f, 4.3f },
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{ 69.5f, 67.4f, 72.8f, -129.8f, -29.0f, 13.2f, -70.9f },
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{ 81.6f, -76.1f, -6.8f, 51.9f, 15.0f, 9.3f, -2.8f, 6.7f },
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{ 24.0f, 8.6f, -16.9f, -3.2f, -20.6f, 13.3f, 11.7f, -16.0f, -2.0f },
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{ 5.4f, 8.8f, 3.1f, -3.1f, 0.6f, -13.3f, -0.1f, 8.7f, -9.1f, -10.5f },
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{ -1.9f, -6.5f, 0.2f, 0.6f, -0.6f, 1.7f, -0.7f, 2.1f, 2.3f, -1.8f, -3.6f },
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{ 3.1f, -1.5f, -2.3f, 2.1f, -0.9f, 0.6f, -0.7f, 0.2f, 1.7f, -0.2f, 0.4f, 3.5f },
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{ -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 } };
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static private final float[][] H_COEFF = new float[][] {
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{ 0.0f },
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{ 0.0f, 4796.2f },
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{ 0.0f, -2845.6f, -642.0f },
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{ 0.0f, -115.3f, 245.0f, -538.3f },
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{ 0.0f, 283.4f, -188.6f, 180.9f, -329.5f },
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{ 0.0f, 47.4f, 196.9f, -119.4f, 16.1f, 100.1f },
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{ 0.0f, -20.7f, 33.2f, 58.8f, -66.5f, 7.3f, 62.5f },
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{ 0.0f, -54.1f, -19.4f, 5.6f, 24.4f, 3.3f, -27.5f, -2.3f },
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{ 0.0f, 10.2f, -18.1f, 13.2f, -14.6f, 16.2f, 5.7f, -9.1f, 2.2f },
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{ 0.0f, -21.6f, 10.8f, 11.7f, -6.8f, -6.9f, 7.8f, 1.0f, -3.9f, 8.5f },
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{ 0.0f, 3.3f, -0.3f, 4.6f, 4.4f, -7.9f, -0.6f, -4.1f, -2.8f, -1.1f, -8.7f },
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{ 0.0f, -0.1f, 2.1f, -0.7f, -1.1f, 0.7f, -0.2f, -2.1f, -1.5f, -2.5f, -2.0f, -2.3f },
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{ 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 } };
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static private final float[][] DELTA_G = new float[][] {
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{ 0.0f },
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{ 10.7f, 17.9f },
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{ -8.6f, -3.3f, 2.4f },
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{ 3.1f, -6.2f, -0.4f, -10.4f },
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{ -0.4f, 0.8f, -9.2f, 4.0f, -4.2f },
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{ -0.2f, 0.1f, -1.4f, 0.0f, 1.3f, 3.8f },
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{ -0.5f, -0.2f, -0.6f, 2.4f, -1.1f, 0.3f, 1.5f },
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{ 0.2f, -0.2f, -0.4f, 1.3f, 0.2f, -0.4f, -0.9f, 0.3f },
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{ 0.0f, 0.1f, -0.5f, 0.5f, -0.2f, 0.4f, 0.2f, -0.4f, 0.3f },
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{ 0.0f, -0.1f, -0.1f, 0.4f, -0.5f, -0.2f, 0.1f, 0.0f, -0.2f, -0.1f },
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{ 0.0f, 0.0f, -0.1f, 0.3f, -0.1f, -0.1f, -0.1f, 0.0f, -0.2f, -0.1f, -0.2f },
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{ 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, -0.1f },
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{ 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 } };
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static private final float[][] DELTA_H = new float[][] {
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{ 0.0f },
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{ 0.0f, -26.8f },
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{ 0.0f, -27.1f, -13.3f },
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{ 0.0f, 8.4f, -0.4f, 2.3f },
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{ 0.0f, -0.6f, 5.3f, 3.0f, -5.3f },
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{ 0.0f, 0.4f, 1.6f, -1.1f, 3.3f, 0.1f },
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{ 0.0f, 0.0f, -2.2f, -0.7f, 0.1f, 1.0f, 1.3f },
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{ 0.0f, 0.7f, 0.5f, -0.2f, -0.1f, -0.7f, 0.1f, 0.1f },
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{ 0.0f, -0.3f, 0.3f, 0.3f, 0.6f, -0.1f, -0.2f, 0.3f, 0.0f },
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{ 0.0f, -0.2f, -0.1f, -0.2f, 0.1f, 0.1f, 0.0f, -0.2f, 0.4f, 0.3f },
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{ 0.0f, 0.1f, -0.1f, 0.0f, 0.0f, -0.2f, 0.1f, -0.1f, -0.2f, 0.1f, -0.1f },
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{ 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, -0.1f },
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{ 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 } };
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static private final long BASE_TIME =
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new GregorianCalendar(2015, 1, 1).getTimeInMillis();
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// The ratio between the Gauss-normalized associated Legendre functions and
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// the Schmid quasi-normalized ones. Compute these once staticly since they
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// don't depend on input variables at all.
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static private final float[][] SCHMIDT_QUASI_NORM_FACTORS =
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computeSchmidtQuasiNormFactors(G_COEFF.length);
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/**
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* Estimate the magnetic field at a given point and time.
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*
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* @param gdLatitudeDeg
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* Latitude in WGS84 geodetic coordinates -- positive is east.
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* @param gdLongitudeDeg
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* Longitude in WGS84 geodetic coordinates -- positive is north.
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* @param altitudeMeters
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* Altitude in WGS84 geodetic coordinates, in meters.
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* @param timeMillis
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* Time at which to evaluate the declination, in milliseconds
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* since January 1, 1970. (approximate is fine -- the declination
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* changes very slowly).
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*/
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public GeomagneticField(float gdLatitudeDeg,
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float gdLongitudeDeg,
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float altitudeMeters,
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long timeMillis) {
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final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients.
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// We don't handle the north and south poles correctly -- pretend that
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// we're not quite at them to avoid crashing.
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gdLatitudeDeg = Math.min(90.0f - 1e-5f,
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Math.max(-90.0f + 1e-5f, gdLatitudeDeg));
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computeGeocentricCoordinates(gdLatitudeDeg,
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gdLongitudeDeg,
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altitudeMeters);
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assert G_COEFF.length == H_COEFF.length;
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// Note: LegendreTable computes associated Legendre functions for
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// cos(theta). We want the associated Legendre functions for
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// sin(latitude), which is the same as cos(PI/2 - latitude), except the
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// derivate will be negated.
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LegendreTable legendre =
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new LegendreTable(MAX_N - 1,
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(float) (Math.PI / 2.0 - mGcLatitudeRad));
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// Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in
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// 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times).
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float[] relativeRadiusPower = new float[MAX_N + 2];
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relativeRadiusPower[0] = 1.0f;
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relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm;
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for (int i = 2; i < relativeRadiusPower.length; ++i) {
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relativeRadiusPower[i] = relativeRadiusPower[i - 1] *
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relativeRadiusPower[1];
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}
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// Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N --
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// this is much faster than calling Math.sin and Math.com MAX_N+1 times.
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float[] sinMLon = new float[MAX_N];
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float[] cosMLon = new float[MAX_N];
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sinMLon[0] = 0.0f;
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cosMLon[0] = 1.0f;
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sinMLon[1] = (float) Math.sin(mGcLongitudeRad);
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cosMLon[1] = (float) Math.cos(mGcLongitudeRad);
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for (int m = 2; m < MAX_N; ++m) {
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// Standard expansions for sin((m-x)*theta + x*theta) and
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// cos((m-x)*theta + x*theta).
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int x = m >> 1;
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sinMLon[m] = sinMLon[m-x] * cosMLon[x] + cosMLon[m-x] * sinMLon[x];
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cosMLon[m] = cosMLon[m-x] * cosMLon[x] - sinMLon[m-x] * sinMLon[x];
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}
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float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad);
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float yearsSinceBase =
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(timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f);
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// We now compute the magnetic field strength given the geocentric
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// location. The magnetic field is the derivative of the potential
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// function defined by the model. See NOAA Technical Report: The US/UK
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// World Magnetic Model for 2015-2020 for the derivation.
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float gcX = 0.0f; // Geocentric northwards component.
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float gcY = 0.0f; // Geocentric eastwards component.
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float gcZ = 0.0f; // Geocentric downwards component.
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for (int n = 1; n < MAX_N; n++) {
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for (int m = 0; m <= n; m++) {
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// Adjust the coefficients for the current date.
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float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m];
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float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m];
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// Negative derivative with respect to latitude, divided by
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// radius. This looks like the negation of the version in the
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// NOAA Techincal report because that report used
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// P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the
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// derivative with respect to theta is negated.
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gcX += relativeRadiusPower[n+2]
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* (g * cosMLon[m] + h * sinMLon[m])
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* legendre.mPDeriv[n][m]
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* SCHMIDT_QUASI_NORM_FACTORS[n][m];
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// Negative derivative with respect to longitude, divided by
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// radius.
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gcY += relativeRadiusPower[n+2] * m
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* (g * sinMLon[m] - h * cosMLon[m])
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* legendre.mP[n][m]
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* SCHMIDT_QUASI_NORM_FACTORS[n][m]
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* inverseCosLatitude;
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// Negative derivative with respect to radius.
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gcZ -= (n + 1) * relativeRadiusPower[n+2]
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* (g * cosMLon[m] + h * sinMLon[m])
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* legendre.mP[n][m]
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* SCHMIDT_QUASI_NORM_FACTORS[n][m];
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}
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}
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// Convert back to geodetic coordinates. This is basically just a
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// rotation around the Y-axis by the difference in latitudes between the
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// geocentric frame and the geodetic frame.
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double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad;
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mX = (float) (gcX * Math.cos(latDiffRad)
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+ gcZ * Math.sin(latDiffRad));
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mY = gcY;
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mZ = (float) (- gcX * Math.sin(latDiffRad)
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+ gcZ * Math.cos(latDiffRad));
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}
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/**
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* @return The X (northward) component of the magnetic field in nanoteslas.
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*/
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public float getX() {
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return mX;
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}
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/**
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* @return The Y (eastward) component of the magnetic field in nanoteslas.
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*/
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public float getY() {
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return mY;
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}
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/**
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* @return The Z (downward) component of the magnetic field in nanoteslas.
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*/
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public float getZ() {
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return mZ;
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}
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/**
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* @return The declination of the horizontal component of the magnetic
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* field from true north, in degrees (i.e. positive means the
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* magnetic field is rotated east that much from true north).
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*/
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public float getDeclination() {
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return (float) Math.toDegrees(Math.atan2(mY, mX));
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}
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/**
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* @return The inclination of the magnetic field in degrees -- positive
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* means the magnetic field is rotated downwards.
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*/
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public float getInclination() {
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return (float) Math.toDegrees(Math.atan2(mZ,
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getHorizontalStrength()));
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}
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/**
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* @return Horizontal component of the field strength in nanoteslas.
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*/
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public float getHorizontalStrength() {
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return (float) Math.hypot(mX, mY);
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}
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/**
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* @return Total field strength in nanoteslas.
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*/
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public float getFieldStrength() {
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return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ);
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}
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/**
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* @param gdLatitudeDeg
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* Latitude in WGS84 geodetic coordinates.
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* @param gdLongitudeDeg
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* Longitude in WGS84 geodetic coordinates.
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* @param altitudeMeters
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* Altitude above sea level in WGS84 geodetic coordinates.
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* @return Geocentric latitude (i.e. angle between closest point on the
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* equator and this point, at the center of the earth.
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*/
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private void computeGeocentricCoordinates(float gdLatitudeDeg,
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float gdLongitudeDeg,
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float altitudeMeters) {
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float altitudeKm = altitudeMeters / 1000.0f;
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float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM;
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float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM;
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double gdLatRad = Math.toRadians(gdLatitudeDeg);
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float clat = (float) Math.cos(gdLatRad);
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float slat = (float) Math.sin(gdLatRad);
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float tlat = slat / clat;
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float latRad =
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(float) Math.sqrt(a2 * clat * clat + b2 * slat * slat);
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mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2)
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/ (latRad * altitudeKm + a2));
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mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg);
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float radSq = altitudeKm * altitudeKm
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+ 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat +
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b2 * slat * slat)
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+ (a2 * a2 * clat * clat + b2 * b2 * slat * slat)
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/ (a2 * clat * clat + b2 * slat * slat);
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mGcRadiusKm = (float) Math.sqrt(radSq);
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}
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/**
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* Utility class to compute a table of Gauss-normalized associated Legendre
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* functions P_n^m(cos(theta))
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*/
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static private class LegendreTable {
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// These are the Gauss-normalized associated Legendre functions -- that
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// is, they are normal Legendre functions multiplied by
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// (n-m)!/(2n-1)!! (where (2n-1)!! = 1*3*5*...*2n-1)
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public final float[][] mP;
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// Derivative of mP, with respect to theta.
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public final float[][] mPDeriv;
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/**
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* @param maxN
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* The maximum n- and m-values to support
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* @param thetaRad
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* Returned functions will be Gauss-normalized
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* P_n^m(cos(thetaRad)), with thetaRad in radians.
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*/
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public LegendreTable(int maxN, float thetaRad) {
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// Compute the table of Gauss-normalized associated Legendre
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// functions using standard recursion relations. Also compute the
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// table of derivatives using the derivative of the recursion
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// relations.
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float cos = (float) Math.cos(thetaRad);
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float sin = (float) Math.sin(thetaRad);
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mP = new float[maxN + 1][];
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mPDeriv = new float[maxN + 1][];
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mP[0] = new float[] { 1.0f };
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mPDeriv[0] = new float[] { 0.0f };
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for (int n = 1; n <= maxN; n++) {
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mP[n] = new float[n + 1];
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mPDeriv[n] = new float[n + 1];
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for (int m = 0; m <= n; m++) {
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if (n == m) {
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mP[n][m] = sin * mP[n - 1][m - 1];
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mPDeriv[n][m] = cos * mP[n - 1][m - 1]
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+ sin * mPDeriv[n - 1][m - 1];
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} else if (n == 1 || m == n - 1) {
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mP[n][m] = cos * mP[n - 1][m];
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mPDeriv[n][m] = -sin * mP[n - 1][m]
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+ cos * mPDeriv[n - 1][m];
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} else {
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assert n > 1 && m < n - 1;
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float k = ((n - 1) * (n - 1) - m * m)
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/ (float) ((2 * n - 1) * (2 * n - 3));
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mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m];
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mPDeriv[n][m] = -sin * mP[n - 1][m]
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+ cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m];
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}
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}
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}
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}
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}
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/**
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* Compute the ration between the Gauss-normalized associated Legendre
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* functions and the Schmidt quasi-normalized version. This is equivalent to
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* sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)!
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*/
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private static float[][] computeSchmidtQuasiNormFactors(int maxN) {
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float[][] schmidtQuasiNorm = new float[maxN + 1][];
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schmidtQuasiNorm[0] = new float[] { 1.0f };
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for (int n = 1; n <= maxN; n++) {
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schmidtQuasiNorm[n] = new float[n + 1];
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schmidtQuasiNorm[n][0] =
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schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n;
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for (int m = 1; m <= n; m++) {
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schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1]
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* (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1)
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/ (float) (n + m));
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}
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}
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return schmidtQuasiNorm;
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}
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}
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