FieldNeQuickParameters.java
/* Copyright 2002-2020 CS GROUP
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* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
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*
* 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,
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package org.orekit.models.earth.ionosphere;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.SinCos;
import org.orekit.time.DateComponents;
import org.orekit.time.DateTimeComponents;
import org.orekit.time.TimeComponents;
/**
* This class perfoms the computation of the parameters used by the NeQuick model.
*
* @author Bryan Cazabonne
*
* @see "European Union (2016). European GNSS (Galileo) Open Service-Ionospheric Correction
* Algorithm for Galileo Single Frequency Users. 1.2."
*
* @since 10.1
*/
class FieldNeQuickParameters <T extends RealFieldElement<T>> {
/** Solar zenith angle at day night transition, degrees. */
private static final double X0 = 86.23292796211615;
/** F2 layer maximum density. */
private final T nmF2;
/** F2 layer maximum density height [km]. */
private final T hmF2;
/** F1 layer maximum density height [km]. */
private final T hmF1;
/** E layer maximum density height [km]. */
private final T hmE;
/** F2 layer bottom thickness parameter [km]. */
private final T b2Bot;
/** F1 layer top thickness parameter [km]. */
private final T b1Top;
/** F1 layer bottom thickness parameter [km]. */
private final T b1Bot;
/** E layer top thickness parameter [km]. */
private final T beTop;
/** E layer bottom thickness parameter [km]. */
private final T beBot;
/** topside thickness parameter [km]. */
private final T h0;
/** Layer amplitudes. */
private final T[] amplitudes;
/**
* Build a new instance.
* @param field field of the elements
* @param dateTime current date time components
* @param f2 F2 coefficients used by the F2 layer
* @param fm3 Fm3 coefficients used by the F2 layer
* @param latitude latitude of a point along the integration path, in radians
* @param longitude longitude of a point along the integration path, in radians
* @param alpha effective ionisation level coefficients
* @param modipGrip modip grid
*/
FieldNeQuickParameters(final Field<T> field, final DateTimeComponents dateTime, final double[][][] f2,
final double[][][] fm3, final T latitude, final T longitude,
final double[] alpha, final double[][] modipGrip) {
// Zero
final T zero = field.getZero();
// MODIP in degrees
final T modip = computeMODIP(latitude, longitude, modipGrip);
// Effective ionisation level Az
final T az = computeAz(modip, alpha);
// Effective sunspot number (Eq. 19)
final T azr = FastMath.sqrt(az.subtract(63.7).multiply(1123.6).add(167273.0)).subtract(408.99);
// Date and Time components
final DateComponents date = dateTime.getDate();
final TimeComponents time = dateTime.getTime();
// Hours
final double hours = time.getSecondsInUTCDay() / 3600.0;
// Effective solar zenith angle in radians
final T xeff = computeEffectiveSolarAngle(date.getMonth(), hours, latitude, longitude);
// Coefficients for F2 layer parameters
// Compute the array of interpolated coefficients for foF2 (Eq. 44)
final T[][] af2 = MathArrays.buildArray(field, 76, 13);
for (int j = 0; j < 76; j++) {
for (int k = 0; k < 13; k++ ) {
af2[j][k] = azr.multiply(0.01).negate().add(1.0).multiply(f2[0][j][k]).add(azr.multiply(0.01).multiply(f2[1][j][k]));
}
}
// Compute the array of interpolated coefficients for M(3000)F2 (Eq. 46)
final T[][] am3 = MathArrays.buildArray(field, 49, 9);
for (int j = 0; j < 49; j++) {
for (int k = 0; k < 9; k++ ) {
am3[j][k] = azr.multiply(0.01).negate().add(1.0).multiply(fm3[0][j][k]).add(azr.multiply(0.01).multiply(fm3[1][j][k]));
}
}
// E layer maximum density height in km (Eq. 78)
this.hmE = field.getZero().add(120.0);
// E layer critical frequency in MHz
final T foE = computefoE(date.getMonth(), az, xeff, latitude);
// E layer maximum density in 10^11 m-3 (Eq. 36)
final T nmE = foE.multiply(foE).multiply(0.124);
// Time argument (Eq. 49)
final double t = FastMath.toRadians(15 * hours) - FastMath.PI;
// Compute Fourier time series for foF2 and M(3000)F2
final T[] cf2 = computeCF2(field, af2, t);
final T[] cm3 = computeCm3(field, am3, t);
// F2 layer critical frequency in MHz
final T foF2 = computefoF2(field, modip, cf2, latitude, longitude);
// Maximum Usable Frequency factor
final T mF2 = computeMF2(field, modip, cm3, latitude, longitude);
// F2 layer maximum density in 10^11 m-3
this.nmF2 = foF2.multiply(foF2).multiply(0.124);
// F2 layer maximum density height in km
this.hmF2 = computehmF2(field, foE, foF2, mF2);
// F1 layer critical frequency in MHz
final T foF1 = computefoF1(field, foE, foF2);
// F1 layer maximum density in 10^11 m-3
final T nmF1;
if (foF1.getReal() <= 0.0 && foE.getReal() > 2.0) {
final T foEpopf = foE.add(0.5);
nmF1 = foEpopf.multiply(foEpopf).multiply(0.124);
} else {
nmF1 = foF1.multiply(foF1).multiply(0.124);
}
// F1 layer maximum density height in km
this.hmF1 = hmF2.add(hmE).multiply(0.5);
// Thickness parameters (Eq. 85 to 89)
final T a = clipExp(FastMath.log(foF2.multiply(foF2)).multiply(0.857).add(FastMath.log(mF2).multiply(2.02)).add(-3.467)).multiply(0.01);
this.b2Bot = nmF2.divide(a).multiply(0.385);
this.b1Top = hmF2.subtract(hmF1).multiply(0.3);
this.b1Bot = hmF1.subtract(hmE).multiply(0.5);
this.beTop = FastMath.max(b1Bot, zero.add(7.0));
this.beBot = zero.add(5.0);
// Layer amplitude coefficients
this.amplitudes = computeLayerAmplitudes(field, nmE, nmF1, foF1);
// Topside thickness parameter
this.h0 = computeH0(field, date.getMonth(), azr);
}
/**
* Get the F2 layer maximum density.
* @return nmF2
*/
public T getNmF2() {
return nmF2;
}
/**
* Get the F2 layer maximum density height.
* @return hmF2 in km
*/
public T getHmF2() {
return hmF2;
}
/**
* Get the F1 layer maximum density height.
* @return hmF1 in km
*/
public T getHmF1() {
return hmF1;
}
/**
* Get the E layer maximum density height.
* @return hmE in km
*/
public T getHmE() {
return hmE;
}
/**
* Get the F2 layer thickness parameter (bottom).
* @return B2Bot in km
*/
public T getB2Bot() {
return b2Bot;
}
/**
* Get the F1 layer thickness parameter (top).
* @return B1Top in km
*/
public T getB1Top() {
return b1Top;
}
/**
* Get the F1 layer thickness parameter (bottom).
* @return B1Bot in km
*/
public T getB1Bot() {
return b1Bot;
}
/**
* Get the E layer thickness parameter (bottom).
* @return BeBot in km
*/
public T getBEBot() {
return beBot;
}
/**
* Get the E layer thickness parameter (top).
* @return BeTop in km
*/
public T getBETop() {
return beTop;
}
/**
* Get the F2, F1 and E layer amplitudes.
* <p>
* The resulting element is an array having the following form:
* <ul>
* <li>double[0] = A1 → F2 layer amplitude
* <li>double[1] = A2 → F1 layer amplitude
* <li>double[2] = A3 → E layer amplitude
* </ul>
* @return layer amplitudes
*/
public T[] getLayerAmplitudes() {
return amplitudes.clone();
}
/**
* Get the topside thickness parameter H0.
* @return H0 in km
*/
public T getH0() {
return h0;
}
/**
* Computes the value of the modified dip latitude (MODIP) for the
* given latitude and longitude.
*
* @param lat receiver latitude, radians
* @param lon receiver longitude, radians
* @param stModip modip grid
* @return the MODIP in degrees
*/
private T computeMODIP(final T lat, final T lon, final double[][] stModip) {
// Zero
final T zero = lat.getField().getZero();
// For the MODIP computation, the latitude and longitude have to be converted in degrees
final T latitude = FastMath.toDegrees(lat);
final T longitude = FastMath.toDegrees(lon);
// Extreme cases
if (latitude.getReal() == 90.0 || latitude.getReal() == -90.0) {
return latitude;
}
// Auxiliary parameter l (Eq. 6 to 8)
final int lF = (int) ((longitude.getReal() + 180) * 0.1);
int l = lF - 2;
if (l < 0) {
l += 36;
} else if (l > 33) {
l -= 36;
}
// Auxiliary parameter a (Eq. 9 to 11)
final T a = latitude.add(90).multiply(0.2).add(1.0);
final T aF = FastMath.floor(a);
// Eq. 10
final T x = a.subtract(aF);
// Eq. 11
final int i = (int) aF.getReal() - 2;
// zi coefficients (Eq. 12 and 13)
final T z1 = interpolate(zero.add(stModip[i + 1][l + 2]), zero.add(stModip[i + 2][l + 2]),
zero.add(stModip[i + 3][l + 2]), zero.add(stModip[i + 4][l + 2]), x);
final T z2 = interpolate(zero.add(stModip[i + 1][l + 3]), zero.add(stModip[i + 2][l + 3]),
zero.add(stModip[i + 3][l + 3]), zero.add(stModip[i + 4][l + 3]), x);
final T z3 = interpolate(zero.add(stModip[i + 1][l + 4]), zero.add(stModip[i + 2][l + 4]),
zero.add(stModip[i + 3][l + 4]), zero.add(stModip[i + 4][l + 4]), x);
final T z4 = interpolate(zero.add(stModip[i + 1][l + 5]), zero.add(stModip[i + 2][l + 5]),
zero.add(stModip[i + 3][l + 5]), zero.add(stModip[i + 4][l + 5]), x);
// Auxiliary parameter b (Eq. 14 and 15)
final T b = longitude.add(180).multiply(0.1);
final T bF = FastMath.floor(b);
final T y = b.subtract(bF);
// MODIP (Ref Eq. 16)
final T modip = interpolate(z1, z2, z3, z4, y);
return modip;
}
/**
* This method computes the effective ionisation level Az.
* <p>
* This parameter is used for the computation of the Total Electron Content (TEC).
* </p>
* @param modip modified dip latitude (MODIP) in degrees
* @param alpha effective ionisation level coefficients
* @return the ionisation level Az
*/
private T computeAz(final T modip, final double[] alpha) {
// Field
final Field<T> field = modip.getField();
// Zero
final T zero = field.getZero();
// Particular condition (Eq. 17)
if (alpha[0] == 0.0 && alpha[1] == 0.0 && alpha[2] == 0.0) {
return zero.add(63.7);
}
// Az = a0 + modip * a1 + modip^2 * a2 (Eq. 18)
T az = modip.multiply(alpha[2]).add(alpha[1]).multiply(modip).add(alpha[0]);
// If Az < 0 -> Az = 0
az = FastMath.max(zero, az);
// If Az > 400 -> Az = 400
az = FastMath.min(zero.add(400.0), az);
return az;
}
/**
* This method computes the effective solar zenith angle.
* <p>
* The effective solar zenith angle is compute as a function of the
* solar zenith angle and the solar zenith angle at day night transition.
* </p>
* @param month current month of the year
* @param hours universal time (hours)
* @param latitude in radians
* @param longitude in radians
* @return the effective solar zenith angle, radians
*/
private T computeEffectiveSolarAngle(final int month,
final double hours,
final T latitude,
final T longitude) {
// Zero
final T zero = latitude.getField().getZero();
// Local time (Eq.4)
final T lt = longitude.divide(FastMath.toRadians(15.0)).add(hours);
// Day of year at the middle of the month (Eq. 20)
final double dy = 30.5 * month - 15.0;
// Time (Eq. 21)
final double t = dy + (18 - hours) / 24;
// Arguments am and al (Eq. 22 and 23)
final double am = FastMath.toRadians(0.9856 * t - 3.289);
final double al = am + FastMath.toRadians(1.916 * FastMath.sin(am) + 0.020 * FastMath.sin(2.0 * am) + 282.634);
// Sine and cosine of solar declination (Eq. 24 and 25)
final double sDec = 0.39782 * FastMath.sin(al);
final double cDec = FastMath.sqrt(1. - sDec * sDec);
// Solar zenith angle, deg (Eq. 26 and 27)
final FieldSinCos<T> scLat = FastMath.sinCos(latitude);
final T coef = lt.negate().add(12.0).multiply(FastMath.PI / 12);
final T cZenith = scLat.sin().multiply(sDec).add(scLat.cos().multiply(cDec).multiply(FastMath.cos(coef)));
final T angle = FastMath.atan2(FastMath.sqrt(cZenith.multiply(cZenith).negate().add(1.0)), cZenith);
final T x = FastMath.toDegrees(angle);
// Effective solar zenith angle (Eq. 28)
final T xeff = join(clipExp(x.multiply(0.2).negate().add(20.0)).multiply(0.24).negate().add(90.0), x, zero.add(12.0), x.subtract(X0));
return FastMath.toRadians(xeff);
}
/**
* This method computes the E layer critical frequency at a given location.
* @param month current month
* @param az ffective ionisation level
* @param xeff effective solar zenith angle in radians
* @param latitude latitude in radians
* @return the E layer critical frequency at a given location in MHz
*/
private T computefoE(final int month, final T az,
final T xeff, final T latitude) {
// The latitude has to be converted in degrees
final T lat = FastMath.toDegrees(latitude);
// Square root of the effective ionisation level
final T sqAz = FastMath.sqrt(az);
// seas parameter (Eq. 30 to 32)
final int seas;
if (month == 1 || month == 2 || month == 11 || month == 12) {
seas = -1;
} else if (month == 3 || month == 4 || month == 9 || month == 10) {
seas = 0;
} else {
seas = 1;
}
// Latitudinal dependence (Eq. 33 and 34)
final T ee = clipExp(lat.multiply(0.3));
final T seasp = ee.subtract(1.0).divide(ee.add(1.0)).multiply(seas);
// Critical frequency (Eq. 35)
final T coef = seasp.multiply(0.019).negate().add(1.112);
final T foE = FastMath.sqrt(coef .multiply(coef).multiply(sqAz).multiply(FastMath.cos(xeff).pow(0.6)).add(0.49));
return foE;
}
/**
* Computes the F2 layer height of maximum electron density.
* @param field field of the elements
* @param foE E layer layer critical frequency in MHz
* @param foF2 F2 layer layer critical frequency in MHz
* @param mF2 maximum usable frequency factor
* @return hmF2 in km
*/
private T computehmF2(final Field<T> field, final T foE, final T foF2, final T mF2) {
// Zero
final T zero = field.getZero();
// Ratio
final T fo = foF2.divide(foE);
final T ratio = join(fo, zero.add(1.75), zero.add(20.0), fo.subtract(1.75));
// deltaM parameter
T deltaM = zero.subtract(0.012);
if (foE.getReal() >= 1e-30) {
deltaM = deltaM.add(ratio.subtract(1.215).divide(0.253).reciprocal());
}
// hmF2 Eq. 80
final T mF2Sq = mF2.multiply(mF2);
final T temp = FastMath.sqrt(mF2Sq.multiply(0.0196).add(1.0).divide(mF2Sq.multiply(1.2967).subtract(1.0)));
final T height = mF2.multiply(1490.0).multiply(temp).divide(mF2.add(deltaM)).subtract(176.0);
return height;
}
/**
* Computes cf2 coefficients.
* @param field field of the elements
* @param af2 interpolated coefficients for foF2
* @param t time argument
* @return the cf2 coefficients array
*/
private T[] computeCF2(final Field<T> field, final T[][] af2, final double t) {
// Eq. 50
final T[] cf2 = MathArrays.buildArray(field, 76);
for (int i = 0; i < cf2.length; i++) {
T sum = field.getZero();
for (int k = 0; k < 6; k++) {
final SinCos sc = FastMath.sinCos((k + 1) * t);
sum = sum.add(af2[i][2 * k + 1].multiply(sc.sin()).add(af2[i][2 * (k + 1)].multiply(sc.cos())));
}
cf2[i] = af2[i][0].add(sum);
}
return cf2;
}
/**
* Computes Cm3 coefficients.
* @param field field of the elements
* @param am3 interpolated coefficients for foF2
* @param t time argument
* @return the Cm3 coefficients array
*/
private T[] computeCm3(final Field<T> field, final T[][] am3, final double t) {
// Eq. 51
final T[] cm3 = MathArrays.buildArray(field, 49);
for (int i = 0; i < cm3.length; i++) {
T sum = field.getZero();
for (int k = 0; k < 4; k++) {
final SinCos sc = FastMath.sinCos((k + 1) * t);
sum = sum.add(am3[i][2 * k + 1].multiply(sc.sin()).add(am3[i][2 * (k + 1)].multiply(sc.cos())));
}
cm3[i] = am3[i][0].add(sum);
}
return cm3;
}
/**
* This method computes the F2 layer critical frequency.
* @param field field of the elements
* @param modip modified DIP latitude, in degrees
* @param cf2 Fourier time series for foF2
* @param latitude latitude in radians
* @param longitude longitude in radians
* @return the F2 layer critical frequency, MHz
*/
private T computefoF2(final Field<T> field, final T modip, final T[] cf2,
final T latitude, final T longitude) {
// One
final T one = field.getOne();
// Legendre grades (Eq. 63)
final int[] q = new int[] {
12, 12, 9, 5, 2, 1, 1, 1, 1
};
// Array for geographic terms
final T[] g = MathArrays.buildArray(field, cf2.length);
g[0] = one;
// MODIP coefficients Eq. 57
final T sinMODIP = FastMath.sin(FastMath.toRadians(modip));
final T[] m = MathArrays.buildArray(field, 12);
m[0] = one;
for (int i = 1; i < q[0]; i++) {
m[i] = sinMODIP.multiply(m[i - 1]);
g[i] = m[i];
}
// Latitude coefficients (Eq. 58)
final T cosLat = FastMath.cos(latitude);
final T[] p = MathArrays.buildArray(field, 8);
p[0] = cosLat;
for (int n = 2; n < 9; n++) {
p[n - 1] = cosLat.multiply(p[n - 2]);
}
// latitude and longitude terms
int index = 12;
for (int i = 1; i < q.length; i++) {
final FieldSinCos<T> sc = FastMath.sinCos(longitude.multiply(i));
for (int j = 0; j < q[i]; j++) {
g[index++] = m[j].multiply(p[i - 1]).multiply(sc.cos());
g[index++] = m[j].multiply(p[i - 1]).multiply(sc.sin());
}
}
// Compute foF2 by linear combination
final T frequency = one.linearCombination(g, cf2);
return frequency;
}
/**
* This method computes the Maximum Usable Frequency factor.
* @param field field of the elements
* @param modip modified DIP latitude, in degrees
* @param cm3 Fourier time series for M(3000)F2
* @param latitude latitude in radians
* @param longitude longitude in radians
* @return the Maximum Usable Frequency factor
*/
private T computeMF2(final Field<T> field, final T modip, final T[] cm3,
final T latitude, final T longitude) {
// One
final T one = field.getOne();
// Legendre grades (Eq. 71)
final int[] r = new int[] {
7, 8, 6, 3, 2, 1, 1
};
// Array for geographic terms
final T[] g = MathArrays.buildArray(field, cm3.length);
g[0] = one;
// MODIP coefficients Eq. 57
final T sinMODIP = FastMath.sin(FastMath.toRadians(modip));
final T[] m = MathArrays.buildArray(field, 12);
m[0] = one;
for (int i = 1; i < 12; i++) {
m[i] = sinMODIP.multiply(m[i - 1]);
if (i < 7) {
g[i] = m[i];
}
}
// Latitude coefficients (Eq. 58)
final T cosLat = FastMath.cos(latitude);
final T[] p = MathArrays.buildArray(field, 8);
p[0] = cosLat;
for (int n = 2; n < 9; n++) {
p[n - 1] = cosLat.multiply(p[n - 2]);
}
// latitude and longitude terms
int index = 7;
for (int i = 1; i < r.length; i++) {
final FieldSinCos<T> sc = FastMath.sinCos(longitude.multiply(i));
for (int j = 0; j < r[i]; j++) {
g[index++] = m[j].multiply(p[i - 1]).multiply(sc.cos());
g[index++] = m[j].multiply(p[i - 1]).multiply(sc.sin());
}
}
// Compute m3000 by linear combination
final T m3000 = one.linearCombination(g, cm3);
return m3000;
}
/**
* This method computes the F1 layer critical frequency.
* <p>
* This computation performs the algorithm exposed in Annex F
* of the reference document.
* </p>
* @param field field of the elements
* @param foE the E layer critical frequency, MHz
* @return the F1 layer critical frequency, MHz
* @param foF2 the F2 layer critical frequency, MHz
*/
private T computefoF1(final Field<T> field, final T foE, final T foF2) {
final T zero = field.getZero();
final T temp = join(foE.multiply(1.4), zero, zero.add(1000.0), foE.subtract(2.0));
final T temp2 = join(zero, temp, zero.add(1000.0), foE.subtract(temp));
final T value = join(temp2, temp2.multiply(0.85), zero.add(60.0), foF2.multiply(0.85).subtract(temp2));
if (value.getReal() < 1.0E-6) {
return zero;
} else {
return value;
}
}
/**
* This method allows the computation of the F2, F1 and E layer amplitudes.
* <p>
* The resulting element is an array having the following form:
* <ul>
* <li>double[0] = A1 → F2 layer amplitude
* <li>double[1] = A2 → F1 layer amplitude
* <li>double[2] = A3 → E layer amplitude
* </ul>
* </p>
* @param field field of the elements
* @param nmE E layer maximum density in 10^11 m-3
* @param nmF1 F1 layer maximum density in 10^11 m-3
* @param foF1 F1 layer critical frequency in MHz
* @return a three components array containing the layer amplitudes
*/
private T[] computeLayerAmplitudes(final Field<T> field, final T nmE, final T nmF1, final T foF1) {
// Zero
final T zero = field.getZero();
// Initialize array
final T[] amplitude = MathArrays.buildArray(field, 3);
// F2 layer amplitude (Eq. 90)
final T a1 = nmF2.multiply(4.0);
amplitude[0] = a1;
// F1 and E layer amplitudes (Eq. 91 to 98)
if (foF1.getReal() < 0.5) {
amplitude[1] = zero;
amplitude[2] = nmE.subtract(epst(a1, hmF2, b2Bot, hmE)).multiply(4.0);
} else {
T a2a = zero;
T a3a = nmE.multiply(4.0);
for (int i = 0; i < 5; i++) {
a2a = nmF1.subtract(epst(a1, hmF2, b2Bot, hmF1)).subtract(epst(a3a, hmE, beTop, hmF1)).multiply(4.0);
a2a = join(a2a, nmF1.multiply(0.8), field.getOne(), a2a.subtract(nmF1.multiply(0.8)));
a3a = nmE.subtract(epst(a2a, hmF1, b1Bot, hmE)).subtract(epst(a1, hmF2, b2Bot, hmE)).multiply(4.0);
}
amplitude[1] = a2a;
amplitude[2] = join(a3a, zero.add(0.05), zero.add(60.0), a3a.subtract(0.005));
}
return amplitude;
}
/**
* This method computes the topside thickness parameter H0.
*
* @param field field of the elements
* @param month current month
* @param azr effective sunspot number
* @return H0 in km
*/
private T computeH0(final Field<T> field, final int month, final T azr) {
// One
final T one = field.getOne();
// Auxiliary parameter ka (Eq. 99 and 100)
final T ka;
if (month > 3 && month < 10) {
// month = 4,5,6,7,8,9
ka = azr.multiply(0.014).add(hmF2.multiply(0.008)).negate().add(6.705);
} else {
// month = 1,2,3,10,11,12
final T ratio = hmF2.divide(b2Bot);
ka = ratio.multiply(ratio).multiply(0.097).add(nmF2.multiply(0.153)).add(-7.77);
}
// Auxiliary parameter kb (Eq. 101 and 102)
T kb = join(ka, one.multiply(2.0), one, ka.subtract(2.0));
kb = join(one.multiply(8.0), kb, one, kb.subtract(8.0));
// Auxiliary parameter Ha (Eq. 103)
final T hA = kb.multiply(b2Bot);
// Auxiliary parameters x and v (Eq. 104 and 105)
final T x = hA.subtract(150.0).multiply(0.01);
final T v = x.multiply(0.041163).subtract(0.183981).multiply(x).add(1.424472);
// Topside thickness parameter (Eq. 106)
final T h = hA.divide(v);
return h;
}
/**
* A clipped exponential function.
* <p>
* This function, describe in section F.2.12.2 of the reference document, is
* recommanded for the computation of exponential values.
* </p>
* @param power power for exponential function
* @return clipped exponential value
*/
private T clipExp(final T power) {
final T zero = power.getField().getZero();
if (power.getReal() > 80.0) {
return zero.add(5.5406E34);
} else if (power.getReal() < -80) {
return zero.add(1.8049E-35);
} else {
return FastMath.exp(power);
}
}
/**
* This method provides a third order interpolation function
* as recommended in the reference document (Ref Eq. 128 to Eq. 138)
*
* @param z1 z1 coefficient
* @param z2 z2 coefficient
* @param z3 z3 coefficient
* @param z4 z4 coefficient
* @param x position
* @return a third order interpolation
*/
private T interpolate(final T z1, final T z2,
final T z3, final T z4,
final T x) {
if (FastMath.abs(2.0 * x.getReal()) < 1e-10) {
return z2;
}
final T delta = x.multiply(2.0).subtract(1.0);
final T g1 = z3.add(z2);
final T g2 = z3.subtract(z2);
final T g3 = z4.add(z1);
final T g4 = z4.subtract(z1).divide(3.0);
final T a0 = g1.multiply(9.0).subtract(g3);
final T a1 = g2.multiply(9.0).subtract(g4);
final T a2 = g3.subtract(g1);
final T a3 = g4.subtract(g2);
final T zx = delta.multiply(a3).add(a2).multiply(delta).add(a1).multiply(delta).add(a0).multiply(0.0625);
return zx;
}
/**
* Allows smooth joining of functions f1 and f2
* (i.e. continuous first derivatives) at origin.
* <p>
* This function, describe in section F.2.12.1 of the reference document, is
* recommanded for computational efficiency.
* </p>
* @param dF1 first function
* @param dF2 second function
* @param dA width of transition region
* @param dX x value
* @return the computed value
*/
private T join(final T dF1, final T dF2,
final T dA, final T dX) {
final T ee = clipExp(dA.multiply(dX));
return dF1.multiply(ee).add(dF2).divide(ee.add(1.0));
}
/**
* The Epstein function.
* <p>
* This function, describe in section 2.5.1 of the reference document, is used
* as a basis analytical function in NeQuick for the construction of the ionospheric layers.
* </p>
* @param x x parameter
* @param y y parameter
* @param z z parameter
* @param w w parameter
* @return value of the epstein function
*/
private T epst(final T x, final T y,
final T z, final T w) {
final T ex = clipExp(w.subtract(y).divide(z));
final T opex = ex.add(1.0);
final T epst = x.multiply(ex).divide(opex.multiply(opex));
return epst;
}
}