NeQuickParameters.java
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* CS licenses this file to You under the Apache License, Version 2.0
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*
* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
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package org.orekit.models.earth.ionosphere;
import org.hipparchus.util.FastMath;
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 NeQuickParameters {
/** Solar zenith angle at day night transition, degrees. */
private static final double X0 = 86.23292796211615;
/** F2 layer maximum density. */
private final double nmF2;
/** F2 layer maximum density height [km]. */
private final double hmF2;
/** F1 layer maximum density height [km]. */
private final double hmF1;
/** E layer maximum density height [km]. */
private final double hmE;
/** F2 layer bottom thickness parameter [km]. */
private final double b2Bot;
/** F1 layer top thickness parameter [km]. */
private final double b1Top;
/** F1 layer bottom thickness parameter [km]. */
private final double b1Bot;
/** E layer top thickness parameter [km]. */
private final double beTop;
/** E layer bottom thickness parameter [km]. */
private final double beBot;
/** topside thickness parameter [km]. */
private final double h0;
/** Layer amplitudes. */
private final double[] amplitudes;
/**
* Build a new instance.
* @param dateTime current date time components
* @param flattenF2 F2 coefficients used by the F2 layer (flatten array)
* @param flattenFm3 Fm3 coefficients used by the F2 layer (flatten array)
* @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
*/
NeQuickParameters(final DateTimeComponents dateTime,
final double[] flattenF2, final double[] flattenFm3,
final double latitude, final double longitude,
final double[] alpha, final double[][] modipGrip) {
// MODIP in degrees
final double modip = computeMODIP(latitude, longitude, modipGrip);
// Effective ionisation level Az
final double az = computeAz(modip, alpha);
// Effective sunspot number (Eq. 19)
final double azr = FastMath.sqrt(167273.0 + (az - 63.7) * 1123.6) - 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 double xeff = computeEffectiveSolarAngle(date.getMonth(), hours, latitude, longitude);
// E layer maximum density height in km (Eq. 78)
this.hmE = 120.0;
// E layer critical frequency in MHz
final double foE = computefoE(date.getMonth(), az, xeff, latitude);
// E layer maximum density in 10^11 m-3 (Eq. 36)
final double nmE = 0.124 * foE * foE;
// Time argument (Eq. 49)
final double t = FastMath.toRadians(15 * hours) - FastMath.PI;
// Compute Fourier time series for foF2 and M(3000)F2
final double[] scT = sinCos(t, 6);
final double[] cf2 = computeCF2(flattenF2, azr, scT);
final double[] cm3 = computeCm3(flattenFm3, azr, scT);
// F2 layer critical frequency in MHz
final double[] scL = sinCos(longitude, 8);
final double foF2 = computefoF2(modip, cf2, latitude, scL);
// Maximum Usable Frequency factor
final double mF2 = computeMF2(modip, cm3, latitude, scL);
// F2 layer maximum density in 10^11 m-3
this.nmF2 = 0.124 * foF2 * foF2;
// F2 layer maximum density height in km
this.hmF2 = computehmF2(foE, foF2, mF2);
// F1 layer critical frequency in MHz
final double foF1 = computefoF1(foE, foF2);
// F1 layer maximum density in 10^11 m-3
final double nmF1;
if (foF1 <= 0.0 && foE > 2.0) {
final double foEpopf = foE + 0.5;
nmF1 = 0.124 * foEpopf * foEpopf;
} else {
nmF1 = 0.124 * foF1 * foF1;
}
// F1 layer maximum density height in km
this.hmF1 = 0.5 * (hmF2 + hmE);
// Thickness parameters (Eq. 85 to 89)
final double a = 0.01 * clipExp(-3.467 + 0.857 * FastMath.log(foF2 * foF2) + 2.02 * FastMath.log(mF2));
this.b2Bot = 0.385 * nmF2 / a;
this.b1Top = 0.3 * (hmF2 - hmF1);
this.b1Bot = 0.5 * (hmF1 - hmE);
this.beTop = FastMath.max(b1Bot, 7.0);
this.beBot = 5.0;
// Layer amplitude coefficients
this.amplitudes = computeLayerAmplitudes(nmE, nmF1, foF1);
// Topside thickness parameter
this.h0 = computeH0(date.getMonth(), azr);
}
/**
* Get the F2 layer maximum density.
* @return nmF2
*/
public double getNmF2() {
return nmF2;
}
/**
* Get the F2 layer maximum density height.
* @return hmF2 in km
*/
public double getHmF2() {
return hmF2;
}
/**
* Get the F1 layer maximum density height.
* @return hmF1 in km
*/
public double getHmF1() {
return hmF1;
}
/**
* Get the E layer maximum density height.
* @return hmE in km
*/
public double getHmE() {
return hmE;
}
/**
* Get the F2 layer thickness parameter (bottom).
* @return B2Bot in km
*/
public double getB2Bot() {
return b2Bot;
}
/**
* Get the F1 layer thickness parameter (top).
* @return B1Top in km
*/
public double getB1Top() {
return b1Top;
}
/**
* Get the F1 layer thickness parameter (bottom).
* @return B1Bot in km
*/
public double getB1Bot() {
return b1Bot;
}
/**
* Get the E layer thickness parameter (bottom).
* @return BeBot in km
*/
public double getBEBot() {
return beBot;
}
/**
* Get the E layer thickness parameter (top).
* @return BeTop in km
*/
public double 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 double[] getLayerAmplitudes() {
return amplitudes.clone();
}
/**
* Get the topside thickness parameter H0.
* @return H0 in km
*/
public double 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 double computeMODIP(final double lat, final double lon, final double[][] stModip) {
// For the MODIP computation, latitude and longitude have to be converted in degrees
final double latitude = FastMath.toDegrees(lat);
final double longitude = FastMath.toDegrees(lon);
// Extreme cases
if (latitude == 90.0 || latitude == -90.0) {
return latitude;
}
// Auxiliary parameter l (Eq. 6 to 8)
final int lF = (int) ((longitude + 180) * 0.1);
int l = lF - 2;
if (l < -2) {
l += 36;
} else if (l > 33) {
l -= 36;
}
// Auxiliary parameter a (Eq. 9 to 11)
final double a = 0.2 * (latitude + 90) + 1.0;
final double aF = FastMath.floor(a);
// Eq. 10
final double x = a - aF;
// Eq. 11
final int i = (int) aF - 2;
// zi coefficients (Eq. 12 and 13)
final double z1 = interpolate(stModip[i + 1][l + 2], stModip[i + 2][l + 2], stModip[i + 3][l + 2], stModip[i + 4][l + 2], x);
final double z2 = interpolate(stModip[i + 1][l + 3], stModip[i + 2][l + 3], stModip[i + 3][l + 3], stModip[i + 4][l + 3], x);
final double z3 = interpolate(stModip[i + 1][l + 4], stModip[i + 2][l + 4], stModip[i + 3][l + 4], stModip[i + 4][l + 4], x);
final double z4 = interpolate(stModip[i + 1][l + 5], stModip[i + 2][l + 5], stModip[i + 3][l + 5], stModip[i + 4][l + 5], x);
// Auxiliary parameter b (Eq. 14 and 15)
final double b = (longitude + 180) * 0.1;
final double bF = FastMath.floor(b);
final double y = b - bF;
// MODIP (Ref Eq. 16)
return interpolate(z1, z2, z3, z4, y);
}
/**
* 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 double computeAz(final double modip, final double[] alpha) {
// Particular condition (Eq. 17)
if (alpha[0] == 0.0 && alpha[1] == 0.0 && alpha[2] == 0.0) {
return 63.7;
}
// Az = a0 + modip * a1 + modip^2 * a2 (Eq. 18)
double az = alpha[0] + modip * (alpha[1] + modip * alpha[2]);
// If Az < 0 -> Az = 0
az = FastMath.max(0.0, az);
// If Az > 400 -> Az = 400
az = FastMath.min(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 double computeEffectiveSolarAngle(final int month,
final double hours,
final double latitude,
final double longitude) {
// Local time (Eq.4)
final double lt = hours + longitude / FastMath.toRadians(15.0);
// 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 SinCos scLat = FastMath.sinCos(latitude);
final double coef = (FastMath.PI / 12) * (12 - lt);
final double cZenith = scLat.sin() * sDec + scLat.cos() * cDec * FastMath.cos(coef);
final double angle = FastMath.atan2(FastMath.sqrt(1.0 - cZenith * cZenith), cZenith);
final double x = FastMath.toDegrees(angle);
// Effective solar zenith angle (Eq. 28)
final double xeff = join(90.0 - 0.24 * clipExp(20.0 - 0.2 * x), x, 12.0, x - 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 double computefoE(final int month, final double az,
final double xeff, final double latitude) {
// The latitude has to be converted in degrees
final double lat = FastMath.toDegrees(latitude);
// Square root of the effective ionisation level
final double 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 double ee = clipExp(0.3 * lat);
final double seasp = seas * ((ee - 1.0) / (ee + 1.0));
// Critical frequency (Eq. 35)
final double coef = 1.112 - 0.019 * seasp;
return FastMath.sqrt(coef * coef * sqAz * FastMath.pow(FastMath.cos(xeff), 0.6) + 0.49);
}
/**
* Computes the F2 layer height of maximum electron density.
* @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 double computehmF2(final double foE, final double foF2, final double mF2) {
// Ratio
final double fo = foF2 / foE;
final double ratio = join(fo, 1.75, 20.0, fo - 1.75);
// deltaM parameter
double deltaM = -0.012;
if (foE >= 1e-30) {
deltaM += 0.253 / (ratio - 1.215);
}
// hmF2 Eq. 80
final double mF2Sq = mF2 * mF2;
final double temp = FastMath.sqrt((0.0196 * mF2Sq + 1) / (1.2967 * mF2Sq - 1.0));
return ((1490.0 * mF2 * temp) / (mF2 + deltaM)) - 176.0;
}
/** Compute sines and cosines.
* @param a argument
* @param n number of terms
* @return sin(a), cos(a), sin(2a), cos(2a) … sin(n a), cos(n a) array
* @since 12.1.3
*/
private double[] sinCos(final double a, final int n) {
final SinCos sc0 = FastMath.sinCos(a);
SinCos sci = sc0;
final double[] sc = new double[2 * n];
int isc = 0;
sc[isc++] = sci.sin();
sc[isc++] = sci.cos();
for (int i = 1; i < n; i++) {
sci = SinCos.sum(sc0, sci);
sc[isc++] = sci.sin();
sc[isc++] = sci.cos();
}
return sc;
}
/**
* Computes cf2 coefficients.
* @param flattenF2 F2 coefficients used by the F2 layer (flatten array)
* @param azr effective sunspot number (Eq. 19)
* @param scT sines/cosines array of time argument
* @return the cf2 coefficients array
*/
private double[] computeCF2(final double[] flattenF2, final double azr, final double[] scT) {
// interpolation coefficients for effective spot number
final double azr01 = azr * 0.01;
final double omazr01 = 1 - azr01;
// Eq. 44 and Eq. 50 merged into one loop
final double[] cf2 = new double[76];
int index = 0;
for (int i = 0; i < cf2.length; i++) {
cf2[i] = omazr01 * flattenF2[index ] + azr01 * flattenF2[index + 1] +
(omazr01 * flattenF2[index + 2] + azr01 * flattenF2[index + 3]) * scT[ 0] +
(omazr01 * flattenF2[index + 4] + azr01 * flattenF2[index + 5]) * scT[ 1] +
(omazr01 * flattenF2[index + 6] + azr01 * flattenF2[index + 7]) * scT[ 2] +
(omazr01 * flattenF2[index + 8] + azr01 * flattenF2[index + 9]) * scT[ 3] +
(omazr01 * flattenF2[index + 10] + azr01 * flattenF2[index + 11]) * scT[ 4] +
(omazr01 * flattenF2[index + 12] + azr01 * flattenF2[index + 13]) * scT[ 5] +
(omazr01 * flattenF2[index + 14] + azr01 * flattenF2[index + 15]) * scT[ 6] +
(omazr01 * flattenF2[index + 16] + azr01 * flattenF2[index + 17]) * scT[ 7] +
(omazr01 * flattenF2[index + 18] + azr01 * flattenF2[index + 19]) * scT[ 8] +
(omazr01 * flattenF2[index + 20] + azr01 * flattenF2[index + 21]) * scT[ 9] +
(omazr01 * flattenF2[index + 22] + azr01 * flattenF2[index + 23]) * scT[10] +
(omazr01 * flattenF2[index + 24] + azr01 * flattenF2[index + 25]) * scT[11];
index += 26;
}
return cf2;
}
/**
* Computes Cm3 coefficients.
* @param flattenFm3 Fm3 coefficients used by the F2 layer (flatten array)
* @param azr effective sunspot number (Eq. 19)
* @param scT sines/cosines array of time argument
* @return the Cm3 coefficients array
*/
private double[] computeCm3(final double[] flattenFm3, final double azr, final double[] scT) {
// interpolation coefficients for effective spot number
final double azr01 = azr * 0.01;
final double omazr01 = 1 - azr01;
// Eq. 44 and Eq. 51 merged into one loop
final double[] cm3 = new double[49];
int index = 0;
for (int i = 0; i < cm3.length; i++) {
cm3[i] = omazr01 * flattenFm3[index ] + azr01 * flattenFm3[index + 1] +
(omazr01 * flattenFm3[index + 2] + azr01 * flattenFm3[index + 3]) * scT[ 0] +
(omazr01 * flattenFm3[index + 4] + azr01 * flattenFm3[index + 5]) * scT[ 1] +
(omazr01 * flattenFm3[index + 6] + azr01 * flattenFm3[index + 7]) * scT[ 2] +
(omazr01 * flattenFm3[index + 8] + azr01 * flattenFm3[index + 9]) * scT[ 3] +
(omazr01 * flattenFm3[index + 10] + azr01 * flattenFm3[index + 11]) * scT[ 4] +
(omazr01 * flattenFm3[index + 12] + azr01 * flattenFm3[index + 13]) * scT[ 5] +
(omazr01 * flattenFm3[index + 14] + azr01 * flattenFm3[index + 15]) * scT[ 6] +
(omazr01 * flattenFm3[index + 16] + azr01 * flattenFm3[index + 17]) * scT[ 7];
index += 18;
}
return cm3;
}
/**
* This method computes the F2 layer critical frequency.
* @param modip modified DIP latitude, in degrees
* @param cf2 Fourier time series for foF2
* @param latitude latitude in radians
* @param scL sines/cosines array of longitude argument
* @return the F2 layer critical frequency, MHz
*/
private double computefoF2(final double modip, final double[] cf2,
final double latitude, final double[] scL) {
// Legendre grades (Eq. 63)
final int[] q = new int[] {
12, 12, 9, 5, 2, 1, 1, 1, 1
};
double frequency = cf2[0];
// MODIP coefficients Eq. 57
final double sinMODIP = FastMath.sin(FastMath.toRadians(modip));
final double[] m = new double[12];
m[0] = 1.0;
for (int i = 1; i < q[0]; i++) {
m[i] = sinMODIP * m[i - 1];
frequency += m[i] * cf2[i];
}
// latitude and longitude terms
int index = 12;
final double cosLat1 = FastMath.cos(latitude);
double cosLatI = cosLat1;
for (int i = 1; i < q.length; i++) {
final double c = cosLatI * scL[2 * i - 1];
final double s = cosLatI * scL[2 * i - 2];
for (int j = 0; j < q[i]; j++) {
frequency += m[j] * c * cf2[index++];
frequency += m[j] * s * cf2[index++];
}
cosLatI *= cosLat1; // Eq. 58
}
return frequency;
}
/**
* This method computes the Maximum Usable Frequency factor.
* @param modip modified DIP latitude, in degrees
* @param cm3 Fourier time series for M(3000)F2
* @param latitude latitude in radians
* @param scL sines/cosines array of longitude argument
* @return the Maximum Usable Frequency factor
*/
private double computeMF2(final double modip, final double[] cm3,
final double latitude, final double[] scL) {
// Legendre grades (Eq. 71)
final int[] r = new int[] {
7, 8, 6, 3, 2, 1, 1
};
double m3000 = cm3[0];
// MODIP coefficients Eq. 57
final double sinMODIP = FastMath.sin(FastMath.toRadians(modip));
final double[] m = new double[12];
m[0] = 1.0;
for (int i = 1; i < 12; i++) {
m[i] = sinMODIP * m[i - 1];
if (i < 7) {
m3000 += m[i] * cm3[i];
}
}
// latitude and longitude terms
int index = 7;
final double cosLat1 = FastMath.cos(latitude);
double cosLatI = cosLat1;
for (int i = 1; i < r.length; i++) {
final double c = cosLatI * scL[2 * i - 1];
final double s = cosLatI * scL[2 * i - 2];
for (int j = 0; j < r[i]; j++) {
m3000 += m[j] * c * cm3[index++];
m3000 += m[j] * s * cm3[index++];
}
cosLatI *= cosLat1; // Eq. 58
}
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 foE the E layer critical frequency, MHz
* @return the F1 layer critical frequency, MHz
* @param foF2 the F2 layer critical frequency, MHz
*/
private double computefoF1(final double foE, final double foF2) {
final double temp = join(1.4 * foE, 0.0, 1000.0, foE - 2.0);
final double temp2 = join(0.0, temp, 1000.0, foE - temp);
final double value = join(temp2, 0.85 * temp2, 60.0, 0.85 * foF2 - temp2);
if (value < 1.0E-6) {
return 0.0;
} 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 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 double[] computeLayerAmplitudes(final double nmE, final double nmF1, final double foF1) {
// Initialize array
final double[] amplitude = new double[3];
// F2 layer amplitude (Eq. 90)
final double a1 = 4.0 * nmF2;
amplitude[0] = a1;
// F1 and E layer amplitudes (Eq. 91 to 98)
if (foF1 < 0.5) {
amplitude[1] = 0.0;
amplitude[2] = 4.0 * (nmE - epst(a1, hmF2, b2Bot, hmE));
} else {
double a2a = 0.0;
double a3a = 4.0 * nmE;
for (int i = 0; i < 5; i++) {
a2a = 4.0 * (nmF1 - epst(a1, hmF2, b2Bot, hmF1) - epst(a3a, hmE, beTop, hmF1));
a2a = join(a2a, 0.8 * nmF1, 1.0, a2a - 0.8 * nmF1);
a3a = 4.0 * (nmE - epst(a2a, hmF1, b1Bot, hmE) - epst(a1, hmF2, b2Bot, hmE));
}
amplitude[1] = a2a;
amplitude[2] = join(a3a, 0.05, 60.0, a3a - 0.005);
}
return amplitude;
}
/**
* This method computes the topside thickness parameter H0.
*
* @param month current month
* @param azr effective sunspot number
* @return H0 in km
*/
private double computeH0(final int month, final double azr) {
// Auxiliary parameter ka (Eq. 99 and 100)
final double ka;
if (month > 3 && month < 10) {
// month = 4,5,6,7,8,9
ka = 6.705 - 0.014 * azr - 0.008 * hmF2;
} else {
// month = 1,2,3,10,11,12
final double ratio = hmF2 / b2Bot;
ka = -7.77 + 0.097 * ratio * ratio + 0.153 * nmF2;
}
// Auxiliary parameter kb (Eq. 101 and 102)
double kb = join(ka, 2.0, 1.0, ka - 2.0);
kb = join(8.0, kb, 1.0, kb - 8.0);
// Auxiliary parameter Ha (Eq. 103)
final double hA = kb * b2Bot;
// Auxiliary parameters x and v (Eq. 104 and 105)
final double x = 0.01 * (hA - 150.0);
final double v = (0.041163 * x - 0.183981) * x + 1.424472;
// Topside thickness parameter (Eq. 106)
return hA / v;
}
/**
* 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 double clipExp(final double power) {
if (power > 80.0) {
return 5.5406E34;
} else if (power < -80) {
return 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 double interpolate(final double z1, final double z2,
final double z3, final double z4,
final double x) {
if (FastMath.abs(2.0 * x) < 1e-10) {
return z2;
}
final double delta = 2.0 * x - 1.0;
final double g1 = z3 + z2;
final double g2 = z3 - z2;
final double g3 = z4 + z1;
final double g4 = (z4 - z1) / 3.0;
final double a0 = 9.0 * g1 - g3;
final double a1 = 9.0 * g2 - g4;
final double a2 = g3 - g1;
final double a3 = g4 - g2;
return 0.0625 * (a0 + delta * (a1 + delta * (a2 + delta * a3)));
}
/**
* 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 double join(final double dF1, final double dF2,
final double dA, final double dX) {
final double ee = clipExp(dA * dX);
return (dF1 * ee + dF2) / (ee + 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 double epst(final double x, final double y,
final double z, final double w) {
final double ex = clipExp((w - y) / z);
final double opex = 1.0 + ex;
return x * ex / (opex * opex);
}
}