/[PAMELA software]/chewbacca/YodaProfiler/inc/sgp4.h
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Annotation of /chewbacca/YodaProfiler/inc/sgp4.h

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Revision 1.1.1.1 - (hide annotations) (download) (vendor branch)
Tue Sep 23 07:20:32 2008 UTC (16 years, 2 months ago) by mocchiut
Branch: v0r00, MAIN
CVS Tags: v1r02, v1r00, v1r01, start, v10RED, v9r00, v9r01, HEAD
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Imported sources, 23/09/2008

1 mocchiut 1.1 //
2     // stdafx.h
3     //
4     #ifndef sgp4_h
5     #define sgp4_h
6    
7     #if !defined(__CINT__) || defined(__MAKECINT__)
8    
9     //#define WIN32_LEAN_AND_MEAN // Exclude rarely-used stuff from Windows headers
10     #include <stdio.h>
11     //#include <tchar.h>
12     #include <ctype.h>
13     #include <string>
14     #include <map>
15     #include <vector>
16     #include <algorithm>
17     #include <assert.h>
18     #include <time.h>
19     #include <math.h>
20    
21     using namespace std;
22     //
23     // globals.h
24     //
25    
26     const double PI = 3.141592653589793;
27     const double TWOPI = 2.0 * PI;
28     const double RADS_PER_DEG = PI / 180.0;
29    
30     const double GM = 398601.2; // Earth gravitational constant, km^3/sec^2
31     const double GEOSYNC_ALT = 42241.892; // km
32     const double EARTH_DIA = 12800.0; // km
33     const double DAY_SIDERAL = (23 * 3600) + (56 * 60) + 4.09; // sec
34     const double DAY_24HR = (24 * 3600); // sec
35    
36     const double AE = 1.0;
37     const double AU = 149597870.0; // Astronomical unit (km) (IAU 76)
38     const double SR = 696000.0; // Solar radius (km) (IAU 76)
39     const double TWOTHRD = 2.0 / 3.0;
40     const double XKMPER_WGS72 = 6378.135; // Earth equatorial radius - km (WGS '72)
41     const double F = 1.0 / 298.26; // Earth flattening (WGS '72)
42     const double GE = 398600.8; // Earth gravitational constant (WGS '72)
43     const double J2 = 1.0826158E-3; // J2 harmonic (WGS '72)
44     const double J3 = -2.53881E-6; // J3 harmonic (WGS '72)
45     const double J4 = -1.65597E-6; // J4 harmonic (WGS '72)
46     const double CK2 = J2 / 2.0;
47     const double CK4 = -3.0 * J4 / 8.0;
48     const double XJ3 = J3;
49     const double E6A = 1.0e-06;
50     const double QO = AE + 120.0 / XKMPER_WGS72;
51     const double S = AE + 78.0 / XKMPER_WGS72;
52     const double HR_PER_DAY = 24.0; // Hours per day (solar)
53     const double MIN_PER_DAY = 1440.0; // Minutes per day (solar)
54     const double SEC_PER_DAY = 86400.0; // Seconds per day (solar)
55     const double OMEGA_E = 1.00273790934; // earth rotation per sideral day
56     const double XKE = sqrt(3600.0 * GE / //sqrt(ge) ER^3/min^2
57     (XKMPER_WGS72 * XKMPER_WGS72 * XKMPER_WGS72));
58     const double QOMS2T = pow((QO - S), 4); //(QO - S)^4 ER^4
59    
60     // Utility functions
61     double sqr (const double x);
62     double Fmod2p(const double arg);
63     double AcTan (const double sinx, double cosx);
64    
65     double rad2deg(const double);
66     double deg2rad(const double);
67     //
68     // coord.h
69     //
70     // Copyright 2002-2003 Michael F. Henry
71     //
72     //////////////////////////////////////////////////////////////////////
73     // Geocentric coordinates.
74     class cCoordGeo
75     {
76     public:
77     cCoordGeo();
78     cCoordGeo(double lat, double lon, double alt) :
79     m_Lat(lat), m_Lon(lon), m_Alt(alt) {}
80     virtual ~cCoordGeo() {};
81    
82     double m_Lat; // Latitude, radians (negative south)
83     double m_Lon; // Longitude, radians (negative west)
84     double m_Alt; // Altitude, km (above mean sea level)
85     };
86    
87     //////////////////////////////////////////////////////////////////////
88     // Topocentric-Horizon coordinates.
89     class cCoordTopo
90     {
91     public:
92     cCoordTopo();
93     cCoordTopo(double az, double el, double rng, double rate) :
94     m_Az(az), m_El(el), m_Range(rng), m_RangeRate(rate) {}
95     virtual ~cCoordTopo() {};
96    
97     double m_Az; // Azimuth, radians
98     double m_El; // Elevation, radians
99     double m_Range; // Range, kilometers
100     double m_RangeRate; // Range rate of change, km/sec
101     // Negative value means "towards observer"
102     };
103    
104     // cVector.h: interface for the cVector class.
105     //
106     // Copyright 2003 (c) Michael F. Henry
107     //
108     //////////////////////////////////////////////////////////////////////
109    
110     class cVector
111     {
112     public:
113     cVector(double x = 0.0, double y = 0.0, double z = 0.0, double w = 0.0) :
114     m_x(x), m_y(y), m_z(z), m_w(w) {}
115     virtual ~cVector() {};
116    
117     void Sub(const cVector&); // subtraction
118     void Mul(double factor); // multiply each component by 'factor'
119    
120     double Angle(const cVector&) const; // angle between two vectors
121     double Magnitude() const; // vector magnitude
122     double Dot(const cVector& vec) const; // dot product
123    
124     // protected:
125     double m_x;
126     double m_y;
127     double m_z;
128     double m_w;
129     };
130     //
131     // cTle.h
132     //
133     // This class will accept a single set of two-line elements and then allow
134     // a client to request specific fields, such as epoch, mean motion,
135     // etc., from the set.
136     //
137     // Copyright 1996-2003 Michael F. Henry
138     //
139     /////////////////////////////////////////////////////////////////////////////
140     class cTle
141     {
142     public:
143     cTle(string&, string&, string&);
144     cTle(const cTle &tle);
145     ~cTle();
146    
147     enum eTleLine
148     {
149     LINE_ZERO,
150     LINE_ONE,
151     LINE_TWO
152     };
153    
154     enum eField
155     {
156     FLD_FIRST,
157     FLD_NORADNUM = FLD_FIRST,
158     FLD_INTLDESC,
159     FLD_SET, // TLE set number
160     FLD_EPOCHYEAR, // Epoch: Last two digits of year
161     FLD_EPOCHDAY, // Epoch: Fractional Julian Day of year
162     FLD_ORBITNUM, // Orbit at epoch
163     FLD_I, // Inclination
164     FLD_RAAN, // R.A. ascending node
165     FLD_E, // Eccentricity
166     FLD_ARGPER, // Argument of perigee
167     FLD_M, // Mean anomaly
168     FLD_MMOTION, // Mean motion
169     FLD_MMOTIONDT, // First time derivative of mean motion
170     FLD_MMOTIONDT2,// Second time derivative of mean motion
171     FLD_BSTAR, // BSTAR Drag
172     FLD_LAST // MUST be last
173     };
174    
175     enum eUnits
176     {
177     U_FIRST,
178     U_RAD = U_FIRST, // radians
179     U_DEG, // degrees
180     U_NATIVE, // TLE format native units (no conversion)
181     U_LAST // MUST be last
182     };
183    
184     void Initialize();
185    
186     static int CheckSum(const string&);
187     static bool IsValidLine(string&, eTleLine);
188     static string ExpToDecimal(const string&);
189    
190     static void TrimLeft(string&);
191     static void TrimRight(string&);
192    
193     double getField(eField fld, // which field to retrieve
194     eUnits unit = U_NATIVE, // return units in rad, deg etc.
195     string *pstr = NULL, // return ptr for str value
196     bool bStrUnits = false) // 'true': append units to str val
197     const;
198     string getName() const { return m_strName; }
199     string getLine1() const { return m_strLine1;}
200     string getLine2() const { return m_strLine2;}
201    
202     protected:
203     static double ConvertUnits(double val, eField fld, eUnits units);
204    
205     private:
206     string getUnits(eField) const;
207     double getFieldNumeric(eField) const;
208    
209     // Satellite name and two data lines
210     string m_strName;
211     string m_strLine1;
212     string m_strLine2;
213    
214     // Converted fields, in atof()-readable form
215     string m_Field[FLD_LAST];
216    
217     // Cache of field values in "double" format
218     typedef int FldKey;
219     FldKey Key(eUnits u, eField f) const { return (u * 100) + f; }
220     mutable map<FldKey, double> m_mapCache;
221     };
222    
223     ///////////////////////////////////////////////////////////////////////////
224     //
225     // TLE data format
226     //
227     // [Reference: T.S. Kelso]
228     //
229     // Two line element data consists of three lines in the following format:
230     //
231     // AAAAAAAAAAAAAAAAAAAAAA
232     // 1 NNNNNU NNNNNAAA NNNNN.NNNNNNNN +.NNNNNNNN +NNNNN-N +NNNNN-N N NNNNN
233     // 2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN
234     //
235     // Line 0 is a twenty-two-character name.
236     //
237     // Lines 1 and 2 are the standard Two-Line Orbital Element Set Format identical
238     // to that used by NORAD and NASA. The format description is:
239     //
240     // Line 1
241     // Column Description
242     // 01-01 Line Number of Element Data
243     // 03-07 Satellite Number
244     // 10-11 International Designator (Last two digits of launch year)
245     // 12-14 International Designator (Launch number of the year)
246     // 15-17 International Designator (Piece of launch)
247     // 19-20 Epoch Year (Last two digits of year)
248     // 21-32 Epoch (Julian Day and fractional portion of the day)
249     // 34-43 First Time Derivative of the Mean Motion
250     // or Ballistic Coefficient (Depending on ephemeris type)
251     // 45-52 Second Time Derivative of Mean Motion (decimal point assumed;
252     // blank if N/A)
253     // 54-61 BSTAR drag term if GP4 general perturbation theory was used.
254     // Otherwise, radiation pressure coefficient. (Decimal point assumed)
255     // 63-63 Ephemeris type
256     // 65-68 Element number
257     // 69-69 Check Sum (Modulo 10)
258     // (Letters, blanks, periods, plus signs = 0; minus signs = 1)
259     //
260     // Line 2
261     // Column Description
262     // 01-01 Line Number of Element Data
263     // 03-07 Satellite Number
264     // 09-16 Inclination [Degrees]
265     // 18-25 Right Ascension of the Ascending Node [Degrees]
266     // 27-33 Eccentricity (decimal point assumed)
267     // 35-42 Argument of Perigee [Degrees]
268     // 44-51 Mean Anomaly [Degrees]
269     // 53-63 Mean Motion [Revs per day]
270     // 64-68 Revolution number at epoch [Revs]
271     // 69-69 Check Sum (Modulo 10)
272     //
273     // All other columns are blank or fixed.
274     //
275     // Example:
276     //
277     // NOAA 6
278     // 1 11416U 86 50.28438588 0.00000140 67960-4 0 5293
279     // 2 11416 98.5105 69.3305 0012788 63.2828 296.9658 14.24899292346978
280    
281     //
282     // cJulian.h
283     //
284     // Copyright (c) 2003 Michael F. Henry
285     //
286     //
287     // See note in cJulian.cpp for information on this class and the epoch dates
288     //
289     const double EPOCH_JAN1_00H_1900 = 2415019.5; // Jan 1.0 1900 = Jan 1 1900 00h UTC
290     const double EPOCH_JAN1_12H_1900 = 2415020.0; // Jan 1.5 1900 = Jan 1 1900 12h UTC
291     const double EPOCH_JAN1_12H_2000 = 2451545.0; // Jan 1.5 2000 = Jan 1 2000 12h UTC
292    
293     //////////////////////////////////////////////////////////////////////////////
294     class cJulian
295     {
296     public:
297     cJulian() { Initialize(2000, 1); }
298     explicit cJulian(time_t t); // Create from time_t
299     explicit cJulian(int year, double day); // Create from year, day of year
300     explicit cJulian(int year, // i.e., 2004
301     int mon, // 1..12
302     int day, // 1..31
303     int hour, // 0..23
304     int min, // 0..59
305     double sec = 0.0); // 0..(59.999999...)
306     ~cJulian() {};
307    
308     double toGMST() const; // Greenwich Mean Sidereal Time
309     double toLMST(double lon) const; // Local Mean Sideral Time
310     time_t toTime() const; // To time_t type - avoid using
311    
312     double FromJan1_00h_1900() const { return m_Date - EPOCH_JAN1_00H_1900; }
313     double FromJan1_12h_1900() const { return m_Date - EPOCH_JAN1_12H_1900; }
314     double FromJan1_12h_2000() const { return m_Date - EPOCH_JAN1_12H_2000; }
315    
316     void getComponent(int *pYear, int *pMon = NULL, double *pDOM = NULL) const;
317     double getDate() const { return m_Date; }
318    
319     void addDay (double day) { m_Date += day; }
320     void addHour(double hr ) { m_Date += (hr / HR_PER_DAY ); }
321     void addMin (double min) { m_Date += (min / MIN_PER_DAY); }
322     void addSec (double sec) { m_Date += (sec / SEC_PER_DAY); }
323    
324     double spanDay (const cJulian& b) const { return m_Date - b.m_Date; }
325     double spanHour(const cJulian& b) const { return spanDay(b) * HR_PER_DAY; }
326     double spanMin (const cJulian& b) const { return spanDay(b) * MIN_PER_DAY; }
327     double spanSec (const cJulian& b) const { return spanDay(b) * SEC_PER_DAY; }
328    
329     static bool IsLeapYear(int y)
330     { return (y % 4 == 0 && y % 100 != 0) || (y % 400 == 0); }
331    
332     protected:
333     void Initialize(int year, double day);
334    
335     double m_Date; // Julian date
336     };
337     //
338     // cEci.h
339     //
340     // Copyright (c) 2003 Michael F. Henry
341     //
342     //////////////////////////////////////////////////////////////////////
343     // class cEci
344     // Encapsulates an Earth-Centered Inertial position, velocity, and time.
345     class cEci
346     {
347     public:
348     cEci() { m_VecUnits = UNITS_NONE; }
349     cEci(const cCoordGeo &geo, const cJulian &cJulian);
350     cEci(const cVector &pos, const cVector &vel,
351     const cJulian &date, bool IsAeUnits = true);
352     virtual ~cEci() {};
353    
354     cCoordGeo toGeo();
355    
356     cVector getPos() const { return m_pos; }
357     cVector getVel() const { return m_vel; }
358     cJulian getDate() const { return m_date; }
359    
360     void setUnitsAe() { m_VecUnits = UNITS_AE; }
361     void setUnitsKm() { m_VecUnits = UNITS_KM; }
362     bool UnitsAreAe() const { return m_VecUnits == UNITS_AE; }
363     bool UnitsAreKm() const { return m_VecUnits == UNITS_KM; }
364     void ae2km(); // Convert position, velocity vector units from AE to km
365    
366     protected:
367     void MulPos(double factor) { m_pos.Mul(factor); }
368     void MulVel(double factor) { m_vel.Mul(factor); }
369    
370     enum VecUnits
371     {
372     UNITS_NONE, // not initialized
373     UNITS_AE,
374     UNITS_KM
375     };
376    
377     cVector m_pos;
378     cVector m_vel;
379     cJulian m_date;
380     VecUnits m_VecUnits;
381     };
382     //
383     // cNoradBase.h
384     //
385     // This class provides a base class for the NORAD SGP4/SDP4
386     // orbit models.
387     //
388     // Copyright (c) 2003 Michael F. Henry
389     //
390     #pragma once
391    
392     //////////////////////////////////////////////////////////////////////////////
393    
394     class cEci;
395     class cOrbit;
396    
397     //////////////////////////////////////////////////////////////////////////////
398    
399     class cNoradBase
400     {
401     public:
402     cNoradBase(const cOrbit&);
403     virtual ~cNoradBase() {};
404    
405     virtual bool getPosition(double tsince, cEci &eci) = 0;
406    
407     protected:
408     cNoradBase& operator=(const cNoradBase&);
409    
410     void Initialize();
411     bool FinalPosition(double incl, double omega, double e,
412     double a, double xl, double xnode,
413     double xn, double tsince, cEci &eci);
414    
415     const cOrbit &m_Orbit;
416    
417     // Orbital parameter variables which need only be calculated one
418     // time for a given orbit (ECI position time-independent).
419     double m_satInc; // inclination
420     double m_satEcc; // eccentricity
421    
422     double m_cosio; double m_theta2; double m_x3thm1; double m_eosq;
423     double m_betao2; double m_betao; double m_aodp; double m_xnodp;
424     double m_s4; double m_qoms24; double m_perigee; double m_tsi;
425     double m_eta; double m_etasq; double m_eeta; double m_coef;
426     double m_coef1; double m_c1; double m_c2; double m_c3;
427     double m_c4; double m_sinio; double m_a3ovk2; double m_x1mth2;
428     double m_xmdot; double m_omgdot; double m_xhdot1; double m_xnodot;
429     double m_xnodcf; double m_t2cof; double m_xlcof; double m_aycof;
430     double m_x7thm1;
431     };
432     //
433     // cOrbit.h
434     //
435     // This is the header file for the class cOrbit. This class accepts a
436     // single satellite's NORAD two-line element set and provides information
437     // regarding the satellite's orbit such as period, axis length,
438     // ECI coordinates/velocity, etc., using the SGP4/SDP4 orbital models.
439     //
440     // Copyright (c) 2002-2003 Michael F. Henry
441     //
442     #pragma once
443    
444     #include "math.h"
445    
446     using namespace std;
447     //////////////////////////////////////////////////////////////////////////////
448    
449     class cVector;
450     class cGeoCoord;
451     class cEci;
452    
453     //////////////////////////////////////////////////////////////////////////////
454     class cOrbit
455     {
456     public:
457     cOrbit(const cTle &tle);
458     virtual ~cOrbit();
459    
460     // Return satellite ECI data at given minutes since element's epoch.
461     bool getPosition(double tsince, cEci *pEci) const;
462    
463     double Inclination() const { return radGet(cTle::FLD_I); }
464     double Eccentricity() const { return m_tle.getField(cTle::FLD_E); }
465     double RAAN() const { return radGet(cTle::FLD_RAAN); }
466     double ArgPerigee() const { return radGet(cTle::FLD_ARGPER); }
467     double BStar() const { return m_tle.getField(cTle::FLD_BSTAR) / AE;}
468     double Drag() const { return m_tle.getField(cTle::FLD_MMOTIONDT); }
469     double mnMotion() const { return m_tle.getField(cTle::FLD_MMOTION); }
470     double mnAnomaly() const { return radGet(cTle::FLD_M); }
471     double mnAnomaly(cJulian t) const; // mean anomaly (in radians) at time t
472    
473     cJulian Epoch() const { return m_jdEpoch; }
474    
475     double TPlusEpoch(const cJulian &t) const; // time span [t - epoch] in secs
476    
477     string SatName(bool fAppendId = false) const;
478    
479     // "Recovered" from the input elements
480     double SemiMajor() const { return m_aeAxisSemiMajorRec; }
481     double SemiMinor() const { return m_aeAxisSemiMinorRec; }
482     double mnMotionRec() const { return m_mnMotionRec; } // mn motion, rads/min
483     double Major() const { return 2.0 * SemiMajor(); } // major axis in AE
484     double Minor() const { return 2.0 * SemiMinor(); } // minor axis in AE
485     double Perigee() const { return m_kmPerigeeRec; } // perigee in km
486     double Apogee() const { return m_kmApogeeRec; } // apogee in km
487     double Period() const; // period in seconds
488    
489     protected:
490     double radGet(cTle::eField fld) const
491     { return m_tle.getField(fld, cTle::U_RAD); }
492    
493     double degGet(cTle::eField fld) const
494     { return m_tle.getField(fld, cTle::U_DEG); }
495    
496     private:
497     cTle m_tle;
498     cJulian m_jdEpoch;
499     cNoradBase *m_pNoradModel;
500    
501     // Caching variables; note units are not necessarily the same as tle units
502     mutable double m_secPeriod;
503    
504     // Caching variables recovered from the input TLE elements
505     double m_aeAxisSemiMinorRec; // semi-minor axis, in AE units
506     double m_aeAxisSemiMajorRec; // semi-major axis, in AE units
507     double m_mnMotionRec; // radians per minute
508     double m_kmPerigeeRec; // perigee, in km
509     double m_kmApogeeRec; // apogee, in km
510     };
511    
512     //
513     // cNoradSGP4.h
514     //
515     // This class implements the NORAD Simple General Perturbation 4 orbit
516     // model. This model provides the ECI coordiantes/velocity of satellites
517     // with orbit periods less than 225 minutes.
518     //
519     // Copyright (c) 2003 Michael F. Henry
520     //
521     #pragma once
522    
523     class cOrbit;
524    
525     //////////////////////////////////////////////////////////////////////////////
526     class cNoradSGP4 : public cNoradBase
527     {
528     public:
529     cNoradSGP4(const cOrbit &orbit);
530     virtual ~cNoradSGP4() {};
531    
532     virtual bool getPosition(double tsince, cEci &eci);
533    
534     protected:
535     double m_c5;
536     double m_omgcof;
537     double m_xmcof;
538     double m_delmo;
539     double m_sinmo;
540     };
541    
542     //
543     // cNoradSDP4.h
544     //
545     // This class implements the NORAD Simple Deep Perturbation 4 orbit
546     // model. This model provides the ECI coordinates/velocity of satellites
547     // with periods >= 225 minutes.
548     //
549     // Copyright (c) 2003 Michael F. Henry
550     //
551     #pragma once
552    
553     class cOrbit;
554    
555     //////////////////////////////////////////////////////////////////////////////
556     class cNoradSDP4 : public cNoradBase
557     {
558     public:
559     cNoradSDP4(const cOrbit &orbit);
560     virtual ~cNoradSDP4() {};
561    
562     virtual bool getPosition(double tsince, cEci &eci);
563    
564     protected:
565     bool DeepInit(double *eosq, double *sinio, double *cosio, double *m_betao,
566     double *m_aodp, double *m_theta2, double *m_sing, double *m_cosg,
567     double *m_betao2,double *xmdot, double *omgdot, double *xnodott);
568    
569     bool DeepSecular(double *xmdf, double *omgadf,double *xnode, double *emm,
570     double *xincc, double *xnn, double *tsince);
571     bool DeepCalcDotTerms (double *pxndot, double *pxnddt, double *pxldot);
572     void DeepCalcIntegrator(double *pxndot, double *pxnddt, double *pxldot,
573     const double &delt);
574     bool DeepPeriodics(double *e, double *xincc, double *omgadf,
575     double *xnode, double *xmam);
576     double m_sing;
577     double m_cosg;
578    
579     // Deep Initialization
580     double eqsq; double siniq; double cosiq; double rteqsq; double ao;
581     double cosq2; double sinomo; double cosomo; double bsq; double xlldot;
582     double omgdt; double xnodot;
583    
584     // Deep Secular, Periodic
585     double xll; double omgasm; double xnodes; double _em;
586     double xinc; double xn; double t;
587    
588     // Variables shared by "Deep" routines
589     double dp_e3; double dp_ee2; double dp_savtsn; double dp_se2;
590     double dp_se3; double dp_sgh2; double dp_sgh3; double dp_sgh4;
591     double dp_sghs; double dp_sh2; double dp_sh3; double dp_si2;
592     double dp_si3; double dp_sl2; double dp_sl3; double dp_sl4;
593     double dp_xgh2; double dp_xgh3; double dp_xgh4; double dp_xh2;
594     double dp_xh3; double dp_xi2; double dp_xi3; double dp_xl2;
595     double dp_xl3; double dp_xl4; double dp_xqncl; double dp_zmol;
596     double dp_zmos;
597    
598     double dp_atime; double dp_d2201; double dp_d2211; double dp_d3210;
599     double dp_d3222; double dp_d4410; double dp_d4422; double dp_d5220;
600     double dp_d5232; double dp_d5421; double dp_d5433; double dp_del1;
601     double dp_del2; double dp_del3; double dp_fasx2; double dp_fasx4;
602     double dp_fasx6; double dp_omegaq; double dp_sse; double dp_ssg;
603     double dp_ssh; double dp_ssi; double dp_ssl; double dp_step2;
604     double dp_stepn; double dp_stepp; double dp_thgr; double dp_xfact;
605     double dp_xlamo; double dp_xli; double dp_xni;
606    
607     bool dp_iresfl;
608     bool dp_isynfl;
609    
610     // DeepInit vars that change with epoch
611     double dpi_c; double dpi_ctem; double dpi_day; double dpi_gam;
612     double dpi_stem; double dpi_xnodce; double dpi_zcosgl; double dpi_zcoshl;
613     double dpi_zcosil; double dpi_zsingl; double dpi_zsinhl; double dpi_zsinil;
614     double dpi_zx; double dpi_zy;
615    
616     };
617    
618     #endif
619     #endif
620    

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