[124] | 1 | |
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| 2 | |
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| 3 | #define CODENAME "NBI" |
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| 4 | #define VERSION "1" |
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| 5 | |
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| 6 | /* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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| 7 | |
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| 8 | NBI |
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| 9 | A set of numerical integrators for the gravitational N-body problem. |
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| 10 | |
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| 11 | (C) Copyright 1996 Ferenc Varadi. All rights reserved. |
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| 12 | This copyright notice is intended to prevent the commercial use of this code. |
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| 13 | The code is free and can be freely distributed. |
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| 14 | Do not remove this copyright notice unless you make changes in the code. |
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| 15 | If you make changes in the code, add your name to the copyright notice. |
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| 16 | |
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| 17 | The usual disclaimers apply, i.e., use the code at your own risk. |
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| 18 | The author does not guarantee anything. |
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| 19 | |
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| 20 | This code was developed by F. Varadi in collaboration |
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| 21 | with M. Ghil, W. I. Newman, W. M. Kaula, K. Grazier, D. Goldstein |
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| 22 | and M. Lessnick. The partial financial support of NSF Grant |
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| 23 | ATM95-23787 (M. Ghil and F. Varadi) is gratefully acknowledged. |
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| 24 | |
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| 25 | If you have any questions, suggestions etc., contact F. Varadi, |
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| 26 | e-mail: varadi@ucla.edu |
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| 27 | WWW: http://www.atmos.ucla.edu/~varadi |
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| 28 | |
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| 29 | |
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| 30 | For the impatient: |
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| 31 | Save this file as NBI.c |
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| 32 | Compile the code as |
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| 33 | cc -o NBI NBI.c -lm |
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| 34 | |
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| 35 | Download the sample input file NBIsampleinput and save it as |
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| 36 | NBIsampleinput. It is an input file for the outer Solar System, with |
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| 37 | the planets from Jupiter through Neptune based on the Jet Propulsion |
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| 38 | Laboratory's DE403 (Digital Ephemeris 403). This was obtained |
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| 39 | from the ftp site navigator.jpl.nasa.gov, updates can be accessed |
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| 40 | there. |
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| 41 | |
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| 42 | Run the code: |
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| 43 | NBI NBIsampleinput |
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| 44 | Take a look at the output in NBIsampleoutput and the log file |
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| 45 | NBIsampleoutput.log Change the MAXNBODIES macro, i.e., the |
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| 46 | maximum number of particles, to suit your needs. It is set to |
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| 47 | 2100 in this version. |
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| 48 | |
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| 49 | 1) Description: |
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| 50 | Four numerical integrators for the gravitational (nonrelativistic) |
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| 51 | N-body problem are bundled into a single source code. The N bodies |
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| 52 | are assumed to be point masses. Particles with zero mass are called |
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| 53 | test particles; they are assumed not to influence each other and |
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| 54 | the particles with nonzero mass. |
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| 55 | |
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| 56 | The integrators are: |
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| 57 | |
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| 58 | a) A Wisdom-Holman-type mapping for hierarchical N-body systems. |
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| 59 | Code name: HWH, maximum global order = 4 |
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| 60 | This can deal with more general arrangements than the standard |
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| 61 | Wisdom-Holman mapping. Hierarchical N-body systems are described |
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| 62 | by Roy (1988). These are represented in the code by binary trees. |
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| 63 | The integrator takes advantage of certain properties of |
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| 64 | symplectic forms and Jacobi coordinates, these will be described |
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| 65 | in a paper (in preparation). We also use singularly weighted |
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| 66 | symplectic forms, these are discussed by Varadi et al. (1995). |
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| 67 | |
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| 68 | b) A modified Cowell-Stormer integrator, with modifications by |
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| 69 | W. I. Newman and his students. |
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| 70 | Code name: CSN, max global order = 15 |
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| 71 | Note: (global order) = (local order) - 2 (Goldstein, 1996) |
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| 72 | |
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| 73 | c) A Gragg-Bulirsch-Stoer integrator, as it is described by |
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| 74 | Hairer et al., (1993). |
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| 75 | Code name: GBS, max order = 20 (max stage = 10) |
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| 76 | IMPORTANT: The user has to specify the number of stages |
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| 77 | in the input file and not the order. Order = 2*(number of stages), |
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| 78 | see the Notes below. |
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| 79 | |
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| 80 | d) A symplectic mapping with Kinetic-Potential energy splitting |
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| 81 | Code name: SKP, max global order = 4 |
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| 82 | This is included for the sake of completeness. |
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| 83 | |
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| 84 | |
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| 85 | 2) References: |
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| 86 | |
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| 87 | Goldstein, D.: 1996, The Near-Optimality of Stormer |
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| 88 | Methods for Long Time Integrations of y''=g(y), |
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| 89 | Ph.D. Dissertation, Univ. of California, Los Angeles, |
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| 90 | Dept. of Mathematics |
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| 91 | |
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| 92 | Hairer, E., Norsett, S. P. and Wanner, G.: 1993, |
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| 93 | Solving Ordinary Differential Equations I. Nonstiff Problems. |
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| 94 | Second Revised Edition |
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| 95 | |
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| 96 | Lessnick, M.: 1996, Stability Analysis of Symplectic |
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| 97 | Integration Schemes, Ph.D. Dissertation, Univ. of California, |
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| 98 | Los Angeles, Dept. of Mathematics |
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| 99 | |
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| 100 | Roy, A. E.: 1988, Orbital Motion, Institute of Physics |
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| 101 | Publishing, Bristol |
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| 102 | |
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| 103 | Varadi, F. De la Barre, Kaula, W. M. and Ghil, M.: 1995, |
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| 104 | Singularly Weighted Symplectic Forms and Applications to |
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| 105 | Asteroid Motion, Celestial Mechanics and Dynamical Astronomy, |
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| 106 | vol. 62, pp. 23-41 |
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| 107 | |
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| 108 | Yoshida, H.: 1993, Recent Progress in The Theory and |
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| 109 | Application of Symplectic Integrators, |
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| 110 | Celestial Mechanics and Dynamical Astronomy, vol. 56, pp. 27-43 |
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| 111 | |
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| 112 | |
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| 113 | |
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| 114 | 3) Notes |
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| 115 | |
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| 116 | All long-term integrations suffer from roundoff errors. |
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| 117 | Symplectic schemes guarantee symplecticity for short |
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| 118 | integrations but they are not strictly symplectic |
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| 119 | for very long integrations. The implementation of |
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| 120 | the Wisdom-Holman mapping in this code was aimed at |
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| 121 | reducing the effects of roundoff errors and thus make |
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| 122 | the scheme as symplectic as possible. |
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| 123 | |
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| 124 | The Cowell-Stormer integrator, being a multistep |
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| 125 | integrator, has to be intialized. In theory, the starting |
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| 126 | points should be computed with machine precision. This |
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| 127 | can be done using quadrupole precision arithmetic but |
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| 128 | the Gragg-Bulirsch-Stoer scheme in double precision |
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| 129 | appers to be quite adequate. It should be noted that |
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| 130 | the stability of the Cowell-Stormer scheme ensures |
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| 131 | that initial errors do not grow due to computational |
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| 132 | limitations (Goldstein, 1996). |
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| 133 | |
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| 134 | In the case of the Gragg-Bulirsch-Stoer scheme one |
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| 135 | specifies the number of stages k in the extrapolation |
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| 136 | scheme. The order of the method is then 2*k. |
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| 137 | This factor of 2 comes from the fact that the |
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| 138 | underlying method (Gragg's) has only even powers |
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| 139 | of the step size in the expansion of the local error |
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| 140 | (cf. Hairer et al., 1993, especially equation 9.22). |
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| 141 | |
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| 142 | All integrators use only G*mass, there is no need for |
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| 143 | the masses themselves nor the value of G. Any set of units |
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| 144 | can be used: |
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| 145 | distance_unit for position, |
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| 146 | time_unit for time and step size, |
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| 147 | distance_unit/time_unit for velocity. |
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| 148 | E.g., one can use AU, day and AU/day as units. |
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| 149 | |
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| 150 | None of the codes is regularized in any sense. We intend |
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| 151 | to provide regularized code in the future. For the Wisdom-Holman |
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| 152 | mapping this involves changing the tree of Jacobian reference |
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| 153 | frames and dealing with the transition region accurately. |
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| 154 | |
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| 155 | In the case of the Wisdom-Holman mapping, the computation of |
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| 156 | acceleration differences between Jacobi and inertial coordinates |
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| 157 | could be improved in order to further reduce roundoff error. |
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| 158 | These differences can be represented by multi-pole expansions |
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| 159 | of the potential but we have not explored the details yet. |
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| 160 | |
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| 161 | The present version of the integrator does not monitor error. |
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| 162 | |
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| 163 | The choice of step size is up to the user. In most cases |
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| 164 | one has to adjust the step size to the shortest orbital |
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| 165 | period T in the system. The Wisdom-Holman mapping at second |
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| 166 | order is usually used with step size of T/10-T/100. |
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| 167 | We recommend T/1000 for Cowell-Stormer integrator |
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| 168 | since this renders the calculation EXACT to double |
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| 169 | precision, even for high (e=0.5) eccentricities. |
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| 170 | The cost of using this short time step is substantially |
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| 171 | compensated by reduced computational complexity (as |
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| 172 | compared to the Wisdom-Holman mapping). For much larger |
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| 173 | step sizes the integrator is not stable. |
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| 174 | |
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| 175 | The Gragg-Bulirsch-Stoer method appears to be stable |
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| 176 | for large orders and step sizes. For order 20 one can |
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| 177 | even use T/5 as the step size and still get accurate results. |
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| 178 | Since this is an accurate but compuationally very expensive |
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| 179 | integrator, it is mainly used by us for short integrations. |
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| 180 | We have not investigated the propagation of roundoff |
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| 181 | error in the GBS method. |
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| 182 | |
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| 183 | |
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| 184 | 4) How to compile: |
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| 185 | Since there is only a single source file, it is very easy to |
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| 186 | compile the code with whatever C compiler is available. The |
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| 187 | code was compiled and tested on Sun SPARCstations (Solaris 2.5.1 |
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| 188 | and earlier) and DEC Alpha workstations (Digital UNIX V3.2). |
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| 189 | For instance, on the SPARCstations, |
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| 190 | |
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| 191 | cc -fast -xO5 -xdepend -o NBI NBI.c -lm |
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| 192 | |
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| 193 | should work with Sun's C compiler. The code uses only the standard |
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| 194 | C library, more exactly: I/O functions, exit, malloc and free for |
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| 195 | the tree, sqrt, cbrt, sin, cos, sinh, cosh. |
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| 196 | |
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| 197 | Caution: optimization may introduce problems with some compilers |
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| 198 | and it is prudent to check the correctness of the optimized code |
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| 199 | by compiling without optimization, e.g., |
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| 200 | cc -g -o NBI_no_op NBI.c -lm |
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| 201 | By comparing the output from NBI and NBI_no_op one can detect if |
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| 202 | the optimization leads to any problems. (It should not but in |
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| 203 | practice the situation is not so clear.) |
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| 204 | |
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| 205 | One also can play with various compiler switches which control |
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| 206 | roundoff but we have not explored these. |
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| 207 | |
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| 208 | 5) How to run |
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| 209 | |
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| 210 | NBI inputfile |
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| 211 | |
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| 212 | (Everything has to be specified in inputfile.) |
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| 213 | |
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| 214 | 6) On hierarchical N-body systems |
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| 215 | |
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| 216 | We can give only a brief introduction into these; a detailed technical |
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| 217 | description is in preparation. Our approach is somewhat different |
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| 218 | from that of Roy (1988). |
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| 219 | |
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| 220 | One starts with the concept of joining subsystems and applies this |
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| 221 | concept recursively to form new systems. When two subsystems are |
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| 222 | joined, the two subsystems are assumed to behave as point masses |
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| 223 | and thus define the appropriate two-body problem for the Wisdom-Holman |
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| 224 | mapping. The subsystems are, in general, not point masses and one |
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| 225 | takes this into account in the perturbation step of the Wisdom-Holman |
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| 226 | mapping. |
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| 227 | |
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| 228 | Instead of a simple chain of Jacobi coordinates, the code uses a |
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| 229 | tree of Jacobi coordinates. This makes it possible to use the code |
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| 230 | e.g., in situations when the massive particles have sattelites, either |
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| 231 | massive ones or not. It also reduces, when carefully specified, the |
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| 232 | integration error since more of the perturbations are absorbed into |
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| 233 | two-body interactions. The tree has to be specified in the input file. |
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| 234 | One can define this tree formally as it is processed by the code which |
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| 235 | works like a simple finite automaton but we did not use lex, yacc or |
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| 236 | any other compiler-compiler tools. |
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| 237 | |
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| 238 | Tree description rules: |
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| 239 | Rule 1) particles are indexed by consecutive natural numbers, from 1 to N, |
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| 240 | Rule 2) particles are subsystems, |
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| 241 | Rule 3) (x y) : join the subsystems x and y to create a new subsystem., |
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| 242 | Rule 4) [i1 - i2] denotes a set of test particles, from index i1 to index i2, |
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| 243 | which are treated the same way, |
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| 244 | Note: the space before and after - is necessary! |
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| 245 | Rule 5) ([i1 - i2] i3) is forbidden, use instead (i3 [i1 - i2]) |
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| 246 | |
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| 247 | Example: 2000 main belt asteroids, from 6 to 2006, and |
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| 248 | Sun, Jupiter, Saturn, Uranus and Neptune (1 - 5) |
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| 249 | can described as |
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| 250 | (((((1 [6 - 2006]) 2) 3) 4) 5) |
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| 251 | |
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| 252 | Another example for the tree specification when test particles between |
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| 253 | Jupiter and Saturn are added with indeces from 6 to 1000 and another set |
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| 254 | of test particles is added between Saturn and Uranus with indices from |
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| 255 | 1001 to 2000. The indices for the massive bodies are: |
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| 256 | Sun 1, Jupiter, 2, Saturn 3, Uranus 4, Neptune 5. |
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| 257 | ((((((1 2) [6 - 1000]) 3) [1001 - 2000]) 4) 5) |
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| 258 | |
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| 259 | Yet another example: the Sun, Earth, Moon, Jupiter and Io with indeces |
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| 260 | 1,2,3,4 and 5, respectively, for which the tree is |
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| 261 | ((1 (2 3)) (4 5)) |
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| 262 | |
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| 263 | |
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| 264 | 7) Format of the input file |
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| 265 | Id method order step_size total_integration_time printing_time |
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| 266 | number_of_particles |
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| 267 | |
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| 268 | tree_description |
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| 269 | |
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| 270 | GMs of particles, possibly zeros |
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| 271 | |
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| 272 | Initial conditions: x,y,z, vx, vy, vz |
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| 273 | |
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| 274 | Explanation: |
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| 275 | |
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| 276 | Id is an arbitrary string which specifies the name of the experiment. |
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| 277 | |
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| 278 | Method can be SKP, HWH, CSN and GBS. |
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| 279 | |
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| 280 | Tree_description is used only when the method is HWH or the HWH is used |
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| 281 | to initialize CSN. One can put a dummy tree description of the form |
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| 282 | (1 2) |
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| 283 | in the input file when HWH is not used. This will satisfy the parser |
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| 284 | which processes the tree description but will not play any role in the |
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| 285 | integration. |
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| 286 | |
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| 287 | |
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| 288 | Example: |
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| 289 | For Sun, Jupiter, Saturn, Uranus and Neptune, |
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| 290 | with indeces 1,2,3,4 and 5, in heliocentric coordinates. |
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| 291 | |
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| 292 | SomeId HWH 4 100.0 365.0e+4 1.0e+4 |
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| 293 | 5 |
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| 294 | ((((1 2) 3) 4) 5) |
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| 295 | |
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| 296 | 0.295912208285591095e-03 |
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| 297 | 0.282534590952422643e-06 0.845971518568065874e-07 |
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| 298 | 0.129202491678196939e-07 0.152435890078427628e-07 |
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| 299 | |
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| 300 | 0.0 0.0 0.0 0.0 0.0 0.0 |
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| 301 | |
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| 302 | -0.538420940678015203e+01 -0.831247035699103631e+00 -0.225095848657298592e+00 |
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| 303 | 0.109236311953937086e-02 -0.652329334256263223e-02 -0.282301443780311710e-02 |
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| 304 | |
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| 305 | 0.788989169798583756e+01 0.459570785756998301e+01 0.155843220515231762e+01 |
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| 306 | -0.321720261683698921e-02 0.433063255278440598e-02 0.192641782724487106e-02 |
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| 307 | |
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| 308 | -0.182698980946940850e+02 -0.116271406901560681e+01 -0.250371938307287545e+00 |
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| 309 | 0.221540447608191936e-03 -0.376765389967669917e-02 -0.165324449144407023e-02 |
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| 310 | |
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| 311 | -0.160595376822070470e+02 -0.239429495784517528e+02 -0.940042953888094424e+01 |
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| 312 | 0.264312302715172384e-02 -0.150349219713705076e-02 -0.681271071793930938e-03 |
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| 313 | |
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| 314 | |
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| 315 | There are 2 output files: |
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| 316 | 1) SomeId contains the actual integration data |
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| 317 | 2) SomeId.log contains a copy of the input data and error messages. |
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| 318 | Some error messages might be sent to the standard output and the user |
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| 319 | has to redirect it in order to capture them. |
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| 320 | |
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| 321 | In the case of the Cowell-Stormer integrator, an additional file, SomeId.lerr |
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| 322 | is created. This contains the LOCAL truncation error of the integration, |
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| 323 | computed for each step but only printed for the last step in the printing |
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| 324 | cycle. This also should help to determine the appropriate step size. |
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| 325 | |
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| 326 | The output is in the original coordinate system, i.e., inertial and not Jacobian. |
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| 327 | Output is produced when time is an integer multiple of the specified printing |
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| 328 | time. The following is printed: |
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| 329 | time relative_change_in_total_energy relative_change_in_ang.mom.z.comp. |
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| 330 | after which |
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| 331 | x y z |
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| 332 | dx dy dz |
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| 333 | for each particle. |
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| 334 | |
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| 335 | |
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| 336 | 9) The uset can change the code, of course. The section MAIN LOOP is where |
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| 337 | this can be done easily. You can insert code to do more things, e.g., |
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| 338 | detecting close approaches. |
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| 339 | |
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| 340 | 10) MACROS TO GIVE SOME CONTROL OVER THINGS. |
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| 341 | Changes in the code that you can make HERE: |
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| 342 | CHANGE the DIM macro to 2 for planar motions. |
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| 343 | (Note: a variables dim is also used, easy to change |
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| 344 | it everywhere to DIM. It is still better to keep |
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| 345 | the Kepler solver in the more general 3-dimensional form.) |
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| 346 | CHANGE the MAXNBODIES macro to whatever you want, |
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| 347 | including test particles. |
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| 348 | |
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| 349 | **************** END OF DESCRIPTION ********************** */ |
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| 350 | |
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| 351 | /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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| 352 | USER-CHANGEABLE MACROS */ |
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| 353 | |
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| 354 | /* dimension of physical space */ |
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| 355 | #define DIM 3 |
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| 356 | /* max number of bodies, obviously */ |
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| 357 | #define MAXNBODIES 2100 |
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| 358 | |
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| 359 | /* TOLERANCES */ |
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| 360 | |
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| 361 | /* the extrapolation scheme stops when |
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| 362 | Tj,k - T(j-1),k becomes smaller than this */ |
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| 363 | #define GBSTOL 5.0e-32 |
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| 364 | |
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| 365 | /* The solution of Kepler's equation is accepted when |
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| 366 | when iterates change by an amount smaller than this */ |
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| 367 | #define KEPLERSOLVERTOLERANCE 5.0e-16 |
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| 368 | |
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| 369 | /* what method and order to use to initialize the CSN integrator, GBS or HWH */ |
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| 370 | #define CSNINITGBS 1 |
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| 371 | #define CSNINITGBSORDER 4 |
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| 372 | #define CSNINITHWH 2 |
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| 373 | #define CSNINITHWHORDER 4 |
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| 374 | int csninit = CSNINITGBS; |
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| 375 | |
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| 376 | |
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| 377 | /* which extrapolation sequence to use in the GBS method */ |
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| 378 | #define EXSEQHARM int extrapolseq[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; |
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| 379 | #define EXSEQBUL int extrapolseq[] = { 0, 1, 2, 3, 4, 6, 8, 12, 16, 24, 32}; |
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| 380 | |
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| 381 | /* cange this line accordingly */ |
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| 382 | EXSEQBUL |
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| 383 | |
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| 384 | |
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| 385 | /* VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV */ |
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| 386 | |
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| 387 | /* The actual code. |
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| 388 | Change things below this line at your own peril. |
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| 389 | |
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| 390 | */ |
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| 391 | |
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| 392 | /* MACROS TO DISTINGUISH BETWEEN TEST PARTICLES AND |
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| 393 | PARTICLES WITH FINITE MASS |
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| 394 | You can add more types here, these values are stored |
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| 395 | in tpstore for each particle |
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| 396 | e.g., you could define stopped test particles, |
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| 397 | but you have to change the code accordingly. |
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| 398 | It is perhaps easier to add more integer arrays. |
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| 399 | IMPORTANT: THE TREE MAINTAINS ITS OWN INTEGER ARRAYS |
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| 400 | WHICH HOLD TEST PARTICLE INDICES. |
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| 401 | */ |
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| 402 | |
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| 403 | #define NOTTESTPARTICLE 1 |
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| 404 | #define TESTPARTICLE 0 |
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| 405 | |
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| 406 | /* the header files we need, only standard stuff */ |
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| 407 | #include <stdio.h> |
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| 408 | #include <stdlib.h> |
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| 409 | #include <string.h> |
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| 410 | #include <math.h> |
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| 411 | #include "omp.h" |
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| 412 | |
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| 413 | /* Macro definitions */ |
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| 414 | #define NUMMETHODS 4 |
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| 415 | #define SKP 1 |
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| 416 | #define HWH 2 |
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| 417 | #define CSN 3 |
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| 418 | #define GBS 4 |
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| 419 | |
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| 420 | /* it is really the number of stages for GBS */ |
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| 421 | char *methodnames[] = { " ", "SKP", "HWH", "CSN", "GBS" }; |
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| 422 | #define MAXCSN 15 |
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| 423 | #define MAXGBS 10 |
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| 424 | int MAXORDERS[] = { 0, 4, 4, MAXCSN, MAXGBS }; |
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| 425 | |
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| 426 | /* |
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| 427 | MACROS WHICH DEFINE WHAT IS STORED FOR THE PARTICLES |
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| 428 | from 1 to 6: x y z vx vy vz |
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| 429 | 7: G*mass |
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| 430 | from 8 to 10: accelerations in x, y and z |
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| 431 | e.g., particle i's y velocity is |
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| 432 | parts[i][5] |
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| 433 | */ |
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| 434 | |
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| 435 | #define TMPSIZE (2*DIM+1) |
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| 436 | /* Note: we need only the G*mass for the actual integrations */ |
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| 437 | #define GMASSCO (7) |
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| 438 | #define ACC (7) |
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| 439 | /* you can add more data for particles here |
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| 440 | but keep NPARTDATA to specify the total number of |
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| 441 | coordinates and other components */ |
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| 442 | #define NPARTDATA (ACC+3) |
---|
| 443 | /* this is used from index 1 in both indeces */ |
---|
| 444 | #define DECLARR [MAXNBODIES+1][NPARTDATA+1] |
---|
| 445 | |
---|
| 446 | /* Cowell-Stormer-Newman array */ |
---|
| 447 | #define DECLSTORMER [MAXNBODIES+1][DIM+1][MAXCSN+2] |
---|
| 448 | /* Gragg-Bulirsch-Stoer array */ |
---|
| 449 | #define DECLBS [MAXNBODIES+1][2*DIM+1][2][MAXGBS+2] |
---|
| 450 | |
---|
| 451 | #define DIM2 (2*DIM) |
---|
| 452 | |
---|
| 453 | /* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 454 | GLOBAL DATA |
---|
| 455 | ARRAYS THAT HOLD THE PARTICLES AND AUXILIARY DATA |
---|
| 456 | */ |
---|
| 457 | |
---|
| 458 | /* ARRAYS THAT HOLD THE PARTICLES' DATA. |
---|
| 459 | This can be moved into main() without |
---|
| 460 | any adverse effect. */ |
---|
| 461 | double parts DECLARR; |
---|
| 462 | |
---|
| 463 | /* This holds test particle indices. |
---|
| 464 | It seems easier to keep this global. It is used, e.g., |
---|
| 465 | by PlainAccel to avoid the computation of force between |
---|
| 466 | test particles. */ |
---|
| 467 | int tpstore[MAXNBODIES+1]; |
---|
| 468 | |
---|
| 469 | /* this is needed for error messages from deep within the integrator */ |
---|
| 470 | FILE *FLOG; |
---|
| 471 | |
---|
| 472 | /* Local error monitoring for the Cowell-Stormer integrator */ |
---|
| 473 | double CSNerror = 0; |
---|
| 474 | |
---|
| 475 | |
---|
| 476 | /* FUNCTION AND STRUCT DECLARATIONS */ |
---|
| 477 | |
---|
| 478 | /* the tree to store Jacobi coordinates */ |
---|
| 479 | struct tree { |
---|
| 480 | double tmass; /* total G*mass */ |
---|
| 481 | double rm1; /* total mass / mass1 */ |
---|
| 482 | double rm2; /* total mass / mass2 */ |
---|
| 483 | double bc[DIM2+1]; /* barycenter: position and velocity |
---|
| 484 | for actual particle these are pos. and vel. */ |
---|
| 485 | double acc[DIM+1]; |
---|
| 486 | /* nonzero particle index indicates that this is one with finite mass |
---|
| 487 | or it is an array of test particles which can be processed in a simple loop, |
---|
| 488 | zero means that this is a node in the tree |
---|
| 489 | */ |
---|
| 490 | int particleindex; /* nonzero indicates actual particle(s) */ |
---|
| 491 | struct tree *p1; |
---|
| 492 | struct tree *p2; |
---|
| 493 | int *testparticles; /* nonzero indicates array of test particles */ |
---|
| 494 | }; |
---|
| 495 | |
---|
| 496 | |
---|
| 497 | int CStep(int ord, double h, int nump, double parts DECLARR, |
---|
| 498 | struct tree *treein); |
---|
| 499 | |
---|
| 500 | int GBSStep(int ord, double h, int nump, double parts DECLARR); |
---|
| 501 | |
---|
| 502 | /* makes a simple chain, usual planetary motion case */ |
---|
| 503 | struct tree *MakeSimpleTree(int nump); |
---|
| 504 | /* makes an arbitrary tree from a textual description, i.e., |
---|
| 505 | parses the text and builds the tree */ |
---|
| 506 | struct tree *MakeTree(FILE *f); |
---|
| 507 | |
---|
| 508 | /* Fill tree with barycenters, used to initialize the tree */ |
---|
| 509 | int FillCMinTree(struct tree *tree, double p DECLARR); |
---|
| 510 | /* copy particle coordinates from tree; |
---|
| 511 | since the tree is the primary storage for the coordinates |
---|
| 512 | of particles with finite mass, one needs to call this |
---|
| 513 | before accessing data in the "parts" array |
---|
| 514 | */ |
---|
| 515 | int ParticlesFromTree(struct tree *tree, double p DECLARR); |
---|
| 516 | |
---|
| 517 | /* The actual HWH integrator */ |
---|
| 518 | int HWHStep(int order, struct tree *tree, double stepsize, double p DECLARR); |
---|
| 519 | |
---|
| 520 | /* Kinetic-potential energy split */ |
---|
| 521 | int SKPStep(int order, double stepsize, int nump, double p DECLARR); |
---|
| 522 | |
---|
| 523 | |
---|
| 524 | /* access integer arrays in trees that hold the indeces |
---|
| 525 | of test particles attached to that point, |
---|
| 526 | returns pointer to testparticles, |
---|
| 527 | included for the sake of completeness, not actually used */ |
---|
| 528 | int **GetTestParticles(struct tree *tree, int ind); |
---|
| 529 | |
---|
| 530 | |
---|
| 531 | /* VERY SIMPLE IO, you can write your own if you need something more */ |
---|
| 532 | int readdata(FILE *f, int num, double p DECLARR) { |
---|
| 533 | int i, j; double tmp; |
---|
| 534 | for ( i = 1; i <= num; ++i ) { |
---|
| 535 | fscanf(f, "%le", &tmp); p[i][GMASSCO] = tmp; } |
---|
| 536 | for ( i = 1; i <= num; ++i ) { |
---|
| 537 | for ( j = 1; j <= 6; ++j ) { |
---|
| 538 | fscanf(f, "%le", &tmp); p[i][j] = tmp; } } |
---|
| 539 | return num; } |
---|
| 540 | |
---|
| 541 | // X |
---|
| 542 | int printdataA(int num, FILE *f, double p DECLARR) { |
---|
| 543 | int i, j; |
---|
| 544 | for ( i = 1; i <= num; ++i ) { |
---|
| 545 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 546 | fprintf(f, "%.14le ", p[i][j]); |
---|
| 547 | } |
---|
| 548 | fprintf(f, "%c", '\n'); |
---|
| 549 | for ( j = DIM+1; j <= 2*DIM; ++j ) { |
---|
| 550 | fprintf(f, "%.14le ", p[i][j]); |
---|
| 551 | } |
---|
| 552 | fprintf(f, "%c", '\n'); |
---|
| 553 | } |
---|
| 554 | return num; |
---|
| 555 | } |
---|
| 556 | |
---|
| 557 | // X |
---|
| 558 | int printdata(int num, FILE *f, double p DECLARR, int c1, int c2) { |
---|
| 559 | int i, j; |
---|
| 560 | for ( i = 1; i <= num; ++i ) { |
---|
| 561 | for ( j = c1; j <= c2; ++j ) { |
---|
| 562 | fprintf(f, "%.14le ", p[i][j]); } |
---|
| 563 | fprintf(f, "%c", '\n'); |
---|
| 564 | } |
---|
| 565 | return num; |
---|
| 566 | } |
---|
| 567 | |
---|
| 568 | //X total energy for particles with finite mass |
---|
| 569 | double energy(int nump, int dim, double p DECLARR, int *tps) { |
---|
| 570 | double h = 0, tmp, tmp2; |
---|
| 571 | int i,j,k; |
---|
| 572 | |
---|
| 573 | for ( i = 1; i <= nump; ++i ) { |
---|
| 574 | if ( tps[i] == 0 ) |
---|
| 575 | continue; |
---|
| 576 | tmp = 0.0; |
---|
| 577 | |
---|
| 578 | #pragma omp parallel for reduction(+:tmp) schedule(runtime) |
---|
| 579 | for ( k = 1; k <= dim; ++k ) { |
---|
| 580 | tmp = tmp + p[i][k+dim]*p[i][k+dim]; |
---|
| 581 | } |
---|
| 582 | tmp = tmp*p[i][GMASSCO]/2.0; |
---|
| 583 | |
---|
| 584 | h = h + tmp; |
---|
| 585 | for ( j = i+1; j <= nump; ++j ) { |
---|
| 586 | tmp = 0.0; |
---|
| 587 | #pragma omp parallel for reduction(+:tmp) schedule(runtime) |
---|
| 588 | for ( k = 1; k <= dim; ++k ) { |
---|
| 589 | tmp2 = p[i][k]-p[j][k]; |
---|
| 590 | tmp = tmp+tmp2*tmp2; |
---|
| 591 | } |
---|
| 592 | tmp = 1/sqrt(tmp); |
---|
| 593 | h = h - tmp*p[i][GMASSCO]*p[j][GMASSCO]; |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | return h; |
---|
| 598 | } |
---|
| 599 | |
---|
| 600 | // X z component of angular momentum |
---|
| 601 | double angmomz(int nump, int dim, double p DECLARR, int *tps) { |
---|
| 602 | double az = 0.0; |
---|
| 603 | int i; |
---|
| 604 | |
---|
| 605 | for ( i = 1; i <= nump; ++i ) { |
---|
| 606 | if ( tps[i] == 0 ) |
---|
| 607 | continue; |
---|
| 608 | // x*vy - y*vx |
---|
| 609 | az = az + (p[i][1]*p[i][2+dim] - p[i][2]*p[i][1+dim]) * p[i][GMASSCO]; |
---|
| 610 | } |
---|
| 611 | return az; |
---|
| 612 | } |
---|
| 613 | |
---|
| 614 | // X transforms all particles to coordinates relative to barycenter |
---|
| 615 | int tobarycenter(int nump, int dim, double p DECLARR) { |
---|
| 616 | double bc[10]; |
---|
| 617 | int i, j; |
---|
| 618 | |
---|
| 619 | #pragma omp parallel private(j) |
---|
| 620 | #pragma omp for schedule(runtime) |
---|
| 621 | for (j = 0; j <= 2*dim; ++j ) |
---|
| 622 | bc[j] = 0.0; |
---|
| 623 | |
---|
| 624 | for ( i = nump; i >= 1; --i ) { |
---|
| 625 | bc[0] += p[i][GMASSCO]; |
---|
| 626 | #pragma omp parallel private(j) |
---|
| 627 | #pragma omp for schedule(runtime) |
---|
| 628 | for (j = 1; j <= 2*dim; ++j ) |
---|
| 629 | bc[j] += p[i][j]*p[i][GMASSCO]; |
---|
| 630 | } |
---|
| 631 | |
---|
| 632 | #pragma omp parallel private(j) |
---|
| 633 | #pragma omp for schedule(runtime) |
---|
| 634 | for (j = 1; j <= 2*dim; ++j ) |
---|
| 635 | bc[j] = bc[j]/bc[0]; |
---|
| 636 | |
---|
| 637 | |
---|
| 638 | for ( i = nump; i >= 1; --i ) { |
---|
| 639 | #pragma omp parallel private(j) |
---|
| 640 | #pragma omp for schedule(runtime) |
---|
| 641 | for (j = 1; j <= 2*dim; ++j ) |
---|
| 642 | p[i][j] -= bc[j]; |
---|
| 643 | } |
---|
| 644 | return 0; |
---|
| 645 | } |
---|
| 646 | |
---|
| 647 | |
---|
| 648 | |
---|
| 649 | |
---|
| 650 | /* """""""""""""""""""""""""""""""""""""""""""""""""""""""""" |
---|
| 651 | MAIN |
---|
| 652 | */ |
---|
| 653 | |
---|
| 654 | int main(int argc, char **argv) { |
---|
| 655 | FILE *f, *fin, *flog, *flocerr; |
---|
| 656 | char sicode[100]; |
---|
| 657 | int icode; /* SKP = 1 HWH = 2 CSN = 3 GBS = 4 */ |
---|
| 658 | struct tree *tree; int num, num2; |
---|
| 659 | int ii, i, order = 1, nin, nps; |
---|
| 660 | double stepsize; |
---|
| 661 | double time = 0.0, ftime, ptime; |
---|
| 662 | char fnamin[1000]; char id[1000]; |
---|
| 663 | double az, az0, toten, toten0; |
---|
| 664 | |
---|
| 665 | // get command-line argument |
---|
| 666 | if ( argc < 2 ) { exit(1); } |
---|
| 667 | sscanf(argv[1], "%s", fnamin); |
---|
| 668 | |
---|
| 669 | // read input file |
---|
| 670 | fin = fopen(fnamin, "r"); |
---|
| 671 | fscanf(fin, "%s", id); strcpy(fnamin, id); |
---|
| 672 | |
---|
| 673 | // create output and log file |
---|
| 674 | // id - name of output file |
---|
| 675 | f = fopen(id, "w"); strcat(fnamin, ".log"); flog = fopen(fnamin, "w"); |
---|
| 676 | FLOG = flog; |
---|
| 677 | |
---|
| 678 | #define FAILEDIN { fclose(fin); fclose(f); fclose(flog); exit(1); } |
---|
| 679 | |
---|
| 680 | fprintf(flog, "ID = %s\n", id); |
---|
| 681 | fscanf(fin, "%s", sicode); |
---|
| 682 | fscanf(fin, "%d", &order); fprintf(flog, "ORDER = %2d\n", order); |
---|
| 683 | icode = 0; |
---|
| 684 | for ( icode = 1; icode <= NUMMETHODS; ++icode ) { |
---|
| 685 | if ( strcmp(sicode, methodnames[icode] ) == 0 ) { |
---|
| 686 | if ( order < 1 || order > MAXORDERS[icode] ) { |
---|
| 687 | fprintf(flog, " Order %2d for method %s is not implemented \n", order, sicode); |
---|
| 688 | FAILEDIN |
---|
| 689 | } |
---|
| 690 | break; |
---|
| 691 | } |
---|
| 692 | } |
---|
| 693 | |
---|
| 694 | if ( icode > NUMMETHODS ) { |
---|
| 695 | fprintf(flog, " Invalid method code %s\n", sicode); |
---|
| 696 | FAILEDIN |
---|
| 697 | } |
---|
| 698 | |
---|
| 699 | |
---|
| 700 | fscanf(fin, "%le", &stepsize); fprintf(flog, "STEPSIZE = %.12f\n", stepsize); |
---|
| 701 | fscanf(fin, "%le", &ftime); fprintf(flog, "FINAL TIME = %.12f\n", ftime); |
---|
| 702 | fscanf(fin, "%le", &ptime); fprintf(flog, "PRINTING TIME = %.12f\n", ptime); |
---|
| 703 | fscanf(fin, "%d", &num); fprintf(flog, "NUMBER OF PARTS = %2d\n", num); |
---|
| 704 | |
---|
| 705 | if ( num > MAXNBODIES ) { |
---|
| 706 | fprintf(flog, " Too many particles, change MAXNBODIES macro in code "); |
---|
| 707 | FAILEDIN |
---|
| 708 | } |
---|
| 709 | |
---|
| 710 | /* initialize tpstore */ |
---|
| 711 | |
---|
| 712 | for ( i = 1; i <= num+2; ++i ) { |
---|
| 713 | tpstore[i] = NOTTESTPARTICLE; |
---|
| 714 | } |
---|
| 715 | |
---|
| 716 | /* this will TESTPARTICLE for test particles in tpstore */ |
---|
| 717 | tree = MakeTree(fin); |
---|
| 718 | |
---|
| 719 | /* For CSN create error file */ |
---|
| 720 | if ( icode == CSN ) { |
---|
| 721 | strcpy(fnamin, id); strcat(fnamin, ".lerr"); flocerr = fopen(fnamin, "w"); |
---|
| 722 | } |
---|
| 723 | |
---|
| 724 | num2 = readdata(fin, num, parts); |
---|
| 725 | /* DONE READING ALL INPUTS */ |
---|
| 726 | fclose(fin); |
---|
| 727 | |
---|
| 728 | /* zero out test particles' tpstore, again, just in case */ |
---|
| 729 | for ( i = 1; i <= num; ++i ) { |
---|
| 730 | if ( parts[i][GMASSCO] == 0.0 ) { |
---|
| 731 | tpstore[i] = TESTPARTICLE; |
---|
| 732 | } |
---|
| 733 | } |
---|
| 734 | |
---|
| 735 | if ( num != num2 ) exit(1); |
---|
| 736 | fprintf(flog, "GMs\n"); |
---|
| 737 | printdata(num, flog, parts, GMASSCO, GMASSCO); |
---|
| 738 | |
---|
| 739 | fprintf(flog, "Inits \n"); |
---|
| 740 | printdataA(num, flog, parts); |
---|
| 741 | |
---|
| 742 | fflush(flog); |
---|
| 743 | |
---|
| 744 | /* WATCH OUT FOR THIS |
---|
| 745 | The transformation to barycenter |
---|
| 746 | tends to improve things. |
---|
| 747 | */ |
---|
| 748 | tobarycenter(num, DIM, parts); |
---|
| 749 | fprintf(flog, "Actual Barycentric Inits \n"); |
---|
| 750 | printdataA(num, flog, parts); |
---|
| 751 | |
---|
| 752 | fprintf(flog, "Actual integrator is %s \n", sicode); |
---|
| 753 | fprintf(flog, "CODE: %s \n", CODENAME); |
---|
| 754 | fprintf(flog, "VERSION: %s \n", VERSION); |
---|
| 755 | fflush(flog); |
---|
| 756 | |
---|
| 757 | |
---|
| 758 | // z component of total angular momentum, it is used to monitor accumulation of roundoff |
---|
| 759 | az0 = angmomz(num, DIM, parts, tpstore); |
---|
| 760 | toten0 = energy(num, DIM, parts, tpstore); |
---|
| 761 | |
---|
| 762 | |
---|
| 763 | |
---|
| 764 | /* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 765 | ACTUAL INTEGRATION |
---|
| 766 | */ |
---|
| 767 | |
---|
| 768 | // the length of the inner loop, i.e., between printing |
---|
| 769 | nin = (int) (fabs(ptime)/fabs(stepsize)); |
---|
| 770 | |
---|
| 771 | if ( nin == 0 ) { |
---|
| 772 | fprintf(flog, "%s\n", " Stepsize is larger than printing time, aborted"); |
---|
| 773 | exit(1); |
---|
| 774 | } |
---|
| 775 | |
---|
| 776 | // the length of the outer loop, i.e., printings from beginning to end |
---|
| 777 | nps = (int) (fabs(ftime)/fabs(ptime)); |
---|
| 778 | |
---|
| 779 | fprintf(flog, "nin = %d nps = %d", nin, nps); |
---|
| 780 | |
---|
| 781 | /* WARNING: VERY LONG INTEGRATIONS CAN PRODUCE VERY LARGE |
---|
| 782 | INTEGERS AND ONE HAS TO MAKE SURE THAT THEY ARE STILL |
---|
| 783 | SMALLER THAN THE LARGEST REPRESENTABLE INTEGER |
---|
| 784 | ANOTHER WARNING: ROUNDOFF EFFECTS MAY CAUSE nin AND/OR nps TO BE |
---|
| 785 | DIFFERENT FROM WHAT THE USER EXPECTS |
---|
| 786 | */ |
---|
| 787 | |
---|
| 788 | |
---|
| 789 | /* print the first data point, i.e., the initial data */ |
---|
| 790 | #define PRINTDATA fprintf(f, "%.12f ", time);\ |
---|
| 791 | az = angmomz(num, DIM, parts, tpstore); \ |
---|
| 792 | toten = energy(num, DIM, parts, tpstore); \ |
---|
| 793 | fprintf(f, "%.16e ", (toten-toten0)/toten0); \ |
---|
| 794 | fprintf(f, "%.16e\n", (az-az0)/az0); \ |
---|
| 795 | printdataA(num, f, parts); |
---|
| 796 | |
---|
| 797 | #define PRINTERROR \ |
---|
| 798 | if ( icode == CSN ) { \ |
---|
| 799 | fprintf(flocerr, "%.12f %.12e\n", time, CSNerror); } |
---|
| 800 | |
---|
| 801 | PRINTDATA |
---|
| 802 | PRINTERROR |
---|
| 803 | |
---|
| 804 | |
---|
| 805 | /* MAIN LOOP */ |
---|
| 806 | for ( ii = 1; ii <= nps; ++ii ) { |
---|
| 807 | for ( i = 1; i <= nin; ++i ) { |
---|
| 808 | switch(icode) { |
---|
| 809 | case SKP: |
---|
| 810 | SKPStep(order, stepsize, num, parts); break; |
---|
| 811 | case HWH: |
---|
| 812 | HWHStep(order, tree, stepsize, parts); break; |
---|
| 813 | case CSN: |
---|
| 814 | CStep(order, stepsize, num, parts, tree); break; |
---|
| 815 | case GBS: |
---|
| 816 | GBSStep(order, stepsize, num, parts); break; |
---|
| 817 | default: |
---|
| 818 | fprintf(flog, "Not implemented\n"); |
---|
| 819 | fclose(flog); fclose(f); exit(1); break; |
---|
| 820 | } |
---|
| 821 | |
---|
| 822 | /* DONE ONE TIME STEP |
---|
| 823 | ADD MORE CODE HERE IF NECESSARY |
---|
| 824 | variables you can use: |
---|
| 825 | double time; |
---|
| 826 | double parts DECLARR; |
---|
| 827 | Note that actual time should be computed as |
---|
| 828 | actualtime = time+stepsize*i |
---|
| 829 | */ |
---|
| 830 | |
---|
| 831 | } |
---|
| 832 | |
---|
| 833 | time += stepsize*nin; |
---|
| 834 | fprintf(f, "end of step, time = %f\n", time); |
---|
| 835 | |
---|
| 836 | if ( icode == HWH ) { ParticlesFromTree(tree, parts); } |
---|
| 837 | |
---|
| 838 | /* CHANGE THIS PART OR ADD YOUR CODE IF NECESSARY */ |
---|
| 839 | |
---|
| 840 | PRINTDATA |
---|
| 841 | PRINTERROR |
---|
| 842 | |
---|
| 843 | if ( stepsize > 0.0 && time > ftime ) break; |
---|
| 844 | if ( stepsize < 0.0 && time < ftime ) break; |
---|
| 845 | |
---|
| 846 | } |
---|
| 847 | |
---|
| 848 | |
---|
| 849 | fclose(f); |
---|
| 850 | fprintf(flog, "\n Finished \n"); |
---|
| 851 | fclose(flog); |
---|
| 852 | if ( icode == CSN ) fclose(flocerr); |
---|
| 853 | |
---|
| 854 | return 0; |
---|
| 855 | } |
---|
| 856 | |
---|
| 857 | |
---|
| 858 | /* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
| 859 | FOR TEST: THE SIMPLE SPLIT, I.E., Kinetic - Potential |
---|
| 860 | It does not provide special treatment for test particles. |
---|
| 861 | */ |
---|
| 862 | int PlainSplitKineticStep(int num, double stepsize, double p DECLARR) { |
---|
| 863 | int i, k; |
---|
| 864 | for ( i = 1; i <= num; ++i ) { |
---|
| 865 | for ( k = 1; k <= DIM; ++k ) { |
---|
| 866 | p[i][k] += stepsize*p[i][k+DIM]; } } |
---|
| 867 | return 0; } |
---|
| 868 | |
---|
| 869 | int PlainSplitPotentialStep(int num, double stepsize, double p DECLARR) { |
---|
| 870 | int i, j, k; |
---|
| 871 | double tmp, tmp2, tmp3; |
---|
| 872 | for ( i = 1; i <= num; ++i ) { |
---|
| 873 | tmp = 0.0; |
---|
| 874 | for ( j = i+1; j <= num; ++j ) { |
---|
| 875 | tmp2 = 0.0; |
---|
| 876 | for ( k = 1; k <= DIM; ++k ) { |
---|
| 877 | tmp3 = p[i][k] - p[j][k]; |
---|
| 878 | tmp2 = tmp2 + tmp3*tmp3; } |
---|
| 879 | tmp3 = 1.0/sqrt(tmp2); |
---|
| 880 | tmp2 = tmp3/tmp2; |
---|
| 881 | for ( k = 1; k <= DIM; ++k ) { |
---|
| 882 | tmp3 = p[i][k] - p[j][k]; |
---|
| 883 | tmp = -tmp3*tmp2*p[j][GMASSCO]*stepsize; |
---|
| 884 | p[i][k+DIM] += tmp; |
---|
| 885 | tmp = tmp3*tmp2*p[i][GMASSCO]*stepsize; |
---|
| 886 | p[j][k+DIM] += tmp; } |
---|
| 887 | } |
---|
| 888 | } |
---|
| 889 | return 0; } |
---|
| 890 | |
---|
| 891 | |
---|
| 892 | |
---|
| 893 | /* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
| 894 | COWELL-STORMER INTEGRATOR */ |
---|
| 895 | |
---|
| 896 | |
---|
| 897 | /* this computes accelerations, used both for CSN and GBS, |
---|
| 898 | not to be confused with Accel used for HWH */ |
---|
| 899 | |
---|
| 900 | int PlainAccel(int num, double p DECLARR) { |
---|
| 901 | int i, j, k; int tpi, tpj; |
---|
| 902 | double tmp, tmp2, tmp3; |
---|
| 903 | double massi, massj; |
---|
| 904 | for ( i = 1; i <= num; ++i ) { |
---|
| 905 | for ( k = 1; k <= DIM; ++k ) { p[i][ACC+k] = 0.0; } } |
---|
| 906 | /* for testing things |
---|
| 907 | for ( i = 1; i <= num; ++i ) { |
---|
| 908 | for ( k = 1; k <= DIM; ++k ) { p[i][ACC+k] = 1.0; } } |
---|
| 909 | return 0; |
---|
| 910 | */ |
---|
| 911 | for ( i = num; i >= 1; --i ) { |
---|
| 912 | tpi = tpstore[i]; |
---|
| 913 | massi = p[i][GMASSCO]; |
---|
| 914 | for ( j = i+1; j <= num; ++j ) { |
---|
| 915 | tpj = tpstore[j]; |
---|
| 916 | if ( tpi == TESTPARTICLE && tpj == TESTPARTICLE ) continue; |
---|
| 917 | tmp2 = 0.0; |
---|
| 918 | for ( k = 1; k <= DIM; ++k ) { |
---|
| 919 | tmp3 = p[i][k] - p[j][k]; |
---|
| 920 | tmp2 = tmp2 + tmp3*tmp3; } |
---|
| 921 | tmp3 = 1.0/sqrt(tmp2); |
---|
| 922 | tmp2 = tmp3/tmp2; |
---|
| 923 | massj = p[j][GMASSCO]; |
---|
| 924 | for ( k = 1; k <= DIM; ++k ) { |
---|
| 925 | tmp3 = p[i][k] - p[j][k]; |
---|
| 926 | tmp = tmp3*tmp2; |
---|
| 927 | if ( tpj == NOTTESTPARTICLE ) { |
---|
| 928 | p[i][ACC+k] -= (tmp*massj); } |
---|
| 929 | if ( tpi == NOTTESTPARTICLE ) { |
---|
| 930 | p[j][ACC+k] += (tmp*massi); } |
---|
| 931 | } |
---|
| 932 | } |
---|
| 933 | } |
---|
| 934 | return 0; } |
---|
| 935 | |
---|
| 936 | /* Cowell-Stormer-Newman 14(6)th order */ |
---|
| 937 | |
---|
| 938 | |
---|
| 939 | /* Newman's 14(6)th order Stormer's coeffs */ |
---|
| 940 | |
---|
| 941 | double CSalpha[] = { 0.0, |
---|
| 942 | 1.000000000000000000000, |
---|
| 943 | 0.000000000000000000000, |
---|
| 944 | 0.083333333333333333333, |
---|
| 945 | 0.083333333333333333333, |
---|
| 946 | 0.079166666666666666666, |
---|
| 947 | 0.075000000000000000000, |
---|
| 948 | 0.071345899470899470899, |
---|
| 949 | 0.068204365079365079365, |
---|
| 950 | 0.065495756172839506172, |
---|
| 951 | 0.063140432098765432098, |
---|
| 952 | 0.061072649861712361712, |
---|
| 953 | 0.059240564123376623376, |
---|
| 954 | 0.057603625837453135733, |
---|
| 955 | 0.056129980884507174190, |
---|
| 956 | 0.054794379107071147139 |
---|
| 957 | }; |
---|
| 958 | |
---|
| 959 | |
---|
| 960 | double CSbeta[] = { 0.0, |
---|
| 961 | 1.50000000000000000000, |
---|
| 962 | 0.33333333333333333333, |
---|
| 963 | 0.37500000000000000000, |
---|
| 964 | 0.35277777777777777777, |
---|
| 965 | 0.33402777777777777777, |
---|
| 966 | 0.31924603174603174603, |
---|
| 967 | 0.30736607142857142857, |
---|
| 968 | 0.29757660934744268077, |
---|
| 969 | 0.28933077050264550264, |
---|
| 970 | 0.28225737868098979210, |
---|
| 971 | 0.27609762576993479771, |
---|
| 972 | 0.27066578505957226195, |
---|
| 973 | 0.26582499331955247133, |
---|
| 974 | 0.26147199790503706399, |
---|
| 975 | 0.25752728193649391773 |
---|
| 976 | }; |
---|
| 977 | |
---|
| 978 | |
---|
| 979 | |
---|
| 980 | double sumfrombottom(double *a, int nr, double *coef) { |
---|
| 981 | int i; |
---|
| 982 | double sum = 0.0; |
---|
| 983 | for ( i = nr; i >= 1; --i ) { |
---|
| 984 | sum += a[i]*coef[i]; } |
---|
| 985 | return sum; } |
---|
| 986 | |
---|
| 987 | int differencing(double *a, int nr, double in) { |
---|
| 988 | int i, j, p; |
---|
| 989 | double tmp1, tmp2; |
---|
| 990 | tmp1 = a[1]; a[1] = in; |
---|
| 991 | for ( i = 2; i <= nr; ++i ) { |
---|
| 992 | tmp2 = a[i]; a[i] = a[i-1]-tmp1; tmp1 = tmp2; } |
---|
| 993 | return 0; } |
---|
| 994 | |
---|
| 995 | |
---|
| 996 | |
---|
| 997 | static int CStepCount = 0; |
---|
| 998 | static int CStepInit = 0; |
---|
| 999 | static struct tree *initCStree; |
---|
| 1000 | |
---|
| 1001 | int CStep(int ord, double h, int nump, |
---|
| 1002 | double parts DECLARR, struct tree *treein) { |
---|
| 1003 | double *a, asav, vx, sum, tmp; int p,j, i; |
---|
| 1004 | static double df DECLSTORMER; |
---|
| 1005 | /* actual local order to determine how terms to sum */ |
---|
| 1006 | if ( CStepInit == 0 ) { |
---|
| 1007 | initCStree = treein; |
---|
| 1008 | CStepInit = 1; |
---|
| 1009 | for ( i = 1; i <= ord+1; ++i ) { |
---|
| 1010 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1011 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 1012 | df[p][j][i] = 0.0; } } } } |
---|
| 1013 | if ( CStepInit == 1 ) { |
---|
| 1014 | /* initialization stage */ |
---|
| 1015 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1016 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 1017 | df[p][j][0] = -parts[p][j]; } } |
---|
| 1018 | |
---|
| 1019 | if ( csninit == CSNINITHWH ) { |
---|
| 1020 | HWHStep(CSNINITHWHORDER, initCStree, h, parts); |
---|
| 1021 | ParticlesFromTree(initCStree, parts); } |
---|
| 1022 | else { GBSStep(CSNINITGBSORDER, h, nump, parts); } |
---|
| 1023 | if ( CStepCount > ord ) CStepInit = 2; |
---|
| 1024 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1025 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 1026 | df[p][j][0] += parts[p][j]; } } |
---|
| 1027 | } |
---|
| 1028 | else { |
---|
| 1029 | /* actual run */ |
---|
| 1030 | CSNerror = 0; |
---|
| 1031 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1032 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 1033 | /* formula: x(n+1) - x(n) = (x(n) - x(n-1)) + h^2*sum |
---|
| 1034 | with X(n) = x(n)-x(n-1) |
---|
| 1035 | X(n+1) = X(n) + h^2*sum |
---|
| 1036 | x(n+1) = X(N+1) + x(n) |
---|
| 1037 | X(n) is in a[0] |
---|
| 1038 | */ |
---|
| 1039 | a = df[p][j]; |
---|
| 1040 | asav = a[0]; |
---|
| 1041 | sum = sumfrombottom(a, ord, CSalpha); |
---|
| 1042 | sum *= h*h; |
---|
| 1043 | a[0] += sum; |
---|
| 1044 | parts[p][j] += a[0]; |
---|
| 1045 | /* vx = (1.0/h)*(x(n)-x(n-1)) + h*sum */ |
---|
| 1046 | sum = h*sumfrombottom(a, ord, CSbeta); |
---|
| 1047 | vx = asav/h + sum; |
---|
| 1048 | parts[p][DIM+j] = vx; |
---|
| 1049 | /* record error */ |
---|
| 1050 | tmp = fabs(CSalpha[ord]*a[ord]*h*h); |
---|
| 1051 | if ( CSNerror < tmp ) CSNerror = tmp; |
---|
| 1052 | } } } |
---|
| 1053 | PlainAccel(nump, parts); |
---|
| 1054 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1055 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 1056 | differencing(df[p][j], ord, parts[p][ACC+j]); |
---|
| 1057 | parts[p][ACC+j] = 0.0; |
---|
| 1058 | } } |
---|
| 1059 | ++CStepCount; |
---|
| 1060 | return 0; } |
---|
| 1061 | |
---|
| 1062 | |
---|
| 1063 | |
---|
| 1064 | /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
---|
| 1065 | BULIRSCH-STOER |
---|
| 1066 | actually, GRAGG-BULIRSCH-STOER, following Hairer et al., 1993 |
---|
| 1067 | */ |
---|
| 1068 | |
---|
| 1069 | /* Gragg's symmetric integrator, this is used to generate Tj,1 */ |
---|
| 1070 | int GStep(int nump, double parts DECLARR, double s DECLARR, double h, int len) { |
---|
| 1071 | int k, j, p, d, knext, kprev, m; |
---|
| 1072 | double dif, difsum, tmp1, astep; |
---|
| 1073 | static double y0 DECLARR; |
---|
| 1074 | static double y1 DECLARR; |
---|
| 1075 | /* save originial in y0 */ |
---|
| 1076 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1077 | y0[p][GMASSCO] = parts[p][GMASSCO]; |
---|
| 1078 | for ( d = 1; d <= DIM; ++d ) { |
---|
| 1079 | y0[p][d] = parts[p][d]; |
---|
| 1080 | y0[p][d+DIM] = parts[p][d+DIM]; } } |
---|
| 1081 | /* consult Hairer et al. why we need this |
---|
| 1082 | in short: we need a method which has only even powers |
---|
| 1083 | of h in the expansion of its error, i.e., a symmetric method |
---|
| 1084 | */ |
---|
| 1085 | h = h/2.0; |
---|
| 1086 | PlainAccel(nump, y0); |
---|
| 1087 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1088 | /* load masses into y1 */ |
---|
| 1089 | y1[p][GMASSCO] = y0[p][GMASSCO]; |
---|
| 1090 | for ( d = 1; d <= DIM; ++d ) { |
---|
| 1091 | y1[p][d] = y0[p][d]+h*y0[p][DIM+d]; |
---|
| 1092 | y1[p][d+DIM] = y0[p][d+DIM]+h*y0[p][ACC+d]; } } |
---|
| 1093 | /* compute y2 (m=1), y3' (m=2), y4 (m=3), y5' (m=4) y(2n+1)' (m=2*n) |
---|
| 1094 | n = len |
---|
| 1095 | */ |
---|
| 1096 | for ( m = 1; m <= 2*len; ++m ) { |
---|
| 1097 | if ( (m%2) ) { |
---|
| 1098 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1099 | for ( d = 1; d <= DIM; ++d ) { |
---|
| 1100 | y1[p][d] = y0[p][d]+2.0*h*y1[p][d+DIM]; |
---|
| 1101 | s[p][d] = y1[p][d]; y0[p][d] = y1[p][d]; |
---|
| 1102 | } } } |
---|
| 1103 | else { |
---|
| 1104 | PlainAccel(nump, y1); |
---|
| 1105 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1106 | for ( d = 1; d <= DIM; ++d ) { |
---|
| 1107 | y0[p][d+DIM] = y1[p][d+DIM]; |
---|
| 1108 | y1[p][d+DIM] = y0[p][d+DIM]+2.0*h*y1[p][ACC+d]; |
---|
| 1109 | s[p][d+DIM] = (y0[p][d+DIM]+y1[p][d+DIM])/2.0; |
---|
| 1110 | } } |
---|
| 1111 | } |
---|
| 1112 | } |
---|
| 1113 | return 0; } |
---|
| 1114 | |
---|
| 1115 | |
---|
| 1116 | int GBSStep(int bsord, double h, int nump, double parts DECLARR) { |
---|
| 1117 | int k, j, jfinal, p, d, jnext, jprev, len; |
---|
| 1118 | static double gbsarr DECLBS; |
---|
| 1119 | double dif, difsum, tmp1, astep; |
---|
| 1120 | int *n = extrapolseq; |
---|
| 1121 | static double s DECLARR; |
---|
| 1122 | /* for testing GStep |
---|
| 1123 | astep = h; len = 1; |
---|
| 1124 | GStep(nump, parts, s, astep, len); |
---|
| 1125 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1126 | for ( d = 1; d <= 2*DIM; ++d ) { parts[p][d] = s[p][d]; } } |
---|
| 1127 | return 0; |
---|
| 1128 | */ |
---|
| 1129 | jfinal = bsord; |
---|
| 1130 | for ( j = 1; j <= bsord; ++j ) { |
---|
| 1131 | difsum = 0.0; |
---|
| 1132 | /* map j and j-1 to storage index */ |
---|
| 1133 | jnext = ((j)%2); |
---|
| 1134 | jprev = ((j-1)%2); |
---|
| 1135 | /* compute Tj,1 */ |
---|
| 1136 | len = n[j]; |
---|
| 1137 | astep = h/len; |
---|
| 1138 | GStep(nump, parts, s, astep, len); |
---|
| 1139 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1140 | for ( d = 1; d <= 2*DIM; ++d ) { gbsarr[p][d][jnext][1] = s[p][d]; } } |
---|
| 1141 | /* compute Tj,k */ |
---|
| 1142 | for ( k = 1; k <= j-1; ++k ) { |
---|
| 1143 | /* Aitken-Neville for nonsymmetric underlying method */ |
---|
| 1144 | tmp1 = ((double) n[j])/((double) n[j-k]); |
---|
| 1145 | /* Aitken-Neville for symmetric underlying method (square of previous) */ |
---|
| 1146 | tmp1 = tmp1*tmp1; |
---|
| 1147 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1148 | for ( d = 1; d <= 2*DIM; ++d ) { |
---|
| 1149 | dif = (gbsarr[p][d][jnext][k] - gbsarr[p][d][jprev][k]); |
---|
| 1150 | if ( k == j-1 ) difsum += fabs(dif); |
---|
| 1151 | gbsarr[p][d][jnext][k+1] = gbsarr[p][d][jnext][k] + dif/(tmp1-1.0); |
---|
| 1152 | } } |
---|
| 1153 | } |
---|
| 1154 | /* stop computing more is reached roundoff level */ |
---|
| 1155 | if ( j > 1 && difsum <= GBSTOL ) { jfinal = j; break; } |
---|
| 1156 | } |
---|
| 1157 | j = jfinal; k = j; jnext = ((j)%2); |
---|
| 1158 | for ( p = 1; p <= nump; ++p ) { |
---|
| 1159 | for ( d = 1; d <= 2*DIM; ++d ) { parts[p][d] = gbsarr[p][d][jnext][k]; } } |
---|
| 1160 | return 0; } |
---|
| 1161 | |
---|
| 1162 | |
---|
| 1163 | |
---|
| 1164 | |
---|
| 1165 | |
---|
| 1166 | |
---|
| 1167 | /* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
| 1168 | Actual HWH integration */ |
---|
| 1169 | int MoveCMandKepler(struct tree *tree, double *cmove, double stepsize, |
---|
| 1170 | double p DECLARR); |
---|
| 1171 | int KeplerOnTree(struct tree *tree, double stepsize, double p DECLARR); |
---|
| 1172 | int RecursivePerturbations(struct tree *tree, double stepsize, double p DECLARR); |
---|
| 1173 | int RecPertAcc(struct tree *tree, double stepsize, double p DECLARR); |
---|
| 1174 | |
---|
| 1175 | /* fourth order coeffs */ |
---|
| 1176 | static double Coeff4x0 = 0.0; |
---|
| 1177 | static double Coeff4x1 = 0.0; |
---|
| 1178 | |
---|
| 1179 | static int SympCalled = 0; |
---|
| 1180 | |
---|
| 1181 | void initSympCoefs() { |
---|
| 1182 | double cbrt2 = cbrt(2.0); |
---|
| 1183 | Coeff4x0 = -cbrt2/(2.0-cbrt2); |
---|
| 1184 | Coeff4x1 = 1.0/(2.0-cbrt2); |
---|
| 1185 | SympCalled = 1; } |
---|
| 1186 | |
---|
| 1187 | |
---|
| 1188 | static int HWHCalled = 0; |
---|
| 1189 | |
---|
| 1190 | // X |
---|
| 1191 | int HWHStep(int order, struct tree *tree, double stepsize, double p DECLARR) { |
---|
| 1192 | if ( SympCalled == 0 ) { |
---|
| 1193 | initSympCoefs(); |
---|
| 1194 | } |
---|
| 1195 | if ( HWHCalled == 0) { |
---|
| 1196 | // initialize tree |
---|
| 1197 | FillCMinTree(tree, p); |
---|
| 1198 | HWHCalled = 1; |
---|
| 1199 | } |
---|
| 1200 | if ( order == 1 ) { |
---|
| 1201 | KeplerOnTree(tree, stepsize, p); |
---|
| 1202 | RecursivePerturbations(tree, stepsize, p); |
---|
| 1203 | return 0; |
---|
| 1204 | } |
---|
| 1205 | if ( order == 2 ) { |
---|
| 1206 | KeplerOnTree(tree, stepsize/2.0, p); |
---|
| 1207 | RecursivePerturbations(tree, stepsize, p); |
---|
| 1208 | KeplerOnTree(tree, stepsize/2.0, p); |
---|
| 1209 | return 0; |
---|
| 1210 | } |
---|
| 1211 | if ( order == 4 ) { |
---|
| 1212 | HWHStep(2, tree, stepsize*Coeff4x1, p); |
---|
| 1213 | HWHStep(2, tree, stepsize*Coeff4x0, p); |
---|
| 1214 | HWHStep(2, tree, stepsize*Coeff4x1, p); |
---|
| 1215 | return 0; |
---|
| 1216 | } |
---|
| 1217 | printf(" Order %2d is not implemented, Aborted", order); |
---|
| 1218 | exit(1); |
---|
| 1219 | } |
---|
| 1220 | |
---|
| 1221 | |
---|
| 1222 | int SKPStep(int order, double stepsize, int nump, double p DECLARR) { |
---|
| 1223 | if ( SympCalled == 0 ) { initSympCoefs(); } |
---|
| 1224 | if ( order == 1 ) { |
---|
| 1225 | PlainSplitKineticStep(nump, stepsize, p); |
---|
| 1226 | PlainSplitPotentialStep(nump, stepsize, p); |
---|
| 1227 | return 0; } |
---|
| 1228 | if ( order == 2 ) { |
---|
| 1229 | PlainSplitKineticStep(nump, stepsize/2.0, p); |
---|
| 1230 | PlainSplitPotentialStep(nump, stepsize, p); |
---|
| 1231 | PlainSplitKineticStep(nump, stepsize/2.0, p); |
---|
| 1232 | return 0; } |
---|
| 1233 | if ( order == 4 ) { |
---|
| 1234 | SKPStep(2, stepsize*Coeff4x1, nump, p); |
---|
| 1235 | SKPStep(2, stepsize*Coeff4x0, nump, p); |
---|
| 1236 | SKPStep(2, stepsize*Coeff4x1, nump, p); |
---|
| 1237 | return 0; } |
---|
| 1238 | printf(" Order %2d is not implemented, Aborted", order); |
---|
| 1239 | exit(1); } |
---|
| 1240 | |
---|
| 1241 | |
---|
| 1242 | |
---|
| 1243 | /* +++++++++++++++++++++++++++++++++++++++++++++++++++++ |
---|
| 1244 | / TREE |
---|
| 1245 | / |
---|
| 1246 | / |
---|
| 1247 | */ |
---|
| 1248 | |
---|
| 1249 | |
---|
| 1250 | int inittree(struct tree *tmp) { |
---|
| 1251 | int i; tmp->tmass = 0.0; tmp->particleindex = 0; |
---|
| 1252 | tmp->p1 = 0; tmp->p2 = 0; |
---|
| 1253 | tmp->testparticles = 0; tmp->rm1 = 0; tmp->rm2 = 0; |
---|
| 1254 | for ( i = 1; i <= DIM2; ++i ) { tmp->bc[i] = 0; } |
---|
| 1255 | for ( i = 1; i <= DIM; ++i ) { tmp->acc[i] = 0; } |
---|
| 1256 | return 0; } |
---|
| 1257 | |
---|
| 1258 | |
---|
| 1259 | struct tree *newtree() { |
---|
| 1260 | struct tree *tmp = (struct tree*) malloc(sizeof(struct tree)); |
---|
| 1261 | inittree(tmp); return tmp; } |
---|
| 1262 | |
---|
| 1263 | void deletetree(struct tree *p) { |
---|
| 1264 | if ( p->p1 ) deletetree(p->p1); |
---|
| 1265 | if ( p->p2 ) deletetree(p->p2); |
---|
| 1266 | free((void *) p); } |
---|
| 1267 | |
---|
| 1268 | |
---|
| 1269 | struct tree *MakeSimpleTree(int nump) { |
---|
| 1270 | int i; |
---|
| 1271 | struct tree *root; |
---|
| 1272 | struct tree *t1, *p1, *p2; |
---|
| 1273 | root = newtree(); |
---|
| 1274 | t1 = root; |
---|
| 1275 | for ( i = nump; i > 1; --i ) { |
---|
| 1276 | p1 = newtree(); |
---|
| 1277 | p2 = newtree(); |
---|
| 1278 | p1->particleindex = 0; |
---|
| 1279 | p2->particleindex = i; |
---|
| 1280 | t1->p1 = p1; t1->p2 = p2; |
---|
| 1281 | t1 = p1; } |
---|
| 1282 | t1->particleindex = 1; |
---|
| 1283 | return root; } |
---|
| 1284 | |
---|
| 1285 | int eatwhite(FILE *f) { |
---|
| 1286 | int c; |
---|
| 1287 | for ( ; ; ) { |
---|
| 1288 | c = getc(f); |
---|
| 1289 | if ( !isspace(c) ) break; |
---|
| 1290 | } |
---|
| 1291 | ungetc(c, f); |
---|
| 1292 | return c; |
---|
| 1293 | } |
---|
| 1294 | |
---|
| 1295 | |
---|
| 1296 | /* just an array to hold indeces read in, |
---|
| 1297 | portions of this are assigned to |
---|
| 1298 | tpa's below */ |
---|
| 1299 | int tmpReadList[MAXNBODIES+1000]; |
---|
| 1300 | /* bookkeeping */ |
---|
| 1301 | int freelist = 0; |
---|
| 1302 | |
---|
| 1303 | int *ReadList(FILE *f) { |
---|
| 1304 | int i1, i2; int c; int i; int *arr; |
---|
| 1305 | c = eatwhite(f); |
---|
| 1306 | if ( c != '[' ) { |
---|
| 1307 | printf(" Error: bad list, aborted \n"); exit(1); |
---|
| 1308 | } |
---|
| 1309 | c = getc(f); |
---|
| 1310 | fscanf(f, "%d - %d", &i1, &i2); |
---|
| 1311 | c = eatwhite(f); |
---|
| 1312 | if ( c != ']' ) { |
---|
| 1313 | printf(" Error: bad list, aborted \n"); exit(1); |
---|
| 1314 | } |
---|
| 1315 | c = getc(f); |
---|
| 1316 | arr = tmpReadList+freelist; |
---|
| 1317 | |
---|
| 1318 | /* put zero in tpstore */ |
---|
| 1319 | for ( i = i1; i <= i2; ++i ) tpstore[i] = TESTPARTICLE; |
---|
| 1320 | for ( i = i1; i <= i2; ++i ) arr[i-i1+1] = i; |
---|
| 1321 | |
---|
| 1322 | arr[0] = i2-i1+1; |
---|
| 1323 | freelist += i2-i1+2; |
---|
| 1324 | return arr; |
---|
| 1325 | } |
---|
| 1326 | |
---|
| 1327 | |
---|
| 1328 | |
---|
| 1329 | struct tree *MakeTree(FILE *f) { |
---|
| 1330 | int i; int c; int pind; int *tpa; |
---|
| 1331 | struct tree *root; |
---|
| 1332 | struct tree *p1, *p2; |
---|
| 1333 | c = eatwhite(f); |
---|
| 1334 | if ( c != '(' ) { |
---|
| 1335 | if ( isdigit(c) ) { |
---|
| 1336 | // single particle |
---|
| 1337 | fscanf(f,"%d", &pind); |
---|
| 1338 | root = newtree(); |
---|
| 1339 | root->particleindex = pind; |
---|
| 1340 | return root; |
---|
| 1341 | } |
---|
| 1342 | // set of test particles |
---|
| 1343 | tpa = ReadList(f); |
---|
| 1344 | root = newtree(); |
---|
| 1345 | root->particleindex = tpa[1]; |
---|
| 1346 | root->testparticles = tpa; |
---|
| 1347 | return root; |
---|
| 1348 | } |
---|
| 1349 | c = getc(f); |
---|
| 1350 | root = newtree(); |
---|
| 1351 | p1 = MakeTree(f); |
---|
| 1352 | p2 = MakeTree(f); |
---|
| 1353 | root->p1 = p1; root->p2 = p2; |
---|
| 1354 | root->particleindex = 0; |
---|
| 1355 | c = eatwhite(f); |
---|
| 1356 | |
---|
| 1357 | if ( c != ')' ) { |
---|
| 1358 | printf(" Error: bad tree, aborted \n"); exit(1); |
---|
| 1359 | } |
---|
| 1360 | c = getc(f); |
---|
| 1361 | return root; |
---|
| 1362 | } |
---|
| 1363 | |
---|
| 1364 | |
---|
| 1365 | |
---|
| 1366 | /* not used now but might come handy */ |
---|
| 1367 | struct tree *getparticleintree(struct tree *tree, int ind) { |
---|
| 1368 | struct tree *tmp; |
---|
| 1369 | if ( tree->particleindex ) { |
---|
| 1370 | if ( tree->particleindex == ind ) { return tree; } |
---|
| 1371 | return 0; } |
---|
| 1372 | tmp = getparticleintree(tree->p1, ind); |
---|
| 1373 | if ( tmp != 0 ) return tmp; |
---|
| 1374 | tmp = getparticleintree(tree->p2, ind); |
---|
| 1375 | if ( tmp != 0 ) return tmp; |
---|
| 1376 | return 0; } |
---|
| 1377 | |
---|
| 1378 | |
---|
| 1379 | /* not used now but might come handy */ |
---|
| 1380 | int **GetTestParticles(struct tree *tree, int ind) { |
---|
| 1381 | struct tree *tmp = getparticleintree(tree, ind); |
---|
| 1382 | if ( tmp == 0 ) return 0; |
---|
| 1383 | return &(tmp->testparticles); } |
---|
| 1384 | |
---|
| 1385 | |
---|
| 1386 | /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
---|
| 1387 | ACTUAL NUMERICAL STUFF ON TREE |
---|
| 1388 | */ |
---|
| 1389 | |
---|
| 1390 | // X fills in initial data: masses, mass ratios, barycenters |
---|
| 1391 | int FillCMinTree(struct tree *tree, double p DECLARR) { |
---|
| 1392 | int j; double *bc = tree->bc; |
---|
| 1393 | int i, ind, tp, num, *tpa = tree->testparticles; |
---|
| 1394 | |
---|
| 1395 | #pragma omp parallel for private(j) schedule(runtime) |
---|
| 1396 | for ( j = 1; j <= DIM; ++j ) |
---|
| 1397 | tree->acc[j] = 0.0; |
---|
| 1398 | |
---|
| 1399 | tree->tmass = 0.0; tree->rm1 = 0.0; tree->rm2 = 0.0; |
---|
| 1400 | #pragma omp parallel for private(j) schedule(runtime) |
---|
| 1401 | for ( j = 1; j <= DIM2; ++j ) |
---|
| 1402 | bc[j] = 0.0; |
---|
| 1403 | |
---|
| 1404 | ind = tree->particleindex; |
---|
| 1405 | if ( ind ) { |
---|
| 1406 | if ( tpa != 0 ) { |
---|
| 1407 | num = tpa[0]; |
---|
| 1408 | for ( tp = 1; tp <= num; ++tp ) { |
---|
| 1409 | ind = tpa[tp]; |
---|
| 1410 | if ( ind < 1 ) |
---|
| 1411 | continue; |
---|
| 1412 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1413 | for ( i = 1; i <= DIM; ++i ) |
---|
| 1414 | p[ind][ACC+i] = 0.0; |
---|
| 1415 | } |
---|
| 1416 | } |
---|
| 1417 | else { |
---|
| 1418 | tree->tmass = p[ind][GMASSCO]; |
---|
| 1419 | #pragma omp parallel for private(j) schedule(runtime) |
---|
| 1420 | for ( j = 1; j <= 2*DIM; ++j ) |
---|
| 1421 | bc[j] = p[ind][j]; |
---|
| 1422 | } |
---|
| 1423 | return 0; |
---|
| 1424 | } |
---|
| 1425 | FillCMinTree(tree->p1, p); |
---|
| 1426 | FillCMinTree(tree->p2, p); |
---|
| 1427 | tree->tmass = tree->p1->tmass + tree->p2->tmass; |
---|
| 1428 | tree->rm1 = (tree->p1->tmass)/(tree->tmass); |
---|
| 1429 | tree->rm2 = (tree->p2->tmass)/(tree->tmass); |
---|
| 1430 | |
---|
| 1431 | #pragma omp parallel for private(j) schedule(runtime) |
---|
| 1432 | for ( j = 1; j <= DIM2; ++j ) { |
---|
| 1433 | bc[j] = tree->p1->bc[j] * tree->rm1 + tree->p2->bc[j] * tree->rm2; |
---|
| 1434 | } |
---|
| 1435 | return 0; |
---|
| 1436 | } |
---|
| 1437 | |
---|
| 1438 | /* copy from tree into p */ |
---|
| 1439 | int ParticlesFromTree(struct tree *tree, double p DECLARR) { |
---|
| 1440 | int j; double *bc = tree->bc; |
---|
| 1441 | int i, ind, *tpa = tree->testparticles; |
---|
| 1442 | ind = tree->particleindex; |
---|
| 1443 | if ( ind ) { |
---|
| 1444 | if ( tpa == 0 ) { |
---|
| 1445 | tree->tmass = p[ind][GMASSCO]; |
---|
| 1446 | for ( j = 1; j <= DIM2; ++j ) p[ind][j] = bc[j]; } |
---|
| 1447 | return 0; } |
---|
| 1448 | ParticlesFromTree(tree->p1, p); |
---|
| 1449 | ParticlesFromTree(tree->p2, p); |
---|
| 1450 | return 0; } |
---|
| 1451 | |
---|
| 1452 | |
---|
| 1453 | /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
---|
| 1454 | KEPLER STEP ON TREE |
---|
| 1455 | */ |
---|
| 1456 | |
---|
| 1457 | /* computes Stumpff functions several ways, depending on x */ |
---|
| 1458 | int StumpffFunctions(double *vals, double x); |
---|
| 1459 | /* advances the Kepler motion 1/2*v^2 - mu/|x| for time deltat */ |
---|
| 1460 | double KeplerStumpffStep(int dim, double mu, double *xv, double deltat); |
---|
| 1461 | /* return only the increment in xv */ |
---|
| 1462 | double IncrementKeplerStumpffStep(int dim, double mu, double *xv, double deltat); |
---|
| 1463 | |
---|
| 1464 | // X NOTE: this does not CHANGE centers of masses |
---|
| 1465 | int KeplerOnTree(struct tree *tree, double stepsize, double p DECLARR) { |
---|
| 1466 | // move the center of mass |
---|
| 1467 | double cmove[10]; |
---|
| 1468 | int i; |
---|
| 1469 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1470 | for ( i = 1; i <= 2*DIM; ++i ) |
---|
| 1471 | cmove[i] = 0.0; |
---|
| 1472 | |
---|
| 1473 | // move by 1/2*(Tmass)*v^2 */ |
---|
| 1474 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1475 | for ( i = 1; i <= DIM; ++i ) |
---|
| 1476 | cmove[i] = (tree->bc[DIM+i])*stepsize; |
---|
| 1477 | |
---|
| 1478 | MoveCMandKepler(tree, cmove, stepsize, p); |
---|
| 1479 | return 0; |
---|
| 1480 | } |
---|
| 1481 | |
---|
| 1482 | |
---|
| 1483 | // X Assume that test particles are attached to 2nd |
---|
| 1484 | int DoTestPartKepler(struct tree *tree, double *cmove, double stepsize, double p DECLARR) { |
---|
| 1485 | int i, tp, num, *tpa, ind; |
---|
| 1486 | double mu, tmpkep[TMPSIZE], *bc; |
---|
| 1487 | tpa = tree->p2->testparticles; |
---|
| 1488 | num = tpa[0]; |
---|
| 1489 | if ( num > 0 ) { |
---|
| 1490 | bc = tree->p1->bc; |
---|
| 1491 | mu = tree->tmass; |
---|
| 1492 | for ( tp = 1; tp <= num; ++tp ) { |
---|
| 1493 | ind = tpa[tp]; |
---|
| 1494 | if ( ind < 1 ) continue; |
---|
| 1495 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1496 | for ( i = 1; i <= DIM2; ++i ) |
---|
| 1497 | tmpkep[i] = p[ind][i] - bc[i]; |
---|
| 1498 | IncrementKeplerStumpffStep(DIM, mu, tmpkep, stepsize); |
---|
| 1499 | for ( i = 1; i <= DIM2; ++i ) |
---|
| 1500 | p[ind][i] += (cmove[i]+tmpkep[i]); |
---|
| 1501 | } |
---|
| 1502 | } |
---|
| 1503 | return 0; |
---|
| 1504 | } |
---|
| 1505 | |
---|
| 1506 | // X move the center of mass and do a Kepler step on relative coordinates, transmit the new "moves" down |
---|
| 1507 | int MoveCMandKepler(struct tree *tree, double *cmove, double stepsize, double p DECLARR) { |
---|
| 1508 | int i, *tpa, ind; |
---|
| 1509 | double tmp[TMPSIZE], tmpkep[TMPSIZE], *xv1, *xv2, mu; |
---|
| 1510 | double *bc = tree->bc; |
---|
| 1511 | |
---|
| 1512 | for ( i = 1; i <= DIM2; ++i ) { |
---|
| 1513 | bc[i] += cmove[i]; |
---|
| 1514 | } |
---|
| 1515 | // do nothing else for actual particles |
---|
| 1516 | if ( tree->particleindex ) { |
---|
| 1517 | return 0; |
---|
| 1518 | } |
---|
| 1519 | if ( tree->p2->testparticles ) { |
---|
| 1520 | // this is a pair where p2 is an array of test particles |
---|
| 1521 | DoTestPartKepler(tree, cmove, stepsize, p); |
---|
| 1522 | MoveCMandKepler(tree->p1, cmove, stepsize, p); |
---|
| 1523 | return 0; |
---|
| 1524 | } |
---|
| 1525 | mu = tree->tmass; |
---|
| 1526 | xv1 = tree->p1->bc; |
---|
| 1527 | xv2 = tree->p2->bc; |
---|
| 1528 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1529 | for ( i = 1; i <= DIM2; ++i ) { |
---|
| 1530 | tmpkep[i] = xv2[i]-xv1[i]; |
---|
| 1531 | } |
---|
| 1532 | // do Kepler step on tmpkep, we get back the increment |
---|
| 1533 | IncrementKeplerStumpffStep(DIM, mu, tmpkep, stepsize); |
---|
| 1534 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1535 | // use only the relative change |
---|
| 1536 | for ( i = 1; i <= DIM2; ++i ) { |
---|
| 1537 | tmp[i] = cmove[i] - tmpkep[i]*(tree->rm2); |
---|
| 1538 | } |
---|
| 1539 | MoveCMandKepler(tree->p1, tmp, stepsize, p); |
---|
| 1540 | #pragma omp parallel for private(i) schedule(runtime) |
---|
| 1541 | for ( i = 1; i <= DIM2; ++i ) { |
---|
| 1542 | tmp[i] = cmove[i] + tmpkep[i]*(tree->rm1); |
---|
| 1543 | } |
---|
| 1544 | MoveCMandKepler(tree->p2, tmp, stepsize, p); |
---|
| 1545 | return 0; |
---|
| 1546 | } |
---|
| 1547 | |
---|
| 1548 | /* ++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
---|
| 1549 | PERTURBATION ACCELERATIONS |
---|
| 1550 | */ |
---|
| 1551 | |
---|
| 1552 | /* X simple acceleration */ |
---|
| 1553 | int Accel(double *x1, double *x2, double *acc) { |
---|
| 1554 | double tmp[10], r = 0.0; int i; |
---|
| 1555 | for ( i = 1; i <= DIM; ++i ) { |
---|
| 1556 | tmp[i] = x1[i]-x2[i]; |
---|
| 1557 | r = r + tmp[i]*tmp[i]; |
---|
| 1558 | } |
---|
| 1559 | r = sqrt(r); |
---|
| 1560 | r = r*r*r; |
---|
| 1561 | for ( i = 1; i <= DIM; ++i ) { |
---|
| 1562 | acc[i] = -tmp[i]/r; |
---|
| 1563 | } |
---|
| 1564 | return 0; |
---|
| 1565 | } |
---|
| 1566 | |
---|
| 1567 | int AdvanceTestParticleVel(struct tree *tree, double stepsize, double p DECLARR) { |
---|
| 1568 | int i, ind, tp, num, *tpa = tree->testparticles; |
---|
| 1569 | if ( tpa == 0 ) return 0; num = tpa[0]; |
---|
| 1570 | for ( tp = 1; tp <= num; ++tp ) { |
---|
| 1571 | ind = tpa[tp]; if ( ind < 1 ) continue; |
---|
| 1572 | for ( i = 1; i <= DIM; ++i ) { |
---|
| 1573 | p[ind][DIM+i] += stepsize*p[ind][ACC+i]; |
---|
| 1574 | p[ind][ACC+i] = 0.0; } |
---|
| 1575 | } |
---|
| 1576 | return 0; } |
---|
| 1577 | |
---|
| 1578 | |
---|
| 1579 | /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
---|
| 1580 | PERTURBATIONS ON TREE |
---|
| 1581 | */ |
---|
| 1582 | // X |
---|
| 1583 | int RecursivePerturbations(struct tree *tree, double stepsize, double p DECLARR) { |
---|
| 1584 | int j, ind; double *bc = tree->bc; |
---|
| 1585 | /* advance attached test particles |
---|
| 1586 | if ( tree->particleindex ) { |
---|
| 1587 | /* if particle we are ready to advance v */ |
---|
| 1588 | if ( tree->testparticles ) { |
---|
| 1589 | AdvanceTestParticleVel(tree, stepsize, p); |
---|
| 1590 | return 0; |
---|
| 1591 | } |
---|
| 1592 | // this is a nonzero mass actual particle, advance v |
---|
| 1593 | for ( j = 1; j <= DIM; ++j ) { |
---|
| 1594 | bc[DIM+j] += stepsize*tree->acc[j]; |
---|
| 1595 | tree->acc[j] = 0.0; |
---|
| 1596 | } |
---|
| 1597 | return 0; |
---|
| 1598 | |
---|
| 1599 | /* if not, first we take care of accs. for pairs with the two parts |
---|
| 1600 | IMPORTANT TO DO THIS FIRST |
---|
| 1601 | */ |
---|
| 1602 | RecPertAcc(tree, stepsize, p); |
---|
| 1603 | // now descend and do the same for both parts |
---|
| 1604 | RecursivePerturbations(tree->p2, stepsize, p); |
---|
| 1605 | RecursivePerturbations(tree->p1, stepsize, p); |
---|
| 1606 | /* now regenerate center of mass etc. */ |
---|
| 1607 | if ( tree->p2->testparticles ) { |
---|
| 1608 | #pragma omp parallel private(j) |
---|
| 1609 | #pragma omp for schedule(runtime) |
---|
| 1610 | for ( j = 1; j <= DIM2; ++j ) { |
---|
| 1611 | bc[j] = tree->p1->bc[j]; |
---|
| 1612 | } |
---|
| 1613 | return 0; |
---|
| 1614 | } |
---|
| 1615 | |
---|
| 1616 | #pragma omp parallel private(j) |
---|
| 1617 | #pragma omp for schedule(runtime) |
---|
| 1618 | for ( j = 1; j <= DIM2; ++j ) { |
---|
| 1619 | bc[j] = tree->p1->bc[j] * tree->rm1 + tree->p2->bc[j] * tree->rm2; |
---|
| 1620 | } |
---|
| 1621 | return 0; |
---|
| 1622 | } |
---|
| 1623 | |
---|
| 1624 | /* assume test particles in tree2 for dir > 1, reverse signs for dir < 0 */ |
---|
| 1625 | int TestParticleAcc(int dir, double *cacc, struct tree *tree1, struct tree *tree2, |
---|
| 1626 | double p DECLARR) { |
---|
| 1627 | int i, ind, tp, num, *tpa = tree2->testparticles; |
---|
| 1628 | double acc[TMPSIZE]; |
---|
| 1629 | double *bc = tree1->bc; |
---|
| 1630 | double tmp, gm1 = tree1->tmass; |
---|
| 1631 | num = tpa[0]; |
---|
| 1632 | for ( tp = 1; tp <= num; ++tp ) { |
---|
| 1633 | ind = tpa[tp]; if ( ind < 1 ) continue; |
---|
| 1634 | /* rewrite this to avoid bad numerical attitude */ |
---|
| 1635 | Accel(bc, &p[ind][0], acc); |
---|
| 1636 | for ( i = 1; i <= DIM; ++i ) { |
---|
| 1637 | /* since test particles are in 2nd */ |
---|
| 1638 | tmp = acc[i]-cacc[i]*dir; |
---|
| 1639 | p[ind][ACC+i] += -gm1*tmp; } |
---|
| 1640 | } |
---|
| 1641 | return 0; } |
---|
| 1642 | |
---|
| 1643 | |
---|
| 1644 | /* X c1 and c2 are for possible future use */ |
---|
| 1645 | int RecPertAccSub(struct tree *tree1, |
---|
| 1646 | struct tree *tree2, double *cacc, double *c1, double *c2, double p DECLARR) { |
---|
| 1647 | /* do the work if both are particles */ |
---|
| 1648 | int i, ind1, ind2; double acc[TMPSIZE]; |
---|
| 1649 | double tmp, gm1 = tree1->tmass, gm2 = tree2->tmass; |
---|
| 1650 | ind1 = tree1->particleindex; |
---|
| 1651 | ind2 = tree2->particleindex; |
---|
| 1652 | if ( ind1 && ind2 ) { |
---|
| 1653 | /* do nothing if both are test particle arrays */ |
---|
| 1654 | if ( tree1->testparticles && tree2->testparticles ) |
---|
| 1655 | return 0; |
---|
| 1656 | /* test particles first */ |
---|
| 1657 | if ( tree2->testparticles ) { |
---|
| 1658 | TestParticleAcc(1, cacc, tree1, tree2, p); |
---|
| 1659 | return 0; |
---|
| 1660 | } |
---|
| 1661 | if ( tree1->testparticles ) { |
---|
| 1662 | TestParticleAcc( -1, cacc, tree2, tree1, p); |
---|
| 1663 | return 0; |
---|
| 1664 | } |
---|
| 1665 | /* if actual particles with nonzero mass */ |
---|
| 1666 | Accel(tree1->bc, tree2->bc, acc); |
---|
| 1667 | for ( i = 1; i <= DIM; ++i ) { |
---|
| 1668 | /* rewrite this to avoid bad numerical attitude */ |
---|
| 1669 | tmp = acc[i]-cacc[i]; |
---|
| 1670 | tree1->acc[i] += gm2*tmp; |
---|
| 1671 | tree2->acc[i] += -gm1*tmp; |
---|
| 1672 | } |
---|
| 1673 | return 0; |
---|
| 1674 | } |
---|
| 1675 | /* if not, descend but only for one branch, the other is taken care in turn */ |
---|
| 1676 | if ( !ind1 ) { |
---|
| 1677 | RecPertAccSub(tree1->p2, tree2, cacc, c1, c2, p); |
---|
| 1678 | RecPertAccSub(tree1->p1, tree2, cacc, c1, c2, p); |
---|
| 1679 | return 0; |
---|
| 1680 | } |
---|
| 1681 | RecPertAccSub(tree1, tree2->p1, cacc, c1, c2, p); |
---|
| 1682 | RecPertAccSub(tree1, tree2->p2, cacc, c1, c2, p); |
---|
| 1683 | return 0; |
---|
| 1684 | } |
---|
| 1685 | |
---|
| 1686 | /* assume test particles in tree2 */ |
---|
| 1687 | int TestParticleAccSpec(double *cm, struct tree *tree1, struct tree *tree2, double p DECLARR) { |
---|
| 1688 | int i, ind, tp, num, *tpa = tree2->testparticles; |
---|
| 1689 | double acc[TMPSIZE], cacc[TMPSIZE]; |
---|
| 1690 | double *bc = tree1->bc; |
---|
| 1691 | double tmp, gm1 = tree1->tmass; |
---|
| 1692 | num = tpa[0]; |
---|
| 1693 | for ( tp = 1; tp <= num; ++tp ) { |
---|
| 1694 | ind = tpa[tp]; if ( ind < 1 ) continue; |
---|
| 1695 | /* rewrite this to avoid bad numerical attitude */ |
---|
| 1696 | Accel(bc, &p[ind][0], acc); |
---|
| 1697 | Accel(cm, &p[ind][0], cacc); |
---|
| 1698 | for ( i = 1; i <= DIM; ++i ) { |
---|
| 1699 | /* since test particles are in 2nd */ |
---|
| 1700 | tmp = acc[i]-cacc[i]; |
---|
| 1701 | p[ind][ACC+i] += -gm1*tmp; |
---|
| 1702 | } |
---|
| 1703 | } |
---|
| 1704 | return 0; |
---|
| 1705 | } |
---|
| 1706 | |
---|
| 1707 | |
---|
| 1708 | /* c1 and c2 are for possible future use */ |
---|
| 1709 | int RecPertAccSubTest(double *cm, struct tree *tree1, struct tree *tree2, double p DECLARR) { |
---|
| 1710 | int ind1; |
---|
| 1711 | ind1 = tree1->particleindex; |
---|
| 1712 | if ( ind1 ) { |
---|
| 1713 | /* do nothing if tree1 has only test particles */ |
---|
| 1714 | if ( tree1->testparticles ) |
---|
| 1715 | return 0; |
---|
| 1716 | TestParticleAccSpec(cm, tree1, tree2, p); |
---|
| 1717 | return 0; |
---|
| 1718 | } |
---|
| 1719 | /* if not, descend for both branches */ |
---|
| 1720 | RecPertAccSubTest(cm, tree1->p1, tree2, p); |
---|
| 1721 | RecPertAccSubTest(cm, tree1->p2, tree2, p); |
---|
| 1722 | return 0; |
---|
| 1723 | } |
---|
| 1724 | |
---|
| 1725 | |
---|
| 1726 | int RecPertAcc(struct tree *tree, double stepsize, double p DECLARR) { |
---|
| 1727 | double cacc[TMPSIZE]; |
---|
| 1728 | /* do nothing if all in p2 are attached to p1: pure Kepler motion */ |
---|
| 1729 | if ( tree->p1->particleindex && tree->p2->particleindex ) |
---|
| 1730 | return 0; |
---|
| 1731 | if ( tree->p2->testparticles == 0 ) { |
---|
| 1732 | /* actual nonzero masses in p2 */ |
---|
| 1733 | Accel(tree->p1->bc, tree->p2->bc, cacc); |
---|
| 1734 | |
---|
| 1735 | RecPertAccSub(tree->p1, tree->p2, cacc, tree->p1->bc, tree->p2->bc, p); |
---|
| 1736 | return 0; |
---|
| 1737 | } |
---|
| 1738 | /* test particles in p2 */ |
---|
| 1739 | RecPertAccSubTest(tree->p1->bc, tree->p1, tree->p2, p); |
---|
| 1740 | return 0; |
---|
| 1741 | } |
---|
| 1742 | |
---|
| 1743 | |
---|
| 1744 | |
---|
| 1745 | |
---|
| 1746 | /* |
---|
| 1747 | // =============================================================================== |
---|
| 1748 | // |
---|
| 1749 | // KEPLER MOTION USING STUMPFF FUCNTIONS |
---|
| 1750 | // FOLLOWING DANBY, 1992 |
---|
| 1751 | // (quartic Newtonian solver, Stumpff function definitions, |
---|
| 1752 | // f and g functions) |
---|
| 1753 | // see also: Stiefel and Sheifele, Linear and Regular |
---|
| 1754 | // Celestial Mechanics |
---|
| 1755 | // |
---|
| 1756 | // =============================================================================== |
---|
| 1757 | |
---|
| 1758 | // Stumpff functions (c0, c1, c2, c3) |
---|
| 1759 | */ |
---|
| 1760 | |
---|
| 1761 | /* CHANGE these numbers to tune accuracy */ |
---|
| 1762 | /* this one can be changed runtime */ |
---|
| 1763 | static double StumpffQSTol = KEPLERSOLVERTOLERANCE; |
---|
| 1764 | |
---|
| 1765 | /* the limit for which trig and hyp. trig functions are used */ |
---|
| 1766 | #define STUMPFFPLAINLIM (5.0) |
---|
| 1767 | /* reduction limit */ |
---|
| 1768 | #define STUMPFFRED (1.0/32.0) |
---|
| 1769 | #define STUMPFFSHORTTOL (1.0e-6) |
---|
| 1770 | |
---|
| 1771 | /* this one is not used now */ |
---|
| 1772 | static double StumpffSerTol = 1.0e-25; |
---|
| 1773 | |
---|
| 1774 | static int StumpffErrorCount = 0; |
---|
| 1775 | static int StumpffErrorCountLimit = 100; |
---|
| 1776 | |
---|
| 1777 | CheckStumpffErrorCount() { |
---|
| 1778 | ++StumpffErrorCount; |
---|
| 1779 | if ( StumpffErrorCount > StumpffErrorCountLimit ) { |
---|
| 1780 | fprintf(FLOG, "\n Too many errors, aborted \n"); |
---|
| 1781 | fflush(FLOG); |
---|
| 1782 | exit(1); |
---|
| 1783 | } |
---|
| 1784 | return 0; |
---|
| 1785 | } |
---|
| 1786 | |
---|
| 1787 | double util_fact(int k) { |
---|
| 1788 | int i; double fact = 1; |
---|
| 1789 | for ( i = 1; i <= k; ++i ) { |
---|
| 1790 | fact *= i; |
---|
| 1791 | } |
---|
| 1792 | return fact; |
---|
| 1793 | } |
---|
| 1794 | |
---|
| 1795 | /* |
---|
| 1796 | In case we need the coefficients, produced by Mathematica |
---|
| 1797 | static double c2_0 = 0.5; |
---|
| 1798 | static double c2_1 = -1.0/24; |
---|
| 1799 | static double c2_2 = 1.0/720; |
---|
| 1800 | static double c2_3 = -1.0/40320; |
---|
| 1801 | static double c2_4 = 1.0/3628800; |
---|
| 1802 | static double c2_5 = -1.0/479001600; |
---|
| 1803 | static double c2_6 = 1.0/87178291200; |
---|
| 1804 | static double c2_7 = -1.0/20922789888000; |
---|
| 1805 | static double c2_8 = 1.0/6402373705728000; |
---|
| 1806 | static double c2_9 = -1.0/2432902008176640000; |
---|
| 1807 | static double c2_10 = 1.0/1124000727777607680000; |
---|
| 1808 | |
---|
| 1809 | static double c3_0 = 1.0/6; |
---|
| 1810 | static double c3_1 = -1.0/120; |
---|
| 1811 | static double c3_2 = 1.0/5040; |
---|
| 1812 | static double c3_3 = -1.0/362880; |
---|
| 1813 | static double c3_4 = 1.0/39916800; |
---|
| 1814 | static double c3_5 = -1.0/6227020800; |
---|
| 1815 | static double c3_6 = 1.0/1307674368000; |
---|
| 1816 | static double c3_7 = -1.0/355687428096000; |
---|
| 1817 | static double c3_8 = 1.0/121645100408832000; |
---|
| 1818 | static double c3_9 = -1.0/51090942171709440000; |
---|
| 1819 | static double c3_10 = 1.0/25852016738884976640000; |
---|
| 1820 | */ |
---|
| 1821 | |
---|
| 1822 | |
---|
| 1823 | /* This is what is actually used, generated by factoring the coefficients */ |
---|
| 1824 | double HornerStumpff2(double x) { |
---|
| 1825 | return |
---|
| 1826 | (1.0 - x*(1 - x*(1 - x*(1 - x*(1 - x *(1 - x |
---|
| 1827 | /* up to degree 10, if you need it |
---|
| 1828 | *(1 - x*(1 - x*(1 - (1 - x/462)*x/380)/306)/240) */ |
---|
| 1829 | /182)/132)/90)/56)/30)/12)/2; |
---|
| 1830 | } |
---|
| 1831 | |
---|
| 1832 | double HornerStumpff3(double x) { |
---|
| 1833 | return |
---|
| 1834 | (1.0 - x*(1 - x*(1 - x*(1 - x*(1 - x*(1 - x |
---|
| 1835 | /* up to degree 10, if you need it |
---|
| 1836 | *(1 - x*(1 - x*(1 - (1 - x/506)*x/420)/342)/272) */ |
---|
| 1837 | /210)/156)/110)/72)/42)/20)/6; |
---|
| 1838 | } |
---|
| 1839 | |
---|
| 1840 | |
---|
| 1841 | /* first 4 terms, ie., up to x^3 */ |
---|
| 1842 | double Stumpff2Short(double x) { |
---|
| 1843 | return (1.0 - x*(1 - x*(1 - x/56)/30)/12)/2; |
---|
| 1844 | } |
---|
| 1845 | |
---|
| 1846 | double Stumpff3Short(double x) { |
---|
| 1847 | return (1.0 - x*(1 - x*(1 - x/72)/42)/20)/6; |
---|
| 1848 | } |
---|
| 1849 | |
---|
| 1850 | |
---|
| 1851 | |
---|
| 1852 | |
---|
| 1853 | // Original for reference |
---|
| 1854 | double StumpffSeriesCk(int k, double x) { |
---|
| 1855 | int i; |
---|
| 1856 | double term, sum = 0.0; |
---|
| 1857 | double terms[100], num; |
---|
| 1858 | term = 1.0; |
---|
| 1859 | for ( i = 1; i <= 50; ++i ) { |
---|
| 1860 | num = (k+2*i-1)*(k+2*i); |
---|
| 1861 | term = term*(-x/num); |
---|
| 1862 | terms[i] = term; |
---|
| 1863 | if ( fabs(term) < StumpffSerTol ) break; |
---|
| 1864 | } |
---|
| 1865 | for ( ; i > 0; --i ) sum += terms[i]; |
---|
| 1866 | sum = (1.0+sum)/util_fact(k); |
---|
| 1867 | return sum; } |
---|
| 1868 | |
---|
| 1869 | // X |
---|
| 1870 | int StumpffFunctions(double *c, double x) { |
---|
| 1871 | double x2, tmp; |
---|
| 1872 | int i; |
---|
| 1873 | /* What this is supposed to be |
---|
| 1874 | c[0] = StumpffSeriesCk(0, x); |
---|
| 1875 | c[1] = StumpffSeriesCk(1, x); |
---|
| 1876 | c[2] = StumpffSeriesCk(2, x); |
---|
| 1877 | c[3] = StumpffSeriesCk(3, x); |
---|
| 1878 | return 0; |
---|
| 1879 | */ |
---|
| 1880 | /* FOR REFERENCE, THIS COULD BE USED FOR LARGE VALUES, MAYBE |
---|
| 1881 | if ( x > STUMPFFPLAINLIM ) { |
---|
| 1882 | x2 = sqrt(x); |
---|
| 1883 | c[0] = cos(x2); |
---|
| 1884 | c[1] = sin(x2)/x2; |
---|
| 1885 | c[2] = (1.0-cos(x2))/x; |
---|
| 1886 | c[3] = (x2-sin(x2))/(x*x2); |
---|
| 1887 | return 0; } |
---|
| 1888 | if ( x < -STUMPFFPLAINLIM ) { |
---|
| 1889 | x2 = sqrt(-x); |
---|
| 1890 | c[0] = cosh(x2); |
---|
| 1891 | c[1] = sinh(x2)/x2; |
---|
| 1892 | c[2] = (cosh(x2)-1.0)/x; |
---|
| 1893 | c[3] = (sinh(x2)-x2)/(x*x2); |
---|
| 1894 | return 0; } |
---|
| 1895 | */ |
---|
| 1896 | if ( fabs(x) < STUMPFFSHORTTOL ) { |
---|
| 1897 | c[2] = Stumpff2Short(x); |
---|
| 1898 | c[3] = Stumpff3Short(x); |
---|
| 1899 | c[1] = 1.0 - x*c[3]; |
---|
| 1900 | c[0] = 1.0 - x*c[2]; |
---|
| 1901 | return 0; |
---|
| 1902 | } |
---|
| 1903 | if ( fabs(x) < STUMPFFRED ) { |
---|
| 1904 | c[2] = HornerStumpff2(x); |
---|
| 1905 | c[3] = HornerStumpff3(x); |
---|
| 1906 | c[1] = 1.0 - x*c[3]; |
---|
| 1907 | c[0] = 1.0 - x*c[2]; |
---|
| 1908 | return 0; |
---|
| 1909 | } |
---|
| 1910 | // reduce value to small |
---|
| 1911 | x2 = x; |
---|
| 1912 | for ( i = 1; i <= 20; ++i ) { |
---|
| 1913 | x2 = x2/4.0; |
---|
| 1914 | if ( fabs(x2) < STUMPFFRED ) |
---|
| 1915 | break; |
---|
| 1916 | } |
---|
| 1917 | if ( i > 20 ) { |
---|
| 1918 | fprintf(FLOG, "%s"," StumpfReduction No Good \n"); |
---|
| 1919 | CheckStumpffErrorCount(); |
---|
| 1920 | fflush(FLOG); |
---|
| 1921 | return 0; |
---|
| 1922 | } |
---|
| 1923 | /* original |
---|
| 1924 | c[2] = StumpffSeriesCk(2, x2); |
---|
| 1925 | c[3] = StumpffSeriesCk(3, x2); |
---|
| 1926 | */ |
---|
| 1927 | c[2] = HornerStumpff2(x2); |
---|
| 1928 | c[3] = HornerStumpff3(x2); |
---|
| 1929 | c[1] = 1.0 - x2*c[3]; |
---|
| 1930 | c[0] = 1.0 - x2*c[2]; |
---|
| 1931 | for ( ; i > 0; --i ) { |
---|
| 1932 | tmp = c[2]; |
---|
| 1933 | c[2] = (c[1]*c[1])/2.0; |
---|
| 1934 | c[3] = (tmp+c[0]*c[3])/4.0; |
---|
| 1935 | c[1] = c[0]*c[1]; |
---|
| 1936 | c[0] = (2.0*c[0]*c[0])-1.0; |
---|
| 1937 | } |
---|
| 1938 | return i; |
---|
| 1939 | } |
---|
| 1940 | |
---|
| 1941 | |
---|
| 1942 | /* =============================================================================== |
---|
| 1943 | */ |
---|
| 1944 | |
---|
| 1945 | /* NOTE: |
---|
| 1946 | It seems that there might be a systematic error here, not sure yet. |
---|
| 1947 | The Newton solvers tend to end up systematically on a preferred side |
---|
| 1948 | of the solution. E.g., for x^2: if starting from above the solution, |
---|
| 1949 | it ends at a slightly larger value than the solution. Starting from |
---|
| 1950 | below, in the first step it will get to the previous case. Since |
---|
| 1951 | the solution cannot be computed to machine precision, we could have |
---|
| 1952 | a systematic error. Since the orbit spends more time near apocenter |
---|
| 1953 | than near pericenter, this seems to lead an increase in energy and |
---|
| 1954 | decrease in angular momentum. Perhaps this could be randomized with |
---|
| 1955 | an additional bisection at the end? |
---|
| 1956 | */ |
---|
| 1957 | // X |
---|
| 1958 | double QuarticStumpffSolverIterator(double mu, double alpha, double s, |
---|
| 1959 | double r0, double u, double deltat) { |
---|
| 1960 | double c[5]; |
---|
| 1961 | double d0, d1, d2, d3, s2, ssav = s, tmp1, tmp2, tmp3; |
---|
| 1962 | double delta1, delta2, delta3; |
---|
| 1963 | int i; |
---|
| 1964 | for ( i = 1; i <= 20; ++i ) { |
---|
| 1965 | s2 = s*s; |
---|
| 1966 | StumpffFunctions(c, alpha*s2); |
---|
| 1967 | tmp1 = s*c[1]; |
---|
| 1968 | tmp2 = s2*c[2]; |
---|
| 1969 | tmp3 = -r0*alpha+mu; |
---|
| 1970 | d0 = u*tmp2+mu*s2*s*c[3]; |
---|
| 1971 | d0 += r0*tmp1; |
---|
| 1972 | d0 -= deltat; |
---|
| 1973 | d1 = u*tmp1+mu*tmp2; |
---|
| 1974 | d1 += r0*c[0]; |
---|
| 1975 | d2 = u*c[0]+tmp3*tmp1; |
---|
| 1976 | d3 = tmp3*c[0]-u*alpha*c[1]; |
---|
| 1977 | delta1 = -d0/d1; |
---|
| 1978 | delta2 = -d0/(d1+delta1*d2/2); |
---|
| 1979 | delta3 = -d0/(d1+delta1*d2/2+delta2*delta2*d3/6); |
---|
| 1980 | ssav= s; |
---|
| 1981 | s = s + delta3; |
---|
| 1982 | if ( fabs(delta3/s) < StumpffQSTol ) return s; |
---|
| 1983 | } |
---|
| 1984 | fprintf(FLOG, "%s"," QUARTIC STUMPFF SOLVER NOT CONVERGENT? \n"); |
---|
| 1985 | fprintf(FLOG, " s = %.16e \n", s); |
---|
| 1986 | fprintf(FLOG, "sprev = %.16e \n", ssav); |
---|
| 1987 | fprintf(FLOG, "delta3/s = %.16e \n", delta3/s); |
---|
| 1988 | fprintf(FLOG, "Stumpff x = %.16e \n", alpha*s2); |
---|
| 1989 | fprintf(FLOG, "deltas = %.16e ", delta1); fprintf(FLOG, "%.16e ", delta2); |
---|
| 1990 | fprintf(FLOG, "%.16e \n", delta3); |
---|
| 1991 | CheckStumpffErrorCount(); |
---|
| 1992 | fflush(FLOG); |
---|
| 1993 | return s; |
---|
| 1994 | } |
---|
| 1995 | |
---|
| 1996 | // X |
---|
| 1997 | double QuarticStumpffSolver(double mu, double alpha, double s, double r0, double u, double deltat) { |
---|
| 1998 | /* initial guess */ |
---|
| 1999 | double tmp = deltat/r0; |
---|
| 2000 | double s0 = tmp; |
---|
| 2001 | double r0dot = u/r0; |
---|
| 2002 | tmp = tmp*tmp; |
---|
| 2003 | s0 -= 0.5*r0dot*tmp; |
---|
| 2004 | /* third order in deltat */ |
---|
| 2005 | tmp = tmp*deltat/r0; |
---|
| 2006 | s0 += (0.5*r0dot*r0dot-1/6*(mu-alpha*r0)/r0)*tmp; |
---|
| 2007 | s = QuarticStumpffSolverIterator( mu, alpha, s0, r0, u, deltat); |
---|
| 2008 | return s; |
---|
| 2009 | } |
---|
| 2010 | |
---|
| 2011 | /* =============================================================================== |
---|
| 2012 | */ |
---|
| 2013 | // X |
---|
| 2014 | void IncfgAndDerivsStumpff(double *vals, double mu, double alpha, double s, |
---|
| 2015 | double r0, double u, double deltat) { |
---|
| 2016 | double r, s2, tmp1, tmp2, tmp3; |
---|
| 2017 | double c[5]; |
---|
| 2018 | s = QuarticStumpffSolver( mu, alpha, s, r0, u, deltat); |
---|
| 2019 | s2 = s*s; |
---|
| 2020 | StumpffFunctions(c, alpha*s2); |
---|
| 2021 | //recompute c[1] from angular mom. |
---|
| 2022 | tmp1 = s*c[1]; |
---|
| 2023 | tmp2 = s2*c[2]; |
---|
| 2024 | tmp3 = u*tmp1+mu*tmp2; |
---|
| 2025 | /* r */ |
---|
| 2026 | r = tmp3+(r0*c[0]); |
---|
| 2027 | vals[0] = r; |
---|
| 2028 | tmp3 = -mu*tmp2; |
---|
| 2029 | /* f */ |
---|
| 2030 | vals[1] = tmp3/r0; |
---|
| 2031 | /* g, this is usually bad in terms of roundoff */ |
---|
| 2032 | vals[2] = r0*tmp1+u*tmp2; |
---|
| 2033 | /* derivs */ |
---|
| 2034 | vals[3] = -(mu*tmp1)/(r0*r); |
---|
| 2035 | vals[4] = tmp3/r; |
---|
| 2036 | return; |
---|
| 2037 | } |
---|
| 2038 | |
---|
| 2039 | void fgAndDerivsStumpff(double *vals, double mu, double alpha, double s, |
---|
| 2040 | double r0, double u, double deltat) { |
---|
| 2041 | IncfgAndDerivsStumpff(vals, mu, alpha, s, r0, u, deltat); |
---|
| 2042 | vals[1] += 1.0; |
---|
| 2043 | vals[4] += 1.0; |
---|
| 2044 | return; } |
---|
| 2045 | |
---|
| 2046 | double KeplerStumpffStep(int dim, double mu, double *xv, double deltat) { |
---|
| 2047 | double fgvals[5], tmp; |
---|
| 2048 | double *x = xv; |
---|
| 2049 | double *v = xv+dim; |
---|
| 2050 | double v02 = 0.0, u = 0.0, r0 = 0.0; |
---|
| 2051 | double r0dot, alpha; |
---|
| 2052 | int i; |
---|
| 2053 | for ( i = 1; i <= dim; ++i ) { |
---|
| 2054 | v02 += v[i]*v[i]; |
---|
| 2055 | u += x[i]*v[i]; |
---|
| 2056 | r0 += x[i]*x[i]; } |
---|
| 2057 | r0 = sqrt(r0); |
---|
| 2058 | r0dot = u/r0; |
---|
| 2059 | /* a = 1.0/(2.0/r0 - v02/mu); alpha = mu/a; */ |
---|
| 2060 | alpha = 2.0*mu/r0 - v02; |
---|
| 2061 | fgAndDerivsStumpff(fgvals, mu, alpha, 0.0, r0, u, deltat); |
---|
| 2062 | /* now update */ |
---|
| 2063 | for ( i = 1; i <= dim; ++i ) { |
---|
| 2064 | tmp = x[i]; |
---|
| 2065 | x[i] = fgvals[1]*x[i]+fgvals[2]*v[i]; |
---|
| 2066 | v[i] = fgvals[3]*tmp+fgvals[4]*v[i]; } |
---|
| 2067 | return 0.0; } |
---|
| 2068 | |
---|
| 2069 | |
---|
| 2070 | // X return only the increment |
---|
| 2071 | double IncrementKeplerStumpffStep(int dim, double mu, double *xv, double deltat) { |
---|
| 2072 | double fg[5], tmp, tmp2; |
---|
| 2073 | double *x = xv; |
---|
| 2074 | double *v = xv+dim; |
---|
| 2075 | double alpha, v02 = 0.0, u = 0.0, r02 = 0.0, r0; |
---|
| 2076 | int i, ii; |
---|
| 2077 | double tmp1, r, delta1; |
---|
| 2078 | for ( i = 1; i <= dim; ++i ) { |
---|
| 2079 | v02 += v[i]*v[i]; |
---|
| 2080 | u += x[i]*v[i]; |
---|
| 2081 | r02 += x[i]*x[i]; |
---|
| 2082 | } |
---|
| 2083 | r0 = sqrt(r02); |
---|
| 2084 | /* a = 1.0/(2.0/r0 - v02/mu); alpha = mu/a; */ |
---|
| 2085 | alpha = 2.0*mu/r0 - v02; |
---|
| 2086 | IncfgAndDerivsStumpff(fg, mu, alpha, 0.0, r0, u, deltat); |
---|
| 2087 | |
---|
| 2088 | // using fg'-gf' = 1 ( ' = dot) or total energy do not help much |
---|
| 2089 | |
---|
| 2090 | // now update |
---|
| 2091 | for ( i = 1; i <= dim; ++i ) { |
---|
| 2092 | tmp = x[i]; |
---|
| 2093 | x[i] = fg[1]*x[i]+fg[2]*v[i]; |
---|
| 2094 | v[i] = fg[3]*tmp+fg[4]*v[i]; |
---|
| 2095 | } |
---|
| 2096 | return 0.0; |
---|
| 2097 | } |
---|
| 2098 | |
---|
| 2099 | /* FOR TEST |
---|
| 2100 | double IncrementKeplerStumpffStep(int dim, double mu, double *xv, double deltat) { |
---|
| 2101 | double tmp[7], tmp2[7]; |
---|
| 2102 | int i; |
---|
| 2103 | for ( i = 1; i <= 2*dim; ++i ) { tmp[i] = tmp2[i] = xv[i]; } |
---|
| 2104 | IncrementKeplerStumpffStepSub(dim, mu, tmp, deltat); |
---|
| 2105 | for ( i = 1; i <= 2*dim; ++i ) tmp2[i] += tmp[i]; |
---|
| 2106 | IncrementKeplerStumpffStepSub(dim, mu, tmp2, -deltat); |
---|
| 2107 | for ( i = 1; i <= 2*dim; ++i ) xv[i] = (tmp[i]-tmp2[i])/2.0; |
---|
| 2108 | return 0.0; } |
---|
| 2109 | */ |
---|
| 2110 | |
---|
| 2111 | |
---|
| 2112 | |
---|
| 2113 | |
---|