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SSPairPotential.cc
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9 
10 /// @file
11 /// @brief
12 /// @author Nobuyasu Koga ( nobuyasu@uw.edu )
13 
14 // Unit header
15 #include <protocols/fldsgn/potentials/sspot/SSPairPotential.hh>
16 
17 // Project headers
18 #include <core/pose/Pose.hh>
19 // AUTO-REMOVED #include <core/conformation/Conformation.hh>
20 #include <core/scoring/Energies.hh>
21 #include <core/scoring/EnergyGraph.hh>
22 #include <protocols/fldsgn/topology/SS_Info2.hh>
23 #include <protocols/fldsgn/topology/BB_Pos.hh>
24 #include <protocols/fldsgn/topology/DimerPairing.hh>
25 #include <protocols/fldsgn/potentials/sspot/util.hh>
26 
27 #include <basic/database/open.hh>
28 #include <basic/Tracer.hh>
29 
30 // Numeric
31 #include <numeric/conversions.hh>
32 
33 // utility
34 #include <utility/io/izstream.hh>
35 
36 // C++ headers
37 #include <cmath>
38 #include <iostream>
39 
40 //#include <ObjexxFCL/FArray1Da.hh>
41 #include <ObjexxFCL/format.hh>
42 
43 #include <utility/vector1.hh>
44 #include <ObjexxFCL/FArray3D.hh>
45 
46 //Auto Headers
47 #include <core/conformation/Residue.hh>
48 #include <core/kinematics/Jump.hh>
49 
50 
51 
52 static basic::Tracer TR("protocols.fldsgn.potentials.sspot.SSPairPotential", basic::t_info);
53 
54 namespace protocols {
55 namespace fldsgn {
56 namespace potentials {
57 namespace sspot {
58 
59 /// @brief default constructor
60 SSPairPotential::SSPairPotential():
61  strand_dist_cutoff_( 6.5 ),
62  dimer_seqsep_cutoff_( 11 ), // Size or 6 ?
63  lowstrand_( 1 ),
64  phithetascore_( 2, 3, 36, 36 ),
65  dotscore_( 6 ),
66  rsigma_dot_( 12, 18, 2, 2, rsigma_dot_initializer )
67 {
68  load_phi_theta_bins();
69  load_dotscore_bins();
70 }
71 
72 /// @brief destructor
73 SSPairPotential::~SSPairPotential()
74 {}
75 
76 /// @brief return score of phitheta
77 core::Real
78 SSPairPotential::calc_phithetascore( Size const strand_seqsep, Real const phi, Real const theta ) const
79 {
80  Size istrand_seqsep;
81  if ( strand_seqsep >= 2 && strand_seqsep <= 10 ) {
82  istrand_seqsep = 2;
83  } else {
84  if ( strand_seqsep > 10 ) {
85  istrand_seqsep = 3;
86  } else {
87  istrand_seqsep = 1;
88  }
89  }
90  Size iphi = static_cast< Size >( 1 + ( phi + 180.0 )/10 );
91  if ( iphi > 36 ) {
92  iphi = 36;
93  } else if ( iphi < 1 ) {
94  iphi = 1;
95  }
96  Size itheta = static_cast< Size >( 1 + ( theta/5 ) );
97  if ( itheta > 36 ) {
98  itheta = 36;
99  } else if ( itheta < 1 ) {
100  itheta = 1;
101  }
102  return phithetascore_( 2, int( istrand_seqsep ), int( iphi ), int( itheta ) );
103 }
104 
105 /// @brief return dot score
106 core::Real
107 SSPairPotential::calc_dotscore( Real const dpall ) const
108 {
109  int idot;
110  if ( dpall > 0.33 && dpall <= 0.66 ) {
111  idot = 2;
112  } else if ( dpall > 0.66 && dpall <= 1.00 ) {
113  idot = 3;
114  } else if ( dpall > 1.00 && dpall <= 1.33 ) {
115  idot = 4;
116  } else if ( dpall > 1.33 && dpall <= 1.60 ) {
117  idot = 5;
118  } else if ( dpall > 1.60 && dpall <= 1.80 ) {
119  idot = 6;
120  } else if ( dpall > 1.80 && dpall <= 2.00 ) {
121  idot = 5;
122  } else {
123  idot = 1;
124  }
125  return dotscore_( idot );
126 }
127 
128 /// @brief return rsigma score
129 core::Real
130 SSPairPotential::calc_rsigmascore( Real sig, Real dist, Size const sign1, Size const sign2 ) const
131 {
132  if ( sig > 179.0 ) {
133  sig = 179.0;
134  } else if ( sig < 0.0 ) {
135  sig = 0.0;
136  }
137  Size isig = static_cast< Size >( sig / 10 ) + 1;
138  if ( dist > 6.4 ) {
139  dist = 6.4;
140  } else if ( dist < 3.5 ) {
141  dist = 3.5;
142  }
143  Size idist = static_cast< Size >( ( dist - 3.5 ) / 0.25 ) + 1;
144 
145  // FIX THIS !!!!!!!!!!!!!!
146  // The definition of dimer signs (sign1,sign2) appears inverted (1 should be 2, vice versa).
147  Real tempscore_rsigma = rsigma_dot_( int( idist ), int( isig ), 3 - sign1, 3 - sign2 );
148 
149  // Modify sigma potential to no longer give an rsigma bonus to strands in wrong register.
150  if ( sign1 == 1 & sign2 == 1 & sig < 110. & sig > 70. ) tempscore_rsigma = 0.0;
151  if ( sign1 == 1 & sign2 == 2 & (sig < 75. | sig > 95.) ) tempscore_rsigma = 0.0;
152  if ( sign1 == 2 & sign2 == 1 & (sig < 90. | sig > 110.)) tempscore_rsigma = 0.0;
153  if ( sign1 == 2 & sign2 == 2 & sig < 120. & sig > 80. ) tempscore_rsigma = 0.0;
154 
155  return tempscore_rsigma;
156 }
157 
158 /// @brief calculate sum of dot product of the co vectors of strand dimers ss1 and ss2
159 /// @brief with the vector connecting the midpoints of the dimer vectors (vdist)
160 /// @brief also determine return the sign of the dot products for each dimer
161 /// @brief to determine which direction the CO groups point
162 void
163 SSPairPotential::pair_dp(
164  Size const & ss1,
165  Size const & ss2,
166  BB_Pos const & bb_pos,
167  Real & dp,
168  Vector const & mid_vector,
169  Size & sign1,
170  Size & sign2
171 ) const
172 {
173  // length of C=O bond
174  static Real const dist_co_inv = { 1.0f / 1.231015f };
175 
176  // unit vector of mid_vector
177  Vector const u_midvec( mid_vector.normalized_or_zero() );
178 
179  //
180  Real dp1( 0.0 );
181  Real sdp1( 0.0 );
182  for ( Size i=ss1; i<=ss1+1; ++i ) {
183  Vector temp;
184  if ( i == ss1+1 ) {
185  temp = dist_co_inv * ( bb_pos.C(i) - bb_pos.O(i) );
186  } else {
187  temp = dist_co_inv * ( bb_pos.O(i) - bb_pos.C(i) );
188  }
189  Real const tempdot = temp.dot( u_midvec );
190  dp1 += std::abs(tempdot);
191  sdp1 += tempdot;
192  }
193  dp1 *= 0.5;
194 
195  //
196  Real dp2( 0.0 );
197  Real sdp2( 0.0 );
198  for ( Size i=ss2; i<=ss2+1; ++i ) {
199  Vector temp;
200  if ( i == ss2+1 ) {
201  temp = dist_co_inv * ( bb_pos.C(i) - bb_pos.O(i) );
202  } else {
203  temp = dist_co_inv * ( bb_pos.O(i) - bb_pos.C(i) );
204  }
205  Real const tempdot = temp.dot( u_midvec );
206  dp2 += std::abs(tempdot);
207  sdp2 += tempdot;
208  }
209  dp2 *= 0.5;
210 
211  dp = dp1 + dp2;
212 
213  //js These signs tell whether the first c=o bond vector of a dimer points
214  //js at the other dimer. sign1 = 1 means that the first c=o bond of dimer1
215  //js points at dimer2. sign2 = 1 means that dimer2 points at dimer1. When
216  //js sign1 or sign2 equals 2, that dimer points away from the other dimer.
217  sign1 = ( sdp1 > 0.0 ? 2 : 1 );
218  sign2 = ( sdp2 < 0.0 ? 2 : 1 );
219 }
220 
221 
222 
223 /// @brief
224 void
225 SSPairPotential::score(
226  Pose const & pose,
227  SS_Info2 const & ss_info,
228  DimerPairings & dimer_pairs,
229  Real & ss_score ) const
230 {
231  using protocols::fldsgn::potentials::sspot::spherical;
232  using protocols::fldsgn::potentials::sspot::get_foldtree_seqsep;
233  using protocols::fldsgn::topology::StrandOP;
234  using protocols::fldsgn::topology::Strands;
235 
236  ss_score = 0.0;
237  Real rsigma_score = 0.0;
238  dimer_pairs.clear();
239 
240  Real ssdist_12_ = -1.6408;
241 
242  Strands const & strands( ss_info.strands() );
243  BB_Pos const & bb_pos( ss_info.bb_pos() );
244 
245  EnergyGraph const & energy_graph( pose.energies().energy_graph() );
246 
247  for( Size istrand=1; istrand<=strands.size(); istrand++ ){
248 
249  StrandOP const strand( strands[ istrand ] );
250  if( strand->length() < 2 ) continue;
251  for( Size ss1=strand->begin(); ss1<strand->end(); ss1++ ){
252 
253  for( core::graph::Graph::EdgeListConstIter
254  iru = energy_graph.get_node( ss1 )->const_upper_edge_list_begin(),
255  irue = energy_graph.get_node( ss1 )->const_upper_edge_list_end();
256  iru != irue; ++iru ) {
257 
258  Size const ss2( (*iru)->get_second_node_ind() );
259  Size jstrand = ss_info.strand_id( ss2 );
260  if( pose.residue_type( ss2 ).is_upper_terminus() ) continue;
261  if( ss_info.strand_id( ss2+1 ) == 0 || jstrand == 0 || istrand == jstrand ) continue;
262 
263  Size const strand_seqsep = get_foldtree_seqsep( pose, strands[ jstrand ]->begin()-1, strands[ istrand ]->end()+1 ) + 1;
264  Size const dimer_seqsep = get_foldtree_seqsep( pose, ss2, ss1 );
265 
266  Vector const & pt1( bb_pos.N( ss1 ) );
267  Vector const & pt2( bb_pos.C( ss1+1 ) );
268  Vector const & pt3( bb_pos.N( ss2 ) );
269  Vector const & pt4( bb_pos.C( ss2+1 ) );
270 
271  // midpoint coordinates of two dimers
272  Vector cen1 = Real( 0.5 )*( pt1 + pt2 );
273  Vector cen2 = Real( 0.5 )*( pt3 + pt4 );
274 
275  // vector between midpoints
276  Vector mid_vector = cen2 -cen1;
277  Real dist_dimers = mid_vector.length();
278 
279  if( dist_dimers < strand_dist_cutoff_ ) {
280 
281  // calc phi and theta score between dimers
282  Real phi, theta;
283  spherical( pt2, pt4, phi, theta, cen1, cen2, mid_vector );
284  Real phithetascore = calc_phithetascore( strand_seqsep, phi, theta );
285 
286  if ( phithetascore < 0.0 ) {
287 
288  // calc dot product and dist score
289  // car if the sequence distance between pairs is too small, don't add this term to the total
290  // car LOCAL STRANDS DON'T GET SO MUCH OF A SCORE BONUS, add terms to pair only if pair separation > dimer_seqsep_cutoff_
291  Real dotscore( 0.0 );
292  Real distscore( 0.0 );
293  Real dimer_pair_score( 0.0 );
294  Real dpall;
295  Size sign1, sign2;
296  pair_dp( ss1, ss2, bb_pos, dpall, mid_vector, sign1, sign2 );
297  dotscore = calc_dotscore( dpall );
298 
299  // rsigma score
300  Real const u21z = ( pt2 - cen1 ).normalized_or_zero().dot( mid_vector.normalized_or_zero() );
301  Real sig = numeric::conversions::degrees( numeric::arccos( u21z ) ); //std::acos( sin_cos_range( u21z ) );
302  Real tempscore_rsigma = calc_rsigmascore( sig, dist_dimers, sign1, sign2 );
303  if ( tempscore_rsigma > 0.0 ) {
304  //car add in all unfavorable rsigma scores (these pairs may not contribute
305  //car to ss_score if they have a favorable dimer_pair_score)
306  //car note there are no positive scores in structure_db.cc as of 7/03
307  rsigma_score += tempscore_rsigma;
308  } else {
309  //car and favorable ones if phitheta and dot score favorable & dist<6.5
310  //car note that rsigma is not subject to the favorable-dimer-interactions-must
311  //car be-consistent-pairwise-strands rule that is applied to the ss_score below
312  if ( dotscore < 0.0 ) rsigma_score += tempscore_rsigma;
313  }
314 
315  //
316  if ( dimer_seqsep >= dimer_seqsep_cutoff_ ) {
317  // dist score
318  if ( lowstrand_ > 0.5 ) { // what is lowstrand ??????
319  distscore = ssdist_12_; // I don't think this make asense
320  }
321  dimer_pair_score = phithetascore + distscore + dotscore;
322  } else {
323  //// rhiju Allow penalty for locally paired strands
324  //Real penalty_localpair( 0.0 );
325  //Real seqsep = std::abs( ss2 - ss1 );
326  //if ( seqsep <= 11 ) penalty_localpair = localstrandpair_penalty_ * SS_penalty( seqsep );
327  // sum all scores
328  //Real dimer_pair_score = phithetascore + distscore + dotscore + penalty_localpair;
329  }
330 
331  if ( dimer_pair_score < 0.0 ) {
332  dimer_pairs.push_back( new DimerPairing( ss1, ss2, dist_dimers, phi, theta,
333  sig, dpall, sign1, sign2, dimer_pair_score ) );
334  } else {
335  ss_score += dimer_pair_score;
336  }
337 
338  } // if phithetascore < 0.0
339  } // if ( dist_dimers < strand_dist_cutoff_ )
340  } //
341  } // for ( ss1 )
342  } // for( istrand )
343 
344  dimer_pairs.finalize( ss_info );
345  for ( DimerPairings::iterator it= dimer_pairs.begin(), ite= dimer_pairs.end(); it != ite; ++it ) {
346  DimerPairing const & pairing( **it );
347  if ( !pairing.valid() ) continue;
348  ss_score += pairing.score();
349 
350  int const res1 ( pairing.res1() );
351  int const res2 ( pairing.res2() );
352  Size const strand1( ss_info.strand_id( res1 ) );
353  Size const strand2( ss_info.strand_id( res2 ) );
354  int const edge1( strands[ strand1 ]->end()+1 );
355  int const edge2( strands[ strand2 ]->begin()-1 );
356 
357  if ( std::abs( res2 - res1 ) > 11 && std::abs( edge2-edge1 ) > 8 ) {
358  ss_score -= 0.2;
359  }
360  }
361 
362  ss_score *= 0.498 * 0.75;
363  ss_score += rsigma_score * 0.1;
364 
365 } // score
366 
367 
368 /// @brief load phi/theta bins for use in secondary structure scoring
369 void
370 SSPairPotential::load_phi_theta_bins( String const & ss_filename )
371 {
372  using ObjexxFCL::fmt::skip;
373  typedef ObjexxFCL::FArray3D< Real > FArray3D_real;
374  FArray3D_real pts_SS( 36, 36, 3 );
375 
376  FArray1D_int iptsn( 36 );
377  for ( int itheta = 1; itheta <= 36; ++itheta ) {
378  iptsn(itheta) = 100;
379  }
380 
381  // FIXME: need equivalent to open_data_file() function here
382  utility::io::izstream SS_stream;
383  basic::database::open( SS_stream, ss_filename );
384  for ( int isep = 1; isep <= 3; ++isep ) {
385  for ( int itheta = 1; itheta <= 36; ++itheta ) {
386  for ( int iph = 1; iph <= 36; ++iph ) {
387  SS_stream >> pts_SS(itheta,iph,isep) >> skip;
388  }
389  }
390  if ( isep == 1 ) SS_stream.seek_beg();
391  }
392  SS_stream.close();
393  SS_stream.clear();
394 
395  for ( int isep = 1; isep <= 3; ++isep ) {
396  Real tot = 0.0;
397  Real totn = 0.0;
398  for ( int iph = 1; iph <= 36; ++iph ) {
399  for ( int itheta = 1; itheta <= 36; ++itheta ) {
400  pts_SS( itheta, iph, isep ) += iptsn( itheta )*0.000001f; // SMALL COUNTS CORRECTION
401  tot += pts_SS( itheta, iph, isep );
402  totn += iptsn( itheta );
403  }
404  }
405  for ( int iph = 1; iph <= 36; ++iph ) {
406  for ( int itheta = 1; itheta <= 36; ++itheta ) {
407  phithetascore_( 2, isep, iph, itheta ) = -std::log( pts_SS( itheta, iph, isep )/tot) + std::log(iptsn( itheta )/totn );
408  }
409  }
410  }
411 
412 } // load_phi_theta_bins
413 
414 /// @brief
415 void
416 SSPairPotential::load_dotscore_bins()
417 {
418  // triangle-2 random numbers
419  // data idsn/56,167,278,278,167,56/
420  // sort of triangle-4 random numbers
421  FArray1D_int idsn( 6 );
422  idsn( 1 ) = 5596;
423  idsn( 2 ) = 16581;
424  idsn( 3 ) = 27823;
425  idsn( 4 ) = 27823;
426  idsn( 5 ) = 16581;
427  idsn( 6 ) = 5596;
428 
429  FArray1D_int ids( 6 );
430  ids( 1 ) = 1;
431  ids( 2 ) = 48;
432  ids( 3 ) = 368;
433  ids( 4 ) = 2378;
434  ids( 5 ) = 7141;
435  ids( 6 ) = 8904;
436 
437  Real tot = 0.0;
438  Real totn = 0.0;
439  for ( int idot = 1; idot <= 6; ++idot ) {
440  tot += ids(idot);
441  totn += idsn(idot);
442  }
443  for ( int idot = 1; idot <= 6; ++idot ) {
444  if ( ids(idot) != 0 ) {
445  dotscore_(idot) = -std::log(ids(idot)/tot) + std::log(idsn(idot)/totn);
446  } else {
447  dotscore_(idot) = 0.0;
448  }
449  }
450 }
451 
452 /// @brief
453 void
454 SSPairPotential::rsigma_dot_initializer(
455  FArray4D_real & rsigma_dot
456 )
457 {
458  // section 12
459  //js --------------------------
460  //js new rsigma stats that take into account whether the first
461  //js c=o bond vector points towards away from the other dimer
462  rsigma_dot( 1, 1, 1, 2 ) = -1.038100;
463  rsigma_dot( 1, 2, 1, 2 ) = -1.038100;
464  rsigma_dot( 1, 3, 1, 2 ) = -1.038100;
465  rsigma_dot( 1, 4, 1, 2 ) = -1.038100;
466  rsigma_dot( 1, 5, 1, 2 ) = -1.038100;
467  rsigma_dot( 1, 6, 1, 2 ) = -1.038100;
468  rsigma_dot( 1, 7, 1, 2 ) = -1.038100;
469  rsigma_dot( 1, 8, 1, 2 ) = -2.984000;
470  rsigma_dot( 1, 9, 1, 2 ) = -3.746110;
471  rsigma_dot( 1, 10, 1, 2 ) = -3.746110;
472  rsigma_dot( 1, 11, 1, 2 ) = -2.647500;
473  rsigma_dot( 1, 12, 1, 2 ) = -1.038100;
474  rsigma_dot( 1, 13, 1, 2 ) = -1.038100;
475  rsigma_dot( 1, 14, 1, 2 ) = -1.038100;
476  rsigma_dot( 1, 15, 1, 2 ) = -1.038100;
477  rsigma_dot( 1, 16, 1, 2 ) = -1.038100;
478  rsigma_dot( 1, 17, 1, 2 ) = -1.038100;
479  rsigma_dot( 1, 18, 1, 2 ) = -1.038100;
480  rsigma_dot( 2, 1, 1, 2 ) = -0.973500;
481  rsigma_dot( 2, 2, 1, 2 ) = -0.973500;
482  rsigma_dot( 2, 3, 1, 2 ) = -0.973500;
483  rsigma_dot( 2, 4, 1, 2 ) = -0.973500;
484  rsigma_dot( 2, 5, 1, 2 ) = -0.973500;
485  rsigma_dot( 2, 6, 1, 2 ) = -0.973500;
486  rsigma_dot( 2, 7, 1, 2 ) = -2.072100;
487  rsigma_dot( 2, 8, 1, 2 ) = -0.973500;
488  rsigma_dot( 2, 9, 1, 2 ) = -4.943820;
489  rsigma_dot( 2, 10, 1, 2 ) = -5.178220;
490  rsigma_dot( 2, 11, 1, 2 ) = -4.823670;
491  rsigma_dot( 2, 12, 1, 2 ) = -2.919400;
492  rsigma_dot( 2, 13, 1, 2 ) = -2.583000;
493  rsigma_dot( 2, 14, 1, 2 ) = -0.973500;
494  rsigma_dot( 2, 15, 1, 2 ) = -0.973500;
495  rsigma_dot( 2, 16, 1, 2 ) = -0.973500;
496  rsigma_dot( 2, 17, 1, 2 ) = -0.973500;
497  rsigma_dot( 2, 18, 1, 2 ) = -0.973500;
498  rsigma_dot( 3, 1, 1, 2 ) = -0.912900;
499  rsigma_dot( 3, 2, 1, 2 ) = -0.912900;
500  rsigma_dot( 3, 3, 1, 2 ) = -0.912900;
501  rsigma_dot( 3, 4, 1, 2 ) = -0.912900;
502  rsigma_dot( 3, 5, 1, 2 ) = -0.912900;
503  rsigma_dot( 3, 6, 1, 2 ) = -0.912900;
504  rsigma_dot( 3, 7, 1, 2 ) = -2.011500;
505  rsigma_dot( 3, 8, 1, 2 ) = -4.048400;
506  rsigma_dot( 3, 9, 1, 2 ) = -5.981810;
507  rsigma_dot( 3, 10, 1, 2 ) = -7.006470;
508  rsigma_dot( 3, 11, 1, 2 ) = -6.696730;
509  rsigma_dot( 3, 12, 1, 2 ) = -4.131780;
510  rsigma_dot( 3, 13, 1, 2 ) = -0.912900;
511  rsigma_dot( 3, 14, 1, 2 ) = -0.912900;
512  rsigma_dot( 3, 15, 1, 2 ) = -0.912900;
513  rsigma_dot( 3, 16, 1, 2 ) = -0.912900;
514  rsigma_dot( 3, 17, 1, 2 ) = -0.912900;
515  rsigma_dot( 3, 18, 1, 2 ) = -0.912900;
516  rsigma_dot( 4, 1, 1, 2 ) = -0.855700;
517  rsigma_dot( 4, 2, 1, 2 ) = -0.855700;
518  rsigma_dot( 4, 3, 1, 2 ) = -0.855700;
519  rsigma_dot( 4, 4, 1, 2 ) = -0.855700;
520  rsigma_dot( 4, 5, 1, 2 ) = -0.855700;
521  rsigma_dot( 4, 6, 1, 2 ) = -2.465200;
522  rsigma_dot( 4, 7, 1, 2 ) = -3.420700;
523  rsigma_dot( 4, 8, 1, 2 ) = -3.900270;
524  rsigma_dot( 4, 9, 1, 2 ) = -6.315330;
525  rsigma_dot( 4, 10, 1, 2 ) = -8.116270;
526  rsigma_dot( 4, 11, 1, 2 ) = -8.329380;
527  rsigma_dot( 4, 12, 1, 2 ) = -5.298390;
528  rsigma_dot( 4, 13, 1, 2 ) = -1.954400;
529  rsigma_dot( 4, 14, 1, 2 ) = -0.855700;
530  rsigma_dot( 4, 15, 1, 2 ) = -0.855700;
531  rsigma_dot( 4, 16, 1, 2 ) = -0.855700;
532  rsigma_dot( 4, 17, 1, 2 ) = -0.855700;
533  rsigma_dot( 4, 18, 1, 2 ) = -0.855700;
534  rsigma_dot( 5, 1, 1, 2 ) = -0.801700;
535  rsigma_dot( 5, 2, 1, 2 ) = -0.801700;
536  rsigma_dot( 5, 3, 1, 2 ) = -0.801700;
537  rsigma_dot( 5, 4, 1, 2 ) = -0.801700;
538  rsigma_dot( 5, 5, 1, 2 ) = -0.801700;
539  rsigma_dot( 5, 6, 1, 2 ) = -1.900300;
540  rsigma_dot( 5, 7, 1, 2 ) = -3.634900;
541  rsigma_dot( 5, 8, 1, 2 ) = -5.119160;
542  rsigma_dot( 5, 9, 1, 2 ) = -6.381410;
543  rsigma_dot( 5, 10, 1, 2 ) = -9.110860;
544  rsigma_dot( 5, 11, 1, 2 ) = -9.615860;
545  rsigma_dot( 5, 12, 1, 2 ) = -6.566870;
546  rsigma_dot( 5, 13, 1, 2 ) = -2.411100;
547  rsigma_dot( 5, 14, 1, 2 ) = -1.900300;
548  rsigma_dot( 5, 15, 1, 2 ) = -0.801700;
549  rsigma_dot( 5, 16, 1, 2 ) = -0.801700;
550  rsigma_dot( 5, 17, 1, 2 ) = -0.801700;
551  rsigma_dot( 5, 18, 1, 2 ) = -0.801700;
552  rsigma_dot( 6, 1, 1, 2 ) = -0.750400;
553  rsigma_dot( 6, 2, 1, 2 ) = -0.750400;
554  rsigma_dot( 6, 3, 1, 2 ) = -0.750400;
555  rsigma_dot( 6, 4, 1, 2 ) = -0.750400;
556  rsigma_dot( 6, 5, 1, 2 ) = -0.750400;
557  rsigma_dot( 6, 6, 1, 2 ) = -2.359800;
558  rsigma_dot( 6, 7, 1, 2 ) = -4.511580;
559  rsigma_dot( 6, 8, 1, 2 ) = -5.325090;
560  rsigma_dot( 6, 9, 1, 2 ) = -6.768980;
561  rsigma_dot( 6, 10, 1, 2 ) = -8.613260;
562  rsigma_dot( 6, 11, 1, 2 ) = -9.405770;
563  rsigma_dot( 6, 12, 1, 2 ) = -7.032650;
564  rsigma_dot( 6, 13, 1, 2 ) = -3.885880;
565  rsigma_dot( 6, 14, 1, 2 ) = -3.315300;
566  rsigma_dot( 6, 15, 1, 2 ) = -0.750400;
567  rsigma_dot( 6, 16, 1, 2 ) = -0.750400;
568  rsigma_dot( 6, 17, 1, 2 ) = -0.750400;
569  rsigma_dot( 6, 18, 1, 2 ) = -0.750400;
570  rsigma_dot( 7, 1, 1, 2 ) = -0.701600;
571  rsigma_dot( 7, 2, 1, 2 ) = -0.701600;
572  rsigma_dot( 7, 3, 1, 2 ) = -0.701600;
573  rsigma_dot( 7, 4, 1, 2 ) = -0.701600;
574  rsigma_dot( 7, 5, 1, 2 ) = -0.701600;
575  rsigma_dot( 7, 6, 1, 2 ) = -2.311000;
576  rsigma_dot( 7, 7, 1, 2 ) = -4.365150;
577  rsigma_dot( 7, 8, 1, 2 ) = -5.446520;
578  rsigma_dot( 7, 9, 1, 2 ) = -6.795160;
579  rsigma_dot( 7, 10, 1, 2 ) = -7.145720;
580  rsigma_dot( 7, 11, 1, 2 ) = -7.527050;
581  rsigma_dot( 7, 12, 1, 2 ) = -6.885740;
582  rsigma_dot( 7, 13, 1, 2 ) = -4.508250;
583  rsigma_dot( 7, 14, 1, 2 ) = -1.800200;
584  rsigma_dot( 7, 15, 1, 2 ) = -2.647500;
585  rsigma_dot( 7, 16, 1, 2 ) = -0.701600;
586  rsigma_dot( 7, 17, 1, 2 ) = -0.701600;
587  rsigma_dot( 7, 18, 1, 2 ) = -0.701600;
588  rsigma_dot( 8, 1, 1, 2 ) = -0.655100;
589  rsigma_dot( 8, 2, 1, 2 ) = -0.655100;
590  rsigma_dot( 8, 3, 1, 2 ) = -0.655100;
591  rsigma_dot( 8, 4, 1, 2 ) = -0.655100;
592  rsigma_dot( 8, 5, 1, 2 ) = -0.655100;
593  rsigma_dot( 8, 6, 1, 2 ) = -3.699600;
594  rsigma_dot( 8, 7, 1, 2 ) = -4.089060;
595  rsigma_dot( 8, 8, 1, 2 ) = -5.417250;
596  rsigma_dot( 8, 9, 1, 2 ) = -6.293430;
597  rsigma_dot( 8, 10, 1, 2 ) = -6.663890;
598  rsigma_dot( 8, 11, 1, 2 ) = -6.788470;
599  rsigma_dot( 8, 12, 1, 2 ) = -6.368800;
600  rsigma_dot( 8, 13, 1, 2 ) = -4.732610;
601  rsigma_dot( 8, 14, 1, 2 ) = -1.753700;
602  rsigma_dot( 8, 15, 1, 2 ) = -0.655100;
603  rsigma_dot( 8, 16, 1, 2 ) = -0.655100;
604  rsigma_dot( 8, 17, 1, 2 ) = -0.655100;
605  rsigma_dot( 8, 18, 1, 2 ) = -0.655100;
606  rsigma_dot( 9, 1, 1, 2 ) = -0.610600;
607  rsigma_dot( 9, 2, 1, 2 ) = -0.610600;
608  rsigma_dot( 9, 3, 1, 2 ) = -0.610600;
609  rsigma_dot( 9, 4, 1, 2 ) = -0.610600;
610  rsigma_dot( 9, 5, 1, 2 ) = -1.709200;
611  rsigma_dot( 9, 6, 1, 2 ) = -3.906460;
612  rsigma_dot( 9, 7, 1, 2 ) = -3.906460;
613  rsigma_dot( 9, 8, 1, 2 ) = -5.355550;
614  rsigma_dot( 9, 9, 1, 2 ) = -6.070210;
615  rsigma_dot( 9, 10, 1, 2 ) = -5.971910;
616  rsigma_dot( 9, 11, 1, 2 ) = -6.070210;
617  rsigma_dot( 9, 12, 1, 2 ) = -5.852370;
618  rsigma_dot( 9, 13, 1, 2 ) = -4.901080;
619  rsigma_dot( 9, 14, 1, 2 ) = -2.807800;
620  rsigma_dot( 9, 15, 1, 2 ) = -2.220100;
621  rsigma_dot( 9, 16, 1, 2 ) = -0.610600;
622  rsigma_dot( 9, 17, 1, 2 ) = -1.709200;
623  rsigma_dot( 9, 18, 1, 2 ) = -0.610600;
624  rsigma_dot( 10, 1, 1, 2 ) = -0.568100;
625  rsigma_dot( 10, 2, 1, 2 ) = -0.568100;
626  rsigma_dot( 10, 3, 1, 2 ) = -0.568100;
627  rsigma_dot( 10, 4, 1, 2 ) = -2.177500;
628  rsigma_dot( 10, 5, 1, 2 ) = -2.765300;
629  rsigma_dot( 10, 6, 1, 2 ) = -4.002050;
630  rsigma_dot( 10, 7, 1, 2 ) = -4.802170;
631  rsigma_dot( 10, 8, 1, 2 ) = -5.598500;
632  rsigma_dot( 10, 9, 1, 2 ) = -5.809810;
633  rsigma_dot( 10, 10, 1, 2 ) = -5.809810;
634  rsigma_dot( 10, 11, 1, 2 ) = -5.732850;
635  rsigma_dot( 10, 12, 1, 2 ) = -5.572010;
636  rsigma_dot( 10, 13, 1, 2 ) = -4.858520;
637  rsigma_dot( 10, 14, 1, 2 ) = -3.935360;
638  rsigma_dot( 10, 15, 1, 2 ) = -1.666700;
639  rsigma_dot( 10, 16, 1, 2 ) = -1.666700;
640  rsigma_dot( 10, 17, 1, 2 ) = -0.568100;
641  rsigma_dot( 10, 18, 1, 2 ) = -1.666700;
642  rsigma_dot( 11, 1, 1, 2 ) = -0.527200;
643  rsigma_dot( 11, 2, 1, 2 ) = -0.527200;
644  rsigma_dot( 11, 3, 1, 2 ) = -0.527200;
645  rsigma_dot( 11, 4, 1, 2 ) = -1.625900;
646  rsigma_dot( 11, 5, 1, 2 ) = -3.746110;
647  rsigma_dot( 11, 6, 1, 2 ) = -4.190800;
648  rsigma_dot( 11, 7, 1, 2 ) = -4.761350;
649  rsigma_dot( 11, 8, 1, 2 ) = -5.897880;
650  rsigma_dot( 11, 9, 1, 2 ) = -5.850250;
651  rsigma_dot( 11, 10, 1, 2 ) = -5.789930;
652  rsigma_dot( 11, 11, 1, 2 ) = -5.371430;
653  rsigma_dot( 11, 12, 1, 2 ) = -5.608640;
654  rsigma_dot( 11, 13, 1, 2 ) = -5.306360;
655  rsigma_dot( 11, 14, 1, 2 ) = -4.288440;
656  rsigma_dot( 11, 15, 1, 2 ) = -3.092200;
657  rsigma_dot( 11, 16, 1, 2 ) = -0.527200;
658  rsigma_dot( 11, 17, 1, 2 ) = -0.527200;
659  rsigma_dot( 11, 18, 1, 2 ) = -0.527200;
660  rsigma_dot( 12, 1, 1, 2 ) = -0.488000;
661  rsigma_dot( 12, 2, 1, 2 ) = -0.488000;
662  rsigma_dot( 12, 3, 1, 2 ) = -0.488000;
663  rsigma_dot( 12, 4, 1, 2 ) = -3.623500;
664  rsigma_dot( 12, 5, 1, 2 ) = -4.722120;
665  rsigma_dot( 12, 6, 1, 2 ) = -4.692710;
666  rsigma_dot( 12, 7, 1, 2 ) = -5.197550;
667  rsigma_dot( 12, 8, 1, 2 ) = -5.544260;
668  rsigma_dot( 12, 9, 1, 2 ) = -5.740290;
669  rsigma_dot( 12, 10, 1, 2 ) = -5.478450;
670  rsigma_dot( 12, 11, 1, 2 ) = -5.347830;
671  rsigma_dot( 12, 12, 1, 2 ) = -5.363220;
672  rsigma_dot( 12, 13, 1, 2 ) = -5.103140;
673  rsigma_dot( 12, 14, 1, 2 ) = -4.722120;
674  rsigma_dot( 12, 15, 1, 2 ) = -3.984530;
675  rsigma_dot( 12, 16, 1, 2 ) = -3.196100;
676  rsigma_dot( 12, 17, 1, 2 ) = -0.488000;
677  rsigma_dot( 12, 18, 1, 2 ) = -0.488000;
678 
679  // section 11
680  rsigma_dot( 1, 1, 1, 1 ) = -0.552300;
681  rsigma_dot( 1, 2, 1, 1 ) = -0.552300;
682  rsigma_dot( 1, 3, 1, 1 ) = -0.552300;
683  rsigma_dot( 1, 4, 1, 1 ) = -0.552300;
684  rsigma_dot( 1, 5, 1, 1 ) = -0.552300;
685  rsigma_dot( 1, 6, 1, 1 ) = -0.552300;
686  rsigma_dot( 1, 7, 1, 1 ) = -0.552300;
687  rsigma_dot( 1, 8, 1, 1 ) = -0.552300;
688  rsigma_dot( 1, 9, 1, 1 ) = -0.552300;
689  rsigma_dot( 1, 10, 1, 1 ) = -1.651000;
690  rsigma_dot( 1, 11, 1, 1 ) = -0.552300;
691  rsigma_dot( 1, 12, 1, 1 ) = -0.552300;
692  rsigma_dot( 1, 13, 1, 1 ) = -0.552300;
693  rsigma_dot( 1, 14, 1, 1 ) = -0.552300;
694  rsigma_dot( 1, 15, 1, 1 ) = -0.552300;
695  rsigma_dot( 1, 16, 1, 1 ) = -0.552300;
696  rsigma_dot( 1, 17, 1, 1 ) = -0.552300;
697  rsigma_dot( 1, 18, 1, 1 ) = -0.552300;
698  rsigma_dot( 2, 1, 1, 1 ) = -0.487800;
699  rsigma_dot( 2, 2, 1, 1 ) = -0.487800;
700  rsigma_dot( 2, 3, 1, 1 ) = -0.487800;
701  rsigma_dot( 2, 4, 1, 1 ) = -0.487800;
702  rsigma_dot( 2, 5, 1, 1 ) = -0.487800;
703  rsigma_dot( 2, 6, 1, 1 ) = -0.487800;
704  rsigma_dot( 2, 7, 1, 1 ) = -0.487800;
705  rsigma_dot( 2, 8, 1, 1 ) = -0.487800;
706  rsigma_dot( 2, 9, 1, 1 ) = -0.487800;
707  rsigma_dot( 2, 10, 1, 1 ) = -1.586400;
708  rsigma_dot( 2, 11, 1, 1 ) = -2.097200;
709  rsigma_dot( 2, 12, 1, 1 ) = -1.586400;
710  rsigma_dot( 2, 13, 1, 1 ) = -0.487800;
711  rsigma_dot( 2, 14, 1, 1 ) = -0.487800;
712  rsigma_dot( 2, 15, 1, 1 ) = -0.487800;
713  rsigma_dot( 2, 16, 1, 1 ) = -0.487800;
714  rsigma_dot( 2, 17, 1, 1 ) = -0.487800;
715  rsigma_dot( 2, 18, 1, 1 ) = -0.487800;
716  rsigma_dot( 3, 1, 1, 1 ) = -0.427200;
717  rsigma_dot( 3, 2, 1, 1 ) = -0.427200;
718  rsigma_dot( 3, 3, 1, 1 ) = -0.427200;
719  rsigma_dot( 3, 4, 1, 1 ) = -0.427200;
720  rsigma_dot( 3, 5, 1, 1 ) = -0.427200;
721  rsigma_dot( 3, 6, 1, 1 ) = -1.525800;
722  rsigma_dot( 3, 7, 1, 1 ) = -2.036600;
723  rsigma_dot( 3, 8, 1, 1 ) = -2.036600;
724  rsigma_dot( 3, 9, 1, 1 ) = -0.427200;
725  rsigma_dot( 3, 10, 1, 1 ) = -2.373100;
726  rsigma_dot( 3, 11, 1, 1 ) = -1.525800;
727  rsigma_dot( 3, 12, 1, 1 ) = -2.992100;
728  rsigma_dot( 3, 13, 1, 1 ) = -2.373100;
729  rsigma_dot( 3, 14, 1, 1 ) = -0.427200;
730  rsigma_dot( 3, 15, 1, 1 ) = -0.427200;
731  rsigma_dot( 3, 16, 1, 1 ) = -0.427200;
732  rsigma_dot( 3, 17, 1, 1 ) = -0.427200;
733  rsigma_dot( 3, 18, 1, 1 ) = -0.427200;
734  rsigma_dot( 4, 1, 1, 1 ) = -0.370000;
735  rsigma_dot( 4, 2, 1, 1 ) = -0.370000;
736  rsigma_dot( 4, 3, 1, 1 ) = -0.370000;
737  rsigma_dot( 4, 4, 1, 1 ) = -0.370000;
738  rsigma_dot( 4, 5, 1, 1 ) = -0.370000;
739  rsigma_dot( 4, 6, 1, 1 ) = -0.370000;
740  rsigma_dot( 4, 7, 1, 1 ) = -2.315900;
741  rsigma_dot( 4, 8, 1, 1 ) = -2.567200;
742  rsigma_dot( 4, 9, 1, 1 ) = -2.767900;
743  rsigma_dot( 4, 10, 1, 1 ) = -3.588900;
744  rsigma_dot( 4, 11, 1, 1 ) = -3.414500;
745  rsigma_dot( 4, 12, 1, 1 ) = -4.033580;
746  rsigma_dot( 4, 13, 1, 1 ) = -3.804010;
747  rsigma_dot( 4, 14, 1, 1 ) = -0.370000;
748  rsigma_dot( 4, 15, 1, 1 ) = -0.370000;
749  rsigma_dot( 4, 16, 1, 1 ) = -0.370000;
750  rsigma_dot( 4, 17, 1, 1 ) = -0.370000;
751  rsigma_dot( 4, 18, 1, 1 ) = -0.370000;
752  rsigma_dot( 5, 1, 1, 1 ) = -0.316000;
753  rsigma_dot( 5, 2, 1, 1 ) = -0.316000;
754  rsigma_dot( 5, 3, 1, 1 ) = -0.316000;
755  rsigma_dot( 5, 4, 1, 1 ) = -0.316000;
756  rsigma_dot( 5, 5, 1, 1 ) = -0.316000;
757  rsigma_dot( 5, 6, 1, 1 ) = -1.925400;
758  rsigma_dot( 5, 7, 1, 1 ) = -3.683200;
759  rsigma_dot( 5, 8, 1, 1 ) = -4.122610;
760  rsigma_dot( 5, 9, 1, 1 ) = -3.812460;
761  rsigma_dot( 5, 10, 1, 1 ) = -3.683200;
762  rsigma_dot( 5, 11, 1, 1 ) = -3.360500;
763  rsigma_dot( 5, 12, 1, 1 ) = -4.969910;
764  rsigma_dot( 5, 13, 1, 1 ) = -4.869830;
765  rsigma_dot( 5, 14, 1, 1 ) = -3.149200;
766  rsigma_dot( 5, 15, 1, 1 ) = -0.316000;
767  rsigma_dot( 5, 16, 1, 1 ) = -0.316000;
768  rsigma_dot( 5, 17, 1, 1 ) = -0.316000;
769  rsigma_dot( 5, 18, 1, 1 ) = -0.316000;
770  rsigma_dot( 6, 1, 1, 1 ) = -0.264700;
771  rsigma_dot( 6, 2, 1, 1 ) = -0.264700;
772  rsigma_dot( 6, 3, 1, 1 ) = -0.264700;
773  rsigma_dot( 6, 4, 1, 1 ) = -0.264700;
774  rsigma_dot( 6, 5, 1, 1 ) = -0.264700;
775  rsigma_dot( 6, 6, 1, 1 ) = -2.829600;
776  rsigma_dot( 6, 7, 1, 1 ) = -5.680760;
777  rsigma_dot( 6, 8, 1, 1 ) = -5.076840;
778  rsigma_dot( 6, 9, 1, 1 ) = -4.271990;
779  rsigma_dot( 6, 10, 1, 1 ) = -4.234950;
780  rsigma_dot( 6, 11, 1, 1 ) = -3.761170;
781  rsigma_dot( 6, 12, 1, 1 ) = -5.567960;
782  rsigma_dot( 6, 13, 1, 1 ) = -6.108200;
783  rsigma_dot( 6, 14, 1, 1 ) = -4.956010;
784  rsigma_dot( 6, 15, 1, 1 ) = -1.874100;
785  rsigma_dot( 6, 16, 1, 1 ) = -0.264700;
786  rsigma_dot( 6, 17, 1, 1 ) = -0.264700;
787  rsigma_dot( 6, 18, 1, 1 ) = -0.264700;
788  rsigma_dot( 7, 1, 1, 1 ) = -0.215900;
789  rsigma_dot( 7, 2, 1, 1 ) = -0.215900;
790  rsigma_dot( 7, 3, 1, 1 ) = -0.215900;
791  rsigma_dot( 7, 4, 1, 1 ) = -0.215900;
792  rsigma_dot( 7, 5, 1, 1 ) = -0.215900;
793  rsigma_dot( 7, 6, 1, 1 ) = -5.011660;
794  rsigma_dot( 7, 7, 1, 1 ) = -7.313420;
795  rsigma_dot( 7, 8, 1, 1 ) = -6.580620;
796  rsigma_dot( 7, 9, 1, 1 ) = -4.726730;
797  rsigma_dot( 7, 10, 1, 1 ) = -4.748470;
798  rsigma_dot( 7, 11, 1, 1 ) = -2.923900;
799  rsigma_dot( 7, 12, 1, 1 ) = -5.700670;
800  rsigma_dot( 7, 13, 1, 1 ) = -6.799280;
801  rsigma_dot( 7, 14, 1, 1 ) = -6.059410;
802  rsigma_dot( 7, 15, 1, 1 ) = -2.161800;
803  rsigma_dot( 7, 16, 1, 1 ) = -0.215900;
804  rsigma_dot( 7, 17, 1, 1 ) = -0.215900;
805  rsigma_dot( 7, 18, 1, 1 ) = -0.215900;
806  rsigma_dot( 8, 1, 1, 1 ) = -0.169300;
807  rsigma_dot( 8, 2, 1, 1 ) = -0.169300;
808  rsigma_dot( 8, 3, 1, 1 ) = -0.169300;
809  rsigma_dot( 8, 4, 1, 1 ) = -0.169300;
810  rsigma_dot( 8, 5, 1, 1 ) = -0.169300;
811  rsigma_dot( 8, 6, 1, 1 ) = -6.132930;
812  rsigma_dot( 8, 7, 1, 1 ) = -8.735140;
813  rsigma_dot( 8, 8, 1, 1 ) = -7.789560;
814  rsigma_dot( 8, 9, 1, 1 ) = -5.199790;
815  rsigma_dot( 8, 10, 1, 1 ) = -4.981530;
816  rsigma_dot( 8, 11, 1, 1 ) = -3.882920;
817  rsigma_dot( 8, 12, 1, 1 ) = -5.059700;
818  rsigma_dot( 8, 13, 1, 1 ) = -7.329420;
819  rsigma_dot( 8, 14, 1, 1 ) = -7.217740;
820  rsigma_dot( 8, 15, 1, 1 ) = -4.723230;
821  rsigma_dot( 8, 16, 1, 1 ) = -0.169300;
822  rsigma_dot( 8, 17, 1, 1 ) = -0.169300;
823  rsigma_dot( 8, 18, 1, 1 ) = -0.169300;
824  rsigma_dot( 9, 1, 1, 1 ) = -0.124900;
825  rsigma_dot( 9, 2, 1, 1 ) = -0.124900;
826  rsigma_dot( 9, 3, 1, 1 ) = -0.124900;
827  rsigma_dot( 9, 4, 1, 1 ) = -1.223500;
828  rsigma_dot( 9, 5, 1, 1 ) = -3.069300;
829  rsigma_dot( 9, 6, 1, 1 ) = -6.756900;
830  rsigma_dot( 9, 7, 1, 1 ) = -8.997660;
831  rsigma_dot( 9, 8, 1, 1 ) = -7.292710;
832  rsigma_dot( 9, 9, 1, 1 ) = -5.704630;
833  rsigma_dot( 9, 10, 1, 1 ) = -4.442390;
834  rsigma_dot( 9, 11, 1, 1 ) = -4.202430;
835  rsigma_dot( 9, 12, 1, 1 ) = -4.567550;
836  rsigma_dot( 9, 13, 1, 1 ) = -7.550850;
837  rsigma_dot( 9, 14, 1, 1 ) = -8.291970;
838  rsigma_dot( 9, 15, 1, 1 ) = -5.617960;
839  rsigma_dot( 9, 16, 1, 1 ) = -1.223500;
840  rsigma_dot( 9, 17, 1, 1 ) = -1.223500;
841  rsigma_dot( 9, 18, 1, 1 ) = -0.124900;
842  rsigma_dot( 10, 1, 1, 1 ) = -0.082300;
843  rsigma_dot( 10, 2, 1, 1 ) = -0.082300;
844  rsigma_dot( 10, 3, 1, 1 ) = -0.082300;
845  rsigma_dot( 10, 4, 1, 1 ) = -1.180900;
846  rsigma_dot( 10, 5, 1, 1 ) = -3.932490;
847  rsigma_dot( 10, 6, 1, 1 ) = -6.858840;
848  rsigma_dot( 10, 7, 1, 1 ) = -8.186740;
849  rsigma_dot( 10, 8, 1, 1 ) = -6.228670;
850  rsigma_dot( 10, 9, 1, 1 ) = -5.720690;
851  rsigma_dot( 10, 10, 1, 1 ) = -4.548250;
852  rsigma_dot( 10, 11, 1, 1 ) = -4.451790;
853  rsigma_dot( 10, 12, 1, 1 ) = -4.548250;
854  rsigma_dot( 10, 13, 1, 1 ) = -7.242410;
855  rsigma_dot( 10, 14, 1, 1 ) = -8.619920;
856  rsigma_dot( 10, 15, 1, 1 ) = -6.349540;
857  rsigma_dot( 10, 16, 1, 1 ) = -3.026800;
858  rsigma_dot( 10, 17, 1, 1 ) = -1.180900;
859  rsigma_dot( 10, 18, 1, 1 ) = -1.180900;
860  rsigma_dot( 11, 1, 1, 1 ) = -0.041500;
861  rsigma_dot( 11, 2, 1, 1 ) = -0.041500;
862  rsigma_dot( 11, 3, 1, 1 ) = -0.041500;
863  rsigma_dot( 11, 4, 1, 1 ) = -1.987400;
864  rsigma_dot( 11, 5, 1, 1 ) = -4.275620;
865  rsigma_dot( 11, 6, 1, 1 ) = -6.582550;
866  rsigma_dot( 11, 7, 1, 1 ) = -6.915710;
867  rsigma_dot( 11, 8, 1, 1 ) = -6.166200;
868  rsigma_dot( 11, 9, 1, 1 ) = -5.483930;
869  rsigma_dot( 11, 10, 1, 1 ) = -4.595390;
870  rsigma_dot( 11, 11, 1, 1 ) = -4.616230;
871  rsigma_dot( 11, 12, 1, 1 ) = -4.931860;
872  rsigma_dot( 11, 13, 1, 1 ) = -6.246070;
873  rsigma_dot( 11, 14, 1, 1 ) = -8.296560;
874  rsigma_dot( 11, 15, 1, 1 ) = -6.734840;
875  rsigma_dot( 11, 16, 1, 1 ) = -3.337400;
876  rsigma_dot( 11, 17, 1, 1 ) = -1.140100;
877  rsigma_dot( 11, 18, 1, 1 ) = -0.041500;
878  rsigma_dot( 12, 1, 1, 1 ) = -0.002300;
879  rsigma_dot( 12, 2, 1, 1 ) = -0.002300;
880  rsigma_dot( 12, 3, 1, 1 ) = -0.002300;
881  rsigma_dot( 12, 4, 1, 1 ) = -2.199500;
882  rsigma_dot( 12, 5, 1, 1 ) = -4.729680;
883  rsigma_dot( 12, 6, 1, 1 ) = -6.131350;
884  rsigma_dot( 12, 7, 1, 1 ) = -5.729140;
885  rsigma_dot( 12, 8, 1, 1 ) = -5.604410;
886  rsigma_dot( 12, 9, 1, 1 ) = -5.211780;
887  rsigma_dot( 12, 10, 1, 1 ) = -4.892640;
888  rsigma_dot( 12, 11, 1, 1 ) = -4.992730;
889  rsigma_dot( 12, 12, 1, 1 ) = -5.275290;
890  rsigma_dot( 12, 13, 1, 1 ) = -5.945090;
891  rsigma_dot( 12, 14, 1, 1 ) = -7.716970;
892  rsigma_dot( 12, 15, 1, 1 ) = -6.693140;
893  rsigma_dot( 12, 16, 1, 1 ) = -3.972590;
894  rsigma_dot( 12, 17, 1, 1 ) = -1.948200;
895  rsigma_dot( 12, 18, 1, 1 ) = -0.002300;
896 
897  // section 22
898  rsigma_dot( 1, 1, 2, 2 ) = -0.550000;
899  rsigma_dot( 1, 2, 2, 2 ) = -0.550000;
900  rsigma_dot( 1, 3, 2, 2 ) = -0.550000;
901  rsigma_dot( 1, 4, 2, 2 ) = -0.550000;
902  rsigma_dot( 1, 5, 2, 2 ) = -0.550000;
903  rsigma_dot( 1, 6, 2, 2 ) = -0.550000;
904  rsigma_dot( 1, 7, 2, 2 ) = -0.550000;
905  rsigma_dot( 1, 8, 2, 2 ) = -2.159400;
906  rsigma_dot( 1, 9, 2, 2 ) = -0.550000;
907  rsigma_dot( 1, 10, 2, 2 ) = -2.159400;
908  rsigma_dot( 1, 11, 2, 2 ) = -0.550000;
909  rsigma_dot( 1, 12, 2, 2 ) = -0.550000;
910  rsigma_dot( 1, 13, 2, 2 ) = -0.550000;
911  rsigma_dot( 1, 14, 2, 2 ) = -0.550000;
912  rsigma_dot( 1, 15, 2, 2 ) = -0.550000;
913  rsigma_dot( 1, 16, 2, 2 ) = -0.550000;
914  rsigma_dot( 1, 17, 2, 2 ) = -0.550000;
915  rsigma_dot( 1, 18, 2, 2 ) = -0.550000;
916  rsigma_dot( 2, 1, 2, 2 ) = -0.485500;
917  rsigma_dot( 2, 2, 2, 2 ) = -0.485500;
918  rsigma_dot( 2, 3, 2, 2 ) = -0.485500;
919  rsigma_dot( 2, 4, 2, 2 ) = -0.485500;
920  rsigma_dot( 2, 5, 2, 2 ) = -0.485500;
921  rsigma_dot( 2, 6, 2, 2 ) = -1.584100;
922  rsigma_dot( 2, 7, 2, 2 ) = -3.050400;
923  rsigma_dot( 2, 8, 2, 2 ) = -2.094900;
924  rsigma_dot( 2, 9, 2, 2 ) = -2.431400;
925  rsigma_dot( 2, 10, 2, 2 ) = -1.584100;
926  rsigma_dot( 2, 11, 2, 2 ) = -0.485500;
927  rsigma_dot( 2, 12, 2, 2 ) = -0.485500;
928  rsigma_dot( 2, 13, 2, 2 ) = -0.485500;
929  rsigma_dot( 2, 14, 2, 2 ) = -0.485500;
930  rsigma_dot( 2, 15, 2, 2 ) = -0.485500;
931  rsigma_dot( 2, 16, 2, 2 ) = -0.485500;
932  rsigma_dot( 2, 17, 2, 2 ) = -0.485500;
933  rsigma_dot( 2, 18, 2, 2 ) = -0.485500;
934  rsigma_dot( 3, 1, 2, 2 ) = -0.424800;
935  rsigma_dot( 3, 2, 2, 2 ) = -0.424800;
936  rsigma_dot( 3, 3, 2, 2 ) = -0.424800;
937  rsigma_dot( 3, 4, 2, 2 ) = -0.424800;
938  rsigma_dot( 3, 5, 2, 2 ) = -0.424800;
939  rsigma_dot( 3, 6, 2, 2 ) = -3.258000;
940  rsigma_dot( 3, 7, 2, 2 ) = -4.231500;
941  rsigma_dot( 3, 8, 2, 2 ) = -3.980180;
942  rsigma_dot( 3, 9, 2, 2 ) = -2.370700;
943  rsigma_dot( 3, 10, 2, 2 ) = -1.523400;
944  rsigma_dot( 3, 11, 2, 2 ) = -2.822700;
945  rsigma_dot( 3, 12, 2, 2 ) = -0.424800;
946  rsigma_dot( 3, 13, 2, 2 ) = -0.424800;
947  rsigma_dot( 3, 14, 2, 2 ) = -0.424800;
948  rsigma_dot( 3, 15, 2, 2 ) = -0.424800;
949  rsigma_dot( 3, 16, 2, 2 ) = -0.424800;
950  rsigma_dot( 3, 17, 2, 2 ) = -0.424800;
951  rsigma_dot( 3, 18, 2, 2 ) = -0.424800;
952  rsigma_dot( 4, 1, 2, 2 ) = -0.367700;
953  rsigma_dot( 4, 2, 2, 2 ) = -0.367700;
954  rsigma_dot( 4, 3, 2, 2 ) = -0.367700;
955  rsigma_dot( 4, 4, 2, 2 ) = -0.367700;
956  rsigma_dot( 4, 5, 2, 2 ) = -3.312100;
957  rsigma_dot( 4, 6, 2, 2 ) = -3.412200;
958  rsigma_dot( 4, 7, 2, 2 ) = -5.509340;
959  rsigma_dot( 4, 8, 2, 2 ) = -4.128880;
960  rsigma_dot( 4, 9, 2, 2 ) = -3.075700;
961  rsigma_dot( 4, 10, 2, 2 ) = -2.765600;
962  rsigma_dot( 4, 11, 2, 2 ) = -2.765600;
963  rsigma_dot( 4, 12, 2, 2 ) = -2.765600;
964  rsigma_dot( 4, 13, 2, 2 ) = -0.367700;
965  rsigma_dot( 4, 14, 2, 2 ) = -0.367700;
966  rsigma_dot( 4, 15, 2, 2 ) = -0.367700;
967  rsigma_dot( 4, 16, 2, 2 ) = -0.367700;
968  rsigma_dot( 4, 17, 2, 2 ) = -0.367700;
969  rsigma_dot( 4, 18, 2, 2 ) = -0.367700;
970  rsigma_dot( 5, 1, 2, 2 ) = -0.313600;
971  rsigma_dot( 5, 2, 2, 2 ) = -0.313600;
972  rsigma_dot( 5, 3, 2, 2 ) = -0.313600;
973  rsigma_dot( 5, 4, 2, 2 ) = -1.412200;
974  rsigma_dot( 5, 5, 2, 2 ) = -3.021700;
975  rsigma_dot( 5, 6, 2, 2 ) = -4.779520;
976  rsigma_dot( 5, 7, 2, 2 ) = -6.825360;
977  rsigma_dot( 5, 8, 2, 2 ) = -4.657420;
978  rsigma_dot( 5, 9, 2, 2 ) = -3.358100;
979  rsigma_dot( 5, 10, 2, 2 ) = -3.609400;
980  rsigma_dot( 5, 11, 2, 2 ) = -4.245440;
981  rsigma_dot( 5, 12, 2, 2 ) = -3.021700;
982  rsigma_dot( 5, 13, 2, 2 ) = -1.412200;
983  rsigma_dot( 5, 14, 2, 2 ) = -0.313600;
984  rsigma_dot( 5, 15, 2, 2 ) = -0.313600;
985  rsigma_dot( 5, 16, 2, 2 ) = -0.313600;
986  rsigma_dot( 5, 17, 2, 2 ) = -0.313600;
987  rsigma_dot( 5, 18, 2, 2 ) = -0.313600;
988  rsigma_dot( 6, 1, 2, 2 ) = -0.262300;
989  rsigma_dot( 6, 2, 2, 2 ) = -0.262300;
990  rsigma_dot( 6, 3, 2, 2 ) = -0.262300;
991  rsigma_dot( 6, 4, 2, 2 ) = -1.871800;
992  rsigma_dot( 6, 5, 2, 2 ) = -2.208200;
993  rsigma_dot( 6, 6, 2, 2 ) = -6.862190;
994  rsigma_dot( 6, 7, 2, 2 ) = -7.463490;
995  rsigma_dot( 6, 8, 2, 2 ) = -4.837030;
996  rsigma_dot( 6, 9, 2, 2 ) = -4.436700;
997  rsigma_dot( 6, 10, 2, 2 ) = -4.916280;
998  rsigma_dot( 6, 11, 2, 2 ) = -5.687270;
999  rsigma_dot( 6, 12, 2, 2 ) = -4.405450;
1000  rsigma_dot( 6, 13, 2, 2 ) = -2.208200;
1001  rsigma_dot( 6, 14, 2, 2 ) = -0.262300;
1002  rsigma_dot( 6, 15, 2, 2 ) = -1.360900;
1003  rsigma_dot( 6, 16, 2, 2 ) = -0.262300;
1004  rsigma_dot( 6, 17, 2, 2 ) = -0.262300;
1005  rsigma_dot( 6, 18, 2, 2 ) = -0.262300;
1006  rsigma_dot( 7, 1, 2, 2 ) = -0.213500;
1007  rsigma_dot( 7, 2, 2, 2 ) = -0.213500;
1008  rsigma_dot( 7, 3, 2, 2 ) = -0.213500;
1009  rsigma_dot( 7, 4, 2, 2 ) = -0.213500;
1010  rsigma_dot( 7, 5, 2, 2 ) = -4.256580;
1011  rsigma_dot( 7, 6, 2, 2 ) = -8.696750;
1012  rsigma_dot( 7, 7, 2, 2 ) = -7.275720;
1013  rsigma_dot( 7, 8, 2, 2 ) = -4.746130;
1014  rsigma_dot( 7, 9, 2, 2 ) = -4.145350;
1015  rsigma_dot( 7, 10, 2, 2 ) = -4.923060;
1016  rsigma_dot( 7, 11, 2, 2 ) = -6.725270;
1017  rsigma_dot( 7, 12, 2, 2 ) = -5.620700;
1018  rsigma_dot( 7, 13, 2, 2 ) = -2.611400;
1019  rsigma_dot( 7, 14, 2, 2 ) = -0.213500;
1020  rsigma_dot( 7, 15, 2, 2 ) = -0.213500;
1021  rsigma_dot( 7, 16, 2, 2 ) = -0.213500;
1022  rsigma_dot( 7, 17, 2, 2 ) = -0.213500;
1023  rsigma_dot( 7, 18, 2, 2 ) = -0.213500;
1024  rsigma_dot( 8, 1, 2, 2 ) = -0.167000;
1025  rsigma_dot( 8, 2, 2, 2 ) = -0.167000;
1026  rsigma_dot( 8, 3, 2, 2 ) = -0.167000;
1027  rsigma_dot( 8, 4, 2, 2 ) = -1.265600;
1028  rsigma_dot( 8, 5, 2, 2 ) = -6.383610;
1029  rsigma_dot( 8, 6, 2, 2 ) = -9.098560;
1030  rsigma_dot( 8, 7, 2, 2 ) = -6.418910;
1031  rsigma_dot( 8, 8, 2, 2 ) = -4.561460;
1032  rsigma_dot( 8, 9, 2, 2 ) = -4.174340;
1033  rsigma_dot( 8, 10, 2, 2 ) = -4.979190;
1034  rsigma_dot( 8, 11, 2, 2 ) = -7.462060;
1035  rsigma_dot( 8, 12, 2, 2 ) = -7.337890;
1036  rsigma_dot( 8, 13, 2, 2 ) = -3.722400;
1037  rsigma_dot( 8, 14, 2, 2 ) = -0.167000;
1038  rsigma_dot( 8, 15, 2, 2 ) = -0.167000;
1039  rsigma_dot( 8, 16, 2, 2 ) = -0.167000;
1040  rsigma_dot( 8, 17, 2, 2 ) = -0.167000;
1041  rsigma_dot( 8, 18, 2, 2 ) = -0.167000;
1042  rsigma_dot( 9, 1, 2, 2 ) = -0.122600;
1043  rsigma_dot( 9, 2, 2, 2 ) = -0.122600;
1044  rsigma_dot( 9, 3, 2, 2 ) = -0.122600;
1045  rsigma_dot( 9, 4, 2, 2 ) = -1.221200;
1046  rsigma_dot( 9, 5, 2, 2 ) = -7.827370;
1047  rsigma_dot( 9, 6, 2, 2 ) = -8.067400;
1048  rsigma_dot( 9, 7, 2, 2 ) = -5.809530;
1049  rsigma_dot( 9, 8, 2, 2 ) = -4.966740;
1050  rsigma_dot( 9, 9, 2, 2 ) = -4.327250;
1051  rsigma_dot( 9, 10, 2, 2 ) = -4.884730;
1052  rsigma_dot( 9, 11, 2, 2 ) = -7.072410;
1053  rsigma_dot( 9, 12, 2, 2 ) = -8.543900;
1054  rsigma_dot( 9, 13, 2, 2 ) = -5.252450;
1055  rsigma_dot( 9, 14, 2, 2 ) = -1.732000;
1056  rsigma_dot( 9, 15, 2, 2 ) = -0.122600;
1057  rsigma_dot( 9, 16, 2, 2 ) = -0.122600;
1058  rsigma_dot( 9, 17, 2, 2 ) = -0.122600;
1059  rsigma_dot( 9, 18, 2, 2 ) = -0.122600;
1060  rsigma_dot( 10, 1, 2, 2 ) = -0.080000;
1061  rsigma_dot( 10, 2, 2, 2 ) = -0.080000;
1062  rsigma_dot( 10, 3, 2, 2 ) = -1.689400;
1063  rsigma_dot( 10, 4, 2, 2 ) = -2.913200;
1064  rsigma_dot( 10, 5, 2, 2 ) = -7.579420;
1065  rsigma_dot( 10, 6, 2, 2 ) = -6.907620;
1066  rsigma_dot( 10, 7, 2, 2 ) = -5.422330;
1067  rsigma_dot( 10, 8, 2, 2 ) = -5.161400;
1068  rsigma_dot( 10, 9, 2, 2 ) = -4.590850;
1069  rsigma_dot( 10, 10, 2, 2 ) = -4.970340;
1070  rsigma_dot( 10, 11, 2, 2 ) = -6.331900;
1071  rsigma_dot( 10, 12, 2, 2 ) = -8.504850;
1072  rsigma_dot( 10, 13, 2, 2 ) = -6.881280;
1073  rsigma_dot( 10, 14, 2, 2 ) = -2.644900;
1074  rsigma_dot( 10, 15, 2, 2 ) = -0.080000;
1075  rsigma_dot( 10, 16, 2, 2 ) = -1.178600;
1076  rsigma_dot( 10, 17, 2, 2 ) = -0.080000;
1077  rsigma_dot( 10, 18, 2, 2 ) = -0.080000;
1078  rsigma_dot( 11, 1, 2, 2 ) = -0.039200;
1079  rsigma_dot( 11, 2, 2, 2 ) = -1.137800;
1080  rsigma_dot( 11, 3, 2, 2 ) = -2.437100;
1081  rsigma_dot( 11, 4, 2, 2 ) = -4.356660;
1082  rsigma_dot( 11, 5, 2, 2 ) = -6.159470;
1083  rsigma_dot( 11, 6, 2, 2 ) = -6.109910;
1084  rsigma_dot( 11, 7, 2, 2 ) = -5.082600;
1085  rsigma_dot( 11, 8, 2, 2 ) = -5.203960;
1086  rsigma_dot( 11, 9, 2, 2 ) = -5.029610;
1087  rsigma_dot( 11, 10, 2, 2 ) = -5.180840;
1088  rsigma_dot( 11, 11, 2, 2 ) = -5.633880;
1089  rsigma_dot( 11, 12, 2, 2 ) = -7.850740;
1090  rsigma_dot( 11, 13, 2, 2 ) = -8.236990;
1091  rsigma_dot( 11, 14, 2, 2 ) = -3.258000;
1092  rsigma_dot( 11, 15, 2, 2 ) = -2.604100;
1093  rsigma_dot( 11, 16, 2, 2 ) = -1.648600;
1094  rsigma_dot( 11, 17, 2, 2 ) = -0.039200;
1095  rsigma_dot( 11, 18, 2, 2 ) = -0.039200;
1096  rsigma_dot( 12, 1, 2, 2 ) = 0.000000;
1097  rsigma_dot( 12, 2, 2, 2 ) = -2.197200;
1098  rsigma_dot( 12, 3, 2, 2 ) = -2.708000;
1099  rsigma_dot( 12, 4, 2, 2 ) = -5.093700;
1100  rsigma_dot( 12, 5, 2, 2 ) = -5.802070;
1101  rsigma_dot( 12, 6, 2, 2 ) = -5.587200;
1102  rsigma_dot( 12, 7, 2, 2 ) = -5.198450;
1103  rsigma_dot( 12, 8, 2, 2 ) = -5.459540;
1104  rsigma_dot( 12, 9, 2, 2 ) = -5.068860;
1105  rsigma_dot( 12, 10, 2, 2 ) = -5.272950;
1106  rsigma_dot( 12, 11, 2, 2 ) = -5.370590;
1107  rsigma_dot( 12, 12, 2, 2 ) = -6.597100;
1108  rsigma_dot( 12, 13, 2, 2 ) = -7.631870;
1109  rsigma_dot( 12, 14, 2, 2 ) = -5.043380;
1110  rsigma_dot( 12, 15, 2, 2 ) = -3.218800;
1111  rsigma_dot( 12, 16, 2, 2 ) = -2.833200;
1112  rsigma_dot( 12, 17, 2, 2 ) = -2.197200;
1113  rsigma_dot( 12, 18, 2, 2 ) = 0.000000;
1114 
1115  // section 21
1116  rsigma_dot( 1, 1, 2, 1 ) = -0.974100;
1117  rsigma_dot( 1, 2, 2, 1 ) = -0.974100;
1118  rsigma_dot( 1, 3, 2, 1 ) = -0.974100;
1119  rsigma_dot( 1, 4, 2, 1 ) = -0.974100;
1120  rsigma_dot( 1, 5, 2, 1 ) = -0.974100;
1121  rsigma_dot( 1, 6, 2, 1 ) = -0.974100;
1122  rsigma_dot( 1, 7, 2, 1 ) = -0.974100;
1123  rsigma_dot( 1, 8, 2, 1 ) = -2.920000;
1124  rsigma_dot( 1, 9, 2, 1 ) = -3.171400;
1125  rsigma_dot( 1, 10, 2, 1 ) = -0.974100;
1126  rsigma_dot( 1, 11, 2, 1 ) = -2.583600;
1127  rsigma_dot( 1, 12, 2, 1 ) = -0.974100;
1128  rsigma_dot( 1, 13, 2, 1 ) = -0.974100;
1129  rsigma_dot( 1, 14, 2, 1 ) = -0.974100;
1130  rsigma_dot( 1, 15, 2, 1 ) = -0.974100;
1131  rsigma_dot( 1, 16, 2, 1 ) = -0.974100;
1132  rsigma_dot( 1, 17, 2, 1 ) = -0.974100;
1133  rsigma_dot( 1, 18, 2, 1 ) = -0.974100;
1134  rsigma_dot( 2, 1, 2, 1 ) = -0.909600;
1135  rsigma_dot( 2, 2, 2, 1 ) = -0.909600;
1136  rsigma_dot( 2, 3, 2, 1 ) = -0.909600;
1137  rsigma_dot( 2, 4, 2, 1 ) = -0.909600;
1138  rsigma_dot( 2, 5, 2, 1 ) = -0.909600;
1139  rsigma_dot( 2, 6, 2, 1 ) = -0.909600;
1140  rsigma_dot( 2, 7, 2, 1 ) = -0.909600;
1141  rsigma_dot( 2, 8, 2, 1 ) = -4.343580;
1142  rsigma_dot( 2, 9, 2, 1 ) = -6.015540;
1143  rsigma_dot( 2, 10, 2, 1 ) = -4.205430;
1144  rsigma_dot( 2, 11, 2, 1 ) = -2.008200;
1145  rsigma_dot( 2, 12, 2, 1 ) = -2.519000;
1146  rsigma_dot( 2, 13, 2, 1 ) = -0.909600;
1147  rsigma_dot( 2, 14, 2, 1 ) = -0.909600;
1148  rsigma_dot( 2, 15, 2, 1 ) = -0.909600;
1149  rsigma_dot( 2, 16, 2, 1 ) = -0.909600;
1150  rsigma_dot( 2, 17, 2, 1 ) = -0.909600;
1151  rsigma_dot( 2, 18, 2, 1 ) = -0.909600;
1152  rsigma_dot( 3, 1, 2, 1 ) = -0.849000;
1153  rsigma_dot( 3, 2, 2, 1 ) = -0.849000;
1154  rsigma_dot( 3, 3, 2, 1 ) = -0.849000;
1155  rsigma_dot( 3, 4, 2, 1 ) = -0.849000;
1156  rsigma_dot( 3, 5, 2, 1 ) = -0.849000;
1157  rsigma_dot( 3, 6, 2, 1 ) = -0.849000;
1158  rsigma_dot( 3, 7, 2, 1 ) = -3.046200;
1159  rsigma_dot( 3, 8, 2, 1 ) = -5.990630;
1160  rsigma_dot( 3, 9, 2, 1 ) = -7.627760;
1161  rsigma_dot( 3, 10, 2, 1 ) = -6.013760;
1162  rsigma_dot( 3, 11, 2, 1 ) = -2.794900;
1163  rsigma_dot( 3, 12, 2, 1 ) = -2.458400;
1164  rsigma_dot( 3, 13, 2, 1 ) = -0.849000;
1165  rsigma_dot( 3, 14, 2, 1 ) = -0.849000;
1166  rsigma_dot( 3, 15, 2, 1 ) = -0.849000;
1167  rsigma_dot( 3, 16, 2, 1 ) = -0.849000;
1168  rsigma_dot( 3, 17, 2, 1 ) = -0.849000;
1169  rsigma_dot( 3, 18, 2, 1 ) = -0.849000;
1170  rsigma_dot( 4, 1, 2, 1 ) = -0.791800;
1171  rsigma_dot( 4, 2, 2, 1 ) = -0.791800;
1172  rsigma_dot( 4, 3, 2, 1 ) = -0.791800;
1173  rsigma_dot( 4, 4, 2, 1 ) = -0.791800;
1174  rsigma_dot( 4, 5, 2, 1 ) = -0.791800;
1175  rsigma_dot( 4, 6, 2, 1 ) = -2.401300;
1176  rsigma_dot( 4, 7, 2, 1 ) = -3.736250;
1177  rsigma_dot( 4, 8, 2, 1 ) = -6.512120;
1178  rsigma_dot( 4, 9, 2, 1 ) = -8.856760;
1179  rsigma_dot( 4, 10, 2, 1 ) = -7.235940;
1180  rsigma_dot( 4, 11, 2, 1 ) = -4.010690;
1181  rsigma_dot( 4, 12, 2, 1 ) = -2.401300;
1182  rsigma_dot( 4, 13, 2, 1 ) = -1.890400;
1183  rsigma_dot( 4, 14, 2, 1 ) = -0.791800;
1184  rsigma_dot( 4, 15, 2, 1 ) = -0.791800;
1185  rsigma_dot( 4, 16, 2, 1 ) = -0.791800;
1186  rsigma_dot( 4, 17, 2, 1 ) = -0.791800;
1187  rsigma_dot( 4, 18, 2, 1 ) = -0.791800;
1188  rsigma_dot( 5, 1, 2, 1 ) = -0.737700;
1189  rsigma_dot( 5, 2, 2, 1 ) = -0.737700;
1190  rsigma_dot( 5, 3, 2, 1 ) = -0.737700;
1191  rsigma_dot( 5, 4, 2, 1 ) = -0.737700;
1192  rsigma_dot( 5, 5, 2, 1 ) = -0.737700;
1193  rsigma_dot( 5, 6, 2, 1 ) = -2.683700;
1194  rsigma_dot( 5, 7, 2, 1 ) = -4.171730;
1195  rsigma_dot( 5, 8, 2, 1 ) = -7.436010;
1196  rsigma_dot( 5, 9, 2, 1 ) = -9.773380;
1197  rsigma_dot( 5, 10, 2, 1 ) = -8.510500;
1198  rsigma_dot( 5, 11, 2, 1 ) = -4.669570;
1199  rsigma_dot( 5, 12, 2, 1 ) = -3.445800;
1200  rsigma_dot( 5, 13, 2, 1 ) = -1.836400;
1201  rsigma_dot( 5, 14, 2, 1 ) = -0.737700;
1202  rsigma_dot( 5, 15, 2, 1 ) = -0.737700;
1203  rsigma_dot( 5, 16, 2, 1 ) = -0.737700;
1204  rsigma_dot( 5, 17, 2, 1 ) = -0.737700;
1205  rsigma_dot( 5, 18, 2, 1 ) = -0.737700;
1206  rsigma_dot( 6, 1, 2, 1 ) = -0.686500;
1207  rsigma_dot( 6, 2, 2, 1 ) = -0.686500;
1208  rsigma_dot( 6, 3, 2, 1 ) = -0.686500;
1209  rsigma_dot( 6, 4, 2, 1 ) = -0.686500;
1210  rsigma_dot( 6, 5, 2, 1 ) = -0.686500;
1211  rsigma_dot( 6, 6, 2, 1 ) = -0.686500;
1212  rsigma_dot( 6, 7, 2, 1 ) = -4.297370;
1213  rsigma_dot( 6, 8, 2, 1 ) = -7.670240;
1214  rsigma_dot( 6, 9, 2, 1 ) = -9.274480;
1215  rsigma_dot( 6, 10, 2, 1 ) = -8.780530;
1216  rsigma_dot( 6, 11, 2, 1 ) = -5.395980;
1217  rsigma_dot( 6, 12, 2, 1 ) = -2.632400;
1218  rsigma_dot( 6, 13, 2, 1 ) = -3.084300;
1219  rsigma_dot( 6, 14, 2, 1 ) = -0.686500;
1220  rsigma_dot( 6, 15, 2, 1 ) = -0.686500;
1221  rsigma_dot( 6, 16, 2, 1 ) = -0.686500;
1222  rsigma_dot( 6, 17, 2, 1 ) = -0.686500;
1223  rsigma_dot( 6, 18, 2, 1 ) = -0.686500;
1224  rsigma_dot( 7, 1, 2, 1 ) = -0.637700;
1225  rsigma_dot( 7, 2, 2, 1 ) = -0.637700;
1226  rsigma_dot( 7, 3, 2, 1 ) = -0.637700;
1227  rsigma_dot( 7, 4, 2, 1 ) = -0.637700;
1228  rsigma_dot( 7, 5, 2, 1 ) = -1.736300;
1229  rsigma_dot( 7, 6, 2, 1 ) = -3.682200;
1230  rsigma_dot( 7, 7, 2, 1 ) = -4.645000;
1231  rsigma_dot( 7, 8, 2, 1 ) = -6.967380;
1232  rsigma_dot( 7, 9, 2, 1 ) = -7.766160;
1233  rsigma_dot( 7, 10, 2, 1 ) = -7.608390;
1234  rsigma_dot( 7, 11, 2, 1 ) = -5.416790;
1235  rsigma_dot( 7, 12, 2, 1 ) = -3.773160;
1236  rsigma_dot( 7, 13, 2, 1 ) = -3.345700;
1237  rsigma_dot( 7, 14, 2, 1 ) = -2.834900;
1238  rsigma_dot( 7, 15, 2, 1 ) = -2.247100;
1239  rsigma_dot( 7, 16, 2, 1 ) = -0.637700;
1240  rsigma_dot( 7, 17, 2, 1 ) = -0.637700;
1241  rsigma_dot( 7, 18, 2, 1 ) = -0.637700;
1242  rsigma_dot( 8, 1, 2, 1 ) = -0.591100;
1243  rsigma_dot( 8, 2, 2, 1 ) = -0.591100;
1244  rsigma_dot( 8, 3, 2, 1 ) = -0.591100;
1245  rsigma_dot( 8, 4, 2, 1 ) = -0.591100;
1246  rsigma_dot( 8, 5, 2, 1 ) = -2.788400;
1247  rsigma_dot( 8, 6, 2, 1 ) = -4.087650;
1248  rsigma_dot( 8, 7, 2, 1 ) = -4.702020;
1249  rsigma_dot( 8, 8, 2, 1 ) = -6.084200;
1250  rsigma_dot( 8, 9, 2, 1 ) = -6.877140;
1251  rsigma_dot( 8, 10, 2, 1 ) = -6.827510;
1252  rsigma_dot( 8, 11, 2, 1 ) = -5.980210;
1253  rsigma_dot( 8, 12, 2, 1 ) = -4.087650;
1254  rsigma_dot( 8, 13, 2, 1 ) = -3.635700;
1255  rsigma_dot( 8, 14, 2, 1 ) = -4.202060;
1256  rsigma_dot( 8, 15, 2, 1 ) = -2.537100;
1257  rsigma_dot( 8, 16, 2, 1 ) = -0.591100;
1258  rsigma_dot( 8, 17, 2, 1 ) = -0.591100;
1259  rsigma_dot( 8, 18, 2, 1 ) = -0.591100;
1260  rsigma_dot( 9, 1, 2, 1 ) = -0.546700;
1261  rsigma_dot( 9, 2, 2, 1 ) = -0.546700;
1262  rsigma_dot( 9, 3, 2, 1 ) = -0.546700;
1263  rsigma_dot( 9, 4, 2, 1 ) = -0.546700;
1264  rsigma_dot( 9, 5, 2, 1 ) = -3.254700;
1265  rsigma_dot( 9, 6, 2, 1 ) = -4.102040;
1266  rsigma_dot( 9, 7, 2, 1 ) = -4.916140;
1267  rsigma_dot( 9, 8, 2, 1 ) = -5.788440;
1268  rsigma_dot( 9, 9, 2, 1 ) = -5.777800;
1269  rsigma_dot( 9, 10, 2, 1 ) = -6.126420;
1270  rsigma_dot( 9, 11, 2, 1 ) = -5.997730;
1271  rsigma_dot( 9, 12, 2, 1 ) = -4.721080;
1272  rsigma_dot( 9, 13, 2, 1 ) = -4.102040;
1273  rsigma_dot( 9, 14, 2, 1 ) = -4.157610;
1274  rsigma_dot( 9, 15, 2, 1 ) = -3.111600;
1275  rsigma_dot( 9, 16, 2, 1 ) = -1.645300;
1276  rsigma_dot( 9, 17, 2, 1 ) = -0.546700;
1277  rsigma_dot( 9, 18, 2, 1 ) = -0.546700;
1278  rsigma_dot( 10, 1, 2, 1 ) = -0.504100;
1279  rsigma_dot( 10, 2, 2, 1 ) = -0.504100;
1280  rsigma_dot( 10, 3, 2, 1 ) = -0.504100;
1281  rsigma_dot( 10, 4, 2, 1 ) = -0.504100;
1282  rsigma_dot( 10, 5, 2, 1 ) = -3.548700;
1283  rsigma_dot( 10, 6, 2, 1 ) = -4.873580;
1284  rsigma_dot( 10, 7, 2, 1 ) = -5.176960;
1285  rsigma_dot( 10, 8, 2, 1 ) = -5.756400;
1286  rsigma_dot( 10, 9, 2, 1 ) = -5.573030;
1287  rsigma_dot( 10, 10, 2, 1 ) = -5.702630;
1288  rsigma_dot( 10, 11, 2, 1 ) = -5.668920;
1289  rsigma_dot( 10, 12, 2, 1 ) = -5.078840;
1290  rsigma_dot( 10, 13, 2, 1 ) = -4.678520;
1291  rsigma_dot( 10, 14, 2, 1 ) = -4.310790;
1292  rsigma_dot( 10, 15, 2, 1 ) = -4.217700;
1293  rsigma_dot( 10, 16, 2, 1 ) = -2.113600;
1294  rsigma_dot( 10, 17, 2, 1 ) = -0.504100;
1295  rsigma_dot( 10, 18, 2, 1 ) = -0.504100;
1296  rsigma_dot( 11, 1, 2, 1 ) = -0.463300;
1297  rsigma_dot( 11, 2, 2, 1 ) = -0.463300;
1298  rsigma_dot( 11, 3, 2, 1 ) = -0.463300;
1299  rsigma_dot( 11, 4, 2, 1 ) = -2.409200;
1300  rsigma_dot( 11, 5, 2, 1 ) = -4.313460;
1301  rsigma_dot( 11, 6, 2, 1 ) = -5.225480;
1302  rsigma_dot( 11, 7, 2, 1 ) = -5.493750;
1303  rsigma_dot( 11, 8, 2, 1 ) = -5.353660;
1304  rsigma_dot( 11, 9, 2, 1 ) = -5.154660;
1305  rsigma_dot( 11, 10, 2, 1 ) = -5.397780;
1306  rsigma_dot( 11, 11, 2, 1 ) = -5.726000;
1307  rsigma_dot( 11, 12, 2, 1 ) = -5.480590;
1308  rsigma_dot( 11, 13, 2, 1 ) = -4.018660;
1309  rsigma_dot( 11, 14, 2, 1 ) = -4.313460;
1310  rsigma_dot( 11, 15, 2, 1 ) = -4.574180;
1311  rsigma_dot( 11, 16, 2, 1 ) = -2.861200;
1312  rsigma_dot( 11, 17, 2, 1 ) = -0.463300;
1313  rsigma_dot( 11, 18, 2, 1 ) = -1.561900;
1314  rsigma_dot( 12, 1, 2, 1 ) = -0.424100;
1315  rsigma_dot( 12, 2, 2, 1 ) = -0.424100;
1316  rsigma_dot( 12, 3, 2, 1 ) = -2.822000;
1317  rsigma_dot( 12, 4, 2, 1 ) = -3.132100;
1318  rsigma_dot( 12, 5, 2, 1 ) = -5.115440;
1319  rsigma_dot( 12, 6, 2, 1 ) = -5.697090;
1320  rsigma_dot( 12, 7, 2, 1 ) = -5.747100;
1321  rsigma_dot( 12, 8, 2, 1 ) = -5.386930;
1322  rsigma_dot( 12, 9, 2, 1 ) = -5.019210;
1323  rsigma_dot( 12, 10, 2, 1 ) = -5.186260;
1324  rsigma_dot( 12, 11, 2, 1 ) = -5.775950;
1325  rsigma_dot( 12, 12, 2, 1 ) = -5.600240;
1326  rsigma_dot( 12, 13, 2, 1 ) = -4.394380;
1327  rsigma_dot( 12, 14, 2, 1 ) = -3.257300;
1328  rsigma_dot( 12, 15, 2, 1 ) = -3.920600;
1329  rsigma_dot( 12, 16, 2, 1 ) = -3.643000;
1330  rsigma_dot( 12, 17, 2, 1 ) = -1.522700;
1331  rsigma_dot( 12, 18, 2, 1 ) = -0.424100;
1332 }
1333 
1334 
1335 } // ns sspot
1336 } // ns potentials
1337 } // ns fldsgn
1338 } // ns protocols
Generated on Sat Jun 1 2013 11:50:07 for Rosetta 3.5 by   doxygen 1.8.4