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  1. /* PROGRAM coupled_oscillators */
  2. /* n 個の質点からなる連成振動子の運動を */
  3. /* 0 < t < TEND の範囲で解く。 */
  4. /* 長さ 2*N の配列 w[0~(N-1)][0~1] を定義して, */
  5. /* j 番目の質点の変位を w[j][0], */
  6. /* 速度を w[j][1] に格納する。 */
  7. /* 質点の質量の逆数に比例する無次元パラメータは */
  8. /* 配列 c[0~(N-1)] に格納する。 */
  9. /* 初期条件は変位ゼロ, */
  10. /* 速度は 1 番目の質点のみ VZERO とする。 */
  11. #include<stdio.h>
  12. #define N 10
  13. #define VZERO 0.1
  14. #define TEND 100.0
  15. void rhs(double f[N][2], double w[N][2], double c[N], int n);
  16. int main(void){
  17. int j;
  18. double t,dt, c[N], w[N][2],p[N][2],
  19. k1[N][2], k2[N][2], k3[N][2], k4[N][2];
  20. /* 時間ステップの刻み幅 dt を標準入力から読み込む。*/
  21. scanf("%lf",&dt);
  22. /* 質量はみんな同じ。*/
  23. for(j=0;j<N;++j)c[j] = 1.0;
  24. /* 未知変数 w と時刻 t の初期化。*/
  25. for(j=0;j<N;++j) w[j][0] = 0.0,
  26. w[j][1] = j==0 ? VZERO : 0.0;
  27. t = 0.0;
  28. /* 時間積分の開始(無限 for loop)。*/
  29. for(;;){
  30. /* 時刻 t での質点の位置を書き出す。*/
  31. printf("%12.7f",t);
  32. for(j=0;j<N;++j)
  33. printf("%16.8e", w[j][0] + (j+1.0)/(N+1.0));
  34. printf("\n");
  35. /* 時刻が TEND を超えたら無限 for loop から脱出する。*/
  36. if ( t >= TEND ) break;
  37. /* 4次ルンゲ・クッタ法。微分方程式を */
  38. /* dw/dt = f(w) だと思って,機械的に */
  39. /* アルゴリズムを適用する。*/
  40. /* まず補助変数 k1 = f(p) を計算する。*/
  41. for(j=0;j<N;++j)
  42. p[j][0]=w[j][0],
  43. p[j][1]=w[j][1];
  44. rhs(k1, p, c, N);
  45. /* 補助変数 k2 = f(p) を計算する。*/
  46. for(j=0;j<N;++j)
  47. p[j][0]=w[j][0] + 0.5*dt*k1[j][0],
  48. p[j][1]=w[j][1] + 0.5*dt*k1[j][1];
  49. rhs(k2, p, c, N);
  50. /* 補助変数 k3 = f(p) を計算する。*/
  51. for(j=0;j<N;++j)
  52. p[j][0]=w[j][0] + 0.5*dt*k2[j][0],
  53. p[j][1]=w[j][1] + 0.5*dt*k2[j][1];
  54. rhs(k3, p, c, N);
  55. /* 補助変数 k4 = f(p) を計算する。*/
  56. for(j=0;j<N;++j)
  57. p[j][0]=w[j][0] + dt*k3[j][0],
  58. p[j][1]=w[j][1] + dt*k3[j][1];
  59. rhs(k4, p, c, N);
  60. /* 未知変数 w と時刻 t を次の時間ステップでの値で上書きする。*/
  61. for(j=0;j<N;++j)
  62. w[j][0]=w[j][0] + (dt/6.0)*(k1[j][0]+k4[j][0]+2.0*(k2[j][0]+k3[j][0])),
  63. w[j][1]=w[j][1] + (dt/6.0)*(k1[j][1]+k4[j][1]+2.0*(k2[j][1]+k3[j][1]));
  64. t = t + dt;
  65. }
  66. return 0;}
  67.  
  68. /* 微分方程式 dw/dt = f(w) の右辺を計算するサブルーチン。*/
  69. void rhs(double f[N][2], double w[N][2], double c[N], int n){
  70. int j;
  71. for(j=0;j<n;++j){
  72. /* du(j)/dt = v(j) */
  73. f[j][0] = w[j][1];
  74. /* dv(j)/dt = -c(j) * (2u(j) - u(j-1) - u(j+1)) */
  75. if ( j == 0 ) {
  76. f[j][1] = - c[j] * (2.0*w[j][0] - w[j+1][0]);
  77. } else if ( j == n-1 ) {
  78. f[j][1] = - c[j] * (2.0*w[j][0] - w[j-1][0]);
  79. } else {
  80. f[j][1] = - c[j] * (2.0*w[j][0] - w[j-1][0] - w[j+1][0]);
  81. }
  82. }
  83. }
Success #stdin #stdout 0s 4404KB
stdin
1.0
stdout
   0.0000000  9.09090909e-02  1.81818182e-01  2.72727273e-01  3.63636364e-01  4.54545455e-01  5.45454545e-01  6.36363636e-01  7.27272727e-01  8.18181818e-01  9.09090909e-01
   1.0000000  1.57575758e-01  1.98484848e-01  2.72727273e-01  3.63636364e-01  4.54545455e-01  5.45454545e-01  6.36363636e-01  7.27272727e-01  8.18181818e-01  9.09090909e-01
   2.0000000  1.29797980e-01  2.34595960e-01  2.89393939e-01  3.65025253e-01  4.54545455e-01  5.45454545e-01  6.36363636e-01  7.27272727e-01  8.18181818e-01  9.09090909e-01
   3.0000000  8.32702020e-02  2.23918876e-01  3.20991162e-01  3.80418771e-01  4.56744529e-01  5.45541351e-01  6.36363636e-01  7.27272727e-01  8.18181818e-01  9.09090909e-01
   4.0000000  8.03959736e-02  1.80786160e-01  3.16998106e-01  4.07994003e-01  4.71269992e-01  5.48319129e-01  6.36575828e-01  7.27277550e-01  8.18181818e-01  9.09090909e-01
   5.0000000  9.33183470e-02  1.68123098e-01  2.76796685e-01  4.08329168e-01  4.96055389e-01  5.62066908e-01  6.39759301e-01  7.27629193e-01  8.18198898e-01  9.09091160e-01
   6.0000000  9.40571654e-02  1.81667494e-01  2.57116640e-01  3.72471705e-01  4.98997183e-01  5.84695203e-01  6.52840600e-01  7.31105316e-01  8.18688937e-01  9.09127308e-01
   7.0000000  9.03009539e-02  1.86505335e-01  2.69323877e-01  3.47865678e-01  4.67313478e-01  5.89331457e-01  6.73748514e-01  7.43604106e-01  8.22379606e-01  9.09745574e-01
   8.0000000  9.01017895e-02  1.81923446e-01  2.78486018e-01  3.56732363e-01  4.39674553e-01  5.61435891e-01  6.79508572e-01  7.63098802e-01  8.34358203e-01  9.13506441e-01
   9.0000000  9.09899746e-02  1.80471752e-01  2.74227014e-01  3.69374044e-01  4.44514621e-01  5.32121253e-01  6.54944873e-01  7.69607906e-01  8.52547145e-01  9.24178190e-01
  10.0000000  9.11034189e-02  1.81770595e-01  2.70851267e-01  3.66928576e-01  4.59349802e-01  5.32864810e-01  6.24892131e-01  7.47792560e-01  8.58626433e-01  9.37417541e-01
  11.0000000  9.09526447e-02  1.82128082e-01  2.72237983e-01  3.61705108e-01  4.59581913e-01  5.48644505e-01  6.21627355e-01  7.16633334e-01  8.35358717e-01  9.34061226e-01
  12.0000000  9.08509028e-02  1.81878128e-01  2.73241242e-01  3.62416241e-01  4.53079403e-01  5.51676520e-01  6.36252682e-01  7.05983839e-01  7.95207224e-01  9.01451829e-01
  13.0000000  9.08683643e-02  1.81766323e-01  2.72878824e-01  3.64179325e-01  4.52232651e-01  5.43544304e-01  6.38260428e-01  7.10850125e-01  7.70824029e-01  8.64579782e-01
  14.0000000  9.09359180e-02  1.81757097e-01  2.72576736e-01  3.63693848e-01  4.53383428e-01  5.37055807e-01  6.21869113e-01  7.05352859e-01  7.76596342e-01  8.66080690e-01
  15.0000000  9.09180808e-02  1.81763478e-01  2.72287482e-01  3.61827477e-01  4.49439944e-01  5.30179591e-01  6.04053307e-01  6.91859768e-01  7.99610684e-01  9.05388019e-01
  16.0000000  9.08194674e-02  1.81434646e-01  2.70953483e-01  3.57599231e-01  4.39345203e-01  5.17913073e-01  5.98557936e-01  6.96929982e-01  8.21855229e-01  9.33835513e-01
  17.0000000  9.04592518e-02  1.79938683e-01  2.66743062e-01  3.48646279e-01  4.26362349e-01  5.09074508e-01  6.09983226e-01  7.23984362e-01  8.32006289e-01  9.23373306e-01
  18.0000000  8.90530413e-02  1.75708073e-01  2.57847323e-01  3.36237711e-01  4.18685761e-01  5.17187829e-01  6.33464257e-01  7.44766944e-01  8.26467685e-01  9.00780157e-01
  19.0000000  8.52570944e-02  1.67162703e-01  2.45779540e-01  3.28367378e-01  4.26364047e-01  5.40758504e-01  6.51612358e-01  7.40015909e-01  8.14476433e-01  8.98470388e-01
  20.0000000  7.83672758e-02  1.55920291e-01  2.38121370e-01  3.35167823e-01  4.48649639e-01  5.60445322e-01  6.49407229e-01  7.23467340e-01  8.10979343e-01  9.10324364e-01
  21.0000000  7.11942141e-02  1.49810890e-01  2.44716820e-01  3.56681637e-01  4.68644163e-01  5.59686610e-01  6.34430202e-01  7.18092446e-01  8.17415456e-01  9.14700373e-01
  22.0000000  7.16659021e-02  1.59448592e-01  2.66834184e-01  3.77551644e-01  4.69708754e-01  5.44815709e-01  6.27232729e-01  7.25712873e-01  8.22070465e-01  9.09704209e-01
  23.0000000  8.73165907e-02  1.87022681e-01  2.91541587e-01  3.81669318e-01  4.56017529e-01  5.36311926e-01  6.33501635e-01  7.31752426e-01  8.19684632e-01  9.06606881e-01
  24.0000000  1.13598681e-01  2.18183758e-01  3.03201806e-01  3.72281686e-01  4.47773537e-01  5.42168204e-01  6.40692188e-01  7.29512184e-01  8.16512680e-01  9.08404482e-01
  25.0000000  1.30407365e-01  2.30732606e-01  3.00766867e-01  3.68903506e-01  4.55960057e-01  5.51735017e-01  6.40130115e-01  7.25766286e-01  8.17154253e-01  9.10073126e-01
  26.0000000  1.19462967e-01  2.15518014e-01  2.96147996e-01  3.81722222e-01  4.71891981e-01  5.55722564e-01  6.37579921e-01  7.26611496e-01  8.19027358e-01  9.09565405e-01
  27.0000000  8.81115688e-02  1.86306137e-01  2.94590500e-01  3.97723711e-01  4.82735335e-01  5.58584944e-01  6.41148654e-01  7.30423345e-01  8.19633251e-01  9.08982705e-01
  28.0000000  6.65529141e-02  1.66072715e-01  2.87617809e-01  3.97255144e-01  4.85357428e-01  5.66925690e-01  6.50577612e-01  7.34762104e-01  8.20655470e-01  9.09723283e-01
  29.0000000  7.42116237e-02  1.65700047e-01  2.70761338e-01  3.77674856e-01  4.80999430e-01  5.76175827e-01  6.60696335e-01  7.41025980e-01  8.24574675e-01  9.11653469e-01
  30.0000000  9.66776740e-02  1.77926403e-01  2.56778304e-01  3.54939803e-01  4.68406047e-01  5.75323391e-01  6.66835933e-01  7.49943585e-01  8.31737962e-01  9.14972052e-01
  31.0000000  1.05730631e-01  1.88440172e-01  2.60153690e-01  3.45977892e-01  4.50301548e-01  5.60533232e-01  6.64582579e-01  7.57057123e-01  8.40137131e-01  9.19954683e-01
  32.0000000  9.52109375e-02  1.89210541e-01  2.75458624e-01  3.53836246e-01  4.38430806e-01  5.40341790e-01  6.51288694e-01  7.55022343e-01  8.45056929e-01  9.24838417e-01
  33.0000000  8.36502475e-02  1.82921583e-01  2.83682632e-01  3.67473805e-01  4.42364414e-01  5.28605046e-01  6.31656400e-01  7.40145340e-01  8.39845262e-01  9.24958288e-01
  34.0000000  8.50602518e-02  1.77816672e-01  2.77413199e-01  3.73212648e-01  4.56113570e-01  5.32192586e-01  6.17409622e-01  7.17286742e-01  8.20865242e-01  9.15418040e-01
  35.0000000  9.28695490e-02  1.78662869e-01  2.67958032e-01  3.67484502e-01  4.63598866e-01  5.43842812e-01  6.16466132e-01  6.98096265e-01  7.93928242e-01  8.96836464e-01
  36.0000000  9.49757433e-02  1.82542756e-01  2.67023305e-01  3.58662320e-01  4.57104032e-01  5.48411871e-01  6.23337782e-01  6.92082012e-01  7.74262511e-01  8.79187052e-01
  37.0000000  9.10500340e-02  1.83779739e-01  2.71961851e-01  3.55521485e-01  4.44214360e-01  5.38320058e-01  6.24604982e-01  6.98482280e-01  7.76058975e-01  8.76817976e-01
  38.0000000  8.83463886e-02  1.81100380e-01  2.72937773e-01  3.56485446e-01  4.35654118e-01  5.21409195e-01  6.15309009e-01  7.08713035e-01  7.99188256e-01  8.95024255e-01
  39.0000000  8.90285702e-02  1.77443584e-01  2.66795234e-01  3.53493660e-01  4.32614520e-01  5.11904006e-01  6.06368921e-01  7.16986607e-01  8.27042076e-01  9.21014713e-01
  40.0000000  8.90862958e-02  1.74236489e-01  2.58082629e-01  3.44110894e-01  4.30176749e-01  5.16219417e-01  6.12235538e-01  7.25012001e-01  8.40123903e-01  9.32941473e-01
  41.0000000  8.58345981e-02  1.69679525e-01  2.50991098e-01  3.35151466e-01  4.28722431e-01  5.30045606e-01  6.32835368e-01  7.34550877e-01  8.32889577e-01  9.21692336e-01
  42.0000000  8.08430060e-02  1.63087727e-01  2.46699645e-01  3.34927145e-01  4.34863749e-01  5.45686283e-01  6.52051493e-01  7.40169557e-01  8.16824840e-01  9.01331454e-01
  43.0000000  7.71178578e-02  1.58235618e-01  2.47386138e-01  3.45616644e-01  4.50629273e-01  5.57115548e-01  6.54738906e-01  7.35238495e-01  8.07564910e-01  8.93615789e-01
  44.0000000  7.73384565e-02  1.61221477e-01  2.57000496e-01  3.62765675e-01  4.67199146e-01  5.59831790e-01  6.42044012e-01  7.23410981e-01  8.10549063e-01  9.03665853e-01
  45.0000000  8.40313619e-02  1.75474622e-01  2.75809249e-01  3.78661186e-01  4.72850778e-01  5.52744686e-01  6.28487056e-01  7.17075110e-01  8.19066390e-01  9.16464447e-01
  46.0000000  9.76857701e-02  1.97910756e-01  2.96597543e-01  3.86352705e-01  4.65685906e-01  5.42167315e-01  6.26326622e-01  7.22512765e-01  8.23719022e-01  9.17351221e-01
  47.0000000  1.13277597e-01  2.18460951e-01  3.08861635e-01  3.84399138e-01  4.56140561e-01  5.38898938e-01  6.35000022e-01  7.32184298e-01  8.21711261e-01  9.08867333e-01
  48.0000000  1.20778752e-01  2.24710791e-01  3.07260455e-01  3.79073894e-01  4.56612412e-01  5.47702801e-01  6.44913357e-01  7.35271242e-01  8.17539056e-01  9.03720479e-01
  49.0000000  1.12420721e-01  2.10864448e-01  2.95548518e-01  3.78842373e-01  4.69197610e-01  5.61943277e-01  6.49036783e-01  7.31626501e-01  8.16782125e-01  9.07085958e-01
  50.0000000  9.13881385e-02  1.84423810e-01  2.82180486e-01  3.84477625e-01  4.83695336e-01  5.71217774e-01  6.49336726e-01  7.30400400e-01  8.20646431e-01  9.12762100e-01
  51.0000000  7.23154020e-02  1.62595401e-01  2.72652903e-01  3.86736198e-01  4.87372047e-01  5.72099252e-01  6.52157056e-01  7.37128160e-01  8.26359974e-01  9.14571207e-01
  52.0000000  6.99240323e-02  1.59067772e-01  2.66886598e-01  3.76745143e-01  4.76431791e-01  5.68339816e-01  6.58936004e-01  7.47496523e-01  8.31380014e-01  9.14218173e-01
  53.0000000  8.49218555e-02  1.72667450e-01  2.63520752e-01  3.58010073e-01  4.58218238e-01  5.62598475e-01  6.63355545e-01  7.53671877e-01  8.35463955e-01  9.16301464e-01
  54.0000000  1.02258387e-01  1.89197020e-01  2.64034829e-01  3.44926348e-01  4.43670934e-01  5.53139383e-01  6.58027575e-01  7.51938338e-01  8.38294599e-01  9.20543630e-01
  55.0000000  1.05767157e-01  1.94887786e-01  2.70138772e-01  3.48085771e-01  4.39058324e-01  5.39838479e-01  6.42663469e-01  7.42725783e-01  8.36767057e-01  9.22005060e-01
  56.0000000  9.45093673e-02  1.88065526e-01  2.78318455e-01  3.62872679e-01  4.43796235e-01  5.29004711e-01  6.24792142e-01  7.27460874e-01  8.26733605e-01  9.16739994e-01
  57.0000000  8.24679724e-02  1.78107579e-01  2.81035620e-01  3.74326814e-01  4.52686728e-01  5.28012061e-01  6.13257229e-01  7.09119567e-01  8.08162932e-01  9.05158291e-01
  58.0000000  8.19761999e-02  1.74485655e-01  2.75127614e-01  3.72381473e-01  4.58635083e-01  5.35783505e-01  6.11574497e-01  6.94217158e-01  7.88068336e-01  8.91626009e-01
  59.0000000  9.06324433e-02  1.78066255e-01  2.66347680e-01  3.60478943e-01  4.55944002e-01  5.42038628e-01  6.16340267e-01  6.90111605e-01  7.77469940e-01  8.82919935e-01
  60.0000000  9.65033380e-02  1.82461974e-01  2.62701854e-01  3.49506829e-01  4.44604913e-01  5.37628984e-01  6.20779945e-01  6.98739632e-01  7.84037389e-01  8.85448336e-01
  61.0000000  9.32586612e-02  1.81803557e-01  2.64585601e-01  3.45695631e-01  4.31509098e-01  5.24573996e-01  6.20708246e-01  7.14267536e-01  8.05646366e-01  9.00264240e-01
  62.0000000  8.58656806e-02  1.75927655e-01  2.64805517e-01  3.46079785e-01  4.25150481e-01  5.14638376e-01  6.18656397e-01  7.27991622e-01  8.30078440e-01  9.19508883e-01
  63.0000000  8.19012604e-02  1.68835616e-01  2.58442669e-01  3.44820134e-01  4.28405518e-01  5.18099730e-01  6.21740291e-01  7.35148348e-01  8.42556295e-01  9.30131635e-01
  64.0000000  8.21576185e-02  1.64074966e-01  2.49572217e-01  3.41600987e-01  4.37560759e-01  5.34332119e-01  6.33609509e-01  7.36564472e-01  8.36609657e-01  9.24369794e-01
  65.0000000  8.23844710e-02  1.62752973e-01  2.46861177e-01  3.42406904e-01  4.47944067e-01  5.52888154e-01  6.48352681e-01  7.34835555e-01  8.19347698e-01  9.07659303e-01
  66.0000000  8.13362048e-02  1.65328708e-01  2.54723504e-01  3.52441256e-01  4.57989720e-01  5.62763776e-01  6.54520337e-01  7.30951928e-01  8.05538618e-01  8.94790353e-01
  67.0000000  8.31025162e-02  1.73380405e-01  2.70499163e-01  3.69503638e-01  4.66990140e-01  5.60573792e-01  6.46741843e-01  7.25438698e-01  8.05057186e-01  8.96401050e-01
  68.0000000  9.14248024e-02  1.87928113e-01  2.88291862e-01  3.85023512e-01  4.71896420e-01  5.51353249e-01  6.32412974e-01  7.21109351e-01  8.15252123e-01  9.08972406e-01
  69.0000000  1.04186858e-01  2.05772776e-01  3.02624896e-01  3.91423852e-01  4.69866621e-01  5.43490062e-01  6.25161141e-01  7.21990574e-01  8.25203465e-01  9.19087654e-01
  70.0000000  1.14308109e-01  2.18695719e-01  3.08994323e-01  3.88233454e-01  4.63715116e-01  5.43145777e-01  6.31629695e-01  7.28641972e-01  8.26899694e-01  9.17691815e-01
  71.0000000  1.15003607e-01  2.18084973e-01  3.04618218e-01  3.81409493e-01  4.61434363e-01  5.51343564e-01  6.45842118e-01  7.36307017e-01  8.21941285e-01  9.08849427e-01
  72.0000000  1.04437338e-01  2.01933425e-01  2.91030172e-01  3.77284757e-01  4.68037885e-01  5.63822419e-01  6.56595900e-01  7.39678546e-01  8.18084637e-01  9.03779079e-01
  73.0000000  8.74359884e-02  1.78083084e-01  2.74828304e-01  3.77007482e-01  4.78793548e-01  5.73373607e-01  6.58770588e-01  7.39058283e-01  8.20723228e-01  9.07960246e-01
  74.0000000  7.36716379e-02  1.60118084e-01  2.63665044e-01  3.76169372e-01  4.82611727e-01  5.74247708e-01  6.56212381e-01  7.39745890e-01  8.28395722e-01  9.16393702e-01
  75.0000000  7.20054391e-02  1.58192690e-01  2.60820176e-01  3.69773017e-01  4.72833710e-01  5.66019660e-01  6.54597960e-01  7.44747944e-01  8.35538945e-01  9.21074527e-01
  76.0000000  8.34646091e-02  1.71555481e-01  2.64039652e-01  3.58242111e-01  4.54132041e-01  5.53328289e-01  6.53823848e-01  7.49830090e-01  8.37862020e-01  9.19966353e-01
  77.0000000  9.90069787e-02  1.88976359e-01  2.69194642e-01  3.48649380e-01  4.38547592e-01  5.41616397e-01  6.48633156e-01  7.47315113e-01  8.34478715e-01  9.16767828e-01
  78.0000000  1.06124995e-01  1.97424682e-01  2.73837183e-01  3.48839727e-01  4.35081189e-01  5.33528511e-01  6.35896921e-01  7.34177867e-01  8.26153478e-01  9.13892692e-01
  79.0000000  9.97357349e-02  1.92224002e-01  2.77037084e-01  3.59204319e-01  4.42902697e-01  5.29349061e-01  6.19688937e-01  7.15222735e-01  8.13585033e-01  9.09164169e-01
  80.0000000  8.68566764e-02  1.79961455e-01  2.77483262e-01  3.70696580e-01  4.53376219e-01  5.29117699e-01  6.08453366e-01  6.98857283e-01  7.98513948e-01  9.00221227e-01
  81.0000000  7.96462774e-02  1.71599839e-01  2.73785458e-01  3.72418834e-01  4.57515737e-01  5.32265083e-01  6.07463524e-01  6.91227527e-01  7.85807812e-01  8.89950376e-01
  82.0000000  8.34338675e-02  1.72396521e-01  2.66877154e-01  3.61824620e-01  4.52026933e-01  5.35593759e-01  6.14430162e-01  6.94065657e-01  7.82532319e-01  8.85498721e-01
  83.0000000  9.20886606e-02  1.78138491e-01  2.60489848e-01  3.46936518e-01  4.40281722e-01  5.34418636e-01  6.22336514e-01  7.05543121e-01  7.93045585e-01  8.91847530e-01
  84.0000000  9.53323797e-02  1.80582753e-01  2.57794145e-01  3.38239332e-01  4.29266484e-01  5.27751878e-01  6.26199632e-01  7.21159612e-01  8.14033980e-01  9.06830461e-01
  85.0000000  8.96353242e-02  1.75843794e-01  2.57929571e-01  3.39113442e-01  4.25327812e-01  5.21505662e-01  6.27081400e-01  7.34714324e-01  8.34711623e-01  9.22042083e-01
  86.0000000  8.09132716e-02  1.67430000e-01  2.57316090e-01  3.44787531e-01  4.30861516e-01  5.24176775e-01  6.29886579e-01  7.41003912e-01  8.43382285e-01  9.28381706e-01
  87.0000000  7.71617945e-02  1.62121677e-01  2.54886350e-01  3.49706257e-01  4.43303943e-01  5.38161279e-01  6.37471598e-01  7.39054073e-01  8.35801188e-01  9.22172312e-01
  88.0000000  8.04222923e-02  1.64070791e-01  2.54827312e-01  3.54019238e-01  4.57036800e-01  5.55991283e-01  6.46824098e-01  7.32461789e-01  8.18586967e-01  9.08060594e-01
  89.0000000  8.68505189e-02  1.72842063e-01  2.62764105e-01  3.61981813e-01  4.67039693e-01  5.66204965e-01  6.51138016e-01  7.26129747e-01  8.04488301e-01  8.96356965e-01
  90.0000000  9.29310419e-02  1.85589830e-01  2.79191156e-01  3.75044800e-01  4.71479022e-01  5.63325093e-01  6.46280836e-01  7.22849284e-01  8.02870637e-01  8.95591818e-01
  91.0000000  9.89824170e-02  1.99334444e-01  2.97506714e-01  3.88268010e-01  4.71430750e-01  5.52274956e-01  6.35753339e-01  7.22932714e-01  8.12967624e-01  9.05520435e-01
  92.0000000  1.06026403e-01  2.10777246e-01  3.08799378e-01  3.94290294e-01  4.69021176e-01  5.43603448e-01  6.28868028e-01  7.25930711e-01  8.25448773e-01  9.17132937e-01
  93.0000000  1.11355681e-01  2.15422667e-01  3.08262347e-01  3.90361068e-01  4.66459180e-01  5.44742370e-01  6.32900545e-01  7.31338129e-01  8.30876197e-01  9.20720403e-01
  94.0000000  1.09584934e-01  2.09164532e-01  2.97418252e-01  3.80835175e-01  4.66055842e-01  5.55037888e-01  6.46289789e-01  7.37702835e-01  8.27554962e-01  9.14820383e-01
  95.0000000  9.85584472e-02  1.92249356e-01  2.81764226e-01  3.72761466e-01  4.69153766e-01  5.67492162e-01  6.59751465e-01  7.42527032e-01  8.21894973e-01  9.07118909e-01
  96.0000000  8.32390339e-02  1.71654401e-01  2.67418920e-01  3.69398459e-01  4.73792424e-01  5.74269862e-01  6.64528969e-01  7.44206350e-01  8.21479099e-01  9.06304853e-01
  97.0000000  7.29203616e-02  1.58205549e-01  2.59051045e-01  3.68138466e-01  4.74443142e-01  5.71377504e-01  6.59567729e-01  7.43679136e-01  8.27793657e-01  9.13377037e-01
  98.0000000  7.41726386e-02  1.59427205e-01  2.58615646e-01  3.64435303e-01  4.66291332e-01  5.60122492e-01  6.50588676e-01  7.42976006e-01  8.35312676e-01  9.21300342e-01
  99.0000000  8.57253504e-02  1.73635697e-01  2.64518364e-01  3.57376896e-01  4.50915237e-01  5.45575608e-01  6.42896698e-01  7.41827510e-01  8.36919822e-01  9.22627271e-01
 100.0000000  9.92656496e-02  1.90560238e-01  2.72339117e-01  3.51235426e-01  4.36872548e-01  5.33470516e-01  6.36323252e-01  7.36755036e-01  8.29770371e-01  9.16353934e-01