>> truncated_normal_rule 30-Jan-2017 09:47:25 TRUNCATED_NORMAL_RULE MATLAB version For the (truncated) Gaussian probability density function pdf(x) = exp(-0.5*((x-MU)/SIGMA)^2) / SIGMA / sqrt ( 2 * pi ) compute an N-point quadrature rule for approximating Integral ( A <= x <= B ) f(x) pdf(x) dx The value of OPTION determines the truncation interval [A,B]: 0: (-oo,+oo) 1: [A,+oo) 2: (-oo,B] 3: [A,B] The user specifies OPTION, N, MU, SIGMA, A, B and FILENAME. FILENAME is used to generate 3 files: filename_w.txt - the weight file filename_x.txt - the abscissa file. filename_r.txt - the region file, listing A and B. Enter OPTION, 0/1/2/3: 2 Enter the rule order N: 10 Enter MU, the mean value of the normal distribution: -6.68 Enter SIGMA, the standard deviation: 1.472 Enter the right endpoint B: -4.6052 FILENAME is the "root name" of the quadrature files. Enter FILENAME as a quoted string: 'junk' OPTION = 2 N = 10 MU = -6.68 SIGMA = 1.472 A = -oo B = -4.6052 FILENAME = "junk" ORDER = 0, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 0, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 1 ORDER = 1, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 1, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -6.91622 ORDER = 2, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 2, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 49.4549 ORDER = 3, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 3, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -365.34 ORDER = 4, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 4, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 2785.02 ORDER = 5, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 5, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -21876.6 ORDER = 6, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 6, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 176798 ORDER = 7, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 7, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -1.46767e+06 ORDER = 8, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 8, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 1.2496e+07 ORDER = 9, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 9, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -1.08962e+08 ORDER = 10, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 10, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 9.71773e+08 ORDER = 11, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 11, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -8.85344e+09 ORDER = 12, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 12, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 8.23075e+10 ORDER = 13, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 13, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -7.80037e+11 ORDER = 14, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 14, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 7.5292e+12 ORDER = 15, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 15, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -7.39579e+13 ORDER = 16, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 16, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 7.38753e+14 ORDER = 17, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 17, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -7.49889e+15 ORDER = 18, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 18, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 7.73049e+16 ORDER = 19, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 19, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = -8.0887e+17 ORDER = 20, B = -4.6052, MU = -6.68, S = 1.472 ORDER = 20, H = 1.40951, H_PDF = 0.14774, H_CDF = 0.920658 MOMENT_PDF = 8.58581e+18 Moments: 1: 1 2: -6.916215625528578 3: 49.4549245772151 4: -365.3404164706679 5: 2785.018746046533 6: -21876.62385746943 7: 176797.7904945071 8: -1467673.951046176 9: 12496016.79193835 10: -108962237.1950604 11: 971773329.715145 12: -8853435593.676079 13: 82307468738.71234 14: -780037174927.5826 15: 7529199889072.648 16: -73957920053443.02 17: 738753252857845.1 18: -7498894801452297 19: 7.730488017152146e+16 20: -8.088695394812941e+17 21: 8.585806039935065e+18 Hankel matrix H: Col: 1 2 3 4 5 Row 1 : 1 -6.91622 49.4549 -365.34 2785.02 2 : -6.91622 49.4549 -365.34 2785.02 -21876.6 3 : 49.4549 -365.34 2785.02 -21876.6 176798 4 : -365.34 2785.02 -21876.6 176798 -1.46767e+06 5 : 2785.02 -21876.6 176798 -1.46767e+06 1.2496e+07 6 : -21876.6 176798 -1.46767e+06 1.2496e+07 -1.08962e+08 7 : 176798 -1.46767e+06 1.2496e+07 -1.08962e+08 9.71773e+08 8 : -1.46767e+06 1.2496e+07 -1.08962e+08 9.71773e+08 -8.85344e+09 9 : 1.2496e+07 -1.08962e+08 9.71773e+08 -8.85344e+09 8.23075e+10 10 : -1.08962e+08 9.71773e+08 -8.85344e+09 8.23075e+10 -7.80037e+11 11 : 9.71773e+08 -8.85344e+09 8.23075e+10 -7.80037e+11 7.5292e+12 Col: 6 7 8 9 10 Row 1 : -21876.6 176798 -1.46767e+06 1.2496e+07 -1.08962e+08 2 : 176798 -1.46767e+06 1.2496e+07 -1.08962e+08 9.71773e+08 3 : -1.46767e+06 1.2496e+07 -1.08962e+08 9.71773e+08 -8.85344e+09 4 : 1.2496e+07 -1.08962e+08 9.71773e+08 -8.85344e+09 8.23075e+10 5 : -1.08962e+08 9.71773e+08 -8.85344e+09 8.23075e+10 -7.80037e+11 6 : 9.71773e+08 -8.85344e+09 8.23075e+10 -7.80037e+11 7.5292e+12 7 : -8.85344e+09 8.23075e+10 -7.80037e+11 7.5292e+12 -7.39579e+13 8 : 8.23075e+10 -7.80037e+11 7.5292e+12 -7.39579e+13 7.38753e+14 9 : -7.80037e+11 7.5292e+12 -7.39579e+13 7.38753e+14 -7.49889e+15 10 : 7.5292e+12 -7.39579e+13 7.38753e+14 -7.49889e+15 7.73049e+16 11 : -7.39579e+13 7.38753e+14 -7.49889e+15 7.73049e+16 -8.0887e+17 Col: 11 Row 1 : 9.71773e+08 2 : -8.85344e+09 3 : 8.23075e+10 4 : -7.80037e+11 5 : 7.5292e+12 6 : -7.39579e+13 7 : 7.38753e+14 8 : -7.49889e+15 9 : 7.73049e+16 10 : -8.0887e+17 11 : 8.58581e+18 Frobenius norm of H-R'*R = 22.716 Cholesky factor R: Col: 1 2 3 4 5 Row 1 : 1 -6.91622 49.4549 -365.34 2785.02 2 : 0 1.27314 -18.3008 202.841 -2053.85 3 : 0 0 2.07596 -46.5221 711.892 4 : 0 0 0 3.89813 -120.613 5 : 0 0 0 0 8.15191 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 : -21876.6 176798 -1.46767e+06 1.2496e+07 -1.08962e+08 2 : 20024.8 -192361 1.84211e+06 -1.7702e+07 1.71361e+08 3 : -9295.77 111821 -1.28441e+06 1.43661e+07 -1.5832e+08 4 : 2382.78 -38463.4 554716 -7.46554e+06 9.60983e+07 5 : -325.249 7938.83 -153640 2.59746e+06 -4.02667e+07 6 : 18.6194 -916.712 26803.6 -607796 1.18343e+07 7 : 0 45.8161 -2699.23 92399.5 -2.41178e+06 8 : 0 0 120.247 -8285.94 326253 9 : 0 0 0 336.18 -26548.7 10 : 0 0 0 0 1173.72 11 : 0 0 0 0 0 Col: 11 Row 1 : 9.71773e+08 2 : -1.67495e+09 3 : 1.73203e+09 4 : -1.20133e+09 5 : 5.88674e+08 6 : -2.08388e+08 7 : 5.33232e+07 8 : -9.66447e+06 9 : 1.1834e+06 10 : -100195 11 : 7122.86 Jacobi matrix J: Col: 1 2 3 4 5 Row 1 : -6.91622 1.27314 0 0 0 2 : 1.27314 -7.45833 1.63058 0 0 3 : 0 1.63058 -8.03538 1.87774 0 4 : 0 0 1.87774 -8.53128 2.09124 5 : 0 0 0 2.09124 -8.95727 6 : 0 0 0 0 2.28406 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 2.28406 0 0 0 0 6 : -9.33571 2.46066 0 0 0 7 : 2.46066 -9.68024 2.62454 0 0 8 : 0 2.62454 -9.99356 2.79575 0 9 : 0 0 2.79575 -10.0639 3.49134 10 : 0 0 0 3.49134 -6.39354 Eigenvector matrix V: Col: 1 2 3 4 5 Row 1 : -0.000578236 -0.00903543 0.0543346 -0.17926 0.374006 2 : 0.00347993 0.0417953 -0.187534 0.428168 -0.523734 3 : -0.0147435 -0.130002 0.400607 -0.516192 0.10649 4 : 0.0483507 0.293948 -0.535863 0.156486 0.417159 5 : -0.12657 -0.484045 0.352421 0.356797 -0.129083 6 : 0.267214 0.546373 0.127544 -0.299469 -0.396537 7 : -0.45182 -0.321114 -0.429483 -0.255558 0.0172185 8 : 0.592667 -0.129893 0.147184 0.307733 0.378214 9 : -0.547742 0.432089 0.333855 0.243915 0.15896 10 : 0.23365 -0.235278 -0.237061 -0.238968 -0.240722 Col: 6 7 8 9 10 Row 1 : -0.53278 0.546474 -0.423779 0.250717 0.00395384 2 : 0.253434 0.206062 -0.474948 0.416036 0.00978868 3 : 0.406119 -0.297504 -0.242631 0.481587 0.0190891 4 : -0.109004 -0.432316 0.0834491 0.467586 0.0349198 5 : -0.417275 -0.165989 0.339247 0.401064 0.0624602 6 : -0.162441 0.212602 0.43868 0.301244 0.110037 7 : 0.267583 0.404599 0.370819 0.182561 0.19117 8 : 0.372356 0.300782 0.180838 0.056782 0.32775 9 : 0.0780051 0.00290265 -0.0567645 -0.0659725 0.550806 10 : -0.241376 -0.237841 -0.219185 -0.144868 0.731397 Creating quadrature files. "Root" file name is "junk". Weight file will be "junk_w.txt". Abscissa file will be "junk_x.txt". Region file will be "junk_r.txt". TRUNCATED_NORMAL_RULE: Normal end of execution. 30-Jan-2017 09:47:46 >> diary off