August 26 2003 2:57:08.468 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "halton_02_00100.txt". The weight data will be read from "halton_02_00100_weight_a.txt". The spatial dimension is 2 The number of points is 100 # halton_02_00100.txt # created by HALTON_DATASET. # # File generated on March 16 2003 9:39:34.875 AM # # Spatial dimension M = 2 # Number of points N = 100 # Bases: 2 3 # Initial values skipped = 0 # The input data file has been read. # halton_02_00100_weight_a.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 10:39:09.595 AM # # Spatial dimension M = 2 # Number of points N = 100 # EPSILON (unit roundoff) = 0.119209E-06 # # Initial SEED = 123456789 # # The generator points were read from the file: "/home/r1/src-samples/datasets/halton/halton_02_00100.txt". # Sampling by UNIFORM. # Number of sample points = 10000 # The file of weights was successfully read. INTEGRAL_TEST_01 Using a set of points in [0,1]^N, approximate integrals from the TESTNINT set. Problem Region Correct Estimated Absolute Relative Index Volume Integral Integral Error Error (%) 1 1.00000 1.16667 1.15155 0.151181E-01 1.29584 2 1.00000 1.06667 1.04549 0.211730E-01 1.98497 4 1.00000 2.28571 2.16477 0.120947 5.29145 6 1.00000 1.00000 0.988208 0.117922E-01 1.17922 8 1.00000 0.500000 0.495760 0.424024E-02 0.848049 9 1.00000 1.68336 1.67689 0.646496E-02 0.384052 10 1.00000 0.500000 0.497520 0.248039E-02 0.496078 11 1.00000 2.95249 2.93107 0.214238E-01 0.725618 14 1.00000 -0.250000 -0.251015 0.101495E-02 0.405979 15 1.00000 0.399576 0.400894 0.131765E-02 0.329762 16 1.00000 0.500000 0.497520 0.248039E-02 0.496078 17 1.00000 0.166667 0.164622 0.204487E-02 1.22692 18 1.00000 0.785398 0.800400 0.150018E-01 1.91009 19 1.00000 0.241265 0.239320 0.194506E-02 0.806194 24 1.00000 1.00000 0.988208 0.117922E-01 1.17922 25 1.00000 1.08030 1.07933 0.962615E-03 0.891067E-01 26 1.00000 0.154818 0.155416 0.597402E-03 0.385874 28 1.00000 0.859876 0.861185 0.130850E-02 0.152173 30 1.00000 0.959521 0.959996 0.474453E-03 0.494468E-01 31 1.00000 0.841679 0.815289 0.263892E-01 3.13531 INTEGRAL_TEST_01: Normal conclusion. INTEGRAL_TEST_02 Using a set of points in [0,1]^N, approximate integrals from the TESTNINT set. The integrands depend on a base point. We randomly vary the base point repeatedly, and look at the average behavior. Because the base point moves, the value of the exact integral changes on each repetition! Number of repetitions = 100 Average Maximum Average Maximum Integral Absolute Absolute Relative Relative Error Error Error % Error % 15 0.002283 0.005561 0.726990 1.950161 16 0.004128 0.007969 0.617170 1.161854 17 0.003432 0.009167 1.040689 2.234056 19 0.002137 0.006081 0.756298 2.064731 INTEGRAL_TEST_02: Normal conclusion. INTEGRAL_TEST_03 Using a set of points in [0,1]^N, approximate integrals from the TESTNINT set. Integrand J has the form: product ( 1 <= I <= J ) X(mod(I,N)+1) Problem Region Correct Estimated Absolute Relative Index Volume Integral Integral Error Error (%) 1 1.00000 1.00000 0.996600 0.339991E-02 0.339991 2 1.00000 0.500000 0.498284 0.171649E-02 0.343299 3 1.00000 0.250000 0.247269 0.273143E-02 1.09257 4 1.00000 0.166667 0.164627 0.204009E-02 1.22405 5 1.00000 0.111111 0.108254 0.285685E-02 2.57117 6 1.00000 0.833333E-01 0.805214E-01 0.281189E-02 3.37426 7 1.00000 0.625000E-01 0.594500E-01 0.304997E-02 4.87996 8 1.00000 0.500000E-01 0.468868E-01 0.311323E-02 6.22645 9 1.00000 0.400000E-01 0.368435E-01 0.315652E-02 7.89129 10 1.00000 0.333333E-01 0.301224E-01 0.321093E-02 9.63278 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 1.06302 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:08.523 PM