August 26 2003 2:57:03.667 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "halton_02_00010.txt". The weight data will be read from "halton_02_00010_weight_d.txt". The spatial dimension is 2 The number of points is 10 # halton_02_00010.txt # created by HALTON_DATASET. # # File generated on March 16 2003 9:25:10.385 AM # # Spatial dimension M = 2 # Number of points N = 10 # Bases: 2 3 # Initial values skipped = 0 # The input data file has been read. # halton_02_00010_weight_d.txt # created by VORONOI_WEIGHT_WRITE # at June 3 2003 8:33:43.074 AM # # Spatial dimension M = 2 # Number of points N = 10 # 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_00010.txt". # Sampling by RANDOM_NUMBER (Fortran90 intrinsic). # Number of sample points = 1000000 # 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 1.05598 0.110685 9.48725 2 1.00000 1.06667 0.935375 0.131292 12.3086 4 1.00000 2.28571 2.85934 0.573630 25.0963 6 1.00000 1.00000 0.869455 0.130545 13.0545 8 1.00000 0.500000 0.475465 0.245354E-01 4.90708 9 1.00000 1.68336 1.64127 0.420904E-01 2.50039 10 1.00000 0.500000 0.474226 0.257743E-01 5.15485 11 1.00000 2.95249 2.80001 0.152483 5.16457 14 1.00000 -0.250000 -0.254488 0.448799E-02 1.79520 15 1.00000 0.399576 0.412824 0.132472E-01 3.31532 16 1.00000 0.500000 0.474226 0.257743E-01 5.15485 17 1.00000 0.166667 0.151966 0.147004E-01 8.82024 18 1.00000 0.785398 0.884635 0.992368E-01 12.6352 19 1.00000 0.241265 0.243993 0.272767E-02 1.13057 24 1.00000 1.00000 0.869455 0.130545 13.0545 25 1.00000 1.08030 1.07122 0.907683E-02 0.840218 26 1.00000 0.154818 0.157802 0.298387E-02 1.92734 28 1.00000 0.859876 0.871112 0.112354E-01 1.30662 30 1.00000 0.959521 0.963057 0.353605E-02 0.368522 31 1.00000 0.841679 0.786623 0.550560E-01 6.54121 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 0.012217 0.027605 3.765531 9.051347 16 0.018764 0.038517 2.925862 6.354361 17 0.018481 0.052630 5.795895 12.900976 19 0.010493 0.033291 3.769710 14.473275 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 0.958195 0.418050E-01 4.18050 2 1.00000 0.500000 0.478358 0.216416E-01 4.32832 3 1.00000 0.250000 0.223870 0.261295E-01 10.4518 4 1.00000 0.166667 0.142171 0.244956E-01 14.6974 5 1.00000 0.111111 0.861053E-01 0.250058E-01 22.5052 6 1.00000 0.833333E-01 0.603188E-01 0.230145E-01 27.6174 7 1.00000 0.625000E-01 0.391381E-01 0.233619E-01 37.3790 8 1.00000 0.500000E-01 0.282595E-01 0.217405E-01 43.4811 9 1.00000 0.400000E-01 0.186452E-01 0.213548E-01 53.3869 10 1.00000 0.333333E-01 0.135906E-01 0.197428E-01 59.2283 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 6.28418 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:03.707 PM