August 26 2003 2:57:08.356 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 "". 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. 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 1.11417 0.525012E-01 4.50010 2 1.00000 1.06667 1.10139 0.347229E-01 3.25527 4 1.00000 2.28571 2.45249 0.166773 7.29631 6 1.00000 1.00000 1.01477 0.147736E-01 1.47736 8 1.00000 0.500000 0.483750 0.162504E-01 3.25008 9 1.00000 1.68336 1.66098 0.223773E-01 1.32932 10 1.00000 0.500000 0.501852 0.185186E-02 0.370371 11 1.00000 2.95249 2.97027 0.177760E-01 0.602068 14 1.00000 -0.250000 -0.251966 0.196561E-02 0.786245 15 1.00000 0.399576 0.399288 0.288039E-03 0.720862E-01 16 1.00000 0.500000 0.501852 0.185186E-02 0.370371 17 1.00000 0.166667 0.167929 0.126192E-02 0.757152 18 1.00000 0.785398 0.790000 0.460136E-02 0.585863 19 1.00000 0.241265 0.239160 0.210476E-02 0.872384 24 1.00000 1.00000 1.01477 0.147736E-01 1.47736 25 1.00000 1.08030 1.07577 0.452554E-02 0.418917 26 1.00000 0.154818 0.156913 0.209440E-02 1.35282 28 1.00000 0.859876 0.859016 0.860810E-03 0.100109 30 1.00000 0.959521 0.959228 0.292897E-03 0.305253E-01 31 1.00000 0.841679 0.821450 0.202290E-01 2.40341 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 0.004401 0.009861 1.452543 4.195054 16 0.009486 0.023407 1.395631 2.723636 17 0.009119 0.022665 2.745150 5.037282 19 0.004337 0.013188 1.485295 3.548720 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 0.989999 0.100006E-01 1.00006 2 1.00000 0.500000 0.488437 0.115627E-01 2.31254 3 1.00000 0.250000 0.236472 0.135282E-01 5.41129 4 1.00000 0.166667 0.155395 0.112720E-01 6.76323 5 1.00000 0.111111 0.101522 0.958908E-02 8.63017 6 1.00000 0.833333E-01 0.750777E-01 0.825562E-02 9.90674 7 1.00000 0.625000E-01 0.551027E-01 0.739728E-02 11.8356 8 1.00000 0.500000E-01 0.434826E-01 0.651741E-02 13.0348 9 1.00000 0.400000E-01 0.338907E-01 0.610929E-02 15.2732 10 1.00000 0.333333E-01 0.278482E-01 0.548515E-02 16.4555 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 1.59945 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:08.417 PM