August 26 2003 2:44:44.867 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "cvt_02_00100.txt". The weight data will be read from "cvt_02_00100_weight_c.txt". The spatial dimension is 2 The number of points is 100 # cvt_02_00100.txt # created by CVT_DATASET # at April 11 2003 12:10:57.078 PM # # Spatial dimension M = 2 # Number of points N = 100 # # Initial SEED = 123456789 # Initialization by UNIFORM. # Sampling by UNIFORM. # Number of sample points = 500000 # Number of sampling iterations = 100 # L2 norm of dataset change on last step = 0.007545 # The input data file has been read. # cvt_02_00100_weight_c.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 1:12:23.150 PM # # Spatial dimension M = 2 # Number of points N = 100 # EPSILON (unit roundoff) = 0.119209E-06 # # Initial SEED = 987654321 # # The generator points were read from the file: "/home/r1/src-samples/datasets/cvt/cvt_02_00100.txt". # Sampling by UNIFORM. # 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 1.16454 0.212729E-02 0.182339 2 1.00000 1.06667 1.03772 0.289465E-01 2.71374 4 1.00000 2.28571 2.17430 0.111410 4.87419 6 1.00000 1.00000 0.990695 0.930482E-02 0.930482 8 1.00000 0.500000 0.499960 0.399649E-04 0.799298E-02 9 1.00000 1.68336 1.68286 0.496268E-03 0.294809E-01 10 1.00000 0.500000 0.497577 0.242326E-02 0.484651 11 1.00000 2.95249 2.93362 0.188737E-01 0.639246 14 1.00000 -0.250000 -0.249958 0.424385E-04 0.169754E-01 15 1.00000 0.399576 0.401235 0.165901E-02 0.415191 16 1.00000 0.500000 0.497577 0.242326E-02 0.484651 17 1.00000 0.166667 0.164841 0.182582E-02 1.09549 18 1.00000 0.785398 0.789112 0.371379E-02 0.472854 19 1.00000 0.241265 0.240621 0.644162E-03 0.266994 24 1.00000 1.00000 0.990695 0.930482E-02 0.930482 25 1.00000 1.08030 1.08023 0.666380E-04 0.616850E-02 26 1.00000 0.154818 0.154790 0.282228E-04 0.182296E-01 28 1.00000 0.859876 0.860989 0.111234E-02 0.129361 30 1.00000 0.959521 0.959943 0.421524E-03 0.439307E-01 31 1.00000 0.841679 0.906802 0.651236E-01 7.73734 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 0.000960 0.002353 0.301345 0.841394 16 0.001845 0.003033 0.287322 0.470230 17 0.001820 0.001978 0.611648 1.073103 19 0.001298 0.004886 0.447460 1.575624 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 1.00000 0.00000 0.00000 2 1.00000 0.500000 0.499861 0.139207E-03 0.278413E-01 3 1.00000 0.250000 0.249903 0.967085E-04 0.386834E-01 4 1.00000 0.166667 0.166123 0.544041E-03 0.326425 5 1.00000 0.111111 0.110363 0.748262E-03 0.673436 6 1.00000 0.833333E-01 0.825314E-01 0.801921E-03 0.962305 7 1.00000 0.625000E-01 0.616869E-01 0.813112E-03 1.30098 8 1.00000 0.500000E-01 0.491664E-01 0.833634E-03 1.66727 9 1.00000 0.400000E-01 0.391636E-01 0.836376E-03 2.09094 10 1.00000 0.333333E-01 0.324885E-01 0.844847E-03 2.53454 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 0.963649 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:44.916 PM