August 26 2003 2:44:49.968 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "cvt_02_01000.txt". The weight data will be read from "cvt_02_01000_weight_a.txt". The spatial dimension is 2 The number of points is 1000 # cvt_02_01000.txt # created by CVT_DATASET # at April 11 2003 12:32:28.499 PM # # Spatial dimension M = 2 # Number of points N = 1000 # # 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 = 0.020973 # The input data file has been read. # cvt_02_01000_weight_a.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 1:16:58.375 PM # # Spatial dimension M = 2 # Number of points N = 1000 # EPSILON (unit roundoff) = 0.119209E-06 # # Initial SEED = 123456789 # # The generator points were read from the file: "/home/r1/src-samples/datasets/cvt/cvt_02_01000.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 1.15686 0.980973E-02 0.840834 2 1.00000 1.06667 1.07698 0.103154E-01 0.967070 4 1.00000 2.28571 2.29352 0.780797E-02 0.341599 6 1.00000 1.00000 0.989989 0.100114E-01 1.00114 8 1.00000 0.500000 0.496478 0.352222E-02 0.704443 9 1.00000 1.68336 1.67872 0.463927E-02 0.275596 10 1.00000 0.500000 0.499160 0.840396E-03 0.168079 11 1.00000 2.95249 2.94184 0.106518E-01 0.360774 14 1.00000 -0.250000 -0.250927 0.927001E-03 0.370800 15 1.00000 0.399576 0.399490 0.861883E-04 0.215699E-01 16 1.00000 0.500000 0.499160 0.840396E-03 0.168079 17 1.00000 0.166667 0.166100 0.566185E-03 0.339711 18 1.00000 0.785398 0.792799 0.740069E-02 0.942285 19 1.00000 0.241265 0.239804 0.146092E-02 0.605527 24 1.00000 1.00000 0.989989 0.100114E-01 1.00114 25 1.00000 1.08030 1.07974 0.553608E-03 0.512460E-01 26 1.00000 0.154818 0.155330 0.511557E-03 0.330424 28 1.00000 0.859876 0.860213 0.336707E-03 0.391576E-01 30 1.00000 0.959521 0.959648 0.127196E-03 0.132562E-01 31 1.00000 0.841679 0.842540 0.861764E-03 0.102386 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 0.002047 0.004485 0.660125 1.600397 16 0.003620 0.006628 0.534250 0.968188 17 0.002743 0.006368 0.801376 1.485574 19 0.001928 0.004326 0.675802 1.508759 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 0.999998 0.166893E-05 0.166893E-03 2 1.00000 0.500000 0.499314 0.686407E-03 0.137281 3 1.00000 0.250000 0.248387 0.161293E-02 0.645173 4 1.00000 0.166667 0.165991 0.675529E-03 0.405318 5 1.00000 0.111111 0.109721 0.139039E-02 1.25135 6 1.00000 0.833333E-01 0.821421E-01 0.119127E-02 1.42952 7 1.00000 0.625000E-01 0.611139E-01 0.138606E-02 2.21769 8 1.00000 0.500000E-01 0.486503E-01 0.134968E-02 2.69936 9 1.00000 0.400000E-01 0.386545E-01 0.134546E-02 3.36366 10 1.00000 0.333333E-01 0.320019E-01 0.133142E-02 3.99424 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 0.471528 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:50.230 PM