August 26 2003 2:44:39.427 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "cvt_02_00010.txt". The weight data will be read from "cvt_02_00010_weight_c.txt". The spatial dimension is 2 The number of points is 10 # cvt_02_00010.txt # created by CVT_DATASET # at April 11 2003 12:04:56.303 PM # # Spatial dimension M = 2 # Number of points N = 10 # # 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 = 0.001501 # The input data file has been read. # cvt_02_00010_weight_c.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 1:11:07.784 PM # # Spatial dimension M = 2 # Number of points N = 10 # 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_00010.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 1.14874 0.179288E-01 1.53676 2 1.00000 1.06667 0.814052 0.252614 23.6826 4 1.00000 2.28571 1.37769 0.908027 39.7262 6 1.00000 1.00000 0.853926 0.146074 14.6074 8 1.00000 0.500000 0.500124 0.124216E-03 0.248432E-01 9 1.00000 1.68336 1.67941 0.395107E-02 0.234714 10 1.00000 0.500000 0.459251 0.407485E-01 8.14971 11 1.00000 2.95249 2.72414 0.228354 7.73429 14 1.00000 -0.250000 -0.250002 0.205636E-05 0.822544E-03 15 1.00000 0.399576 0.439622 0.400451E-01 10.0219 16 1.00000 0.500000 0.459251 0.407485E-01 8.14971 17 1.00000 0.166667 0.149610 0.170570E-01 10.2342 18 1.00000 0.785398 0.831464 0.460658E-01 5.86528 19 1.00000 0.241265 0.254137 0.128722E-01 5.33528 24 1.00000 1.00000 0.853926 0.146074 14.6074 25 1.00000 1.08030 1.07990 0.397682E-03 0.368124E-01 26 1.00000 0.154818 0.154515 0.303090E-03 0.195771 28 1.00000 0.859876 0.870192 0.103154E-01 1.19963 30 1.00000 0.959521 0.963469 0.394732E-02 0.411384 31 1.00000 0.841679 0.794219 0.474592E-01 5.63864 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 0.010655 0.040443 3.350676 13.432423 16 0.016732 0.047493 2.578663 6.923224 17 0.017051 0.017359 5.729681 9.944868 19 0.012500 0.067114 4.410595 21.907207 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 0.499736 0.264317E-03 0.528634E-01 3 1.00000 0.250000 0.249734 0.266388E-03 0.106555 4 1.00000 0.166667 0.161754 0.491273E-02 2.94764 5 1.00000 0.111111 0.104794 0.631752E-02 5.68577 6 1.00000 0.833333E-01 0.764146E-01 0.691877E-02 8.30253 7 1.00000 0.625000E-01 0.556123E-01 0.688766E-02 11.0203 8 1.00000 0.500000E-01 0.428838E-01 0.711616E-02 14.2323 9 1.00000 0.400000E-01 0.329847E-01 0.701532E-02 17.5383 10 1.00000 0.333333E-01 0.262257E-01 0.710761E-02 21.3228 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 7.22762 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:39.469 PM