August 26 2003 2:57:08.672 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 "halton_02_00100_weight_c.txt". 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. # halton_02_00100_weight_c.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 10:39:14.428 AM # # 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/halton/halton_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 1.16082 0.584984E-02 0.501415 2 1.00000 1.06667 1.02854 0.381231E-01 3.57404 4 1.00000 2.28571 2.13074 0.154978 6.78029 6 1.00000 1.00000 0.993526 0.647360E-02 0.647360 8 1.00000 0.500000 0.499309 0.691354E-03 0.138271 9 1.00000 1.68336 1.68134 0.202000E-02 0.119998 10 1.00000 0.500000 0.497892 0.210845E-02 0.421691 11 1.00000 2.95249 2.93659 0.159028E-01 0.538621 14 1.00000 -0.250000 -0.250056 0.560284E-04 0.224113E-01 15 1.00000 0.399576 0.401061 0.148460E-02 0.371544 16 1.00000 0.500000 0.497892 0.210845E-02 0.421691 17 1.00000 0.166667 0.164919 0.174753E-02 1.04852 18 1.00000 0.785398 0.797948 0.125498E-01 1.59788 19 1.00000 0.241265 0.240402 0.863090E-03 0.357735 24 1.00000 1.00000 0.993526 0.647360E-02 0.647360 25 1.00000 1.08030 1.07985 0.445604E-03 0.412484E-01 26 1.00000 0.154818 0.154913 0.945926E-04 0.610992E-01 28 1.00000 0.859876 0.861007 0.113052E-02 0.131475 30 1.00000 0.959521 0.959929 0.407457E-03 0.424646E-01 31 1.00000 0.841679 0.807370 0.343082E-01 4.07616 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 0.000903 0.002051 0.275638 0.642200 16 0.001763 0.002637 0.277660 0.492370 17 0.001733 0.003283 0.578549 1.128356 19 0.000955 0.002637 0.344842 0.926726 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 0.996381 0.361902E-02 0.361902 2 1.00000 0.500000 0.498878 0.112161E-02 0.224322 3 1.00000 0.250000 0.248822 0.117767E-02 0.471067 4 1.00000 0.166667 0.165086 0.158040E-02 0.948241 5 1.00000 0.111111 0.109294 0.181701E-02 1.63531 6 1.00000 0.833333E-01 0.813359E-01 0.199742E-02 2.39690 7 1.00000 0.625000E-01 0.604113E-01 0.208873E-02 3.34197 8 1.00000 0.500000E-01 0.477984E-01 0.220162E-02 4.40323 9 1.00000 0.400000E-01 0.377376E-01 0.226236E-02 5.65590 10 1.00000 0.333333E-01 0.309896E-01 0.234376E-02 7.03128 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 0.959082 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:08.727 PM