12 August 2008 5:45:23.818 PM TEST_NINT_PRB FORTRAN90 version Test the routines in the TEST_NINT library. TEST01 GET_PROBLEM_NUM returns the number of problems. P00_NAME(#) returns the name for problem #. We use these two routines to print a directory of all the problems. The number of problems available is 32 1 "SquareSum". 2 "QuadSum". 3 "QuintSum". 4 "HexSum". 5 "ST04". 6 "DR4061". 7 "DR4062". 8 "RC01". 9 "Patterson #7". 10 "Patterson #4". 11 "Patterson #2, exp(sum(abs(X)))". 12 "BFN02". 13 "BFN03". 14 "BFN04". 15 "Partial product ( X(1:N) )". 16 "L1(X-Z)". 17 "L2(X-Z)^2". 18 "Disk". 19 "Sqrt-Prod". 20 "Sum^P". 21 "SphereMonomial". 22 "BallMonomial". 23 "SimplexMonomial". 24 "(|4X-2|+c)/(1+c)". 25 "Patterson #3, exp(c*X)". 26 "Patterson #1". 27 "Genz #1 / Patterson #5, Oscillatory". 28 "Genz #2 / Patterson #6, Product Peak". 29 "Genz #3 / Patterson #8, Corner Peak". 30 "Genz #4 / Patterson #9, Gaussian". 31 "Genz #5, Continuous". 32 "Genz #6, Discontinuous". TEST02 GET_PROBLEM_NUM returns the number of problems. P00_TITLE(#) prints the title for problem #. We use these two routines to print a directory of all the problems. The number of problems available is 32 Problem 01 Name: SquareSum Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( X(i) ) )^2 Problem 02 Name: QuadSum Davis, Rabinowitz, page 370, #1. Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( 2 * X(i) - 1 ) )^4 Problem 03 Name: QuintSum Davis, Rabinowitz, page 370, #3. Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( X(i) ) )^5 Problem 04 Name: HexSum Davis, Rabinowitz, page 370, #2. Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( 2 * X(i) - 1 ) )^6 Problem 05 Name: ST04 Stroud #4, page 26. Region: 0 <= X(i) <= 1 Integrand: F(X) = 1 / ( 1 + sum ( 2 * X(i) ) ) Problem 07 Name: DR4061 Davis, Rabinowitz, page 406, #1. Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( abs ( 4 * X(i) - 2 ) ) Problem 07 Name: DR4062 Davis, Rabinowitz, page 406, #2. Region: 0 <= X(i) <= 1 Integrand: F(X) = prod ( pi * sin ( pi * X(i) ) / 2 ) Problem 08 Name: RC01 Crandall, page 49, #1 Region: 0 <= X(i) <= 1 Integrand: F(X) = sin^2 ( pi/4 * sum ( X(i) ) ) Problem 09 Name: Patterson #7 Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( sum ( C(i) * X(i) ) ) Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Problem 10 Name: Patterson #4 Stroud, page ? Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( abs ( X(i) - 0.5 ) ) Problem 11 Name: Patterson #2, exp(sum(abs(X))) Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( sum ( abs ( X(i) ))) Problem 12 Name: BFN02 Bratley, Fox, Niederreiter, #2 Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( i * cos ( X(i) ) ) Problem 13 Name: BFN03 Bratley, Fox, Niederreiter, #3 Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( low order Chebyshevs ) Problem 14 Name: BFN04 Bratley, Fox, Niederreiter, #4 Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( -1^I * product(X(1:I)) ) Problem 15 Name: Partial product ( X(1:N) ) Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( X(1:N) ) Parameters: N, defaults to 1 Problem 16 Name: L1(X-Z) Lipschitz continuous. Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( | X(i) - Z(i) | ) Parameters: Z(1:DIM_NUM) defaults to (0.5,0.5,...) Problem 17 Name: L2(X-Z)^2 Zero at point Z. Radially symmetric. Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( ( X(i) - Z(i) )^2 ) Parameters: Z(1:DIM_NUM) defaults to (0.5,0.5,...) Problem 18 Name: Disk Disk of radius R centered at Z. Region: 0 <= X(i) <= 1 Integrand: F(X) = sphere interior characteristic Parameters: R, defaults to 0.5 Z(1:DIM_NUM) defaults to (0.5,0.5,...0.5) Problem 19 Name: Sqrt-Prod Region: 0 <= X(i) <= 1 Integrand: F(X) = prod ( sqrt ( | X(i) - Z(i) | ) ) Parameters: Z(1:DIM_NUM) defaults to (1/3,1/3,...,1/3) Problem 20 Name: Sum^P Region: A <= X(i) <= B Integrand: F(X) = ( sum ( X(i) ) )^p Parameters: A, defaults to 0.0. B, defaults to 1.0. P, defaults to 2.0. Problem 21 Name: SphereMonomial Region: Sphere surface, radius 1, center 0 Integrand: F(X) = C * product ( X(i)^E(i) ) Parameters: C, defaults to 1.0. E(1:DIM_NUM) defaults to 2. Problem 22 Name: BallMonomial Region: Sphere interior, radius R, center 0 Integrand: F(X) = C * product ( X(i)^E(i) ) Parameters: C, defaults to 1.0. R, defaults to 1.0. E(1:DIM_NUM) defaults to 2. Problem 23 Name: SimplexMonomial Region: Interior of unit simplex Integrand: F(X) = C * product ( X(i)^E(i) ) Parameters: C, defaults to 1.0. E(1:DIM_NUM) defaults to 2. Problem 24 Name: (|4X-2|+C)/(1+C) Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( ( |4*X(i)-2| + C(i) ) / ( 1 + C(i) ) ) Parameters: C(1:DIM_NUM) defaults to 0.0 Problem 25 Name: Patterson #3, exp(c*X) Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( C * product ( X(i) ) ) Parameters: C, defaults to 0.3. Problem 26 Name: Patterson #1 Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( C(i) * exp ( - C(i) * X(i) ) ) Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Problem 27 Name: Genz #1 / Patterson #5, Oscillatory Region: 0 <= X(i) <= 1 Integrand: F(X) = cos ( 2 * pi * R + sum ( C(i) * X(i) ) ) Parameters: R, defaults to 0.3 C(1:DIM_NUM) defaults to 1/DIM_NUM Problem 28 Name: Genz #2 / Patterson #6, Product Peak Region: 0 <= X(i) <= 1 Integrand: F(X) = 1 / product ( C(i)^2 + ( X(i) - Z(i) )^2 ) Parameters: C(1:DIM_NUM) defaults to DIM_NUM^(9/4)/sqrt(170) Z(1:DIM_NUM) defaults to 0.5. Problem 29 Name: Genz #3 / Patterson #8, Corner Peak Region: 0 <= X(i) <= 1 Integrand: F(X) = 1 / ( 1 + sum( C(i) * X(i) ) )^R Parameters: R, defaults to 0.3 C(1:DIM_NUM) defaults to 1/DIM_NUM. Problem 30 Name: Genz #4 / Patterson #9, Gaussian Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( - sum ( C(i)^2 * ( X(i) - Z(i) )^2 ) Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Z(1:DIM_NUM) defaults to 0.5. Problem 31 Name: Genz #5, Continuous Nondifferentiable peak at point Z. Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( -sum ( C(i) * | X(i) - Z(i) | )) Parameters: C(1:DIM_NUM) defaults to 2.0; Z(1:DIM_NUM) defaults to 0.5; Problem 32 Name: Genz #6, Discontinuous Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( C(i) * X(i) ) if X <= Z, 0 otherwise. Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Z(1:DIM_NUM) defaults to 0.5. TEST03 Use a simple product rule on box regions. Use a fixed spatial dimension. Prob Dim Subs Approx Exact Error 1 3 1 2.50000 2.50000 0.444089E-15 1 3 3 2.50000 2.50000 0.754952E-14 1 3 5 2.50000 2.50000 0.133227E-14 2 3 1 2.60000 2.60000 0.444089E-15 2 3 3 2.60000 2.60000 0.226485E-13 2 3 5 2.60000 2.60000 0.142553E-12 3 3 1 -0.197065E-14 0.00000 0.197065E-14 3 3 3 -0.922102E-14 0.00000 0.922102E-14 3 3 5 -0.354294E-14 0.00000 0.354294E-14 4 3 1 9.76190 9.76190 0.888178E-14 4 3 3 9.76190 9.76190 0.497380E-13 4 3 5 9.76190 9.76190 0.113687E-12 5 3 1 2.15214 2.15214 0.315880E-06 5 3 3 2.15214 2.15214 0.478373E-10 5 3 5 2.15214 2.15214 0.453415E-12 6 3 1 0.843508 1.00000 0.156492 6 3 3 0.981729 1.00000 0.182708E-01 6 3 5 0.993397 1.00000 0.660336E-02 7 3 1 1.00000 1.00000 0.165427E-06 7 3 3 1.00000 1.00000 0.194289E-11 7 3 5 1.00000 1.00000 0.266454E-13 8 3 1 0.758012 0.758012 0.306248E-10 8 3 3 0.758012 0.758012 0.455191E-14 8 3 5 0.758012 0.758012 0.177636E-13 9 3 1 1.67176 1.67176 0.444089E-15 9 3 3 1.67176 1.67176 0.133227E-14 9 3 5 1.67176 1.67176 0.479616E-13 10 3 1 0.708638 0.750000 0.413622E-01 10 3 3 0.745404 0.750000 0.459580E-02 10 3 5 0.748346 0.750000 0.165449E-02 11 3 1 4.83433 5.07321 0.238888 11 3 3 5.04614 5.07321 0.270711E-01 11 3 5 5.06345 5.07321 0.976102E-02 12 3 1 0.107978 0.107978 0.366118E-08 12 3 3 0.107978 0.107978 0.451167E-13 12 3 5 0.107978 0.107978 0.117961E-14 13 3 1 0.769784E-16 0.00000 0.769784E-16 13 3 3 -0.102397E-15 0.00000 0.102397E-15 13 3 5 0.721824E-15 0.00000 0.721824E-15 14 3 1 -0.375000 -0.375000 0.111022E-15 14 3 3 -0.375000 -0.375000 0.499600E-15 14 3 5 -0.375000 -0.375000 0.432987E-14 15 3 1 0.833333E-01 0.833333E-01 0.277556E-16 15 3 3 0.833333E-01 0.833333E-01 0.416334E-16 15 3 5 0.833333E-01 0.833333E-01 0.111022E-15 16 3 1 0.708638 0.750000 0.413622E-01 16 3 3 0.745404 0.750000 0.459580E-02 16 3 5 0.748346 0.750000 0.165449E-02 17 3 1 0.250000 0.250000 0.00000 17 3 3 0.250000 0.250000 0.333067E-15 17 3 5 0.250000 0.250000 0.449640E-14 18 3 1 0.501831 0.523599 0.217678E-01 18 3 3 0.538509 0.523599 0.149100E-01 18 3 5 0.531268 0.523599 0.766915E-02 19 3 1 0.130655 0.118506 0.121487E-01 19 3 3 0.118682 0.118506 0.175632E-03 19 3 5 0.119561 0.118506 0.105459E-02 20 3 1 2.50000 2.50000 0.444089E-15 20 3 3 2.50000 2.50000 0.754952E-14 20 3 5 2.50000 2.50000 0.133227E-14 24 3 1 0.843508 1.00000 0.156492 24 3 3 0.981729 1.00000 0.182708E-01 24 3 5 0.993397 1.00000 0.660336E-02 25 3 1 1.03924 1.03924 0.00000 25 3 3 1.03924 1.03924 0.133227E-14 25 3 5 1.03924 1.03924 0.333067E-14 26 3 1 0.227780E-01 0.227780E-01 0.104083E-16 26 3 3 0.227780E-01 0.227780E-01 0.104083E-16 26 3 5 0.227780E-01 0.227780E-01 0.457967E-15 27 3 1 -0.717110 -0.717110 0.111022E-15 27 3 3 -0.717110 -0.717110 0.333067E-15 27 3 5 -0.717110 -0.717110 0.355271E-14 28 3 1 0.797361 0.797359 0.197503E-05 28 3 3 0.797359 0.797359 0.137879E-11 28 3 5 0.797359 0.797359 0.182077E-13 29 3 1 0.287607 0.287607 0.822067E-10 29 3 3 0.287607 0.287607 0.743849E-14 29 3 5 0.287607 0.287607 0.660583E-14 30 3 1 0.972704 0.972704 0.589084E-12 30 3 3 0.972704 0.972704 0.388578E-14 30 3 5 0.972704 0.972704 0.555112E-15 31 3 1 0.286876 0.252580 0.342960E-01 31 3 3 0.256268 0.252580 0.368801E-02 31 3 5 0.253905 0.252580 0.132417E-02 32 3 1 2.06810 1.35153 0.716572 32 3 3 1.29697 1.35153 0.545545E-01 32 3 5 1.39548 1.35153 0.439507E-01 TEST04 Use a Monte Carlo rule on box regions. Use a fixed spatial dimension. Repeatedly multiply the number of points by 16. Prob Dim Points Approx Exact Error 1 3 1 1.35235 2.50000 1.14765 1 3 16 1.87331 2.50000 0.626686 1 3 256 2.35297 2.50000 0.147029 1 3 4096 2.46314 2.50000 0.368552E-01 1 3 65536 2.49418 2.50000 0.582490E-02 2 3 1 0.206599 2.60000 2.39340 2 3 16 1.37111 2.60000 1.22889 2 3 256 2.64084 2.60000 0.408358E-01 2 3 4096 2.42224 2.60000 0.177758 2 3 65536 2.61799 2.60000 0.179944E-01 3 3 1 -0.139287 0.00000 0.139287 3 3 16 -1.56742 0.00000 1.56742 3 3 256 -1.65872 0.00000 1.65872 3 3 4096 -0.121269 0.00000 0.121269 3 3 65536 -0.946982E-01 0.00000 0.946982E-01 4 3 1 0.939056E-01 9.76190 9.66800 4 3 16 2.68402 9.76190 7.07789 4 3 256 10.1655 9.76190 0.403546 4 3 4096 8.72314 9.76190 1.03876 4 3 65536 9.89633 9.76190 0.134428 5 3 1 2.40543 2.15214 0.253286 5 3 16 2.34091 2.15214 0.188764 5 3 256 2.22047 2.15214 0.683300E-01 5 3 4096 2.15793 2.15214 0.578634E-02 5 3 65536 2.15530 2.15214 0.315490E-02 6 3 1 1.56695 1.00000 0.566951 6 3 16 0.894436 1.00000 0.105564 6 3 256 0.910032 1.00000 0.899675E-01 6 3 4096 0.978412 1.00000 0.215883E-01 6 3 65536 0.998756 1.00000 0.124443E-02 7 3 1 0.960367E-01 1.00000 0.903963 7 3 16 1.07681 1.00000 0.768064E-01 7 3 256 1.04651 1.00000 0.465133E-01 7 3 4096 1.01574 1.00000 0.157424E-01 7 3 65536 0.998635 1.00000 0.136514E-02 8 3 1 0.626554 0.758012 0.131459 8 3 16 0.680048 0.758012 0.779643E-01 8 3 256 0.739658 0.758012 0.183538E-01 8 3 4096 0.755785 0.758012 0.222719E-02 8 3 65536 0.757446 0.758012 0.565833E-03 9 3 1 1.47349 1.67176 0.198266 9 3 16 1.55948 1.67176 0.112282 9 3 256 1.64415 1.67176 0.276064E-01 9 3 4096 1.66559 1.67176 0.616638E-02 9 3 65536 1.67066 1.67176 0.109850E-02 10 3 1 0.957111 0.750000 0.207111 10 3 16 0.736981 0.750000 0.130185E-01 10 3 256 0.732635 0.750000 0.173646E-01 10 3 4096 0.746003 0.750000 0.399695E-02 10 3 65536 0.750335 0.750000 0.335111E-03 11 3 1 6.78166 5.07321 1.70845 11 3 16 4.97377 5.07321 0.994402E-01 11 3 256 4.89893 5.07321 0.174288 11 3 4096 5.02552 5.07321 0.476932E-01 11 3 65536 5.07400 5.07321 0.788616E-03 12 3 1 -0.156896 0.107978 0.264873 12 3 16 0.409110 0.107978 0.301133 12 3 256 0.138670 0.107978 0.306927E-01 12 3 4096 0.864920E-01 0.107978 0.214856E-01 12 3 65536 0.104032 0.107978 0.394554E-02 13 3 1 -0.326496 0.00000 0.326496 13 3 16 -0.114433 0.00000 0.114433 13 3 256 0.190695 0.00000 0.190695 13 3 4096 -0.723087E-02 0.00000 0.723087E-02 13 3 65536 0.417571E-02 0.00000 0.417571E-02 14 3 1 -0.745586E-02 -0.375000 0.367544 14 3 16 -0.289459 -0.375000 0.855411E-01 14 3 256 -0.359688 -0.375000 0.153119E-01 14 3 4096 -0.369182 -0.375000 0.581830E-02 14 3 65536 -0.373913 -0.375000 0.108698E-02 15 3 1 0.708057E-04 0.833333E-01 0.832625E-01 15 3 16 0.377175E-01 0.833333E-01 0.456159E-01 15 3 256 0.737390E-01 0.833333E-01 0.959432E-02 15 3 4096 0.807121E-01 0.833333E-01 0.262124E-02 15 3 65536 0.828995E-01 0.833333E-01 0.433848E-03 16 3 1 0.957111 0.750000 0.207111 16 3 16 0.736981 0.750000 0.130185E-01 16 3 256 0.732635 0.750000 0.173646E-01 16 3 4096 0.746003 0.750000 0.399695E-02 16 3 65536 0.750335 0.750000 0.335111E-03 17 3 1 0.356893 0.250000 0.106893 17 3 16 0.247543 0.250000 0.245678E-02 17 3 256 0.242365 0.250000 0.763479E-02 17 3 4096 0.247614 0.250000 0.238580E-02 17 3 65536 0.250155 0.250000 0.155022E-03 18 3 1 0.00000 0.523599 0.523599 18 3 16 0.562500 0.523599 0.389012E-01 18 3 256 0.570313 0.523599 0.467137E-01 18 3 4096 0.526611 0.523599 0.301255E-02 18 3 65536 0.521484 0.523599 0.211440E-02 19 3 1 0.228508E-01 0.118506 0.956556E-01 19 3 16 0.954622E-01 0.118506 0.230441E-01 19 3 256 0.108245 0.118506 0.102616E-01 19 3 4096 0.115624 0.118506 0.288230E-02 19 3 65536 0.118458 0.118506 0.485371E-04 20 3 1 1.35235 2.50000 1.14765 20 3 16 1.87331 2.50000 0.626686 20 3 256 2.35297 2.50000 0.147029 20 3 4096 2.46314 2.50000 0.368552E-01 20 3 65536 2.49418 2.50000 0.582490E-02 24 3 1 1.56695 1.00000 0.566951 24 3 16 0.894436 1.00000 0.105564 24 3 256 0.910032 1.00000 0.899675E-01 24 3 4096 0.978412 1.00000 0.215883E-01 24 3 65536 0.998756 1.00000 0.124443E-02 25 3 1 1.00132 1.03924 0.379204E-01 25 3 16 1.02142 1.03924 0.178201E-01 25 3 256 1.03563 1.03924 0.361246E-02 25 3 4096 1.03813 1.03924 0.111291E-02 25 3 65536 1.03908 1.03924 0.162376E-03 26 3 1 0.251356E-01 0.227780E-01 0.235757E-02 26 3 16 0.242094E-01 0.227780E-01 0.143146E-02 26 3 256 0.231589E-01 0.227780E-01 0.380888E-03 26 3 4096 0.228441E-01 0.227780E-01 0.661075E-04 26 3 65536 0.227932E-01 0.227780E-01 0.151984E-04 27 3 1 -0.645589 -0.717110 0.715209E-01 27 3 16 -0.674194 -0.717110 0.429162E-01 27 3 256 -0.705884 -0.717110 0.112261E-01 27 3 4096 -0.715142 -0.717110 0.196821E-02 27 3 65536 -0.716667 -0.717110 0.443249E-03 28 3 1 0.720050 0.797359 0.773093E-01 28 3 16 0.800335 0.797359 0.297595E-02 28 3 256 0.802901 0.797359 0.554151E-02 28 3 4096 0.799039 0.797359 0.167989E-02 28 3 65536 0.797232 0.797359 0.127093E-03 29 3 1 0.339228 0.287607 0.516210E-01 29 3 16 0.324231 0.287607 0.366240E-01 29 3 256 0.299381 0.287607 0.117736E-01 29 3 4096 0.288908 0.287607 0.130071E-02 29 3 65536 0.288112 0.287607 0.505026E-03 30 3 1 0.961121 0.972704 0.115832E-01 30 3 16 0.972987 0.972704 0.283017E-03 30 3 256 0.973529 0.972704 0.824947E-03 30 3 4096 0.972961 0.972704 0.257074E-03 30 3 65536 0.972687 0.972704 0.169928E-04 31 3 1 0.147456 0.252580 0.105124 31 3 16 0.258001 0.252580 0.542078E-02 31 3 256 0.259989 0.252580 0.740878E-02 31 3 4096 0.254030 0.252580 0.144952E-02 31 3 65536 0.252302 0.252580 0.278733E-03 32 3 1 0.00000 1.35153 1.35153 32 3 16 2.11020 1.35153 0.758674 32 3 256 1.47110 1.35153 0.119575 32 3 4096 1.36116 1.35153 0.962710E-02 32 3 65536 1.34896 1.35153 0.256667E-02 TEST05 Demonstrate problems that use a "base point" by moving the base point around. Use a Monte Carlo rule on box regions. Use a fixed spatial dimension. Problem number = 16 Run number 1 Basis point Z = 0.9571 0.9352 Prob Dim Points Approx Exact Error 16 2 10 0.993653 0.898343 0.953107E-01 16 2 1000 0.898769 0.898343 0.426003E-03 16 2 100000 0.898849 0.898343 0.506313E-03 Run number 2 Basis point Z = 0.1959 0.1788 Prob Dim Points Approx Exact Error 16 2 10 0.744480 0.695653 0.488272E-01 16 2 1000 0.688970 0.695653 0.668335E-02 16 2 100000 0.695751 0.695653 0.977319E-04 Run number 3 Basis point Z = 0.0918 0.9687 Prob Dim Points Approx Exact Error 16 2 10 0.862028 0.886329 0.243011E-01 16 2 1000 0.883626 0.886329 0.270317E-02 16 2 100000 0.886044 0.886329 0.285256E-03 Problem number = 17 Run number 1 Basis point Z = 0.6367 0.1665 Prob Dim Points Approx Exact Error 17 2 10 0.330243 0.296580 0.336635E-01 17 2 1000 0.290950 0.296580 0.562973E-02 17 2 100000 0.295671 0.296580 0.908404E-03 Run number 2 Basis point Z = 0.0534 0.2132 Prob Dim Points Approx Exact Error 17 2 10 0.387597 0.448389 0.607922E-01 17 2 1000 0.455837 0.448389 0.744751E-02 17 2 100000 0.448189 0.448389 0.199875E-03 Run number 3 Basis point Z = 0.9204 0.0142 Prob Dim Points Approx Exact Error 17 2 10 0.646630 0.579453 0.671770E-01 17 2 1000 0.597896 0.579453 0.184430E-01 17 2 100000 0.580542 0.579453 0.108832E-02 Problem number = 18 Run number 1 Basis point Z = 0.8962 0.0923 Prob Dim Points Approx Exact Error 18 2 10 0.300000 0.785398 0.485398 18 2 1000 0.338000 0.785398 0.447398 18 2 100000 0.304830 0.785398 0.480568 Run number 2 Basis point Z = 0.7357 0.6399 Prob Dim Points Approx Exact Error 18 2 10 0.500000 0.785398 0.285398 18 2 1000 0.609000 0.785398 0.176398 18 2 100000 0.580340 0.785398 0.205058 Run number 3 Basis point Z = 0.6558 0.4055 Prob Dim Points Approx Exact Error 18 2 10 0.600000 0.785398 0.185398 18 2 1000 0.688000 0.785398 0.973982E-01 18 2 100000 0.670930 0.785398 0.114468 Problem number = 19 Run number 1 Basis point Z = 0.2594 0.5231 Prob Dim Points Approx Exact Error 19 2 10 0.260424 0.242009 0.184148E-01 19 2 1000 0.244268 0.242009 0.225932E-02 19 2 100000 0.241858 0.242009 0.151028E-03 Run number 2 Basis point Z = 0.1394 0.6593 Prob Dim Points Approx Exact Error 19 2 10 0.359765 0.277505 0.822599E-01 19 2 1000 0.275868 0.277505 0.163738E-02 19 2 100000 0.277787 0.277505 0.281917E-03 Run number 3 Basis point Z = 0.0265 0.8779 Prob Dim Points Approx Exact Error 19 2 10 0.224671 0.370999 0.146328 19 2 1000 0.371206 0.370999 0.207623E-03 19 2 100000 0.371288 0.370999 0.289029E-03 Problem number = 31 Run number 1 Basis point Z = 0.8937 0.1204 Prob Dim Points Approx Exact Error 31 2 10 0.290096 0.266739 0.233570E-01 31 2 1000 0.260932 0.266739 0.580664E-02 31 2 100000 0.267404 0.266739 0.665482E-03 Run number 2 Basis point Z = 0.5357 0.2670 Prob Dim Points Approx Exact Error 31 2 10 0.418436 0.373314 0.451224E-01 31 2 1000 0.367671 0.373314 0.564285E-02 31 2 100000 0.373205 0.373314 0.108791E-03 Run number 3 Basis point Z = 0.0819 0.5277 Prob Dim Points Approx Exact Error 31 2 10 0.321622 0.313164 0.845833E-02 31 2 1000 0.300570 0.313164 0.125938E-01 31 2 100000 0.313921 0.313164 0.757094E-03 TEST06 Use a simple product rule on a box region. Use a fixed problem; Let the spatial dimension increase. Prob Dim Subs Approx Exact Error Calls 6 1 1 0.944850 1.00000 0.055150 5 6 1 3 0.993872 1.00000 0.006128 15 6 1 5 0.997794 1.00000 0.002206 25 6 2 1 0.892742 1.00000 0.107258 25 6 2 3 0.987782 1.00000 0.012218 225 6 2 5 0.995593 1.00000 0.004407 625 6 3 1 0.843508 1.00000 0.156492 125 6 3 3 0.981729 1.00000 0.018271 3375 6 3 5 0.993397 1.00000 0.006603 15625 6 4 1 0.796989 1.00000 0.203011 625 6 4 3 0.975713 1.00000 0.024287 50625 6 4 5 0.991205 1.00000 0.008795 390625 6 5 1 0.753035 1.00000 0.246965 3125 6 5 3 0.969735 1.00000 0.030265 759375 6 5 5 0.989019 1.00000 0.010981 9765625 6 6 1 0.711506 1.00000 0.288494 15625 6 6 3 0.963792 1.00000 0.036208 11390625 6 6 5 0.986837 1.00000 0.013163 244140625 TEST_NINT_PRB Normal end of execution. 12 August 2008 5:49:17.042 PM