30-Mar-2019 17:13:31 test_nint_test MATLAB version Test test_nint. 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, C0 Pseudo-Gaussian"; 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) = prod ( (|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, C0 Pseudo-Gaussian 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 2.500000 2.500000 0.000000 1 3 3 2.500000 2.500000 0.000000 1 3 5 2.500000 2.500000 0.000000 2 3 1 2.600000 2.600000 0.000000 2 3 3 2.600000 2.600000 0.000000 2 3 5 2.600000 2.600000 0.000000 3 3 1 -0.000000 0.000000 0.000000 3 3 3 -0.000000 0.000000 0.000000 3 3 5 -0.000000 0.000000 0.000000 4 3 1 9.761905 9.761905 0.000000 4 3 3 9.761905 9.761905 0.000000 4 3 5 9.761905 9.761905 0.000000 5 3 1 2.152143 2.152143 0.000000 5 3 3 2.152143 2.152143 0.000000 5 3 5 2.152143 2.152143 0.000000 6 3 1 0.843508 1.000000 0.156492 6 3 3 0.981729 1.000000 0.018271 6 3 5 0.993397 1.000000 0.006603 7 3 1 1.000000 1.000000 0.000000 7 3 3 1.000000 1.000000 0.000000 7 3 5 1.000000 1.000000 0.000000 8 3 1 0.758012 0.758012 0.000000 8 3 3 0.758012 0.758012 0.000000 8 3 5 0.758012 0.758012 0.000000 9 3 1 1.671758 1.671758 0.000000 9 3 3 1.671758 1.671758 0.000000 9 3 5 1.671758 1.671758 0.000000 10 3 1 0.708638 0.750000 0.041362 10 3 3 0.745404 0.750000 0.004596 10 3 5 0.748346 0.750000 0.001654 11 3 1 4.834326 5.073214 0.238888 11 3 3 5.046143 5.073214 0.027071 11 3 5 5.063453 5.073214 0.009761 12 3 1 0.107978 0.107978 0.000000 12 3 3 0.107978 0.107978 0.000000 12 3 5 0.107978 0.107978 0.000000 13 3 1 0.000000 0.000000 0.000000 13 3 3 -0.000000 0.000000 0.000000 13 3 5 0.000000 0.000000 0.000000 14 3 1 -0.375000 -0.375000 0.000000 14 3 3 -0.375000 -0.375000 0.000000 14 3 5 -0.375000 -0.375000 0.000000 15 3 1 0.083333 0.083333 0.000000 15 3 3 0.083333 0.083333 0.000000 15 3 5 0.083333 0.083333 0.000000 16 3 1 0.708638 0.750000 0.041362 16 3 3 0.745404 0.750000 0.004596 16 3 5 0.748346 0.750000 0.001654 17 3 1 0.250000 0.250000 0.000000 17 3 3 0.250000 0.250000 0.000000 17 3 5 0.250000 0.250000 0.000000 18 3 1 0.501831 0.523599 0.021768 18 3 3 0.538509 0.523599 0.014910 18 3 5 0.531268 0.523599 0.007669 19 3 1 0.130655 0.118506 0.012149 19 3 3 0.118682 0.118506 0.000176 19 3 5 0.119561 0.118506 0.001055 20 3 1 2.500000 2.500000 0.000000 20 3 3 2.500000 2.500000 0.000000 20 3 5 2.500000 2.500000 0.000000 24 3 1 0.843508 1.000000 0.156492 24 3 3 0.981729 1.000000 0.018271 24 3 5 0.993397 1.000000 0.006603 25 3 1 1.039240 1.039240 0.000000 25 3 3 1.039240 1.039240 0.000000 25 3 5 1.039240 1.039240 0.000000 26 3 1 0.022778 0.022778 0.000000 26 3 3 0.022778 0.022778 0.000000 26 3 5 0.022778 0.022778 0.000000 27 3 1 -0.717110 -0.717110 0.000000 27 3 3 -0.717110 -0.717110 0.000000 27 3 5 -0.717110 -0.717110 0.000000 28 3 1 0.797361 0.797359 0.000002 28 3 3 0.797359 0.797359 0.000000 28 3 5 0.797359 0.797359 0.000000 29 3 1 0.287607 0.287607 0.000000 29 3 3 0.287607 0.287607 0.000000 29 3 5 0.287607 0.287607 0.000000 30 3 1 0.972704 0.972704 0.000000 30 3 3 0.972704 0.972704 0.000000 30 3 5 0.972704 0.972704 0.000000 31 3 1 0.286876 0.252580 0.034296 31 3 3 0.256268 0.252580 0.003688 31 3 5 0.253905 0.252580 0.001324 32 3 1 2.068101 1.351529 0.716572 32 3 3 1.296975 1.351529 0.054555 32 3 5 1.395480 1.351529 0.043951 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 4.738306 2.500000 2.238306 1 3 16 2.333167 2.500000 0.166833 1 3 256 2.411636 2.500000 0.088364 1 3 4096 2.503311 2.500000 0.003311 1 3 65536 2.489950 2.500000 0.010050 2 3 1 3.356382 2.600000 0.756382 2 3 16 2.649185 2.600000 0.049185 2 3 256 2.646058 2.600000 0.046058 2 3 4096 2.685483 2.600000 0.085483 2 3 65536 2.570220 2.600000 0.029780 3 3 1 4.542964 0.000000 4.542964 3 3 16 0.387068 0.000000 0.387068 3 3 256 -0.603234 0.000000 0.603234 3 3 4096 0.182542 0.000000 0.182542 3 3 65536 -0.036307 0.000000 0.036307 4 3 1 6.149037 9.761905 3.612867 4 3 16 8.177445 9.761905 1.584460 4 3 256 10.576972 9.761905 0.815067 4 3 4096 10.178562 9.761905 0.416658 4 3 65536 9.587000 9.761905 0.174905 5 3 1 1.494341 2.152143 0.657802 5 3 16 2.220892 2.152143 0.068749 5 3 256 2.179803 2.152143 0.027660 5 3 4096 2.156061 2.152143 0.003918 5 3 65536 2.154190 2.152143 0.002047 6 3 1 0.188293 1.000000 0.811707 6 3 16 0.575097 1.000000 0.424903 6 3 256 0.844929 1.000000 0.155071 6 3 4096 0.993615 1.000000 0.006385 6 3 65536 0.984073 1.000000 0.015927 7 3 1 0.074372 1.000000 0.925628 7 3 16 1.209017 1.000000 0.209017 7 3 256 1.027181 1.000000 0.027181 7 3 4096 0.985171 1.000000 0.014829 7 3 65536 1.007163 1.000000 0.007163 8 3 1 0.980850 0.758012 0.222837 8 3 16 0.715272 0.758012 0.042740 8 3 256 0.750944 0.758012 0.007068 8 3 4096 0.754731 0.758012 0.003282 8 3 65536 0.757248 0.758012 0.000765 9 3 1 2.065946 1.671758 0.394188 9 3 16 1.639449 1.671758 0.032310 9 3 256 1.656364 1.671758 0.015395 9 3 4096 1.671820 1.671758 0.000062 9 3 65536 1.670051 1.671758 0.001707 10 3 1 0.676765 0.750000 0.073235 10 3 16 0.674002 0.750000 0.075998 10 3 256 0.728122 0.750000 0.021878 10 3 4096 0.751583 0.750000 0.001583 10 3 65536 0.747283 0.750000 0.002717 11 3 1 3.871066 5.073214 1.202148 11 3 16 4.168932 5.073214 0.904282 11 3 256 4.769223 5.073214 0.303991 11 3 4096 5.068655 5.073214 0.004559 11 3 65536 5.039460 5.073214 0.033754 12 3 1 -2.217899 0.107978 2.325876 12 3 16 0.613654 0.107978 0.505676 12 3 256 0.189021 0.107978 0.081043 12 3 4096 0.141975 0.107978 0.033997 12 3 65536 0.111308 0.107978 0.003330 13 3 1 -0.219208 0.000000 0.219208 13 3 16 -0.216625 0.000000 0.216625 13 3 256 0.055759 0.000000 0.055759 13 3 4096 -0.007192 0.000000 0.007192 13 3 65536 0.000523 0.000000 0.000523 14 3 1 -0.639027 -0.375000 0.264027 14 3 16 -0.437793 -0.375000 0.062793 14 3 256 -0.364729 -0.375000 0.010271 14 3 4096 -0.378620 -0.375000 0.003620 14 3 65536 -0.373677 -0.375000 0.001323 15 3 1 0.221531 0.083333 0.138198 15 3 16 0.095640 0.083333 0.012307 15 3 256 0.078314 0.083333 0.005019 15 3 4096 0.084729 0.083333 0.001396 15 3 65536 0.082466 0.083333 0.000868 16 3 1 0.676765 0.750000 0.073235 16 3 16 0.674002 0.750000 0.075998 16 3 256 0.728122 0.750000 0.021878 16 3 4096 0.751583 0.750000 0.001583 16 3 65536 0.747283 0.750000 0.002717 17 3 1 0.264996 0.250000 0.014996 17 3 16 0.210241 0.250000 0.039759 17 3 256 0.238198 0.250000 0.011802 17 3 4096 0.250388 0.250000 0.000388 17 3 65536 0.248561 0.250000 0.001439 18 3 1 0.000000 0.523599 0.523599 18 3 16 0.625000 0.523599 0.101401 18 3 256 0.562500 0.523599 0.038901 18 3 4096 0.516846 0.523599 0.006753 18 3 65536 0.527176 0.523599 0.003577 19 3 1 0.206047 0.118506 0.087541 19 3 16 0.109865 0.118506 0.008641 19 3 256 0.113298 0.118506 0.005208 19 3 4096 0.118730 0.118506 0.000224 19 3 65536 0.117613 0.118506 0.000893 20 3 1 4.738306 2.500000 2.238306 20 3 16 2.333167 2.500000 0.166833 20 3 256 2.411636 2.500000 0.088364 20 3 4096 2.503311 2.500000 0.003311 20 3 65536 2.489950 2.500000 0.010050 24 3 1 0.188293 1.000000 0.811707 24 3 16 0.575097 1.000000 0.424903 24 3 256 0.844929 1.000000 0.155071 24 3 4096 0.993615 1.000000 0.006385 24 3 65536 0.984073 1.000000 0.015927 25 3 1 1.109175 1.039240 0.069935 25 3 16 1.038966 1.039240 0.000274 25 3 256 1.037501 1.039240 0.001739 25 3 4096 1.039783 1.039240 0.000543 25 3 65536 1.038984 1.039240 0.000256 26 3 1 0.017927 0.022778 0.004851 26 3 16 0.023267 0.022778 0.000489 26 3 256 0.022962 0.022778 0.000184 26 3 4096 0.022793 0.022778 0.000015 26 3 65536 0.022797 0.022778 0.000019 27 3 1 -0.862276 -0.717110 0.145166 27 3 16 -0.702113 -0.717110 0.014997 27 3 256 -0.711623 -0.717110 0.005487 27 3 4096 -0.716621 -0.717110 0.000489 27 3 65536 -0.716536 -0.717110 0.000574 28 3 1 0.787193 0.797359 0.010166 28 3 16 0.826242 0.797359 0.028882 28 3 256 0.804981 0.797359 0.007622 28 3 4096 0.796866 0.797359 0.000494 28 3 65536 0.798342 0.797359 0.000982 29 3 1 0.165237 0.287607 0.122370 29 3 16 0.301187 0.287607 0.013580 29 3 256 0.292339 0.287607 0.004732 29 3 4096 0.288333 0.287607 0.000726 29 3 65536 0.288021 0.287607 0.000414 30 3 1 0.970985 0.972704 0.001719 30 3 16 0.976989 0.972704 0.004284 30 3 256 0.973965 0.972704 0.001260 30 3 4096 0.972659 0.972704 0.000045 30 3 65536 0.972859 0.972704 0.000154 31 3 1 0.258327 0.252580 0.005746 31 3 16 0.282168 0.252580 0.029588 31 3 256 0.257722 0.252580 0.005142 31 3 4096 0.250625 0.252580 0.001955 31 3 65536 0.253751 0.252580 0.001171 32 3 1 0.000000 1.351529 1.351529 32 3 16 2.008780 1.351529 0.657251 32 3 256 1.439567 1.351529 0.088038 32 3 4096 1.343556 1.351529 0.007974 32 3 65536 1.364737 1.351529 0.013207 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 = ( 0.082632, 0.178923 ) Prob Dim Points Approx Exact Error 16 2 10 0.828392 0.777287 0.051105 16 2 1000 0.775504 0.777287 0.001783 16 2 100000 0.778530 0.777287 0.001243 Run number 2 Basis point Z = ( 0.646896, 0.563017 ) Prob Dim Points Approx Exact Error 16 2 10 0.485964 0.525550 0.039586 16 2 1000 0.524224 0.525550 0.001325 16 2 100000 0.526232 0.525550 0.000682 Run number 3 Basis point Z = ( 0.187520, 0.700506 ) Prob Dim Points Approx Exact Error 16 2 10 0.780443 0.637846 0.142597 16 2 1000 0.632846 0.637846 0.005000 16 2 100000 0.637118 0.637846 0.000728 Problem number = 17 Run number 1 Basis point Z = ( 0.562647, 0.778201 ) Prob Dim Points Approx Exact Error 17 2 10 0.330324 0.247987 0.082337 17 2 1000 0.245958 0.247987 0.002029 17 2 100000 0.247295 0.247987 0.000693 Run number 2 Basis point Z = ( 0.615997, 0.948237 ) Prob Dim Points Approx Exact Error 17 2 10 0.321626 0.381039 0.059412 17 2 1000 0.394866 0.381039 0.013828 17 2 100000 0.381322 0.381039 0.000284 Run number 3 Basis point Z = ( 0.029920, 0.845367 ) Prob Dim Points Approx Exact Error 17 2 10 0.435544 0.506920 0.071376 17 2 1000 0.504355 0.506920 0.002565 17 2 100000 0.507770 0.506920 0.000850 Problem number = 18 Run number 1 Basis point Z = ( 0.355576, 0.400390 ) Prob Dim Points Approx Exact Error 18 2 10 0.900000 0.785398 0.114602 18 2 1000 0.669000 0.785398 0.116398 18 2 100000 0.676850 0.785398 0.108548 Run number 2 Basis point Z = ( 0.712823, 0.623711 ) Prob Dim Points Approx Exact Error 18 2 10 0.900000 0.785398 0.114602 18 2 1000 0.604000 0.785398 0.181398 18 2 100000 0.607400 0.785398 0.177998 Run number 3 Basis point Z = ( 0.041589, 0.974324 ) Prob Dim Points Approx Exact Error 18 2 10 0.400000 0.785398 0.385398 18 2 1000 0.241000 0.785398 0.544398 18 2 100000 0.232230 0.785398 0.553168 Problem number = 19 Run number 1 Basis point Z = ( 0.104494, 0.440174 ) Prob Dim Points Approx Exact Error 19 2 10 0.236703 0.278425 0.041722 19 2 1000 0.278565 0.278425 0.000141 19 2 100000 0.279091 0.278425 0.000666 Run number 2 Basis point Z = ( 0.349801, 0.544056 ) Prob Dim Points Approx Exact Error 19 2 10 0.199993 0.230455 0.030462 19 2 1000 0.230245 0.230455 0.000210 19 2 100000 0.230910 0.230455 0.000455 Run number 3 Basis point Z = ( 0.062563, 0.839596 ) Prob Dim Points Approx Exact Error 19 2 10 0.338115 0.342051 0.003937 19 2 1000 0.343015 0.342051 0.000964 19 2 100000 0.342624 0.342051 0.000572 Problem number = 31 Run number 1 Basis point Z = ( 0.703346, 0.495708 ) Prob Dim Points Approx Exact Error 31 2 10 0.323730 0.380071 0.056341 31 2 1000 0.379865 0.380071 0.000206 31 2 100000 0.380090 0.380071 0.000020 Run number 2 Basis point Z = ( 0.448199, 0.657152 ) Prob Dim Points Approx Exact Error 31 2 10 0.333264 0.386782 0.053519 31 2 1000 0.392355 0.386782 0.005573 31 2 100000 0.387310 0.386782 0.000527 Run number 3 Basis point Z = ( 0.110267, 0.128820 ) Prob Dim Points Approx Exact Error 31 2 10 0.194670 0.270680 0.076010 31 2 1000 0.268740 0.270680 0.001940 31 2 100000 0.270116 0.270680 0.000564 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 1.000000 0.055150 5 6 1 3 0.993872 1.000000 0.006128 15 6 1 5 0.997794 1.000000 0.002206 25 6 2 1 0.892742 1.000000 0.107258 25 6 2 3 0.987782 1.000000 0.012218 225 6 2 5 0.995593 1.000000 0.004407 625 6 3 1 0.843508 1.000000 0.156492 125 6 3 3 0.981729 1.000000 0.018271 3375 6 3 5 0.993397 1.000000 0.006603 15625 6 4 1 0.796989 1.000000 0.203011 625 6 4 3 0.975713 1.000000 0.024287 50625 6 4 5 0.991205 1.000000 0.008795 390625 test_nint_test Normal end of execution. 30-Mar-2019 17:17:04