24 December 2011 11:55:19 AM
TEST_NINT_PRB
C++ version
Test 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, 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) = product ( 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, 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 2.5 2.5 4.44089e-16
1 3 3 2.5 2.5 7.54952e-15
1 3 5 2.5 2.5 1.33227e-15
2 3 1 2.6 2.6 4.44089e-16
2 3 3 2.6 2.6 2.26485e-14
2 3 5 2.6 2.6 1.42553e-13
3 3 1 -2.41474e-15 0 2.41474e-15
3 3 3 -9.22513e-15 0 9.22513e-15
3 3 5 -3.48654e-15 0 3.48654e-15
4 3 1 9.7619 9.7619 8.88178e-15
4 3 3 9.7619 9.7619 4.61853e-14
4 3 5 9.7619 9.7619 1.1191e-13
5 3 1 2.15214 2.15214 3.1588e-07
5 3 3 2.15214 2.15214 4.78373e-11
5 3 5 2.15214 2.15214 4.53415e-13
6 3 1 0.843508 1 0.156492
6 3 3 0.981729 1 0.0182708
6 3 5 0.993397 1 0.00660336
7 3 1 1 1 1.65427e-07
7 3 3 1 1 1.94289e-12
7 3 5 1 1 2.66454e-14
8 3 1 0.758012 0.758012 3.06247e-11
8 3 3 0.758012 0.758012 4.77396e-15
8 3 5 0.758012 0.758012 1.77636e-14
9 3 1 1.67176 1.67176 4.44089e-16
9 3 3 1.67176 1.67176 1.33227e-15
9 3 5 1.67176 1.67176 4.79616e-14
10 3 1 0.708638 0.75 0.0413622
10 3 3 0.745404 0.75 0.0045958
10 3 5 0.748346 0.75 0.00165449
11 3 1 4.83433 5.07321 0.238888
11 3 3 5.04614 5.07321 0.0270711
11 3 5 5.06345 5.07321 0.00976102
12 3 1 0.107978 0.107978 3.66118e-09
12 3 3 0.107978 0.107978 4.51167e-14
12 3 5 0.107978 0.107978 1.22125e-15
13 3 1 7.69784e-17 0 7.69784e-17
13 3 3 -1.02397e-16 0 1.02397e-16
13 3 5 7.21824e-16 0 7.21824e-16
14 3 1 -0.375 -0.375 1.11022e-16
14 3 3 -0.375 -0.375 4.996e-16
14 3 5 -0.375 -0.375 4.32987e-15
15 3 1 0.0555556 0.0833333 0.0277778
15 3 3 0.0555556 0.0833333 0.0277778
15 3 5 0.0555556 0.0833333 0.0277778
16 3 1 0.708638 0.75 0.0413622
16 3 3 0.745404 0.75 0.0045958
16 3 5 0.748346 0.75 0.00165449
17 3 1 0.25 0.25 0
17 3 3 0.25 0.25 3.33067e-16
17 3 5 0.25 0.25 4.4964e-15
18 3 1 0.501831 0.523599 0.0217678
18 3 3 0.538509 0.523599 0.01491
18 3 5 0.531268 0.523599 0.00766915
19 3 1 0.130655 0.118506 0.0121487
19 3 3 0.118682 0.118506 0.000175632
19 3 5 0.119561 0.118506 0.00105459
20 3 1 2.5 2.5 4.44089e-16
20 3 3 2.5 2.5 7.54952e-15
20 3 5 2.5 2.5 1.33227e-15
24 3 1 0.843508 1 0.156492
24 3 3 0.981729 1 0.0182708
24 3 5 0.993397 1 0.00660336
25 3 1 1.03924 1.03924 0
25 3 3 1.03924 1.03924 1.33227e-15
25 3 5 1.03924 1.03924 3.33067e-15
26 3 1 0.022778 0.022778 1.04083e-17
26 3 3 0.022778 0.022778 1.04083e-17
26 3 5 0.022778 0.022778 4.57967e-16
27 3 1 -0.71711 -0.71711 0
27 3 3 -0.71711 -0.71711 4.44089e-16
27 3 5 -0.71711 -0.71711 3.44169e-15
28 3 1 0.797361 0.797359 1.97503e-06
28 3 3 0.797359 0.797359 1.37912e-12
28 3 5 0.797359 0.797359 1.85407e-14
29 3 1 0.287607 0.287607 8.22067e-11
29 3 3 0.287607 0.287607 7.43849e-15
29 3 5 0.287607 0.287607 6.60583e-15
30 3 1 0.972704 0.972704 5.89084e-13
30 3 3 0.972704 0.972704 3.88578e-15
30 3 5 0.972704 0.972704 5.55112e-16
31 3 1 0.286876 0.25258 0.034296
31 3 3 0.256268 0.25258 0.00368801
31 3 5 0.253905 0.25258 0.00132417
32 3 1 2.0681 1.35153 0.716572
32 3 3 1.29697 1.35153 0.0545545
32 3 5 1.39548 1.35153 0.0439507
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 4.017 2.5 1.517
1 3 16 1.98069 2.5 0.519314
1 3 256 2.51538 2.5 0.0153838
1 3 4096 2.46408 2.5 0.0359208
1 3 65536 2.48823 2.5 0.0117677
2 3 1 1.0344 2.6 1.5656
2 3 16 1.97205 2.6 0.627951
2 3 256 2.19528 2.6 0.404718
2 3 4096 2.52913 2.6 0.0708695
2 3 65536 2.6071 2.6 0.00710206
3 3 1 1.04318 0 1.04318
3 3 16 -2.99187 0 2.99187
3 3 256 -0.7862 0 0.7862
3 3 4096 -0.441875 0 0.441875
3 3 65536 -0.0880609 0 0.0880609
4 3 1 1.05203 9.7619 8.70987
4 3 16 7.26339 9.7619 2.49851
4 3 256 7.52632 9.7619 2.23559
4 3 4096 9.11323 9.7619 0.648678
4 3 65536 9.83619 9.7619 0.0742864
5 3 1 1.59729 2.15214 0.554855
5 3 16 2.32895 2.15214 0.176805
5 3 256 2.12889 2.15214 0.0232496
5 3 4096 2.16561 2.15214 0.0134657
5 3 65536 2.15723 2.15214 0.00509
6 3 1 2.70969 1 1.70969
6 3 16 1.39964 1 0.399639
6 3 256 0.927314 1 0.0726859
6 3 4096 1.01947 1 0.0194699
6 3 65536 0.988955 1 0.0110454
7 3 1 0.171452 1 0.828548
7 3 16 0.84167 1 0.15833
7 3 256 1.04765 1 0.0476485
7 3 4096 1.00357 1 0.00356759
7 3 65536 1.00419 1 0.0041861
8 3 1 0.999989 0.758012 0.241977
8 3 16 0.689194 0.758012 0.0688182
8 3 256 0.773012 0.758012 0.0149998
8 3 4096 0.754223 0.758012 0.0037896
8 3 65536 0.756453 0.758012 0.00155909
9 3 1 1.95049 1.67176 0.278734
9 3 16 1.57779 1.67176 0.0939654
9 3 256 1.67642 1.67176 0.0046567
9 3 4096 1.66522 1.67176 0.00653733
9 3 65536 1.66957 1.67176 0.00219179
10 3 1 1.06741 0.75 0.317409
10 3 16 0.810449 0.75 0.0604495
10 3 256 0.736137 0.75 0.0138628
10 3 4096 0.752979 0.75 0.00297908
10 3 65536 0.747869 0.75 0.00213106
11 3 1 8.4555 5.07321 3.38229
11 3 16 5.7675 5.07321 0.69429
11 3 256 4.93312 5.07321 0.140091
11 3 4096 5.11274 5.07321 0.0395218
11 3 65536 5.05083 5.07321 0.0223889
12 3 1 1.55949 0.107978 1.45151
12 3 16 0.833615 0.107978 0.725638
12 3 256 0.137672 0.107978 0.0296946
12 3 4096 0.118813 0.107978 0.0108351
12 3 65536 0.11386 0.107978 0.00588253
13 3 1 0.111466 0 0.111466
13 3 16 -0.65298 0 0.65298
13 3 256 -0.178717 0 0.178717
13 3 4096 -0.0365333 0 0.0365333
13 3 65536 0.0173751 0 0.0173751
14 3 1 -0.182807 -0.375 0.192193
14 3 16 -0.310928 -0.375 0.064072
14 3 256 -0.37366 -0.375 0.00133984
14 3 4096 -0.37087 -0.375 0.00412971
14 3 65536 -0.372828 -0.375 0.00217178
15 3 1 0.0361912 0.0833333 0.0471421
15 3 16 0.025008 0.0833333 0.0583253
15 3 256 0.0538751 0.0833333 0.0294582
15 3 4096 0.0528793 0.0833333 0.030454
15 3 65536 0.0549606 0.0833333 0.0283727
16 3 1 1.06741 0.75 0.317409
16 3 16 0.810449 0.75 0.0604495
16 3 256 0.736137 0.75 0.0138628
16 3 4096 0.752979 0.75 0.00297908
16 3 65536 0.747869 0.75 0.00213106
17 3 1 0.39609 0.25 0.14609
17 3 16 0.275293 0.25 0.0252929
17 3 256 0.244171 0.25 0.00582935
17 3 4096 0.251083 0.25 0.00108302
17 3 65536 0.249087 0.25 0.000912782
18 3 1 0 0.523599 0.523599
18 3 16 0.625 0.523599 0.101401
18 3 256 0.527344 0.523599 0.00374497
18 3 4096 0.522949 0.523599 0.000649557
18 3 65536 0.525803 0.523599 0.00220384
19 3 1 0.188471 0.118506 0.0699647
19 3 16 0.101971 0.118506 0.0165355
19 3 256 0.114447 0.118506 0.0040589
19 3 4096 0.117241 0.118506 0.0012655
19 3 65536 0.11768 0.118506 0.00082618
20 3 1 4.017 2.5 1.517
20 3 16 1.98069 2.5 0.519314
20 3 256 2.51538 2.5 0.0153838
20 3 4096 2.46408 2.5 0.0359208
20 3 65536 2.48823 2.5 0.0117677
24 3 1 2.70969 1 1.70969
24 3 16 1.39964 1 0.399639
24 3 256 0.927314 1 0.0726859
24 3 4096 1.01947 1 0.0194699
24 3 65536 0.988955 1 0.0110454
25 3 1 1.05335 1.03924 0.0141146
25 3 16 1.0253 1.03924 0.0139381
25 3 256 1.03907 1.03924 0.000170837
25 3 4096 1.03816 1.03924 0.0010826
25 3 65536 1.03896 1.03924 0.00028111
26 3 1 0.0189886 0.022778 0.00378942
26 3 16 0.0240013 0.022778 0.00122333
26 3 256 0.0226612 0.022778 0.000116791
26 3 4096 0.0228626 0.022778 8.46653e-05
26 3 65536 0.022808 0.022778 3.00166e-05
27 3 1 -0.831744 -0.71711 0.114634
27 3 16 -0.680456 -0.71711 0.036654
27 3 256 -0.72077 -0.71711 0.00366041
27 3 4096 -0.714615 -0.71711 0.00249475
27 3 65536 -0.716219 -0.71711 0.000891248
28 3 1 0.69175 0.797359 0.10561
28 3 16 0.779424 0.797359 0.0179354
28 3 256 0.801944 0.797359 0.004585
28 3 4096 0.796695 0.797359 0.000664494
28 3 65536 0.798027 0.797359 0.000667379
29 3 1 0.184792 0.287607 0.102815
29 3 16 0.320299 0.287607 0.0326922
29 3 256 0.283335 0.287607 0.0042717
29 3 4096 0.290027 0.287607 0.00241961
29 3 65536 0.2885 0.287607 0.00089336
30 3 1 0.956944 0.972704 0.01576
30 3 16 0.969986 0.972704 0.00271879
30 3 256 0.973337 0.972704 0.000632361
30 3 4096 0.97259 0.972704 0.000114316
30 3 65536 0.972803 0.972704 9.84143e-05
31 3 1 0.118266 0.25258 0.134314
31 3 16 0.221384 0.25258 0.0311968
31 3 256 0.259995 0.25258 0.00741418
31 3 4096 0.251361 0.25258 0.00121901
31 3 65536 0.25344 0.25258 0.00085948
32 3 1 0 1.35153 1.35153
32 3 16 1.0341 1.35153 0.317429
32 3 256 1.36951 1.35153 0.0179842
32 3 4096 1.35156 1.35153 3.08634e-05
32 3 65536 1.36334 1.35153 0.0118134
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 = 0.218418 0.956318
Prob Dim Points Approx Exact Error
16 2 10 0.840784 0.787514 0.0532697
16 2 1000 0.793654 0.787514 0.00613983
16 2 100000 0.787792 0.787514 0.000277882
Run number 2
Basis point Z = 0.829509 0.561695
Prob Dim Points Approx Exact Error
16 2 10 0.745229 0.612383 0.132847
16 2 1000 0.614758 0.612383 0.0023755
16 2 100000 0.612616 0.612383 0.000233775
Run number 3
Basis point Z = 0.415307 0.0661187
Prob Dim Points Approx Exact Error
16 2 10 0.616367 0.695426 0.0790589
16 2 1000 0.689503 0.695426 0.00592292
16 2 100000 0.69359 0.695426 0.00183558
Problem number = 17
Run number 1
Basis point Z = 0.257578 0.109957
Prob Dim Points Approx Exact Error
17 2 10 0.299242 0.377569 0.0783266
17 2 1000 0.372033 0.377569 0.00553584
17 2 100000 0.375314 0.377569 0.00225471
Run number 2
Basis point Z = 0.043829 0.633966
Prob Dim Points Approx Exact Error
17 2 10 0.387798 0.392705 0.00490725
17 2 1000 0.392704 0.392705 1.89028e-06
17 2 100000 0.39118 0.392705 0.00152562
Run number 3
Basis point Z = 0.0617272 0.449539
Prob Dim Points Approx Exact Error
17 2 10 0.319277 0.361296 0.0420187
17 2 1000 0.359104 0.361296 0.00219181
17 2 100000 0.359354 0.361296 0.0019422
Problem number = 18
Run number 1
Basis point Z = 0.401306 0.754673
Prob Dim Points Approx Exact Error
18 2 10 0.5 0.785398 0.285398
18 2 1000 0.587 0.785398 0.198398
18 2 100000 0.58835 0.785398 0.197048
Run number 2
Basis point Z = 0.797287 0.00183837
Prob Dim Points Approx Exact Error
18 2 10 0.3 0.785398 0.485398
18 2 1000 0.324 0.785398 0.461398
18 2 100000 0.29785 0.785398 0.487548
Run number 3
Basis point Z = 0.897504 0.350752
Prob Dim Points Approx Exact Error
18 2 10 0.3 0.785398 0.485398
18 2 1000 0.444 0.785398 0.341398
18 2 100000 0.44269 0.785398 0.342708
Problem number = 19
Run number 1
Basis point Z = 0.0945448 0.0136169
Prob Dim Points Approx Exact Error
19 2 10 0.261655 0.38842 0.126766
19 2 1000 0.381927 0.38842 0.00649348
19 2 100000 0.387221 0.38842 0.00119932
Run number 2
Basis point Z = 0.859097 0.840847
Prob Dim Points Approx Exact Error
19 2 10 0.394038 0.314958 0.0790801
19 2 1000 0.317779 0.314958 0.00282142
19 2 100000 0.316299 0.314958 0.00134091
Run number 3
Basis point Z = 0.123104 0.00751236
Prob Dim Points Approx Exact Error
19 2 10 0.260874 0.380081 0.119208
19 2 1000 0.374378 0.380081 0.00570331
19 2 100000 0.379008 0.380081 0.00107332
Problem number = 31
Run number 1
Basis point Z = 0.260303 0.912484
Prob Dim Points Approx Exact Error
31 2 10 0.278917 0.294324 0.0154068
31 2 1000 0.293259 0.294324 0.00106485
31 2 100000 0.293668 0.294324 0.000655911
Run number 2
Basis point Z = 0.113664 0.351629
Prob Dim Points Approx Exact Error
31 2 10 0.348145 0.318205 0.02994
31 2 1000 0.318928 0.318205 0.000722404
31 2 100000 0.319552 0.318205 0.00134675
Run number 3
Basis point Z = 0.822887 0.267132
Prob Dim Points Approx Exact Error
31 2 10 0.29974 0.326926 0.0271858
31 2 1000 0.332656 0.326926 0.00573047
31 2 100000 0.326865 0.326926 6.06648e-05
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 0.94485 1 0.0551496 5
6 1 3 0.993872 1 0.00612773 15
6 1 5 0.997794 1 0.00220598 25
6 2 1 0.892742 1 0.107258 25
6 2 3 0.987782 1 0.0122179 225
6 2 5 0.995593 1 0.0044071 625
6 3 1 0.843508 1 0.156492 125
6 3 3 0.981729 1 0.0182708 3375
6 3 5 0.993397 1 0.00660336 15625
6 4 1 0.796989 1 0.203011 625
6 4 3 0.975713 1 0.0242865 50625
6 4 5 0.991205 1 0.00879477 390625
6 5 1 0.753035 1 0.246965 3125
6 5 3 0.969735 1 0.0302654 759375
6 5 5 0.989019 1 0.0109814 9765625
6 6 1 0.711506 1 0.288494 15625
6 6 3 0.963792 1 0.0362077 11390625
6 6 5 0.986837 1 0.0131631 244140625
TEST_NINT_PRB
Normal end of execution.
24 December 2011 11:56:19 AM