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sparse_grid_cc_prb_output.txt
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12 March 2013 03:27:43 PM
SPARSE_GRID_CC_PRB
C++ version
Test the SPARSE_GRID_CC library.
TEST01
SPARSE_GRID_CFN_SIZE returns the number of distinct
points in a sparse grid of Closed Fully Nested rules.
Each sparse grid is of spatial dimension DIM,
and is made up of all product grids of levels up to LEVEL_MAX.
DIM: 1 2 3 4 5
LEVEL_MAX
0 1 1 1 1 1
1 3 5 7 9 11
2 5 13 25 41 61
3 9 29 69 137 241
4 17 65 177 401 801
5 33 145 441 1105 2433
6 65 321 1073 2929 6993
7 129 705 2561 7537 19313
8 257 1537 6017 18945 51713
9 513 3329 13953 46721 135073
10 1025 7169 32001 113409 345665
12 March 2013 03:27:43 PM
TEST01
SPARSE_GRID_CFN_SIZE returns the number of distinct
points in a sparse grid of Closed Fully Nested rules.
Each sparse grid is of spatial dimension DIM,
and is made up of all product grids of levels up to LEVEL_MAX.
DIM: 6 7 8 9 10
LEVEL_MAX
0 1 1 1 1 1
1 13 15 17 19 21
2 85 113 145 181 221
3 389 589 849 1177 1581
4 1457 2465 3937 6001 8801
5 4865 9017 15713 26017 41265
6 15121 30241 56737 100897 171425
7 44689 95441 190881 361249 652065
8 127105 287745 609025 1218049 2320385
9 350657 836769 1863937 3918273 7836545
10 943553 2362881 5515265 12133761 25370753
12 March 2013 03:27:43 PM
TEST01
SPARSE_GRID_CFN_SIZE returns the number of distinct
points in a sparse grid of Closed Fully Nested rules.
Each sparse grid is of spatial dimension DIM,
and is made up of all product grids of levels up to LEVEL_MAX.
DIM: 100
LEVEL_MAX
0 1
1 201
2 20201
3 1353801
4 68074001
12 March 2013 03:27:45 PM
TEST01
SPARSE_GRID_CCS_SIZE returns the number of distinct
points in a Clenshaw Curtis Slow-Growth sparse grid.
Each sparse grid is of spatial dimension DIM,
and is made up of all product grids of levels up to LEVEL_MAX.
DIM: 1 2 3 4 5
LEVEL_MAX
0 1 1 1 1 1
1 3 5 7 9 11
2 5 13 25 41 61
3 9 29 69 137 241
4 9 49 153 369 761
5 17 81 297 849 2033
6 17 129 545 1777 4833
7 17 161 881 3377 10433
8 17 225 1361 5953 20753
9 33 257 1953 9857 38593
10 33 385 2721 15361 67425
12 March 2013 03:27:45 PM
TEST01
SPARSE_GRID_CCS_SIZE returns the number of distinct
points in a Clenshaw Curtis Slow-Growth sparse grid.
Each sparse grid is of spatial dimension DIM,
and is made up of all product grids of levels up to LEVEL_MAX.
DIM: 6 7 8 9 10
LEVEL_MAX
0 1 1 1 1 1
1 13 15 17 19 21
2 85 113 145 181 221
3 389 589 849 1177 1581
4 1409 2409 3873 5929 8721
5 4289 8233 14689 24721 39665
6 11473 24529 48289 88945 155105
7 27697 65537 141601 284209 536705
8 61345 159953 377729 823057 1677665
9 126401 361665 930049 2192865 4810625
10 244289 765089 2136577 5436321 12803073
12 March 2013 03:27:45 PM
TEST01
SPARSE_GRID_CCS_SIZE returns the number of distinct
points in a Clenshaw Curtis Slow-Growth sparse grid.
Each sparse grid is of spatial dimension DIM,
and is made up of all product grids of levels up to LEVEL_MAX.
DIM: 100
LEVEL_MAX
0 1
1 201
2 20201
3 1353801
4 68073201
12 March 2013 03:27:48 PM
TEST02:
SPARSE_GRID_CC_INDEX returns all grid indexes
whose level value satisfies
0 <= LEVEL <= LEVEL_MAX.
Here, LEVEL is the sum of the levels of the 1D rules,
and the order of the rule is 2**LEVEL + 1.
LEVEL_MAX = 3
Spatial dimension DIM_NUM = 2
Number of unique points in the grid = 29
Grid index:
0 4 4
1 0 4
2 8 4
3 4 0
4 4 8
5 2 4
6 6 4
7 0 0
8 8 0
9 0 8
10 8 8
11 4 2
12 4 6
13 1 4
14 3 4
15 5 4
16 7 4
17 2 0
18 6 0
19 2 8
20 6 8
21 0 2
22 8 2
23 0 6
24 8 6
25 4 1
26 4 3
27 4 5
28 4 7
TEST02:
SPARSE_GRID_CC_INDEX returns all grid indexes
whose level value satisfies
0 <= LEVEL <= LEVEL_MAX.
Here, LEVEL is the sum of the levels of the 1D rules,
and the order of the rule is 2**LEVEL + 1.
LEVEL_MAX = 4
Spatial dimension DIM_NUM = 2
Number of unique points in the grid = 65
Grid index:
0 8 8
1 0 8
2 16 8
3 8 0
4 8 16
5 4 8
6 12 8
7 0 0
8 16 0
9 0 16
10 16 16
11 8 4
12 8 12
13 2 8
14 6 8
15 10 8
16 14 8
17 4 0
18 12 0
19 4 16
20 12 16
21 0 4
22 16 4
23 0 12
24 16 12
25 8 2
26 8 6
27 8 10
28 8 14
29 1 8
30 3 8
31 5 8
32 7 8
33 9 8
34 11 8
35 13 8
36 15 8
37 2 0
38 6 0
39 10 0
40 14 0
41 2 16
42 6 16
43 10 16
44 14 16
45 4 4
46 12 4
47 4 12
48 12 12
49 0 2
50 16 2
51 0 6
52 16 6
53 0 10
54 16 10
55 0 14
56 16 14
57 8 1
58 8 3
59 8 5
60 8 7
61 8 9
62 8 11
63 8 13
64 8 15
TEST02:
SPARSE_GRID_CC_INDEX returns all grid indexes
whose level value satisfies
0 <= LEVEL <= LEVEL_MAX.
Here, LEVEL is the sum of the levels of the 1D rules,
and the order of the rule is 2**LEVEL + 1.
LEVEL_MAX = 0
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 1
Grid index:
0 0 0 0
TEST02:
SPARSE_GRID_CC_INDEX returns all grid indexes
whose level value satisfies
0 <= LEVEL <= LEVEL_MAX.
Here, LEVEL is the sum of the levels of the 1D rules,
and the order of the rule is 2**LEVEL + 1.
LEVEL_MAX = 2
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 25
Grid index:
0 2 2 2
1 0 2 2
2 4 2 2
3 2 0 2
4 2 4 2
5 2 2 0
6 2 2 4
7 1 2 2
8 3 2 2
9 0 0 2
10 4 0 2
11 0 4 2
12 4 4 2
13 2 1 2
14 2 3 2
15 0 2 0
16 4 2 0
17 0 2 4
18 4 2 4
19 2 0 0
20 2 4 0
21 2 0 4
22 2 4 4
23 2 2 1
24 2 2 3
TEST02:
SPARSE_GRID_CC_INDEX returns all grid indexes
whose level value satisfies
0 <= LEVEL <= LEVEL_MAX.
Here, LEVEL is the sum of the levels of the 1D rules,
and the order of the rule is 2**LEVEL + 1.
LEVEL_MAX = 2
Spatial dimension DIM_NUM = 6
Number of unique points in the grid = 85
Grid index:
0 2 2 2 2 2 2
1 0 2 2 2 2 2
2 4 2 2 2 2 2
3 2 0 2 2 2 2
4 2 4 2 2 2 2
5 2 2 0 2 2 2
6 2 2 4 2 2 2
7 2 2 2 0 2 2
8 2 2 2 4 2 2
9 2 2 2 2 0 2
10 2 2 2 2 4 2
11 2 2 2 2 2 0
12 2 2 2 2 2 4
13 1 2 2 2 2 2
14 3 2 2 2 2 2
15 0 0 2 2 2 2
16 4 0 2 2 2 2
17 0 4 2 2 2 2
18 4 4 2 2 2 2
19 2 1 2 2 2 2
20 2 3 2 2 2 2
21 0 2 0 2 2 2
22 4 2 0 2 2 2
23 0 2 4 2 2 2
24 4 2 4 2 2 2
25 2 0 0 2 2 2
26 2 4 0 2 2 2
27 2 0 4 2 2 2
28 2 4 4 2 2 2
29 2 2 1 2 2 2
30 2 2 3 2 2 2
31 0 2 2 0 2 2
32 4 2 2 0 2 2
33 0 2 2 4 2 2
34 4 2 2 4 2 2
35 2 0 2 0 2 2
36 2 4 2 0 2 2
37 2 0 2 4 2 2
38 2 4 2 4 2 2
39 2 2 0 0 2 2
40 2 2 4 0 2 2
41 2 2 0 4 2 2
42 2 2 4 4 2 2
43 2 2 2 1 2 2
44 2 2 2 3 2 2
45 0 2 2 2 0 2
46 4 2 2 2 0 2
47 0 2 2 2 4 2
48 4 2 2 2 4 2
49 2 0 2 2 0 2
50 2 4 2 2 0 2
51 2 0 2 2 4 2
52 2 4 2 2 4 2
53 2 2 0 2 0 2
54 2 2 4 2 0 2
55 2 2 0 2 4 2
56 2 2 4 2 4 2
57 2 2 2 0 0 2
58 2 2 2 4 0 2
59 2 2 2 0 4 2
60 2 2 2 4 4 2
61 2 2 2 2 1 2
62 2 2 2 2 3 2
63 0 2 2 2 2 0
64 4 2 2 2 2 0
65 0 2 2 2 2 4
66 4 2 2 2 2 4
67 2 0 2 2 2 0
68 2 4 2 2 2 0
69 2 0 2 2 2 4
70 2 4 2 2 2 4
71 2 2 0 2 2 0
72 2 2 4 2 2 0
73 2 2 0 2 2 4
74 2 2 4 2 2 4
75 2 2 2 0 2 0
76 2 2 2 4 2 0
77 2 2 2 0 2 4
78 2 2 2 4 2 4
79 2 2 2 2 0 0
80 2 2 2 2 4 0
81 2 2 2 2 0 4
82 2 2 2 2 4 4
83 2 2 2 2 2 1
84 2 2 2 2 2 3
TEST03:
SPARSE_GRID_CC makes a sparse Clenshaw Curtis grid.
LEVEL_MAX = 3
Spatial dimension DIM_NUM = 2
Number of unique points in the grid = 29
Grid weights:
0 -1.269841
1 -0.190476
2 -0.190476
3 -0.190476
4 -0.190476
5 0.203175
6 0.203175
7 -0.066667
8 -0.066667
9 -0.066667
10 -0.066667
11 0.203175
12 0.203175
13 0.292437
14 0.723436
15 0.723436
16 0.292437
17 0.177778
18 0.177778
19 0.177778
20 0.177778
21 0.177778
22 0.177778
23 0.177778
24 0.177778
25 0.292437
26 0.723436
27 0.723436
28 0.292437
Grid points:
0 0.000000 0.000000
1 -1.000000 0.000000
2 1.000000 0.000000
3 0.000000 -1.000000
4 0.000000 1.000000
5 -0.707107 0.000000
6 0.707107 0.000000
7 -1.000000 -1.000000
8 1.000000 -1.000000
9 -1.000000 1.000000
10 1.000000 1.000000
11 0.000000 -0.707107
12 0.000000 0.707107
13 -0.923880 0.000000
14 -0.382683 0.000000
15 0.382683 0.000000
16 0.923880 0.000000
17 -0.707107 -1.000000
18 0.707107 -1.000000
19 -0.707107 1.000000
20 0.707107 1.000000
21 -1.000000 -0.707107
22 1.000000 -0.707107
23 -1.000000 0.707107
24 1.000000 0.707107
25 0.000000 -0.923880
26 0.000000 -0.382683
27 0.000000 0.382683
28 0.000000 0.923880
TEST03:
SPARSE_GRID_CC makes a sparse Clenshaw Curtis grid.
LEVEL_MAX = 0
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 1
Grid weights:
0 8.000000
Grid points:
0 0.000000 0.000000 0.000000
TEST03:
SPARSE_GRID_CC makes a sparse Clenshaw Curtis grid.
LEVEL_MAX = 1
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 7
Grid weights:
0 -0.000000
1 1.333333
2 1.333333
3 1.333333
4 1.333333
5 1.333333
6 1.333333
Grid points:
0 0.000000 0.000000 0.000000
1 -1.000000 0.000000 0.000000
2 1.000000 0.000000 0.000000
3 0.000000 -1.000000 0.000000
4 0.000000 1.000000 0.000000
5 0.000000 0.000000 -1.000000
6 0.000000 0.000000 1.000000
TEST04:
Compute the weights of a Clenshaw Curtis sparse grid .
As a simple test, sum these weights.
They should sum to exactly 2^DIM_NUM.
LEVEL_MAX = 4
Spatial dimension DIM_NUM = 2
Number of unique points in the grid = 65
Weight sum Exact sum Difference
4.000000 4.000000 0.000000
TEST04:
Compute the weights of a Clenshaw Curtis sparse grid .
As a simple test, sum these weights.
They should sum to exactly 2^DIM_NUM.
LEVEL_MAX = 0
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 1
Weight sum Exact sum Difference
8.000000 8.000000 0.000000
TEST04:
Compute the weights of a Clenshaw Curtis sparse grid .
As a simple test, sum these weights.
They should sum to exactly 2^DIM_NUM.
LEVEL_MAX = 1
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 7
Weight sum Exact sum Difference
8.000000 8.000000 0.000000
TEST04:
Compute the weights of a Clenshaw Curtis sparse grid .
As a simple test, sum these weights.
They should sum to exactly 2^DIM_NUM.
LEVEL_MAX = 6
Spatial dimension DIM_NUM = 3
Number of unique points in the grid = 1073
Weight sum Exact sum Difference
8.000000 8.000000 0.000000
TEST04:
Compute the weights of a Clenshaw Curtis sparse grid .
As a simple test, sum these weights.
They should sum to exactly 2^DIM_NUM.
LEVEL_MAX = 3
Spatial dimension DIM_NUM = 10
Number of unique points in the grid = 1581
Weight sum Exact sum Difference
1024.000000 1024.000000 0.000000
TEST05
Check the exactness of a Clenshaw Curtis sparse grid quadrature rule,
applied to all monomials of orders 0 to DEGREE_MAX.
LEVEL_MAX = 0
Spatial dimension DIM_NUM = 2
The maximum total degree to be checked is DEGREE_MAX = 3
We expect this rule to be accurate up to and including total degree 1
Number of unique points in the grid = 1
Error Total Monomial
Degree Exponents
0.000000 0 0 0
0.000000 1 1 0
0.000000 1 0 1
0.250000 2 2 0
0.000000 2 1 1
0.250000 2 0 2
0.500000 3 3 0
0.250000 3 2 1
0.250000 3 1 2
0.500000 3 0 3
TEST05
Check the exactness of a Clenshaw Curtis sparse grid quadrature rule,
applied to all monomials of orders 0 to DEGREE_MAX.
LEVEL_MAX = 1
Spatial dimension DIM_NUM = 2
The maximum total degree to be checked is DEGREE_MAX = 5
We expect this rule to be accurate up to and including total degree 3
Number of unique points in the grid = 5
Error Total Monomial
Degree Exponents
0.000000 0 0 0
0.000000 1 1 0
0.000000 1 0 1
0.000000 2 2 0
0.000000 2 1 1
0.000000 2 0 2
0.000000 3 3 0
0.000000 3 2 1
0.000000 3 1 2
0.000000 3 0 3
0.041667 4 4 0
0.000000 4 3 1
0.062500 4 2 2
0.000000 4 1 3
0.041667 4 0 4
0.125000 5 5 0
0.041667 5 4 1
0.125000 5 3 2
0.125000 5 2 3
0.041667 5 1 4
0.125000 5 0 5
TEST05
Check the exactness of a Clenshaw Curtis sparse grid quadrature rule,
applied to all monomials of orders 0 to DEGREE_MAX.
LEVEL_MAX = 2
Spatial dimension DIM_NUM = 2
The maximum total degree to be checked is DEGREE_MAX = 7
We expect this rule to be accurate up to and including total degree 5
Number of unique points in the grid = 13
Error Total Monomial
Degree Exponents
0.000000 0 0 0
0.000000 1 1 0
0.000000 1 0 1
0.000000 2 2 0
0.000000 2 1 1
0.000000 2 0 2
0.000000 3 3 0
0.000000 3 2 1
0.000000 3 1 2
0.000000 3 0 3
0.000000 4 4 0
0.000000 4 3 1
0.000000 4 2 2
0.000000 4 1 3
0.000000 4 0 4
0.000000 5 5 0
0.000000 5 4 1
0.000000 5 3 2
0.000000 5 2 3
0.000000 5 1 4
0.000000 5 0 5
0.001042 6 6 0
0.000000 6 5 1
0.010417 6 4 2
0.000000 6 3 3
0.010417 6 2 4
0.000000 6 1 5
0.001042 6 0 6
0.004167 7 7 0
0.001042 7 6 1
0.031250 7 5 2
0.020833 7 4 3
0.020833 7 3 4
0.031250 7 2 5
0.001042 7 1 6
0.004167 7 0 7
TEST05
Check the exactness of a Clenshaw Curtis sparse grid quadrature rule,
applied to all monomials of orders 0 to DEGREE_MAX.
LEVEL_MAX = 3
Spatial dimension DIM_NUM = 2
The maximum total degree to be checked is DEGREE_MAX = 9
We expect this rule to be accurate up to and including total degree 7
Number of unique points in the grid = 29
Error Total Monomial
Degree Exponents
0.000000 0 0 0
0.000000 1 1 0
0.000000 1 0 1
0.000000 2 2 0
0.000000 2 1 1
0.000000 2 0 2
0.000000 3 3 0
0.000000 3 2 1
0.000000 3 1 2
0.000000 3 0 3
0.000000 4 4 0
0.000000 4 3 1
0.000000 4 2 2
0.000000 4 1 3
0.000000 4 0 4
0.000000 5 5 0
0.000000 5 4 1
0.000000 5 3 2
0.000000 5 2 3
0.000000 5 1 4
0.000000 5 0 5
0.000000 6 6 0
0.000000 6 5 1
0.000000 6 4 2
0.000000 6 3 3
0.000000 6 2 4
0.000000 6 1 5
0.000000 6 0 6
0.000000 7 7 0
0.000000 7 6 1
0.000000 7 5 2
0.000000 7 4 3
0.000000 7 3 4
0.000000 7 2 5
0.000000 7 1 6
0.000000 7 0 7
0.000000 8 8 0
0.000000 8 7 1
0.000260 8 6 2
0.000000 8 5 3
0.001736 8 4 4
0.000000 8 3 5
0.000260 8 2 6
0.000000 8 1 7
0.000000 8 0 8
0.000000 9 9 0
0.000000 9 8 1
0.001042 9 7 2
0.000521 9 6 3
0.005208 9 5 4
0.005208 9 4 5
0.000521 9 3 6
0.001042 9 2 7
0.000000 9 1 8
0.000000 9 0 9
TEST05
Check the exactness of a Clenshaw Curtis sparse grid quadrature rule,
applied to all monomials of orders 0 to DEGREE_MAX.
LEVEL_MAX = 4
Spatial dimension DIM_NUM = 2
The maximum total degree to be checked is DEGREE_MAX = 11
We expect this rule to be accurate up to and including total degree 9
Number of unique points in the grid = 65
Error Total Monomial
Degree Exponents
0.000000 0 0 0
0.000000 1 1 0
0.000000 1 0 1
0.000000 2 2 0
0.000000 2 1 1
0.000000 2 0 2
0.000000 3 3 0
0.000000 3 2 1
0.000000 3 1 2
0.000000 3 0 3
0.000000 4 4 0
0.000000 4 3 1
0.000000 4 2 2
0.000000 4 1 3
0.000000 4 0 4
0.000000 5 5 0
0.000000 5 4 1
0.000000 5 3 2
0.000000 5 2 3
0.000000 5 1 4
0.000000 5 0 5
0.000000 6 6 0
0.000000 6 5 1
0.000000 6 4 2
0.000000 6 3 3
0.000000 6 2 4
0.000000 6 1 5
0.000000 6 0 6
0.000000 7 7 0
0.000000 7 6 1
0.000000 7 5 2
0.000000 7 4 3
0.000000 7 3 4
0.000000 7 2 5
0.000000 7 1 6
0.000000 7 0 7
0.000000 8 8 0
0.000000 8 7 1
0.000000 8 6 2
0.000000 8 5 3
0.000000 8 4 4
0.000000 8 3 5
0.000000 8 2 6
0.000000 8 1 7
0.000000 8 0 8
0.000000 9 9 0
0.000000 9 8 1
0.000000 9 7 2
0.000000 9 6 3
0.000000 9 5 4
0.000000 9 4 5
0.000000 9 3 6
0.000000 9 2 7
0.000000 9 1 8
0.000000 9 0 9
0.000000 10 10 0
0.000000 10 9 1
0.000000 10 8 2
0.000000 10 7 3
0.000043 10 6 4
0.000000 10 5 5
0.000043 10 4 6
0.000000 10 3 7
0.000000 10 2 8
0.000000 10 1 9
0.000000 10 010
0.000000 11 11 0
0.000000 11 10 1
0.000000 11 9 2
0.000000 11 8 3
0.000174 11 7 4
0.000130 11 6 5
0.000130 11 5 6
0.000174 11 4 7
0.000000 11 3 8
0.000000 11 2 9
0.000000 11 110
0.000000 11 011
TEST05
Check the exactness of a Clenshaw Curtis sparse grid quadrature rule,
applied to all monomials of orders 0 to DEGREE_MAX.
LEVEL_MAX = 5
Spatial dimension DIM_NUM = 2
The maximum total degree to be checked is DEGREE_MAX = 13
We expect this rule to be accurate up to and including total degree 11
Number of unique points in the grid = 145
Error Total Monomial
Degree Exponents
0.000000 0 0 0
0.000000 1 1 0
0.000000 1 0 1
0.000000 2 2 0
0.000000 2 1 1
0.000000 2 0 2
0.000000 3 3 0
0.000000 3 2 1
0.000000 3 1 2
0.000000 3 0 3
0.000000 4 4 0
0.000000 4 3 1
0.000000 4 2 2
0.000000 4 1 3
0.000000 4 0 4
0.000000 5 5 0
0.000000 5 4 1
0.000000 5 3 2
0.000000 5 2 3
0.000000 5 1 4
0.000000 5 0 5
0.000000 6 6 0
0.000000 6 5 1
0.000000 6 4 2
0.000000 6 3 3
0.000000 6 2 4
0.000000 6 1 5
0.000000 6 0 6
0.000000 7 7 0
0.000000 7 6 1
0.000000 7 5 2
0.000000 7 4 3
0.000000 7 3 4
0.000000 7 2 5
0.000000 7 1 6
0.000000 7 0 7