06 November 2014 07:39:06 PM
LPP_PRB:
C++ version
Test the LEGENDRE_PRODUCT_POLYNOMIAL library.
I4_CHOOSE_TEST
I4_CHOOSE evaluates C(N,K).
N K CNK
0 0 1
1 0 1
1 1 1
2 0 1
2 1 2
2 2 1
3 0 1
3 1 3
3 2 3
3 3 1
4 0 1
4 1 4
4 2 6
4 3 4
4 4 1
I4_UNIFORM_AB_TEST
I4_UNIFORM_AB computes pseudorandom values
in an interval [A,B].
The lower endpoint A = -100
The upper endpoint B = 200
The initial seed is 123456789
1 -35
2 187
3 149
4 69
5 25
6 -81
7 -23
8 -67
9 -87
10 90
11 -82
12 35
13 20
14 127
15 139
16 -100
17 170
18 5
19 -72
20 -96
I4VEC_PERMUTE_TEST
I4VEC_PERMUTE reorders an integer vector
according to a given permutation.
Using initial random number seed = 0
A, before rearrangement:
0: 2
1: 12
2: 10
3: 7
4: 5
5: 0
6: 3
7: 1
8: 0
9: 8
10: 0
11: 5
Permutation vector P:
0: 4
1: 9
2: 1
3: 3
4: 11
5: 7
6: 6
7: 5
8: 0
9: 8
10: 10
11: 2
A, after rearrangement:
0: 5
1: 8
2: 12
3: 7
4: 5
5: 1
6: 3
7: 0
8: 2
9: 0
10: 0
11: 10
I4VEC_PRINT_TEST
I4VEC_PRINT prints an I4VEC
Here is the I4VEC:
0: 91
1: 92
2: 93
3: 94
I4VEC_SORT_HEAP_INDEX_A_TEST
I4VEC_SORT_HEAP_INDEX_A creates an ascending
sort index for an I4VEC.
Unsorted array:
0: 13
1: 58
2: 50
3: 34
4: 25
5: 4
6: 15
7: 6
8: 2
9: 38
10: 3
11: 27
12: 24
13: 46
14: 48
15: 0
16: 54
17: 21
18: 5
19: 0
Sort vector INDX:
0: 15
1: 19
2: 8
3: 10
4: 5
5: 18
6: 7
7: 0
8: 6
9: 17
10: 12
11: 4
12: 11
13: 3
14: 9
15: 13
16: 14
17: 2
18: 16
19: 1
I INDX(I) A(INDX(I))
0 15 0
1 19 0
2 8 2
3 10 3
4 5 4
5 18 5
6 7 6
7 0 13
8 6 15
9 17 21
10 12 24
11 4 25
12 11 27
13 3 34
14 9 38
15 13 46
16 14 48
17 2 50
18 16 54
19 1 58
I4VEC_SUM_TEST
I4VEC_SUM sums the entries of an I4VEC.
The vector:
0: 2
1: 10
2: 9
3: 6
4: 4
The vector entries sum to 31
I4VEC_UNIFORM_AB_NEW_TEST
I4VEC_UNIFORM_AB_NEW computes pseudorandom values
in an interval [A,B].
The lower endpoint A = -100
The upper endpoint B = 200
The initial seed is 123456789
The random vector:
0: -35
1: 187
2: 149
3: 69
4: 25
5: -81
6: -23
7: -67
8: -87
9: 90
10: -82
11: 35
12: 20
13: 127
14: 139
15: -100
16: 170
17: 5
18: -72
19: -96
R8VEC_PERMUTE_TEST
R8VEC_PERMUTE permutes an R8VEC in place.
Original Array X[]:
0 1
1 2
2 3
3 4
4 5
Permutation Vector P[]:
0: 1
1: 3
2: 4
3: 0
4: 2
Permuted array X[P[]]:
0 2
1 4
2 5
3 1
4 3
TEST1335
R8VEC_PRINT prints an R8VEC.
The R8VEC:
0 123.456
1 5e-06
2 -1e+06
3 3.14159
R8VEC_UNIFORM_AB_NEW_TEST
R8VEC_UNIFORM returns a random R8VEC
with entries in a given range [ A, B ]
For this problem:
A = 10
B = 20
Input SEED = 123456789
Random R8VEC:
0 12.1842
1 19.5632
2 18.2951
3 15.617
4 14.1531
5 10.6612
6 12.5758
7 11.0996
8 10.4383
9 16.3397
Input SEED = 1361431000
Random R8VEC:
0 10.6173
1 14.4954
2 14.0131
3 17.5467
4 17.9729
5 10.0184
6 18.975
7 13.5075
8 10.9454
9 10.1362
Input SEED = 29242052
Random R8VEC:
0 18.591
1 18.4085
2 11.231
3 10.0751
4 12.603
5 19.1248
6 11.1366
7 13.5163
8 18.2289
9 12.6713
R8MAT_PRINT_TEST
R8MAT_PRINT prints an R8MAT.
The R8MAT:
Col: 0 1 2 3
Row
0: 11 12 13 14
1: 21 22 23 24
2: 31 32 33 34
3: 41 42 43 44
4: 51 52 53 54
5: 61 62 63 64
R8MAT_PRINT_SOME_TEST
R8MAT_PRINT_SOME prints some of an R8MAT.
The R8MAT, rows 2:4, cols 1:2:
Col: 0 1
Row
1: 21 22
2: 31 32
3: 41 42
R8MAT_UNIFORM_AB_NEW_TEST
R8MAT_UNIFORM_AB_NEW returns a random R8MAT in [A,B].
The random R8MAT:
Col: 0 1 2 3
Row
0: 3.74735 2.52895 2.49382 2.01471
1: 9.65054 4.06062 5.59631 9.18003
2: 8.63607 2.87965 5.21045 4.80602
3: 6.49356 2.35063 8.03739 2.75636
4: 5.32246 7.07173 8.3783 2.10894
PERM_UNIFORM_TEST
PERM_UNIFORM randomly selects a permutation.
2 9 8 6 3 5 7 4 0 1
6 1 5 2 8 4 0 9 3 7
0 1 8 2 4 5 7 9 3 6
3 8 4 7 0 9 2 5 6 1
1 7 5 4 0 6 8 2 3 9
COMP_ENUM_TEST
COMP_ENUM counts compositions;
1 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10
1 3 6 10 15 21 28 36 45 55
1 4 10 20 35 56 84 120 165 220
1 5 15 35 70 126 210 330 495 715
1 6 21 56 126 252 462 792 1287 2002
1 7 28 84 210 462 924 1716 3003 5005
1 8 36 120 330 792 1716 3432 6435 11440
1 9 45 165 495 1287 3003 6435 12870 24310
1 10 55 220 715 2002 5005 11440 24310 48620
1 11 66 286 1001 3003 8008 19448 43758 92378
COMP_NEXT_GRLEX_TEST
A COMP is a composition of an integer N into K parts.
Each part is nonnegative. The order matters.
COMP_NEXT_GRLEX determines the next COMP in
graded lexicographic (grlex) order.
Rank: NC COMP
----: -- ------------
1: 0 = 0 + 0 + 0
----: -- ------------
2: 1 = 0 + 0 + 1
3: 1 = 0 + 1 + 0
4: 1 = 1 + 0 + 0
----: -- ------------
5: 2 = 0 + 0 + 2
6: 2 = 0 + 1 + 1
7: 2 = 0 + 2 + 0
8: 2 = 1 + 0 + 1
9: 2 = 1 + 1 + 0
10: 2 = 2 + 0 + 0
----: -- ------------
11: 3 = 0 + 0 + 3
12: 3 = 0 + 1 + 2
13: 3 = 0 + 2 + 1
14: 3 = 0 + 3 + 0
15: 3 = 1 + 0 + 2
16: 3 = 1 + 1 + 1
17: 3 = 1 + 2 + 0
18: 3 = 2 + 0 + 1
19: 3 = 2 + 1 + 0
20: 3 = 3 + 0 + 0
----: -- ------------
21: 4 = 0 + 0 + 4
22: 4 = 0 + 1 + 3
23: 4 = 0 + 2 + 2
24: 4 = 0 + 3 + 1
25: 4 = 0 + 4 + 0
26: 4 = 1 + 0 + 3
27: 4 = 1 + 1 + 2
28: 4 = 1 + 2 + 1
29: 4 = 1 + 3 + 0
30: 4 = 2 + 0 + 2
31: 4 = 2 + 1 + 1
32: 4 = 2 + 2 + 0
33: 4 = 3 + 0 + 1
34: 4 = 3 + 1 + 0
35: 4 = 4 + 0 + 0
----: -- ------------
36: 5 = 0 + 0 + 5
37: 5 = 0 + 1 + 4
38: 5 = 0 + 2 + 3
39: 5 = 0 + 3 + 2
40: 5 = 0 + 4 + 1
41: 5 = 0 + 5 + 0
42: 5 = 1 + 0 + 4
43: 5 = 1 + 1 + 3
44: 5 = 1 + 2 + 2
45: 5 = 1 + 3 + 1
46: 5 = 1 + 4 + 0
47: 5 = 2 + 0 + 3
48: 5 = 2 + 1 + 2
49: 5 = 2 + 2 + 1
50: 5 = 2 + 3 + 0
51: 5 = 3 + 0 + 2
52: 5 = 3 + 1 + 1
53: 5 = 3 + 2 + 0
54: 5 = 4 + 0 + 1
55: 5 = 4 + 1 + 0
56: 5 = 5 + 0 + 0
----: -- ------------
57: 6 = 0 + 0 + 6
58: 6 = 0 + 1 + 5
59: 6 = 0 + 2 + 4
60: 6 = 0 + 3 + 3
61: 6 = 0 + 4 + 2
62: 6 = 0 + 5 + 1
63: 6 = 0 + 6 + 0
64: 6 = 1 + 0 + 5
65: 6 = 1 + 1 + 4
66: 6 = 1 + 2 + 3
67: 6 = 1 + 3 + 2
68: 6 = 1 + 4 + 1
69: 6 = 1 + 5 + 0
70: 6 = 2 + 0 + 4
71: 6 = 2 + 1 + 3
COMP_RANDOM_GRLEX_TEST
A COMP is a composition of an integer N into K parts.
Each part is nonnegative. The order matters.
COMP_RANDOM_GRLEX selects a random COMP in
graded lexicographic (grlex) order between indices RANK1 and RANK2.
28: 4 = 1 + 2 + 1
59: 6 = 0 + 2 + 4
54: 5 = 4 + 0 + 1
43: 5 = 1 + 1 + 3
37: 5 = 0 + 1 + 4
COMP_RANK_GRLEX_TEST
A COMP is a composition of an integer N into K parts.
Each part is nonnegative. The order matters.
COMP_RANK_GRLEX determines the rank of a COMP
from its parts.
Actual Inferred
Test Rank Rank
1 28 28
2 59 59
3 54 54
4 43 43
5 37 37
COMP_UNRANK_GRLEX_TEST
A COMP is a composition of an integer N into K parts.
Each part is nonnegative. The order matters.
COMP_UNRANK_GRLEX determines the parts
of a COMP from its rank.
Rank: -> NC COMP
----: -- ------------
1: 0 = 0 + 0 + 0
----: -- ------------
2: 1 = 0 + 0 + 1
3: 1 = 0 + 1 + 0
4: 1 = 1 + 0 + 0
----: -- ------------
5: 2 = 0 + 0 + 2
6: 2 = 0 + 1 + 1
7: 2 = 0 + 2 + 0
8: 2 = 1 + 0 + 1
9: 2 = 1 + 1 + 0
10: 2 = 2 + 0 + 0
----: -- ------------
11: 3 = 0 + 0 + 3
12: 3 = 0 + 1 + 2
13: 3 = 0 + 2 + 1
14: 3 = 0 + 3 + 0
15: 3 = 1 + 0 + 2
16: 3 = 1 + 1 + 1
17: 3 = 1 + 2 + 0
18: 3 = 2 + 0 + 1
19: 3 = 2 + 1 + 0
20: 3 = 3 + 0 + 0
----: -- ------------
21: 4 = 0 + 0 + 4
22: 4 = 0 + 1 + 3
23: 4 = 0 + 2 + 2
24: 4 = 0 + 3 + 1
25: 4 = 0 + 4 + 0
26: 4 = 1 + 0 + 3
27: 4 = 1 + 1 + 2
28: 4 = 1 + 2 + 1
29: 4 = 1 + 3 + 0
30: 4 = 2 + 0 + 2
31: 4 = 2 + 1 + 1
32: 4 = 2 + 2 + 0
33: 4 = 3 + 0 + 1
34: 4 = 3 + 1 + 0
35: 4 = 4 + 0 + 0
----: -- ------------
36: 5 = 0 + 0 + 5
37: 5 = 0 + 1 + 4
38: 5 = 0 + 2 + 3
39: 5 = 0 + 3 + 2
40: 5 = 0 + 4 + 1
41: 5 = 0 + 5 + 0
42: 5 = 1 + 0 + 4
43: 5 = 1 + 1 + 3
44: 5 = 1 + 2 + 2
45: 5 = 1 + 3 + 1
46: 5 = 1 + 4 + 0
47: 5 = 2 + 0 + 3
48: 5 = 2 + 1 + 2
49: 5 = 2 + 2 + 1
50: 5 = 2 + 3 + 0
51: 5 = 3 + 0 + 2
52: 5 = 3 + 1 + 1
53: 5 = 3 + 2 + 0
54: 5 = 4 + 0 + 1
55: 5 = 4 + 1 + 0
56: 5 = 5 + 0 + 0
----: -- ------------
57: 6 = 0 + 0 + 6
58: 6 = 0 + 1 + 5
59: 6 = 0 + 2 + 4
60: 6 = 0 + 3 + 3
61: 6 = 0 + 4 + 2
62: 6 = 0 + 5 + 1
63: 6 = 0 + 6 + 0
64: 6 = 1 + 0 + 5
65: 6 = 1 + 1 + 4
66: 6 = 1 + 2 + 3
67: 6 = 1 + 3 + 2
68: 6 = 1 + 4 + 1
69: 6 = 1 + 5 + 0
70: 6 = 2 + 0 + 4
71: 6 = 2 + 1 + 3
MONO_NEXT_GRLEX_TEST
MONO_NEXT_GRLEX computes the next monomial
in M variables, in grlex order.
Let M = 4
0 3 3 2
0 3 4 1
0 3 5 0
0 4 0 4
0 4 1 3
0 4 2 2
1 0 1 0
1 1 0 0
2 0 0 0
0 0 0 3
0 0 1 2
0 0 2 1
0 2 0 1
0 2 1 0
0 3 0 0
1 0 0 2
1 0 1 1
1 0 2 0
1 3 3 0
1 4 0 2
1 4 1 1
1 4 2 0
1 5 0 1
1 5 1 0
3 1 0 0
4 0 0 0
0 0 0 5
0 0 1 4
0 0 2 3
0 0 3 2
3 3 0 0
4 0 0 2
4 0 1 1
4 0 2 0
4 1 0 1
4 1 1 0
1 3 0 1
1 3 1 0
1 4 0 0
2 0 0 3
2 0 1 2
2 0 2 1
3 1 2 2
3 1 3 1
3 1 4 0
3 2 0 3
3 2 1 2
3 2 2 1
3 1 3 2
3 1 4 1
3 1 5 0
3 2 0 4
3 2 1 3
3 2 2 2
0 3 1 0
0 4 0 0
1 0 0 3
1 0 1 2
1 0 2 1
1 0 3 0
MONO_PRINT_TEST
MONO_PRINT can print out a monomial.
Monomial [5]:x^(5).
Monomial [5]:x^(-5).
Monomial [2,1,0,3]:x^(2,1,0,3).
Monomial [17,-3,199]:x^(17,-3,199).
MONO_RANK_GRLEX_TEST
MONO_RANK_GRLEX returns the rank of a monomial in the sequence
of all monomials in M dimensions, in grlex order.
Print a monomial sequence with ranks assigned.
Let M = 3
N = 4
1 0 0 0
2 0 0 1
3 0 1 0
4 1 0 0
5 0 0 2
6 0 1 1
7 0 2 0
8 1 0 1
9 1 1 0
10 2 0 0
11 0 0 3
12 0 1 2
13 0 2 1
14 0 3 0
15 1 0 2
16 1 1 1
17 1 2 0
18 2 0 1
19 2 1 0
20 3 0 0
21 0 0 4
22 0 1 3
23 0 2 2
24 0 3 1
25 0 4 0
26 1 0 3
27 1 1 2
28 1 2 1
29 1 3 0
30 2 0 2
31 2 1 1
32 2 2 0
33 3 0 1
34 3 1 0
35 4 0 0
Now, given a monomial, retrieve its rank in the sequence:
1 0 0 0
4 1 0 0
2 0 0 1
7 0 2 0
15 1 0 2
24 0 3 1
77 3 2 1
158 5 2 1
MONO_UNRANK_GRLEX_TEST
MONO_UNRANK_GRLEX is given a rank, and returns the corresponding
monomial in the sequence of all monomials in M dimensions
in grlex order.
For reference, print a monomial sequence with ranks.
Let M = 3
N = 4
1 0 0 0
2 0 0 1
3 0 1 0
4 1 0 0
5 0 0 2
6 0 1 1
7 0 2 0
8 1 0 1
9 1 1 0
10 2 0 0
11 0 0 3
12 0 1 2
13 0 2 1
14 0 3 0
15 1 0 2
16 1 1 1
17 1 2 0
18 2 0 1
19 2 1 0
20 3 0 0
21 0 0 4
22 0 1 3
23 0 2 2
24 0 3 1
25 0 4 0
26 1 0 3
27 1 1 2
28 1 2 1
29 1 3 0
30 2 0 2
31 2 1 1
32 2 2 0
33 3 0 1
34 3 1 0
35 4 0 0
Now choose random ranks between 1 and 35
8 1 0 1
34 3 1 0
30 2 0 2
20 3 0 0
15 1 0 2
MONO_UPTO_ENUM_TEST
MONO_UPTO_ENUM can enumerate the number of monomials
in M variables, of total degree 0 up to N.
N:
0 1 2 3 4 5 6 7 8
m +------------------------------------------------------
1 | 1 2 3 4 5 6 7 8 9
2 | 1 3 6 10 15 21 28 36 45
3 | 1 4 10 20 35 56 84 120 165
4 | 1 5 15 35 70 126 210 330 495
5 | 1 6 21 56 126 252 462 792 1287
6 | 1 7 28 84 210 462 924 1716 3003
7 | 1 8 36 120 330 792 1716 3432 6435
8 | 1 9 45 165 495 1287 3003 6435 12870
MONO_UPTO_NEXT_GRLEX_TEST
MONO_UPTO_NEXT_GRLEX can list the monomials
in M variables, of total degree up to N,
in grlex order, one at a time.
We start the process with (0,0,...,0,0).
The process ends with (N,0,...,0,0)
Let M = 3
N = 4
1 0 0 0
2 0 0 1
3 0 1 0
4 1 0 0
5 0 0 2
6 0 1 1
7 0 2 0
8 1 0 1
9 1 1 0
10 2 0 0
11 0 0 3
12 0 1 2
13 0 2 1
14 0 3 0
15 1 0 2
16 1 1 1
17 1 2 0
18 2 0 1
19 2 1 0
20 3 0 0
21 0 0 4
22 0 1 3
23 0 2 2
24 0 3 1
25 0 4 0
26 1 0 3
27 1 1 2
28 1 2 1
29 1 3 0
30 2 0 2
31 2 1 1
32 2 2 0
33 3 0 1
34 3 1 0
35 4 0 0
MONO_UPTO_RANDOM_TEST
MONO_UPTO_RANDOM selects at random a monomial
in M dimensions of total degree no greater than N.
Let M = 3
N = 4
8 1 0 1
34 3 1 0
30 2 0 2
20 3 0 0
15 1 0 2
POLYNOMIAL_COMPRESS_TEST
POLYNOMIAL_COMPRESS compresses a polynomial.
Uncompressed P(X) =
+ 7 * x^(0,0,0)
- 5 * x^(0,0,1)
+ 5 * x^(0,0,1)
+ 9 * x^(1,0,0)
+ 11 * x^(0,0,2)
+ 3 * x^(0,0,2)
+ 6 * x^(0,0,2)
+ 0 * x^(0,1,2)
- 13 * x^(3,0,1)
+ 1e-20 * x^(4,0,0).
Compressed P(X) =
+ 7 * x^(0,0,0)
+ 0 * x^(0,0,1)
+ 9 * x^(1,0,0)
+ 20 * x^(0,0,2)
- 13 * x^(3,0,1).
POLYNOMIAL_PRINT_TEST
POLYNOMIAL_PRINT prints a polynomial.
P1(X) =
+ 7 * x^(0,0,0)
- 5 * x^(0,0,1)
+ 9 * x^(1,0,0)
+ 11 * x^(0,0,2)
+ 0 * x^(0,1,2)
- 13 * x^(3,0,1).
POLYNOMIAL_SORT_TEST
POLYNOMIAL_SORT sorts a polynomial by exponent index.
Unsorted polynomial:
+ 0 * x^(0,1,2)
+ 9 * x^(1,0,0)
- 5 * x^(0,0,1)
- 13 * x^(3,0,1)
+ 7 * x^(0,0,0)
+ 11 * x^(0,0,2).
Sorted polynomial:
+ 7 * x^(0,0,0)
- 5 * x^(0,0,1)
+ 9 * x^(1,0,0)
+ 11 * x^(0,0,2)
+ 0 * x^(0,1,2)
- 13 * x^(3,0,1).
POLYNOMIAL_VALUE_TEST
POLYNOMIAL_VALUE evaluates a polynomial.
P(X) =
+ 7 * x^(0,0,0)
- 5 * x^(0,0,1)
+ 9 * x^(1,0,0)
+ 11 * x^(0,0,2)
+ 0 * x^(0,1,2)
- 13 * x^(3,0,1).
P(1,2,3) = 61
P(-2,4,1) = 99
LP_COEFFICIENTS_TEST
LP_COEFFICIENTS: coefficients of Legendre polynomial P(n,x).
P(0,x) =
+ 1 * x^(0).
P(1,x) =
+ 1 * x^(1).
P(2,x) =
- 0.5 * x^(0)
+ 1.5 * x^(2).
P(3,x) =
- 1.5 * x^(1)
+ 2.5 * x^(3).
P(4,x) =
+ 0.375 * x^(0)
- 3.75 * x^(2)
+ 4.375 * x^(4).
P(5,x) =
+ 1.875 * x^(1)
- 8.75 * x^(3)
+ 7.875 * x^(5).
P(6,x) =
- 0.3125 * x^(0)
+ 6.5625 * x^(2)
- 19.6875 * x^(4)
+ 14.4375 * x^(6).
P(7,x) =
- 2.1875 * x^(1)
+ 19.6875 * x^(3)
- 43.3125 * x^(5)
+ 26.8125 * x^(7).
P(8,x) =
+ 0.273438 * x^(0)
- 9.84375 * x^(2)
+ 54.1406 * x^(4)
- 93.8438 * x^(6)
+ 50.2734 * x^(8).
P(9,x) =
+ 2.46094 * x^(1)
- 36.0938 * x^(3)
+ 140.766 * x^(5)
- 201.094 * x^(7)
+ 94.9609 * x^(9).
P(10,x) =
- 0.246094 * x^(0)
+ 13.5352 * x^(2)
- 117.305 * x^(4)
+ 351.914 * x^(6)
- 427.324 * x^(8)
+ 180.426 * x^(10).
LP_VALUE_TEST:
LP_VALUE evaluates a Legendre polynomial.
Tabulated Computed
O X L(O,X) L(O,X) Error
0 0.25 1 1 0
1 0.25 0.25 0.25 0
2 0.25 -0.40625 -0.40625 0
3 0.25 -0.335938 -0.335938 0
4 0.25 0.157715 0.157715 0
5 0.25 0.339722 0.339722 0
6 0.25 0.0242767 0.0242767 0
7 0.25 -0.279919 -0.279919 0
8 0.25 -0.152454 -0.152454 -2.77556e-17
9 0.25 0.176824 0.176824 0
10 0.25 0.2212 0.2212 2.77556e-17
3 0 0 -0 0
3 0.1 -0.1475 -0.1475 0
3 0.2 -0.28 -0.28 0
3 0.3 -0.3825 -0.3825 0
3 0.4 -0.44 -0.44 -5.55112e-17
3 0.5 -0.4375 -0.4375 0
3 0.6 -0.36 -0.36 5.55112e-17
3 0.7 -0.1925 -0.1925 1.11022e-16
3 0.8 0.08 0.08 -2.22045e-16
3 0.9 0.4725 0.4725 -1.11022e-16
3 1 1 1 0
LP_VALUES_TEST:
LP_VALUES stores values of
the Legendre polynomial P(o,x).
Tabulated
O X L(O,X)
0 0.25 1
1 0.25 0.25
2 0.25 -0.40625
3 0.25 -0.335938
4 0.25 0.157715
5 0.25 0.339722
6 0.25 0.0242767
7 0.25 -0.279919
8 0.25 -0.152454
9 0.25 0.176824
10 0.25 0.2212
3 0 0
3 0.1 -0.1475
3 0.2 -0.28
3 0.3 -0.3825
3 0.4 -0.44
3 0.5 -0.4375
3 0.6 -0.36
3 0.7 -0.1925
3 0.8 0.08
3 0.9 0.4725
3 1 1
LPP_TO_POLYNOMIAL_TEST:
LPP_TO_POLYNOMIAL is given a Legendre product polynomial
and determines its polynomial representation.
Using spatial dimension M = 2
LPP #1 = L(0,X)*L(0,Y) =
+ 1 * x^(0,0).
LPP #2 = L(0,X)*L(1,Y) =
+ 1 * x^(0,1).
LPP #3 = L(1,X)*L(0,Y) =
+ 1 * x^(1,0).
LPP #4 = L(0,X)*L(2,Y) =
- 0.5 * x^(0,0)
+ 1.5 * x^(0,2).
LPP #5 = L(1,X)*L(1,Y) =
+ 1 * x^(1,1).
LPP #6 = L(2,X)*L(0,Y) =
- 0.5 * x^(0,0)
+ 1.5 * x^(2,0).
LPP #7 = L(0,X)*L(3,Y) =
- 1.5 * x^(0,1)
+ 2.5 * x^(0,3).
LPP #8 = L(1,X)*L(2,Y) =
- 0.5 * x^(1,0)
+ 1.5 * x^(1,2).
LPP #9 = L(2,X)*L(1,Y) =
- 0.5 * x^(0,1)
+ 1.5 * x^(2,1).
LPP #10 = L(3,X)*L(0,Y) =
- 1.5 * x^(1,0)
+ 2.5 * x^(3,0).
LPP #11 = L(0,X)*L(4,Y) =
+ 0.375 * x^(0,0)
- 3.75 * x^(0,2)
+ 4.375 * x^(0,4).
LPP_VALUE_TEST:
LPP_VALUE evaluates a Legendre product polynomial.
Evaluate at X = -0.563163 0.912635 0.659018
Rank I1 I2 I3: L(I1,X1)*L(I2,X2)*L(I3,X3) P(X1,X2,X3)
1 0 0 0 1 1
2 0 0 1 0.659018 0.659018
3 0 1 0 0.912635 0.912635
4 1 0 0 -0.563163 -0.563163
5 0 0 2 0.151458 0.151458
6 0 1 1 0.601443 0.601443
7 0 2 0 0.749354 0.749354
8 1 0 1 -0.371135 -0.371135
9 1 1 0 -0.513963 -0.513963
10 2 0 0 -0.0242705 -0.0242705
11 0 0 3 -0.27299 -0.27299
12 0 1 2 0.138226 0.138226
13 0 2 1 0.493838 0.493838
14 0 3 0 0.531388 0.531388
15 1 0 2 -0.0852956 -0.0852956
16 1 1 1 -0.338711 -0.338711
17 1 2 0 -0.422009 -0.422009
18 2 0 1 -0.0159947 -0.0159947
19 2 1 0 -0.0221501 -0.0221501
20 3 0 0 0.398223 0.398223
LPP_PRB:
Normal end of execution.
06 November 2014 07:39:06 PM